DEVELOPMENTS IN SURFACE CONTAMINATION AND CLEANING
Developments in Surface Contamination and Cleaning Fundamentals an...
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DEVELOPMENTS IN SURFACE CONTAMINATION AND CLEANING
Developments in Surface Contamination and Cleaning Fundamentals and Applied Aspects
Edited by Rajiv Kohli Houston, Texas and K. L. Mittal Consultant, Adhesion and Surface Cleaning Hopewell Junction, New York
Norwich, NY, USA
Copyright # 2008 by William Andrew, Inc. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the Publisher. Library of Congress Cataloging-in-Publication Data Developments in surface contamination and cleaning : fundamentals and applied aspects / edited by Rajiv Kohli and K.L. Mittal. p. cm. Includes bibliographical references and index. ISBN 978-0-8155-1555-5 (978-0-8155) 1. Surfaces (Technology)–Inspection. 2. Surface contamination–Prevention. 3. Particles–Measurement. 4. Cleaning. 5. Coatings. 6. Dust control. I. Kohli, Rajiv, 1947- II. Mittal, K. L., 1945TA418.7.D876 620'.44–dc22
2008 2007034322
Printed in the United States of America This book is printed on acid-free paper. 10 9 8 7 6 5 4 3 2 1 Published by: William Andrew Inc. 13 Eaton Avenue Norwich, NY 13815 1-800-932-7045 www.williamandrew.com NOTICE To the best of our knowledge the information in this publication is accurate; however the Publisher does not assume any responsibility or liability for the accuracy or completeness of, or consequences arising from, such information. This book is intended for informational purposes only. Mention of trade names or commercial products does not constitute endorsement or recommendation for their use by the Publisher. Final determination of the suitability of any information or product for any use, and the manner of that use, is the sole responsibility of the user. Anyone intending to rely upon any recommendation of materials or procedures mentioned in this publication should be independently satisfied as to such suitability, and must meet all applicable safety and health standards.
Contents
Introduction ............................................................................... Rajiv Kohli and Kash Mittal PART I
xxxiii
FUNDAMENTALS. . . . . . . . . . . . . . . . . . . . . . . . . .
1
1 The Physical Nature of Very, Very Small Particles and its Impact on Their Behavior . . . . . . . . . . . . . . . . . . . . . . . . . Othmar Preining
3
1.1 1.2 1.3
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Spectrum of Aerosol Particle Sizes . . . . . . . . . . Atoms and Molecules—Concepts and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 The Model of a Gas . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Particles and Gas Molecules . . . . . . . . . . . . . . . . . . 1.6 Particle Interactions . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1 Coagulation . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.2 Homogeneous nucleation . . . . . . . . . . . . . . . 1.6.3 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Nanoparticles as Molecular Clusters . . . . . . . . . . . . 1.8 An Interaction Model for Nanometer–Sized Particles 1.9 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 8 10 15 15 15 17 18 19 21 23 23
2 Elucidating the Fundamental Interactions of Very Small Particles: Ultrafast Science . . . . . . . . . . . . . . . . . . . . . . . . . . Carlo Altucci and Domenico Paparo
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Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Techniques for the Generation of Ultrashort Pulses. 2.2.1 Basic concepts: mode locking and early generations of ultrashort laser sources . . . . . 2.2.2 Sub-100-fs pulses and chirped pulse amplification . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 The few-optical-cycle regime . . . . . . . . . . . . v
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CONTENTS 2.2.4 The carrier-envelope-phase (CEP) . . . . . . . 2.2.5 Techniques for ultrashort pulse measurements . . . . . . . . . . . . . . . . . . . . . 2.3 Dynamics of Atoms and Molecules in Strong Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.1 Perturbative regime . . . . . . . . . . . 2.3.1.2 The strong field regime . . . . . . . . 2.3.1.3 High-order harmonic generation . . 2.3.2 Attosecond pulse generation and characterization: the present border line of ultrafast science . . . . . . . . . . . . . . . . . . . . 2.3.3 Molecules . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.1 The birth of femtochemistry: probing the transition states . . . . . 2.3.3.2 Some basic theoretical concepts on wave-packet formation and dynamics. . . . . . . . . . . . . . . . . . . 2.3.3.3 Diatomic molecule and lasermolecule interaction . . . . . . . . . . . 2.3.4 Simple properties of a wave-packet . . . . . . 2.3.4.1 Wavepacket generation and influence of chirping . . . . . . . . . . 2.4 Bond-breaking in Single Molecules . . . . . . . . . . . 2.5 Controlling Molecular Populations and Chemical Reactions by Ultrafast Pulses . . . . . . . . . . . . . . . 2.6 Polyatomic Molecules and Nonadiabatic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Recent Results in Ultrafast Crystallography: UED and Time-resolved X-rays . . . . . . . . . . . . . . . . . . 2.8 New Nonlinear Optical Techniques for Probing Surfaces: Surface Second-harmonic and Sum-frequency Generation . . . . . . . . . . . . . . . . . 2.8.1 Theoretical considerations . . . . . . . . . . . . . 2.8.2 Local-field-induced enhancement of SSHG on metal surfaces . . . . . . . . . . . . . . . . . . . 2.8.3 Metal nanoparticles . . . . . . . . . . . . . . . . . 2.8.4 Femtochemistry of surfaces probed by pump-probe SSFG and SSHG. . . . . . . . . . 2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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vii
CONTENTS 3 Transport and Deposition of Aerosol Particles . . . . . . . . . . . . Daniel J. Rader and Anthony S. Geller 3.1 3.2 3.3
3.4 3.5
3.6
3.7
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . Noncontinuum Considerations . . . . . . . . . . . . . Lagrangian Particle Equation of Motion . . . . . . 3.3.1 Fluid–particle drag force . . . . . . . . . . . . . 3.3.1.1 Fluid-drag force: assumptions and practical considerations . . . . 3.3.2 Gravitational force . . . . . . . . . . . . . . . . . 3.3.3 Thermophoretic force . . . . . . . . . . . . . . . 3.3.3.1 Continuum regime limit . . . . . . . 3.3.3.2 Free molecule regime limit . . . . . 3.3.4 Electrostatic force. . . . . . . . . . . . . . . . . . Inertial Effects . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Nondimensionalization . . . . . . . . . . . . . . Drift Velocity. . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Gravitational drift velocity . . . . . . . . . . . 3.5.2 Thermophoretic drift velocity . . . . . . . . . 3.5.3 Electric drift velocity . . . . . . . . . . . . . . . Eulerian Formulation . . . . . . . . . . . . . . . . . . . . 3.6.1 Particle diffusion coefficient . . . . . . . . . . 3.6.2 Nondimensional formulation . . . . . . . . . . Particle Transport and Deposition in a Parallel Plate Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Fluid transport equations . . . . . . . . . . . . 3.7.1.1 Flow field in the showerhead holes. . . . . . . . . . . . . . . . . . . . . 3.7.1.2 Fluid transport between parallel plates . . . . . . . . . . . . . . 3.7.1.3 Summary: fluid flow analysis for the parallel plate geometry . . . . . 3.7.2 Particle collection efficiency. . . . . . . . . . . 3.7.3 Particles entering through the showerhead 3.7.3.1 External force limit . . . . . . . . . . 3.7.4 Particle traps/in situ nucleation . . . . . . . . 3.7.4.1 Efficiency for the Lagrangian formulation . . . . . . . . . . . . . . . . 3.7.4.2 Efficiency for the Eulerian formulation . . . . . . . . . . . . . . . . 3.7.4.3 External force limit . . . . . . . . . .
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viii
CONTENTS
3.7.5 Diffusion-enhanced deposition from traps or in situ nucleation . . . . . . . . . . . . . . . . . 3.7.5.1 Problem definition . . . . . . . . . . . . 3.7.5.2 Solution of the Eulerian particle transport equation . . . . . . . . . . . . 3.7.5.3 Particle collection efficiency . . . . . 3.7.5.4 Particle flux. . . . . . . . . . . . . . . . . 3.7.6 Nondimensional results. . . . . . . . . . . . . . . 3.7.6.1 Efficiency at intermediate Peclet numbers . . . . . . . . . . . . . . . . . . . 3.7.7 Dimensional results . . . . . . . . . . . . . . . . . 3.7.7.1 Trap height effects . . . . . . . . . . . . 3.7.7.2 Pressure effects . . . . . . . . . . . . . . 3.7.7.3 Mass flow rate effects . . . . . . . . . 3.7.7.4 Effect of thermophoresis . . . . . . . 3.7.8 Summary: diffusion-enhanced deposition . . 3.8 Inertia-Enhanced Deposition . . . . . . . . . . . . . . . . 3.8.1 Particle transport in the showerhead holes . 3.8.2 Particle transport between parallel plates . . 3.8.2.1 Asymptotic limit of critical Stokes number . . . . . . . . . . . . . . . . . . . . 3.8.3 Coupled transport—nondimensional results 3.8.3.1 Critical Stokes numbers . . . . . . . . 3.8.3.2 Grand design curves . . . . . . . . . . 3.8.3.3 External forces . . . . . . . . . . . . . . 3.8.3.4 Parabolic profile . . . . . . . . . . . . . 3.8.4 Coupled transport—dimensional results . . . 3.9 Chapter Summary and Practical Guidelines . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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247 249 250 252 254 255 258 261 264
4 Relevance of Particle Transport in Surface Deposition and Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao-Hsin Lin and Chao Zhu
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4.1 4.2 4.3 4.4 4.5 4.6
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle–solid Surface Interactions . . . . . . . . . . . . . . . . Dry Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermophoresis and Its Relevance in Surface Cleaning . Electrostatic Force and Its Relevance in Surface Cleaning Dielectrophoresis and Its Relevance in Surface Cleaning
267 268 273 280 285 286
ix
CONTENTS 4.7 Abrasive Erosion and Its Relevance in Surface Cleaning 4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
288 292 294
5 Tribological Implication of Particles . . . . . . . . . . . . . . . . . . . Koji Kato
299
5.1 5.2 5.3
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Micro-Site for Generation of Wear Particles. . . . Wear Modes and Particles. . . . . . . . . . . . . . . . . . . . 5.3.1 Adhesive transfer of atoms in contact and separation . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Adhesive transfer of flake-like particles in sliding contact . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Micro-cutting and generation of fine feather-like particles in abrasive sliding. . . . . . 5.3.4 Surface plastic flow and a thin filmy wear particle generation by repeated contacts . . . . . 5.3.5 Crack initiation and propagation in the subsurface of contact and generation of a flake-like particle by repeated contact . . . . . . 5.3.6 Tribo-oxidation and generation of particles of oxides by repeated contacts in air and water . . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Wear particles generated in sliding of steels in oil with additives . . . . . . . . . . . . . . . . . . . 5.4 Wear Rate and Number of Generated Wear Particles 5.5 The Size Distribution of Wear Particles . . . . . . . . . . 5.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Solid wear particles . . . . . . . . . . . . . . . . . . . 5.6.2 Gas molecules by wear . . . . . . . . . . . . . . . . . 5.6.3 Triboemission of electrons, ions, photons, and particles . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Airborne Molecular Contamination: Contamination on Substrates and the Environment in Semiconductors and Other Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taketoshi Fujimoto, Kikuo Takeda and Tatsuo Nonaka
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x
CONTENTS 6.1
6.2
6.3
6.4
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Changes in semiconductor integration . . . . 6.1.3 Changes in target contaminant . . . . . . . . . Definitions, Types and Sources of AMCs . . . . . . . 6.2.1 Definition of ‘‘Airborne Molecular Contamination’’ . . . . . . . . . . . . . . . . . . . . 6.2.2 Examples of AMC-induced problems in the manufacturing process . . . . . . . . . . . . . . . 6.2.3 Nature of AMC-induced effects . . . . . . . . . 6.2.4 Classification of airborne molecular contaminants . . . . . . . . . . . . . . . . . . . . . . 6.2.4.1 SEMATECH technology transfer report No. 95052812A-TR . . . . . . 6.2.4.2 International technology roadmap for semiconductor (ITRS) 1999 . . . . . . . . . . . . . . . . Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Substrate surface analysis . . . . . . . . . . . . . 6.3.1.1 Quantitative analysis . . . . . . . . . . 6.3.1.2 Surface (instrumental) analysis . . . 6.3.2 Air analysis . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.1 Acids . . . . . . . . . . . . . . . . . . . . . 6.3.2.2 Bases: ammonia (NH3) and amines. . . . . . . . . . . . . . . . . . . . . 6.3.2.3 Condensables: organic compounds 6.3.2.4 Dopants: boron, phosphorus, and metals . . . . . . . . . . . . . . . . . 6.3.3 Outgassing evaluation method for construction materials. . . . . . . . . . . . . . . . 6.3.3.1 IEST WG 031 . . . . . . . . . . . . . . . 6.3.3.2 JACA No. 34-1999 . . . . . . . . . . . Nature of Airborne Molecular Contamination and Its Effects . . . . . . . . . . . . . . . 6.4.1 Investigation of the properties of AMCs. . . 6.4.1.1 Effects of rinsing the outdoor air . 6.4.1.2 Acids . . . . . . . . . . . . . . . . . . . . . 6.4.1.3 Bases . . . . . . . . . . . . . . . . . . . . . 6.4.1.4 Condensables: siloxanes, phthalates, phosphates and other organic compounds . . . . . . . . . . .
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CONTENTS
6.5
6.4.2 Examples of problems caused by AMC contamination . . . . . . . . . . . . . . . . . . . . . 6.4.2.1 General. . . . . . . . . . . . . . . . . . . . 6.4.2.2 Effects of ammonia . . . . . . . . . . . 6.4.2.3 Effects of siloxanes . . . . . . . . . . . 6.4.2.4 Effects of HMDS . . . . . . . . . . . . 6.4.3 Chemistry of AMCs . . . . . . . . . . . . . . . . . 6.4.3.1 Monolayer and sub-monolayer contamination . . . . . . . . . . . . . . . 6.4.3.2 Clausius–Clapeyron relation . . . . . 6.4.3.3 Outgassing phenomenon: two-phase exponential model of vaporization and diffusion of contaminants . . . . . . . 6.4.3.4 Sticking probability, sticking coefficient, and staying tendency . . 6.4.3.5 Investigation of contamination based on the ‘‘Organic Conceptual Diagram’’ . . . . . . . . . . . . . . . . . . Examples of Application of Knowledge and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Excursion of AMCs . . . . . . . . . . . . . . . . . 6.5.1.1 Data analysis . . . . . . . . . . . . . . . 6.5.1.2 Investigation of contaminant sources in cleanroom . . . . . . . . . . 6.5.2 Selection of construction materials with fewer AMC contaminant sources . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Chemical filter for air cleaning . . . . . . . . . 6.5.3.1 Change of total organic concentration with time . . . . . . . . 6.5.3.2 Change of siloxanes concentration in cleanroom air . . . . . . . . . . . . . 6.5.3.3 Effect of chemical filter . . . . . . . . 6.5.3.4 Published reports on removal mechanisms. . . . . . . . . . . . . . . . . 6.5.3.5 Other issues. . . . . . . . . . . . . . . . . 6.5.4 Removal from the substrate surface (carbon chemistry) . . . . . . . . . . . . . . . . . . 6.5.4.1 Cleaning technology using UV photoelectron with catalyst . . . . . .
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xii
CONTENTS 6.5.4.2 Other cleaning technology . . . . . . 6.5.5 Monitoring systems . . . . . . . . . . . . . . . . . 6.5.6 Recent developments . . . . . . . . . . . . . . . . 6.5.6.1 Cleanliness requirements for Si wafer . . . . . . . . . . . . . . . . . . . 6.5.6.2 Trends in standardization . . . . . . . 6.5.6.3 New analytical techniques . . . . . . 6.5.6.4 Achieving cleanroom cleanliness at low AMCs level (DOP 0.1 ng/m3) . . . . . . . . . . . . . 6.6 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Technology for cleanliness of AMCs . . . . . 6.6.2 Advances in analytical methods . . . . . . . . . 6.6.3 Application of air cleanliness technology to various fields . . . . . . . . . . . . . . . . . . . . . . 6.6.3.1 Sick house syndrome . . . . . . . . . . 6.6.3.2 Endocrine disrupters . . . . . . . . . . 6.6.3.3 Cleanliness of experiment and analysis environments . . . . . . . . . 6.6.3.4 Other applications . . . . . . . . . . . . 6.6.4 Contribution of the analyst/chemist to troubleshooting . . . . . . . . . . . . . . . . . . . . 6.7 Summary of the Chapter. . . . . . . . . . . . . . . . . . . Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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7 Aspects of Particle Adhesion and Removal. . . . . . . . . . . . . . . David J. Quesnel, Donald S. Rimai and David M. Schaefer
475
7.1 7.2 7.3 7.4 7.5
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . Interactions Giving Rise to Particle Adhesion . . . Mechanics of Particle Adhesion . . . . . . . . . . . . . Factors Affecting Particle Adhesion . . . . . . . . . . Methods of Measuring the Adhesion of Particles to Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8 Relevance of Electrostatic Discharge Controls to Particle Contamination in Cleanroom Environments . . . . . . . . . . . . . . Larry Levit and Arnold Steinman
503
xiii
CONTENTS 8.1 8.2 8.3 8.4 8.5 8.6
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . Electrostatic Charge Problems in Cleanrooms . Static Charge Generation . . . . . . . . . . . . . . . Insulators Versus Conductors . . . . . . . . . . . . Cleanroom Electrostatic Management . . . . . . Air Ionization for Static Charge Control . . . . 8.6.1 Corona ionization . . . . . . . . . . . . . . . 8.6.1.1 AC ionizer . . . . . . . . . . . . . . 8.6.1.2 DC ionizer . . . . . . . . . . . . . . 8.6.2 Photoelectric ionization. . . . . . . . . . . . 8.6.3 Radioisotope ionization . . . . . . . . . . . 8.6.4 Measuring ionizer performance . . . . . . 8.7 Air Ionizer Applications . . . . . . . . . . . . . . . . 8.7.1 Discharge in process tools . . . . . . . . . . 8.7.2 Flow benches and work surfaces . . . . . 8.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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503 504 508 510 511 514 515 515 517 519 520 521 521 524 525 526 527
CHARACTERIZATION OF SURFACE CONTAMINANTS . . . . . . . . . . . . . . . . . . . . . . . .
529
9 Electron Microscopy Techniques for Imaging and Analysis of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . .
531
PART II
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. . . . . . . . . . . . . . . . .
Zhong Lin Wang and Jean L. Lee 9.1
9.2
Scanning Electron Microscopy. . . . . . . . . . . . . . . . . . .
531
9.1.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1.1 Environmental scanning electron microscope . . . . . . . . . . . . . . . . . . . . . 9.1.2 Signals produced by the SEM . . . . . . . . . . . . . . 9.1.2.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . 9.1.2.2 Composition analysis . . . . . . . . . . . . . . High-resolution Transmission Electron Microscopy . . . . 9.2.1 Main components of a transmission electron microscope . . . . . . . . . . . . . . . . . . . . . 9.2.2 The physics for atomic resolution lattice imaging 9.2.2.1 Phase contrast imaging. . . . . . . . . . . . . 9.2.2.2 Image formation . . . . . . . . . . . . . . . . . 9.2.2.3 Image interpretation of very thin samples. . . . . . . . . . . . . . . . . . . . . . . .
531 535 536 536 541 545 546 548 548 550 551
xiv
CONTENTS 9.2.2.4 Dynamic theory and image simulation. Shapes of Nanocrystals . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Polyhedral shapes. . . . . . . . . . . . . . . . . . . . . . 9.3.2 Twining structure and stacking faults . . . . . . . 9.3.3 Multiply twinned particles—decahedron and icosahedron . . . . . . . . . . . . . . . . . . . . . . 9.4 Nanodiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Optics for nanodiffraction . . . . . . . . . . . . . . . 9.4.2 Experimental procedure to obtain a nanodiffraction pattern . . . . . . . . . . . . . . . . . 9.5 Scanning Transmission Electron Microscopy . . . . . . . 9.5.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Imaging modes . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Composition-sensitive imaging . . . . . . . . . . . . 9.5.4 Nanoscale microanalysis . . . . . . . . . . . . . . . . 9.6 In-situ TEM and Nanomeasurements . . . . . . . . . . . . 9.6.1 Thermodynamic properties of nanocrystals . . . . . . . . . . . . . . . . . . . . . . . . . 9.7 Electron Energy-loss Spectroscopy of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7.1 Quantitative nanoanalysis . . . . . . . . . . . . . . . 9.7.2 Near edge fine structure and bonding in transition metal oxides . . . . . . . . . . . . . . . . . 9.8 Energy Dispersive X-ray Microanalysis (EDS). . . . . . 9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . .
552 555 555 558
. . .
559 562 562
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563 564 564 566 568 569 570
.
570
. .
576 577
. . . .
578 581 582 583
10 Surface Analysis Methods for Contaminant Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David A. Cole and Lei Zhang
585
9.3
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Auger Electron Spectroscopy (AES) . . . . . . . . 10.2.1 Background of AES. . . . . . . . . . . . . . 10.2.2 Basic principles of AES . . . . . . . . . . . 10.2.3 AES instrumentation . . . . . . . . . . . . . 10.2.4 Applications of AES for characterizing surface contaminants . . . . . . . . . . . . . 10.2.5 Recent developments and future directions of AES . . . . . . . . . . . . . . . 10.3 X-ray Photoelectron Spectroscopy (XPS). . . . .
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585 586 586 586 593
.....
594
..... .....
600 601
xv
CONTENTS 10.3.1 10.3.2 10.3.3 10.3.4
Background of XPS. . . . . . . . . . . . . . . Basic principles of XPS . . . . . . . . . . . . XPS instrumentation . . . . . . . . . . . . . . Applications of XPS for characterizing surface contaminants . . . . . . . . . . . . . . 10.3.5 Recent developments and future directions of XPS . . . . . . . . . . . . . . . . 10.4 Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) . . . . . . . . . . . . . . . . 10.4.1 Background of TOF-SIMS . . . . . . . . . . 10.4.2 Basic principles of TOF-SIMS . . . . . . . 10.4.3 TOF-SIMS instrumentation . . . . . . . . . 10.4.4 Applications of TOF-SIMS for characterizing surface contaminants . . . 10.4.5 Recent developments and future directions of TOF-SIMS . . . . . . . . . . . 10.5 Low-energy Ion Scattering (LEIS) . . . . . . . . . . 10.5.1 Background of LEIS . . . . . . . . . . . . . . 10.5.2 Basic principles of LEIS. . . . . . . . . . . . 10.5.3 LEIS instrumentation . . . . . . . . . . . . . 10.5.4 Applications of LEIS for characterizing surface contaminants . . . . . . . . . . . . . . 10.5.5 Recent developments and future directions of LEIS . . . . . . . . . . . . . . . . 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.... .... ....
601 602 611
....
613
....
620
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. . . .
622 622 622 628
....
630
. . . . .
. . . . .
634 635 635 635 640
....
641
.... .... ....
645 646 647
11 Ionic Contamination and Analytical Techniques for Ionic Contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beverly Newton
653
11.1 What is an Ion? . . . . . . . . . . . . . . . . . . . . . . . 11.2 Sources and Effects of Ionic Contamination in Electronics Manufacturing . . . . . . . . . . . . . . . . 11.3 How Does Corrosion Begin? . . . . . . . . . . . . . . 11.4 Sources and Effects of Ionic Contamination for Semiconductor and MEMS Manufacturing . . . . 11.5 Ionic Contamination of Data Storage Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Ionic Contamination of Cleanroom and Packaging Materials . . . . . . . . . . . . . . . . . . . .
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. . . . .
. . . .
. . . . .
....
653
.... ....
654 656
....
656
....
658
....
658
xvi
CONTENTS 11.7 Analytical Techniques . . . . . . . . . . . . . . . . . . 11.8 Selection Criteria. . . . . . . . . . . . . . . . . . . . . . 11.9 Instrumentation Selection. . . . . . . . . . . . . . . . 11.9.1 Ultraviolet photoelectric emission . . . . 11.9.2 Phase imaging . . . . . . . . . . . . . . . . . . 11.9.3 Energy dispersive X-ray spectroscopy (EDS/EDX) . . . . . . . . . . . . . . . . . . . 11.9.4 Graphite furnace atomic absorption (GFAA) . . . . . . . . . . . . . . . . . . . . . . 11.9.5 Inductively coupled plasma/mass spectrometry (ICP/MS) . . . . . . . . . . . 11.9.6 Optically stimulated electron emission (OSEE). . . . . . . . . . . . . . . . . . . . . . . 11.9.7 Secondary ion mass spectroscopy (SIMS) . . . . . . . . . . . . . . . . . . . . . . . 11.9.8 Auger electron spectroscopy (AES) . . . 11.9.9 X-ray photoelectron spectroscopy/ electron spectroscopy for chemical analysis (XPS/ESCA). . . . . . . . . . . . . 11.9.10 Total reflection X-ray fluorescence (TXRF) . . . . . . . . . . . . . . . . . . . . . 11.9.11 Ion chromatography (IC) . . . . . . . . . . 11.9.12 Capillary ion electrophoresis (CIE) . . . 11.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . .
660 660 661 661 661
.....
662
.....
663
.....
664
.....
665
..... .....
665 666
.....
666
. . . . .
. . . . .
667 667 671 671 672
12 Relevance of Colorimetric Interferometry for Thin Surface Film Contaminants . . . . . . . . . . . . . . . . . . . . . . . . Michel Querry, Philippe Vergne and Je´r^ ome Molimard
675
12.1 Introduction . . . . . . . . . . . . . . . . . . 12.2 Interferometry. . . . . . . . . . . . . . . . . 12.2.1 Elementary phenomena . . . . 12.2.2 White light interferometry . . 12.3 Colorimetry . . . . . . . . . . . . . . . . . . 12.3.1 Definition of the problem. . . 12.3.2 Colorimetric encoding . . . . . 12.3.3 Detectors . . . . . . . . . . . . . . 12.4 Colorimetric Interferometry . . . . . . . 12.4.1 Methods using colorimetric interferometry in lubrication.
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675 676 676 679 680 680 681 683 684
............
684
xvii
CONTENTS 12.4.2 New developed method . . . . . . . . . . . . . . . . 12.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
684 689 690
13 Wettability Techniques to Monitor the Cleanliness of Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . William Birch, Alain Carre´ and Kashmiri L. Mittal
693
13.1 Background and Introduction. . . . . . . . . . . 13.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . 13.3 Theoretical and Experimental Investigations 13.4 Instrumentation. . . . . . . . . . . . . . . . . . . . . 13.5 Examples of Applications. . . . . . . . . . . . . . 13.6 Recent Developments . . . . . . . . . . . . . . . . 13.7 Future Directions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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693 694 696 700 705 716 718 721
PART III METHODS FOR REMOVAL OF SURFACE CONTAMINATION . . . . . . . . . . . . . . . . . . . . . . .
725
14 The Use of Surfactants to Enhance Particle Removal from Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Michael L. Free 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 14.1.1 Industrial perspective . . . . . . . . . . . . 14.1.2 Historical perspective . . . . . . . . . . . . 14.2 Surfactant Behavior in Solution . . . . . . . . . . 14.3 Interfacial Forces and Particle Removal . . . . 14.3.1 Introduction to interfacial forces. . . . 14.3.2 Measurement of surface forces . . . . . 14.3.3 Adhesion. . . . . . . . . . . . . . . . . . . . 14.3.4 Particle removal forces . . . . . . . . . . 14.3.5 Modification of surface forces using surfactants . . . . . . . . . . . . . . . . . . 14.3.6 Measurement of particle removal . . 14.3.7 Enhanced-particle removal results associated with surfactant use . . . . . 14.3.8 Post-cleaning surfactant removal . . . 14.3.9 Selection of surfactants for cleaning purposes . . . . . . . . . . . . . . . . . . . .
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727
. . . . . . . . .
727 727 728 728 734 734 736 738 739
...... ......
739 744
...... ......
745 749
......
750
xviii
CONTENTS
14.3.10 Mathematical modeling of enhanced-particle removal using surfactants . . . . . . . . . . . . . . . . . . . . . . . . 14.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Cleaning with Solvents. . . . . . . . . . . . . . . . . . . . . . . . . . . . John B. Durkee 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Environmental and Regulatory Issues . . . . . . . 15.2.1 Ozone-depleting solvents (chemicals) . . . . . . . . . . . . . . . . . . . . 15.2.1.1 Regulation of ozonedepleting chemicals . . . . . . . 15.2.2 Reactions of ozone depletion in the stratosphere . . . . . . . . . . . . . . . . . . . 15.2.3 VOC solvents . . . . . . . . . . . . . . . . . . 15.2.3.1 Definition of a VOC . . . . . . 15.2.3.2 Definition of VOC exempt. . 15.2.3.3 Reactions leading to smog formation . . . . . . . . . . . . . . 15.2.3.4 Smog formed from VOCs . . 15.2.4 Global warming . . . . . . . . . . . . . . . . 15.2.4.1 Regulation of solvent cleaning because of global warming. . . . . . . . . . . . . . . 15.2.4.2 Specific regulations affecting solvent cleaning . . . . . . . . . 15.2.5 Relationship of solvent characteristics ODP, VOC, and GWP. . . . . . . . . . . . 15.3 Potential Health Consequences of Solvent Use in Cleaning. . . . . . . . . . . . . . . . . . . . . . . 15.3.1 Flammability issues . . . . . . . . . . . . . . 15.3.1.1 Flash point . . . . . . . . . . . . 15.3.1.2 Combustion . . . . . . . . . . . 15.3.1.3 Static discharge . . . . . . . . . 15.3.1.4 Procedures recommended to avoid fires . . . . . . . . . . 15.3.1.5 Body contact . . . . . . . . . . 15.3.1.6 Skin contact . . . . . . . . . . .
750 753 753 759
..... .....
759 760
.....
761
.....
762
. . . .
. . . .
772 776 776 780
..... ..... .....
782 785 789
.....
789
.....
792
.....
795
. . . . .
. . . . .
796 797 797 802 807
..... ..... .....
809 810 812
. . . .
. . . . .
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. . . .
. . . . .
xix
CONTENTS 15.3.1.7 Carcinogenicity . . . . . . . . . . 15.3.1.8 Protection from hazards. . . . 15.3.1.9 Taking action . . . . . . . . . . . 15.3.1.10 Legal or regulatory hazards . 15.3.1.11 Economic hazards . . . . . . . . 15.4 Solvent Selection via Solubility Parameters . . . . 15.4.1 Background . . . . . . . . . . . . . . . . . . . . 15.4.2 The Kauri Butanol test . . . . . . . . . . . . 15.4.3 The Hildebrand Solubility Parameter . . 15.4.3.1 A one-dimensional solubility parameter. . . . . . . . . . . . . . . 15.4.3.2 Molecular forces . . . . . . . . . . 15.4.4 Hansen Solubility Parameters (HSP) . . . 15.4.4.1 Solvent substitution with HSP 15.4.5 Solvent substitution . . . . . . . . . . . . . . . 15.4.5.1 Multiple components. . . . . . . 15.4.5.2 HSP data and calculations . . . 15.5 Choosing Cleaning Solvents and Cleaning Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.5.1 Choices of solvents . . . . . . . . . . . . . . . 15.5.1.1 Chemical structure and atomic composition . . . . . . . . 15.5.1.2 Technical data . . . . . . . . . . . 15.5.2 Cleaning/rinsing/drying processes . . . . . 15.5.2.1 Solvent cleaning processes . . . 15.5.2.2 Rinsing processes . . . . . . . . . 15.5.2.3 Drying processes . . . . . . . . . . 15.5.2.4 Design features for environmental control . . . . . . 15.5.2.5 Multiple-stage processes . . . . 15.5.2.6 Selection of design features . . 15.6 Control of Quality in Solvent Cleaning . . . . . . . 15.7 Avoiding Common Mistakes . . . . . . . . . . . . . . 15.8 The Future of Solvents and Cleaning . . . . . . . . 15.8.1 Customer preferences . . . . . . . . . . . . . . 15.8.2 Environmental regulations . . . . . . . . . . 15.8.3 Innovation . . . . . . . . . . . . . . . . . . . . . 15.8.3.1 Business innovation. . . . . . . . 15.8.3.2 Technical innovation . . . . . . . 15.8.3.3 Regulatory innovation. . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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814 815 820 821 821 822 823 823 825
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826 827 829 830 831 831 833
.... ....
839 840
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840 851 851 852 853 853
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854 855 856 858 862 863 864 865 866 866 866 867 868
xx
CONTENTS
16 Removal of Particles by Chemical Cleaning . . . . . . . . . . . . . Philip G. Clark and Thomas J. Wagener 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 16.2 Particle/Surface Interactions . . . . . . . . . . . . 16.2.1 van der Waals Force . . . . . . . . . . . 16.2.2 Electrostatic force . . . . . . . . . . . . . 16.2.3 Hydrodynamic force . . . . . . . . . . . 16.3 Process Applications and Chemistries . . . . . 16.3.1 Particle challenge wafer preparation 16.3.2 dHF clean. . . . . . . . . . . . . . . . . . . 16.3.3 SC-1 Clean . . . . . . . . . . . . . . . . . . 16.3.4 Single-step clean . . . . . . . . . . . . . . 16.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
873 876 876 878 880 881 881 882 883 886 886 887
17 Cleaning Using a High-speed Impinging Jet . . . . . . . . . . . . . Kuniaki Gotoh
889
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Fundamentals of Air Jet Removal . . . . . . . . 17.2.1 Apparatus and parameters . . . . . . . . 17.2.2 Definition of removal efficiency . . . . 17.2.3 Effect of operating conditions on the removal efficiency . . . . . . . . . . . . . 17.2.3.1 Pressure drop Pn and distance d . . . . . . . . . . . . . 17.2.3.2 Impinging angle . . . . . . . 17.2.4 Condition of the environment. . . . . . 17.3 New Removal Methods Using the Air Jet Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.1 Pre-charging method . . . . . . . . . . . . 17.3.2 Vibrating air jet method. . . . . . . . . . 17.3.3 Other removal methods . . . . . . . . . . 17.4 Remaining Problems . . . . . . . . . . . . . . . . . . 17.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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889 890 890 894
......
896
...... ...... ......
896 897 903
. . . . . . .
. . . . . . .
906 906 909 913 914 916 916
18 Microabrasive Precision Cleaning and Processing Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rajiv Kohli
919
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. . . . . . . . . . . .
873
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. . . . . . .
xxi
CONTENTS 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Microabrasive Technology . . . . . . . . . . . . . . . . . . 18.3 Fundamental Considerations . . . . . . . . . . . . . . . . 18.3.1 Removal of films . . . . . . . . . . . . . . . . . . . 18.3.1.1 Removal by delamination . . . . . 18.3.1.2 Removal by mechanical erosion . 18.3.2 Removal of particles . . . . . . . . . . . . . . . . 18.4 System Description . . . . . . . . . . . . . . . . . . . . . . . 18.4.1 Nozzle materials and design . . . . . . . . . . . 18.4.2 Type of abrasives . . . . . . . . . . . . . . . . . . 18.4.2.1 Selection of the abrasive . . . . . . 18.4.2.2 Abrasive quality . . . . . . . . . . . . 18.4.3 Air treatment . . . . . . . . . . . . . . . . . . . . . 18.4.3.1 Air drying . . . . . . . . . . . . . . . . 18.4.3.2 Oil contamination . . . . . . . . . . . 18.4.4 Dust collection . . . . . . . . . . . . . . . . . . . . 18.4.5 Recycling and secondary waste . . . . . . . . . 18.4.6 Static charging . . . . . . . . . . . . . . . . . . . . 18.4.7 Scalability . . . . . . . . . . . . . . . . . . . . . . . . 18.4.8 Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5.1 Removal of conformal coatings . . . . . . . . 18.5.2 Thin film removal . . . . . . . . . . . . . . . . . . 18.5.3 Removal of coatings on dental components. . . . . . . . . . . . . . . . . . . . . . . 18.5.4 Cutting brittle materials . . . . . . . . . . . . . . 18.5.5 Precision deburring of metal components. . 18.5.6 Demarking . . . . . . . . . . . . . . . . . . . . . . . 18.5.7 Micromachining of three-dimensional structures . . . . . . . . . . . . . . . . . . . . . . . . 18.5.8 Decorative engraving, etching, and frosting . . . . . . . . . . . . . . . . . . . . . . 18.5.9 Miscellaneous applications . . . . . . . . . . . . 18.6 Advantages and Disadvantages. . . . . . . . . . . . . . . 18.6.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . 18.6.2 Disadvantages . . . . . . . . . . . . . . . . . . . . . 18.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
919 920 921 922 922 923 924 925 926 927 931 932 933 933 935 935 935 936 937 938 938 938 939
. . . .
. . . .
940 940 941 942
..
944
. . . . . . . .
945 946 946 946 947 947 947 947
. . . . . . . .
xxii
CONTENTS
19 Cleaning Using Argon/Nitrogen Cryogenic Aerosols . . . . . . . Wayne T. McDermott and Jeffery W. Butterbaugh 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 19.2 Aerosol Jet Cleaning Mechanisms . . . . . . . . 19.2.1 Adhesion and hydrodynamic forces. 19.2.2 Particle collision . . . . . . . . . . . . . . 19.3 Production of Argon/Nitrogen Cryogenic Aerosol Jets . . . . . . . . . . . . . . . . . . . . . . . 19.3.1 Equipment requirements . . . . . . . . 19.3.2 Operating conditions . . . . . . . . . . . 19.3.3 Cleaning systems . . . . . . . . . . . . . . 19.4 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.5 Effectiveness and Applications . . . . . . . . . . 19.5.1 Kinetics of cleaning . . . . . . . . . . . . 19.5.2 Cleaning performance . . . . . . . . . . 19.5.3 Applications . . . . . . . . . . . . . . . . . 19.6 Future Directions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
951
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
951 953 955 956
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
958 961 964 965 969 970 970 974 981 984 984
20 Carbon Dioxide Snow Cleaning . . . . . . . . . . . . . . . . . . . . . Robert Sherman
987
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . 20.2 Thermodynamic Properties. . . . . . . . . . . 20.3 Cleaning Mechanisms . . . . . . . . . . . . . . 20.3.1 Particle removal . . . . . . . . . . . . 20.3.2 Organic removal . . . . . . . . . . . . 20.3.3 Other mechanisms . . . . . . . . . . . 20.4 Proof of Process . . . . . . . . . . . . . . . . . . 20.5 Equipment . . . . . . . . . . . . . . . . . . . . . . 20.5.1 Nozzles. . . . . . . . . . . . . . . . . . . 20.5.2 Other equipment items . . . . . . . . 20.5.2.1 Moisture control . . . . . 20.5.2.2 Static control . . . . . . . 20.5.3 Input pressure control . . . . . . . . 20.6 Process Parameters . . . . . . . . . . . . . . . . 20.6.1 Redeposition . . . . . . . . . . . . . . . 20.6.2 Recontamination sources . . . . . . 20.6.2.1 CO2 impurities . . . . . . 20.6.2.2 Moisture condensation
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . .
987 988 989 990 990 991 992 994 995 997 997 998 999 1000 1000 1001 1001 1002
xxiii
CONTENTS 20.6.2.3 Static charge. . . . . . . . . . . . . . . . 20.6.2.4 Cleaning technique . . . . . . . . . . . 20.6.3 Surface damage . . . . . . . . . . . . . . . . . . . . . 20.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.2 Vacuum technologies . . . . . . . . . . . . . . . . . 20.7.3 Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.7.4 Hard drive disks assemblies and components 20.7.5 Cleanrooms, process equipment, and tooling 20.7.6 Other applications . . . . . . . . . . . . . . . . . . . 20.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1002 1002 1003 1003 1004 1007 1007 1008 1009 1009 1010 1011
21 Coatings for Prevention or Deactivation of Biological Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joerg C. Tiller
1013
21.1 21.2 21.3 21.4 21.5
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Contaminations . . . . . . . . . . . . . . . . . Means of Contamination . . . . . . . . . . . . . . . . . . General Requirements for Self-cleaning Coatings . Laboratory Tests for Antimicrobial Activity of Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 Agents Against Biological Contaminations . . . . . 21.7 Coating Methods . . . . . . . . . . . . . . . . . . . . . . . 21.7.1 Brush, pad, and roll coating . . . . . . . . . . 21.7.2 Dip and flow coatings . . . . . . . . . . . . . . 21.7.3 Spin coating . . . . . . . . . . . . . . . . . . . . . 21.7.4 Spray application . . . . . . . . . . . . . . . . . 21.7.5 Electroplating . . . . . . . . . . . . . . . . . . . . 21.7.6 Electroless plating . . . . . . . . . . . . . . . . . 21.7.7 Sputtering . . . . . . . . . . . . . . . . . . . . . . . 21.7.8 Physical vapor deposition. . . . . . . . . . . . 21.7.9 Chemical vapor deposition . . . . . . . . . . . 21.7.10 Surface modification . . . . . . . . . . . . . . . 21.8 Non-adhesive Coatings . . . . . . . . . . . . . . . . . . . 21.8.1 Coatings with hydrophilic polymers and hydrogels . . . . . . . . . . . . . . . . . . . . . . . 21.8.2 Ultrahydrophobic coatings . . . . . . . . . . .
. . . .
. . . .
1013 1015 1016 1016
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
1017 1019 1020 1020 1020 1020 1020 1021 1021 1021 1022 1022 1022 1022
.. ..
1023 1026
xxiv
CONTENTS
21.8.3 Influence of surface net charge on microbial adhesion. . . . . . . . . . . . . . . . 21.8.4 Proteins . . . . . . . . . . . . . . . . . . . . . . . 21.9 Microbe Killing or Growth Inhibiting Coatings . 21.9.1 Release systems . . . . . . . . . . . . . . . . . . 21.9.1.1 Diffusion systems . . . . . . . . . 21.9.2 Contact active antimicrobial surfaces. . . 21.9.2.1 Chemical action . . . . . . . . . . 21.9.2.2 Physicochemical action . . . . . 21.10 Metal Coatings . . . . . . . . . . . . . . . . . . . . . . . 21.11 Antifouling Paints . . . . . . . . . . . . . . . . . . . . . 21.12 Antimicrobial Surfaces with Multiple Action . . 21.13 Antiviral Coatings . . . . . . . . . . . . . . . . . . . . . 21.14 Surface Cleaning by Coating. . . . . . . . . . . . . . 21.15 Application Examples . . . . . . . . . . . . . . . . . . 21.15.1 Biomedical applications . . . . . . . . . . 21.15.2 Food protection . . . . . . . . . . . . . . . . 21.15.3 Textiles . . . . . . . . . . . . . . . . . . . . . . 21.15.4 Daily life products . . . . . . . . . . . . . . 21.15.5 Construction and ships . . . . . . . . . . . 21.16 Future Developments . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
1026 1027 1027 1028 1029 1038 1039 1042 1044 1045 1047 1047 1048 1049 1049 1052 1052 1052 1053 1053 1053
22 A Detailed Study of Semiconductor Wafer Drying . . . . . . . Wim Fyen, Frank Holsteyns, Twan Bearda, Sophia Arnauts, Jan Van Steenbergen, Geert Doumen, Karine Kenis, and Paul W. Mertens
1067
22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 22.1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . 22.1.2 Approach followed in this work . . . . 22.1.3 Drying techniques commonly used in semiconductor manufacturing . . . . . . 22.1.3.1 Spin drying . . . . . . . . . . . 22.1.3.2 Surface tension gradient (Marangoni) based drying . 22.2 Theoretical Background . . . . . . . . . . . . . . . . 22.2.1 Stability of wetting films on silica . . . 22.2.1.1 Surface forces . . . . . . . . . . 22.2.1.2 Disjoining pressure . . . . . .
. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .
..... ..... .....
1067 1067 1068
..... .....
1070 1070
. . . . .
1071 1074 1074 1074 1074
. . . . .
. . . . .
. . . . .
. . . . .
xxv
CONTENTS 22.2.1.3 Importance of short range repulsive interactions . . . . . . . . . 22.2.2 Adsorption of ions on silica surfaces . . . . . 22.2.2.1 Structure of the silica–water interface . . . . . . . . . . . . . . . . . . 22.2.2.2 Interaction between metal cations and a silica surface. . . . . 22.2.3 Literature models describing wafer drying . 22.2.3.1 Spin drying . . . . . . . . . . . . . . . 22.2.3.2 Vertical Marangoni-based wafer drying . . . . . . . . . . . . . . . 22.2.3.3 Applicability of the model for vertical drying to a rotating wafer system. . . . . . . . . . . . . . . 22.2.3.4 Limitations of the model for Marangoni-based drying . . . . . . 22.2.4 Salt tracer tests . . . . . . . . . . . . . . . . . . . . 22.2.4.1 Interpretation of salt tracer tests. 22.2.4.2 Available literature data . . . . . . 22.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . 22.3.1 Setups for wafer drying . . . . . . . . . . . . . . 22.3.1.1 Spin drying . . . . . . . . . . . . . . . 22.3.1.2 Vertical Marangoni-based drying 22.3.1.3 Marangoni-based drying of horizontally rotating wafer. . . . . 22.3.2 Analytical techniques . . . . . . . . . . . . . . . . 22.3.2.1 Metal surface concentration by TXRF . . . . . . . . . . . . . . . . . 22.3.2.2 Surface tension by Wilhelmy plate method . . . . . . . . . . . . . . 22.3.3 Characterization of materials and products 22.3.3.1 Wafers . . . . . . . . . . . . . . . . . . . 22.3.3.2 Liquid chemicals . . . . . . . . . . . . 22.3.3.3 Metal salts . . . . . . . . . . . . . . . . 22.3.4 Procedure for the salt tracer tests . . . . . . . 22.3.4.1 Spin drying . . . . . . . . . . . . . . . 22.3.4.2 Vertical Marangoni-based drying 22.3.4.3 Marangoni-based drying on a rotating wafer. . . . . . . . . . . . . . 22.4 Results of Salt Tracer Tests . . . . . . . . . . . . . . . . . 22.4.1 Spin drying . . . . . . . . . . . . . . . . . . . . . . .
. .
1075 1077
.
1078
. . .
1079 1081 1081
.
1086
.
1089
. . . . . . . .
1090 1091 1091 1093 1094 1094 1094 1095
. .
1097 1098
.
1098
. . . . . . . .
1100 1101 1101 1101 1102 1102 1102 1102
. . .
1103 1103 1103
xxvi 22.4.1.1 Spin-off vs. evaporation. . . . . . 22.4.1.2 Uniformity of the evaporated film . . . . . . . . . . . . . . . . . . . . 22.4.1.3 Effect of the rotation speed on evaporation . . . . . . . . . . . . 22.4.1.4 Investigation of adsorption . . . 22.4.2 Vertical Marangoni-based drying . . . . . . 22.4.2.1 Histogram of salt test results . . 22.4.2.2 Effect of IPA flow rate . . . . . . 22.4.2.3 Effect of withdrawal speed. . . . 22.4.3 Marangoni-based drying on a rotating wafer . . . . . . . . . . . . . . . . . . . . 22.4.3.1 Effect of liquid dispensation during drying . . . . . . . . . . . . . 22.4.3.2 Effect of nozzle speed . . . . . . . 22.4.3.3 Effect of liquid surface tension . 22.4.3.4 Investigation of adsorption . . . 22.5 Discussion of Experimental Data . . . . . . . . . . . . 22.5.1 Spin drying . . . . . . . . . . . . . . . . . . . . . . 22.5.1.1 Spin-off vs. evaporation. . . . . . 22.5.1.2 Effect of high rotation speeds. . 22.5.1.3 Wafer topography and surface heterogeneity . . . . . . . . 22.5.2 Marangoni-based drying . . . . . . . . . . . . 22.5.2.1 Limits to the use of salt tests . . 22.5.2.2 Mean surface tension gradient for Marangonibased drying. . . . . . . . . . . . . . 22.5.2.3 Drying speed . . . . . . . . . . . . . 22.5.2.4 Wafer topography and surface heterogeneity . . . . . . . . 22.5.2.5 Alternatives to IPA as a suitable tensioactive component 22.5.2.6 Residues of organic species after Marangoni-based drying . 22.6 Summary and Conclusions . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CONTENTS ..
1103
..
1105
. . . . . .
. . . . . .
1106 1108 1110 1110 1111 1113
..
1114
. . . . . . . .
. . . . . . . .
1114 1115 1117 1118 1120 1120 1120 1121
.. .. ..
1122 1123 1123
.. ..
1124 1126
..
1126
..
1127
.. .. ..
1128 1128 1130
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1137
Contributors
Carlo Altucci Dipartimento di Scienze Fisiche Complesso Universitario di Monte S. Angelo Napoli Italy Sophia Arnauts IMEC Leuven Belgium Twan Bearda IMEC Leuven Belgium William Birch Institute for Materials Research and Engineering (IMRE) Singapore Jeffery W Butterbaugh FSI International Inc. Chaska, MN USA Alain Carre´ Corning S.A. Corning European Technology Center Avon France Philip G Clark 3M, Electronics Markets Materials Division 3M Center St. Paul, MN USA xxvii
xxviii David A Cole Evans Analytical Group LLC East Windsor, NJ USA Geert Doumen IMEC Leuven Belgium John B Durkee Hunt, TX USA Michael L Free Department of Metallurgical Engineering University of Utah Salt Lake City, UT USA Taketoshi Fujimoto Sumika Chemical Analysis Service Ltd. Osaka Japan Wim Fyen K. U. Leuven Research & Development (LRD) Katholieke Universiteit Leuven Leuven Belgium Anthony S Geller Sandia National Laboratories New Mexico Albuquerque, NM USA Kuniaki Gotoh Department of Applied Chemistry Okayama University Okayama Japan
CONTRIBUTORS
CONTRIBUTORS Frank Holsteyns IMEC Leuven Belgium Koji Kato Department of Mechanical Engineering College of Engineering Nihon University Koriyama City Japan Karine Kenis IMEC Leuven Belgium Rajiv Kohli Houston, TX USA Jean L Lee Nano-SciTech Norcross, GA USA Larry Levit MKS, Ion Systems Alameda, CA USA Chao-Hsin Lin Environmental Control Systems Boeing Commercial Airplanes Group Seattle, WA USA Wayne T McDermott Air Products and Chemicals Inc. Allentown, PA USA
xxix
xxx Paul W Mertens IMEC Leuven Belgium Kashmiri L Mittal Hopewell Junction, NY USA Je´r^ ome Molimard Centre SMS Ecole Nationale Supe´rieure des Mines de Saint Etienne Saint Etienne France Beverly Newton Rohnert Park, CA USA Tatsuo Nonaka Sumika Chemical Analysis Service Ltd. Osaka Japan Domenico Paparo Dipartimento di Scienze Fisiche Complesso Universitario di Monte S. Angelo Napoli Italy Othmar Preining Austrian Academy of Sciences Clean Air Commission Vienna Austria Michel Querry LaMCoS UMR CNRS/INSA INSA de Lyon Villeurbanne France
CONTRIBUTORS
CONTRIBUTORS David J Quesnel Department of Mechanical Engineering University of Rochester Rochester, NY USA Daniel J Rader Sandia National Laboratories New Mexico Albuquerque, NM USA Donald S Rimai Eastman Kodak Company Rochester, NY USA David M Schaefer Department of Physics Towson University Towson, MD USA Robert Sherman Applied Surface Technologies New Providence, NJ USA Jan Van Steenbergen IMEC Leuven Belgium Arnold Steinman MKS, Ion Systems Alameda, CA USA Kikuo Takeda Sumika Chemical Analysis Service Ltd. Osaka Japan
xxxi
xxxii Joerg C Tiller Freiburg Materials Research Center University of Freiburg Freiburg Germany Philippe Vergne LaMCoS UMR CNRS/INSA INSA de Lyon Villeurbanne France Thomas J Wagener FSI International Inc. Chaska, MN USA Zhong Lin Wang School of Materials Science and Engineering Georgia Institute of Technology Atlanta, GA USA Lei Zhang DuPont Central Research and Development Wilmington, DE USA Chao Zhu Departmental of Mechanical Engineering New Jersey Institute of Technology Newark, NJ USA
CONTRIBUTORS
I Introduction Rajiv Kohli and Kash L. Mittal
Contaminants on surfaces are of fundamental interest in a wide variety of industries due to their proclivity for causing the failure of critical components. These contaminants can be small particles, thin films, molecular species, ionic species, or microbiological species. Particulate contamination most often is present in the form of dust, for example, lint from clothing and lens tissue, or fine airborne particles. Tiny particles of abrasive or other machining debris also can become embedded in a surface during polishing or other processing operations. On the other hand, film contamination can originate from a variety of sources, including airborne pollutants (water vapor, organic materials, and cleanroom construction materials), outgassing of plastic containers holding finished components, residues from protective strip coatings, dried liquid residue following an improper cleaning operation, and fingerprints left during handling.
I.1
The Impact of Contaminants
In the form of contaminants, small particles can have a major impact on the performance of precision and other products. For example, the presence of impurities such as boron and phosphorous in the parts per billion range can result in the irrecoverable loss of an entire production lot of semiconductor wafers. In a hard disk drive, a particle of dimensions similar to the nominal flying height trapped between the head and the disk can lead to catastrophic failure of the drive. Similarly, the presence of low levels of hydrocarbon contaminants in the components for oxygen service can cause catastrophic damage to spacecraft due to autoignition. Film contaminant layers on the surface of high-quality metallic mirrors or other optical components can increase scattering. Particles on a surface can act as nucleation sites and produce larger cone-shaped defects in the film with increased scattering. Furthermore, contaminant layers on
R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, xxxiii–xliii ª 2008 William Andrew Inc.
xxxiii
xxxiv
I: INTRODUCTION
optical surfaces intended to be further coated with thin films, will affect the adhesion of the films. Similarly, airborne molecular contaminants (AMCs) on a silicon wafer can affect the performance of the device incorporating chips fabricated from such a contaminated wafer. Even on mechanical parts, such as precision gears or other precision metal components, that must be coated with a protective or performance coating, the presence of contaminant films or particles can lead to poor coating adhesion and subsequent failure of the critical component.
I.2
Size Range of Particles
For a detailed characterization, it is first necessary to resolve the particles by their sizes. Discrete particles can be generally classified by size according to Table I.1. Most precision technology applications require characterization of microsize and smaller particles. For example, civilian and defense space agencies in the United States (NASA, National Aeronautics and Space Administration) and Europe (ESA, European Space Agency) specify surface cleanliness levels for space hardware in the micro-particle size range. The cleanliness levels commonly used to specify particulates and nonvolatile residue (NVR) for hardware used for oxygen service are given in Table I.2. Table I.1 Range of Particle Sizes and Selected Techniques for Resolution of Particles for Characterization
Particle Class
Particle Size (nm)
Resolution Techniques
Macro Micro Submicrometer
>50,000 100–50,000 10–100
Nano Atomic
1–10 0.01–1
Subatomic
<0.01
Unaided eye Conventional optical microscopy Near-field optical microscopy and surface plasmon microscopy Electron and probe microscopies Electron and probe microscopies, holography, and resonance force microscopy Femtosecond to attosecond spectroscopy and atomic force microscopy
I: INTRODUCTION
xxxv
However, for other applications, such as the NASA Genesis and Stardust missions, the surface cleanliness levels for the sample return canister are specified at more stringent levels, level 10 for particles and A/5 or A/10 for NVR as shown in Table I.3. These missions collected Table I.2 Common Surface Cleanliness Levels for NASA Aerospace Components for Oxygen Service
Level
300
100
50
Particulate Level Particle Maximum Size (mm) Count per m2 <100 100–250 250–300 >300 <25 25–50 50–100 >100 <10 15–25 25–50 >50
Unlimited* 930 30 0 Unlimited* 680 110 0 Unlimited* 170 80 0
NVR Level Level Quantity (mg/cm2) A B C D
1 2 3 4
*Particles in this size range are not counted.
Table I.3 Surface Cleanliness Levels for the Return Canister for the NASA Genesis Mission
Level 10
5
Particulate Level Particle Maximum size (mm) Count per m2 1 2 5 10 1 2 5
90 80 33 10 30 25 10
Level A/5 A/10
NVR Level Quantity (mg/cm2) 0.2 0.1
xxxvi
I: INTRODUCTION
and returned to Earth samples of unperturbed solar wind and cometary dust.
I.3
Scope of the Book
The individual contributions in the present book discuss in some detail various critical topics regarding the fundamental nature of contaminants, as well as the characterization of contaminants and available methods for removal of contaminants. Each chapter has been contributed by one or more subject-matter experts in surface contamination and precision cleaning. The book does not profess to be all inclusive, but we believe the present contributions provide in a single volume a broad overview of the subject of surface contamination and precision cleaning, as well as reflect the current trends in this arena. The book deals with the fundamental aspects, characterization, and methods for removal of surface contaminants.
I.3.1 Fundamental aspects As semiconductor and electronic device sizes shrink, nanoparticle contamination will become increasingly critical to high yield and high performance. For example, to achieve a data density higher than 77.5 Gb/cm2 (500 Gb/in2), hard disk drive manufacturers will have to make their magnetic bits a mere 15–20 nm across with just 25 nm between the bits. At these sizes, the overall behavior of nanosize particles (<20 nm) is governed by the surface and binding energies of the molecules in the particle. These particles are regarded as complex structures whose behavior depends on the position of the individual molecules and the combined electronic charge distribution. The physical nature of these very small particles is discussed by Othmar Preining in his contribution. In addition, developments in new materials and processes also depend increasingly on an understanding of the application of nanosize components, atomic and molecular scale manipulation, and ultrafast interactions. These interactions in atomic, electronic and even nuclear processes occur at femtosecond (10 15 s) to subzeptosecond (10 21 s) time scales. Here too electron and probe microscopic techniques are being combined with ultrashort laser pulses to track and characterize individual atoms and molecules. The results from these research activities have application to understanding nanoparticle behavior. The contribution by Carlo Altucci
I: INTRODUCTION
xxxvii
and Domenico Paparo discusses the worldwide efforts to elucidate the nature of very small particles by means of ultrafast techniques at the femtosceond and attosecond time scales. Particles smaller than 10 mm adhere to a surface by very strong bonding interactions. These interactions can be covalent or ionic bonding, van der Waals forces, hydrogen bonding, dipole–dipole and electrostatic interactions, or a combination of these interactions. The theoretical forces of adhesion are proportional to particle size, while the removal force varies as the second or third power of the particle diameter, thus requiring an increasingly larger force to overcome the adhesion force between the particle and the substrate as the particle size is reduced. The nature and contribution of these forces are discussed in detail from the particle removal perspective in the contribution from David Quesnel, Donald Rimai and David Schaefer. Particle transport and deposition on surfaces are the subjects of two contributions. Daniel Rader and Anthony Geller discuss the fundamental mechanisms and conditions for the transport of aerosol particles and their deposition onto surfaces. In their contribution, Chao-Hsin Lin and Chao Zhu consider the particle-surface interaction mechanisms in particle transport and deposition and their effect on precision cleaning by mechanical means. When two solid surfaces are brought into contact followed by separation, rolling or sliding in vacuum, in air or in liquid, wear particles are generated at the contact interface that behave as contaminants for the contacting surfaces and surroundings. Koji Kato discusses the mechanisms of wear particle generation and the wear models for adhesive, abrasive, fatigue, and corrosive wear, as well as plastic flow. Thin films are a particularly insidious form of contamination and are very difficult to remove. Examples of such contaminant films are AMCs (airborne molecular contaminants) that are becoming increasingly significant in the semiconductor and other precision industries. The effects of AMCs are often catastrophic. As little as 1 ppb of a contaminant such as boron or phosphorous can result in a 100% yield loss of the silicon wafer. The contribution by Taketoshi Fujimoto, Kikuo Takeda and Tatsuo Nonaka is a comprehensive overview of the nature and effects of AMCs and the techniques for mitigating their effects. From a contamination perspective, electrostatic forces on small particles tend to adhere them very strongly to a substrate. This is of great concern in cleanroom manufacturing. Larry Levit and Arnold Steinman discuss the issues of concern for charged particles and the techniques to mitigate their effects in their contribution.
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I.3.2 Characterization Characterization of surface contaminants present in the form of submicrometer and subnanometer size particles and surface films is essential to understanding their fundamental interactions and their behavior. To develop control and remediation strategies for particle contaminants, it is essential to physically and chemically characterize particles ranging in size from 100 mm to 0.1 nm, as well as thin films. These control strategies are also critical to achieving and maintaining high product yields. As noted earlier, in high technology applications across many industrial sectors, component and feature sizes are continually shrinking. The development of new materials for many of these applications involves particle interactions at the nanometer or even smaller scale. At the same time, there is increasing realization that further advances in the medical field will require understanding of cellular phenomena at atomic and molecular levels. There is a need for real-time imaging of biological processes occurring at the molecular and electronic levels to improve our understanding of human physiology and of the breakdown in the human immune systems. This understanding will help in the development of the next generation of diagnostic and therapeutic technologies. In the semiconductor industry, the critical need is to characterize particles and features in the nanometer and sub-nanometer size range. For example, the next generation of semiconductors in five years or so will be at the 32-nm node. One of the many technology challenges facing the semiconductor industry for the 45-nm node and beyond is the selection of the best critical dimension (CD) metrology equipment to meet the needs of process equipment suppliers and semiconductor manufacturers. The direct measurement of parameters such as lens aberrations, line-edge roughness and overlays will require a host of new metrology capabilities, and the late availability of the means for measurement could delay the introduction of the new technologies. At the same time, alternative materials are being investigated for integrated circuits that will overcome the fundamental limitations of silicon and silica. The materials of choice are oxides and ionic materials. The electronic properties of these materials can be controlled with nanoscale precision, as shown recently by imaging and manipulating the oxygen vacancies in films of fully oxidized SrTiO3 and of SrTiO3 x [1]. The ability to dope oxide films without introducing impurities is very attractive for commercial semiconductor applications. In support of these needs, many methods have been developed for chemical and physical characterization of particles with near-atomic
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scale resolution. These methods take advantage of the complete range of the structure and properties of materials. For medically significant molecules, direct observation at the atomic level would reveal the molecular structure of macromolecules in their natural forms, embedded in their natural environments. By combining the chemical specificity of magnetic resonance spectroscopy with the atomic resolution of probe microscopy, the goal of obtaining 3-dimensional images of individual biological molecules could be achieved. A major milestone in this quest was reached by the recent measurement of the magnetic force from a single electron spin [2]. Electron microscopy techniques are available to image and analyze nanoparticles. Detailed information can be obtained on particle size, size distribution, morphology, surface structure, particle shape, crystal structure, phase transformation, and chemical composition. Zhong Wang and Jean Lee review the available electron microscopy techniques for particle analysis, including scanning electron microscopy, transmission electron microscopy, and scanning transmission electron microscopy. The contribution by David Cole and Lei Zhang presents four classical surface analysis methods: Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), time-of-flight secondary ion mass spectrometry (TOF-SIMS), and low energy ion scattering (LEIS). These methods are uniquely suited for contaminant analysis on contemporary products due to the need to examine materials of ever decreasing concentration and size. These techniques have been developed to a very high degree of sophistication for identification and chemical characterization of surface particles and film contaminants in the nanometer size range. The varying ability of these techniques to determine elemental composition, chemical bonding, and exact compound identification is highlighted in terms of the utility of each method in characterizing industrially significant surface contaminants. There also are a number of different instruments and techniques available to analyze surface ionic contamination. The choice of the instrument or technique can influence the outcome of an investigation, so it is important to understand which technique is best for the type of contamination encountered. In the contribution by Beverly Newton, the nature and effects of ionic contamination on electronic products such as printed circuit boards, semiconductor wafers, and data storage products are described. It also outlines the various techniques available for analysis of ionic contaminants, describes the instrumentation used, and discusses their advantages and disadvantages, and provides examples of application.
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Colorimetric interferometry is a technique used to measure the thickness of thin surface films in the range 1 nm to 1 mm. Michel Querry, Philippe Vergne and Jer^ ome Molimard outline the basic concepts related to visible light interferometry and the main elements of colorimetry in their contribution. The use of these combined techniques is applicable to film-type surface contaminants. The chapter by William Birch, Alain Carre and Kash Mittal presents the importance of monitoring surface cleanliness using wettability techniques. It reviews the fundamentals of surface thermodynamics and the basic theoretical aspects of wetting, followed by the methods for measuring surface wettability. The authors provide some practical examples of the application of contact angle measurements for monitoring cleanliness, and discuss recent developments and future directions in this area with the emergence of new analytical tools for solid surfaces.
I.3.3 Contaminant removal Careful cleaning of critical components is essential to ensure that the performance of the part or the system is not adversely affected. Dust particles larger than 10 mm often can be removed simply by blowing them off with air or nitrogen, or with an aerosol can that has a filter to prevent liquid droplets from escaping. Wet chemical and aqueous cleaning techniques are well established for removal of contaminants. In his contribution, Michael Free describes the use of surfactants to enhance particle removal from surfaces. Surfactants enhance small particle removal from substrates by altering the associated interaction forces between the particle and the substrate, primarily by adsorption of the surfactant on both the particle surface as well as the substrate surface. Although Freon cleaning has also been very effective for removal of contaminants, it is no longer an acceptable cleaning practice due to its high ozone depletion potential and potential adverse effect on the environment. A variety of alternative solvent cleaning agents have been developed to replace Freon as described in the contribution from John Durkee. However, all chemical solvents can have adverse impact on human health and the environment on exposure. The exposure consequences and the regulation of cleaning solvents are also discussed in the contribution by John Durkee. The contributions by Philip Clark and Thomas Wagener is devoted to particle removal by chemical solution methods, including the two most
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common chemistries in use today in production, SC-1 and dilute HF, which are discussed in detail. As noted earlier, aqueous cleaning techniques are well established for removal of surface contaminants; however, they are approaching the limits to remove submicrometer particles (<0.3 mm). In addition, in the semiconductor wafer fabrication industry, water and chemicals usage and chemical recycling and/or disposal can make up as much as 80% of the annual operating costs of a wafer cleaning tool. Furthermore, there are other cleaning applications for which aqueous cleaning or wet chemical methods cannot be used, or for which a non-aqueous technique would be desirable. In response, several non-aqueous precision cleaning and processing techniques have been developed for a wide range of manufacturing applications. One technique that is a sophisticated variation of air or nitrogen blowoff is the use of a high-speed impinging air jet which can remove submicrometer size solid particle contaminants from a surface. As described in the contribution from Kuniaki Gotoh, the efficiency of removal by the high-speed impinging air jet depends on the operating conditions, including air pressure in the jet nozzle, the distance between the nozzle tip and the surface on which particles are deposited, the jet impinging angle, and the humidity of the operating environment. Other dry cleaning techniques use the basic principle of removing particles from a surface by momentum transfer from an impacting source. These techniques have been developed to a very high degree of sophistication for precision cleaning. These impacting sources include microabrasives and argon/nitrogen aerosols. Each of these cleaning techniques is discussed at length in the contributions by Rajiv Kohli and Wayne McDermott and Jeff Butterbaugh. Most common fluids cannot penetrate the stagnant boundary layer on the surface (1–2 mm) that traps the contaminant particles that are smaller than the boundary layer. However, an innovative cleaning system, such as carbon dioxide snow cleaning, employs a cleaning agent that has low surface tension as a fluid to penetrate the boundary layer and also has sufficient accelerating momentum as a solid to dislodge the particles from the surface. Particles as small 30 nm have been successfully removed from a wafer surface, as described in the contribution on CO2 snow cleaning by Robert Sherman. Biological contaminants can result in numerous highly undesirable events such as clogging of industrial fluid flow systems, infection of biomedical devices, or mold growth on various surfaces. A biocidal surface coating is an effective means of preventing biological contamination
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since it acts to alter the surface to prevent microorganisms from attaching to the surface. Joerg Tiller describes the various coatings that have been developed for preventing biological contamination, provides examples of their applications, and discusses their advantages and disadvantages. Drying of cleaned parts is critical to ensure the absence of residual cleaning agents on the surface of the part. Wim Feyn and his colleagues address in detail the issues associated with the drying techniques commonly used in semiconductor manufacturing, including spin drying and Marangoni drying.
I.4
About the Book
In essence, this book addresses many ramifications of surface contamination and cleaning — sources of contaminants; detection, analysis, and characterization of various types of contaminants; as well as ways to monitor the level of cleanliness. It should be underscored that in the world of shrinking dimensions, such as the ever-decreasing size of microelectronic devices, the particles which were cosmetically undesirable but functionally innocuous a few years ago are ‘‘killer defects’’ today, with serious implications for yield and reliability of the components. All indications are that even much smaller size particles will be of concern in the future. So in this book special emphasis is placed on understanding the behavior of nanoscale particles. In conclusion, this book containing bountiful information represents a commentary on many different aspects of this technologically highly important topic. The book further reflects the cumulative wisdom of many experts in this arena. Also, it should be mentioned that the book is copiously referenced and profusely illustrated. Anyone interested (centrally or tangentially) in learning about important recent developments and the current status of the topic of surface contamination and cleaning will find this book an excellent source of much value. The information in this book should be relevant to government, academia and industry personnel involved in research and development, manufacturing, quality control, processing, and procurement specifications in microelectronics, aerospace, optics, xerography, joining (adhesive bonding), biomedical and other industries.
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Acknowledgements First and foremost, we would like to express our heartfelt thanks to all the authors in this book for their contributions, patience, enthusiasm and cooperation during the tenure of this project. Our appreciation goes to the staff of William Andrew for transforming the raw material (manuscripts) in this book form. Rajiv Kohli would also like to thank Jody Mantell for help in locating obscure references and Jeanette Siggins for assistance with preparation of some of the manuscripts for publication.
References 1. D. A. Muller, N. Nakagawa, A. Ohtomo, J. L. Garzul and H. Y. Hwang, ‘‘AtomicScale Imaging of Nanoengineered Oxygen Vacancy Profiles in SrTiO3,’’ Nature 430, 657 (2004). 2. D. Rugar, R. Budakian, H. J. Mamin and B. W. Chui, ‘‘Single Spin Detection by Magnetic Resonance Force Microscopy,’’ Nature 430, 329 (2004).
PART I FUNDAMENTALS
1
The Physical Nature of Very, Very Small Particles and its Impact on Their Behavior Othmar Preining Austrian Academy of Sciences, Clean Air Commission, Vienna, Austria
1.1
Introduction
In aerosol science, particle size is the most important property in governing many aspects of particle behavior. Yet it is a quantity which is not uniquely defined since, depending on the relevant aspect of particle behavior, it may be defined in terms of either its linear geometric dimension or equivalent geometric sizes (i.e. for an equivalent spherical particle) based on the particle volume or surface area, or equivalent sizes for a sphere exhibiting equivalent physical behaviors (e.g. particle aerodynamic diameter and optical diameters). For particles large enough to consider their surfaces or their volumes as continua (larger than about 20 nm), such definitions of particle size are satisfactory. But for much smaller particles, their physical nature—and hence the way in which we think of particle size—needs to be treated differently. In turn, the way in which they interact physically, chemically, and biologically with their surroundings needs to be reconsidered; molecules from the gas phase statistically associated with the particle may change their physical, chemical and even their mechanical properties. Figure 1.1 indicates the spectrum of particle sizes ranging from less than 1 nm to 100 mm where the lower end is close to the size of individual molecules and this makes their behavior so distinctly different from that of larger particles.
1.2
The Spectrum of Aerosol Particle Sizes
To place into perspective the range of particle sizes pertaining to aerosol science in its widest sense, we first consider how particles have been classiR. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 3–24 ª 2008 William Andrew, Inc.
3
4
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Figure 1.1 The aerosol size classes: coarse mode, particles larger than about 1 mm mainly produced by diminution processes; fine aerosol, particles smaller than about 1 mm mainly built up by nucleation, condensation, and coagulation; Nucleation mode and ultrafine aerosol, particles smaller than about 100 nm; Nanosize aerosol, particles smaller than about 20 nm; very, very small aerosol, particles smaller than about 5 nm, particle behavior dominated by surface effects, total number of molecules less than 500; molecular size aerosol, particles smaller than about 1 nm, less than 10 molecules in the particle.
fied and defined in terms of their size. The most used classification of the particle size spectrum for atmospheric aerosol is the three-mode distribution proposed by Whitby (1975), including the coarse mode, the nucleation mode, and the intermediate accumulation mode (see Figure 1.1). The latter is most prominent in atmospheric aerosols because the mechanisms which remove these particles from the atmosphere are the weakest. On the one hand, for the very fine mode, the lifetime of particles in the atmosphere is limited by the mechanisms of diffusion and coagulation (and finally deposition). On the other hand, for the coarse mode, the lifetime of particles is limited by gravitational sedimentation. The intermediate mode contains particles with sizes ranging from about 100 nm to 1 mm. Of course, the size ranges associated with the three modes cannot be defined exactly. So it is irrelevant whether we define size in terms of particle radii or diameter. For present purposes, however, we shall use the term diameter since this provides perhaps the most appropriate overall sense of physical dimension. More generally, beyond discussion of the modes associated with atmospheric aerosol, the size of particles having a diameter less than about 1000
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nm may be discussed in terms of how it relates to various physical phenomena. For example, the diameters of particles in the range 0.3–0.7 mm are of the same size as the wavelengths of visible light, and this clearly influences the way in which such particles interact with it. Particles with diameters smaller than about 100 nm are now referred to as ‘‘ultrafine’’ (deviating from an earlier definition due to the need to distinguish more subclasses; Preining, 1992). Further, ‘‘nanometer size’’ defines particles with diameters less than about 20 nm; it may be useful to define very, very small particles, smaller than about 5 nm (containing only up to 500 molecules), and finally molecular-size for particles with diameters less than 1 nm.
1.3 Atoms and Molecules—Concepts and Dimensions At the smaller sizes in this overall spectrum of aerosols, the physics and chemistry—as well as their interactions with biological systems—are of particular interest for those very small particles. Specifically, for particles with dimensions less than 10 nm the question is posed: how can their surfaces be defined? This relates to how we might define the surface of a molecule or an atom. This requires considering the basic physics of simple atoms, e.g. the hydrogen atom. Figure 1.2 illustrates the radial density distribution of the negative charge (electron) outside the atomic nucleus for two states. Typically for the ground state (i.e. the 1s-state), the radius of the maximum lies approximately at r a0 = 0.053 nm, with a0 being the radius of the electron orbit at the lowest quantum state in the Bohr model (in the Bohr model, the electrons circle the molecules held by electrostatic attraction against centrifugal forces). Hence, an effective diameter of the hydrogen atom may be said to be about 0.1 nm. However, as shown in Figure 1.2, the probability distribution is a continuous function (the charge distribution, a probability density can be calculated from the respective solution of the Schro¨dinger equation, see textbooks of physics, e.g. the Feynman lecture, Vol. III, 1965 or Bergmann Schaefer, Vol. 4, 1992) with finite values extending to considerably greater distances. So the diameter of the hydrogen atom cannot be ascribed any exact value valid for all interactions. Although the probability density falls off rapidly for r > a0, the atom—in the mathematical sense—has no actual sharply defined outer boundary. Now, if the hydrogen atom is given sufficient energy (e.g. by colliding ions, free electrons, or photons) it may become excited (the electronic
6
FUNDAMENTALS
Figure 1.2 Hydrogen atom, s states, spherical symmetry: Upper-half, charge distribution of the electron (probability density) over cross-section, vertical axis arbitrary units, radius in units of a0 = 0.053 nm (first Bohr radius, white bands); Lower-half, inner sphere at the maximum of the charge distribution, outer sphere at the density of the outer break off of the charge distribution. (a) The 1s-state, break off at r = 3a0 the indicated maximum at r = a0; (b) the 2s-state, break off at r = 10a0 the indicated maximum at r = 5.5a0.
charge is elevated to an excitation level, e.g. the 2s-state). The probability density distribution of the electronic charge is then modified and the maximum of probability density is now at r 6a0 = 0.3 nm for the 2s-state. Hence, the effective diameter of the atom might now be said to be close to 0.6 nm. Thus, by simply changing the electronic state of the
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hydrogen atom its physical size has effectively been increased by a factor of about 6. In reality, the situation is more complex, however. In general, it is important to underline the point that the definition of atomic or molecular sizes requires applications of quantum mechanics in considering charge distributions for the electronic cloud surrounding the atomic nucleus. Thus, it is the structure of the electron cloud which really defines the atomic size. So, at this level, we cannot speak of atoms or of molecules as solid entities in the way we do of particles in classical aerosol science. Further, the effective atomic diameter is approximately the same for all elements (a few tenths of a nanometer, a range within a factor of three), even, for example, for a heavy element such as uranium whose atom has as many as 92 electrons. This is because the positive charge of the nucleus increases correspondingly, leading to greater attractive forces and bringing the peak of the respective distribution of the electronic charge closer to the nucleus. The picture becomes even more complicated when atoms are brought together to build molecules. In order to discuss molecular size it is necessary to consider the distance between the centers of the atoms, the bond lengths, and this in turn depends on how we view the particular structure in which the atoms are brought together. The bond lengths are derived mainly from spectroscopy and are often known accurately (up to four decimal places). Table 1.1 shows the bond lengths for some cases (CRC Handbook, 1995). In a chemical bond, some of the electronic charges are distributed around the (2 or more) positively charged atomic nuclei providing the attractive force. In the water molecule the single electronic charge of each hydrogen atom is partly associated with the Table 1.1 Selected Bond Lengths in nm
Compound
Bond
Length
C2 CO CO2 H2O CH4 CH3 O2 C6H6
C–C C–O C–O O–H C–H C–H O–O C–C C–H
0.1242 0.1128 0.1160 0.0957 0.1087 0.108 0.1207 0.1399 0.1101
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FUNDAMENTALS
Figure 1.3 H2O molecule, the rigid structure symbolizes the well-known distances and angle, the 3D-cloud: the charge distribution of the upper (binding) electrons.
oxygen molecule bringing the total charge of the outer electronic shell of the oxygen close to 10 (the ionic portion of this bond is about one-third) (Pauling, 1960; German translation published in 1962). In addition to these bond lengths, however, it is important to note that the overall size of the entity is also governed by the size of the individual atoms as defined by their electronic charge distributions, and this distribution is complex. Consider, for example, a water molecule made up of two hydrogen atoms and a single oxygen atom. Although the effective size of an isolated single hydrogen atom is of the order of 0.1 nm, its size in the water molecule is considerably smaller. When joined with an oxygen molecule, the respective bond length is about 0.1 nm but the overall size of the water molecule is accordingly larger. The water molecule is intrinsically asymmetric, and the hydrogen atoms are mutually located with respect to the oxygen atom at an angle of 104.45 (instead of 90 due to the p-electron structure) as a consequence of their positive net charge of about 1/3e. The molecule is now an electric dipole. The net result is an asymmetric entity whose size is of the order of 0.2–0.3 nm (see Figure 1.3).
1.4
The Model of a Gas
The physics of a gas comprising many such molecules is described by the classical kinetic theory. This embodies a somewhat different approach
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to how molecular sizes are defined, relating to their dimensions (called ‘‘cross-sections’’) which govern how they interact in collisions. The classical model of a gas involves considering the individual molecules as small, hard spherical particles, in random motion and colliding with one another—and in this process exchanging momentum. This model identifies what is known as an ideal gas. The number of molecules in such a system is vast (there are about 6 · 1026 molecules kmol1, Avogadro’s number) and one mole at standard temperature and pressure (STP) occupies 22.41. The molecular density (N) is about 3 · 1025 molecules m–3; from simple geometrical considerations it may be estimated that the mean distance between centers of molecules is about 3 nm. It is interesting to note that this is only about one order of magnitude greater than the overall geometric dimension of the individual molecules, hence, the density of a gas is about 1/1000 of the density of a liquid or a solid. The thermal speeds of the individual molecules are distributed according to Maxwell–Boltzmann distribution. This means that phenomena arising from the molecular motions depend on parameters pffiffiffiffiffiffiffiffi of this distribution, e.g. the root mean-square thermal speed ð hv2 iÞ. The value of this velocity for molecules between collisions (at STP) is high, for example, about 1700 m s1 for hydrogen molecules and about 500 m s1 for air molecules. It is of interest to consider the distance travelled by a molecule between collisions, the mean free path (l). At STP, l is about 70 nm, which is considerably larger than the average distance between molecules. The concept of l requires the definition of the collision cross-section denoted by p s2, with s the (collision) radius of the molecule, equal to the sum of the radii of the colliding molecules—or if these are of the same kind, simply the diameter. The concept requires the hard sphere model and the Maxwellian velocity distribution. The mean free path multiplied with the collision crosssection lp s2 is simply the volume not containing another molecule on average, the sweep volume. This must be equal to 1/N with N being the number concentration of molecules. The classical kinetic thepffiffiffi ory yields for l p ¼ffiffiffið 2Np s2 Þ1 . The factor 1= 2 comes in by the averaging process and is valid only for an ideal gas (see any textbook on kinetic theory of gases, e.g. Weizel, 1958). Since in this expression, s is the molecular diameter for the equivalent hard sphere in the kinetic theory model and ps2 is the cross-section of the molecule for inter-molecular collisions, the other molecules are considered as points without extension. Note that although s/2 may be closely related to the molecular radius introduced earlier, it is not physically the same since it relates to the behavior of
10
FUNDAMENTALS
Table 1.2 Molecular Diameters from Viscosities
Molecule H O H2 He Ne Xe Air CO2
s (nm) 0.092 0.13 0.29 0.29 0.28 0.40 0.36 0.40
Molecule SO2 CH4 C2H2 C6H6 Cyclohexane [NH4]+ [OH]–
s (nm) 0.43 0.38 0.42 0.3 0.61 0.29 0.26
the ideal gas and not specifically to the microscopic properties of each individual molecule. From the kinetic theory of gases, the pressure (P) is given by P = Nm hn2i/3 in which m is the molecular mass. (This is equivalent to P T, with T the gas temperature.) Since P N in this equation, the previous equation for l yields Pl = constant. Finally, the gas viscosity (h) is given by h = 0.217m(hn2i)1/2/p s2. The collision crosssection as defined by the preceding relations can be evaluated by measuring the macroscopic viscosity. Typical molecular diameters derived in this way are given in Table 1.2 (Ro¨mpp, 1977–1988).
1.5
Particles and Gas Molecules
The preceding discussion provides the basis for thinking about the physical nature of very, very small aerosol particles. Consider first as a molecule a hypothetical model sphere with diameter d = 0.5 nm and density 1000 kg m–3. Its mass is about 6.5 · 10–26 kg and it occupies a volume of about 6.5 · 10–29 m3. Its geometrical cross-section is about 2 · 10–19 m2. In terms of atomic mass, the sphere would have a mass of about 40 amu (where 1 amu = 1.67 · 10–27 kg). So this might be considered as a moderately heavy single molecule. We now consider the broad molecular properties of multi-molecule particles, extending into the nanometer range. Table 1.3 summarizes the cross-section, mass, number of molecules, and the fraction of molecules present at the surface of the particle (where d is again the particle diameter). The latter is calculated in two ways: (a) using the relatively simple method which can be applied for
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Table 1.3 Size Fraction of Molecules at the Surface
Size (nm)
Cross-section (10–8 m2)
Mass (10–25 kg)
Number of Molecules
0.5 1.0 2.0 5.0 10.0 20.0
0.2 0.8 3.2 20 80 320
0.65 5.2 42 650 5,200 42,000
1 8 64 1,000 8,000 64,000
Fraction of Molecules at Surface (%) (a) (b) – 100 90 50 25 12
– 99 80 40 20 –
dense structures and (b) by the method reported by Jimbo (1990). It is seen that they are in reasonable agreement (Preining, 1992). In Table 1.3 it is seen that the smaller particles contain only a few molecules practically all at the surface. As particle size increases from 1 to 10 nm, cross-section increases by a factor of 100, and mass and number of molecules by a factor of 1000. Meanwhile, the proportion of molecules at the surface falls from 100% to just 25%. At 20 nm, only about 12% of the molecules are located at the surface of the particle. Of course, if particles are formed by larger molecules (like large organic molecules) the number of molecules per particle will decrease and their surface fraction will increase. Now consider what happens to the electronic structures of the individual molecules when they come together in these particles. By combining in this way, their electronic structures will mutually interact so that the overall chemical behavior of the particles will be different from that of individual molecules—or indeed from free molecules in the gas. They will also be different from the macroscopic bulk state of the substance in question under the same conditions of temperature and pressure. For these very, very small particles the physical situation is therefore unfamiliar. On the one hand, they are not, and do not behave like, individual molecules; but on the other hand, because they contain so few molecules, they cannot be said to be either liquid or solid. They must therefore be regarded as a state of matter which is distinct in its own right. In this state of matter, in particular, we cannot—unlike for much larger entities—approach particles by thinking of them simply in terms of a solid, well-defined surface. There is no such continuum-based description. Rather, the particle must now be regarded as a complex structure
12
FUNDAMENTALS
whose properties, and resultant behavior, will depend on the relative positions of the individual molecules in the particle and finally on the structure of the combined electronic charge distribution (probability density). Consequently, it now becomes apparent that we need to discuss the particle in terms of binding and surface energies of molecules in the particles. Although in the chemistry of materials it is common to express such energy in terms of the units kJ mol1, it is useful here to express it in terms of eV molecule1, where 1 kJ mol1 = 1.036427 · 10–2 eV molecule1 (1 J = 6.24151 · 1018 eV). Table 1.4 shows the energy associated with some simple inter-molecular chemical bonds (CRC Handbook, 1995). From this it is seen that weak bonds may be characterized by energies in the range of about 0.1 eV molecule1 and strong bonds by energies of the order of several eV molecule1. Note here that 1 eV corresponds to a temperature of about 11,605 K, so it corresponds to a very large energy compared to the kinetic energy of molecules at STP (at STP 1/2kT 0.025 eV). Surface tension for bulk materials may also be expressed in the same way, and it is interesting to note that, for most liquids at STP, it ranges from about 0.01 to 0.07 eV molecule1, assuming a molecular surface density in the bulk medium from about 1019–1020 molecules m–2. In the light of this, we now return to the hypothetical particle introduced earlier and consider gold (Au) and water (H2O) particles. Here the binding energy of the particle is estimated by multiplying the single bond energy by the number of molecules; note that this is a crude estimate Table 1.4 Bond Strength at 298 K
Bond C–C Au–Au Cu–O He–He N–O H–H H–CH3 H–OH CH3–CH3 O=CO
kJ mol–1
eV molecule–1
607 225 269 4 631 430 439 498 376 532
6.29 2.33 2.79 0.04 6.53 4.45 4.55 5.16 3.90 5.51
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because the binding energy in a small cluster would be considerably different from that for the bulk material of the same substance. Although the figures shown in Table 1.5 are for the latter, they serve as a useful first approximation for the small cluster more appropriate to very, very small particles. The surface energies for gold and water are 1000 mN m1 (CRC Handbook, 1974) and 72 mN m1 (CRC Handbook, 1995). Under the assumption of about 1019 molecules m–2 this figure yields for gold and water about 1 and 0.07 eV molecule1, respectively. The binding energy for the water molecule corresponds roughly to the H-bridge or to a fraction of the evaporation entropy, the binding energy of Au to about 2/3 of the Au–Au bond. In Table 1.5, the figures in the column marked ‘‘Jimbo’’ are estimates made by Jimbo (1990) for metallic particles in general. It is interesting to note that these are markedly different from those calculated for gold. In this range, the particles may be considered as large molecules—in which case their molecular mean velocities can be estimated by means of kinetic theory. In this way, we find a mean velocity of about 150 m s1 for a particle with d = 1 nm, falling to about 5 m/s for d = 10 nm. Associated with such mean random thermal velocity is the equivalent cross-section as the particle sweeps through a given volume per unit time. This thermal sweep volume provides an estimate of the rate of collisions the particle makes with other molecules (at STP, the molecular density is 2.7 · 1025 molecules m–3). Table 1.6 summarizes these quantities associated with the motion of the small particle, also including the Knudsen number which is Table 1.5 Binding and Surface Energies and their Ratios
ES
EB d (nm) 1 2 5 10 20
Au (eV)
H 2O (eV)
Au (eV)
H2O (eV)
Au (%)
2.3* 18 147 2,300 18,300 147,000
0.2* 1.6 12.8 200 1,600 12,800
1* 8 56 500 2,000 7,700
0.07* 0.56 3.92 35 140 540
– 44 38 22 11 5
Note: EB is the binding energy and Es is the surface energy. * Hypothetical value for one molecule.
R = 100ES/EB Jimbo H 2O (%) (%) – 18.9 10.0 4.2 2.0 –
– 35 30 17.5 8.8 4.2
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Table 1.6 Collisions of Molecules with Particles
d (nm)
0.5 1 2 5 10 20
Thermal Velocity (ms–1) 432 153 54 14 4.8 1.7
Thermal Sweep Volume (10–16 m3 s–1)
Collisions per ns
Knudsen Number (= 2l/d)
3.4 2.7 2.7 3.2 4.2 5.6
9.1 7.2 7.2 8.2 11.3 15.1
280 140 70 28 14 7
defined as a ratio between the molecular mean free path and the particle radius. In Table 1.6, the thermal random velocity of the particle falls as the particle gets bigger. On the other hand, the thermal sweep volume is fairly constant. We see that a particle with d = 1 nm has about 7 collisions per ns, rising only to about 10 for d = 10 nm. This is a very high collision frequency, and so this becomes an important consideration when we think, for example, about particles and their reactions with pollutant gas molecules in the atmosphere. Here, therefore, even if the partial pressure of a pollutant gas species is minute, the chance that a very, very small particle will interact with a molecule of that species within 1 s is itself very high. Conversely, the mean free path of the particle between collisions with gas molecules—of any species—is very small; so is the relaxation time of the particles. Thus, from all the preceding calculations, we must think in terms of very large numbers of events happening in very short time intervals. The particle now considered as a large molecule acquires by collision with gas molecules the same average kinetic energy (equipartition of energy). Since the particle can also rotate it will acquire an average rotational energy accordingly. This rotational energy is stored in an angular velocity of the particle corresponding to its momentum of inertia. Brownian displacement and Brownian rotation play a significant role in the interactions between particles and gas molecules. Table 1.7 summarizes the respective displacements and rotational motions for particles of the given sizes assuming they are spheres with uniform density of r = 1000 kg m–3. The momentum of inertia of a sphere is I = prd 5/60.
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Table 1.7. Brownian Motion
d (nm)
0.5 1 2 5 10 20
1.6
I kg m2
Brownian Displacement nmffiffiffiffiffiffiffi mm p pffiffiffiffiffi ð 1nsÞ1 ð 1sÞ1
5.23 2.64 1.31 0.53 0.24 0.13
165 84 41 17 8.3 4.1
1.65 5.24 1.68 1.64 5.24 1.68
· · · · · ·
10–45 10–44 10–42 10–40 10–39 10–37
Brownian Rotation Rad in Mean 1 ns Equatorial Velocity (ms–1) 1,570 278 49 4.9 0.9 0.15
393 139 49 12 5 1.5
Particle Interactions
1.6.1 Coagulation If 1 g, 1 mg, 1 mg and 1 ng, respectively, of material of density 1000 kg m–3 is dispersed into 1 m–3, then, depending on the size of the individual particles, the number of particles is very large indeed. The half-life of the particles as limited by coagulation can be calculated, given that each collision leads to attachment and coagulation, following the simple equation, dn/dt = – Kn2 (Hinds, 1982). The results are summarized in Table 1.8 (Preining, 1992). Here it is seen, for example, that the half-life for 1 g m–3 of particles with d = 1 nm is of the order of 1 ms. So, the process of coagulation for this aerosol is almost instantaneous. Even for 1 mg/m–3 the half-life is still as short as about 1 ms. At this concentration, the half-life rises to about 1 s when d is as large as 10 nm. From such considerations it becomes apparent that coagulation is a very fast process for very, very small particles, so that in practical situations the lifetime of such particles is mostly very short.
1.6.2 Homogeneous nucleation The conversion of vapor to the particle phase during homogeneous nucleation is very sensitive to the supersaturation ratio (S). The particle
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Table 1.8 Coagulation Constant, Concentration, and Half-life for Very Small Particles
d (nm)
0.5 1 2 5 10 20
K (10–16 m3 s–1)
2.4 3.4 4.8 7.6 10.7 15.1
Particle Number for 1 gm–3
1.5 1.9 2.4 1.5 1.9 2.4
· · · · · ·
1022 1021 1020 1019 1018 1017
Half-life 1 gm–3
1 mg m–3
1 mg m–3
· · · · · ·
3.9 · 10–4 2.2 · 10–3 1.2 · 10–2 1.2 · 10–1 7.0 · 10–1 3.8 ·100
3.9 · 10–1 2.2 · 100 1.2 · 101 1.2 · 102 7.0 · 102 3.8 · 103
3.9 2.2 1.2 1.2 7.0 3.8
10–7 10–6 10–5 10–4 10–4 10–3
1 ng m–3 3.9 2.2 1.2 1.2 7.0 3.8
· · · · · ·
102 103 104 105 105 106
Figure 1.4 Nucleation rate (I) and supersaturation ratio (S) for very small particles.
production rate, I (in m–3 s1), at temperature T = 300 K is given for water by I = C1 exp [ – C2/T 3(ln S )2]. The constants C1 and C2 for water are: C1 = 9 · 1032 s1 m–3 and C2 = 2.15 · 109 K3. Figure 1.4 shows I as a function of S for water where the number of particles produced rises by 15 orders of magnitude as S goes from somewhat less than 3 to about 4. This production rate of primary particles in the nanometer range is so large that, as seen in the preceding discussion, their coagulation must in turn be very fast. In practice, therefore, this means that if there is a process with significant supersaturation (e.g. during expansion) it is not possible to separate the homogeneous nucleation to form nanometer particles from the coagulation of those particles.
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1.6.3 Adsorption Now consider the interaction of very small particles with molecules. As already mentioned, molecules of even a minor gaseous constituent have a high probability of interacting with such a particle. Here, the nature of the interaction depends on the adsorption energy of the molecule at the surface. This may be expressed in terms of the residence time of the molecule at the surface (de Boer, 1953). As shown in Table 1.9, the relatively small adsorption energy of 0.0044 eV molecule1 (i.e. equivalent to 100 cal mol1 in the units usually applied to such situations) corresponds to a residence time of about 1013 s. This should be compared with the collision time between molecules which from knowledge of molecular mean random velocities and molecule size may be shown to be of the order of 10–12 s. However, as the adsorption energy rises to 0.44 eV molecule1, the residence time rises steeply to a value which is about 5–6 orders of magnitude larger than the molecular collision time (Preining, 1995). What happens in such molecular collisions with longer residence times? In effect, molecules may be regarded as staying longer in the vicinity of the particle surface. Although this effect has been postulated since the 1930s (e.g. Zewail and Bernstein, 1992), only during the 1980s physicochemical techniques have become available to measure residence times and reactions as functions of the orientations of molecules. Now, it is known that for asymmetric molecules the reaction between them is strongly dependent on the molecular orientation (Gonzalez-Ure~ na and Vetter, 1995; Orr-Ewing, 1996). Importantly, molecules with long residence times near the particle migrate over the surface of the particle and encounter regions of different electronic structure. This means that the probability of finding a configuration favorable for a reaction is Table 1.9 Adsorption Energies and Residence Times of Molecules
Adsorption Energy (kcal mol1) 0.1 1.5 3.5 10 20 30
Adsorption Energy (eV molecule1)
Residence Time at the Surface (s)
0.0044 0.066 0.154 0.44 0.88 1.32
1.2 · 1013 1.3 · 1012 4.0 · 1011 3.2 · 106 1.0 · 102 4.0 · 10
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increased. This leads to a framework for describing the nature of nanoparticle–molecule interactions.
1.7
Nanoparticles as Molecular Clusters
The properties of a molecular cluster may also be thought of in terms of cluster or condensed matter physics. If the entity is a cluster of several molecules, the binding energy will depend on the number of molecules and their orientation. As mentioned earlier, the system needs to be thought of in terms of its electronic structure. Consider a hypothetical sodium cluster of 20 atoms. Sodium is a metal and each atom contributes one electron to the whole system. So the 20-atom particle has 20 free electrons; however these form a shell-like structure in analogy to the shell structures of atomic nulcei following quantum mechanics. If we look now at the properties of these clusters as a function of the number of sodium atoms, one will find energy extremes for closed shells. Hence, in a random formation process clusters with closed shell structures always even numbered (paired electrons) will be formed more likely than clusters with unpaired electrons. On the other hand, it can be anticipated that clusters with unpaired electrons will be more reactive, hence, their lifetime is reduced and they will be less frequently found. The shell structure has been numerically modelled using a structure of relatively densely packed positively charged nuclei called jellium. The free electrons reside in the potential of this structure. They are now in a field similar to a proton in an atomic nucleus. Hence, a closer analogy exists to the shell model of nuclear physics than to that of atoms. Such a model yields the energy levels schematically given in Figure 1.5 (see Bergmann Schaefer, 1992). The situation is different for positively charged clusters. Now the binding energy is larger for odd-numbered clusters as recently found, see Table 1.10 (Bonacic-Koutecky et al., 1996). The importance of quantum mechanics for describing the (mechanical) properties of nanostructures has been recognized. However, new numerical techniques such as internal coordinate quantum Monte Carlo methods are just yielding first results and progress can be expected in the near future (Noid et al., 1997). Newly formed clusters, particularly cluster aggregates, may have a loose structure containing voids. Such structures can appropriately be described by their fractal dimension. Heat treatment can compact these clusters so they finally get the structure of a solid with a fractal dimension of three (Schmidt-Ott, 1988; Weber et al., 1997; Kleinwechter et al., 1997).
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Figure 1.5 Energy scheme of electrons in a sodium cluster.
Table 1.10 Binding Energy Per Atom for Na+ Clusters
n
E (eV)
n
E (ev)
2 3 4 5
0.49 0.72 0.64 0.71
6 7 8 9
0.67 0.72 0.70 0.72
1.8 An Interaction Model for Nanometer–Sized Particles Which model is appropriate for describing particle–molecule interactions in the gas phase for an entity with dimensions of a few nanometers or less? We cannot define the surface of the entity as being in any sense a continuum or its volume as being a dense system of atoms or molecules. It is neither liquid nor solid and its structure may not be constant with time. The particle itself is very small compared to the mean free path of the gas molecules, and, when the adsorption energy is greater than about 0.1 eV molecule1, the particle will carry adsorbed molecules, which in
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turn may change the particle properties. The physical picture is portrayed in Figure 1.6, where the so-called nanoparticle phase is surrounded by a gas-phase boundary layer comprising the molecules which have collided with the particle and are migrating over its surface, and where molecular adsorption has taken place at some part of the particle’s surface under favorable electronic conditions. The particle is surrounded in its immediate vicinity by a cloud whose molecules are continuously changing within nanoseconds based on the residence time of molecules near the particle. So it can be said that this cloud belongs to the particle. The particle size has a strong influence on all features of particle– molecule interactions. One example is the Kelvin-equivalent diameter of silver and sodium chloride particles. Such diameters have been measured by Porstendo¨rfer et al. (1985). The results are given in Table 1.11. Sodium chloride particles behave in the same way as water droplets
Figure 1.6 The very, very small particle. The white band with a width of about 0.05 nm indicates the outer electronic structure of the molecules forming the particle, the cloud around it shows molecules dynamically adsorbed for periods large compared with ideal molecular collision times but small compared to observations (timescale seconds), the black section indicates permanently adsorbed molecules (two-dimensional condensate).
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Table 1.11 Kelvin-Equivalent Diameters of NaCl and Ag Particles
Geometric Diameter Kelvin-Equivalent Diameter TEM NaCl Ag dk (nm) dk/dG dk (nm) dG (nm) 6 8 12 18
14 21 29 40
2.3 2.6 2.4 2.2
3.2 4.0 5.0 7.1
dk/dG 0.53 0.50 0.42 0.39
of a much larger size and silver particles of a much smaller size. These results show that particle surface and gas reactions are very sensitive to preparation, and small particles behave differently than bulk material of the same substance.
1.9
Concluding Remarks
What may be learned from the basic physics of gases and molecules to identify the main properties of nanometer-sized particles which might have a significant bearing on their behavior, making them distinct from molecules themselves at one end of the size spectrum and from the much larger particles most familiar to aerosol scientists at the other end. A particle in the size range below about 5 nm comprises a relatively small number of molecules. So it is no longer appropriate to think of the particle as an entity which exhibits the properties of the bulk material from which it is derived. Now we cannot speak of it in terms of a volume or a surface which derives from the assumption that the structure of the particle is a continuum. As has been stated more than once, the nature of the particle, unlike for large particles, cannot be regarded as that of either the liquid or the solid state. The nanoparticle is therefore a molecular cluster which must be regarded as an entirely distinct phase of matter, the nanophase. In this phase, the character of the particle is governed by the properties of the individual atoms and molecules: their configuration, their individual, combined, and mutually influenced electronic states. Therefore, considerations of particle behavior and the way the particle interacts with other entities must be based on both quantum mechanics and classical kinetic theory.
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The dynamic properties of the nanophase are extremely important. Nanoparticles are formed in very large numbers during nucleation. But coagulation of such particles occurs very rapidly even at very low mass concentrations. So the lifetime of such particles under normal conditions is very short. This in turn imposes constraints on the kinetics of how such particles interact with other entities—physically, chemically, or biologically. Currently, only simple interactions are well understood. But we are now beginning to anticipate significant scientific advances based on the very special nature of nanoparticles. It is expected that during the years ahead, kinetic theory, quantum mechanics, and aerosol dynamics, together with applications arising from advancing knowledge of these fundamental disciplines, will enable us to predict the interactions in much more complicated systems. Such basic understanding of the different molecular configurations, their orientation, their Brownian rotation, and their chemical interactions will change our perception of atmospheric and gas chemistry. This will also force us to think about new approaches in the development of chemical reactors towards the production of new and more advanced materials. One particularly important aspect of small particles is the way in which they might interact with cells in biological systems. In relation to air pollution, for example, there is increasing concern about the role of small atmospheric particles in the observed increases in disease and mortality in the human populations (e.g. Seaton et al., 1995). In this regard, it seems relevant that Donaldson et al. (1997) have demonstrated in vitro that some types of very small particles can generate hydroxyl radicals to a far greater extent than larger particles of the same substance. In case such particles are inhaled and deposited in the deep lung, this suggests a mechanism for the generation of harmful oxidants which may be precursors of the types of ill-health observed. In summary, aerosol scientists and their colleagues in the other disciplines will discover and eventually understand interactions involving nanoparticles which have not yet even been thought about. This will provide great opportunities for advances in aerosol science. As Friedlander (1996) remarked at the 1996 Annual Conference of the American Association of Aerosol Research in Orlando, Florida: ‘‘... From a scientific point of view it combines the field of aerosol dynamics with aspects of solid state physics and chemistry at the nanometer scale. This will be a very challenging scientific task, both theoretically and experimentally.’’
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Acknowledgements The author thanks J. H. Vincent and G. Breschar for their help in preparing the paper from a transcription of the lecture, as well as A. Kasimir for creating the graphics. This work was supported by the Austrian Academy of Sciences, Clean Air Commission.
References Bergmann, L. and Schaefer, C. (1992). Lehrbuch der Experimentalphysik, Vol. 4, Teilchen, Vol. 5, Vielteilchen-Systeme (Edited by Raith, W.). Walter de Gruyter, Berlin. Bonacic-Koutecky, V., Pittner, J. and Fuchs, C. (1996) Ab initio predictions of structural and optical response properties of Na+n clusters. Interpretation of depletion spectra at low temperature. J. Chem. Phys. 104, 1427–1440. CRC Handbook of Materials Science, Vol.1, C. T. Lynch (Ed.), CRC Press, Boca Raton, FL (1974). CRC Handbook of Chemistry and Physics (1995) 75th Edition. CRC Press, Boca Raton, FL. de Boer, J. H. (1953) The Dynamical Character of Adsorption. Clarendon Press, Oxford. Donaldson, K., Li, X. Y. and MacNee, W. (1998) Ultrafine (nanometre) particle mediated lung injury. J. Aerosol Sci. 29, 553–560. Feynman, R. P., Leighton, R. B. and Sands, M. (1965) The Feynman Lectures of Physics, Vol. III. Quantum Mechanics. Addison-Wesley, Reading, MA. Friedlander, S. K. (1996) Aerosol technology: pushing the frontiers. Paper Presented at the Annual Conference of the American Association for Aerosol Research, Orlando. Gonzalez-Ure~ na, A. and Vetter, R. (1995) Reactive collisions with excited-state atoms. J. Chem. Soc. Faraday Trans. 91, 389–398. Hinds, W. C. (1982) Aerosol Technology. Wiley, New York. Jimbo, G. (1990) Funtai, powder, particle and beyond. Proc. 2nd World Congress on Particle Technology, 19–22 September, 1990, Kyoto, Japan. Kleinwechter, H., Friedlander, S. K. and Schmidt-Ott, A. (1997) Investigation of agglomerate restructuring. J. Aerosol Sci. 28, 763–764. Noid, D. W., Tuzun, R. E. and Sumpter, B. G. (1997) On the importance of quantum mechanics for nanotechnology. Nanotechnology 8, 119–125. Orr-Ewing, A. J. (1996) Dynamical stereochemistry of bimolecular reactions. J. Chem. Soc., Faraday Trans. 92, 881–900. Pauling, L. (1960) The Nature of the Chemical Bond, 3rd Edition. Cornell Univ. Press, (German edition, translated by H. Noller (1962) Verlag Chemie, Weinheim). Porstendo¨rfer, J., Scheibel, H. G., Pohl, F. G., Preining, O., Reischl, G. and Wagner, P. E. (1985) Heterogeneous nucleation of water vapor on monodispersed Ag and NaCl particles with diameters between 6 and 18nm. Aerosol Sci. Technol. 4, 65–79. Preining, O. (1992) The science of ultrafine particles. Pure & Appl. Chem. 64, 1679–1684. Preining, O. (1995) The Fuchs award lecture 1994. J. Aerosol Sci. 26, 529–534.
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Ro¨mpp Chemie Lexikon (1979–1988) (Edited by Neum€ uller, O. A.) 8. Aufl. Franckh, Stuttgart. Seaton, A., MacNee, W., Donaldson, K. and Godden, D. (1995) Particulate air pollution and acute health effects. Lancet 345, 176–178. Schmidt-Ott, A. (1988) New approaches to in situ characterization of ultrafine agglomerates. J. Aerosol Sci. 19, 553–563. Weber, A. P. and Friedlander, S. K. (1997) In situ determination of the activation energy for restructuring of nanometer aerosol agglomerates. J. Aerosol Sci. 28, 179–192. Weizel, W. (1958) Lehrbuch der Theoretischen Physik, Vol. 2, Struktur der Materie. Springer, Berlin. Whitby, K. T. (1975) Modelling of Atmospheric Aerosol Size Distribution. Particle Technology Laboratory Pub. No. 253, University of Minnesota, Minneapolis. Zewail, A. and Bernstein, R. (1992) Real time laser femtochemistry. In The Chemical Bond (Edited by Zewail, A.), pp. 223–279. Academic Press, San Diego.
2 Elucidating the Fundamental Interactions of Very Small Particles: Ultrafast Science Carlo Altucci1,2 and Domenico Paparo1,3 1
Dipartimento di Scienze Fisiche, Complesso Universitario di Monte S. Angelo, Napoli, Italy 2
Consorzio Nazionale Interuniversitario di Struttura della Materia – CNISM, Napoli, Italy 3
Coherentia-CNR-INFM, Napoli, Italy
2.1
Introduction
This chapter is essentially written as a tool for those scientists who, dealing with nanoparticles and thin films topics, need to employ ultrafast optical techniques in order to investigate the system under study. In fact, with feature sizes shrinking in semiconductor devices and the increasing interest in nano-scale processes and systems, contamination from nanoparticles and molecular films is becoming increasingly critical to high yield and performance of electronic devices. Thus, this chapter concerns a number of physical concepts and experimental methods which we believe to have a more direct impact and are directly useful for the abovementioned community of scientists. A complete review on the very wide subject represented by Ultrafast Science is well beyond the purpose of this chapter. Moreover, the so-called ultrafast science is also currently a very hot topic in impressive and tumultuous development whose actual and potential applications diffuse toward a lot of fields, sometimes far from each other. Amongst these fields, the so-called Nano-Science is presently one of the hottest and most dynamic. It is also impressively interdisciplinary, collecting the physical, chemical, and biological behavior of systems characterized by having nanometric spatial extension. In order to have an idea of how enormous the challenges nano-science is facing at the moment, let us just remind the reader of the most important R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 25–187 ª 2008 William Andrew, Inc.
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environmental issue of the next decade, i.e. the role of combustiongenerated particles, either in causing increased respiratory and cardiovascular weakness and/or mortality, or in affecting the radiative balance of the atmosphere. Therefore, an extensive review of the applications of techniques and methods, typical of ultrafast science, to investigate the physical systems of the nano-science and nano-technology is a formidable task and very far beyond the reasonable extension of a chapter. Thus, trying to match the necessary limits imposed by a reasonable length of our topic and to focus the attention on the most important techniques borrowed from the ultrafast science, each concept or experimental technique is usually briefly explained throughout the chapter with the aim to enlighten both the most important physical features and the possible practical consequences for applications. In many cases details are just cited. An effort has been made to provide a wide and complete bibliography, mainly with the intention of catching the attention of the reader, and possibly offering ideas and fundamental bibliographic references for solving specific problems. Just to give here a first quick example of the wide potential applications of ultrashort pulses to the study of nanoparticles, it is worth mentioning the possibility of determining the nanoparticle radius by means of time-resolved fluorescence investigation. It is well known, in fact, that for nanoparticles in solution the Stokes–Einstein relation connects the fluorescence decay time tf, of the nanoparticle species to the viscosity of the solution h = 3t f kbT/4pr3, r being the average hydrodynamic radius of the nanoparticle and T is the absolute temperature of the solution. Thus, with the help of a laser source delivering pulses much shorter than the fluorescence decay time of the system under study, it is possible to investigate the time-resolved fluorescence response of the solution and to determine the nanoparticle average linear size. This optical technique has two remarkable advantages when compared to other investigation tools, such as X-ray or neutron scatterings, which directly access the nanometric scale of the particle size through the radiation wavelength. First, it is much simpler, demanding a much more compact and low-cost experimental apparatus and, second, it also allows one to study the dynamics of the nanoparticle radius, which may be an interesting task, for instance, during sol–gel glass formation in order to better understand the mechanism of the nanoparticle growth [1]. This method has been widely employed also in more complicated and sophisticated versions such as time-resolved fluorescence anisotropy induced by one photon (see for example [2]) and multiphoton excitations [1]. Several other methods and tools for studying
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the nanoparticle properties, based on the ultrafast techniques, will be treated and explained in detail in the following sections. This introduction is followed by eight other sections, the first two of which are more detailed and developed. In fact, Sections 2.2 and 2.3 are dedicated to the techniques employed for ultrashort pulse generation and to the dynamics of atoms and molecules in strong fields, respectively. In a sense, these two first sections can be thought of as the basis for the following subjects, as they treat the fundamental tools of ultrafast science, i.e. the ultrashort laser source, and its basic interactions with matter, namely the interactions with atoms and molecules. Some more detail is often provided for those topics which are presently really at the frontier of science, and which may, hopefully, open the way for new intriguing techniques for the time-resolved investigation of more complicated and quasimacroscopic systems. Hence, the hot topics of attosecond pulse generation and few-optical cycle pulse characterization are explained in more detail. Successively four other shorter sections follow, which deal with the bond-breaking dynamics in single molecules (Section 2.4), with controlling the molecular populations and chemical reactions by using ultrafast pulses (Section 2.5), with nonadiabatic processes in polyatomic molecules (Section 2.6), and with the latest results in ultrafast crystallography (Section 2.7). These sections are, indeed, devoted to the most recent advances in more complex molecular dynamics and crystallography and also referring to rather new techniques such as Time-Resolved Electron Diffraction (UED). The following section (Section 2.8) is more specifically dedicated to nonlinear optical time-resolved techniques for probing properties of surfaces. It is mostly based on two extremely powerful tools: the Second Harmonic Generation by Surfaces (SSHG) and the SumFrequency Generation from Surfaces (SSFG). Special subsections concern the investigation of metal nanoparticles (MNPs) and thin films by the use of these two techniques. The conclusions are presented in Section 2.9.
2.2 Techniques for the Generation of Ultrashort Pulses 2.2.1 Basic concepts: mode locking and early generations of ultrashort laser sources The whole field of ultrashort laser sources was given a boost by the invention and implementation of the technique called mode locking
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(see for example [3–6] for a recent and exhaustive review). The mode locking technique consists essentially in locking in phase a large number of longitudinal modes simultaneously oscillating in a laser cavity, the frequency separation between two adjacent nodes being the inverse of the resonator round-trip time 1/Tr. In fact, the time-dependent radiation intensity circulating into a cavity of length l, produced by N such modes having the same amplitude and phase is proportional to 2 + N1 k0X sin2 ðNvt=2Þ eikvt = IðtÞ k=k sin2 ðvt=2Þ 0
Eq. (2-1)
where v is the central angular frequency, k0 is the first-order longitudinal mode of the gain curve of the cavity, and c is the speed of light in vacuum. Therefore, I(t) is a periodic function of period given by the round-trip time of the cavity, Tr = 2p/v = 2l/c. It consists of a succession of sharp peaks having amplitude proportional to the square of the number of locked modes N2, namely the peak power is N times the average power; the full width at half maximum diminishes with N as DTFWHM ’ Tr/N. Such a regular structure of I(t) is preserved even when the locked modes do not have the same phase, but they have a constant phase difference between adjacent modes. As shown in [7], the mode-locked feature of the radiation intensity is instead completely spoiled when the phase difference between longitudinal modes is not regular but rather randomly distributed or fluctuating in time as it happens for nonmode-locked lasers. Thus, in a mode-locked laser source the entire radiation energy content trapped into the cavity is concentrated in a sequence of short regular spikes equally spaced in time. Each time when a pulse hits a partially reflecting mirror, a portion of its energy is coupled out of the oscillator, leading to a train of ultrashort pulses, as schematically represented in Figure 2.1. By relying on the mode-locking technique, the first generation of mode-locked, solidstate lasers (Nd:glass, Nd:YAG, and ruby) could deliver pulses having durations even shorter than 100 ps. The mode-locking of longitudinal modes in the cavity was achieved either by active or passive techniques. In the first case some external electronic oscillator drives an active loss or a frequency modulation [8, 9], while in the latter case a passive loss modulation is induced by a fast response saturable absorber [10, 11]. A saturable absorber is a nonlinear element exhibiting increased transmittance for increased laser intensity. The latter technique, illustrated in Figure 2.2, is more efficient in producing shorter pulses even though less stable; thus, in most cases, it was implemented together with the active mode-locking.
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Tr
I(t)
DTFWHM
l DTFWHM ªTr /N N: Number of locked modes
Figure 2.1 Schematic of a mode-locked laser source. The radiation power is delivered as a train of short, regular, intense peaks, separated in time by the round-trip time of the cavity, Tr. The time-averaged output power of the laser is, of course, the N th fraction of the peak power, N being the number of locked modes in the cavity. Initial state (free running)
Intensity-dependent transmission T(I(t))
I(t) t
t+Tr
Final state (mode locked) T(I(t)) I(t) t
t+Tr
Figure 2.2 Principle of passive mode-locking. The upper drawing represents the initial state of the laser pulse, born in the cavity in the free running operation mode. Therefore, the transmissivity (upper bold line) of the saturable absorber, being still linear, perfectly follows in time the time-dependent intracavity laser intensity (lower continuous line). The lower drawing shows the time-dependent saturable absorber transmissivity and transmitted laser intensity when the intracavity laser intensity is high enough to saturate on the top the saturable absorber: therefore only the most intense part of the pulse, very short in time, is fully transmitted and can be successively amplified by other round-trips in the cavity.
The picosecond response time of organic saturable absorbers utilized for passive mode-locking sets a limit to the pulse duration. A second generation of mode-locked laser sources appeared when saturable absorbers were employed for mode-locking of continuous-wave (cw) operation
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organic dye lasers [12, 13]. The picosecond barrier of the pulse duration, imposed by the response time of the saturable absorber, was broken thanks to the active role of the gain saturation in pulse formation [14– 16]. Sub-picosecond laser pulses could be produced for the first time [17]. Successively, the adoption of intracavity dispersion control techniques, such as low-loss Brewster-angled prism pairs [18, 19], allowed to shorten the pulse duration down to sub-100 fs pulses. The most widely used organic dye as active medium was Rhodamine 6G (Rh6G) emitting at around 620 nm, but a number of other cw dye lasers were successfully mode-locked to produce femtosecond pulses in the visible and near infrared spectral domain and were used mostly for femtosecond spectroscopy (for a review of ultrashort pulse dye lasers see [20, 21]). Together with the noticeable progress of the ultrafast dye laser sources, solid-state materials knowledge also advanced considerably. In particular, a number of new laser media emerged, characterized by laser transitions with enormous bandwidths in the near infrared spectral range, and therefore were good candidates for delivering ultrashort laser pulses. Most of these materials are constituted by host crystals (YAG, sapphire, forsterite, and LiSAF) doped with transition metals (titanium and chromium) ions. Such materials exhibit extremely wide fluorescence emission spectra, over 100 THz, as shown in Figure 2.3 [22–24]. Continuous-wave passive mode-locking of broadband solid-state lasers was achieved by using either resonant [25] or nonresonant [26] optical nonlinearities. The simultaneous interplay, in soliton-type regime, between negative intracavity group delay dispersion (GDD) and self-phase modulation (SPM) due to nonresonant Kerr effect led to the generation of optical radiation pulses very much shorter than the sub-picosecond absorber recovery time [27]. New fast-response
Figure 2.3 Fluorescence spectra emitted by four of the main transition-metaldoped broadband solid-state laser crystals.
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saturable absorbers, based on nonresonant optical nonlinearities, were implemented, which removed the picosecond barrier of the solid-state laser pulse duration. The most important of these new saturable absorbers was constituted by a single-mode fused silica fiber mode-locker that introduces intracavity Kerr nonlinearity. The technique, called coupled-cavity or additive-pulse mode-locking, has essentially the effect of introducing a fast saturable absorption over a large range of wavelengths irrespective of the fiber dispersion [28–31]. In the additive-pulse mode-locking, in fact, the saturable absorber effect results from the coherent superposition of the intracavity pulse with its self-phase-modulated replica [32, 33], thus leading to cw self-starting passive mode-locking solid-state femtosecond lasers [34, 35]. The same technique was also employed in all-fiber femtosecond lasers [36–40] (see also [41, 42] for recent reviews).
2.2.2 Sub-100-fs pulses and chirped pulse amplification The real breakthrough which made it possible to strongly boost the ultrafast laser source technology was the discovery of self-mode-locking [22, 43, 44] in a titanium-doped sapphire (Ti:Sa) laser. Successive experiments [45] and theoretical studies [46–49] indicated that self-focusing [50, 51] due to the Kerr nonlinearity of the laser crystal is transformed by an intracavity aperture into an ultrafast saturable-absorber-like selfamplitude-modulation (SAM). This technique, called Kerr-lens modelocking (KLM) always associated with SPM, together with some negative GDD, constitutes the basis for the generation of sub-100-fs laser pulses. The optical Kerr effect in the laser host crystal results in a fast change, proportional to the cycle-averaged laser intensity I(r, t) (W.cm2), of the crystal refractive index: Dnðr; tÞ = n2 Iðr; tÞ
Eq. (2-2)
n2 (W.cm2) being the nonlinear refractive index. Thus, KLM results in a lensing effect, due to the radial intensity profile of the laser beam, which tends to more tightly focus the most intense part of the beam. A proper aperture placed at a suitable position in the cavity transmits a larger portion of the laser beam at instants of higher intensity (Figure 2.4), thus behaving as a fast saturable-absorber which reduces loss for higher intensities. This KLM effect, therefore, triggers and keeps the formation of an ultrashort radiation pulse in Ti:Sa and other solid-state lasers. At the
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FUNDAMENTALS
Low Laser beam
n=n0+n2I(r,t) High intensity
Figure 2.4 KLM technique: fast saturable-absorber behavior of an intracavity aperture. The change of the trasmissivity of the intracavity aperture, induced by self-focusing, favors the most intense part of the beam while high losses are introduced for the low intensity part.
same time, Dn(r, t) directly modulates the phase of the laser beam (SPM). SAM and SPM changes, upon each round trip of the laser pulse oscillating in the resonator cavity, are simply proportional to the complex amplitude envelope A(t), the time t being measured in the retarded frame of reference where the pulse always peaks at t = 0, according to: DAðtÞ = kSAM pðtÞAðtÞ
Eq. (2-3)
DAðtÞ = ikSPM pðtÞAðtÞ
Eq. (2-4)
and
respectively. In Eqs. (2-3) and (2-4), A(t) is related to the laser electric field by EðtÞ = AðtÞeiv0 t + if0 + c:c:, where v0 and f0 are the laser carrier angular frequency and phase, respectively, while p(t) j A(t) j 2 is the cycleaveraged time-dependent radiation power carried by the laser beam and kSAM, kSPM(W1), denote the SAM and SPM coefficients, respectively (see [52] for a recent complete analysis of KLM). For SPM an easy calculation gives [53]: kSPM = g SPM L ; g SPM =
2n2 l0 w20
Eq. (2-5)
where l0 is the carrier wavelength of the laser pulse, L is the Kerr medium length assumed to be shorter than the confocal parameter 2z0 = 2pw20 =l0 , and w0 is the beam radius at 1/e2 of maximum. Typical values of kSPM and
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kSAM in KLM Ti:Sa lasers are 106 and 107 W1, respectively [26]. Since typical intracavity peak powers are on the order of 105–106 W in the femtosecond regime, KLM introduces, mostly via SPM, an amplitude modulation of just few percent which is unable to stop the severe pulse broadening caused by dispersion of the laser medium. Thus, in order to shorten the pulse duration well below the 100 fs limit, which is of course allowed by the broad gain bandwidth in Ti:Sa lasers, a negative GDD must be introduced which compensates dispersion induced pulse broadening. Dispersion corresponds to the change of the phase retardation of the optical system with respect to the frequency, f(v), and, therefore, can be analyzed by expanding the group delay Tg(v) = f0(v) around the central frequency of the pulse spectrum, v0: 1 Tg ðvÞ = f0 ðv0 Þ + f00 ðv0 Þðv v0 Þ + f000 ðv0 Þðv v0 Þ2 2 1 0000 + f ðv0 Þðv v0 Þ + + 6
Eq. (2-6)
where the constant term f0(v0) represents the time it takes for the peak of the pulse to propagate through the dispersive medium. f00 (v0) namely the linear term, is referred to as the GDD and denoted by D, whereas the higher order dispersion terms are denoted by f000 (v0) = D3, f0000 (v0) = D4 and so on. Dispersion coefficients reach a critical value, above which dispersion causes a serious pulse deformation according to the simple scaling law fðnÞ = t nlaser . Thus, for instance, a GDD of f00 = t2laser implies a pulse broadening of more than a factor of 2 and reveals how dramatic dispersion-induced broadening can be for ultrafast pulses which have a large frequency content. Most laser media and optical material usually exhibit positive GDD, namely a group delay increasing with frequency. Therefore, an ultrashort pulse which propagates through one of these media assumes a positive frequency sweep or, as it is usually termed, chirp. For example, a sub-100-fs pulse tends to broaden while traversing even few mm of quartz or sapphire, and the shorter the pulse duration or the higher the pulse energy the more the pulse broadens, until self-phasemodulation due to optical Kerr effect can be triggered. The same phenomenon can also be viewed in the temporal domain, where a chirped pulse is represented by having a phase term, F, of the form: FðtÞ = v0 t + fðtÞ; fðtÞ = f0 + at2 + bt3 +
Eq. (2-7)
where the coefficient a (rad fs2), is usually named the linear term chirp coefficient as it implies a frequency sweep which is linear in time, and the
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FUNDAMENTALS
other coefficients, b (rad fs3) and so on, are the higher order term chirp coefficients. Thus, in order to compensate for dispersion effects, some negative intracavity GDD is needed, for example by inserting a pair of prisms [18]. By properly using the interplay between Kerr-induced SPM and negative intracavity GDD, a regime characterized by pulse durations well below 100 fs can be accessed [54] until reaching, nowadays, the fewoptical cycle regime. Since kSPM >> kSAM, solitary pulse shaping in the presence of a net negative intracavity GDD determines the steady-state pulse duration in KLM Ti:Sa lasers. In this condition and by relying on the weak pulse-shaping approximation j DA(t)/A(t) j << 1, it turns out that [49, 55] the steady-state pulse amplitude takes the form A(t) = A0 sech(t/t 0) with: t0 =
2jDj kSPM Wp
Eq. (2-8)
having a pulse duration, tlaser, full width at half maximum of the pulse power p(t) j A(t) j 2, of 1.76 t 0. In Eq. (2-8) Wp stands for the intracavity pulse energy and D < 0 (fs2) is the net intracavity GDD, assumed to be independent of frequency. The requirement of materials characterized by the smallest ratio third-order dispersion (and in general higher order dispersion) to GDD, D3/D, greatly stimulated research in material science. Fused silica was found to be the best candidate to be employed in prism-controlled KLM Ti:Sa lasers. For Ti:Sa laser oscillator a pulse duration of 10 fs was reached ([56, 57] among the others). The limitation due to higher order dispersion terms (see Eq. (2-6)), which prevented from obtaining even shorter pulse durations approaching the gain-bandwidth limit of Ti:Sa, was finally overcome with the invention and realization of chirped multilayer dielectric mirrors [58, 59]. These dielectric mirrors are based on proper modulation of the multilayer period which results in a wavelength-dependent penetration depth of the incident radiation [58], as shown in Figure 2.5. Correspondingly, the group delay introduced by the multilayer mirror depends on the radiation frequency; thus, it can be properly modeled to give the required amount of GDD and higher order dispersions over the entire, broad high-reflectivity bandwidth of the mirror. By relying on the recent noticeable advances of this technology, resonators providing high reflectivity and nearly constant negative GDD over the whole gain band of Ti:Sa (600– 1000 nm) have been assembled. Compact mirror-dispersion-controlled (MDC) KLM Ti:Sa lasers nowadays routinely generate sub-10-fs pulses having peak power which exceeds 1 MW (see for instance [60]) and exhibiting very high spatial optical quality. Recently, the combination
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Figure 2.5 Schematic representation of a multilayer mirror. Different spectral components of the broad wave packet of an ultrashort pulse penetrate to different depths before reflection, due to a modulation of the multilayer period. In the figure the multilayer period increases with increasing the distance from the mirror surface. As a consequence spectral components having longer wavelength penetrate more deeply than shorter wavelengths before being reflected, since reflection originates from constructive interference of partial waves reflected from interfaces between low and high refractive index layers. Therefore, the group delay increases with increasing wavelength, namely decreasing frequency, thus resulting in a negative GDD.
of the two techniques, prism-dispersion-control and chirped mirrors, yielded Ti:Sa oscillator pulse durations below 6 fs [61–63] and sub-5fs pulses from optical parametric amplifiers [64, 65], both obtained by controlling dispersion over a spectral interval as wide as >150 THz. Moreover, a proper combination of mirror dispersion control and the extension of the laser cavity by a telescope [66] allowed the generation of stable sub-10-fs Ti:Sa oscillator pulses with peak powers in excess of 3 MW [67]. Thanks to the absence of any intracavity component other than the gain medium, the KLM/MDC Ti:Sa laser oscillators now exhibit rather good noise performances [68] which allow one to use this laser source in metrology and high resolution spectroscopy experiments [69, 70], besides the more common applications of time-resolved spectroscopy and nonlinear optics. In many interesting experiments, it is required to have an ultrashort laser source with a much higher intensity. In these cases, it is necessary to amplify the pulses delivered by the above described cw mode-locked oscillators. The first demonstration of femtosecond pulse amplification was obtained by using dye cells or jets pumped by Q-switched Nd:YAG lasers and copper-vapor lasers [71, 72] (see also the review [73]). However, the maximum pulse energy that can be achieved by using dye amplifiers is 1 mJ due to the low saturation fluence, Fsat = rv0/se, of such laser media, se being the peak stimulated-emission cross-section. In fact, se is typically very large in dye lasers. Furthermore, the fundamental relationship: tf se Dn0 = k
l20 n2
Eq. (2-9)
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FUNDAMENTALS
which connects se and the gain bandwidth Dn0 with the fluorescence lifetime tf and the refractive index n of the gain medium, k 1 being a numerical factor depending on the emission line shape, shows that the higher se the shorter t f [74]. The short energy-storage time together with the strong amplified spontaneous emission represent additional disadvantages of dye amplifiers. Excimer amplifiers have similar features, but, due to their much larger uniformly inverted apertures, can amplify pulses up to hundreds of millijoules in the ultraviolet spectral region at pulse durations of the order of 100 fs [75–77] (see also [78] for a review). Thus, thanks to their high peak power (1 TW), good beam quality and short wavelength, excimer-amplified pulses can be focused down to less than 1 mm, reaching peak intensities at focus of the order of 1018 W cm2 or even higher [78]. Solid-state media are, however, even more promising than excimers for producing higher peak power pulses, due to their much larger energy fluences and broader bandwidths (see Figure 2.3). Nevertheless, solid-state amplifiers have the relevant drawback of dramatic effects due to optical Kerr effect which induces a strong accumulated intensitydependent phase shift well before the saturation fluence is reached [74]. The problem was solved by means of a clever idea: the chirped pulse amplification (CPA) [79, 80]. The principle of CPA is illustrated in Figure 2.6. An ultrashort pulse having a low-energy content (typically few tens of femtoseconds long with an energy in the range of nanojoules) is first temporally stretched to several hundreds of picoseconds, then it is amplified by a factor which can be as high as 106 or higher without risk of
Oscillator
Prism
Stretcher
Amplifier
Figure 2.6 Principle of Chirped Pulse Amplification (CPA) [79]. The ultrafast, low-energy, seed pulse is first temporally stretched before amplification and final recompression in order to avoid reaching too high peak power in the amplifier system.
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catastrophic effects induced by too high peak power. Finally, it is recompressed down to almost the same duration as the seed pulse. By using diffraction-grating based stretchers [81] and compressors [82], it was possible in the early 1990s to routinely generate pulses in the 100-fs range with peak powers in the 1–10 TW range [83, 84] or higher from laboratory scale laser systems such as Ti:Sa or Cr:LiSAF (for instance 1 J, 50 fs, 20 TW for the recently upgraded Ti:Sa system available at the Lund Laser Centre in Sweden) [85–87]. The basic idea of a grating-based stretcher, illustrated in Figure 2.7, is that different spectral components of the broad ultrashort seed pulse are first spatially dispersed and then overlapped again, traveling, in both cases, paths of different lengths. Thus, at the output of the stretcher different spectral components are temporally delayed with respect to each other to give a stretched pulse. The gratingbased compressor acts in the same way as the stretcher with the only difference that it reverses the paths traveled by the bluish and reddish spectral components of the amplified pulse. Successive progress in the Ti: Sa seed oscillators technology [56, 57, 60] and stretcher/compressor design [88–90] opened the way to the availability of Ti:Sa CPA systems which deliver 20 fs multiterawatt pulses at 10 Hz repetition rate [89, 91]. Nowadays, the most up to date and powerful Ti:Sa CPA systems generate 20 fs pulses carrying a peak power 100 TW [92] capable of reaching at focus the enormous peak intensity of 1020–1021 W cm2. Thanks to the recent
Stretcher Mirror
Grating
Grating
Compressor Mirror
Grating
Grating Mirror
Figure 2.7 Schematic view of a grating based stretcher/compressor.
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FUNDAMENTALS
progress in CPA (see [93, 94] for a review) laboratory-scale systems based on Ti:Sa or Yb:glass [95] are expected to deliver petawatt peak power pulses in the very near future (very promising progress has been recently made at the Lawrence Livermore National Laboratory in the United States [96]). Furthermore, by employing the very good thermal conductivity and suitable electro-optic properties of a Ti:Sa laser source pumped by a recently available kHz-rate Q-switched solid-state system, it is possible to set up ultrashort CPA sources at kHz repetition rate, such as the high performance Ti:Sa sources described in [97–99]. These sources generate 20-fs pulses of several hundred gigawatts at 1 kHz repetition rate. The recent advances in the field suggest the feasibility of kHz-repetition-rate TW sources in the near future [100]. It is worth mentioning that CPA has been recently successfully used also for generating ultrafast, ultraintense laser pulses by diode-pumped doped-fiber laser systems. An advantage of such laser sources beyond the compactness is that they can operate at repetition rates much higher than the solid-state, ultrashort laser sources. Thus, when pulse energies in the range 10 mJ–1 mJ and a very high repetition rate are required, such as in many commercial applications, in medicine or production technology, ultrafast, dopedfiber laser systems represent a more appropriate choice than ultraintense, solid-state laser sources. CPA has been utilized for producing ultraintense pulses at >1 MHz repetition rate [101–103], and recently sub-ps (850 fs), high energy (100 mJ), nearly diffraction-limited pulses at a repetition rate of 32 kHz, and a 1060-nm central wavelength [104]. In this last case, a 150-fs, 25-pJ seed pulse, emitted by a Nd:glass based on a semiconductor saturable absorber (SESAM [105]), was coupled into a dispersive, 2-km-long, step-index, single-mode fiber delay line, which stretched the pulse to a width of about 800 ps and broadened the spectrum (Dl = 9.9 nm compared with 6.9 nm of the oscillator pulse), thanks to considerable self-phase-modulation. Such a pulse is then amplified by means of two fused-silica, double-clad, Nd2O3-doped fiber preamplifiers, followed by two power amplifiers consisting of two ytterbium-doped, double-clad fibers, which can raise the pulse energy up to 130 mJ at a repetition rate of 128 kHz, i.e. an average power of 16.5 W. The pulse is finally temporally compressed by means of a diffraction grating to give an 850-fs FWHM pulse width, with a very good optical quality resulting in a nearly diffraction-limited spatial mode. The limiting factor for pulse compression was represented by the third-order dispersion effect of the fiber stretcher, which could not be compensated by a grating compressor since the third-order dispersion of a grating pair has the same sign (positive) as the third-order dispersion of the fiber.
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Another interesting and novel pulse compression effect has been observed by focusing an ultrashort laser pulse onto a photonic crystal (PC) [106]. In this experiment, a small part of an amplified Ti:Sa laser pulse (270 fs of pulse duration, 8 nm of spectral width centered at l0 = 815 nm) with 3.5 mW of average power at 200 kHz repetition rate was focused onto a few micrometers 1D PC. This crystal consisted of eight layers of high refractive index (ZnS, n1 = 2.29) alternated with seven layers of low refractive index (SrF2, n2 = 1.46) deposited on a glass substrate, the whole structure strongly reflecting light in the range 745–830 nm at normal incidence, [107]. The incoming laser pulse duration could be varied by translating one of the mirrors of the gratingbased compressor. A different amount of either positive or negative chirp to the laser pulse could be given in such a way. An average pulse duration of t inc = 550 fs was used throughout the experiment. Depending on the incidence angle of the incoming laser pulse on the PC, the transmitted pulse duration was modulated between 1.1 tinc (positive chirp) and 0.85 t inc (negative chirp). The effect was ascribed to purely dispersive properties of the thin PC. In particular, due to the wide bandwidth of the femtosecond incoming laser pulse, higher-order dispersion effects also had to be taken into account for a full explanation of the observed experimental results. Pulse compression in PC appears to be even more interesting because it depends not only on the dispersion properties of the PC near the photonic band gap (PBG) [108], where linear propagation of light is forbidden [109], but also on the intensity of the laser electric field inside the structure [110]. This dynamical pulse compression originates by a perturbation of the refractive index due to the nonlinear interaction of the ultrashort laser pulse with the PC periodic media. The compression effect occurs where and when the laser field is localized inside the layers with high refractive index [111], and assumes noticeable importance for understanding pulse nonlinear compression in photonic structures with a large modulation of the refractive index [112].
2.2.3 The few-optical-cycle regime In this section the principal physical mechanisms and techniques that underlie the generation of few-optical-cycle laser pulses will be reviewed. As it has been mentioned in the previous section, pulse compression is essentially based on the interplay of two phenomena: Kerr-induced SPM of an ultrashort, ultraintense laser pulse which propagates through a
40
FUNDAMENTALS
nonlinear medium and negative GDD. The former effect acts as a new frequency generator: the time-dependent nonlinear phase shift accumulated by the pulse propagating through the Kerr medium is, in fact, DFnl ðtÞ = 2p l0 n2 IðtÞL, I(t) being the laser pulse intensity vs. the retarded time t defined above, and L is the propagation length. Therefore, SPM broadens the pulse spectrum: the higher the laser intensity or the nonlinear medium refractive index or the longer the propagation length, the larger time-dependent phase shift and, hence, pulse broadening (see among the others [113, 114]). SPM also implies relevant drawbacks such as phase aberrations introduced by the radial dependence of the nonlinear induced phase shift through the laser intensity I, which can lead to substantial spoiling of the spatial mode quality of the laser beam. But under proper experimental conditions spatial aberrations can be minimized and the induced DFnl can be used for generating ultrashort pulses. The new red-shifted and blue-shifted spectral components emerge at different positions of the pulse temporal envelope. Consequently, a proper delay line must introduce shorter group delay for the new components born in correspondence of the trailing edge of the laser pulse as compared to the delays given to the new components emerging in the leading edge of the pulse. This is, in effect, the role of a negative GDD delay line; naturally such an effect implies pulse compression, as shown in Figure 2.8. The frequency time variation d Fnl/dt, namely the laser pulse chirp, is linear with good approximation near the top of the pulse envelope (t = 0), where most of the energy content of the pulse is concentrated. As a consequence, optimizing temporal compression requires a group delay Tg(v) nearly linear with frequency in the delay line. Furthermore, since the nonlinear refractive index n2 is usually positive (unless some medium resonance falls rather close to the laser central wavelength l0), a negative GDD is needed for temporal compression (dTg/dv < 0). While the negative GDD delay line, although relying on several different but equivalent methods, essentially acts in the same manner, either when low-energy laser pulse compression is regarded (pulses generated by ultrashort laser oscillators have typically energies in the 1–50 nJ range) or when dealing with high energy (‡1 mJ) pulse compression, such as compression of amplified pulses, SPM is obtained in substantially different physical parameter regimes, depending on whether low energy or high energy laser pulses are concerned. First, let us briefly summarize the main properties of SPM in air or, more generally in a uniform medium. The general requirements in order to optimize pulse compression efficiency and to preserve the good optical quality of the laser beam are: (i) highest possible phase shift induced by
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Frequency domain
Time domain
∆ω(τ)
SPM
GDD
n2>0
D<0
+
0
–
Figure 2.8 Illustration of the principle of the optical pulse compression. The upper graph describes the pulse evolution in the frequency domain while the middle one follows the schematic temporal evolution of the electric field of the pulse, and the lower drawing shows the instantaneous frequency vinst(t) behavior vs. time and the temporal variation of the laser bandwidth Dv(t) = vinst(t)v0. Thus, the passage through a transparent ordinary Kerr medium, where SPM takes place with n2 > 0, imposes spectral broadening in frequency, pulse positive chirping in time, and an instantaneous frequency decreasing in time along the pulse envelope, with vinst = v0 just at the top of the pulse (t = 0). The action of the subsequent dispersive delay line with negative GDD consists in leaving unchanged the spectrum, but temporally compressing the pulse by compensating for the chirp, i.e. restoring vinst = v0 at any time during the pulse envelope.
SPM in order to maximize the spectrum bandwidth, and (ii) small depletion of the fundamental TEM00 mode when part of the incident pulse energy is transferred to higher order modes in the nonlinear interaction with the Kerr medium. This latter point implies keeping the peak power of the pulse, p0, well below the critical power in the uniform medium, pc,unif, at which self-focusing tends to heavily distort the laser beam. It has been shown that, in the perturbative approach where just a small fraction of the energy content carried by the fundamental beam is converted into higher order modes, the coupled-mode propagation equations can be analytically solved both in free space, i.e. in a uniform medium [115] and in a hollow waveguide [116]. Within this approximation the maximum energy transferred to the first excited TEM01 mode at the beam waist, G(0), and the peak nonlinear phase shift carried by the pulse exiting the Kerr
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FUNDAMENTALS
medium, Dfnl,out (t = 0), is [116]: k2 p0 2 ; Dfnl;out ðt = 0Þ = pk Gð0Þ = = 4 pc;unif
Eq. (2-10)
where k=
z0 l2 ; pc;unif = 0 Lnl pn2
Eq. (2-11)
z0 = pw20 =l0 being the Rayleigh length, w0 the 1/e2-radius at the beam waist, and Lnl = (gSPMp0)1 the so-called nonlinear length, which turns out to be a useful scale parameter for the nonlinear interaction. Thus, if Lnl >> z0, just a small fraction of the energy carried by the incoming light is coupled into the nonlinear medium to higher order modes, and, for a sufficiently long medium (L >> z0) the perturbative approach can be followed. From Eq. (2-10) it is directly seen that the small depletion of the fundamental mode implies (p0/pc,unif)2 << 1, where the power pc,unif worked out by the coupled-mode analysis agrees with the well-known critical power for self-focusing in a bulk medium pc = afs l20 =ð8pn2 Þ where afs 3.8–6.4 is an opportune correction factor [117]. Moreover, the requirement k2/4 << 1, which also has to be fulfilled for spatially uniform SPM in order not to degrade the spatial mode of the beam, implies that Dfnl,out (t = 0) at maximum can be of the order of p. Such an SPMinduced peak nonlinear phase shift for a near-bandwidth-limited pulse can at maximum double the spectral bandwidth of the pulse [118]. This determines the maximum compression factor in spatially uniform temporal compression, achievable after a single pass through a bulk nonlinear medium. Therefore, to obtain large compression factors the process needs to be repeated several times with many passes in the bulk medium, thus becoming expensive in terms of necessary optics and also impractical. On the other hand, in the opposite limit L << Lnl the perturbative approach fails resulting in an overlapping of an infinite number of excited higher order modes, many of which have amplitudes comparable to that of the fundamental beam. In this condition, the nonlinear phase shift resembles not only the temporal shape of the pulse, but also the transverse intensity distribution of the fundamental mode. This latter phenomenon causes strong self-focusing as p0 ! pc,unif, so that, in order to avoid catastrophic effects which result in a permanent damage of Kerr medium or in an enormous distortion of the fundamental mode, L must be
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significantly shorter than z0. This latter regime, strongly nonperturbative, is typical of temporal compression of the passively mode-locked femtosecond Ti:Sa and other solid-state laser oscillators. These systems delivers ultrashort pulses in the fundamental TEM00 mode, which is apparently in contradiction to what has been just reported above about coupling a considerable amount of the energy carried by the fundamental mode to the higher order modes due to the radial variation of the nonlinear phase shift Dfnl (r, t). Actually, it is the filtering action of the laser resonator to resolve this apparent paradox: in fact, the oscillator resonator behaves like an efficient spatial filter which suppresses the high order spatial modes by setting for them a very high oscillation-threshold and leads to a TEM00 output beam, despite the presence of strong nonlinearities in the cavity. So, both the compression and filtering processes, repeated very many times in the buildup of oscillations of the laser pulse into the laser cavity (see Figure 2.9), represent the basis of few opticalcycle pulse generation in the low-energy regime, characterized by a medium length shorter than the Rayleigh length, L < z0 and by a pulse peak power comparable to the critical power p0 pc. With reference to the simple scheme of Figure 2.9, SPM in the laser crystal and negative GDD in the chirped mirrors M1–M4 occur alternatively many thousands of times before the stationary pulse duration in the sub-10-fs regime is reached. The limiting factor to pulse shortening in the steady state is set by the finite bandwidth over which the negative GDD introduced by the chirped mirrors remains nearly constant and can be balanced by the finite laser medium gain and resonator bandwidth. Instead as reported above, when temporal compression of amplified pulses is concerned, the scheme of compression by using SPM in uniform media and subsequent negative
Figure 2.9 Schematic of a mirror-dispersion-controlled Ti:Sa laser constituted by chirped mirrors (M1–M4), a broadband output coupler (OC), and a thin highly doped Ti:Sapphire crystal; for details see [423].
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GDD appears to be seriously inconvenient. In fact, the amount of pulse broadening, which can be imparted to the laser pulse without strong depletion of the fundamental mode, turns out to be rather small. As a result of this drawback, a severe spoiling of the spatial quality of the outcoming beam occurs. The high peak power of the amplified pulses would require that, in order to avoid all the cited troubles, the total large nonlinear phase shift needed for a strong temporal compression was imparted by adding up in series small amounts of phase shift obtained by repeating the passage of a loosely focused pulse through the Kerr medium several times. On the other hand, hollow waveguides are known to efficiently guide high-power laser pulses [119]. Moreover, filling the waveguide with some gas can introduce the nonlinearity (Kerr effect in most cases) needed for spectral broadening of the high-power pulses and their successive compression [120]. By properly focusing the Gaussian input beam corresponding to the waveguide entrance, it is possible to excite the fundamental linearly polarized mode LP01 of the fiber with almost 100% efficiency [121]. Then, during the propagation into the hollow fiber, the energy content oscillates between the LP01 mode and the higher order excited LPmn modes (with m = 0 to have nonvanishing mode-coupling and n ‡ 2) over a spatial period comparable with the Rayleigh length, z0, of the input beam [116]. Thus, as depicted in Figure 2.10 for the LP01–LP02 30 fs
hollow waveguide
Argon p=0.6 bar
Chirped-mirror compressor 5.5 fs 0.3 mJ
Figure 2.10 Layout of a hollow-fiber chirped-mirror high-energy pulse compressor. The input pulse is first spectrally broadened by SPM into the hollow fiber which is filled in with gas that acts like a Kerr medium. Successively the pulse is temporally compressed by means of reflection off broadband chirped-mirrors which temporally re-compacts different spectral components of the broadened pulse.
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energy exchange, the beam energy continuously flows from the fundamental mode to the excited ones and then back again to the fundamental mode over twice a coherence length, Ln, which accounts for the coupling between the LP0n and the fundamental LP01 modes. Under proper focusing conditions of the input beam, namely when w0 23 a, where a is the bore radius of the hollow waveguide and w0 is the waist of the input beam [121], it turns out that L2 1.1z0 whereas the higher order mode coherence lengths, Ln, decreases with increasing mode order n, and so does the maximum transferred energy, which scales as Ln2. It has been shown [116] that for low depletion, the maximum fractional energy coupled to the LP02 mode and the peak nonlinear phase shift, which is uniform across the beam, is: GðL2 Þ =
k 2 p 2 z z 0 = ; Dfnl ðz; t = 0Þ = k pc;wg p L2 z0
Eq. (2-12)
respectively, where pc;wg =
l20 2n2
Eq. (2-13)
is the critical power for self-focusing in the multimode hollow waveguide and pc,wg pc,unif, i.e. self-focusing in uniform, bulk media and waveguides comes up at about the same power level [115]. Moreover for w0 23a the coupling coefficient k is approximately given by k z0 p0LkSPM (see Eqs. (2-5) and (2-11)) with w0 replaced by a [116]. The most important difference between Eq. (2-12) and its analog for a uniform bulk medium, Eq. (2-10), is represented by the z-dependence of the nonlinear phase shift Dfnl, which is proportional to z in the case of SPM in a filled-in fiber, and is z-independent for SPM in bulk media. This makes it possible to accumulate a relevant spatially uniform SPM in a filled-in fiber, which still meets the requirement of weak fundamental mode depletion by letting the pulse propagate into the hollow fiber for distances of the order of z 20z0 and obtaining a nonlinear phase shift induced in the output beam of the order of 10p when (k/p)2 = 1/4. Such a Dfnl implies a remarkable relative pulse spectral broadening by a factor 10–20. Further SPM enhancement is only limited by the propagation loss suffered by the fundamental mode propagating along the leaky waveguide and eventually by distortion of the pulse envelope temporal profile. It is worth pointing out that as previously illustrated, the formation of a solitonic pulse inside a laser oscillator also requires the action of a
46
FUNDAMENTALS
fast saturable-absorber-like SAM, which in typical Ti:Sa oscillators, for example, is played by the KLM. The action of SAM is twofold: (i) it gives rise to and sustains the formation of a short pulse in the cavity, and (ii) it stabilizes the SPM/GDD interplay in shortening the pulse duration by filtering low-intensity noise sources due to residual gain and positive feedback in the pulse wings. On the contrary, when an extracavity pulse compression scheme is adopted, in the absence of a quasiperiodic evolution the noise of instabilities cannot grow; therefore, SAM action is not needed in this case. The two different physical regimes which characterize SPM/GDD-dominated temporal pulse compression are summarized in Table 2.1. KLM/MDC Ti:Sa oscillators, based on the setup represented in Figure 2.9 or similar, nowadays generate pulses with temporal duration in the range 5–10 fs at multi-MHz repetition rate (typically 80–100 MHz). Extending the cavity with a telescope and reducing the repetition rate allows one to enhance considerably both the pulse energy, reaching
Table 2.1 Ranges of the Most Important Parameters for Few-cycle Pulses in KLM/MDC Ti:Sa Oscillators at Low-energy Levels and in Hollowwaveguide/Chirped-mirror Compressors at High-energy Levels [53]
Systems Parameters
KLM/MDC Multimode Hollow-waveguide/ Ti:Sa Oscillator Chirped-mirror Compressor
Nonlinear interaction length p0/pc pc Dfnl(t = 0) Spectral broadening/ pass Net Negative GDD Compression factor/ pass Self-amplitude modulation depth Output pulse energy Output pulse duration Output peak power Peak intensity at focus Up
z0
‡1 2.5 MW 0.1p–0.5p 1.1–1.3
1 10 GW–1 TW 5p–10p 5–10
10–30 fs2 1.1–1.3
10–30 fs2 5–10
1–3%
–
3–30 nJ 5–8 fs 0.3–3 MW to 1014 W cm2
0.01–1 mJ 4–7 fs 1 GW–0.2 TW Up to 1018 W cm2
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values in excess of 30 nJ at 25 MHz repetition rate with sub-10-fs pulse duration by implementing the setup described in [67], and to further compress the pulse duration below 5 fs [122–124]. Although strong-field physics phenomena are typically triggered at laser intensities approaching 1014 W cm2, which are reached by the highest peak intensities achievable with sub-10-fs laser oscillators [67, 125, 126], many of the most intriguing effects arising in strong-field physics call for intensities far beyond the above value and which are only available with external laser amplification. This additional amplification cannot preserve the few-optical-cycle duration of the seed pulses, even if laser media with the broadest amplification bandwidth are used. In fact, high gain in the amplifier laser medium typically implies gain narrowing, setting a limit of the relative amplified bandwidth, Dv0/v0, to few percent or less, whereas few-optical-cycle seed pulses exhibit Dv0/v0 > 0.1. Hence, amplified pulses need to be compressed after amplification in order to reach the few-optical-cycle duration regime. To this end an excellent method is the multimode gas-filled hollow fiber technique previously described [120, 127, 128], followed by temporal compression upon reflection of chirped mirrors [129, 130] (see Figure 2.10). By this technique seed pulses of 25–30 fs in duration and 1.5 mJ in energy can be compressed to 5 fs in duration with an energy of 0.6–0.7 mJ, thus resulting in a peak power of 0.1–0.15 TW at a repetition rate of 1 kHz. Moreover, this compression technique will likely be scalable to peak powers on the order of 1 TW. Figure 2.11 shows a second-order autocorrelation trace of Ti:Sa pulses having average energy of 0.5 mJ and FWHM pulse duration of about 5 fs, whereas in Figure 2.12 the time-dependent behavior of amplitude and phase of the same laser pulse electric field is illustrated for a carrier phase f0 arbitrarily set to 0. The electric field amplitude (solid curve) appears to be a well-behaved function having a bell-like shape, very much resembling the most commonly assumed analytical sech or Gaussian profiles, while the phase (dotted curve) is very flat at a constant value over the entire temporal extension of the field amplitude. The inset of Figure 2.12 completes the ultrashort pulse characterization by showing the pulse spectrum (solid curve) and the behavior of the phase vs. wavelength, the so-called spectral phase. While the spectral phase is rather constant, the pulse spectrum looks extremely broad and structured by covering an extension of more than 250 nm around the Ti:Sa central wavelength l0 = 800 nm. It is worth mentioning that all the curves shown in Figure 2.12 are obtained by means of a SPIDER measurement (Spectral Phase Interferometry
48
FUNDAMENTALS
SH Intensity (a.u.)
8 τ = 5.5 fs
6
4
2
0 -20
-10
0 Delay (fs)
10
20
Figure 2.11 Measured second order autocorrelation trace of Ti:Sa laser pulses having average pulse energy of 0.5 mJ, compressed by the multimode hollow waveguide/chirped-mirrors technique (courtesy of M. Nisoli). The measured FWHM of the autocorrelation curve is about 7 fs yielding a FWHM intensity pulse duration of 5 fs.
for Direct Electric-field Reconstruction) [131–133] which will be briefly reviewed in Section 2.2.5, together with other methods for characterizing ultrashort laser pulses, such as interferometric autocorrelation and others.
2.2.4 The carrier-envelope-phase (CEP) When dealing with few-optical-cycle laser pulses, whose duration approaches the single optical period Topt, it is worth stressing the importance of a parameter, the absolute phase f0 of Eq. (2-7), which has not received very much consideration until recently. In fact, the absolute phase or carrier-envelope phase, as it also referred to, does not affect the large part of the optical phenomena and it has not been detectable and under control until very recently. But as will be shown shortly, it becomes important in the interaction of intense few-cycle radiation with matter, and its control in broadband, ultrashort laser oscillators is highly necessary for precision measurements of light frequency and atomic transitions. A number of questions arise when the laser pulse duration approaches the single optical cycle: Can the techniques used for characterizing the multicycle
pulses still work for few-optical-cycle pulses?
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(a)
(b) 4
0.8 2 0.6 0 0.4 -2 0.2
Spectral phase (rad)
Normalized intensity
1.0
-4 0.0
600
700
800 900 Wavelength (nm)
1000
Figure 2.12 Amplitude (solid curve) and phase (dotted curve) of a Ti:Sa, 0.5 mJ laser pulse as measured by the SPIDER technique. The measurement is taken by averaging 200 laser shots. In the inset the laser pulse spectrum and the laser pulse phase vs. wavelength are displayed as reconstructed by SPIDER (courtesy of M. Nisoli).
Do these techniques completely characterize few-optical-
cycle pulses, or are there special features of the few-opticalcycle pulses which are missed? Do the fundamental concepts of carrier and envelope of a multicycle radiation field still make sense in the few-optical cycle regime and can they still be used for describing fewoptical-cycle pulses? All these questions have been recently addressed and satisfactorily answered in [53]. By following the argument developed in [53], in fact,
50
FUNDAMENTALS
let us reiterate that the electric field E(t) is expressed in terms of amplitude envelope A(t), carrier frequency v0, and carrier phase f0 as: EðtÞ = AðtÞeiv0 t + if0 + c:c:
Eq. (2-14)
A(t) generally is a complex, time-dependent, well-behaved amplitude which can be derived from E(t) by first Fourier transformation: 1 EðvÞ = pffiffiffiffiffiffi 2p ^
Z
¥
EðtÞeivt dt
Eq. (2-15)
¥
and then coming back to the time domain by introducing the time-depen~ as: dent, complex field EðtÞ ~ = p1ffiffiffiffiffiffi EðtÞ 2p
Z
¥
ivt ^ EðvÞe dv
Eq. (2-16)
0
~ + c:c: Hence, A(t) is fully determined from EðtÞ ~ which obeys EðtÞ = EðtÞ once v0 and f0 are known. One possible definition of v0 is the frequency intensity-weighted mean value [134]: Z
^ 2 vEðvÞ dv v0 = Z0 ¥ ^ 2 EðvÞ dv ¥
Eq. (2-17)
0
However, the conclusions of the following considerations do not depend on the particular choice of v0, provided it falls roughly at the center of the pulse spectrum in order to avoid fast oscillations for A(t). Once v0 is defined, the carrier phase f0 is chosen, for instance, in such a way that A(t) is real at t = 0, instant of time which is often chosen for the sake of simplicity to coincide with the center of gravity of j E(t) j 2. Then, by knowing both v0 and f0, it is possible to reconstruct A(t) from E(t). The main point is that f0 is really unknown, since there is no way to experimentally determine it. None of the methods used for characterizing ultrashort pulses, neither the interferometric autocorrelation, nor Frequency Resolved Optical Gating (FROG), nor SPIDER are sensitive to f0. Thus, for the concepts of envelope and carrier frequency to make sense, we have to require that A(t) and v0 are invariant under an arbitrary transformation Df of f0. It is clearly shown in [53] that, by assuming Df = p/2 in order to maximize the phase transformation effects, both A(t) and v0 remain unchanged until the pulse duration
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tlaser approaches and becomes shorter than the optical cycle Topt. This interesting finding holds true for any of the most common pulse shapes, Gaussian, sech or Lorentzian. Another useful property of A(t), which is preserved as t laser ! Topt, is to directly give the cycle-averaged R radiation 2 intensity I(t) j A(t) j , and therefore the energy fluence F = IðtÞ dt. In fact, by integrating the instantaneous energy density flow, proportional to E2(t) over the laser pulse, it has been demonstrated the carrier phase invariance of F as long as t laser ‡ Topt [135]. Thus, describing electromagnetic pulses in terms of envelope and carrier phase remains valid, self-consistent, and unambiguous until tlaser ‡ Topt. Moreover, being all nonlinear optical phenomena in the regime of many cycle pulses insensitive to the absolute phase f0, they are fully controlled and described by relying on just the two concepts of amplitude envelope, A(t), and pulse carrier frequency, v0. As the interaction time between radiation pulses and material systems, atoms, molecules, clusters or nanoparticles, becomes comparable to the optical period, the radiation electric field (and even the magnetic field when the radiation intensity approaches the relativistic regime, see Section 2.3.1.2) and not the radiation intensity starts dominating the nonlinear light-matter interaction. Under these conditions, nonlinear interactions lasting just a few optical cycles become sensitive also to f0, thus requiring a way to access and control the absolute phase in order to obtain precise control of the physically observable quantities. The first experimental investigation on the fluctuations of the few-cycle pulses absolute phase was performed by Xu et al. [136]. This experiment showed that the absolute phase, in a pulse train emitted by a modelocked laser oscillator, is rapidly varying. The variation results in a change of the position of the carrier oscillation with respect to the envelope (Figure 2.13) from which the name CEP originates. The pulse-to-pulse variation of f0 results from the sum of linear and nonlinear terms. The linear term Df0,lin is due to dispersion in the active medium of the laser oscillator, and accounts for the fact that the pulse envelope travels at the group velocity vg = ðc=v0 Þ½Reðqn=qvÞv0 1 , while the frequency carrier component travels at the phase velocity nph = c/Re [n(v0)]. Thus, for a medium of length L, the linear term reads: Df0;lin = 2p
qn L ql l0
Eq. (2-18)
From Eq. (2-18), we can introduce the dephasing length [136] Ldeph = 0:5jqn=qlj1 l0 , namely the propagation distance over which the
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FUNDAMENTALS A(t)=sech(1.76)τ/τlaser)
Normalized Electric Field
1.0
E(t,φ0=0) E(t,φ0=π/2)
0.5
0.0
-0.5
-1.0 -20
-10
0 Time (fs)
10
20
Figure 2.13 Carrier-Envelope-Phase (CEP) representation. Electric field evolution in time for a 5-fs Ti:Sa laser pulse (l0 = 800 nm) having the absolute phase f0 = 0 (dashed line) and f0 = p/2 (dotted line). The amplitude envelope A(t) = sech(1.76t/t laser), unchanged, is represented by the black curve. t laser = 5 fs is the FWHM intensity temporal profile.
carrier dephasing with respect to the envelope amounts to p. For Ti:Sa pulses Ldeph can be as short as 29 and 19 mm in quartz and sapphire, respectively, thus implying a Df0,lin shift of tens of times 2p for an entire round-trip of the laser in the cavity. The nonlinear phase shift term may arise from drifts and fluctuations of the pulse power which mostly affect the pulse spectral broadening by SPM and finally may also change f0 [136–138]. By denoting Dfr = Dfn+1 Dfn the carrier phase shift with respect to the envelope accumulated during the nth roundtrip, the actual carrier phase shift is Df0r = Dfr 2pm, where m is an integer such that 0 < Df0r < 2p. Df0r can be measured in several ways as suggested in [139]. The first measurement of Df0r [136] was based on interferometric cross-correlation of two successive laser pulses in a nonlinear crystal. In more recent experiments the carrier phase shift has been measured and controlled by operating in the frequency domain. The actual carrier phase shift leads to a frequency offset [135, 139], Tr being the round-trip time in the oscilf0 = ðDf0r =2pÞT1 r lator cavity of the frequency comb emitted by the mode-locked laser. f0 usually falls in the microwave frequency range. Thus, the frequency comb is constituted by equally spaced frequency peaks written as fm = f0 + mfr, where m is a (large) positive integer and fr = Tr1 . Thanks to the experiments cited hereafter performed in the frequency domain for measuring the absolute phase, ultrashort laser source field and strong field optics have surprisingly approached the stabilized laser
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source field, mostly devoted to a complementary use such as high resolution spectroscopy and metrology. Thus, in [135, 140], f0 was measured by locking different frequency modes of the frequency comb emitted by the mode-locked laser to different harmonics of a narrow-line reference source. In [141, 142], optical frequencies were measured in terms of the cesium primary standard. In fact, an air–silica microstructure optical fiber broadened the frequency comb of a fs-laser to span the optical octave from 1064 to 532 nm, enabling measurement of the 282 THz frequency of an iodine-stabilized Nd:YAG cw laser directly in terms of f0. In [137], laser pulses of a 9-fs, 20-nJ, 24-MHz repetition rate Ti:Sa oscillator were first spectrally broadened, then a portion of the broadened spectrum was directly frequency converted and coherently mixed with the fundamental laser field at the shifted frequency, thus allowing measurement of both Df0r and f0. In [138], Df0r of a 4.3-fs Ti:Sa oscillator was determined and stabilized by using direct second-order and third-order nonlinear optical processes. In [143], CEP was measured and controlled by employing optical parametric amplification; thanks to the phase link between signal, idler, and pump waves in parametric interaction, the phase of the idler pulse can be made independent of the pump pulse. Then, by seeding the optical parametric amplifier with an ultrashort white light generated by SPM in a CaF2 window, a selfstabilized source of few-cycle, idler pulses is realized in which the phase of the electric field is reproduced within p/10 in each laser shot. Strong field processes lend themselves as very good candidates to detect and possibly stabilize the absolute phase of few-cycle pulses thanks to their phase sensitivity. Unfortunately, the most well-known among these processes, such as optical-field ionization and harmonic generation in atomic gases, discussed in Sections 2.3.1.2 and 2.3.1.3, respectively, come into play typically at intensities ‡1014 W cm2 which are too high to be achieved by simply using ultrashort laser oscillators without successive amplification. Amplification is performed at a strongly reduced repetition rate (typically on the order of 1 kHz), which so far has not supported carrier phase stabilization by simply using a servo loop for stabilizing the oscillator phase, as in the above-mentioned methods. In fact, intensity-dependent drifts and fluctuations of the round-trip phase delay and group delay may destroy phase stabilization on a time scale of microseconds, by accumulating a jitter of f0 [136], unless possibly one of the very recent methods described in [137, 138] will be used. However, even without control of the absolute phase of the amplified ultrashort laser pulse, the first experimental evidence of an absolute phase effect in the interaction between laser light and matter has been observed lately in
54
FUNDAMENTALS
the above threshold ionization (ATI) of krypton atoms by a 6-fs, 1-kHz repetition rate Ti:Sa, amplified laser pulse [144]. In this experiment, the direction of emission of photoelectrons is, in fact, affected by the absolute phase which leads to an anti-correlation between the number of electrons emitted in one direction and the number of electrons emitted in the opposite direction. Furthermore, other nonlinear optical phenomena expected to be phase sensitive, such as photoemission from the surface of a metal in the tunneling regime [145, 146], occur at intensities reachable by the stateof-art sub-10-fs Ti:Sa oscillators and might provide another way to measure the absolute phase by using strong field optics. Finally, it is clear why controlling the absolute phase of few-cycle light pulses is of extreme importance both for precision frequency-domain spectroscopy and for high-field physics and represents, mainly in the latter case, still an open challenge for researchers in modern optics. In the former case, where noticeable progress has already been made, it allows spanning an unprecedented spectral range constituted by harmonics of the laser repetition rate, each of them known with the precision of a reference frequency standard. In the latter case, where the extension of the phase stabilization technique to amplified pulses is highly demanded and yet missing, it gives access to coherent control of the dynamics of atoms, molecules, and plasmas via the radiation and electric fields (and perhaps also magnetic fields in the near future).
2.2.5 Techniques for ultrashort pulse measurements The task of measuring the duration of short radiation pulses has been performed with conventional radiation detectors whose output signal was read by means of fast oscilloscopes until the nanosecond duration regime has been concerned. Successively, when picosecond pulses came up, electronics were not fast enough and the streak camera was widely employed for measuring the duration of such short pulses. The streak camera is based on the photoelectric effect: the radiation pulse is essentially transformed into an electron bunch by the photoelectric effect in some photocathode material. The electron bunch passes through an intense rump-like electric field stage which spatially broadens the bunch. Spatial extension and temporal duration of the electron bunch are proportional, which makes it easy to measure the temporal duration by measuring the size of the bunch when it strikes a fluorescent screen. Nowadays, the availability of shorter and shorter laser pulse sources,
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first entering the femtosecond regime and then accessing the limit of fewoptical-cycle domain, calls for accurate and nonconventional methods for measuring the pulse duration and, more in general, for characterizing the main radiation pulse features. Moreover, accessing the few-opticalcycle domain has made even more urgent the need for developing techniques for the characterization of the full electric field of the ultrashort pulse (see Section 2.2.4). In fact, several methods have been developed in recent years which are used to measure amplitude and phase of an ultrashort radiation pulse. Throughout this section, we will first concentrate on a classical technique to measure the temporal envelope of ultrashort laser pulses such as second-order autocorrelation. We will then describe the two most widely used methods to measure both amplitude and phase of ultrashort pulses: FROG and Spectral Phase Interferometry for Direct Electric-Field Reconstruction (SPIDER). The second-order autocorrelator, based on the second harmonic generation (SHG) in nonlinear crystals, was first realized in 1967 [147]. Figure 2.14 schematically illustrates the basic principle of operation of a SHG autocorrelation measurement: an incident radiation pulse is split into two sub-pulses by a 50/50 beam-splitter at the center of a Michelson interferometer. The sub-pulse trains, E1 and E2, reflected in each arm and then recombined at the beam splitter, are finally focused onto a nonlinear frequency doubling crystal. The resulting second harmonic signal is generated in the propagation direction of E1 and E2 and is detected by a photomultiplier, the fundamental radiation having been blocked by a filter. The intensity of the SHG is proportional to the square of the
Input beam Doubling crystal
beam splitter
Filter
E2 E1 E1 PMT τ E2 Variable delay
Figure 2.14 Scheme of an interferometric second harmonic generation autocorrelator.
56
FUNDAMENTALS
intensity of the fundamental radiation. This nonlinear dependence of the SHG signal on the fundamental intensity makes it possible to measure the duration of an arbitrarily fast coherent optical signal by means of an interferometer. Several different second-order autocorrelator configurations maybeused.Type-Iphase-matching(ordinary–ordinary,parallelsubtrain polarization) or type-II phase-matching (ordinary–extraordinary, perpendicular sub-train polarization) may be employed in the birefringent nonlinear SHG crystal. In case of collinear beams with type-I phase-matching, by imposing E2(t) = E1 (t t) (autocorrelation), the SHG measured signal is proportional to I12(t) which is given by [148]: Z I12 ðtÞ =
¥ ¥
j½E1 ðtÞ + E1 ðt tÞ2 j2 dt
Eq. (2-19)
t being the delay between the two sub-pulses, varied by varying the mismatch length between the two arms of the interferometer. By averaging out the cos(v0t) carrier fringes, which is usually done because of the integration of the detector over its response time and because of possible mechanical instabilities, it can be seen that I12(t), no matter whether the pulse is transform-limited and/or chirped or not, reads [148]: 3 I12 ðtÞ = 4
(Z
¥
¥
"R ¥ 2
IðtÞ dt 1 + 2
¥
IðtÞIðt tÞdt R¥ 2 ¥ IðtÞ
#!) Eq. (2-20)
where I(t) is the cycle-averaged fundamental intensity. It should be noted that the term in square brackets is the second-order normalized autocorrelation function of the pulse. From Eq. (2-20), it is immediately seen that peak-to-background contrast ratio for the autocorrelation measurement is 3:1. It should also be stressed that the second-order autocorrelation function is always symmetric and, therefore, can only give limited information concerning the pulse shape and chirp; typical experimental traces are shown in Figure 2.15, where a free-running laser trace (a) is compared with typical traces due to a partially mode-locked laser (b), and a fully mode-locked laser (c). Thus, with no mode-locking the autocorrelation trace exhibits just a small coherent spike representing the coherence time and therefore the inverse of the noise bandwidth, having a contrast ratio of 3:2. The case (b) displays the same small coherent spike over a broader feature which indicates the width of the pulse envelope. The contrast ratio of three levels, the central spike, the broad pedestal, and the background is 3:2:1. The last case (c) refers to a fully modelocked laser pulse and exhibits the characteristic contrast ratio of 3:1,
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Figure 2.15 Typical second order autocorrelation traces for different degrees of mode-locking [148]. Traces (a)–(c) refer to a free-running laser, to a partially mode-locked laser, and to fully mode-locked laser, respectively.
Table 2.2 Autocorrelation Deconvolution Values and k Values
Pulse Shape Rectangular Gaussian Sech2 Single-sided exponential
D t/t pulse
k D v t pulse
1 1.414 1.543 2
0.886 0.441 0.315 0.110
even though no definite information can be gained about the possible laser chirp (i.e. the pulse spectral bandwidth) or the exact shape of the pulse temporal envelope. As with the interferometric autocorrelation function, where interference fringes are visible, there is no information about pulse asymmetry; in the case of cycle-averaged autocorrelation, there is no information about the phase structure of the pulse. Neither is it possible to count carrier fringes, but one must make an assumption about the pulse shape and divide the autocorrelation FWHM, Dt, by the appropriate deconvolution factor in order to obtain the pulse duration t pulse. An indication of the pulse temporal profile can be obtained by calculating autocorrelation profiles, corresponding to different pulse shapes, and observing the best fit. Since no information is obtained about the chirp of the pulse, it is useful to measure the associated spectral pulse profile and to compare the experimental time-bandwidth product, Dnt pulse, with the minimum value, k, corresponding to the case of chirp-free, transform-limited pulses. This is done in Table 2.2, where the autocorrelation deconvolution
58
FUNDAMENTALS
factors and k values are reported for the most commonly assumed pulses [149]. An excessive time-bandwidth product may indicate either frequency chirp of the pulse or incomplete mode-locking. As seen above, the contrast ratio in a second-order autocorrelator, cycle-averaged signal is 3:1 in the ideal case and may significantly decrease as soon as the interferometer is not perfectly aligned. Thus, a number of methods have been developed in order to obtain background-free autocorrelation traces, where the contrast ratio is 1:0. One of these methods relies on two noncollinear sub-pulses which are overlapped in the SHG crystal to produce a second harmonic signal in a type-I phase matching configuration [4, 150]. It is also easy to realize in this way, a single shot, background-free, second-order autocorrelation that is very helpful to characterize amplified system pulses, which operate at much lower repetition rate with respect to ultrashort laser oscillators and may exhibit a much higher instability from shot to shot. Therefore, single shot monitoring is often very useful and needed to fully characterize amplified systems. A scheme of a noncollinear single shot autocorrelator is illustrated in Figure 2.16 [151]. The second harmonic signal at frequency 2v0
Figure 2.16 Principle of type-I phase-matching, second order, single shot, noncollinear autocorrelator [424]. The second harmonic signal is generated by a KDP crystal irradiated by two beams intersecting at an angle F. The crossing of the pulse wavefronts induces a second order process and transforms autocorrelation in time into a spatial intensity distribution S(x) along the x-axis.
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is generated by a KDP nonlinear crystal oriented for type-I SHG for the two sub-pulses intersecting at an angle F. Since the two beams are noncollinear, the second harmonic is generated along the bisecting line z only when both pulses coincide in time and space. The spatial distribution of the second harmonic signal along the vertical direction, S(x), is imaged by means of a linear CCD array. S(x) turns out to be equivalent to the second-order autocorrelation function. In fact, if the two beams are uniform, with I1(t) and I2(t) their intensities respectively, the radiated field at the harmonic frequency at a given distance x0 from the center of the crystal is proportional to I1 (t t(x0))I2(t + t(x0)), where the delay t(x0) is given geometrically by tðx0 Þ = 1c nx0 sinðF=2Þ. As a result, one obtains for S(x): Z SðxÞ =
¥
¥
I1 ðt tðxÞÞI2 ðt + tðxÞÞ dt
Eq. (2-21)
which is directly proportional to the second-order autocorrelation function in case the two beams originate from the same pulse and have the same intensity I1(t) = I2(t). Turning to more recent techniques, by utilizing the FROG, one can directly measure the full intensity I(t) and phase F(t) of a single femtosecond pulse. By using second- or third-order nonlinear instantaneous interactions of two replicas of the ultrashort pulse to be measured, FROG measures the spectrum of the signal pulse as a function of the delay between the two replicas. The typical output trace of a FROG measurement is a contour plot reporting the pulse intensity vs. frequency and delays as illustrated in Figure 2.17, where traces for negatively chirped, unchirped, and positively chirped Gaussian pulses are displayed. FROG traces reflect the instantaneous frequency of the pulse, v(t) = d F(t)/dt, in all three cases, black tone indicating high intensity and white indicating low intensity. The following step, which can be considered as a complex two-dimensional phase-retrieval problem, consists in inverting the FROG trace to obtain the pulse intensity and phase. Four main FROG geometries have been demonstrated, three of them based on third-order processes, thus involving x(3), the fourth one being a second-order process related to x(2) (for the definition of x (2) and x (3) see Section 2.3.1.1):
polarization-gate (PG) [152, 153]; self-diffraction (SD) [154, 155]; third-harmonic generation (THG) [156]; second-harmonic generation (SHG) [157–159].
60
FUNDAMENTALS
Figure 2.17 FROG traces for negatively, unchirped, and positively chirped Gaussian [153] pulses. The top figures show the instantaneous frequency vs. the delay time, v(t) = d F/d t between the two replicas. The FROG traces (bottom plots) are density plots, the black and white indicating high and low intensity areas, respectively.
Other geometries have also been tried [160]. Since E(t) is the electric field associated with the ultrashort laser pulse and t is the time delay between the two replicas, the signal field, in the four cases, has the following forms [161]: 2 E PG sig ðt; tÞ = EðtÞjEðt tÞj 2 E SD sig ðt; tÞ = E ðtÞE ðt tÞ 2 E THG sig ðt; tÞ = E ðtÞEðt tÞ
Eq. (2-22)
E SHG sig ðt; tÞ = EðtÞEðt tÞ The signal field is then frequency-resolved by a spectrometer to yield the FROG trace: Z IFROG ðv; tÞ =
¥ ¥
2 dt Esig ðt; tÞexpðivtÞ
Eq. (2-23)
The FROG trace is thus a spectrogram of the pulse, namely a time (delay time)–frequency distribution which contains all relevant information about the pulse. In Figures 2.18–2.20 we show the basic principle of PG-, THG-, and SHG-FROG, respectively. With reference to Figure 2.18(a), two pulse replicas E(t) and E(t t) overlap in an instantaneously
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responding nonlinear medium. In this PG arrangement, the probe pulse E(t) passes through crossed polarizers and is gated at the nonlinear sample medium by the gate pulse E(t t). Figure 2.18(b) shows a schematic of the PG-FROG for two interacting Gaussian pulses. The generated signal pulse turns out to be Gaussian as well and is centered at the time 2t/3. Since the phase of the signal pulse is entirely due to E(t) (proportional to square of the absolute value of E(t t)), the signal pulse will reflect the instantaneous frequency of E(t) at the time 2t/3 [153]. When the phase dependence becomes very complicated and the instantaneous frequency description becomes meaningless, the signal pulse reflects the short time spectrum of the probe pulse. In Figure 2.19, the experimental setup for surface THG-FROG measurements is reported. In this case the two replicas are focused onto the back surface of 160-mm-thick cover glass [156]; the THG signal is highly localized at the air–dielectric interface and disappears completely when the interface is traversed away from the beam focus. Figure 2.20 shows the experimental setup for the SHG-FROG used in [159].
Figure 2.18 Schematic of the experimental setup used for PG FROG [153] (a) and interaction in time between the two Gaussian replica pulses (b).
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Figure 2.19 Experimental setup for surface THG FROG technique [156].
Figure 2.20 Experimental setup for noncollinear SHG FROG measurements [159].
Here a 30-mm-thick KDP nonlinear crystal was used to produce the second harmonic by the two replicas focused at a very small crossing angle (2 ) and a 13-fs near-transform-limited Ti:Sa laser pulse could be characterized. In the sub-10-fs range two serious problems arise with the FROG technique. The first is bandwidth limitation of the optics and the detection system involved, in particular the bandwidth limitation of the SHG process. This problem is resolved by utilizing extremely thin nonlinear optical crystals. The second problem, typical of the noncollinear configuration, is more fundamental and it is related to the reduction of temporal resolution due to the finite beam-crossing angle in the nonlinear crystal. In fact, in any noncollinear geometry the two replicas wavefronts
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interact to generate the signal field along the bisecting direction. Any of the two ultrashort replicas can be regarded as a very thin radiation bullet which propagates forming an angle 2u0 with the propagation direction of the other bullet, the thickness of the single bullet being dl = ct pulse. The temporal overlapping of the two bullets occurs along the bisecting direction for a stretched spatial projection given by cdt = u0 w0, w0 being the beam radius in the focal plane inside the nonlinear crystal. It qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi turns out that the measured pulse duration, t M = t 2pulse + dt2 , is biased by dt with respect to the ‘‘true’’ value tpulse. This dictates the minimum acceptable choice of u0, imposes a constraint on the value of w0, and represents a severe limitation for apparatus temporal resolution. In practice, spatial beam distortion and poor focusability may often result in an increased beam diameter, w0, in the focal plane and may possibly require an increased value of u0. In order to circumvent these disadvantages an alternative approach has been followed in [162]. Such a scheme is based on a collinear geometry in combination with type-II phase-matching. A scheme of the experimental layout used in [162] is shown in Figure 2.21. By means of this apparatus laser pulse durations as short as 6.6 fs have been measured with a temporal resolution of less than 1.2 fs limited by
Figure 2.21 Collinear type-II SHG FROG setup [162]. BS = beam splitters; PR = periscope for polarization rotation; HA = periscope for height adjustment; FM = focusing mirror; SHG = nonlinear crystal; OMA = optical multichannel analyzer. Dots and arrows on the beam path represents the polarization state of the beam.
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the group-velocity-mismatch (GVM) in the nonlinear crystal between the orthogonally polarized fundamental pulses. Typical results obtained by using both an SHG and a THG FROG are shown in Figure 2.22 where the retrieved intensity and phase for a nearly transform-limited oscillator pulse (100 fs) are reported, whereas the insets show the corresponding experimental SHG FROG and THG FROG traces. Figure 2.23 illustrates the interferometric autocorrelations calculated from the retrieved pulses (solid line) and the independently measured data (circles) for a Ti:Sa laser pulse having a transform limit of 7.4 fs. The plots refer to half trace due to the symmetry of the curve and the data: the left side plot reports results obtained by using a collinear, type-II phase-matching SHG FROG, whereas the right side plot displays data and calculation based on the SPIDER method. The agreement between calculated autocorrelations and measurements and between the two methods is very good. In Figure 2.24 the retrieved intensity and phase of a 4.5 fs laser pulse are plotted vs. time (a) and frequency (b). These results [163] have been obtained by use of a noncollinear SHG FROG. Lately, another nonlinear technique SPIDER has been implemented for measuring intensity and phase of an ultrashort laser pulse [132]. SPIDER stands for Spectral Phase Interferometry for Direct Electric-Field Reconstruction. The principle of operation of the method is rather simple
Figure 2.22 Retrieved intensity and phase for a quasi-transform-limited laser oscillator pulse [156]. The insets reveal the corresponding experimental SHG FROG and THG FROG traces, both nearly symmetrical in time.
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Figure 2.23 Interferometric autocorrelations calculated from the retrieved pulses (solid lines) and measured data (circles) with FROG (left) and SPIDER (right) for a Ti:Sa laser pulse having a transform limit of 7.4 fs [162].
Figure 2.24 Retrieved intensity and phase vs. time (a) and vs. frequency (b) for a 4.5 fs Ti:Sa pulse [163]. FROG-retrieved intensity and phase are displayed as shaded contours and dashed curves, respectively. Independently measured spectrum (filled circles) and computed residual phase of the pulse compressor (dash–dotted curve) are shown in (b) for comparison.
as illustrated in Figure 2.25, where the SPIDER experimental setup is shown: two replicas of the input pulse are generated with a fixed time delay t. These two replicas are converted up by means of sum-frequency generation with a strongly chirped pulse which is derived from the
66
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Figure 2.25 SPIDER setup [61]. GDD = SF10 glass block which stretches the pulse by a huge amount of chirp imparted by Group Delay Dispersion; PR = periscope for polarization rotation; BS = beam splitters; TS1 = translation stage for adjustment of the delay t; TS2 = translation stage for adjustment of temporal overlap of the short pulse pair with the stretched pulse; HA = periscope for height adjustment; FM = focusing mirror (30-cm radius of curvature); SFG = upconversion crystal (30-mm-thick type-II b-barium borate in the experiment [61]); OMA = optical multichannel analyzer. The filled shapes stand for silver-coated mirrors, whereas filled circles and arrows along the beam path display the polarization state of the beam.
same input pulse. Owing to their temporal separation, the two replicas beat with two different quasi-cw slices of the stretched pulse, thus resulting in two identical versions of the input pulse that are frequency shifted with respect to each other by a spectral shear dv. The resulting interferogram is recorded with a spectrometer. SPIDER is a self-referencing interferometric technique in the sense that there is no need for a wellcharacterized reference. Moreover, no moving parts are required and only one interferogram, S(vc), has to be measured: Sðvc Þ = jEðvc Þj2 + jEðvc + dvÞj2 + 2jEðvc ÞEðvc + dvÞjcos½Fv ðvc + dvÞ Fv ðvc Þ + vc t (Eq. 2-24) where E(v) is the radiation pulse electric field in frequency, Fv(v) the spectral phase of the pulse, and vc the passband frequency of the spectrometer. Thanks to a fast noniterative algorithm the phase of the oscillatory cosine term in Eq. (2-24) is extracted. The linear term vct is separately
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measured by conventional spectral interferometry and subtracted from the cosine phase term in a calibration measurement which needs to be done just once. Finally, one obtains the spectral phase F(v) by adding up the appropriate phases. By use of the SPIDER technique sub-6-fs pulses generated by a Kerr-lens mode-locked Ti:Sa oscillator in the nanojoule energy range have been successfully characterized [61]. Lately SPIDER has also been employed for measuring intensity and phase of amplified sub-10-fs pulses. As an example, in Figure 2.12, the amplitude and phase of 6.5-fs, amplified Ti:Sa pulse (pulse energy 0.5 mJ), as reconstructed by a SPIDER apparatus, are shown as a function of time (a) and frequency (b). The SPIDER accuracy in reconstructing the pulse is also very high, estimated to be a phase error of 0.062 rad corresponding to less than 2% error in the pulsewidth reconstruction [133].
2.3 Dynamics of Atoms and Molecules in Strong Fields 2.3.1 Atoms The recent advances in ultrashort laser sources nowadays enable the availability of light packets that are extremely confined in time and space. For instance, the spatial extension of a t pulse = 100 fs diffraction-limited light pulse along its propagation direction, delivered by a commercial Titanium–Sapphire laser system, is of the order of ct pulse 30 mm, whereas transversally a spot size comparable to the field wavelength (=0.5–1 mm in the visible and near infrared spectral domain) can be obtained at focus. Light slices few microns thick can be achieved when using few optical cycle laser pulses (tpulse 5 fs). Due to this spatial and temporal confinement, light pulse peak intensities as high as 1014–1015 W cm2 can result even from relatively moderate laser pulse energies (1 mJ), giving rise to electric field amplitudes which approach the static Coulomb field strength experienced by the atomic outer-shell electrons (109 V cm1). Under such conditions, the atomic response to the optical field is strongly nonlinear, as the induced polarization field, namely the atomic dipole moment times the density of atoms, exhibits a nonlinear dependence on the inducing electric field. The nonlinearity arises from different processes, depending on the field intensity level. At moderate intensities, the laser field is much weaker than the static atomic Coulomb field and, consequently, the atom is just slightly perturbed under nonresonant excitations. The atomic energy levels are slightly shifted by an
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amount proportional to the laser intensity (ac Stark shift [164]) and the atom essentially remains in its ground state. This regime of nonlinear interactions between atoms and ultrashort laser fields is well described by a perturbative approach. Within this framework, ionization of the atom takes place through a sequential absorption of a number of photons of the laser field sufficient to push an electron above the atomic coulombic barrier (Multiphoton Ionization (MPI), Figure 2.26(a)). If the laser electric field strength becomes comparable to or higher than the static Coulomb field experienced by the outer-shell electrons, severe ionization of the atom occurs as one of the outer-shell electrons can escape with high probability from its bound state, either by tunneling out from the coulombic barrier (Tunnel Ionization, Figure 2.26(b)) or, if the laser electric field is intense enough to completely remove the coulombic barrier temporarily, by simply being liberated in the laser field (Above-Barrier Ionization, Figure 2.26(c)). In the last case, the electron wave-function diffuses out from the atomic potential well before the laser electric field reverses its sign. Subsequently, the liberated electron wiggles in the laser electric field gaining cycle-averaged kinetic energy which can be much higher than the atomic binding energy. This regime of the ultrashort laser field-atom nonlinear interactions is referred to as the strong field regime. In the strong field regime the atomic polarization is dominated by the ionization process and the contribution from bound electrons is negligible.
x
(a) Multiphoton ionization
x
(b) Tunnel ionization
x
(c) Above-Barrier ionization
Energy
-IP
-IP
-IP
Figure 2.26 Representative scheme of the Multiphoton Ionization (a), the Tunnel Ionization (b), and the Above Barrier Ionization (c) processes in atoms.
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Perturbative regime
Strong field regime
µE/∆<1 Bound electrons
γ <1 optical field ionization Free electrons
c(2) processes:
Multiphoton
Second harmonic generation Above-threshold ionization Optical parametric generation
High harmonic generation
Relativistic regime vosc → c
Optical rectification Laser ablation c
(3)
processes:
Sub-fs x-ray and electron pulses
Hard x-rays Multi MeV electrons
Third harmonic generation Stimulated Raman scattering Self-phase modulation
Long-distance selfchanneling
Self-focusing Self-defocusing & channeling
Self-focusing 1011
1012
1013
1014 1015 Intensity (W/cm2)
1016
1017
1018
Figure 2.27 Regimes of nonlinear optics with intensity scale applied to the visible and near infrared spectral domain. The boundaries between different regimes are not sharply traced. Only nonresonant interactions have been considered, by assuming the typical energy separation, Dr, between two levels of the atomic system to be larger than the photon energy (1 eV).
The induced polarization is nonlinear as long as the electron moves in the neighborhood of its parent ion. Once the ionized electron moves far from the parent ion free in the laser electric field, its trajectory is Newtonian and the atomic response substantially turns back to linear. New nonlinear features arise only at orders of magnitude higher intensities, when either a second electron can be stripped to the once ionized atom by optical-field ionization, or the wiggle energy of the liberated electron in the laser electric field, namely the electron ponderomotive energy, becomes comparable to or even higher than the electron rest energy mc2, thus setting up the onset of the relativistic nonlinear optics. Figure 2.27 shows how to position some of the most common nonlinear optics phenomena according to their typical intensity threshold.
2.3.1.1 Perturbative regime At laser peak intensities typically lower than 1013 W cm2 the polarization field, P, of an ensemble of atoms interacting with a laser field can be expanded in a power series of the electric field, E, assumed to be linearly
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polarized for simplicity, and represented as the superposition of the linear and nonlinear responses, P(A.s/m2) = e0x(1) E + Pnl where As stands for ampere · seconds, and: Pnl = e0 x ð2Þ E2 + e0 x ð3Þ E3 + + e0 xðkÞ Ek +
Eq. (2-25)
e0 = 8.85 · 1012 A s V1 m1 being the vacuum permeability and x (k) the kth-order susceptibility (see for instance [165]), which is a kth-rank tensor relating the components of E and Pnl for the general case of an anisotropic response of the medium. In Eq. (2-25) Pnl has been assumed to instantly follow the electric field dynamics. Such an assumption is very well fulfilled in atoms where the transition frequency from even the ground state to the lowest order excited state significantly exceeds the laser carrier frequency in the visible and near infrared range, so that the transition time is usually shorter than 1 fs; however, the assumption can fail in molecules and condensed matter where nuclear motion can significantly contribute to the induced dipole moment with a response time ranging from hundreds of femtoseconds to several picoseconds, and a more complicated expression for Pnl has to be used (see for example [166, 167]). Within the framework of the quantum theory of optical susceptibilities, by neglecting bound-free transitions, the ratio of two consecutive terms of the series in Eq. (2-25) yields: xðk + 1Þ E k + 1 mik A eAaB = abb rD rD xðkÞ E k
Eq. (2-26)
A(t) is always the time-dependent amplitude of the radiation field, r = 1.06 · 1034 Js is Planck’s constant, aB is the Bohr radius, and e = 1.6 · 1019 C the absolute value of the electron charge. Thus, for abb << 1 bound–bound transitions are weak enough to allow the expansion in Eq. (2-25) to converge. When ionization occurs bound-to-free transitions have to be considered. In this case the so-called Keldysh parameter [168], defined as the ratio between the time it takes for the active electron to tunnel out from the potential barrier, Tcross, and the electric field period Topt, determines whether the expansion in Eq. (2-25) converges or not and whether the perturbation theory holds true or not. In fact, the Keldysh parameter is given by Tcross = g= Topt
rffiffiffiffiffiffiffiffiffi IP eEa eA eAaB = abf = pffiffiffiffiffiffiffiffiffiffiffiffiffi = pffiffiffiffiffiffiffiffiffiffiffiffiffi = 2UP v0 2me IP v0 2me IP rv0
Eq. (2-27)
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where me = 9.11 · 1031 kg is the electron rest mass, v0 is the laser potential of the atom. carrier frequency, and Ip >> rv0 is the ionization ffi pffiffiffiffiffiffiffiffiffiffiffiffi Use has been made of the relation aB = r= 2me IP which generalizes the definition of the Bohr radius for atomic number greater than one. Hence, if abf << 1 bound-to-free transitions can also be treated perturbatively. Equations (2-26) and (2-27) also reveal that abb and abf are simply related by the ratio D/v0, namely by the detuning to the laser frequency. In the following we will mostly concentrate on the case D/v0 which for atoms refers to the near infrared and visible spectral range where most of the ultrashort radiation sources are available. As Figure 2.27 shows, many nonlinear optical phenomena, such as Self-Focusing, SPM, and MPI are described by Eq. (2-25) for radiation intensities not exceeding 1013 W cm2. Self-focusing and SPM, in particular, are very much concerned with nonlinear processes for femtosecond pulse generation in solid-state lasers as has been discussed in Sections 2.2.2 and 2.2.3. At intensities as high as 1013 W cm2, MPI of atoms becomes relevant [169–171]. A schematic picture of MPI is represented in Figure 2.26(a): the active electron very quickly absorbs N, N + 1, N + 2, etc. photons from the laser field, N being the minimum of photons needed to reach the continuum threshold. Increasing the laser intensity favors the absorption of number of photons higher than N: in this case, MPI gives rise to ATI ([172], see [173] for a review). Due to the relevant number of atomic electrons liberated into the continuum by MPI at these intensities, self-defocusing comes into play and competes with self-focusing caused by the optical Kerr effect. As a consequence, the two effects can balance each other under proper conditions and give rise to so-called self-channeling, when intense femtosecond laser pulses can propagate collimated with no diffraction over hundreds of meters [174, 175]. In this intensity regime, in between the perturbative and the strong field framework, the polarization of the medium becomes difficult to calculate analytically, and the time-dependent Schro¨dinger equation is solved by means of special numerical techniques, either directly [176] or indirectly by the Floquet ansatz [177, 178].
2.3.1.2 The strong field regime When the Keldysh parameter is smaller than one, the laser field suppresses the Coulomb potential (see Figure 2.26(b, c)) so heavily that the wave function of the outermost atomic electron of energy Ip, penetrates
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Figure 2.28 Quasistatic total potential felt by the most weakly bound atomic electron in presence of an intense laser field. The total potential results from the superposition of the Coulomb-like static potential and the potential E x due to the linearly polarized laser field. One of the two potential curve arms bends down thus allowing for the electron to tunnel through the barrier. Successively the electron, born at x0 with some drift velocity [181], follows the oscillation of the laser field. The maximum amplitude during the first electron excursion is indicated by aw.
through the barrier and reaches the exterior at x0 in a fraction of the laser period Topt, as shown in Figure 2.28. Consequently, the resultant ionization rate, w(E), follows adiabatically the laser field variation and depends only on the instantaneous electric field and the ground state which the active electron is escaping from. This process, which is drastically different from MPI, is usually referred to as Optical Field Ionization (OFI) and substantially includes Tunnel Ionization and, as an extreme case, ATI. Once the electron is freed in the continuum, essentially it follows the electric field oscillation according to the Newtonian motion laws. By neglecting the Coulomb field of the parent ion, the classical equations of motion are solved to give aw = eA=mv20 for the amplitude, aw, of the wiggling motion in the linearly polarized laser field, while the release position is x0 Ip/eE(tion), tion being the ionization instant of time. The cycle-averaged kinetic energy of the wiggling motion, namely the so-called ponderomotive potential is given by UP = e2 A2 =4mv20
Eq. (2-28)
Thus, for example, at the Titanium–Sapphire wavelength l = 800 nm 15 W fficm2, we have Up = 116 eV and aw = and at a peak intensity I =p10 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 15.4 nm. Therefore, g = IP =2UP < 1 implies that the kinetic energy gained by the active electron in the laser field largely exceeds the atomic pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi bound energy. Moreover, from Eq. (2-27), g = 2x0 =aw , g < 1 means
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also that the oscillation amplitude of the electron is larger than the spatial extension of the barrier: the electron wiggles freely for most of the time after ionization far from the parental ion, acquiring a large kinetic energy within a small fraction of Topt. The influence of the static Coulomb-like field becomes negligible compared to the optical field effect immediately after ionization, which marks the strong field regime of nonlinear optics. Moreover, classical mechanics is sufficient to correctly describe the temporal evolution of the wave packet center of gravity of the freed electron on the time scale of the laser period, since quantum diffusion contributes to the wave function spreading at a typical rate of less than 1 nm fs1 [179, 180]. Thus, the wave packet spatial extension remains small when compared to aw, considering that Topt 2.7 fs, for instance, at the Titanium–Sapphire wavelength. The subsequent mixed motion of the electron, drift and wiggling in the optical field, is accurately described by combining the tunneling rate w(E(t)), obtained from quantum mechanics with the solutions of the Newtonian classical equations of motion of the wave packet center of gravity. With substantially zero initial velocity, they provide the correct temporal evolution and trajectories of the active electron in the strong field regime. Thus, this is the recipe used for describing most of the strong field phenomena, such as ATI electron energy spectra [181, 182] and high-order harmonic generation [182–184]. It is easily seen by following the approach developed in [53] that, as long as the nonrelativistic strong field regime is concerned, x(t) being the position of the wave packet center of gravity larger than the Bohr radius, the first time derivative of the macroscopic polarization P(t) of an atomic ensemble is determined by the current density due to the electrons liberated in the linearly polarized optical _ _ field, PðtÞP nl ðtÞ = Jfree = ene ðtÞ x + ene x0 , where the dot denotes the first partial time derivative and ne(t) the density of free electrons. The first term is due to the just liberated electrons that move away from the parent ion, while the second term arises from the appearance of new free electrons at x0. As for the second time derivative one obtains: 2 €P nl ðtÞ = e ne ðtÞEðtÞ + IP q m qt
_ n e ðtÞ EðtÞ
Eq. (2-29)
where Z ne ðtÞ = n0 1 exp
t ¥
dt0 w½Eðt 0 Þ
Eq. (2-30)
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and use has been made of the nonrelativistic equation of motion m€x = eEðtÞ. _ = 0Þ = v0 0, while n0 The term ene x_ in Eq. (2-29) vanishes since xðt stands for the density of neutral atoms. Equations (2-29) and (2-30) together with the quantistic expression of the ionization rate w[E(t)] represent an explicit and exhaustive constitutive law of the ionizing media. The two terms of Eq. (2-29) play different roles: in fact, while the first one affects the phase of the propagating optical field, causing spectral blue-shift and broadening (see for instance [185, 186]), the second term, proportional to Ip and taken into consideration in [53] for the first time, accounts for the energy loss of the optical field due to ionization. It is worth stressing that Eq. (2-29) can be generalized to an arbitrary polarization of the optical field and that in deriving Eq. (2-29) recombination of the electron into its bound state about one half laser cycle after its detachment has been neglected. Such a process, in fact, occurs with a rather low probability and has very little influence on the spectral domain of the fundamental field, whereas it plays an essential role in harmonic generation. Moreover, it can be shown [53] that Eq. (2-29) is also energy conserving. The polarization field of the macroscopic atomic medium, obtained in Eq. (2-29), is also based on the implicit assumption that the medium response is local, namely at a stated position in space; P(t) depends only on the strength of the electric field E(t 0) for t 0 £ t at the same location. This circumstance, which allows one to omit the spatial dependence of the functions in Eqs. (2-29) and (2-30), is referred to as the electric dipole approximation, and it holds true as long as the interaction is nonrelativistic. When the electric field strength is sufficiently intense to accelerate the liberated electrons to velocities comparable to c, the magnetic component of the Lorentz force is not negligible anymore and the electrons can travel distances comparable to the optical wavelength over a laser period. Consequently, in this case the medium response becomes nonlocal, the relativistic regime being approached when [187] eEmax = arel = mcv0
rffiffiffiffiffiffiffiffiffi 4UP ‡1 mc2
Eq. (2-31)
In the visible and near infrared spectral range, the condition of Eq. (2-31) implies optical intensities as high as 1018 W cm2 or higher (arel 0.9 for I = 1018 W cm2 at l = 1 mm). At these intensities, a number of peculiar phenomena occur, such as relativistic self-channeling [188],
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generation of multi-MeV electron jets [189, 190], and nonlinear Thomson scattering [191].
2.3.1.3 High-order harmonic generation When ultraintense laser pulses interact with atoms (see for example Refs. [192–194] for the first experimental evidence), atom clusters [195, 196], and molecules [197, 198], odd high-order harmonics of the fundamental wavelength are emitted in the extreme ultraviolet (XUV) and softX-ray spectral range. For recent reviews, see Refs. [53, 199, 200]. The moderate pump energy required for efficient nonlinear conversion, compared to other extreme nonlinear optics phenomena, the short pulse duration (shorter than that of the fundamental laser pulse), and the nearly laser-like spatial [201–205] and temporal [206, 207] coherence, make highharmonic radiation a very promising, compact, bright, table-top shortwavelength source. Thus, over the last few years high-order harmonics have already found considerable number of applications, among which we cite: atomic and molecular core-level [208, 209], photo-ionization
[210], and plasma [211, 212] spectroscopy; X-ray fluorescence analysis [213]; time-resolved solid-state physics of surface states [214] and
of ultraviolet photoemission spectroscopy [215]; nano and micro-structured material characterization, such as porous silicon [216]; XUV interferometry for the diagnostics of dense plasmas [211], where a 2D map of electronic densities as high as 2 1020 electrons cm3 was achieved [217]. A major drawback of high harmonic generation (HHG) is the efficiency of the process, which is still too low for many potential applications. A severe limitation is due to the fact that for OFI (Section 2.3.1.2), high-order harmonic generation is strictly linked to the generation of free electrons in the nonlinear medium. Free electrons originate a phase mismatch between the fundamental and the harmonic beams, thus setting a limit for the maximum coherence length over which harmonic radiation can grow because of constructive interference of the local contribution to the harmonic field. Moreover, shorter wavelengths are generated mostly at the top of the laser pulse, when the free-electron
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density is higher. Thus, phase mismatch increases with harmonic order and limits the highest achievable harmonics. Solving this problem may open the way to a number of exciting applications such as laboratoryscale X-ray microscopy, holography, and fs-time-resolved X-ray diffraction and absorption experiments. Using ultrashort laser pulses, down to the few-optical-cycle regime, has been demonstrated to reduce phase mismatch [218, 219], to enhance conversion efficiency, and to extend the spectral range of high harmonics into the water window (2.3–4.4 nm) [220–222]. Furthermore, as will be discussed throughout the next section, theoretical analysis predicts that high harmonics are generated in the temporal domain, either as a train of attosecond pulses [223–225], or as a single attosecond, XUV-radiation burst [226–228]. In this section, we will briefly review the main features of high-order harmonic generation both from a microscopic point of view by analyzing the dynamics of the atomic dipole moment strongly driven by the laser field, and from a macroscopic point of view by addressing the propagation through the nonlinear medium of the generated harmonic field. Atomic units will be used in the following analysis, essentially based on the approach reported in [229]. The results of the simulations will be compared with available experimental findings, mostly obtained with the 1 kHz-harmonic generator apparatus developed at the Politecnico of Milano (Italy). The results obtained with this setup, based on a sub-10-fs Ti:Sa laser source, are described in [230–232]. The gas target was constituted by a pulsed jet about 1 mm long with a local pressure throughout the experiments of 50–60 Torr, whose geometrical form and pressure field have been characterized in detail in [233]. Harmonic radiation was analyzed with a grazing incidence (86 ) Rowland mounting monochromator based on a platinum-coated, 300-grooves mm1, spherical grating (2-m radius of curvature). In a second experiment, harmonics were analyzed and detected by means of a high-resolution flat-field soft X-ray spectrometer and a high-resolution CCD detector, designed for the simultaneous acquisition of the spectrum and the far field pattern of harmonic beam [234]. The spectrometer had been calibrated in order to provide absolute measurements of the emitted photon flux. A schematic of this experimental setup is shown in Figure 2.29. Emission of harmonic radiation from a single atom or molecule is 2 determined by the dipole acceleration, dtd 2 hcjrjci, where r is the position vector and c the electron wave function which results from the solution of the nonrelativistic time-dependent Schro¨dinger equation. The HHG problem has been considerably simplified, still within a fully quantum mechanical approach, in the analysis of Lewenstein and
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Detector: CEM, MCP
Condensing optics Grazing incidence monochromator
Medium length ª 1 mm Confocal parameter ª 6 mm
High resolving power ~ 1500
Figure 2.29 Schematic of the experimental setup of a typical high harmonic generation experiment. The laser beam is focused into the interaction chamber, onto a noble gas jet. The generated high harmonic radiation, emitted collinearly to fundamental laser beam, is measured either by a grazing incidence Rowland mounting monochromator or by a high-resolution flat-field soft X-ray spectrometer followed by a high-resolution CCD detector, designed for the simultaneous acquisition of the spectrum and the far field pattern of the harmonic beam.
co-workers [183], which constitutes the basis of the so-called strong field approximation (SFA) applied to HHG. Such an approach is based on two assumptions: (i) in the continuum, the single active electron behaves as a free particle moving in the laser electric field, with no influence of the atomic, Coulomb-like potential; (ii) the contribution of all other bound states to the evolution of the system except the ground state is neglected. This is fulfilled in the strong field limit g < 1 (see Section 2.3.1.2) where excited bound states are smeared out due to a huge Stark shift, and intermediate resonances do not affect the transition from the ground state to the positive-continuum states. Therefore, this approach has been shown to agree well with the numerical solution of the Schro¨dinger equation, especially for harmonic photon energies significantly larger than the atomic ionization potential, Ip. A generalization of the Lewenstein theory to the nonadiabatic case is necessary when the laser pulse used in HHG experiments approaches the fewoptical-cycle regime and can be found in [229, 235]. Essentially, in the nonadiabatic case the single atom response is sensitive to the full electric field of the laser pulse and not only to the pulse amplitude envelope A(t). By following the model of Priori et al. [229], the nonlinear
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dipole moment reads: ( Z dnl ðtÞ = 2Re i
t
dt0
¥
3=2 p e + iðt t0 Þ=2
· d ½pst ðt0 ; tÞ Vðt0 Þd½ pst ðt0 ; tÞ VðtÞ ) Z t 0 0 0 0 wðt Þdt · exp½iSst ðt ; tÞEðt Þ exp ¥
Eq. (2-32)
In Eq. (2-32), E(t) is the electric field of the laser pulse (assumed to be linearly polarized), V(t) is its associated vector potential, e a positive regularization constant, pst and Sst are the stationary values of the momentum and quasi-classical action, respectively, and d is the dipole matrix element for bound-free transitions. pst is given by Z t 1 0 pst ðt ; tÞ = Vðt00 Þ dt00 Eq. (2-33) t t0 t0 and the corresponding stationary action is 1 1 Sst ðt0 ; tÞ = ðt t0 ÞIP p2st ðt0 ; tÞðt t0 Þ + 2 2
Z
t t0
V2 ðt00 Þ dt00
Eq. (2-34)
The dipole matrix element for transitions from the ground state to the continuum state, characterized by the momentum p, can be approximated, for hydrogen-like atoms, as [183]: d ðpÞ = i
27=2 ð2IP Þ5=4 p 2 p ðp + 2IP Þ3
Eq. (2-35)
The last exponential factor in Eq. (2-32) takes into account the ground state depletion by using the Ammosov–Delone–Krainov (ADK) theory for tunnel ionization [236], which is still valid as long as a laser peak intensity significantly higher than 1015 W cm2 is reached [237]. Thus, the ADK ionization rate reads 4vp 2n 1 4vp exp wðtÞ = vp jCn j vt 3v0 2
Eq. (2-36)
where IP ejEðtÞj Ihyd: 1=2 22n ; jCn j2 = vp = ; vt = pffiffiffiffiffiffiffiffiffiffiffiffiffi ; n = Z r IP n Gðn + 1ÞGðn Þ 2me IP
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where Z is the net resulting charge of the atom, Ihyd is the ionization potential of the hydrogen atom, and e and me are the electron charge and mass, respectively. It must be stressed that Eq. (2-32) still preserves the nice physical interpretation which can be given to the nonlinear dipole moment in the adiabatic case [183] and which was the basis of the semiclassical HHG interpretation [182, 238]. In fact, the term d½pst ðt0 ; tÞ Vðt0 ÞEðt0 Þ is the probability amplitude for an electron to make a transition to the continuum at the time t0 with the canonical momentum pst(t0, t) associated with the classical electronic trajectory which makes the action S stationary. Moreover, exp[iSst(t0, t)] represents the free particle propagator of the electronic wave function since the electron time of birth t0 until the time t, when the active electron 0 recombines with the parental ion with probability amplitude R t d *[p0 st(t0 , t)V(t)]. The whole amplitude is scaled by the factor exp½ ¥ wðt Þ dt which takes into account ionization as a leakage of the electronic wave function amplitude. The semiclassical interpretation, or three-step model, is graphically depicted in Figure 2.30. The electron wave packet is liberated at the
Non-perturbative regime 1014 < Iin < 1016 W/cm2 Tunneling ionization Ep
3rd hν=IP+3.2Up
2nd
x -Ip i
Up ≡ ponderomotive energy Iin ≡ intensity of the incident radiation Ep ≡ potential energy associated to the laser in the dipole approximation
1st
Figure 2.30 Illustration of the three step model: the single active electron, under the action of the laser field, first escapes from the atomic core by tunnel or above threshold ionization (first), then propagates oscillating in the laser field (second). During the second step the electron gains an amount of energy from the field ponderomotive potential which depends on its phase at the time of birth in the continuum. Finally (third), the electron recombines to the ground state of the parental ion emitting an XUV photon for energy conservation.
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time t0 (1), by tunnel or barrier-suppression ionization (see Section 2.3.1.2), then propagates in the strong laser field (2), gaining some additional energy from the ponderomotive potential of the field, and finally recombines to the ground state (3) upon releasing, as a high-energy photon Ip plus the energy gained in the laser field. Due to quasi-periodic repetition of this process in a multicycle laser field, the emitted dipole spectrum is discrete, consisting of odd harmonics of the laser frequency v0. Nevertheless, while previous studies (see for example [183]) indicate that for multicycle laser pulses the single atom spectrum is discrete with well-resolved odd harmonics and closely resembles the measured macroscopic spectra [186], with much shorter laser pulses, especially approaching the few-optical-cycle regime, the single atom spectrum is very chaotic as a result of nonadiabatic effects caused by the variation of the driving pulse intensity over one optical cycle [239], thus substantially breaking the periodicity of the phenomenon. In Figure 2.31, the calculated single Neon atom spectra provides evidence that for 100 fs Ti:Sa laser pulses the spectral structure is regular with well defined odd harmonics, whereas for 30 fs and mostly for sub-10-fs driving pulses, the spectrum appears constituted by spikes rather than being randomly distributed. As a very general feature of measured harmonics spectra, a typical spectrum consists of three main regions, as illustrated in the drawing
Figure 2.31 Single atom harmonic calculated spectrum generated in Helium by many-cycle laser pulses [186]. The laser peak intensity and pulse duration are 2 · 1015 W cm2 and 200 fs, respectively. The harmonic structure is very regular: the lowest order harmonics peaks decrease very quickly with the harmonic order and are followed by a long plateau having rather constant photon yield. The cut-off position is in good agreement with IP + 3.17 UP according to Eq. (2-37).
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in Figure 2.32(a): the very first harmonics, whose intensity is much higher than the other spectral components, follow rather well the lowest-order perturbative theory (LOPT), since their conversion efficiency is proportional to the laser intensity raised to the perturbative nonlinear order of the process [240]; the plateau harmonics, constituting a wide band of harmonic peaks having nearly constant height, and the cut-off harmonics, at the end of the plateau consisting of a small group of the highest-order emitted harmonics, rapidly decreasing in height with the harmonic order. In Figure 2.32(b), a typical measured harmonic spectrum is shown. In this case, the very first harmonics, still following the LOPT and the first harmonics of the plateau, are not visible because of the poor grating (a)
Plateau harmonics: nonperturbative behavior
Log(Intensity)
Low-order harmonics: perturbative behavior Iq~Ilaserq
The cut-off law: Ip+3.17Up
Cut-off harmonics
Harmonic order
(b)
Figure 2.32 Drawing of how a typical measured harmonic spectrum can appear (a). The three regions of low-order harmonics, still following the Lowest Order Perturbation Theory (LOPT) Iq Iqlaser being Ilaser the laser peak intensity, the plateau, and the cut-off harmonics are clearly distinct. (b) Typical measured harmonic spectrum in 50 Torr of Neon, generated by a 30 fs Ti–Sa laser pulse at a laser peak intensity of Ilaser 6.5 · 1014 W cm2 [425].
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efficiency at long wavelengths in spectrometers optimized for short wavelength detection. The great success of the semiclassical model, beyond its simplicity, is due to the correct prediction of the highest-possible emitted harmonic, namely to the correct location of the cut-off in the harmonic spectrum. The most energetic harmonic photon is indeed predicted to have an energy given by [182, 238, 241]: rvmax = IP + 3:17UP ðtÞ
Eq. (2-37)
where Up(t) is the ponderomotive potential as defined in Eq. (2-28) evaluated at the generation time, t, of the harmonic photon. When ionization of the ground state is weak and depletion is negligible, the highest order harmonic is emitted at the top of the pulse (t = 0). This is mostly the case for short driving pulses [242]. On the contrary, with multicycle fundamental pulses ionization can be much more severe and depletion of the ground state can occur much earlier than the top of the pulse. In this second case, the effective laser peak intensity at which the cut-off harmonics are emitted can be much lower than the peak intensity at the top of the pulse. In fact, the harmonic cut-off could be extended below 4.37 nm into the water window in Neon by increasing the peak intensity of 7-fs driving pulses [221], which could not be achieved with 30-fs pump pulses because of early depletion of the ground state. While in the multicycle regime, it turns out that most of the important features of HHG experiments can be understood simply from the single atom theory. In the few-optical-cycle regime, a macroscopic theory which includes propagation effects is essential in order to understand and describe the observed properties, starting with the well resolved discrete structure of the measured spectra. Indeed, it turns out that in the few-optical-cycle domain the propagation acts as a filter which selects the effective electron trajectories contributing to the harmonic signal. Thus, although the single atom spectrum is noisy and irregular, propagation cleans up the final spectrum, resulting essentially in the formation of the ordered structure constituted by odd harmonics of the fundamental beam [229]. Moreover, the filtering action is more effective when the full 3D propagation is considered, as illustrated in Figure 2.33. The partial cleanup obtained in 1D can be attributed to free-electron-induced phase-mismatch, which selectively reduces the contribution of a class of trajectories. In three dimensions, additional mechanisms, due to longitudinal and radial variations of both intensity and phase of the driving pulse, affect the nonlinear polarization phase [243, 244], thus leading to additional phase-mismatch and more effective trajectory selection. The most important propagation effects, extensively
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(a)
Intensity (arb. units)
|dnl|
2
7 fs
60
80
100
120
140
160
Photon energy (eV)
60
80
100
120
140
160
Photon energy (eV) (b)
Intensity (arb. units)
7 fs
60
80
100 120 140 Photon energy (eV)
160
Figure 2.33 Calculated harmonic macroscopic spectra, by using 1D and 3D propagation models, generated by a 7-fs-Ti:Sa laser pulse in 50 mbar of Neon, corresponding to a uniform atomic density n0 = 1.3 · 1018 atoms cm3. (a) The propagation model is 1D and the laser peak intensity is 9 · 1014 W cm2. The inset shows the very chaotic single atom emission spectrum. (b) Calculated harmonic spectrum in the same condition as (a) but using a 3D propagation model [229].
studied in a number of articles [186, 225, 228, 245–247], can be summarized as: (i) absorption, (ii) dephasing, and (iii) defocusing. Altogether, this sets a limit to the maximum achievable harmonic yield. Of course, absorption occurs due to the possibility of harmonic radiation exciting the core electron states and being re-absorbed. Recently, it has been outlined that, for very short driving pulses when ionization becomes negligible, XUV harmonic radiation can reach the absorption-limited regime down to
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FUNDAMENTALS Gaseous medium
fundamental photon
XUV photon P2
P1 Laser beam
±
z
Figure 2.34 Drawing of the possible mismatch effects. All the possible interference conditions, depending on the overall mismatch factor, can be obtained from adding up two harmonic photons generated in two different points of the gaseous medium. More photons of the fundamental beam generate one XUV photon in different points of the medium. Different XUV photons can interfere constructively or destructively depending on the phase matching.
the 10 nm spectral region [248, 249]. Dephasing is caused by the difference between the phase velocities of the driving and the high harmonics fields (see Figure 2.34 for a schematic drawing of the mechanism). The propagation length, corresponding to a mismatch factor of p is defined as the coherence length, indicating the maximum propagation distance over which coherent growth of the macroscopic harmonic output can occur. Three main factors influence the harmonic coherence length. The phase shift imposed by the laser-induced free electron
plasma on the laser pulse. The corresponding coherence length is given by: Lfe =
2pcv0 vp ðtÞ2 q
Eq. (2-38)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where vp ðtÞ = e2 ne ðtÞ=me e0 is the plasma frequency, ne(t) being the free electron density evaluated at the time t when the qth harmonic is generated [186]. A geometric source of dephasing is represented by the curved wave front of the driving field, which introduces a phase advance. Such an additional phase term is known as Gou€y when the laser driving pulse has a Gaussian spatial mode and leads to a coherence length given by [246, 250]: Lg;G
pb p2 w20 q ql0
Eq. (2-39)
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for propagation near focus and in free space, where b = pw20 =l0 is the laser confocal parameter, and w0 is the 1/e2 laser beam radius at focus. A similar effect arises also in HHG in a hollow waveguide due to the wavelength dependence of the propagation constant [251]. In this latter case the coherence length reads: Lg;wg =
4p2 a2 u211 ql20
Eq. (2-40)
a being the bore radius of the waveguide and u11 = 2.405 [119]. For optimum coupling w0 23 a, yielding Lg,wg 1.56 Lg,G. The single atom dipole moment exhibits a phase which approximately decreases linearly with the laser peak intensity, scaling as [243]: fdip
Up v0
Eq. (2-41)
Thus, depending on space through Up, fdip also introduces dephasing between the generated harmonic and the driving field. Moreover, being time-dependent, fdip contributes to chirp harmonic pulses [252, 253], thus limiting temporal coherence of the harmonics. A recent, quite complete study of the interplay of the different cited factors contributing to the final coherence length of high-order harmonics can be found in [254], whereas the influence of nonlinear medium pressure and length is investigated in [233] and more recently in [255].
2.3.2 Attosecond pulse generation and characterization: the present border line of ultrafast science First picosecond and then femtosecond radiation pulses have allowed us to analyze fast dynamics of microscopic processes. The typically utilized technique for high temporal resolution studies is a two beam scheme called pump-probe: a first, short excitation pulse (pump) triggers the process at a t0 time, and a second, short probe pulse takes snapshots of the evolution of the process at different delay times after t0. It is, thus,
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possible to track changes in the nuclear structure of the molecules, such as vibrations or breaking and formation of the chemical bonds, since the characteristic time-scale for atomic motion on an atomic scale length (0.1 nm) ranges from few femtoseconds to few picoseconds [256, 257]. But accessing the temporal evolution of a wide range of electron dynamics in the atomic shells has been, so far, frustrated because the electronic wave-function evolves on an attosecond time-scale (1 as = 1018 seconds). This is, for example, the case of ionization or the creation of inner-shell vacancy. Only an indirect insight into such processes has been gained, so far, thanks to measurements of transition line-widths in the frequency domain [258]. Just to get a first idea of the order of magnitude of the electronic evolution times, let us consider an electron in the ground state of the hydrogen atom, thus having an energy j E0 j = 13.6 eV. If we treat the electron as a classical particle, orbiting on a circle of radius equal to the Bohr radius, aB = 0.55 A˚, the revolution period of the electron is: sffiffiffiffiffiffiffiffiffi 2me Tel = 2pa0 Eq. (2-42) hEk i me = 9.11 · 1031 kg being the electron mass and hEki the cycle-averaged kinetic energy associated with the circular motion of the electron in its ground state. By relying on the virial theorem the cycle-averaged kinetic energy equals the average potential energy of the electron in the Coulombic potential of the proton, hEki = 12hVi = j E0 j , leading to a revolution period Tel 1.9 · 1016 seconds 190 as! Following the dynamics of bound electrons, thus implies breaking the femtosecond wall and going down to the attosecond time scale. At the other extreme, recently Kaplan and Shkolnikov [259] proposed a method for obtaining electromagnetic radiation bursts having sub-attosecond duration. In fact, by focusing petawatt or multiterawatt circularly polarized laser beams on a sub-wavelength-size solid particle or a thin wire, the excited electrons of the target are expected to reach an ultrarelativistic regime such that they can radiate pulses having zeptosecond (zs) duration (1 zs = 1021 seconds). Nevertheless, although even the attosecond barrier seems to be breakable in the near future, the attosecond time regime presently represents the border line of ultrafast science. Trains of attosecond pulses have been first generated at ultrahigh 1 1 or 2Topt ) by superposing frequency-converted repetition rates (Topt coherent radiation [260–262]: the driving field, its second and third
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harmonics, for instance, in the simplest case. Nevertheless, this scheme is substantially limited by the very short pulse interval (1–2 fs) within the train. Another approach to generate sub-femtosecond pulses was followed in [263, 264]. In this approach, a large number of mode-locked solitons, equally spaced in frequency and generated by cascade stimulated Raman scattering (CSRS), is predicted to form a radiation burst lasting 0.2 fs, having a broad spectral content centered at the wavelength of the exciting laser [263]. This phenomenon has actually been observed in [264], where collinear generation of mutually coherent equidistant sidebands in molecular deuterium has been demonstrated, by using two synchronized driving lasers. The huge spectral bandwidth excited by the Raman effect, constituted by the first thirteen anti-Stokes and two Stokes sidebands, ranged from 2.94 to 0.195 mm. Isolated bursts of radiation on the order of 1 fs or shorter are necessary to trace the above cited extremely fast electronic dynamics. Moreover, the most suitable spectral range for such bursts is the XUV or soft X-ray to access the fast spectroscopy of bound atomic electrons. High-order harmonics using few-cycle pulses is thus ideal for this purpose, as discussed in detail in Section 2.3.1.3. In particular, the rather high-order harmonics, whose spectral range covers the XUV region, are emitted only within a small fraction of the laser period near the peak of the pulse, thus leading to the generation of a single XUV/X-ray pulse of 100 as duration, emitted in a collimated laser-like beam [219, 226, 186]. Even when using longer driving pulse durations in the range of ffi 50 fs, high-order harmonics are predicted to lead to the generation of a train of attosecond pulses, in case they are locked in phase (see Section 2.2.1). If this is correct, in fact, a group of neighboring harmonics could add together to form a very short intensity spike, provided they all add constructively at the same instant, in the same way as several excited modes of a laser cavity, once mode-locked, add together constructively in time to form an ultrashort laser pulse. Since harmonics are equally spaced in frequency, this would happen twice per optical cycle of the fundamental field. The duration of the spike, then, could be as short as Topt/2N, N being the number of phase-locked harmonics [261, 262]. At the Ti:Sa wavelength of 800 nm for N = 5, the output pulse would be in the attosecond regime. Theoretical and numerical calculations for the single atom response predict that harmonics are not emitted exactly in phase, rather, they are generated not only in one but several spikes per optical half-cycle [223]. Then, propagation of the fundamental field through the medium affects the spatial and temporal coherence properties of the harmonic radiation, acting as a filter: only one per half-cycle of the interference
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spikes survives the propagation, thus leading to the formation of a train of attosecond pulses spaced by the period of the driving field [223–225, 229]. The first experimental evidence of attosecond pulse generation was achieved by Papadogiannis et al. [265], essentially by observing the autocorrelation effect of a 60-fs Ti:Sa pulse on the harmonic, XUVradiation produced in Ar gas. Despite the simplicity of this experiment, the obtained results have been debated for long time and still their interpretation is uncertain because attosecond production and measurement are intertwined [266, 267]. The experiment consists in creating two collinear, time-delayed Ti:Sa pulses of about 100 mJ pulse energy and 60 fs duration, the second pulse being slightly weaker than the first one, which are focused into an Ar gas laminar flow cell, kept at constant pressure (5 mbar). The peak intensity at focus for the first pulse is measured to be 1.7 · 1014 W cm2. Odd harmonics of the fundamental field are produced in the cell passed through a 150-nm-thick Al-Si(1%) filter, and detected with a microchannel plate (MCP). The filter was used just to realize the idea of mode-locked harmonics: intense lower order harmonics and fundamental were cut, thus selecting harmonics in the energy region up to the energy cut-off value, 51.5 eV under the experimental conditions, which are supposed to be locked in phase. Finally, the total intensity transmitted through the filter was detected as a function of the time delay between the two subsequent pulses. By the correspondence of the temporal overlap of the leading and trailing edges of the two pulses, the trace, shown in Figure 2.35, evidenced a train of sub-femtosecond oscillations whose width at half maximum was about 400 as. But the most striking feature observed was a narrow structure located at the leading front of the recorded trace. Its width, at the limit of the temporal resolution of the apparatus, was estimated to be on the order of 60 as. The Fourier transform of the total XUV temporal trace consisted in harmonic peaks from the 23rd to the 33rd order, superimposed on a continuous background. Therefore, the authors attributed the 400-asbeat to the constructive temporal interference of the six, locked-in-phase harmonic peaks from the 23rd to 33rd order, and the 60-as narrow line to the coherent continuum radiation background emitted in the spectral region 25–60 eV. Paul et al. [268] have also recently observed a train of attosecond pulses by generating phase-locked harmonics in Ar gas from a 40-fs Ti: Sa laser source. In this experiment, the approach developed in [269] has been followed: the phase between pairs of phase-locked harmonics has been determined by relating it to the phase of the infra-red (IR) driving field according to how the combined fields, XUV + IR, ionize atoms.
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Figure 2.35 Total visible-UV-XUV signal filtered with an Al–Si filter as a function of the delay between the two generating laser fields [265]. The inset shows an expanded area at around 60 fs delay, when a narrow feature having a width at half maximum of ’60 as is clearly visible.
Thus, the basic idea followed in [268] is a cross-correlation technique: Ar atoms are ionized by single XUV-photon ionization, in the presence of the IR driving field, which can induce additional multiphoton transitions in the continuum [270]. As a consequence, ionization with harmonic photon can be accompanied by absorption as well as emission of different numbers of IR photons. In the energy spectrum of the photo-electrons, this results in the appearance of sidebands located in between just any two peaks corresponding to ionization by absorption of a single photon from a determined harmonic, as the lower part of Figure 2.36 shows. The upper part of Figure 2.36 illustrates the experimental setup used in [268]. The incoming laser beam of central frequency vlaser was divided by a mask and an iris into an annular intense part used for the generation of the harmonics and a weak central part used as a dressing field [271]. The two pulses could be delayed with respect to each other by using two glass, delay plates, both having a thickness of 6 mm. The path of a beam through its plate depended on the incidence angle, so by tilting one plate or the other any of the pulses could be delayed with great accuracy. The annular beam, focused on a continuous-flow Ar jet at an intensity of 100 TW cm2, generated odd harmonics, which afterward propagated on-axis. The outcoming intense IR-outer-ring field was blocked by a 2.5-mm pinhole, and only the on-axis radiation, both harmonics and IR field could reach a magnetic-bottle spectrometer chamber. Here the two collinear beams were
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Figure 2.36 Upper part: experimental setup used in [268]. A Ti:Sa laser pulse (800 nm, 40 fs, 1 kHz rep. rate) is split by a mask into an outer, annular part (3 mJ) and a small central part (30 mJ). Both beams are focused into an Ar jet, where the smaller focus of the intense annular part generates harmonic radiation. The annular fundamental field is then blocked by a pinhole, and only the central part of the IR pulse and its harmonics propagate into a magnetic-bottle spectrometer. The light is then refocused by a spherical tungsten-coated mirror onto a second Ar jet. Electrons produced by photoionization in this second jet are detected at the end of a time-of-flight spectrometer (TOF) by microchannel plates (MCP). Lower part: quantum paths contributing to the photoelectrons generated in the second Ar jet by mixed-color two-photon ionization, vlaser being the IR field frequency and vq = qvlaser.
refocused on a second Ar jet by means of a spherical, off-axis, tungstencoated mirror, having a short wavelength cut-off around the 19th harmonic order (42.1 nm). The energy spectrum of photoelectrons produced in the second, low-pressure, Ar jet was measured by using a time-of-flight (TOF) spectrometer equipped with a MCP. When the intensity of the dressing IR-field is low enough to treat the problem within the second-order perturbation theory, each harmonic has only a single sideband on each side. Only the two nearest harmonics contribute to each sideband peak, each through two quantum paths (see Figure 2.36) that differ in the order in which the various photons are
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participating. Due to the quantum interference among different paths contributing to the same probability amplitude, a purely interference term appears in the transition probability from the Ar ground state, j cii, having energy E0, to all final states j cfi, representing the angular quantum numbers of the continuum electron, at the sideband energy Eq = E0 + qrvlaser. Such an interference term, Pquantum, is proportional to [268]: Pquantum cosð2fIR + fq1 fq + 1 + Dffatomic Þ
Eq. (2-43)
where fIR is the phase delay of the dressing IR-field with respect to the one that generates harmonics, fq – 1 are the intrinsic q – 1th order harmonic phases respectively, and Dffatomic is an intrinsic atomic phase, consequence of the intrinsic complex phase of the matrix element coupling the atomic ground state to a state in the continuum [272, 273]. Dffatomic is small and obtained from well-known theory with high precision [268]. Moreover, delaying the IR field by a time t with respect to the harmonics sets fIR = vlasert. By experimentally recording the magnitude of the sideband peak as a function of t, and fitting a cosine to the measured oscillations the phase difference between two consecutive harmonics, fq1 fq+1 could be determined. The measured sideband peak area normalized to the total photoelectron signal is shown as a function of t in Figure 2.37 for the first four sidebands. The curves oscillate nearly in phase with a periodicity of 1.35 fs (i.e. half the IR field period). The good modulation depth (a factor of 2) indicated that the relative phases did not fluctuate too much over the beam profile between shots, or within the profile of a single pulse. Once the relative phases were determined, along with the harmonic relative intensities obtained by the normalized areas of the peaks corresponding to a single harmonic photon absorption in the photoelectron energy spectrum, the temporal intensity profile of the total XUV field was uniquely determined. This profile, plotted in Figure 2.38, was found to be a sequence of 250-as peaks (FWHM) spaced by 1.35 fs. Repeating this reconstruction several times with phases randomly modified according to the experimental standard error led to similar results, with a standard deviation of 20 as in the FWHM pulse duration. Moreover, the phase differences of the first four harmonics were close but not identical, thus implying that attosecond pulses were not fully bandwidth limited. A similar approach to generate and detect attosecond pulses was also followed by Drescher et al. [274]. This time, as different from the above cited experiments, it was possible to generate just a single, XUV,
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Figure 2.37 Area of the first four sideband peaks (to higher energies from top to bottom) as a function of the time delay between the IR pulse and the harmonics [268]. The first three curves oscillate in phase, whereas the lowest is shifted forward by 0.35 fs. The vertical lines are spaced by 1.35 fs, half the cycle of the laser field.
attosecond burst per laser pulse, thanks to the few-optical-cycle Ti:Sa laser source employed. In fact, the harmonic radiation produced only within a fraction of the laser cycle near the peak of the pulse was selected by passing harmonics through a filter that transmitted only the highest frequencies. As in [268] the scheme adopted throughout the experiment is based on a cross-correlation technique: an X-ray photon excites a bound atomic electron into a positive-energy state in the presence of a laser field. Laser-induced transitions from this state or a laser-induced shift in its energy (Stark shift) provide the nonlinearity which links the X-ray to the laser pulse, thus permitting to compare the X-ray pulse duration with
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Figure 2.38 Temporal intensity profile of a sum of five harmonics from the 11th order to the 19th order, as reconstructed from measured phases and amplitude [268]. The FWHM of each peak is ’ 250 as. The cosine dashed curve represents the IR probe field for zero delay. The reconstruction assumes that all pulses are identical, but, in reality, the pulse properties might have some variation around this average.
that of the visible pulse, according to the scheme proposed by Schins and co-workers [270, 271, 275–277]. A difficulty intrinsic to the methods suggested by Schins and co-workers is that in order to identify the Stark shift amongst the resulting sidebands in the photoelectron energy spectrum, or to measure the amplitude of the sidebands, the X-ray spectral width must be kept well below the laser photon energy rvlaser 1.6eV to avoid overlap of the sidebands with the main peak. Thus, the methods suggested in [270, 271, 275–277] could not be used for measuring X-ray pulses having durations tx shorter than the laser cycle Topt without significant modifications. The key idea, used in [274], which makes the laser-assisted X-ray photoionization suitable for detecting X-ray pulses shorter than the laser cycle, is using a lateral observation geometry. Within a semiclassical analysis of the laser-assisted photoelectric effect [181, 182, 278], in fact, the final kinetic energy (after the laser pulse), Ef, of the emitted electron, in the limit vx >> vlaser can be written as [274]: Ef Ei UP ðtÞ + UP ðtÞcos ð2vlaser tÞ + 4UP ðtÞ cos 2 u sin2 ðvlaser tÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi + 8Ei UP ðtÞ cos usinðvlaser tÞ Eq. (2-44)
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where Ei = 12 mv2i IP is the initial electron energy in the continuum, v2i being the electron release velocity, Ip the atomic ionization potential, u the angle between the final electron momentum, pf, and the laser polarization (see Eq. 2-39), and Up(t) the ponderomotive energy gained by the ionized electron in the laser field corresponding to the cycle-averaged electron quiver energy Eq. (2-28). Therefore, the final kinetic energy equals the atomic ionization potential reduced by the quiver energy evaluated at the electron instant of birth, plus three terms which account for absorption and emission of laser photons in a quantum description (Figure 2.39). When the X-ray spectral bandwidth is larger than rvlaser, the sidebands of the electron energy spectrum completely coalesce forming a single broad spectral feature described by Eq. (2-44). In this condition neither
t1 EL
θ
EL
t2
pf(θ) t1
t3
t2 Wf hωx
td
W0
τ x>T0/2 τ x<
t3 Kinetic energy spectrometer
Figure 2.39 Semiclassical modeling of laser-assisted photoionization. The electrons, liberated at different instants (t1, t2, t3) by an X-ray photon, are ejected with different angle distributions of their final momenta pf (u) in the presence of the laser field. The momentum transferred along the laser polarization is responsible for a downshift of the final kinetic energy, Ef, of the electrons observed within a small solid angle orthogonally to the laser polarization. The variation of Ef with the time delay, t, between the instant of X-ray absorption and the peak of the laser pulse (assuming an X-ray pulse duration t x << Topt/2 and observation near u = 90 ) exhibits a modulation at twice the laser frequency and an envelope following the temporal evolution of the laser intensity. For t x > Topt/2 the oscillations average out (dashed line).
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the individual sideband amplitudes nor the ponderomotive shift of the spectrum center-of-gravity can be reliably acquired. In particular, the ponderomotive shift tends to be obscured by an upshift of the centerof-gravity of the overall spectrum (fourth term in Eq. (2-44)); upshift is pffiffiffiffiffiffiffiffiffiffiffiffiffi more pronounced for u 0. Moreover, rvxIp Up implies 8Ei UP UP , i.e. the photoelectron energy spectrum smears out over a range much broader than Up, thus preventing an accurate measurement of its shift on the order of Up(t). Electrons emitted at u 90 are special since their energy spectrum does not get distorted by absorption or emission of laser photons, but is shifted just by the oscillating laser field. Restricting the observation geometry at u 90 , i.e. the direction orthogonal to the laser polarization, makes the ponderomotive shift Up(t) clearly observable. As Up(t) is proportional to the instantaneous laser intensity, measuring the ponderomotive shift vs. the delay t yields the cross-correlation between the temporal intensity profiles of the X-ray and laser pulses. Moreover, it also provides a sub-Topt/4 probe for measuring the X-ray emission characteristics on an attosecond time scale, by fitting the oscillations in the electron energy shift predicted by the third term in Eq. (2-44). These oscillations wash out on average for t x ‡ Topt/2. Thus, based on this central remark, in the experiment of Drescher et al. [274] the photoelectron detection angle was confined to a small solid angle around u = 90 , different from laser-assisted photoionization experiments performed previously [181, 182, 278]. The apparatus used throughout the experiment carried out by Drescher et al. [274] is schematically represented in Figure 2.40. Few-cycle, Ti:Sa laser pulses (llaser = 770 nm, tpulse = 7 fs, 0.5 mJ/pulse, 1 kHz rep. rate [129]) were focused into a quasi-static neon gas cell kept to a local pressure of 4 · 102 mbar. Harmonics generated into the cell having photon energies up to 120 eV and a beam divergence of ’0.7 mrad, collinearly propagated with the fundamental beam, passing through a pellicle with a central disk formed by a zirconium foil which is transparent for the X-rays but blocks laser and low-order harmonic radiation. The resulting annular laser beam and the concentric harmonic beam were then refocused, at the same position by a Mo/Si spherical multilayer mirror into an effusive, low-pressure Kr atomic jet. At the focus the harmonic diameter was measured to be 2 mm [213], a factor of ten smaller than the laser beam waist. The Mo/Si multilayer mirror exhibited a peak reflectivity of 60% at 90 eV with a bandwidth of 5 eV and consisted of two piezo-controlled concentric parts. Thus, by slightly separating the two parts the X-ray beam could be delayed with respect to the laser beam. The maximum scan range of this delay stage was ’50 fs whereas the reproducibility was estimated to be 0.1 fs.
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Figure 2.40 Schematic diagram of the experimental setup used in [274]. The focused 7-fs laser beam drills its way through the walls of a metallic tube (diameter 3 mm) by ablation and interacts with Neon atoms inside the tube to produce highorder harmonic radiation. The inset shows the trace of the ionizing Neon gas, whose fluorescence emission can be photographed, leaking out from the tube. The laser and the highly collimated X-ray beam emerge from the interaction region and co-propagate collinearly through a 2-m beamline. Differential pumping stages keep the pressure at around 4 · 102 mbar in the X-ray source chamber and 105 mbar in the experimental chamber. The ionization detector in the higher-pressure part of the beamline monitors the spectrally integrated high-harmonic flux. Laser and harmonic beams pass through a 100-nm-thick, 3-mm diameter zirconium foil deposited on a 5-mm-thick nitrocellulose pellicle to cover a hole of 2-mm diameter. The energy content of the out-coming annular laser beam can be adjusted with a motorized iris between fractions of microjoule and a few tens of microjoules. The X-ray multilayer Mo/Si mirror consists of two concentric parts: the position of the central part is controlled by means of a PZT, which is mounted on a quadrant piezo stage. Such a mechanism allows alignment and translation of the central part with respect to the external part of the mirror. Finally, the energy spectra of the photoelectrons produced by laser-assisted photoionization of Kr are detected by means of a TOF spectrometer.
The Kr target was closely followed by a TOF spectrometer (TOF entrance at 5 mm) having an acceptance angle of 0.3 mrad. The TOF axis was aligned perpendicularly to the laser beam and to the laser polarization (u = 90 ). It is worth pointing out that krypton, whose ionization potential is Ip = 14 eV, was chosen as a target because of the nearly isotropic momentum distribution of 4p electrons at rvx = 90 eV photon energy [258]. The Mo/Si mirror reflects the 55th and 57th harmonic of the fundamental field: assuming no spectral phase modulation, Fourier transformation of the 4p-photoelectron energy spectra in absence of laser field
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yields an X-ray pulse duration of 0.4 fs (FWHM). The laser peak intensity was adjusted so as to give a maximum ponderomotive energy of Up 2 eV, ensuring negligible ATI effect. Hence, thanks to the lateral observation geometry, a contour plot of a typical, time-resolved photoelectron energy spectrum obtained at u 90 , shown in Figure 2.41 (average over 1000 laser shots), reveals two clearly separated lines, at 73 and 77 eV, corresponding to the absorption of one X-ray photon from the 55th and 57th harmonic, respectively, with a remarkable downshift of the center-ofgravity on the order of Up 2 eV, confined to a delay range shorter then 10 fs around t = 0 (second term of Eq. (2-44)). Instead, by integrating the photoelectron energy spectrum in all directions, it would lead for thepconditions of the experiment [274] to a spectral broadening of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 8Ei UP ðt = 0Þ 60 eV, thus impeding the ability to accurately detect any shift of the center-of-gravity on the order of Up 2 eV. By measuring the position of the photoelectron energy spectrum center-of-gravity as a function of the delay, a temporal convolution of the X-ray and the laser pulses was obtained. The laser pulse temporal shape was calculated by propagating the initial unperturbed 7-fs pulse through the neon target, and obtaining the actual temporal profile of the IR-pulse which interacts with Kr atoms. Finally, the X-ray pulse temporal profile was worked out by de-convoluting the laser temporal
Figure 2.41 Contour plot of the 4p spectrum of Kr vs. the delay time between the X-ray and laser pulse. Blue areas denote low-spectral electron density, whereas red areas indicate high-spectral electron density [274]. For delays larger than 5 fs a spectral redistribution of X-ray energy in favor of the 57th harmonic is observable.
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profile from the behavior of the center-of-gravity vs. t. The X-ray pulse FWHM was estimated to be t x = 1.8(+0.7/1.2) fs. The strong limitation of the measurement performed in [274] is represented by its temporal resolution, essentially determined by the slope of the laser pulse rise time, estimated to be as steep as 5 fs. It is not possible to shape laser temporal profiles very much steeper than that. A sub-Topt/4 probe, as is the case of the oscillatory third term of Eq. (2-44), would certainly solve this problem. A partial trace of these oscillations is still observable in Figure 2.41, but due to laser pulse-shape and CEP fluctuations from shot to shot, it is very hard to measure a reliable influence of the third term of Eq. (2-44) on the position of the center-of-gravity vs. t. An improved version of the above cited experiment [274] was recently realized by Hentschel et al. [279]. This time the authors, instead of measuring the position of the photoelectron energy spectra center-ofgravity vs. the delay t, measured the spectral broadening, DEf (t), of the photoelectron energy. In fact, such spectral width strongly depends on the instant of birth of the electron through the light field oscillation. Thus, changing the delay t between the light and the X-ray pulses results in a modulation of DEf (t) with a period equal to one-half of the laser oscillation period Topt [279]. The key advantage of exploiting the broadening of the spectrum instead of the center-of-gravity is that this effect is enhanced by increasing the detection aperture. The signal yield and modulation amplitude are thus enhanced in comparison with what is obtained for the center-of-gravity, provided by the third term in Eq. (244). By measuring DEf (t) as the FWHM of the photoelectron energy distribution (assumed to be Gaussian) for different delays t, the oscillating behavior of DEf (t) is clearly evident (upper plot of Figure 2.42). In Figure 2.43, the 4p-Kr photoelectron energy spectral width subtracted from the cycle-averaged value, DEf (t) hDEfic.a.(t), is plotted vs. t (experimental points). The full red line in the plot is the result of a simulation based on the quasi-classical theory of two-color X-ray photoionization, by assuming a 7.5 fs, 750 nm linearly polarized laser field of 5 · 1013 W cm2 peak intensity and a 650 as, 90 eV Gaussian X-ray pulse. The inset of the same figure represents the result of the same simulation for different X-ray pulse durations, t x = 500, 650, and 800 as. The model includes a Gaussian frequency sweep at the pulse peak and a weak quadratic chirp component, and assumes uniform detection efficiency within the aperture of the TOF spectrometer. The remarkable asymmetry in the calculated and measured DEf(t) around t = 0 is attributed by the authors to a change of the light carrier frequency
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Figure 2.42 Cross-correlation of X-ray pulse with few-cycle laser pulse [279]. The lower panel contour plot represents the Kr 4p photoelectron spectra (vertical axis) as a function of the delay between the X-ray and the laser pulse (horizontal axis), the white/black areas referring to high/low photoelectron energy. The upper panel shows the spectral width DEf as a function of t, evaluated as the FWHM of a Gaussian fit of the spectrum for every delay time.
occurring on the time scale of the optical period, induced by strong instantaneous SPM of the laser pulse upon its interaction with the neon gas X-ray source. The t x-value which best fits with the experimental points turned out to be 650 – 150 as, in rather good agreement with the calculated single X-ray burst duration of 530 as, emitted by focusing a 7fs, 750-nm Gaussian laser pulse to a peak intensity of 9 · 1014 W cm2 into a 3-mm-long 200-mbar neon gas volume. Before ending the present section it is worth stressing that, although promising, all these results concern sub-femtosecond X-ray pulses not yet sufficiently intense to support X-ray-pump/X-ray-probe spectroscopy. However, the generalization of the present concept of light-field-controlled X-ray photoemission should allow the substitution of either the X-ray pump or the X-ray probe pulse by a strong few-cycle laser field without loosing attosecond resolution. This approach, of course, relaxes requirements on the X-ray pulse fluence, and lends itself as a promising tool benefiting from the next generation of high-harmonic sources, which are expected to extend the X-ray photon energy up to about 1 keV!
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Figure 2.43 Energy spectral width reduced by its cycle-averaged value DEf (t) hDEfic.a.(t) of the Kr 4p photoelectron spectra as a function of t [279]. The dots represent the measured oscillating component of DEf (t) hDEfic.a.(t), whereas the full red line is the result of simulations based on the quasi-classical theory of two-color X-ray photoionization by assuming a 7.5-fs, 750-nm linearly polarized light field of 5 · 1013 W cm2 peak intensity and a 650-as, 90-eV Gaussian X-ray pulse. The inset shows the result of the same simulations for different X-ray pulse durations near t = 0 (colored lines), revealing that tx = 650 as is the X-ray pulse duration which best fits the data.
2.3.3 Molecules In the last few decades a large amount of work has been done for investigating ultrafast dynamics occurring in chemical reactions and bond-breaking of molecules thanks to the advent of more flexible laser systems with femtosecond resolution (see Section 2.2.2 for an overview on the subject). The progress done in these fields is so impressive that a short review like this cannot be fully comprehensive. In the next sections we report a description of those experiments that in our opinion can be considered representative of the significant progress made in the last few decades with a special focus on experiments which have reached femtosecond resolution. For more details on the previous advances we refer the readers to good reviews existing in literature and the references therein [256, 280–288]. Before reviewing these experimental reports, we will give some details on the theoretical approach used for addressing the investigated problems. We refer the reader to the optimum paper of Garraway and Souminen and references therein for a more accurate description of the used numerical methods [287].
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2.3.3.1 The birth of femtochemistry: probing the transition states The birth of femtochemistry is due to the seminal work of the Zewail group that probed the coherent oscillations of a superposition of vibrational states by investigating time-resolved fluorescence from cooled anthracene jets [289]. The idea behind this experiment was that an ultrafast pump pulse could excite the molecule to a superposition of two vibrational levels belonging to the excited-state vibrational manifold. Quantum mechanically this coupling gives rise to an oscillatory energy flow between the two states, analogously to what observed for two coupled pendulums. In polyatomic molecules there are several such states that can be excited at the same time. This leads to interference effects that can cancel the quantum coherent oscillations. In usual fluorescence experiments this results in signals decaying in time with no oscillatory features. However, Zewail and co-workers used supersonic jets of polyatomic molecules. This technique leads to a simplification of the vibrational spectra by decreasing the molecules mean temperature. Nevertheless, a high molecular density may be maintained in order to achieve a good signal to noise ratio. For the first time, a timeresolved fluorescence technique in connection with molecular jet technology led to the observation of quantum beats as shown in Figure 2.45. In this figure two time decay signals with a phase difference of p are shown. In order to explain these experimental findings, let us consider two initial vibrational eigenstates j a > and j b> of the molecular electronic excited state. Let us also suppose that they become coupled via anharmonic terms of the Hamiltonian upon light excitation. This leads to the formation of two new normal states jc1 i = ajai + bjbi jc2 i = bjai ajbi
Eq. (2-45)
where a2 + b2 = 1. The fluorescence intensity is then given by [288] IðtÞ
2 h X X
e e mjgihgj^ e e mjcj ihcj j^ e d mjf ihf j^ e d mjci i: hci j^
f = fa ;fb i;j = 1
i
· expðt=tivij Þ
Eq. (2-46)
where g and f represent the ground and final state, respectively (see Figure 2.44 for a schematic representation of the different states
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0 0
1
Hab
|a>
|b>
µafa µbfb
µga µbg |fa> |g>
|f b> 1
0
0
1
Figure 2.44 Schematic representation of the different states involved in the fluorescence of anthracene. g and f represent the ground and final states, respectively. Hab is the Hamiltonian element describing the coupling between states j ai and j bi. For the meaning of the other symbols see the text. Note that the colors of the fluorescence emission are different for the two states, stressing the possibility of isolating the two contributions by adjusting the detection wavelength range. In the two insets the modulation for the two emissions is drawn according to formulas (2.47) and (2.48). Note the p rad phase difference and the partial modulation for the de-excitation through the a channel.
involved in the fluorescent emission). The directions for the excitation and emission polarizations are ^ee and ^ed, respectively. t is the fluorescence lifetime. The energy difference between the two levels c1 and c2 is given by vij/r and m is the transition moment operator in the dipole approximation. With simple calculations, it can be shown that, if mbg = mbfb = 0 and mafa „ 0, the signal is given by [288] IðtÞ expðt=tÞjmag j2 j mafa j2 f1 + b2 ½cosðv12 tÞ 1g
Eq. (2-47)
In this case both absorption and de-excitation occur via the ‘a’ channel. On the contrary, if mbg = mafa = 0 and mbfb „ 0, the signal is given by IðtÞ expðt=tÞjmag j2 jmbfb j2 a2 b2 ½1 cosðv12 tÞ
Eq. (2-48)
The last equation shows that in this case the signal may be modulated at 100% of its amplitude and that it is p rad out of phase with the ‘a’ channel modulation. If the experimental geometry does not permit to
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Figure 2.45 Fluorescence decays from anthracene in a molecular jet. Note the quantum beats superimposed to the temporal exponential decay. The two signals emitted at different wavelengths are p rad out of phase. From Ref. [289] with permission.
distinguish between the two signals, quantum beats from the two channels wash out each other. However, if the experimental geometry is accurately selected, this technique becomes sensitive to the phase between the two vibrational states that superpose. In particular, by selecting a suitable narrow interval of detected wavelengths, the fluorescence signal induced by each of this state can be probed separately (see Figure 2.45). These results indicated that coherence had not previously been detected in complex systems, not because of its absence, but due to the inability to devise selective probes [256]. The same coherence effects were observed among rotational levels [290–294]. The latter experimental reports provided a powerful tool for studying the rotational inertial motions of several molecules. The molecular inertial momentum depends on the atomic masses and their positions. Therefore, a measure of rotational inertia brings information
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on the molecular structure. This technique is known as Rotational Coherence Spectroscopy and has given the possibility of drawing several molecular structures [256]. Thanks to this first experiment a very important concept was introduced: the coherent excitation of molecular wavepackets. This concept is central in connecting quantum mechanics with the classical picture of chemical bonds as individual springs of different strengths and characteristic frequencies. For clarifying this point, let us consider a diatomic molecule. A key concept in chemical reactions dynamics, in general, is the potential energy surface (PES). The PES determines the electronic energy of the system as a function of the different degrees of freedom of the system. For instance, in the case of the diatomic molecule, the degree of freedom to be considered is the inter-nuclear distance. Initially, the molecule is in a ground-state PES. By external excitation, it may be promoted to an excited PES leading to its dissociation, i.e. to bondbreaking. A PES is characterized by the presence of several discrete roto-vibrational sub-levels. When several quantum mechanical rotovibrational eigenstates are coherently excited with a fixed phase relationship, the resulting wave function is a wavepacket localized in space, whose center of mass propagates on PES according to the classical equations of motion. When this happens, the wave-packet motion is in strict analogy with the classical concept of stretching or squeezing a chemical bond. The concept of wave-packet was introduced in early times by Schro¨dinger [295] in order to provide a link between the quantum and the macroscopic world. The concept was considered of no practical interest until the advent of ultrafast laser systems which showed the possibility of using fast laser pulses for creating wave-packets. This possibility relies on the unique property of an ultrafast laser pulse of containing many spectral portions with a well defined phase relationship. Therefore, during excitation every wavelength excites different roto-vibrational levels with their phases locked together. Another ultrafast probe pulse is then used for following the dynamics of this wavepacket. Within this framework the classical concept of the transition state [296, 297] of a chemical reaction may also get a more precise definition. An elementary reaction is generally written as A + BC!½ABC !AB + C
Eq. (2-49)
where A, B, and C are the molecular complexes involved in the reaction. [ABC]* is the transition state of the reaction. This transition state can
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be associated to a nonstationary wave-packet of the form C=
X
ci ðtÞci ðxÞ expðiEi t=rÞ
Eq. (2-50)
i
which evolves in time similarly to the two level problem discussed for anthracene fluorescence. The big difference here is the appearance of the spatial localization x because of the sum over many energy states. In Figure 2.46 a schematic representation of what happens in a laser induced chemical dissociation of a molecule is shown for the paradigm case of ICN. A laser pulse promotes the stationary wavepacket describing the reagents system to an excited dissociative potential surface where the wavepacket is not anymore in an equilibrium
t=200 fs
t=100 fs I
C N t=0
Broadband ultrafast pulse
R
Figure 2.46 A schematic representation of what happens in a laser induced chemical dissociation of a molecule of ICN. A broadband ultrafast pulse promotes the stationary wave-packet describing the reagents system to an excited dissociative potential surface where the wavepacket is not anymore in an equilibrium configuration. Therefore, it starts to move on the PES like a marble on a real surface. R is the reaction coordinate that in our simple case is the internuclear distance of the two atomic complexes. By probing the wavepacket motion on the dissociative PES, the evolution of the reaction transition state can be studied. On the top of figure the different phases of ICN dissociation are shown. Note the rotation of the CN fragments.
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configuration. Therefore, it starts to move on the surface like marble on a real surface. R is the reaction coordinate that in our simple case is the internuclear distance between the I atom and the CN molecule. By probing the wavepacket motion on the dissociative PES the evolution of the reaction transition state can be studied. The whole path from reagents to products involves changes in internuclear separation of the order of 10 A˚. If the atoms move at 104–105 cm seconds1 the entire trip would take 1012–1011 seconds. If we look for a resolution on the reaction coordinate of 0.1 A˚ we need a probe pulse ranging from 10 to 100 fs. This reveals why such studies could appear a dream before the advent of ultrafast laser sources. Indeed the short duration of the laser pulse plays a double role for creating a well suitable wave-packet, as it will be discussed in more detail in the following. First, during the excitation of the wavepacket to the dissociative potential surface, the remaining ground state wave-packet starts to rearrange itself. In the meanwhile that part of the wave-packet already promoted to the excited state starts evolving on it (dispersion effect). If the laser excitation is not instantaneous for all the wave-packet components this leads to a deformation of the replica in the excited state of the initial ground-state wavepacket. A very short laser pulse is needed for avoiding this dispersive deformation of the initial excited wavepacket. Second, the initial ground-state stationary packet is distributed around the minimum of the potential well so that each part of the wavepacket is characterized by a different resonance frequency with respect to the excited potential surface. In order to transfer the wave-packet unmodified from the ground state to the excited state it is important that the pulse spectral content is broad enough to have simultaneously all the wavepacket spectral components in resonance with the excited potential surface (see Figure 2.46 for a schematic representation of these two features).
2.3.3.2 Some basic theoretical concepts on wave-packet formation and dynamics In the previous section, we have qualitatively discussed some important concepts such as PES, wave-packet, and so on. In this section, we wish to briefly introduce some theoretical concepts useful for a formal description of wavepacket formation and dynamics. We will not discuss too many details. We refer to the optimum paper of Garraway and Suominen [287] for a more exhaustive review of the theoretical approaches to this topic.
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The standard way to obtain the dynamics of molecular wavepackets is by the use of the Born–Oppenheimer potential surfaces. These surfaces correspond to the different electronic configurations of the molecule. Since the electron mass is at least three orders of magnitude smaller than that of nuclei, the adiabatic approximation may be applied. This hypothesis states that any change in the electronic configuration is instantaneous with respect to the timescale of the nuclear motion. As a consequence, it is possible to average over the electronic coordinates, obtaining potential surfaces that depend only on the nuclear coordinates. This approximation does not always holds true as in the case of nonadiabatic interactions which will be briefly reviewed in the following. The wavepacket contains information about the position and the momentum of the atoms. This can be formalized through the following steps. The Hamiltonian operator for a molecule in an external laser field is H = Te ðrÞ + TN ðRÞ + Vee ðrÞ + VNN ðRÞ + VeN ðr; RÞ DE
Eq. (2-51)
where T is the kinetic energy, V is the Coulomb interaction. N and e subscripts label electronic and nuclear variables. The interaction with the electric field E is described in the framework of dipole approximation, where D is the dipole operator. The corresponding Schro¨dinger equation for the molecular wave function j Fi is written ir
q jFi = H jFi qt
Eq. (2-52)
Following the adiabatic approximation the set of electronic states f j fni} for a fixed nuclear configuration is a solution for the following eigenvalue problem: Hel jfn i = Un ðRÞjfn i
Eq. (2-53)
where Hel = Te ðrÞ + Vee ðrÞ + VNN ðRÞ + VeN ðr; RÞ
Eq. (2-54)
By using this eigenstates base, the time-dependent molecular wave function can be expanded in the following series: jFi =
X n
cn ðR; tÞjfn i
Eq. (2-55)
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Within the Born–Oppenheimer approximation the following relation is assumed as satisfied: TN ½cðR; tÞjfn i ½TN cðR; tÞjfn i
Eq. (2-56)
By applying the last relationship, we get the following Schro¨dinger equation for each wave function component, cm: ir
q c ðR; tÞ = TN cm ðR; tÞ + Um ðRÞcm ðR; tÞ qt m X hfm jDEjfn icn ðR; tÞ
Eq. (2-57)
n
When the external field is absent this equation describes the time evolution of the mth component of the wavepacket residing on the potential surface Um(R), which corresponds to the electronic state j fmi. Within the Born–Oppenheimer approximation this evolution is completely independent of the other states and their possible occupation. In the following section, we will describe some simple applications of Eq. (2-57) in order to give some insight on the way to approach this kind of problem. We refer the readers to Ref. [287] and references therein for a more extensive account of this subject.
2.3.3.3 Diatomic molecule and laser-molecule interaction In the case of a diatomic molecule, only one nuclear reaction coordinate is involved, i.e. the interatomic distance R. By introducing the function Cm defined as Cm ðR; tÞ =
cm ðR; tÞ R
Eq. (2-58)
we can write the Schro¨dinger equation for the mth mode in the diatomic case as ir
q r2 q 2 Cm ðR; tÞ + Um ðRÞCm ðR; tÞ Cm ðR; tÞ = 2m qR2 qt X nm EðR; tÞCn ðR; tÞ + m
Eq. (2-59)
n
In Eq. (2-59), we have used the dipole transition matrix nm = hfn jDejfm i, where e is the polarization unit vector for a linearly m polarized electric field E = eE(R, t).
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In many interesting applications the laser-field usually couples only two potential surfaces (let us call them 1 and 2). Moreover, in many cases the semiclassical approach can be used. This means that quantization of the electromagnetic field is not needed and it is possible to assume E(R, t) E(t) cos (vt). Here we are not considering any change of v during the molecular system evolution as it may happen in the interesting case of chirping (this case will be briefly described in the next section). The potential surfaces depend strongly on the coordinate R, so the laser field brings the two surfaces into a resonance only at certain values of R. Incidentally, this is the main reason why femtosecond laser pulses are important in femtochemistry since their broad spectrum permits to bring into resonance the entire wavepacket (all its roto-vibrational components). Being at resonance means that in the optical-field there is a spectral component which contrasts with the quantum oscillations, i.e. 12 ð1=2Þm12 EðtÞ expðiðU2 ðRÞ U1 ðRÞ rvÞt=rÞ m = ð1=2Þm12 EðtÞ expðiDðRÞt=rÞ
Eq. (2-60)
where D(R) = U2(R) U1(R) rv is the local detuning and m12 is the timeindependent dipole moment, which may depend on R. In Eq. (2-60), the fastest oscillating components have been not included since they usually average to zero. If the following wave-function vector CðR; tÞ =
C1 ðR; tÞ eivt C2 ðR; tÞ
Eq. (2-61)
is introduced, the system (Eq. 2-59) can be transformed into the following matricial relationship: q ir qt
C1 ðR; tÞ C2 ðR; tÞ
=
TðRÞ + U1 ðRÞ V V TðRÞ + U2 ðRÞ rv
C1 ðR; tÞ C2 ðR; tÞ
Eq. (2-62) r q is the kinetic energy operator. The surface where TðRÞ = 2m qR2 coupling V = rO12/2 is defined being real with Onm = mnm(R)E(t)/r, which is the local Rabi frequency for the surfaces n and m [298]. E(t) stands for the pulse envelope. 2
2
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2.3.4 Simple properties of a wave-packet A wavepacket describes a quantum system that is localized in a limited region of its position coordinate. A simple form for a wavepacket is the Gaussian one: " # ðR R0 Þ2 Eq. (2-63) CðRÞ exp ikR 4s2 where rk, s = DR, and R0 represent the wavepacket momentum, width, and central position, respectively. If only the dynamics over a single potential surface is considered, the Schro¨dinger equation (2-62) for the position and momentum mean values, hRi and hki, becomes q rhki hRi = qt m D qUðRÞ E q r hki = qt qR
Eq. (2-64)
The pair of equations in system (Eq. (2-64)) describes the trajectory of the wavepacket. It is worth noting that in general D qUðRÞ E qR
„
qUðhRiÞ qhRi
Eq. (2-65)
indicating that the ‘‘quantum trajectory,’’ namely the trajectory of hRi and hki, may differ from the classical trajectory. However, in many interesting cases the classical trajectory describes very well the mean motion of the wave-packet. Moreover, for spatially uniform, linear, and quadratic potentials the equality holds exactly. If U = 0 the wave-packet moves with constant speed rk/m, but it also spreads. The spreading, or dispersion, is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r Eq. (2-66) DRðtÞ = hR2 ðtÞi hRðtÞi2 = s 1 + t2 2ms2 This equation leads to the definition of a characteristic quantum diffusion time given by td =
2ms2 2m DR2 ð0Þ = r r
Eq. (2-67)
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For other wavepacket shapes it can be demonstrated that the wave-packet spreads with the same time-dependent behavior and with a time-scale that differs by only a numerical factor. The dispersion time scale is important for understanding the interval of time during which wavepacket dynamics can be observed. It is worth noting that the spreading effect has been found for U = 0. In the case of a harmonic potential there is no spreading of this kind. However, it can be shown that the spreading plays still an important role in realistic potentials and during dissociation. If we take m as the mass of I2 molecule and consider for the width of the ground state wave function, DR(0), the reasonable value of 0.1 A˚, then t d 805 fs. This sets the time-scale for studying the dynamics of I2 and gives an order of magnitude for the temporal scale in femtochemistry.
2.3.4.1 Wavepacket generation and influence of chirping An important method for creating a well defined quantum mechanical wave-packet consists in shining a short laser pulse onto a molecule in its equilibrium state. The wave-packet of the initial state is stationary and narrow because in many experiments it corresponds to the molecule ground-state. This wave-packet can be put in movement if the molecule is promoted to an excited state. However, during this process one would like to preserve the wave-packet properties, i.e. temporally short and well localized at the time zero right after the pulse excitation. This can be achieved only if the laser pulse is short enough that the complete wavepacket can be excited before it starts evolving. On the other hand, a pulse with a short duration is characterized also by having a wide spectrum of wavelengths. This kind of excitation is also known as Franck–Condon excitation, as it follows the principle of no changes in nuclear configuration during the excitation process. In the following, we report from Ref. [287] a simple semiclassical argument for understanding when this kind of excitation occurs. For simplicity let us assume that the potential surface for the ground and the excited state are, respectively, 1 Ug ðRÞ = mv20 ðR R0 Þ2 2 Ue ðRÞ = aðR R0 Þ + b
Eq. (2-68)
where R0 is the equilibrium position of the initial ground-state wavepacket that we assume Gaussian in shape as given by Eq. (2-63).
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FUNDAMENTALS
The wavepacket promoted to the excited-state surface experiences the following acceleration a=
1 D qUe ðRÞ E a = m qR m
Eq. (2-69)
During a pulse with a duration of t each component of the excited wave-packet travels approximately the distance DR
a 2 t 2m
Eq. (2-70)
This distance must be compared with the width s of the wavepacket. This leads to the introduction of a first characteristic time, t ex, corresponding to the time necessary for any spectral component to travel a distance equal to the initial, intrinsic width of the Gaussian wavepacket. This time is given by rffiffiffiffiffiffiffiffiffiffi 2ms tex a
Eq. (2-71)
Another characteristic time comes from the spreading phenomenon discussed in the previous section, i.e. td
2ms2 r
Eq. (2-72)
Finally, in the case of incomplete excitation the unexcited components of the initial ground-state packet start reorganizing with a characteristic time t gr v1 = 2ms2 =r = td : In order to achieve a complete Franck–Condon excitation it is necessary that the pulse duration is much shorter than any of these characteristic times. Actually a further condition on the resonant excitation must be added to these temporal requirements: the spectral content of the laser pulse must be wide enough so that all the roto-vibrational components of the ground-state wavepacket may be simultaneously brought in resonance with the final electronic state. However the pulses which fulfill the time-scale requirements are so short and, hence, so wide spectrally that the last constraint results less important. With these particular PESs it is possible to calculate the excited-state population as a function of time. When this is done, it shows a coherent oscillatory behavior analogous to that observed in the experiment on anthracene fluorescence [287].
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Let us come now to the last topic of this section, i.e. the influence of chirping on wavepacket motion. Pulse chirping and the most sophisticated techniques of pulse shaping are very important for the coherent control of reactions. In other sections of this chapter these techniques and some important experiments on the coherent control of reactions are discussed in detail. Details on the mathematics can be found in Ref. [287]. Here we report only some results of this calculation. A simple model uses a hyperbolic-secant pulse-envelope and a hyperbolic-tangent form for the chirp VðtÞ = V0 sechðt=TÞ dhðtÞ = F tanhðt=TÞ dt
Eq. (2-73)
where V(t) has the same meaning as in Eq. (2-62) and h(t) is the timedependent optical-field phase that produces the chirp in frequency with respect to its mean value v. The hyperbolic tangent form for the chirp becomes a linear change in time when the chirp amplitude F is much larger than the pulse amplitude V0. In Figure 2.47 some results of this model are shown (these results are reported from Ref. [299]). They clearly demonstrate how the chirp can strongly influence the population transfer to the excited electronic state. With ultrashort pulses, the pulse area determines the population distribution between the levels [298]. In particular, only pulses with areas equal to odd multiples of p can deplete the ground-state completely. In Figure 2.47 (panel a) the pulse area is equal to p when F = 0, but because of the long pulse duration the excitation is not complete. In panel (a) of Figure 2.47 the excited wavepacket is not left free to evolve. When the pulse is chirped, the resonance point moves along the ground-state frequency content leading to a more efficient transfer of the wavepacket. However, for large F this process becomes too fast and the resonant point is out of the wavepacket before the pulse–molecule interaction is over. Therefore, for large F the population transfer eventually diminishes. This behavior can give the appearance of an optimum chirp value for pulses with long duration (solid line). For short pulses, given the large wavelength bandwidth of the pulse, the resonance points argument becomes less important since in the limit of ultrashort pulses all the components are simultaneously resonant. This leads to the disappearance of an optimum chirping (broken line). If the excited wavepacket can evolve during the pulse duration, a clear dependence on the chirp direction is observed (panel b of Figure 2.47). The direction of the chirp is determined by the sign of F. Negative F
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FUNDAMENTALS (a)
(b)
Figure 2.47 Influence of chirp on population transfer to the excited electronicstate (from Ref. [287] with permission). The direction of the chirp is determined by the sign of F. Negative F corresponds to a red-shift in the pulse bandwidth (positive chirp) and vice versa. In panel (a), the pulse area is equal to p when F = 0, but, because of the long pulse duration, the excitation is not complete. The wavepacket is not left free to evolve during the excitation. Results refer to pulses with long (solid line) and short (dashed line) duration, respectively (see text for a qualitative explanation of the different behaviors). If the wavepacket can evolve during the pulse, a clear dependence on the chirp direction is observed (panel b). In this case the pulse area is 2p. A chirp-induced enhancement of the population transfer is clearly seen. The full line refers to a pulse two times longer than that of the dashed line and 10 times longer than that of the dotted line. Note that for the very short pulse (dotted line) the area theorem applies again and the symmetry is recovered.
corresponds to a red-shift in the pulse bandwidth (positive chirp) and vice versa. This asymmetry of population transfer is marked when the excitedstate potential surface is very steep around the equilibrium position R0. In this case the excited components experience a strong acceleration toward larger R (see Eq. (2-69)). For a negative chirp (positive F), the resonant point moves together with the excited components. This leads to a less efficient excitation since resonant excitation couples to final levels that
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simultaneously become partially occupied by the already excited wavepacket components. The situation is reversed for the case of positive chirp (negative F). Finally, for very short pulses the area theorem applies again and the symmetry is recovered. This brief discussion has shown how a simple chirped pulse is able to induce dramatic changes in the process of population excitation by means of short pulses. This is an effect that has important consequences for coherent control of chemical reactions. This topic will be reviewed in Section 2.5 where the influence of pulse shaping on the control of bond-breaking and chemical reactions will be discussed by illustrating several recent and interesting experiments.
2.4
Bond-breaking in Single Molecules
In the previous sections we have pointed out the importance of using femtosecond pump pulses for bringing quantum wavepackets from the ground to the excited state, where they start moving. It is also worthwhile to remember that up to now we have limited our considerations to molecular jets where a suitable ground-state wavepacket can be generated. A second (or more than one) ultrafast pulse serves for probing the temporal evolution of the excited wavepacket. For probing these dynamics, several experimental techniques have been employed, such as Laser Induced Fluorescence (LIF) [300–305], Multi Photon Ionization (MPI) [306], or Time Resolved Photoelectron Spectroscopy (TRPES) [307]. These techniques have been demonstrated to be very powerful for resolving complex transition-state dynamics of chemical bond-breaking and chemical reactions in the gas phase. In the following we will describe some experiments on dissociation of single molecules. Details of LIF, MPI, and TRPES, will be also discussed in connection with the experiments. One of the first investigations on bond breaking was performed in the ICN complex by means of LIF [305]. In this dissociative process the covalent bond between the iodine atom and the CN group is broken. The transition state is characterized by a reaction coordinate that, in this case, is simply the distance R between I and CN. The general technique scheme is shown in Figure 2.48. A first pump pulse of wavelength lpump promotes the ground-state wave-packet to a dissociative potential-energy-surface. A second tunable probe pulse brings the CN group to a fluorescent excited state from which it decays by radiative photon emission. In the experiment both the temporal delay and
FUNDAMENTALS LIF signal
LIF signal
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Pump-probe delay
Pump-probe delay
Tunable probe λ(R0)
λ(R1)
Fluorescence λ(R∞)
Broadband ultrafast pulse
R
Figure 2.48 General scheme for LIF technique. A first pump pulse promotes the ground-state wave-packet to a dissociative PES (in general the excited PES may have also a bound character). A second tunable probe pulse brings some moiety of the molecule to an excited state from which it decays by radiative photon emission. In the experiment both the temporal delay and the wavelength of the probe are adjusted. By tuning the probe-wavelength the transition state wavepacket can be followed in time during its motion on PES (l(R) indicates the probe wavelength suitable for probing wavepacket at position R). R ¥ is the distance at which dissociation has occurred. At a fixed probe-wavelength l(R), the passage of the wavepacket on the dissociative PES through the R(l) position can be resolved in time by varying the pump-probe time-delay. In the insets the timeresolved fluorescence signals for two probe wavelengths, i.e. at two positions, are shown (see text for a qualitative explanation).
the wavelength of the probe are adjusted. By tuning the probe-wavelength the transition state wavepacket can be monitored to each position during its motion on PES. At a fixed probe-wavelength l, the passage of the wavepacket on the dissociative PES through the R(l) position can be resolved in time by varying the pump-probe time-delay. When the wavelength is adjusted in order to probe the fragment at the final stage, the fluorescence signal grows up and then reaches a constant level. Then it decays with the characteristic time of the CN excitedstate lifetime which is long compared to the reaction time-scale. In the intermediate positions R(l) the signal grows and then decays after the wavepacket passage. The bond-breaking time is obtained by measuring
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the temporal delay at which the signal peak appears for different position R(l). For ICN dissociation a decay-time of 205 fs is measured, corresponding to a repulsion length parameter of 0.8 A˚. In this experiment a perfect timing between the zero time and the probe arrival is necessary. This calibration should be performed without readjusting the experimental setup since small misalignment can induce appreciable time delays as compared to the required temporal resolution. This can be achieved by using an in-situ clocking of the time. In order to account for the finite response function of both pump- and probe-pulse, the Multiphoton Ionization signal of N,N-diethylaniline (DEA) is detected. This process is instantaneous with respect to the pump and probe response and may also be used for fixing the temporal zero [305]. This experiment opened the way to probing bond-breaking process in molecules. A second seminal experiment in a more complex system (NaI) followed. This molecular system involves two PESs along the reaction coordinate, i.e. the separation distance between Na and I. One of the PES’s describes a chemical bond covalent in nature. The other PES describes the ionic bond. These two PES’s cross at distances larger than 3 A˚. As a consequence, along the reaction coordinate, the chemical bond changes character from being covalent at short distances to being ionic at larger distances (see Figure 2.49). In this experiment the transition-state dynamics is followed by means of LIF with different probe wavelengths (see Figure 2.49). A very interesting result of this experiment is the observation of quantum beats or oscillations, due to the fact that the excited wavepacket starts to oscillate forward and backward in the dissociative well. At the crossing point, part of the wavepacket is reflected back, while a small fraction, 0.1, passes through it leading to the dissociation of the molecule in Na and I fragments. This back and forth oscillations lead to the observation of a modulated fluorescence signal of the Na excited atom (Na*) as shown in Figure 2.50. In this experiment the free Na fragments are detected and analyzed. In this case the signal shows a characteristic step-like increase due to the formation of fragments after each wavepacket trip (see Figure 2.50). The spreading of the wavepacket is very small on a relatively long temporal interval (3 ps), so that in this experiment the pump pulse induces a real coherence in the molecular ensemble. For this reason the wavepacket motion can be treated as occurring along a classical trajectory. We wish to conclude this section by briefly reviewing some results of the so-called barrier reactions. This happens when the reaction dynamics involve more than one nuclear coordinate. The most simple reaction for studying such dynamics is of the type [ABA]y ! AB + A, where [ABA]y is
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FUNDAMENTALS I Na
I-
Na+
I
Na
Covalent: Na*+I λ(R0)
λ(R1)
Fluorescence λ(R∞) Ionic: Na++I-
Covalent: Na+I
Broadband ultrafast pulse
Figure 2.49 Scheme of a LIF experiment on NaI molecule. The wavepacket promoted to the excited PES starts to move back and forth in the quantum well. The latter results from the avoided crossing of two PES’s: one ionic in nature and the other covalent. Therefore the molecule bond changes nature during the wavepacket motion. At the crossing point part of the wavepacket is almost entirely reflected back while a small fraction, 0.1, passes through it leading to the dissociation of the molecule in Na and I fragments. The LIF probe excites the Na atom whose emitted fluorescence is time resolved.
the excited molecular complex. In these systems, a symmetric stretching mode, an asymmetric one, and a bending mode are involved. The symmetric stretch leads to the formation of A + B + A products, while the asymmetric one leads to the formation of AB + A products. The existence of these two reaction paths gives rise to a saddle-point transition [308– 310]. The IHgI molecule may be considered a paradigm case for such kind of reactions. The wavepacket is promoted by pump excitation on the steep repulsive wall right above the saddle point. At this point the
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Figure 2.50 LIF signal from NaI vapor excited with pulses with 65 fs of duration and a wavelength of 310 nm (from Ref. [256] with permission). At a probe wavelength of 580 nm the fluorescence emitted from Na atom in the activated complex is detected (bottom panel). The signal shows a characteristic oscillatory behavior due to the back and forth wavepacket motion in the PES well. At 589 nm the fluorescence is from the Na free fragment (top panel). The signal shows a step-like increase due to the accumulation of dissociated Na atoms after each wavepacket round-trip.
transition state may evolve along a path that leads to the following reaction IHgI + hn ! ½IHgIy ! I + HgI
Eq. (2-74)
or toward three fragments production IHgI + hn ! ½IHgIy ! I + Hg + I
Eq. (2-75)
For the first time coherence in both vibrational and rotational spectra could be observed in so complex a reaction involving multiple bond breakage (see Figure 2.51). As the bond of the activated complex breaks during the descent, both the vibrational motion (300 fs) of the separating diatom and the rotational motion (1.3 ps) show coherent oscillations in time. These studies of the dynamics provided the initial geometry of the transition state, which is found to be bent, and the nature of the final torque, which induces rotations in the nascent HgI fragment.
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Figure 2.51 Femtochemistry of the IHgI molecule that is a paradigm for saddlepoint transition state or barrier reactions (from Ref. [285] with permission). As the bond of the activated complex breaks during the descent, both the vibrational motion (300 fs) of the separating diatom and the rotational motion (1.3 ps) show coherent oscillations in time.
2.5 Controlling Molecular Populations and Chemical Reactions by Ultrafast Pulses One of the most interesting aspects of these studies on the quantum coherence in molecular systems, from both a fundamental and applications point of view, is the possibility of using ultrafast pulses for driving the transition state along a given reaction path after excitation. This leads to the possibility of selectively breaking a specific chemical bond in the molecular system. This idea was born before the advent of femtochemistry. It was thought that this could also be achieved by simply using CW lasers with a wavelength resonant with the vibrational mode of the specific bond. By transferring sufficient energy in such mode it would be possible to break the bond. However, this strategy is not suitable because of the very fast process of internal vibrational redistribution of energy. This means that energy released by the laser
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excitation is ergodically redistributed among all the vibrational modes of the molecule. This process, as pointed out in the previous section, occurs on time scale of hundreds of femtoseconds. Therefore, excitation of a reaction by an ultrafast pulse can instead give the chance of releasing energy in a specific bond in a controlled way before the energy randomization occurs. Generally, there are two schemes which can be applied for an efficient control of a chemical reaction. The first one relies on the possibility of selecting the reagents in a specific energetic state before they collide with the consequent product formation. Very recently, Park et al. [311] have selectively prepared beams of molecular ions containing only a specific isomer of the C3H7I molecule. To this end, they have used ultrashort coherent vacuum ultraviolet radiation (VUV) (see also Section 2.3.1.3 for details on the state of the art of VUV sources). By tuning the wavelength of the VUV radiation, ionic states with a specific isomer conformation could be excited. Since the two isomers have different reaction paths, only the products of the reaction associated with the selected isomer may be formed. The second scheme is more subtle and will be the main subject addressed throughout this section. It relies on the possibility of using more than one ultrafast pulse for quantum interference in the motion of a wavepacket excited on a dissociative PES. Ultrashort pulses, spectrally wide, provide a wide range of frequencies, all locked in phase. In this way, a coherent excitation of several rotovibrational modes can be achieved, leading to the formation of a wavepacket as already discussed in previous sections. This wavepacket can then be allowed to evolve until a favorable molecular configuration is reached. At this point, a second ultrafast pulse, arriving after a suitable delay, can control the excitation toward a given product. This is the so-called Tannor–Kosloff–Rice scheme [312–314]. A first demonstration of its feasibility was given by Baumert et al. [315] through the use of resonant three-photon ionization and fragmentation of Na2. The first control of a bimolecular reaction (Xe + I2 ! XeI + I) was indeed obtained by Zewail et al. [316] in 1992. The principle of this experiment is schematically shown in Figure 2.52. A first ultrafast pump pulse excites the I2 molecule. Then the wavepacket motion follows along the I–I vibrational coordinate. Given the wavelength of the probe pulse, the wavepacket can be lifted up to the well turning point. It is not yet completely clear if the excitation leads to the formation of the ionic pair I+I [256]. However, in this region, if a collision between Xe and I atoms occurs, an ionic IXe+ pair is formed. Then I and Xe+ incur Coulomb attraction and are
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(a) Reagents
Xe I
I
+
I-
I
Probe pulse
Pump pulse
Reaction coordinate: I-I distance (b) Transition state I
I-
+ Xe
Coulomb
Probe pulse
Pump pulse
Reaction coordinate: I2-Xe distance (c) Products
Chemioluminescence
Reaction coordinate: I-Xe distance
Figure 2.52 A possible scheme for pump-probe control of the reaction I2 + Xe ! I + IXe. First, an ultrafast pump pulse excites the I2 molecule. Then the wavepacket motion follows along the I–I vibrational coordinate. Given the wavelength of the probe pulse, the wavepacket can be lifted up to the well turning point, where the ionic pair I+I is formed. A collision between Xe and the I+I pair leads to the formation of an ionic IXe+ pair. Then I and Xe+ feel the Coulomb attraction and bound together. The successive deexcitation leads to the formation of the XeI molecule ground-state. The formation of the latter can be followed by timeresolving the chemiluminescence that is emitted upon deexcitation. (a) Reagents; (b) Transition state; (c) Products.
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bound together. The successive deexcitation leads to the formation of the ground state XeI molecule. The formation of the latter product can be monitored by time-resolving the chemiluminescence that is emitted upon deexcitation. This emission is strongly dependent on the time delay between the pump and probe, since the maximum of the emission occurs only when the wavepacket reaches the turning point of the excited-state well (see Figure 2.53). For comparison the fluorescence signal emitted by I2 reagent at 340 nm is also monitored. The temporal evolution of these two signals is perfectly in phase. A more sophisticated scheme relies on the control of the phase difference between pump and probe. By controlling the delay between two fs pulses with high accuracy by means of a piezoelectric stage, it is possible keeping constant the phase between the two pulses. This can be used for phase-controlling the wavepacket motion [286]. The first pulse excites the wavepacket which reflects the phase content of the pulse. The second pulse excites a second wavepacket which can interfere with the first if this has reached the Franck–Condon region again. Depending on the difference of phase between the two pulses and that accumulated by the first wavepacket during the motion, destructive
Figure 2.53 Temporal behavior of the chemiluminescence emitted upon deexcitation to the ground-state of the molecule XeI. The fluorescence signal from bare iodine is also shown for comparison (from Ref. [316] with permission).
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FUNDAMENTALS
or constructive interference can occur. If the time delay is varied slowly and continuously, the transient signal shows oscillations at the optical frequency. This contribution may be isolated by frequency filtering the signal around the optical frequency. This is shown in Figure 2.54 for the dissociation of Na2 molecule. In the same figure the signal averaged over the optical cycle is also shown. It is clearly seen that it decays more slowly than the filtered signal. This shows that the information about the wavepacket phase is lost much more quickly than that about the location of the vibrational wavepacket on the excited PES. The latter is measured by the optical cycle averaged transient, which is only sensitive to the synchronization of the second pulse with the arrival of the wavepacket in the Franck–Condon region. The control achieved by using phase-locked pulses is one of the simplest ways. An interesting advance comes from the use of laser
Figure 2.54 Frequency-filtered Na2+ pump-probe signal compared to the signal averaged over the optical cycle (from Ref. [286] with permission). The filtered signal measures that part of signal that is modulated at the optical frequency. In the inset the signal power spectrum is shown.
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pulses that are tailored with a specific temporal profile of the field phase and amplitude. This advance started with the simple generation of chirped pulses and ended with the possibility of tailoring any kind of phase pattern by means of sophisticated light shapers made with liquid crystal devices. This kind of control is very complicated when dealing with femtosecond or shorter pulses and also requires sophisticated diagnostic tools for single-shot pulse analysis, such as those reviewed in Section 2.2.5 of this chapter. Here we describe some of the most interesting achievements in controlling chemical reactions. Important results on the selective excitations of wavepacket by chirped pulses have been obtained by Kohler et al. [317] and Bardeen et al. [318]. The basic principles of chirping have been described in Section 2.2.2, while its connection with the wavepacket dynamics has been reported in Section 2.3.4.1. As an example, recent work by Pastirk and co-workers [319] has shown the possibility of influencing the concerted elimination of I2 molecule from the CH2I2 molecule. An increase in the yield of the I2 products is observed for a chirp of about 500 fs2. However all these experiments are characterized by a number of parameters which can be varied: phase difference or time-delay between two laser pulses or chirp. This is not sufficient in more complex systems. The advance in the technology of fs pulse shaping has made it possible to realize an adaptive quantum control of chemical reactions. By using a feedback parameter and a liquid crystal shaper, it is possible to tailor the most efficient pulse suitable for increasing the yield of a given reaction or of a population transfer. This has been shown very recently by Gerber’s group [320]. They have studied the dissociation of the Fe (CO)5 molecule, used as a test for the method, and of the more complex CpFe(CO)2Cl molecule. In the first case, they have used the yield ratio Fe(CO)5+/Fe+ as feedback parameter for the pulse shaper and are able either to maximize and minimize it. Qualitatively, the same result is obtained for the second compound, as shown in Figure 2.55. In this figure the interferometric autocorrelation of the pulse is also shown, demonstrating that it is necessary to design nontrivial pulse shapes in order to influence the reaction yield. These results also show that adaptive control does not need a detailed knowledge of the PESs involved in the reaction. The system ‘‘learns’’ by itself. Vice versa adaptive control may be used for retrieving back information on PES’s. This adaptive technique has been applied very recently also for a selective excitation of molecules in liquids [321]. The authors of this beautiful work have used two dye molecules which have an identical absorption efficiency in the wavelength interval of the ultrafast
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Figure 2.55 In panel (a) the product yields relative to compound CpFe(CO)2Cl are shown (adapted from Ref. [320] with permission). The ratio between CpFeCOCl+ and FeCl+ is maximized (solid blocks) as well as minimized (open blocks) by the optimization algorithm. In panel (b) autocorrelation traces of the optimized pulses (A and B) are shown together with the trace for a bandwidth limited pulse. The insets show clearly that complex field patterns are necessary in order of achieving an optimized control of the reaction yield.
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laser pulse. This eliminates the possibility of selectively pumping one molecular species by tuning the pump wavelength. Moreover, the authors also find a substantial inefficient selective excitation by using pump pulses with different intensity or with linear chirp. However, pulses with very complicated shapes can selectively excite these molecules as clearly shown in Figure 2.56 (panel c at the bottom of figure). With such complicated electric field patterns it has been possible to increase the yield ratio of the two molecular species to about 50%. Most of the control schemes suggested so far change the coherent composition of the initial packet and hence the evolution in different channels. However, the dynamics of these states is still driven by the natural forces of the atoms: the surface energy potential is not modified. This is because all these experiments work in the perturbative limit. This is not the case when an intense laser field is used which can modify the PESs. The perturbative scheme leads to small amounts of the desired products while an intense laser field could potentially increase it significantly.
Figure 2.56 Control of molecular excitation in solution (adapted from Ref. [321] with permission). By varying pulse energy of unshaped pulse (panel a) and linear chirp (panel b), a selective excitation of dye in solution is not possible. This can be achieved only by using a very complex optical-field pattern (panel c at the bottom of figure). Each panel of the bottom figure indicates the optical field pattern corresponding to each experimental data-set in the top panels.
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FUNDAMENTALS
As an example of a control scheme based on Rabi-type cycles, we show in Figure 2.57 the transient signal of Na2 ionization for different values of the pump intensity [322]. In the top panel of the figure the time-resolved transient spectra of Na2+ production upon probe induced ionization are shown. Their Fourier-transformed spectra are shown in the bottom panel of the same figure. The different peaks are a measure of how strong is the contribution of each intermediate PES to the ionic dissociation. In the perturbative limit the main contribution is given from the state A1Su+ . However, at higher intensities things change until the production from 21Pg state overtakes the other production channels. At the highest intensities, contributions from the ground state X1Sg+ start to appear. This kind of investigation offers new opportunities for the future.
2.6 Polyatomic Molecules and Nonadiabatic Processes Up to now we have focused our attention on the application of femtosecond spectroscopy to relatively simple systems, such as single molecules made of a relatively small number of atoms. However, for reaching an efficient control of complex reactions, it is also necessary to develop spectroscopic tools that can provide a more complete picture of the reactive process. This is especially needed when investigating polyatomic molecules where the occurrence of nonadiabatic transitions to their excited state may be barely studied with the help of all-optical techniques. Nonadiabatic dynamics occurs essentially when the Born– Oppenheimer approximation of the unchanged electronic distribution during the nuclear motion breaks down. This happens when a given nuclear configuration is coupled to different electronic excited states. In this case a jump from an electronic state to another with a general different symmetry may suddenly occur. This is the case of a very important class of phenomena such as trans-cis isomerization of molecules. This topic has a great importance in a wide class of biological as well as technological applications [323–325]. In order to study these molecular processes new techniques have been developed. Two of the most powerful ones are the time and kineticenergy resolved TOF mass-spectroscopy (KETOF) and the time-resolved photo-electron spectroscopy (TRPES). These techniques base their success on the fact that photo-ionization is always an allowed process. At the beginning of their development, it was thought that for studying
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Figure 2.57 In the top panel of the figure the time-resolved transient spectra of Na2+ production upon probe induced ionization are shown (from Ref. [286] with permission). Their Fourier transform spectra are shown in the bottom panel of the same figure. The different peaks are a measure of how strong is the contribution of each intermediate PES to the ionic dissociation. In the perturbative limit the main contribution is given from the state A1S u+. However, at higher intensities things change until the production from 21Pg state overtakes the other production channels. At the highest intensities, contributions from the ground state X1S g+ start to appear.
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polyatomic molecules it would have been sufficient to follow the temporal dynamics of ion or electron production. However, time-resolved signal alone can lead to misleading results as pointed out well in the paper of Blanchet and Stolow [326]. This is because photo-ionization cross-sections strongly depend on the correlations between the electronic excited state to be ionized and the resulting ion ground state. For example, if a given excited state correlates electronically with the ground state of the ion, the photoionization cross-section is much larger than if it does not. The latter case would involve a two-electron process, as another electron must simultaneously rearrange in order to achieve the ground state electronic configuration. Such a state will preferentially ionize into an electronically excited state of the ion with the correct core electronic symmetry. Therefore, excited state nonadiabatic effects must have a strong influence on ionization cross-sections as revealed by TRPES. In fact, a nonadiabatic process may bring the molecule in an electronic excited state with a symmetry different from that of the initial excited state. This state is possibly coupled no more to the ground state of the ion but to the excited state which has the correct core electronic symmetry. In this case, by resolving the energetic spectrum as well as the angular distribution of the photo-produced ions or of the photo-emitted electrons, it is possible to follow nonadiabatic interactions. In this section we review some of the experiments performed by means of KETOF and TRPES techniques. For further details we refer to the recent reviews of Zewail and Zhong [284] and Neumark [280]. A schematic picture of a possible setup for KETOF and of its principle is shown in Figures 2.58 and 2.59. The pump pulse l1 brings the AB complex on a dissociative covalent PES. A second probe pulse is then used to ionize the AB*y complex via MPI (in the following the asterisk is used to indicate the excited state and y the transition complex). The resulting cation AB+* then fragments. In KETOF the dynamics of the fragment formation is temporally probed. From the study of the translational energy distribution of the different fragments one obtains several types of information on the system. Moreover, one can also get information about the angular velocity distribution by using different pump polarizations with respect to the TOF axis, which permits discrimination among different reaction scenarios as discussed below. KETOF offers two main advantages: a very large amount of information about the system under investigation can be obtained and, with respect to LIF, the possibility of using only one wavelength for the probe beam. In the following we will discuss some experimental examples for pointing out the amount of information that this technique can provide.
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Multichannel plate Ionization chamber and Mass-spectrometer
Ions Pump
+V d
Probe
Pump polarization
+Va
E +Vr
Lens Beam Mirror splitter
Figure 2.58 A scheme of a possible setup for KETOF measurements. Collinear pump and probe pulses interact with molecules in the ionization chamber. Molecules ionize by multiphoton ionization. The ions are then accelerated by the electrostatic field E. They pass through a capacitor for mass spectroscopy. The ions are collected on the multichannel plate where their kinetic energies may be resolved by measuring the time of flight. In the figure it is shown an example where the dipole transition moment of the dissociative reaction and the pump polarization are parallel to the time-of-flight (TOF) axis. In this case ions recoil in opposed directions along the TOF axis (note the turnaround of one of the ion). If the dissociation is prompt this results in a distribution with a double peak for the velocity component along TOF axis.
Important information about the molecular processes is reflected in the symmetry properties of the distribution of the fragment recoil-velocities with respect to the transition dipole moment, as discussed in the following example. Let us suppose that no molecular processes occur to destroy the initial dipole moment alignment induced by the pump pulse. If the transition moment is parallel to the fragment recoil direction, for a pump polarization parallel to the TOF axis (x = 0, where x is the angle between pump polarization and TOF axis) we find a double-peak distribution. This is because the recoil direction is parallel to the TOF axis. In this case some of the fragments initially move toward a direction opposed to the acceleration imposed by the static electric field. These ions are thus
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V2+
E+avl(t0)
A++B
λ
Ionizing Ultrafast probe
λ λ V1
E+avl(t1)
Broadband ultrafast pulse
E+avl(tf) A+B
V0
AB
R
Figure 2.59 General scheme for multiphoton ionization by a single-color ultrafast pulse employed in KETOF experiments. The probe wavelength l is tuned to ionize A. The same wavelength can also ionize the molecule AB by promoting it to V2+ PES. The change of the translational energy distribution of A+ vs. time + reflects the temporal evolution of the total available energy from E avl at t = 0 to Eavl at t = tf. This permits of resolving the temporal evolution of the nuclear
delayed with respect to those which recoil in the same direction as the accelerating field. For x = p/2 the fragments are expelled along a direction perpendicular to the accelerating field. In this case the distribution of the recoil-velocity components along the TOF-axis (or z) will be symmetric around zero. For longer delays, when the molecule is dissociating, the probe gives information about the excitation transition moment since the distribution reflects the initial alignment induced by the pump. The last
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statement is not generally true for probe excitation at intermediate time instants. In this case the probe excitation may promote the molecule to an ionic bound state which takes a long time before leading to ionic dissociation. During this interval of time the ion rotation may destroy the initial pump induced alignment. This is shown in Figure 2.60 where the time evolution of KETOF spectra for I2 (panel a) and CH3I (panel b) molecule dissociation are shown. First, we observe that the different direction of the transition moments may be measured by observing the velocity distributions at long delays for different values of the pump polarization. Second, for the CH3I molecule the velocity distribution at early times has a similar anisotropy as at the end of the reaction, demonstrating that in this molecule the ion fragmentation is very prompt. This is one example of the information that this technique can provide. Another example is the possibility of distinguishing between the case of a direct-mode dissociation or a dissociative process that follows after an initial incoherent internal vibrational redistribution of energy. This is the case for the reaction C6 H5 I + hn ! ½C6 H5 Iy ! C6 H5 + IðI Þ ! ½C6 H5 Iy ! C6 H5 + I
Eq. (2-76)
Figure 2.60 The temporal evolution of KETOF spectra for I2 (panel a) and CH3I (panel b) molecule dissociation is shown (adapted from Ref. [284] with permission). See text for a detailed explanation of the spectra features.
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where by pumping at a wavelength of 277 nm two states are excited simultaneously: one is a repulsive (n, s*) excitation in the C–I bond and the other is a bound 3(p, p*) benzene ring excitation. Given the different products associated with these two reactions (I/I* and I), these two modes can be probed directly. In this way information on the incoherent dynamics and also on the nonadiabatic coupling between 3 (p, p*) and (n, s*) may be obtained. At this pump wavelength, excitation of the phenyl system is to the 3(p, p*) state, which has a significant oscillator strength because of the presence of the heavy iodine atoms. The optical excitation to the 3(p, p*) state at t0 does not deposit appreciable vibrational energy into the reaction coordinate (the length of the CI bond). With this high vibronic energy in the 3(p, p*) phenyl ring mode, the wavepacket spreads rapidly among all vibrational modes and the C–I mode can quickly become activated at t1y through Internal Vibrational Redistribution (IVR). This excitation then couples nonadiabatically to the dissociative (n, s*) PES, where the C–I bond is broken with high total available energy. The observed I+ KETOF signal shows a distribution peaked at large velocities and highly anisotropic. The C–I stretching motion can also couple with other bath modes. After a certain time, the energy flows back to the C–I coordinate and it breaks with low total available energy. This dynamic destroys the initial coherence of the process and results in delayed emission of I ions with much less available energy. Experimentally, this is shown clearly by the appearance at later times in the I+ KETOF distribution of a double peak with less energy. By gating the medium energy and the low energy ions, one gets the temporal evolution shown in Figure 2.61 where the coherent and incoherent decays are clearly distinguishable. Analogous results can be obtained by TRPES. A recent interesting work on NO dimers has shown how TRPES can resolve nonadiabatic transitions [327]. This possibility is explained well in Figure 2.62, where it is seen that the photoaccesible excited state S2 is coupled with the ionic ground state D0, while the forbidden S1 state, which can only be populated by nonadiabatic interaction coupling, correlates with the excited ionic state D1. This leads to the temporal evolution of the electronic spectra shown in Figure 2.62. A drawback of this technique is when both the excited electronic states correlate with the same ionic state. In this case there is no possibility of distinguishing among the two states. An important improvement of this technique was achieved by correlating the energetic spectra with the angular distribution of the emitted electrons [328], the latter being particularly sensitive to the symmetry and shape of the excited
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Figure 2.61 Temporal evolution of the I+ KETOF distribution produced in iodobenzene dissociation (from Ref. [284] with permission). By gating the low and medium energy ions one gets the temporal evolution of the incoherent (panel C) and coherent (panel B) decays. See text for details.
state wave functions. Therefore, different angular distributions are found even if the two excited states couple with the same final ionic state. This has been successfully demonstrated in a recent experiment by Hayden and co-workers [329].
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Figure 2.62 Time-resolved vibrational and electronic dynamics during internal conversion in all- trans 2,4,6,8 decatetraene (from Ref. [327] with permission). In panel a it is shown that the photoaccesible excited state S2 is coupled with the ionic ground state D0 while the forbidden S1 state, which can be only populated by nonadiabatic interaction coupling, correlates with the excited ionic state D1. This leads to the temporal evolution of the electronic spectra shown in panel b. The nonadiabatic transition is clearly seen by the appearance of the e2 spectrum.
Other interesting improvements of this technique can come from the implementation of fs laser pulses with very short wavelength. Some of the recent results in this field are reviewed in the following section together with other techniques of imaging.
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2.7 Recent Results in Ultrafast Crystallography: UED and Time-resolved X-rays One of the most important challenges in femtochemistry is the possibility of following structural changes occurring in molecular complexes in gas, solid and liquid phases on an ultrafast time-scale. Obtaining an ultrafast real-time imaging of the structural changes is important for a wide variety of phenomena. Recently, different techniques that use soft X-ray sources have led to very interesting results. There are several problems in generating soft X-rays sources with femtosecond resolution. Here we will discuss only the technical requirements necessary in the framework of femtochemistry. We refer the readers to Section 2.3.1.3 for a comprehensive description of techniques and methods for generating ultrafast soft X-rays. Soft X-rays sources can be applied as a direct probe by using the technique of X-rays diffraction or in connection with photoelectron spectroscopy. In the latter case the dissociative dynamics of neutral molecules can be followed by using a single probe photon that may induce a direct ionization of the state under investigation. Most of the results obtained by TRPES regard negatively charged ions that, given the lower ionization threshold, permit probing directly the ground-state dynamics. This does not apply for neutral molecules which have a too high binding energy. This can be done by using X-rays probe pulse. In this respect recent advances in high-harmonic generation techniques (see Section 2.3.1.3 for a detailed account on this topics) have given the possibility of performing experiments based on photo-electron spectroscopy with the use of fs Xray probes. The first time-resolved experiment using soft X-ray pulses has been reported by Probst and Haight [330]. These authors have studied electron–phonon interactions on the surface of organic thin films. In a recent experiment, Bauer et al. [331] have used high harmonics with a temporal resolution £25 fs for studying the change in chemical bond between platinum and oxygen adsorbed on the platinum-surface. In another experiment Nugent et al. [332] use the 17th harmonic of a Ti: Sa fundamental (wavelength of 800 nm) generated in a noble gas in order to probe dissociation of Br2 molecules The other important application of X-ray sources is time-resolved X-ray diffraction. X-ray diffraction has the potentiality of giving a complete, global picture of structural changes, without any ambiguity in the interpretation. In fact, X-ray diffraction spectrum is the result of
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contributions from all the electrons in the atoms. Since most of the electrons follow the nuclei motion, the diffracted spectra give directly the position of all the atoms and hence a direct imaging of the molecule structure. The possibility of following the structural conformational changes in real time on a fs time-scale is one of the greatest challenge of nowadays. In solid materials there occur many structural changes that might be monitored by this technique. One example is provided by the perovskite KNbO3, which experiences a rhombohedral–orthorhombic–tetragonal– cubic sequence as it is heated. At the Curie transition temperature the cubic phase shows a symmetry breaking and ferroelectricity arises. This transition occurs on a sub-picosecond time-scale and it is not yet clear what is the intimate nature of this transition. Other phenomena regard melting processes occurring in solids also at temperature below the melting point [333, 334]. In other amorphous materials, like GeSb, the generation of high concentration of carriers by laser pulses can induce an ultrafast crystallization of these materials [335, 336]. All these kinds of ultrafast phase transitions, ‘cold’ melting or ultrafast crystallization, can be studied by real time X-ray diffraction. The same important advances are expected for the study of many fundamental events in biology. One example for all is represented by cis-trans conformation changes which occur on a time-scale ranging from femtosecond in gas phase to picosecond in solution. Cis-trans transitions are key mechanisms in many biological processes. Cis-trans phase transition consists in a structural transformation of a molecule to its conformer upon rotation around a given covalent bond. There are several problems associated to the possibility of performing ultrafast X-ray diffraction experiments. For an extensive review we refer to the recent paper by Rousse et al. [337]. Some important results in this direction start to be collected. The first experiment of X-ray diffraction with sub-picosecond resolution has been published some years ago in Nature [338]. The investigation was performed on a Langmuir–Blodgett (LB) film of cadmium arachide, which is a fatty acid salt with a polar head on one side and an hydrophobic tail. LB films of such kind of molecules have great relevance as model system for biological systems such as micelles or cellular membranes. The X-rays with a lowest wavelength of 7.12 A˚ were obtained by making an intense ultrashort laser pulse to impinge on a silicon target. By heating the LB film with the energy deposited by an ultrafast pump pulse, a variation in time of the diffraction curves is observed (see Figure 2.63). A very slight shift and a decrease of the peak
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Figure 2.63 Stationary and transient X-ray diffraction spectra of LB films (from Ref. [337] with permission). The reduction of the peak intensity is indicative of a larger disorder due to the heating induced by an ultrafast pump-pulse.
are detected. This shows that the ultrafast heating leads to an immediate disordering of the LB film before that a film expansion can occur, as observed in slow heating of these samples. In fact, a bigger disorder in the system leads to a reduction of the peak intensity since diffraction is more efficient in materials where crystalline order is present. On the other hand, an ordered expansion of the film should lead to a shift of the diffraction spectrum. Interesting experiments with ps resolution have been reported in solid-state physics. Rose-Patruck et al. [339] have observed coherent acoustic motions in a GaAs crystal by means of a laser-induced plasma X-ray source. Recently experiments with a resolution of few ps have shown the first coherent lattice oscillation analogous to the coherent effects discussed previously in single-molecule experiments [340]. This interesting dynamics is shown in Figure 2.64. More recently great interest has been devoted to the study of ultrafast melting of semiconductors, which arises from a strong modification of the inter-atomic forces due to the laser-induced promotion of a large fraction of electrons from the valence to the conduction-band. This transition to the disorder of the atoms in the lattice can be efficiently probed by time-resolved X-ray diffraction since, in contrast with usual
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Figure 2.64 X-ray transient signal upon ultrafast excitation of an InSb sample (from Ref. [340] with permission). This spectrum clearly shows for the first time the coherent lattice oscillation in InSb. This phenomenon is analogous to the coherent effects discussed previously in single-molecule experiments in gases.
optical techniques, it detects directly the change in the atomic structure. In a paper by Rousse et al. [341], it has been demonstrated that the disordering occurs on a sub-picosecond scale (see Figure 2.65). This rules out the possibility of explaining ultrafast melting with the ordinary process of thermally excited atomic motion. The latter is characterized by a diffusive motion of atoms across activation barriers that typically determines kinetic rates on slower timescales (many picoseconds). On the contrary, the ultrafast character of this phenomenon must be ascribed to the excitation of a direct and deterministic motion of the atoms in the lattice (a nonergodic wavepacket excitation analogous to that observed in molecules [284, 342]). The dependence of the de-excitation time on the laser fluence shown in Figure 2.65 suggests the existence of an energy barrier. At intermediate fluences the atoms must perform many complete phononic vibrations before going to the liquid phase. Since, as already stressed, these phonons (lattice vibrations) are far from the equilibrium we are in presence of a new kind of nonthermally activated process. Another alternative technique for structural imaging that deserves being mentioned is based on time-resolved electron diffraction (UED) which, however, has not yet reached sub-picosecond resolution. The ultimate spatial and temporal resolutions obtained in ultrafast electron diffraction are 0.01 A˚ and 1 ps, respectively, in the gas phase [343, 344]. The general philosophy of this technique is the following. Part of an ultrafast laser pulse is used for initiating the chemical reaction while the
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Figure 2.65 Time-resolved X-ray diffracted spectra of semiconductor crystals for three different pump-pulse fluences (from Ref. [341] with permission). Open circles, filled circles, and open triangles correspond to laser fluences of 130, 119, and 110 mJcm2, respectively.
remaining part is directed on a silver photocathode. The laser–cathode interaction generates pulses of electrons. These pulses are directed onto the sample. The electrons, diffracted from the sample, are recorded by an ultrasensitive CCD camera. Here we review briefly two interesting applications of this technique: the study of iodine bond breaking in C2F4I2 and the ring opening in 1,3cyclohexadiene (CHD). In the first case the time-resolved UED spectra provide a signature of the conformational configuration of the molecule after the expulsion of the first iodine atom. Previous experimental data were consistent with two alternative pictures of the transition state: a ‘bridged’ radical structure, in which iodine is shared between the two CF2 moieties, and a ‘classical’ structure, where iodine is localized on one of the two CF2 groups (see Figure 2.66). With UED it has been possible to solve the puzzle of the intermediate structure by following the temporal evolution of the UED spectra. Theoretical calculations based on the two transition state pictures can be effectively compared with the measured spectra in order to find the real transition conformation. This comparison is shown in Figure 2.66 and indicates that the intermediate state is characterized by a ‘classical’ molecular structure.
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Figure 2.66 Temporal evolution of the UED spectrum for the transient C2F4I radical (adapted from Ref. [343] with permission). Df(r) is the difference between the spectrum recorded after the expulsion of the first iodine atom and a spectrum recorded at later time. The experimental result (solid line) is compared with theoretical predictions (dashed line) for two hypothetical structural configurations of the transition state: ‘bridged’ with iodine atom shared among the two C atoms (panel a) and ‘unbridged’ with iodine atom bound to a single C atom (panel b).
The same kind of analysis has been applied to the reaction which leads to the opening of the ring in CHD. Figure 2.67 shows the CHD ground-state diffraction pattern and the difference (bottom panel) with that recorded at later times after pump irradiation. It is clearly seen a decrease in the number of covalent C–C pairs and next-nearest-neighbor C–C pairs. Moreover, positive peaks may be observed in correspondence of a radius of 3.5 A˚. This indicates the simultaneous formation of new pairs with a larger mean bond-length. These observations are consistent with the ring opening of CHD and subsequent formation of 1,3,5-hexatriene on a picosecond time-scale. Due to very many degrees of freedom involved in this complex reaction, a better analysis of the experimental results needs an improvement in the theoretical interpretation of the diffraction spectra evolution. We believe that this technique can be fruitful in the next future.
2.8 New Nonlinear Optical Techniques for Probing Surfaces: Surface Second-harmonic and Sum-frequency Generation Interfaces are present everywhere in our life. They exist both between two different materials or between two different phases of the same material.
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Figure 2.67 UED results of CHD (adapted from Ref. [343] with permission). In the top panel the initial UED spectrum of CHD is shown. In the bottom panel the Df(r) signal is reported (Df(r) has the same meaning as in Figure 2.66). It is clearly seen a decrease in the number of covalent C–C pairs and next-nearestneighbor C–C pairs. Moreover, positive peaks may be observed in correspondence of a radius of 3.5 A˚. This indicates the simultaneous formation of new pairs with a larger mean bond-length. These observations are consistent with the ring opening of CHD and subsequent formation of 1,3,5-hexatriene on a picosecond time-scale.
Interfaces are so interesting since they display physical and chemical properties that are very different from those of the adjacent bulk phases [345, 346]. Despite the diversity of experimental issues related to interface science, generally their investigation requires very sensitive techniques. This is because the surface under study reduces to a single monolayer containing no more than 1015 molecules or atoms per cm2. At the same time, the probing techniques should be applicable under nonvacuum
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conditions in order to investigate so-called ‘‘realistic’’ and able to probe ‘‘buried’’ interfaces. This constraint makes optical techniques the only suitable and rules out a series of standard surface analytical tools, such as electron and neutron diffraction. On the other side, standard optical technique are usually not specific for investigating surfaces since they reach an ultimate resolution which is often not better than the wavelength. Moreover, for standard optical techniques, it is impossible to be selective for surfaces when the atoms and molecules that constitute the interface are also present in much larger quantities in the corresponding bulk phases. One of the most mature and powerful optical technique is IR spectroscopy, which consists into measuring the transmissivity or reflectivity of an IR probe beam. Such technique is sensitive to vibrational excitations, which are good markers for molecules and other elementary processes in liquids, solid, metals, semiconductors and super-conductors. However, the above mentioned technique shows several drawbacks that often can lead to the impossibility of studying some particular system. One of the major drawbacks is the difficulty of having very sensitive detectors for the infrared range. This is especially true when very thin monolayers are studied that give very small signals. In this case the detection must be performed in the so-called photon-counting regime. Another important point that we wish to underline here for its relevance in the study of rough metal surfaces is that IR reflectometry is a differential technique which needs a good reference in order to resolve very low signals. This is not a big problem for flat surfaces where s-polarized signal serves as a reference, but may encounter several limitations when applied to rough surfaces [347]. A comprehensive review of IR-spectroscopy is beyond the scope of this section. For more details we refer the readers to a very recent review on this topics and references therein [348]. Recently the nonlinear optical phenomenon of second-harmonic and sum-frequency generation has proven being suitable for probing surface properties with sub-monolayer sensitivity [349–351]. For a comprehensive list of the applications in which both surface second-harmonic generation (SSHG) and surface sum frequency generation (SSFG) have been used, see the optimum Table I of Ref. [347]. In the following sections, after a brief description of the theoretical framework, we will present an overview of some emerging research areas where the application of these techniques has proven to be promising. Moreover, we will limit ourselves to applications which require temporal resolutions of ps and/or fs. We stress that this section must not be considered as a comprehensive review of the field. For more details we remind the readers to the following list of optimum reviews [345, 347, 349–364].
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2.8.1 Theoretical considerations Optical second harmonic generation is a second-order nonlinear optical process, occurring when the response of the material, characterized by the electric polarization vector P, acquires a component that is quadratic in the electric field E0 of the input wave. This component is described by a third-rank tensor x(2), called second-order nonlinear optical susceptibility, characterizing the material. Under the dipole-approximation the second-harmonic polarization is defined by the relationship [166, 167] Pi ð2vÞ = e0
X
ð2Þ
xijh E0j ðvÞE0h ðvÞ
Eq. (2-77)
jh
where e0 is the vacuum dielectric constant and v is the optical frequency. The latter relation is true for monochromatic plane-waves but this argument may be generalized to optical pulses limited in duration by rewriting the equations in a new reference system which travels with a speed equal to the group velocity of the wave-packet [166]. The polarization oscillating at the second-harmonic frequency 2v is then the source of an outgoing optical wave oscillating at the same frequency. By measuring the intensity, polarization and phase of this outgoing wave one can determine all the elements of x(2). In many cases, by using phenomenological models or ab-initio calculations, these macroscopic quantities may be related to the microscopic properties of the material in study. However, the possibility of this link between the macroscopic and microscopic quantities is still a difficult task for many physical systems of interest [365]. Perhaps this is the main limitation of SSHG and SSFG. What turns the SSHG measurement into a surface-specific technique is the fact that x (2) must vanish in centrosymmetric media, being a thirdorder tensor. Therefore, with the notable exception of noncentrosymmetric crystals and of chiral substances, x(2) will vanish perfectly in the bulk of all materials. However, in proximity to an interface between two centrosymmetric media the inversion symmetry is perturbed and a nonzero x(2) may appear. In most cases, this perturbation is significant only within a molecular distance from the interface. Therefore, by measuring the second harmonic wave generated at an interface one acquires information about it on a scale of only one or two molecular layers across the interface. However, we must stress that this is the case only if dipoleapproximation holds. Indeed, beyond this approximation there are bulk quadrupole terms that also may contribute to the second-harmonic signal. In many cases these contributions are negligible. In other cases, it is
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possible to exploit the differences existing between surfaces and bulk: structural reconstructions, symmetries changes, and different electronic and/or vibrational resonances. However, when the condition for singling out the surface signal is fulfilled, SSHG and SSFG may become invaluable tools for investigating interfacial properties. The interface-generated second harmonic component can be traced both in the transmitted and reflected beams emerging from the interface, usually with comparable magnitudes. The choice of which is the component to be measured is then mainly a question of experimental convenience. However, in many cases, when the dipole-approximation is weak and bulk quadrupolar contributions mix with the signal generated from the interface, the reflection geometry may be more useful for minimizing the bulk contribution with respect to the searched interface signal. Figure 2.68 provides a schematic picture of SSHG phenomenon at the interface between two media. In Eq. (2-77), local-field effects have not a)
ω
2ω
ω
Incidence plane
b)
^ z
p
p
s
s k(ω)
Surface
^y
k(2ω)
^ x
Figure 2.68 In panel (a) a schematic picture of the nonlinear optical process of second-harmonic generation from surface is illustrated. The particular coordinate system used for the theoretical calculations reported in the text is shown in panel (b). x–z is the light incidence plane. The symbols p and s indicate optical-field
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been considered. In order to account for these effects, a further step is needed. After long and straightforward calculations, for which we refer to [351], we can obtain for a linearly polarized monochromatic plane-wave the following expression for the reflected second-harmonic intensity Ia ð2vÞ =
2 v2 2 eff ð2vÞ Ia0 ðvÞ x 0 2c3 ne0 cos2 b aa
Eq. (2-78)
where a and a0 indicate the different field components, b the angle of incidence, n the refractive index of the medium in which the incident beam propagates. In the latter we have introduced an effective tensor describing the interface polarization generating the second harmonic, i.e. ð2Þ
^ai Lij ð2vÞxjhk ð2vÞLhl ðvÞLkm ðvÞ^ e a0 l e^a0 m x eff aa0 = e
Eq. (2-79)
where ^ea are the unit vectors indicating the field polarization, Lij are the Fresnel factors as can be found defined for different geometries in Ref. [366]. In usual SSHG experiments the signal level is so low that the so called photon-counting regime applies. Therefore, it is worth giving an expression for the number of generated SSHG photons Sa(2v), i.e. Sa ð2vÞ =
2 S 2 ðvÞ rv3 a0 eff ð2vÞ x 0 4c3 ne0 cosb aa AT
Eq. (2-80)
where A is the surface area illuminated by the laser beam and T is the laser pulse duration. Equation (2-80) shows the importance of having short pulses in order to increase the SSHG signal. In many cases, Eq. (2-79) may be largely simplified by taking into account the symmetry properties of the surface. For example, in the case of an isotropic surface (invariant for rotation around its normal), it is straightforward to demonstrate that the following relationships hold true xeff ss = 0 xeff ps = 0
Eq. (2-81)
This may be understood qualitatively with the following classical argument. For simplicity let us consider a flat metallic surface where electrons may oscillate freely. For a p-polarized excitation the electrons motion has a component perpendicular to the surface. This component is
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strongly influenced by the presence of the surface that leads to an anharmonic potential experienced by electrons along the direction normal to the surface. In presence of a strong optical field this anharmonic potential may induce second-harmonic generation. On the contrary, any component in the surface oscillates symmetrically with respect to the incident plane and no SSHG is observed. The same argument applies for an spolarized pump. Equation (2-78) refers to an experimental geometry where the sole intensity of the generated second-harmonic is measured. This basic version of the SSHG technique provides only information on the absolute values of the elements of xeff aa0 . However, it is possible to improve SSHG by implementing an interferometric scheme as described, for example, in Ref. [367]. The interferometric SSHG technique is a powerful tool suitable for determining both the real and imaginary parts of the xeff aa0 elements. This technique consists of measuring the interference between the second harmonic signals generated from both the sample surface and a bulk reference. The reference (for example a crystalline quartz plate) is placed along the optical path of the fundamental beam: it may be inserted both before or after the sample surface. In order to define the ideas, let us suppose that the reference is inserted after the sample. Starting from the point where SSHG occurs, the second harmonic and fundamental beams travel collinearly but with different optical paths due to the dispersion of the mean interposed between the sample surface and the reference (the dispersing medium may also be simply air). When these two beams impinge onto the reference, they have two different phases. This phase difference reflects the difference of phase between the second harmonic signals generated from the sample surface and the bulk reference. Its magnitude depends on the distance between the surface and the reference. By varying the distance between the sample and the reference it is possible to modulate the detected interferential signal. This modulation pattern furnishes information on the phase of the sample surface signal with respect to the reference. Hence, by using a well characterized reference, one can measures the phase xeff aa0 elements. In the case of ultrashort pulses, things are a bit complicated from the different group velocities of the second harmonic and fundamental beams. In the case of ultrashort pulses this can lead to a time delay large enough to have a complete temporal nonoverlapping of the two pulses. As a consequence the interference disappears. Therefore, in this case, it is necessary to artificially compensate for these temporal delays or to use different detection schemes such as those proposed in Ref. [368].
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SSHG can provide important information on the microscopic properties of the constituents of the thin layer emitting the second harmonic. However, for most materials, this task is still tough from a theoretical point of view. For example, despite the huge theoretical work existing both on bulk as well as interface properties of semiconductors, it is still not trivial relating the band structures to the measured second harmonic spectra. Till recently, even within the framework of the basic independent-particle model, it was not fully understood how to handle this problem from a theoretical point of view. This is due to the fact that, while in linear optics only interband processes are important, in nonlinear optics a fundamental role is played also by the intraband transitions. This aspect was only very recently clarified by Sipe and coworkers [369–373]. Before this work, it was not possible to solve the divergences appearing in the quantum expression for the x (2) except for the simplest case of cubic crystals. Due to this initial difficulty only few publications have tried going beyond the independent-particle model. In any case they are limited to the dc limit or to the region below the absorption threshold [374–379]. This makes the ab-initio calculation of SSHG response still a largely unexplored area of optics. We would like to conclude this section by briefly citing an important improvement of SSHG:sum frequency generation from surface (SSFG). This is also a nonlinear effect of the second order; hence, it can be described by the same second-order susceptibility. The main difference is that the two initial photons may have two different frequencies v1 and v2. This leads to the generation of radiation at frequency v3 = v1 + v2. SSHG is a degenerate case of SSFG when v1 = v2. Despite the major complexity of SSFG, the possibility of using two input beams gives several advantages. First, if a noncollinear geometry for the input beams is used, the sum-frequency light is emitted along a direction different from those of the reflected input beams. This is due to the conservation of the field wave vectors that holds in the surface plane k3jj = k1jj + k2jj
Eq. (2-82)
where || indicates the wave vector component parallel to the surface. In this way one can select an experimental geometry that minimizes the background contributions coming from the two input beams (straylight, fluorescence, etc.). Moreover SSFG allows one to perform vibrational spectroscopy of the surface by tuning one of the two input beams in the infrared region [380]. If the second beam has a frequency in the visible range, the sum frequency
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generated falls still in the visible range. This gives the possibility of performing infrared spectroscopy by detecting light in the visible where very sensitive photomultiplier detectors may be used. In the case of molecules adsorbed at interfaces, one can investigate the vibrational resonances of all moieties of the molecule. Recently, by resolving the vibrational resonances of all the substitutes of complex molecules, a complete map of the molecule orientation and conformation has been drawn [381]. Some important and very recent development of SSFG within the ultrafast science field will be mentioned in the following sections.
2.8.2 Local-field-induced enhancement of SSHG on metal surfaces In this section, we will consider the interesting case of metal surfaces where a strong enhancement of SSHG due to local-field effects may occur. It can be shown that in this case the macroscopic local-field factors are much larger than the microscopic local-field factors [382]. For these reasons, in the following we will neglect the microscopic local-field corrections. Then let us recall Eq. (2-78) for a p-polarized pump beam and a flat surface Ið2vÞ =
2 v2 ð2Þ p p L ð2vÞL ðvÞL ðvÞ x cos2 b sin2 bI2 ðvÞ Eq. (2-83) ? jj?jj jj jj 3 2c ne0
where the symbols k and ? indicate the components parallel and perpendicular to the surface, respectively. We also assume that the only main ð2Þ contribution to the polarization comes from the term x? . Usually surfaces are not perfectly flat. Therefore, a realistic model for describing SSHG from metal surfaces consists in considering a small hemispherical or hemispheroidal boss on a flat metal surface. The hemispherical or hemispheroidal boss model can also qualitatively account for local field enhancement of SSHG from nanoparticles. Let us first consider a hemispherical boss. If its radius is much smaller than the wavelength, electrostatics can be applied for solving the boundary condition problem. It can be shown that the local field correction factors are given by [382] L? =
e 3e m e0 em + 2e
3e Ljj = em + 2e
Eq. (2-84)
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where em and e are the complex dielectric constant of the metal and of the dielectric medium above the metal surface, respectively. These formulas are valid in general also for a layer of dielectric material deposited on the metal surface with dielectric constant e0. If only the metal surface is investigated then e0 = em. It is worth noting that the macroscopic local-field tensor L assumes this diagonal form when considering a coordinate system in any given point on the hemisphere with the parallel plane tangent to the hemisphere. Equation (2-84) shows that when the denominator em + 2e approaches zero the SSHG is particularly enhanced. Since the imaginary part is always positive, the greatest enhancement is obtained when ´[em + 2e] = 0. This relationship corresponds to the excitation of a local surface plasmon. Noble metals have a dielectric constant with a small imaginary part and a negative real part. Therefore, they can induce a large enhancement of the SSHG. Analogous results can be obtained for a hemispheroidal boss on a flat metal surface. The electrostatic solution of this problem gives the following local-field factors [383]: L? = Ljj =
e
e m e 0 e + ðem eÞD
3e e + ðem eÞD
Eq. (2-85)
where D is the depolarization factor related to the geometric anisotropy of the spheroid. It takes the value of 1/3 for a sphere and zero for a very slender prolate spheroid. In this case the local surface-plasmon resonance is given by ´½e + ðem eÞD = 0
Eq. (2-86)
For highly elongated spheroids the local-field enhancement may be particularly large because for D ! 0 `½e + ðem eÞD!0 [384, 385]. Local-field effects can lead to enhancement factors for SSHG as large as two orders of magnitude [382].
2.8.3 Metal nanoparticles Metal nanoparticles in transparent matrices have attracted in the last decades a large amount of interest from both a fundamental and a practical point of view. This is due to the fact that, showing spectrally selective optical absorption [386, 387], they can be used for surface
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enhanced Raman scattering [388] and are expected to be interesting as nonlinear optical media in all optical switching devices [389]. Moreover, metal nanostructures give the possibility of overcoming the present miniaturization limits of light-guiding and light-handling optical devices. This could be of relevant technological interest for a further miniaturization of optoelectronic systems in communication technology [390, 391], and for increasing the present resolution of optical microscopy [392]. Moreover, MNPs might be used in optochemical sensorics, as for example, for enhancing the signals of optically monitored immunoreactions [393]. Very recently, second harmonic generation enhanced by a 1-nm gold nanoparticle has been used for measuring membrane potential around single molecules at selected cellular sites [394]. Finally, we mention that in a very recent paper [395], it has been suggested a theoretical scheme similar to those discussed in Section 2.5 in order to coherently control by phase modulation of ultrafast laser pulses the spatial distribution of the excitation energy. From an applicative point of view, this would be a fundamental achievement for future applications in ultrafast computing and ultrawide-band transmission of information. All these applications are possible thanks to the particular capability of MNPs of creating structural resonances of the collective oscillation of the electron plasma of the metal, usually called localized surface plasmon or particle plasmon. This is possible in the visible part of the spectrum, where the resonance frequency is mainly determined by the real part of the dielectric constant of the metal and the shape of the particle [396]. The reason for this structural resonance, which is not possible in extended bulk metal, is the spatial confinement of the electron plasma (dielectric confinement): when the quasi-free metal electrons are shifted by the incident light field, repulsion forces are built up by surface charging and they cause restorative forces. This leads to resonances. The electron-plasma resonance in MNPs leads to two important physical effects: (i) spectral selective absorption and (ii) remarkable enhancement of the light-field strength close to the surface of the particle (see previous section on local field enhancement). For applications it is essential to characterize quantitatively the resonance behavior of the surface plasma oscillation (surface ‘‘plasmons’’). In particular, it is fundamentally important to know the characteristic decay time of these plasmons. Such information cannot be obtained by absorption measurements. In fact, the absorption spectrum is inhomogeneously broadened due to the presence of nanoparticles of different sizes and shapes. This problem may be overcome, for example, by using techniques that are able to detect signals from a single nanoparticle [397],
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as has been done recently [398]. Another general way for achieving this information consists in time-resolving the plasmon decay by means of a pump-probe scheme with ultrafast pulses. A very surface specific technique is also needed. Another important requirement is that the pump energy must not be too strong in order to avoid any effect due to the thermal heating of the electrons. In this section, we will focus on the application of SSHG for investigating optical properties of MNPs. Moreover, we will focus on the femtosecond time-resolved regime referring the readers for a more exhaustive review to very recent papers on the subject [386, 399, 400]. During this last decade measurements of SSHG autocorrelation has proven being a powerful technique for probing plasmons in MNPs. We also mention that interesting results have been obtained with autocorrelation measurements of photoelectron emission [401]. Autocorrelated SSHG technique is analogous to that used for measuring the temporal width of laser pulses. It is based on a Michelson-like interferometer as shown in Figure 2.69. An ultrafast beam is divided in two parts. One of the two beams is temporally delayed with respect to the Oscilloscope
Chopper
Lock-in
MNPs sample
Interferential filter
Photomultiplier
Figure 2.69 A possible scheme for a fs interferometric autocorrelation measurement of SSHG from metal nanoparticles (MNPs).
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other. The interference of the two second harmonic signals gives rise to a fast beating whose envelope brings information about the plasmons lifetime. Moreover, by measuring also the absolute value of the second-harmonic reflected signal, it is possible to distinguish between thermal effects and plasmon dynamics [402, 403]. In the following, we give some theoretical details of the technique by reporting the arguments of Ref. [404]. In absence of any nonlinear interaction, the collective motion of electrons on the surface of a MNP may be described by the following classical equation for a given eigenmode with frequency O ~ x€ + 2G x_ + O 2 x = fðtÞexpðivtÞ
Eq. (2-87)
where G is the damping rate, x the collective electronic coordinate, f~ is proportional to the amplitude of the optical electric field whose frequency is v. The steady-state solution of Eq. (2-87) is x(t) = x0 exp(ivt), where x0 x0 =
~ fðtÞ O2 v2 2ivG
Eq. (2-88)
Under the hypothesis of near-resonance (v O) and for a damping rate much lower than the characteristic plasmon frequency (G << O), it is possible to replace Eq. (2-87) with the following simplified form [404] x_ + ðiO + GÞx = fðtÞexpðivtÞ
Eq. (2-89)
~ where fðtÞ = if=ð2OÞ. In the last equation, we have also supposed that f(t) does not vary too rapidly. More precisely, ðO + vÞ>>1
Eq. (2-90)
where t is the pulse duration. From a physical point of view this relation says that the laser pulse should contain a sufficient large number of optical cycles. In general, Eq. (2-89) must be solved numerically. However, when the electric field frequency is not resonant with that of plasmons, an approximate solution is provided by the steady-state solution given in Eq. (2-88). The deviation from the exact solution is of the order of [405] 1 t maxfG; j O vjg
Eq. (2-91)
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For describing second harmonic generation it is necessary to introduce in Eq. (2-89) an anharmonic term of the form ax2. If a is not too big, the equation may be solved with a perturbative method. If we limit only to the second order, we can write x = x1 + x2, where x1 >> x2.x1 and x2 satisfy the following two coupled equations x1 ðtÞ + ði O + GÞx1 ðtÞ = fðtÞexpðivtÞ x2 ðtÞ + ði O + GÞx2 ðtÞ = ax21 ðtÞ
Eq. (2-92)
Two cases must be considered. In the first case, the fundamental is resonant with O whereas the second harmonic is not. In the second case the opposite occurs. This is important in order to simplify the solution. In fact, as already stated, for the nonresonant case the steady-state solution can be used. In the case of resonant second harmonic, the solution of the first of Eq. (2-92) is straightforward. x1 is simply proportional to f(t). As a consequence the second of Eq. (2-92) becomes x2 ðtÞ + ðiO + GÞx2 ðtÞ = bf 2 ðtÞ
Eq. (2-93)
where b = a/(iO+G ). The general solution of Eq. (2-93) is given by Z
¥
x2 ðtÞ = b expði2vtÞ 2
expf½G + iðO 2vÞt0 g½fðt t0 Þ dt0 2
0
Eq. (2-94) The second harmonic optical field is then proportional to this solution, i.e. Z
¥
Eðt; OÞ expði2vtÞ
expf½G + iðO 2vÞt0 g½ fðt t0 Þ dt0 2
0
Eq. (2-95) In the autocorrelation experiment, if g(t) is the amplitude of the first pulse, then fðtÞ = gðtÞ + expðivtÞgðt TÞ
Eq. (2-96)
where T is the temporal difference between the two optical arms of the Michelson interferometer. The autocorrelation signal is given by Z SðTÞ =
+ ¥
¥
2 EðtÞ dt
Eq. (2-97)
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In Figure 2.70, the result of a numerical simulation is shown by using a Gaussian function for the optical field amplitude. In this simulation a plasmon lifetime of 10 fs and a laser pulse duration of 50 fs are used. By knowing the autocorrelation response of the optical pulse it is possible to measure the plasmon lifetime. This was measured for the first time by Steinm€ uller et al. [406] in islands of Ag on indium tin oxide. The result of this experiment is shown in Figure 2.71. In this experiment, the first direct measurement of the plasma-oscillation relaxation in a solid was obtained. This result has recently been confirmed by other measurements concerning an array of nanolithographically designed silver posts that have given a more accurate value of the plasmon lifetime, which results to be of 10 fs [396]. Very recently the same technique has been used for studying the influence of nanoparticle size on the plasmon lifetime in clusters of alkali metals leading to very interesting results [402, 407].
1
autocorrelation signal (arb. un.)
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -60
-40
-20
0 Time (fs)
20
40
60
Figure 2.70 The result of a numerical simulation for the autocorrelation of a SSHG signal. Here a Gaussian function is used for modelizing the laser pulse. In this simulation a plasmon lifetime of 10 fs and a laser pulse duration of 50 fs is used.
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Figure 2.71 Solid line shows the envelope of a SSHG autocorrelation signal on Ag island film (from Ref. [406] with permission). For comparison the pulse autocorrelation signal from a KDP crystal is also reported (dotted line). The response of KDP is almost instantaneous since in this case the SHG is not resonant.
2.8.4 Femtochemistry of surfaces probed by pump-probe SSFG and SSHG Over the last few decades surface science has made large progress thanks also to the advent of new sophisticated techniques with surface sensitivity. The chemical composition, the electronic and geometric structure of many interfaces have been extensively studied and a significant progress in the knowledge of their features has been achieved. However, most of this information refers to the static equilibrium properties of the surface. Problems related to the dynamics of chemical bond rearrangement on surfaces, as well as solvation and molecular reorientation dynamics at interfaces, have not yet been addressed extensively. Studies on bond dynamics at interfaces might answer important questions, as for example, from where the energy for the rearrangement of bonds comes, or how fast is this energy flow. For these reasons, in the last years both theoretical and experimental studies on the mechanisms and rates of energy transfer at surfaces between the adsorbates and the substrate have been boosted up. In these processes both the electronic and phonon degrees of freedom of substrate and adsorbates are involved. The substrate may transfer energy from these degrees of freedom to the adsorbate and vice versa. A detailed knowledge of the time scale of these processes and their resulting rates is essential for a fully
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understanding of reactions at surfaces, and possibly for their control. The progress in this field over the last few years has been possible thanks to the advent of ultrafast laser technology. The first experiment that probed ultrafast dynamics at surfaces was performed by Budde and co-workers who studied desorption of NO from Pd(111) by means of a two-pulse correlation measurement [408]. Shortly after this work, the desorption of CO from a Cu surface was the first chemical reaction to be monitored in real time [409]. In this work, for the first time in such types of experiments, the authors used time-resolved SSHG. Recently, interesting results about this reaction, which can be considered a model for catalysis, have been obtained by means of time-resolved pump-probe IR spectroscopy [410] and photo-electron spectroscopy [411]. Interesting perspectives have been opened recently by the use of timeresolved nonlinear optical techniques for the study of orientational dynamics at interfaces on a ps timescale. Eisenthal and co-workers have been the first to apply time-resolved SSHG for monitoring the reorientation of molecules at air–water interface [355, 412]. In this work the first pump-pulse is used for aligning molecules at interface, while the SSHG induced by a second probe-pulse is monitored at adjustable temporal delay for obtaining information in real time on the molecular orientational dynamics. Other interesting examples in this field are given by Refs. [413, 414]. On a femtosecond temporal scale, very recently time-resolved SSHG proved to be a powerful tool for investigating solvation dynamics at interfaces where usual experimental tools like time-resolved fluorescence fail [415]. While these studies regard the orientational properties of a molecule as a whole, SSFG could raise the possibility of studying the orientational dynamics of single moieties within the whole molecule because of its capability of performing vibrational spectroscopy. The latter property is of great importance for investigating reaction intermediates and the coupling between different vibrational modes during the course of a surface reaction. In fact, molecular vibrations of adsorbates provide direct insights into the formation and breaking of chemical bonds at interface. Even if only few examples exist to date, femtosecond pulse technology has opened up new perspectives in this field, and it is expected that femtosecond pump–probe SSFG may give significant contributions in tracing short lived intermediates in interfacial chemical reactions and in probing their dynamics [347]. Several experimental schemes can be proposed for time-resolved SSFG [416]. However, the only suitable technique for having both tem-
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poral and frequency resolution is the one shown in Figure 2.72. In this clever scheme a first ultrafast pulse induces a surface reaction and the resulting transient changes of an adsorbate vibrational mode are probed by broadband-IR SSFG (bIR-SSFG) spectroscopy by varying the temporal delay between the pump-pulse and the pair of SSFG probe pulses. The time delay between the two beams of this pair is kept fixed. bIRSSFG is used for obtaining a high frequency resolution. This is because as wide is the temporal pulse is as narrow is its spectrum. The broadband IR probe-pulse induces an IR-polarization. This polarization decays typically in few ps due to dephasing. The second visible probe pulse, temporally wider, up converts the vibrational excitation to a virtual electronic level. The width of the resulting spectrum of the emitted SSFG signal is determined by the vibrational resonance because the
Temporally narrow IR pump pulse Temporal delay Temporally narrow IR probe pulse
SSFG signal
Temporally narrowspectrally broadband VIS probe pulse
Figure 2.72 Scheme of setup for time- and frequency-resolved SSFG spectroscopy. A first ultrafast pulse induces a surface reaction. The resulting transient changes of an adsorbate vibrational mode are probed by bIR-SSFG spectroscopy by varying the temporal delay between the pump-pulse and the pair of SSFG probe pulses. The time delay between the two beams of this pair is kept fixed. bIRSSFG is used for obtaining a high frequency resolution. This is because temporally wider pulses are spectrally narrow. In this probing technique the broadband IR pulse (temporally short) induces an IR-polarization. This polarization decays typically in few ps due to dephasing. The second visible probe pulse, temporally wider (spectrally narrower), upconverts the vibrational excitation to a virtual electronic level. The width of the resulting spectrum of the emitted SSFG signal is determined by the vibrational resonance because the SSFG is enhanced only in correspondence of the frequency components of the spectrally narrow visible pulse. The temporal resolution is achieved by varying the temporal delay between the pump pulse and the bIR-SSFG pair. The delay between the beams of the pair is kept fixed.
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SSFG is enhanced only in correspondence to that frequency component that matches with the wavelength of the spectrally narrow visible pulse. Then the temporal resolution is achieved by varying the temporal delay between the pump pulse and the bIR-SSFG pair. The resolution of this technique amounts to 500 fs in time and of 8 cm1 in frequency. Another recent study concerns the CO stretch vibration of carbon monoxide adsorbed on a single-crystal Ru(001) surface [417, 418]. In Figure 2.73, the SSFG spectra obtained at different temporal delays with respect to an IR pumping pulse initiating CO desorption are shown. The main features are the initial red-shifting, a successive blue-shifting, a broadening and a lowering of the resonance peak in time. The set of these findings permit of singling out the fundamental role in the initial desorption process of the coupling between the internal CO stretching and the CO rotational mode which is frustrated by the substrate.
Figure 2.73 Transient SSFG spectra of the C–O stretch mode on a Ru(001) surface at pump energy inducing CO desorption (from Ref. [416] with permission). The main features are the initial red-shifting, a successive blue-shifting, a broadening and a lowering of the resonance peak in time. These findings together permit of singling out the fundamental role in the initial desorption process of the coupling between the internal CO stretching of the CO rotational mode which is frustrated by the substrate.
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It is worthwhile to mention, even if it is not a time-resolved SSFG experiment, that very recently SSFG spectroscopy has been used for studying the transition to delocalization of elementary excitation of CO on Ru surfaces [417]. As we have explained in Section 2.5, localization of vibrational energy in a specific bond is of fundamental importance in achieving mode-selective chemistry. The results of this important study are summarized in Figure 2.74 for different values of CO coverage over the Ru surface. For low values of CO coverage two resonant peaks are clearly seen. The principal one corresponds to SSFG signal coming from IR excitation from the ground state (v = 0) to the first excited vibrational level (v = 1). However, at high enough pump energy, absorption from the first to the second (v = 2) vibrational level can occur leading to the appearance of a new peak in the SSFG spectrum. This peak probes directly the n = 1 ! 2 stretching mode. However, by increasing the surface coverage dipole–dipole interactions between the neighbor molecules leads to delocalization of this elementary excitation all over the
Figure 2.74 On the left, SSFG spectra of the C–O stretch mode as a function of CO coverage (from Ref. [417] with permission). For low values of the CO coverage two resonant peaks are clearly seen. The principal one corresponds to SSFG signal coming from IR excitation from the ground state (v = 0) to the first excited vibrational level (v = 1). However, at high enough pump energy, absorption from the first vibrational level to the second (v = 2) can occur leading to the appearance of a new peak in the SSFG spectrum. This peak probes directly the v = 1 ! 2 stretching mode. By increasing the surface coverage dipole–dipole interactions between the neighbor molecules bring to a delocalization of this elementary excitation all over the molecular monolayer. On the right side, theoretical predictions are compared with experimental results (for details see Ref. [417]).
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molecular monolayer. This result has been recently confirmed by using a novel technique, the so-called ‘Infrared-Infrared-Visible’ SSFG [419]. Other interesting experimental examples of applications of timeresolved SSFG are provided in refs. [420–422]. This field is in its infancy and we believe that all the potential of time-resolved SSFG has not yet been completely exploited.
2.9
Summary
The investigation of nanoparticle properties and surface science, specifically the investigation of the chemical and physical behavior of these systems, has greatly benefited over this last decade from the use of many ultrafast optical techniques. Latest technological advances have pushed nanoscience to study smaller and smaller objects, whose linear size typically ranges nowadays from 1 to 20 nm. Just to cite an example taken from the day-to-day life, let us consider the very recent progresses of the car industry that have made possible the construction of cleaner and cleaner diesel engines, characterized by very high performances and low fuel consumption with apparently almost zero particulate matter emission. Recent studies are demonstrating that a noticeable part of the final products emitted during the combustion occurring in the last generation diesel engines contains organic carbon in the form of hydrocarbon nanoparticles or nanoparticle aggregates which, due to their very small size (1–20 nm), often escape common analytical techniques. Thus, both the amount of such nano-particulate matter present in the atmosphere and its impact on the environment and human health are, at the moment, relatively unknown. Consequently, a growing demand is arising for the implementation of new experimental techniques sensitive to the features of these new nano-materials. Many of these new methods, which mostly characterize the optical response of the system under investigation, are borrowed from ultrafast science. The detailed knowledge of the optical properties of the system often allows one to reconstruct its microscopic structure and its basic interactions with the rest of the world. Fortunately, ultrafast science has also rapidly developed over the past decade, now accessing the unprecedented temporal resolution of sub-femtosecond time-scale. This chapter, far from being a complete review of both ultrafast and nano-sciences, intends to bridge the gap between these two topics. To this purpose, we have illustrated the most widely used and most promising experimental techniques borrowed from ultrafast science and applied
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to the study of nanoparticles and thin films. The initial sections are dedicated to the basis of ultrafast science, namely ultrashort laser sources and their basic interactions with matter, i.e. with atoms and molecules. Special attention is devoted to the very hot topics, such as attosecond and few-optical-cycle pulse generation and characterization, which are presently at the border of science and may open the way for new intriguing techniques of time-resolved investigation. Some applications of ultrafast optical techniques to the study of interfacial properties are discussed. In particular, we describe two nonlinear optical techniques that recently have proven very promising for the study of interfaces: SSHG and SSFG. We briefly compare these two techniques with other classical optical techniques. However, given the limits of space of this chapter, we refer to the bibliography for a more complete review on the applications of optics to the study of interfaces. We provide the reader with some theoretical considerations about SSHG and SSFG. Special attention is devoted to describe those aspects of theory that are of interest for the chemistry and physics of nanoparticles. However, once again, these considerations cannot represent an exhaustive review of the subject and the reader is referred to a series of excellent articles existing in the literature. Finally, we have dealt with one of the hottest topics in ultrafast science, i.e. femtochemistry of surfaces. The latter is of fundamental importance, for example, in the study of nanoparticle contaminants and molecular films, catalysis, and other chemical reactions occurring at interfaces. Also in this case, given the vastness of the scientific literature on this topic, we focus on the very recent applications of SSHG and SSFG in surface femtochemistry. We stress that the application of these techniques in this particular field is still in its initial stage and a lot of work has to be done in order to fully exploit its potential.
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380. X. D. Zhu, H. Suhr and Y. R. Shen, ‘‘Surface Vibrational Spectroscopy by Infrared-Visible Sum Frequency Generation,’’ Phys. Rev. B 35, 3047 (1987). 381. X. Zhuang, P. B. Miranda, D. Kim and Y. R. Shen, ‘‘Mapping Molecular Orientation and Conformation at Interfaces by Surface Nonlinear Optics,’’ Phys. Rev. B 59, 12632 (1999). 382. C. K. Chen, T. F. Heinz, D. Ricard and Y. R. Shen, ‘‘Surface-Enhanced SecondHarmonic Generation and Raman Scattering,’’ Phys. Rev. B 27, 1965 (1983). 383. J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941). 384. J. Gersten and A. Nitzan, ‘‘Electromagnetic Theory of Enhanced Raman Scattering by Molecules Adsorbed on Rough Surfaces,’’ J. Chem. Phys. 73, 3023 (1981). 385. P. F. Liao and A. Wokaun, ‘‘Lightning Rod Effect in Surface Enhanced Raman Scattering,’’ J. Chem. Phys. 76, 751 (1982). 386. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin and Heidelberg, Germany (1995). 387. C. P. Collier, R. J. Saykally, J. J. Shiang, S. E. Henrichs and J. R. Heath, ‘‘Reversible Tuning of Silver Quantum Dot Monolayers through the MetalInsulator Transition,’’ Science 277, 1978 (1997). 388. R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering, Plenum Press, New York (1981). 389. R. F. Haglund, Jr., L. Yang, R. H. Magruder III, J. E. Wittig, K. Becker and R. A. Zuhr, ‘‘Picosecond Nonlinear Optical Response of a Cu:Silica Nanocluster Composite,’’ Opt. Lett. 18, 373 (1992). 390. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto and T. Kobayashi, ‘‘Guiding of a One-Dimensional Optical Beam with Nanometer Diameter,’’ Opt. Lett. 22, 475 (1997). 391. M. Quinten, A. Leitner, J. R. Krenn and F. R. Aussenegg, ‘‘Electromagnetic energy transport via Linear Chains of Silver Nanoparticles,’’ Opt. Lett. 23, 1331 (1998). 392. O. Marti and R. Moeller (Eds.), Photons and Local Probes, Volume 300 of NATO ASI Series E: Applied Science, Kluver, Dordrecht, The Netherlands (1994). 393. T. Schalkhammer, ‘‘Metal Nanoclusters as Transducers for Bioaffinity Interactions,’’ Chem. Mon. 129, 1067 (1998). 394. G. Peleg, A. Lewis, M. Linial and L. M. Loew, ‘‘Non-Linear Optical Measurement of Membrane Potential around Single Molecules at Selected Cellular Sites,’’ Proc. Natl. Acad. Sci. USA 96, 6700 (1999). 395. M. I. Stockman, S. V. Faleev and D. J. Bergman, ‘‘Coherent Control of Femtosecond Energy Localization in Nanosystems,’’ Phys. Rev. Lett. 88, 067402 (2002). 396. B. Lamprecht, A. Leitner and F. R. Aussenegg, ‘‘Femtosecond Decay Time Measurement of Electron Plasma Oscillation in Nanolithographically Designed Silver Particles,’’ Appl. Phys. B 64, 269 (1997). 397. S. Nie and S. R. Emory, ‘‘Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,’’ Science 275, 1102 (1997). 398. T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl and J. Feldmann, ‘‘Surface-Plasmon Resonances in Single Metallic Nanoparticles,’’ Phys. Rev. Lett. 80, 4249 (1998).
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399. C. Voisin, N. D. Fatti, D. Christofilos and F. Vallee, ‘‘Ultrafast Electron Dynamics and Optical Nonlinearities in Metal Nanoparticles,’’ J. Phys. Chem. B 105, 2264 (2001). 400. J. T. Lue, ‘‘A Review of Characterization and Physical Property Studies of Metallic Nanoparticles,’’ J. Phys. Chem. Solids 62, 1599 (2001). 401. J. Lehmann, M. Merschdorf, W. Pfeiffer, A. Thon, S. Voll and G. Gerber, ‘‘Surface Plasmon Dynamics in Silver Nanoparticles Studied by Femtosecond Time-Resolved Photoemission,’’ Phys. Rev. Lett. 85, 2921 (2000). 402. J. H. Klein-Wiele, P. Simon and H. G. Rubahn, ‘‘Size-Dependent Plasmon Lifetimes and Electron-Phonon Coupling Time Constants for Surface Bound Na Clusters,’’ Phys. Rev. Lett. 80, 45 (1998). 403. J. Hohlfeld, U. Conrad and E. Matthias, ‘‘Does Femtosecond Time-Resolved Second-Harmonic Generation Probe Electron Temperatures at Surfaces,’’ Appl. Phys. B 63, 541 (1996). 404. T. Vartanyan, M. Simon and F. Tra¨ger, ‘‘Femtosecond Optical Second Harmonic Generation by Metal Clusters: The Influence of Inhomogeneous line broadening on the Dephasing Time of Surface Plasmon Excitation,’’ Appl. Phys. B 68, 425 (1999). 405. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics, Cambridge University Press, Cambridge, UK (1990). 406. D. Steinmueller-Nethl, R. A. Hoepfel, E. Gornik, A. Leitner and F. R. Aussenegg, ‘‘Femtosecond Relaxation of Localized Plasma Excitations in Ag Islands,’’ Phys. Rev. Lett. 68, 389 (1992). 407. M. Simon, F. Tra¨ger, A. Assion, B. Lang, S. Voll and G. Gerber, ‘‘Femtosecond Time-Resolved Second Harmonic Generation at the Surface of Alkali Metal Clusters,’’ Chem. Phys. Lett. 296, 579 (1998). 408. F. Budde, T. F. Heinz, M. M. T. Loy, J. A. Misewich, F. de Rougemont and H. Zacharias, ‘‘Femtosecond Time-Resolved Measurement of Desorption,’’ Phys. Rev. Lett. 66, 3024 (1991). 409. J. A. Prybylla, H. W. K. Tom and G. D. Aumiller, ‘‘Femtosecond TimeResolved Surface Reaction: Desorption of Co from Cu(111) in <325 fsec,’’ Phys. Rev. Lett. 68, 503 (1992). 410. M. Bonn, S. Funk, C. Hess, D. N. Denzler, C. Stampfl, M. Scheffler, M. Wolf and G. Ertl, ‘‘Phonon-Versus Electron-Mediated Desorption and Oxidation of CO on Ru(0001),’’ Science 285, 1042 (1999). 411. H. Petek, M. J. Weida, H. Nagano and S. Ogawa, ‘‘Real-Time Observation of Adsorbate Atom Motion Above a Metal Surface,’’ Science 288, 1402 (2000). 412. A. Castro, E. V. Sitzmann, D. Zhang and K. B. Eisenthal, ‘‘Rotational Relaxation at the Air/Water Interface by Time-Resolved Second Harmonic Generation,’’ J. Phys. Chem. 95, 6752 (1991). 413. R. Antoine, A. A. Tamburello-Luca, P. Hebert, P. F. Brevet and H. H. Girault, ‘‘Picosecond Dynamics of Eosin B at the Air/Water Interface by Time-Resolved Second Harmonic Generation: Orientational Randomization and Rotational Relaxation,’’ Chem. Phys. Lett. 288, 138 (1998). 414. D. Zimdars, J. I. Dadap, K. B. Eisenthal and T. F. Heinz, ‘‘Anisotropic Orientational Motion of Molecular Adsorbates at the Air-Water Interface,’’ J. Phys. Chem. B 103, 3425 (1999).
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415. D. Zimdars, J. I. Dadap, K. B. Eisenthal and T. F. Heinz, ‘‘Femtosecond Dynamics of Solvation at the Air/Water Interface,’’ Chem. Phys. Lett. 301, 112 (1999). 416. C. Hess, M. Wolf, S. Roke and M. Bonn, ‘‘Femtosecond Time-Resolved Vibrational SFG-Spectroscopy of CO/Ru(001),’’ Surf. Sci. 503, 304 (2002). 417. C. Hess, S. Funk, M. Bonn, D. N. Denzler, M. Wolf and G. Ertl, ‘‘Femtosecond Dynamics of Chemical Reactions at Surfaces,’’ Appl. Phys. A 71, 477 (2000). 418. M. Bonn, C. Hess, S. Funk, J. H. Miners, B. N. J. Persson and M. Wolf, ‘‘Femtosecond Surface Vibrational Spectroscopy of CO on Ru(001) During Desorption,’’ Phys. Rev. Lett. 84, 4653 (2000). 419. M. Bonn, C. Hess, J. H. Miners, T. F. Heinz, H. J. Bakker and M. Cho, ‘‘Novel Surface Vibrational Spectroscopy: Infrared-Infrared-Visible Sum-Frequency Generation,’’ Phys. Rev. Lett. 86, 1566 (2001). 420. A. Bandara, J. Kubota, A. Wada, K. Domen and C. Hirose, ‘‘Adsorption and Reactions of Formic Acid on (2·2)-NiO(111)/Ni(111) Surface. 2. IRAS Study under Catalytic Steady-State Conditions,’’ J. Phys. Chem. B 101, 361 (1998). 421. A. Bandara, J. Kubota, K. Onda, A. Wada, S. S. Kano and K. D. C. Hirose, ‘‘Time-Resolved SFG Study of the Vibrational Excitation of Adsorbed CO on Ni (111) and NiO(111) Surface under the Irradiation of UV and Visible Photons,’’ Surf. Sci. 427–428, 331 (1999). 422. K. Domen, A. Bandara, J. Kubota, K. Onda, A. Wada, S. S. Kano and C. Hirose, ‘‘SFG Study of Unstable Surface Species by Picosecond Pump-Probe Method,’’ Surf. Sci. 427–428, 349 (1999). 423. L. Xu, G. Tempea, A. Poppe, M. Lenzner, C. Spielmann, F. Krausz, A. Stingl and K. Ferencz, ‘‘High-Power Sub-10-fs Ti:Sapphire Oscillators,’’ Appl. Phys. B: Laser Opt. 65, 151 (1997). 424. L. Sarger and J. Oberle, ‘‘How to Measure the Characteristics of Laser Pulses,’’ in Femtosecond Laser Pulses, C. Rulliere (Ed.), Chapter 7, p. 196, Springer, Heidelberg, Germany (1998). 425. P. Ceccherini, A. Boscolo, L. Poletto, G. Tondello, P. Villoresi, C. Altucci, R. Bruzzese, C. de Lisio, M. Nisoli, S. Stagira, S. D. Silvestri and O. Svelto, ‘‘Gas Medium Ionization and Harmonic Wavelength Tunability in HighOrder Harmonic Generation with Ultrashort Laser Pulses,’’ Laser Part. Beams 18, 477 (2000).
3
Transport and Deposition of Aerosol Particles Daniel J. Rader and Anthony S. Geller Sandia National Laboratories New Mexico, Albuquerque, NM, USA
3.1
Introduction
This chapter reviews the theoretical models available to describe particle transport in typical semiconductor processing environments. Recent or classic references have been provided wherever possible for additional background. In all of the discussion that follows, particle concentrations are assumed to be low enough so that the influence of the particle on fluid transport can be neglected; particle–particle interactions are also neglected. Under this assumption, the fluid and thermal fields are calculated first (in the absence of particles), and then used as input for subsequent particle transport calculations. The theoretical underpinnings for both the Lagrangian approach (where individual particle trajectories are calculated) and the Eulerian approach (where the particle concentration field is modeled as a continuum) are presented. The strength of the Lagrangian formulation is in predicting particle transport resulting from external forces including particle inertia; but the current implementation cannot describe the chaotic effect of particle Brownian motion (i.e., particle diffusion) on particle transport. On the other hand, the Eulerian formulation can describe particle transport resulting from applied forces and particle diffusion, but the current implementation cannot account for particle inertia. This chapter begins with a discussion of noncontinuum effects which play a key role in the transport of small particles at low pressure. Next follows a description of the Lagrangian particle transport equation, which basically describes how a particle responds when external forces are applied to it. Brief summaries of some of these forces (which are likely to be important inside a semiconductor process tool) are also included. The concept of particle relaxation time is then introduced, which leads to a R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 189–266 ª 2008 William Andrew, Inc.
189
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discussion of particle drift velocity. The chapter includes a description of the Eulerian particle transport equations for predicting diffusion contributions to particle deposition and concludes with a detailed analysis of particle transport in a parallel plate reactor as an illustration of the utility of these models.
3.2
Noncontinuum Considerations
In the following discussion, frequent mention will be made of the continuum and free molecular regimes. These terms are used here to distinguish between the two limiting cases characterizing the nature of the particle/gas interaction.1 In the continuum limit (large particles or high gas pressures), the gas surrounding the particle appears as a continuous fluid and traditional continuum fluid dynamics apply—such as the Navier–Stokes equations for fluid motion. In the free molecular limit (small particles or low gas pressures), however, the discrete nature of the gas becomes important and individual molecule/particle collisions must be considered. Discrimination between these two regimes is made by comparing the particle diameter to the gas mean free path (which is defined as the average distance a molecule travels between collisions with other gas molecules); a dimensionless parameter known as the Knudsen number is commonly used for these comparisons: Kn ¼
2l dp
Eq. (3-1)
where l gas mean free path (cm) ¼ m/(frc) dp particle diameter (cm) m gas viscosity (g cm1 s1) r gas density (g/cm3) ¼ PM/RT (for ideal gas) 1
The flow field entraining the particle can also be either molecular or continuum in nature. In this case, discrimination between the two flow regimes is made by comparing some characteristic length associated with the reactor geometry to the gas mean free path. For example, a Knudsen number for the flow field could be defined by replacing the particle diameter in Eq. (3-1) with a characteristic reactor length scale. For small particles, it is frequently the case that the flow regime can be considered continuum while the fluid-particle interaction is characterized as freemolecular.
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c mean thermal velocity of the gas molecules (cm/s) ¼ (8RT/pM)1/2 R universal gas constant (8.31451 · 107 g cm2 s2 K1 mol1) M gas molecular weight (g/mol) P gas pressure (dyne/cm2 or g cm1 s2) (1 atm ¼ 760 torr ¼ 1.01325 · 106 dyne/cm2) T gas temperature (K) Also, f is a dimensionless parameter that depends on the kinetic-theory model used to define the gas mean free path: in this work the value f ¼ 0.491 has been adopted [1]. At atmospheric pressures, the mean free path is typically less than 0.1 mm. Gas mean free path is inversely proportional to pressure at constant temperature; for example, the mean free path in air is 0.674 mm at 76 torr, 6.74 mm at 7.6 torr, and 67.4 mm at 760 mtorr at 296 K. Thus, for low-pressure applications, the Knudsen number for submicron particles can be large. A large Knudsen number (say >10) corresponds to the free-molecular regime, while a small Knudsen number (say <0.1) corresponds to the continuum regime. Typically, verified theoretical expressions are available in the literature for the forces acting on particles in both the continuum and free-molecular limits. Unfortunately, theoretical force expressions are difficult to formulate in the transition regime that lies between the continuum and free-molecular regimes (particle size of the order of the mean free path, Kn ¼ 1). Instead, interpolating or correlating functions are used which go to both the continuum and free-molecular expressions in the limit and match experimental data (if available) in between.
3.3
Lagrangian Particle Equation of Motion
In the Lagrangian approach to particle transport, particle Brownian motion is neglected and individual particle trajectories (position and velocity as a function of time) are determined by integrating the following system of ordinary differential vector equations: dxp ¼ Vp dt
mp
X dVp ¼ FD þ FG þ FT þ FE þ Fi dt
Eq. (3-2)
Eq. (3-3)
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FUNDAMENTALS
where xp is the particle position vector, Vp is the particle velocity vector, mp is the particle mass, and FD, FG, FT, FE, and Fi are the fluid-drag, gravitational, thermophoretic, electric, and any additional forces (diffusiophoresis, wall drag, etc.) acting on the particle. The forces explicitly listed in Eq. (3-3) are those of the greatest interest in analysing parallel-plate tools (Section 3.7); additional forces can be added linearly as needed. A brief review of these forces follows (for greater detail see [2–4]). Because of the low pressures (typically less than 100 torr) and small particle sizes (diameters typically less than one micron) of interest in semiconductor processing, particles are usually sufficiently smaller than the gas mean free path, l, so that the freemolecular limit of the various force expressions apply. The free-molecule assumption is well justified for particle Knudsen numbers (Kn ¼ 2l/dp) larger than 10, and is acceptable (accurate within about 20%) for Knudsen numbers as small as two. For Knudsen numbers less than two, force expressions that extend into the transition or continuum regime should be used.
3.3.1 Fluid–particle drag force A particle moving at a different velocity than the surrounding gas will experience a gas resistance or fluid-drag force. A great deal of research has been devoted to describing fluid-drag; only a brief review of this body of literature is reported here. For a rigid sphere of diameter dp moving at constant velocity Vp through a fluid with local velocity U and viscosity m, the drag force is given by (e.g., [5], p. 105): FD ¼
3pmdp Rep ðVp UÞCD ðRep Þ CðKnÞ 24
Eq. (3-4)
where CD(Rep) Rep/24 is a non-Stokesian correction for fluid inertial effects and C(Kn) is a slip correction factor for noncontinuum effects. A fairly simple correlating equation for the non-Stokesian correction has been suggested by Turton and Levenspiel [6]: CD ðRep Þ
Rep 0:01721Rep þ ¼ 1 þ 0:173Re0:657 p 24 1 þ 16; 300Rep1:09
where the particle Reynolds number is given as
Eq. (3-5)
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rdp jVp Uj m
193 Eq. (3-6)
and jVp Uj ¼ ½ðup uÞ2 þ ðvp vÞ2 þ ðwp wÞ2 1=2
Eq. (3-7)
where u, v, and w are the x, y, and z components of velocity for the fluid (without subscript) and the particle (with subscript p). This correlation applies for particle Reynolds number up to about 200,000. Note that only moderate particle Reynolds numbers (say 10 at most) are expected for most semiconductor process applications, so that the far right terms in Eq. (3-5) are small compared to unity. In fact, for submicron particles in typical processing environments, the slip-corrected Stokes drag law [Eq. (3-4) with CD(Rep) Rep/24 ¼ 1] can generally be used with negligible error. It has already been explained that for small particles or at low gas pressures (large value of Kn) the continuum approximation eventually breaks down and the molecular nature of the gas must be considered. Cunningham [7] was the first to propose that a correction factor (called the Cunningham or slip correction factor), C(Kn), be included in Eq. (3-4) to account for noncontinuum effects. The functional form first suggested by Knudsen and Weber [8] is in common use: g CðKnÞ ¼ 1 þ Kn a þ bexp Kn
Eq. (3-8)
where a, b, and g are the parameters that depend on the nature of the gas-particle interaction at the particle surface, and so are affected by both gas composition and particle surface roughness. For example, Ishida [9] used a Millikan apparatus to determine the coefficient a for oil-drops in nine common gases. His results were recently re-evaluated by Rader [10] using modern, more accurate values for the electric charge and gas properties; the corrected values for a are given in Table 3.1. Based on theoretical considerations [11] and experimental data [12], Rader [10] recommends that the expression a + b ¼ 1.647 can be used to accurately calculate b for most gas and particle–surface combinations; b values calculated by this formula using Ishida’s measured values for a are given in Table 3.1. The choice of the third constant, g, is more difficult as there are no theoretical techniques for estimating it, and as complete data for empirically determining it are limited. Rader [10] fits the available
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Table 3.1 Gas Properties. Density, Viscosity, Molecular Weight, Mean Free Path, and Slip Correction Constants (for Oil Drops) for Nine Common Gases at T ¼ 296.15 K and P ¼ 760 torr [10]
Gases
m0 (poise)
M (g mol1)
ro (g cm3)
l0 (mm)
a ()
Air Ar He H2 CH4 C2H6 i-C4H10 N 2O CO2
183.47(6) 224.80(6) 197.11(6) 88.61(6) 110.75(6) 93.37(6) 75.06(6) 147.88(6) 148.12(6)
28.966 39.948 4.003 2.016 16.043 30.069 58.123 44.013 44.010
1.192(3) 1.645(3) 0.165(3) 0.826(3) 0.661(3) 1.251(3) 2.406(3) 1.818(3) 1.823(3)
0.0674 0.0703 0.1943 0.1240 0.0545 0.0333 0.0193 0.0493 0.0438
1.207 1.227 1.277 1.141 1.154 1.254 1.186 1.207 1.150
b ()
g ()
0.440 0.78 0.420 – 0.370 2.00 0.506 – 0.493 – 0.393 – 0.461 – 0.440 – 0.497 0.92
data for air, carbon dioxide, and helium and found g values of 0.78, 0.92, and 2.0, respectively. For other gases, Rader [10] suggests g ¼ 0.85. Note that the correlation for the slip correction factor given by Eq. (3-8) is not very sensitive to the value of g used. In fact, only small errors typically result if the slip factor is calculated using the fitted constants for oildroplets in air (a ¼ 1.207, b ¼ 0.440, and g ¼ 0.78) for different gases or for particles of different surface roughness. A plot of the C(Kn) against Kn is given in Figure 3.1 using these constants. Note that C(Kn) approaches unity in the continuum limit, and approaches (a + b)Kn in the free molecule limit.
3.3.1.1 Fluid-drag force: assumptions and practical considerations All of the above formulae assume solid, homogeneous, spherical particles, while real particles may be far from spherical in shape (flakes, rods, deformed droplets, etc.) and may be porous or inhomogeneous in composition. These variations from ideality can result in particle rotation, modifications to the drag law, etc. Two methods are commonly used to account for nonsphericity: the use of an equivalent diameter or the correction of the drag law with a dynamic shape factor. Hinds [4] and Fuchs [13] provide discussion of both of these approaches. Techniques are
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im it ole cu le L
10
ee M
C(Kn)
100
Fr
Full Slip Correction
1 0.01
Continuum Limit
0.1
1 Kn
10
100
Figure 3.1 Slip correction factor. Dependence of the slip correction factor on particle Knudsen number (solid curve). The free molecule limit for the slip correction factor is also shown (dotted curve).
becoming available for more accurately modeling the transport of certain classes of nonspherical particles (including flakes, rods, chains of spheres, etc.), but these greatly increase the complexity of the problem. In adopting Eq. (3-4), resistance terms resulting from fluid inertia (e.g., the virtual mass and Basset history integral terms) have been neglected, which has been shown [13, 14] to be a reasonable approximation for aerosol particles (where the particle density is much larger than the fluid density) at particle Reynolds numbers not exceeding a few hundred. The uncertainty in Eq. (3-4) becomes greater at higher Reynolds numbers, but high Reynolds numbers are not expected in semiconductor applications. Equation (3-4) strictly applies to the uniform (nonaccelerating), straightline motion of a sphere in a quiescent fluid. In the present application, however, the drag on an accelerating particle in a nonuniform flow field is needed. Fuchs ([13], Chapter 3) and Clift et al. ([14], Chapter 11) review the issues related to the nonuniform rectilinear motion of aerosol particles. Although it will introduce some inaccuracy, the instantaneous drag acting on an accelerating particle can be estimated with the above constant-velocity drag expression with the fluid and particle velocities taken as their local, instantaneous velocities. Strictly speaking, the combination of the slip C(Kn) and non-Stokesian (CD(Rep) Rep/24) corrections in Eq. (3-4) as a product is on flimsy grounds. Henderson [15], for example, presents a correlation that adds
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the corrections.2 Unfortunately, there is little or no data available for Re 1 where slip is appreciable, so the proper formulation cannot be decided. For typical semiconductor process environments, however, particle Reynolds numbers are likely to be low so that the non-Stokesian correction is near one and Eq. (3-4) is likely to be quite satisfactory.3 Thus, in the rest of this work, the slip-corrected Stokes drag law (Eq. (3-4) with CD(Rep) Rep/24 ¼ 1) will be used.
3.3.1.1.1 Continuum regime limit In the continuum limit (large particles and/or near-atmospheric process pressures) and assuming non-Stokesian effects can be neglected, Eq. (3-4) for the gas resistance reduces to Stokes law (e.g., see [4], p. 41): FD; continuum ¼ 3pmdp ðVp UÞ
Eq. (3-9)
The continuum regime drag force is seen to be directly proportional to particle size and to the velocity difference between the particle and the gas; it is independent of process pressure (the dependence of fluid viscosity on pressure is very weak) and depends on temperature only through the temperature dependence of viscosity.
3.3.1.1.2 Free molecule regime limit In the free molecular limit (small particles and/or low process pressures) and assuming non-Stokesian effects can be neglected, Eq. (3-4) for the gas resistance reduces to the following free molecular result (similar to that originally derived by Epstein [16]) in the limit of large Kn: FD; molecular ¼
3pf rcd 2p ðVp UÞ 2ða þ bÞ
Eq. (3-10)
As in the continuum limit, free-molecular drag force is directly proportional to the gas-particle velocity difference. Unlike the continuum result,
2
C is removed from Eq. (3-4) and the expression 1/C replaces ‘‘1’’ as the first term on the right-hand side of Eq. (3-5). 3 In practice, non-Stokesian effects can be neglected when the particle Reynolds number is less than about 0.3.
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however, free-molecular drag shows a much stronger (squared) dependence on particle diameter. Another difference is that free-molecular drag is directly proportional to process pressure (through the fluid density term). Temperature dependencies arise implicitly through the fluid density and the mean gas velocity.
3.3.2 Gravitational force The gravitational force acting on a spherical particle is given by Hinds ([4], p.42): FG ¼
p 3 d ðr rÞg 6 p p
Eq. (3-11)
where rp and r are the particle and gas density, respectively, and g is the gravitational acceleration vector. The gas density is typically much smaller than the particle density, and can be neglected in Eq. (3-11). The gravitational force is independent of the gas mean free path.
3.3.3 Thermophoretic force Because of the thermophoretic force, particles suspended in a gas with a temperature gradient will migrate in the direction opposite to the gradient, i.e. away from hot regions and toward cold regions. This phenomenon results in the preferential deposition of particles on a cold wall, and explains the appearance of a particle free zone near a hot wall. A formulation for the thermophoretic force on a spherical particle was developed by Talbot et al. [17] in a review of thermophoresis: FT ¼ 3pmdp nKT
HT T
Eq. (3-12)
where
kg 2Cs þ Ct Kn kp KT ¼ kg ð1 þ 3Cm KnÞ 1 þ 2 þ 2Ct Kn kp
Eq. (3-13)
and where KT is the temperature gradient in the gas, T is the mean gas temperature about the particle, n ¼ m/r, kg and kp are the gas and
198
FUNDAMENTALS
particle thermal conductivities,4 and Ct, Cs, Cm are the thermal creep coefficient, temperature jump coefficient, and velocity jump coefficient, respectively (Cs ¼ 1.147, Ct ¼ 2.20, and Cm ¼ 1.146 are recommended by Batchelor and Shen [18]). Talbot et al. [17] compared their correlation with other experimenters’ data over a wide range of Knudsen numbers, and found it agrees with available experimental data to within 20%.
3.3.3.1 Continuum regime limit In the continuum limit of small Kn the thermophoretic force approaches: FT; continuum ¼ 6pm2 dp
Cs kg HT kp þ 2kg rT
Eq. (3-14)
which depends on temperature, pressure, gas and particle thermal conductivities, and is proportional to particle diameter.
3.3.3.2 Free molecule regime limit In this limit, Eq. (3-12) approaches the limit first derived by Waldmann and Schmitt [19]: FT; molecular ¼
p HT fmcd 2p 2 T
Eq. (3-15)
Note that in this limit the thermophoretic force is proportional to diameter squared and is independent of the particle thermal conductivity.5
3.3.4 Electrostatic force A charged particle suspended in a region with an electric field E will experience a force ([4], p. 286): FE ¼ np eE ¼ qE
Eq. (3-16)
where np is the number of elementary charge units e (4.803 · 1010 esu in cgs) on the particle giving a total charge q. This equation is deceptively 4
For polyatomic gases, Talbot et al. [17] recommend the use of the ‘translational’ thermal conductivity, which is given by simple kinetic theory as kg = (15/4)mR/M. 5 The gas conductivity does play a role, but has been eliminated from Eq. (3-15) by the expression in footnote 4.
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simple, in that the determination of either the charge on the particle or the surrounding electric field can be exceedingly challenging (experimentally or theoretically). In a plasma tool, for example, np and E will change with time and position and may not be independent.
3.4
Inertial Effects
Using the particle fluid-drag force relationship (Eq. (3-4) with CD(Rep) Rep/24 ¼ 1), the particle force balance of Eq. (3-3) can be rewritten as: t
dVp CðKnÞ ðFG þ FT þ FE þ SFi Þ ¼ UVp þ dt 3pmdp ¼ UVp þ VtG þ VtT þ VtE þ SVti
Eq. (3-17)
where we have introduced a particle response or relaxation time t¼
rp d 2p CðKnÞ 18m
Eq. (3-18)
and the particle drift velocity, V ti , which is discussed below in Section 3.5. Particles characterized by small relaxation times respond rapidly to changes in the flow or in the applied forces, while particles with large relaxation times respond slowly to such changes. For large relaxation times, particle transport is dominated by particle inertia.
3.4.1 Nondimensionalization It is often convenient to nondimensionalize Eqs. (3-2) and (3-17). For this purpose, a characteristic length and velocity must be specified. For example, for parallel plate geometry (see Figure 3.2), we could chose the inter-plate separation S as the characteristic length, and the magnitude of the mean face velocity U0 as the characteristic velocity, for which Eqs. (3-2) and (3-3) become: d~ xp ¼ V~ p dt~
St
dV~ p ~ V~ p þ ðV~ t þ V~ t þ V~ t þ SV~ t Þ ¼ U G T E i dt~
Eq. (3-19)
Eq. (3-20)
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~ ¼ U=U0 , and V~ t ¼ V t =U0 where x~p ¼ xp =S, t~ ¼ tUo =S, V~ p ¼ Vp =U0 , U i i t where V i is the particle drift velocity described below. We have also introduced the particle Stokes number, St, a dimensionless quantity defined as: St ¼
tUo rp d 2p CðKnÞUo ¼ S 18mS
Eq. (3-21)
where t is the particle relaxation time. The Stokes number is a convenient measure of the importance of particle inertia in a specific reactor; for small St inertial effects can be neglected, while for large St inertial effects a)
r z
Ujet
b)
C L
djet
L
S
SHOWERHEAD
−Uo
z r
SUSCEPTOR
RW Figure 3.2 Parallel-plate reactor geometry. Schematic of the reactor geometry assumed in this work: (a) top view of a showerhead and (b) side view of a parallelplate reactor.
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must be considered. Physically, the Stokes number can be interpreted as the ratio of the particle stopping distance6 to the characteristic length of system. The continuum and free molecule limits of St are as follows: Continuum regime limit: Stcontinuum ¼
rp d 2p Uo 18mS
Eq. (3-22)
Free molecule regime limit: Stmolecular ¼
3.5
rp dp U0 pRT 1=2 a þ b rp dp U0 ¼ 0:373 rcS PS 9f 8M
Eq. (3-23)
Drift Velocity
The manipulation of Eq. (3-3) into Eq. (3-17) resulted in the derivation of the particle drift velocity, Vti , which is the particle velocity at which the ith force (neglecting all others) acting on the particle exactly balances the fluid drag force retarding the motion. At this balance point, the particle acceleration vanishes and the particle would move at a steady (or terminal) velocity—the drift velocity. The time required for the particle to reach the drift velocity is short for particles characterized by small particle response times (small Stokes numbers). For small Stokes numbers, particle inertia can be neglected and the acceleration term on the left-hand side of Eq. (3-17) can be dropped, so that particle velocity can be expressed as: Vp ¼ U þ V tp ¼ U þ V tG þ V tT þ V tE þ SV ti
Eq. (3-24)
where the net particle drift velocity is obtained by summing over all external forces, i.e.: V tp ¼ V tG þ V tT þ V tE þ SV ti ¼
CðKnÞ ðFG þ FT þ FE þ SFi Þ 3pmdp Eq. (3-25)
Equations (3-24) and (3-25) show that, neglecting inertia, the particle will move with the fluid velocity plus the vector sum of the individual drift The particle stopping distance, tU0, is defined as the distance a particle would travel before stopping if injected into a quiescent fluid at an initial velocity of U0. 6
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velocities from all of the applied external forces. In the absence of any external forces (and having neglected particle diffusion), a noninertial particle will exactly follow flow streamlines. For isothermal flow between horizontal, parallel plates, all the V ti are constant and are directed normal to the plates. Expressions are given below for the drift velocities for each of the forces listed in Section 3.3.
3.5.1 Gravitational drift velocity The drift velocity for a spherical particle settling under gravity can be found from Eqs. (3-4) and (3-11) with buoyancy and non-Stokesian effects neglected: V tG ¼
rp d 2p gCðKnÞ 18m
Eq. (3-26)
Although the form of the gravitational force is the same in both the continuum and free molecule regime limits, expressions for the two drift velocity limits differ due to the differing drag law contribution: Continuum regime limit: V tG; continuum ¼
rp d 2p g 18m
Eq. (3-27)
Free molecule regime limit: VtG; molecular ¼
rp dp g pRT 1=2 a þ b rp d p g ¼ 0:373 rc P 9f 8M
Eq. (3-28)
Note that the settling speed of a particle in the free molecule limit varies directly as particle diameter and inversely with pressure, while in the continuum limit the settling speed varies as diameter squared and is independent of pressure. Example. The gravitational drift velocity for a unit density spherical particle as a function of particle size is shown in Figure 3.3 for six different process pressures in argon at 293 K. For pressures below 100 torr and particle diameters below 1 mm, note that the lines are parallel and straight with a slope of one, as predicted by the free molecule regime limit. Thus, for most of the pressures and particle sizes of interest in
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Figure 3.3 Gravitational deposition velocity. Dependence of the gravitational deposition velocity on particle diameter for six process pressures (argon at 293 K, particle density rp ¼ 1 g/cm3).
semiconductor processing, the free molecule regime limit—Eq. (3-28)—can be used to predict particle settling rates, greatly simplifying calculations.
3.5.2 Thermophoretic drift velocity The thermophoretic drift velocity resulting from the balance of thermophoretic and drag forces (neglecting non-Stokesian effects) alone can be found by equating Eqs. (3-4) and (3-12): V tT ¼ KT CðKnÞ
mHT mRHT ¼ KT CðKnÞ rT PM
Eq. (3-29)
Interestingly, the drift velocity given by Eq. (3-29) depends on particle diameter only implicitly through the slip correction factor and KT; specifically, in both the large and small particle limits the thermophoretic velocity becomes independent of particle size. Continuum regime limit V tT; continuum ¼
2Cs kg mHT 2Cs kg mRHT ¼ kp þ 2kg rT kp þ 2kg PM
Eq. (3-30)
The continuum limit for thermophoretic drift velocity does not depend on particle size.
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Free molecule regime limit In the free molecular limit, the thermophoretic drift velocity reduces to: V tT;molecular ¼
Cs ða þ bÞ mHT Cs ða þ bÞ mRHT mRHT ¼ ¼ 0:549 3Cm rT 3Cm PM PM Eq. (3-31)
which is the same result as given by Waldmann and Schmitt [19]. The free molecule limit is independent of particle size and gas/particle thermal conductivities. The numerical constant 0.549 in the final equality is very general as the sum a + b is nearly constant for most gases and particle surfaces. Example. The thermophoretic drift velocity for a spherical particle as a function of particle size and pressure is shown in Figure 3.4 for an assumed temperature gradient of HT ¼ 1 K/cm. For the calculations, the ratio of gas to particle thermal conductivities was taken as kg/kp ¼ 0.001, representative of a metal particle suspended in argon (the thermophoretic drift velocity is not very sensitive to this ratio). Even for this small temperature gradient, the drift velocity can become large at low pressures. For pressures below 100 torr and particle diameters below 1 mm, note that the drift velocity becomes independent of particle diameter and inversely proportional to process pressure, as predicted for the
Figure 3.4 Thermophoretic deposition velocity. Dependence of the thermophoretic deposition velocity on particle diameter for six process pressures (argon at 293 K, kg/kp ¼ 0.001, HT ¼ 1 K/cm).
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free molecule regime limit. Thus, for most of the pressures and particle sizes of interest in semiconductor processing, the free molecule regime limit—Eq. (3-31)—can be used to predict particle thermophoretic deposition rates. Because of the simple relationship of drift velocity to pressure and T, calculating the drift velocity for other pressures and temperature gradients is easily done in the free molecule regime limit.
3.5.3 Electric drift velocity The drift velocity for a spherical particle moving under an applied electric field is given by: V tE ¼
CðKnÞ qE 3pmdp
Eq. (3-32)
Although the electrical force is independent of process conditions such as temperature and pressure, these quantities enter the expression for drift velocity through the drag-law contribution.
3.6
Eulerian Formulation
While the Lagrangian (particle tracking) method predicts particle transport by considering single particle motion, the Eulerian formulation predicts particle transport by viewing the particle concentration field as a continuum. In this case, the solution of the particle transport problem becomes very much like that posed by the flow field, i.e., there is one continuous equation for particle mass (concentration) conservation and one continuous equation for particle momentum (velocity) conservation for each particle size. Particle transport by diffusion (Brownian motion) is naturally included in this formulation. A great simplification is obtained if particle inertia is neglected, i.e., it is assumed that the particle instantaneously reaches the drift velocity where drag and imposed forces are in balance.7 In this case, the particle momentum equation is no longer needed, and only the particle continuity equation for particle concentration 7
The requirement that the characteristic time for particle diffusion is much longer than the particle characteristic time, t >> t, is also essential to the development of the basic equations of particle transport by Brownian motion (see [13], Section 35).
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FUNDAMENTALS
n (particles/cm3) remains ([13], p. 190; [20]): qn þ UHn ¼ HD HnHðV tp nÞ þ L qt
Eq. (3-33)
where D (cm2/second) is the Stokes–Einstein particle diffusion coefficient (discussed below) and L (#/cm3/second) is a particle source/sink term to account for particle generation/consumption. The net drift velocity, Vti , appearing in Eq. (3-33) is the same one discussed previously. Although we will not make further use of the fact, it is interesting to note that Eq. (3-33) is applicable to either the Brownian motion of an individual particle or to the diffusion of a particle cloud taken from the continuum point of view ([13], p. 191). For a single particle, n is interpreted as the probability of finding a particle at position (x, y, z) at time t given that the particle was initially located at position (x0, y0, z0) at time t0. Thus, although semiconductor applications are likely characterized by very low particle concentration levels, the continuum approach can still be applied if we continue to associate the particle concentration with a probability distribution (for example, we may find particle concentrations less than 1 cm3, which is acceptable from a probabilistic point of view). For boundary conditions, it is assumed that particles which contact the wall stick and are thus instantly removed from the gas, so that the concentration n equals zero at all walls. Only one-way coupling between the fluid flow and particle concentration fields is used in this work; i.e., the flow field is coupled to particle transport through the velocity field U which appears in Eq. (3-33), while the influence of the particle phase upon the flow is neglected. In practice, the flow field is calculated first (in the absence of a particle phase) and the resulting velocity field is supplied to Eq. (3-33) as a known solution.
3.6.1 Particle diffusion coefficient A more complete discussion of the Stokes–Einstein particle diffusion and its derivation is available in any aerosol text (e.g., [13], Chapter 5). The diffusion coefficient for a spherical particle is: D¼
kTCðKnÞ 3pmdp
Eq. (3-34)
where C(Kn) is defined by Eq. (3-8). The validity of Eq. (3-34) rests on several assumptions: (1) the particles move independently of one another
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and (2) the movements of a particle in consecutive time intervals are independent [16]. The latter assumption is met only if the condition t >> t holds true; in other words, the expression for the diffusion coefficient given in Eq. (3-34) is only valid for observation times much longer than the particle response time. Continuum regime limit The continuum regime limit for the diffusion coefficient is Dcontinuum ¼
kT 3pmdp
Eq. (3-35)
which is inversely proportional to particle diameter and independent of pressure. Free molecule regime limit In the free molecular limit, the diffusion coefficient reduces to Dmolecular
1 ða þ bÞ RT 2 kT ¼ 3f 2pM Pd2p
Eq. (3-36)
which is inversely proportional to particle diameter squared and pressure. Example. The particle diffusion coefficient for a spherical particle as a function of particle size and pressure is shown in Figure 3.5 for a temperature of 293 K. For pressures below 100 torr and particle diameters below 1 mm, note that the lines are parallel and straight with a slope of negative two, as
Figure 3.5 Diffusion coefficient. Dependence of the particle diffusion coefficient on particle diameter for six process pressures in argon at 293 K.
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predicted for the free molecule regime limit. Thus, for most of the pressures and particle sizes of interest in semiconductor processing, the free molecule regime limit—Eq. (3-36)—can be used to calculate the particle diffusion coefficient.
3.6.2 Nondimensional formulation For generality, Eq. (3-33) can be nondimensionalized by choosing a characteristic length (taken here as S, the distance between the showerhead and wafer, Figure 3.2), velocity (taken here as U0, the mean inlet velocity of the flow at the showerhead, Figure 3.2), and concentration (n0¼Lh/U0, the trap source strength divided by inlet velocity). For steady state, and assuming a constant diffusion coefficient, Eq. (3-33) can be written as [20] ~ n ¼ 1 H2 n~HðV~ t n~Þ þ 1 UH~ p Pe
Eq. (3-37)
where the Peclet number (the ratio of convective to diffusive transport) is defined as Pe ¼
SU0 : D
Eq. (3-38)
The continuum regime limit for the Peclet number is Pecontinuum ¼
3pmdp SU0 kT
Eq. (3-39)
which is proportional to particle diameter. Thus, in the continuum limit, the Peclet number can be used as a dimensionless particle diameter. In the free molecular limit: Pemolecular
1 3f 2pM 2 Pd 2p SU0 ¼ kT ða þ bÞ RT
Eq. (3-40)
which is proportional to particle diameter squared and to pressure. In the free molecular limit, the square root of the Peclet number can be used as a dimensionless particle diameter. In standard problems of species mass transfer, the Peclet number would be sufficient to completely characterize the problem for a given
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geometry and flow field. For particles, however, the presence of a drift velocity term (the second term on the right-hand side) means that the Peclet number no longer uniquely specifies the solution and a dimensionless drift velocity ratio must also be considered: V~ tp ¼
Vtp Uo
Eq. (3-41)
3.7 Particle Transport and Deposition in a Parallel Plate Reactor To illustrate an application of the particle transport models, this section analyzes particle transport in an enclosed, parallel-plate reactor geometry characteristic of a wide range of single-wafer process tools. The axisymmetric geometry we consider consists of uniform flow exiting a showerhead separated by a small gap from a parallel susceptor, as shown in Figure 3.2. The wafer would rest on the susceptor, but for the present analysis the wafer is assumed to be thin enough to be ignored. The showerhead consists of a material (usually a metal or ceramic) through which a large number of holes are drilled (see Figure 3.2a). As one major function of the showerhead is to evenly distribute the flow across its face, the holes are usually made very small in diameter and are very numerous (hundreds to thousands for an 8 inch wafer process tool). Ideally, a showerhead would produce a flow characterized by a mean axial (or face) velocity that does not vary in the radial direction; such flow uniformity is needed to accomplish uniform deposition or etching of the wafer surface. In practice, however, commercial showerheads are typically designed empirically to improve process parameters (such as uniformity); the resulting showerhead designs often create nonuniform flow fields which compensate for other system deficiencies - such as radial temperature or reactive species gradients. Various flow fields can be obtained by manipulation of showerhead hole sizes, numbers, and positions. One common feature of showerhead design is that the area available to the flow is constricted inside the showerhead; consequently, the velocity of the gas inside the holes of the showerhead is much larger than the face velocity in the gap below. Particles originating upstream of the showerhead and suspended in the flow can be dramatically accelerated while passing through the showerhead, so that at the exit of the showerhead particle velocities much larger than the fluid face velocity are possible.
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FUNDAMENTALS
Depending on conditions, particle acceleration by the showerhead can lead to inertia-enhanced particle deposition on the wafer below [21]. Thus, a complete description of particle deposition on a wafer in a parallel-plate reactor must include a description of particle transport through the showerhead as well as an analysis of particle transport in the inter-plate region. No attempt is made here to analyze particle generation mechanisms; for the present discussion, particles are assumed to originate either: (1) upstream of the showerhead with a known concentration or (2) from a specified position between the plates with a fixed number or at a known generation rate. The determination of particle transport in a reactor must always begin with a determination of the fluid flow and temperature fields. Particle concentrations are assumed to be low enough to allow a dilute approximation, for which the coupling between the fluid and particle phases is one-way. The fluid/thermal transport equations can be solved either analytically or numerically neglecting the particle phase. The resulting velocity and temperature fields are then used as input for the particle transport calculations.8 In all of the present work isothermal flow is assumed, although small temperature differences are allowed to drive particle thermophoresis. Both analytical and numerical solutions of the flow field are presented. To provide a single parameter that can be used to compare particle deposition among many cases, a particle collection efficiency is defined as the fraction of particles that deposit on the wafer. Particles are presumed to either enter the reactor through the showerhead (uniformly spread between r ¼ 0 and RW), or to originate in a plane parallel to the wafer. The latter case would correspond to particles being released from a plasma trap upon plasma extinction; in this case the particles are initially assumed to be uniformly spread radially between r ¼ 0 and RW at some distance h from the wafer. Analytical expressions for collection efficiency are presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Particle transport is predicted using both a Lagrangian approach (where individual particle trajectories are calculated) and an Eulerian approach (where the particles are modeled as a continuum phase). The strength of the Eulerian formulation is in predicting particle transport 8
The dilute mixture approximation is certainly valid for simulations of commercial semiconductor process tools, as the particle concentrations are typically controlled to very low levels.
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resulting from the combination of applied external forces (including the fluid drag force) and the chaotic effect of particle Brownian motion (i.e., particle diffusion), although the current implementation cannot account for particle inertia. In particular, the Eulerian formulation cannot accommodate particle acceleration effects within the showerhead, and is therefore restricted to particle transport in the inter-plate region. The Eulerian formulation yields an analytical description of particle deposition for the case where the flow field between the plates can be approximated analytically with a creeping-flow assumption and where the particles are assumed to originate from a planar trap located between the plates. The Lagrangian formulation can account for inertia-enhanced deposition resulting from particles which originate upstream of the showerhead and which are accelerated while passing through it. The problem is treated in two steps: (1) within a showerhead-hole and (2) between the showerhead and susceptor.
3.7.1 Fluid transport equations In both of the domains considered (flow within the showerhead and between two parallel plates), the geometry will be axisymmetric. With constant fluid properties, and incompressible, laminar, steady flow, the governing equations for axisymmetric flow are the conservation of mass: qu 1 q þ ðrvÞ ¼ 0 qz r qr
Eq. (3-42)
and conservation of momentum: 2 qv qv qv qP q v 1 qv q2 v v þ þv þu ¼ þm þ qt qr qz qr qr2 r qr qz2 r2 2 qu qu qu qP q u 1 qu q2 u þ r þv þu ¼ þm þ qt qr qz qz qr2 r qr qz2 r
Eq. (3-43)
where u and v are the axial and radial components of the fluid velocity, P is the pressure, r is the fluid density, and m is the fluid viscosity ([22], p. 85). Boundary conditions are needed to complete the problem specification. In all of the following, no-slip (zero velocity) conditions are taken at all solid walls (i.e., on the showerhead, susceptor, and walls of the
212
FUNDAMENTALS
showerhead holes), zero radial velocity is assumed along the centerline, and zero traction is assumed at all outflows. For the two flow domains, specific boundary conditions and methods for solving the governing equations are discussed in greater detail below. Note that for convenience, a different coordinate system is used for describing the flow through a showerhead hole than in the region between the parallel plates (see Figure 3.2b). The generality of the present results are improved if the fluid equations are solved in nondimensional form. Because there are two domains of interest, there are two choices for a characteristic length and velocity. For flow in the showerhead holes, the hole diameter djet and the magnitude of the mean velocity Ujet are used as the characteristic length and velocity, for which the tube Reynolds number is defined as Rejet ¼ rUjetdjet/m. For the flow between two plates, the inter-plate separation S and the magnitude of the mean face velocity U0 are the appropriate choices, and the inter-plate flow is then characterized by a separate Reynolds number: Re ¼ rU0S/m
3.7.1.1 Flow field in the showerhead holes The idealized geometry and the coordinate system for fluid and particle transport in the showerhead holes is shown in the inset in Figure 3.2b. As seen, z is taken as increasing in the direction of flow (toward the wafer), so that all fluid and particle axial velocities considered in this part of the solution are positive. The flow in the showerhead holes is assumed laminar with parallel streamlines, thereby neglecting any axial variations in velocity. For laminar flow in a tube with a uniform inlet velocity, however, it is well known that a fully developed parabolic velocity profile develops over an entrance length given approximately by 0.04 djet Rejet ([5], p. 72). For many showerheads this entrance length is much less than the hole length (showerhead thickness) and so may be safely neglected; for thin showerheads, however, this may not be the case. In the present analysis, we consider two limiting velocity profiles that meet the above assumptions: (1) plug flow (constant velocity profile) and (2) fully developed laminar flow (parabolic velocity profile). For laminar flow, the velocity profile anywhere along the hole will fall somewhere between these two limiting cases. In case one, the velocity is constant throughout the tube and, for incompressible flow, is equal to the mean velocity in the hole, U jet ¼ 4Q=ðNjet pd 2jet Þ where Q is the total gas volumetric flow rate through the
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showerhead and Njet is the number of individual holes in the showerhead. By mass conservation it can be shown that the ratio of the mean axial velocity in a hole and the face velocity is the ratio of the showerhead area to the total hole area: U jet Ashowerhead D 2W ¼ ¼ Uo SAjet Njet d2jet
Eq. (3-44)
For case two, fully developed laminar flow in a tube is given by Ujet ðrÞ ¼ 2U jet
2 ! r 1 ajet
Eq. (3-45)
where r is the radial distance from the tube centerline and ajet is the radius of the hole. The maximum velocity for parabolic flow is twice the mean velocity and occurs on the centerline.
3.7.1.2 Fluid transport between parallel plates Both analytical and numerical techniques have been used to calculate the fluid flow between the showerhead and susceptor. For both methods we assume axisymmetric, incompressible, constant property, laminar, steady flow between two parallel plates (Figure 3.2b). The flow enters through the showerhead (z ¼ S) and is assumed to spread immediately, so that the inlet boundary condition is assumed to be a uniform axial velocity, U0, with zero radial velocity. Both the radial and axial components of velocity vanish at the lower plate (z ¼ 0). The analytical approach assumes that the plates are infinite in the radial direction and that the Reynolds number is small; the numerical technique is used for finite plates and is valid for higher Reynolds numbers. The numerical technique is relied on here to define the conditions over which the simpler analytical solution is valid. The assumption of constant-property flow requires further comment. Although the numerical methods used here can solve for coupled fluidthermal transport, we have not used this capability in the present analysis. For cases where temperature differences are large or where more accurate solutions are needed for a specific application, the reader is advised to solve the coupled fluid–temperature problem. As mentioned above, a modest temperature gradient is allowed to drive particle
214
FUNDAMENTALS
thermophoresis (the magnitude of all particle drift velocities will be calculated using fluid properties evaluated at the susceptor temperature). Under the above assumptions, the flow between the plates is entirely determined by the geometry and the Reynolds number Re ¼ rU0S/m. For the range of conditions encountered in semiconductor reactor processes, the associated Reynolds numbers are typically less than one, and seldom greater than 10. For small Reynolds numbers, viscous effects dominate fluid inertial effects and the ‘‘creeping flow’’ or Stokes flow regime is encountered; it is this regime that allows an analytical solution. The numerical method used for calculating the fluid velocity field was the commercial fluid dynamics analysis code FIDAP (Version 7, Fluid Dynamics International, Evanston, IL, USA). The numerical technique was used to calculate flow fields for Reynolds numbers up to eight. With fixed values for plate separation (S ¼ 1), mean inlet velocity (U0 ¼ 1), and fluid viscosity (m ¼ 1), the fluid density r was varied to obtain flow field solutions for Reynolds numbers between one and eight. The FIDAP option of solving the Stokes flow equations (Re ¼ 0) was also used. The results of these calculations are given in Figure 3.6, which shows axial and radial velocity profiles at r ¼ 1 for Re ¼ 0, 1, 2, 4, and 8 as a function of the dimensionless axial coordinate z/S. Note that all velocities have been normalized by the magnitude of the inlet velocity U0, and that the radial velocity is also normalized by radius. For Re ¼ 0, the radial velocity profile is found to be parabolic and symmetric around z/S ¼ 0.5. As Reynolds number increases, the symmetry vanishes and the maximum in the radial velocity moves closer to the plate (z/S ¼ 0). Variations in the axial and radial velocity profiles are seen to be quite small for Reynolds numbers less than two. As in previous work in a similar geometry [26], it was found that the flow was quasi-1-D: the axial velocity is independent of radius, while the radial velocity is found to scale with radius such that v/r is independent of radius. An analytical simplification is gained if the flow between the plates can be approximated as a quasi-1-D stagnation point flow. Terrill and Cornish [23] give an asymptotic solution to the problem of axisymmetric, laminar, incompressible, constant property and steady flow between two co-axial infinite parallel disks with constant injection across the disks (a uniform gas inlet velocity across the showerhead). Under these assumptions, a similarity solution reduces the 3-D Navier–Stokes equations to a system of ordinary differential equations; for low Reynolds numbers, these equations can be solved with a power series in Reynolds number [23]. The first two terms of their asymptotic expansion (translated into
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the present problem definition) are: uð~ zÞ Re ¼ 2~ z 3 3~ z2 þ z 6 þ 18~ z 3 13~ z2Þ ð2~ z 7 7~ Uo 70 Eq. (3-46) vð~r ; z~Þ 2 Re 6 5 2 v~ð~ r ; z~Þ ¼ ¼ r~ 3~ z 3~ z z þ 27~ z 13~ zÞ ð7~ z 21~ Uo 70 u~ð~ zÞ ¼
Figure 3.6 Flow field results for various Reynolds numbers. Axial (a) and radial (b) velocity profiles for Re ¼ 0, 1, 2, 4, and 8 calculated on a refined (30 elements) mesh. (r/S ¼ 1 for all curves).
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where z~ ¼ z=S and r~ ¼ r=S. These two equations exactly satisfy all boundary conditions. The quasi-1-D nature of the result is clearly seen as the axial velocity is independent of radius, while the radial velocity scales linearly with radius. In the limit of vanishingly small Reynolds number, Eq. (3-46) reduces to a symmetric, parabolic profile for radial velocity, in excellent agreement with the Stokes flow solution (Re ¼ 0) obtained by FIDAP (this limit has also been previously reported by Houtman et al. [24]). Equation (3-46) does a very good job of approximating the axial velocity profile—agreeing with FIDAP solutions to better than 1% for Reynolds numbers less than 4, and to better than about 4% for Reynolds numbers up to 8. The success of Eq. (3-46) in predicting radial velocity is not nearly so good. Although the error is better than 1% for Re < 1, the maximum observed error quickly grows, reaching 15% for Re ¼ 4 and 70% at Re ¼ 8. As can be seen, the largest errors are found near the showerhead (z/S ¼ 1), where the magnitude of the radial velocity is quite small. Thus, although the relative error is quite large, the absolute error is small. In any case, our treatment of the region near the showerhead is only approximate because we have neglected the effect of the discrete jets issuing from the showerhead. Strictly from a fluid velocity point of view, Eq. (3-46) provides a very good approximation of the flow for Reynolds numbers less than two, and a reasonable approximation up to a Reynolds number of four.
3.7.1.3 Summary: fluid flow analysis for the parallel plate geometry This section has defined the parallel-plate geometry which will be used to approximate the flow inside a showerhead-type etch or CVD reactor. The acceleration of the gas flow as it passes through the showerhead will later be found to play a key role in enhancing particle deposition by particle inertia; for this reason, solutions for flow within the showerhead holes have been presented. The two limiting cases which were considered, plug and fully developed parabolic flow, should bracket the range of flows likely to be encountered in semiconductor applications. Laminar, incompressible, constant-property flow between two infinite, parallel plates was used to approximate the inter-plate flow in real reactors which are certainly more complicated. Reynolds number and edge effects were discussed, and an analytical solution was found that should provide
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a fairly accurate description of the flow for Reynolds numbers less than about four when the plate separation is much smaller than the overall system radial dimension. Variable temperature effects have not been considered.
3.7.2 Particle collection efficiency Particle collection efficiency is defined as the fraction of particles present in the inter-plate region that deposit on the wafer. The collection efficiency is introduced to provide a single parameter that can be used to compare particle transport and deposition results among many cases. Note that the use of collection efficiency side-steps the important issue of the particle source term. Thus, while the present transport analysis addresses the question of the fraction of gas-borne particles that deposit on the wafer, a prediction of the number of particles that deposit on the wafer additionally requires a clear understanding of the controlling particle generation mechanisms. In practical terms, the present analysis helps identify strategies for reducing the probability that particles are transported to and deposit on a wafer; a complete strategy for reduction of total particle-on-wafer counts also requires that particle source terms be understood and controlled. Three particle-source scenarios are considered: (1) a continuous source of particles entering the inter-plate region through the showerhead with known concentration (such as for contaminated process gases), (2) a discrete number of particles that are originally trapped between the plates (such as by a plasma) but are subsequently released (such as at plasma extinction), and (3) a continuous source of particles which are created between the plates at a known generation rate (such as by particle nucleation). General collection efficiency expressions for these cases are defined below. In addition, analytical expressions are provided for the limiting case where external forces control particle deposition—i.e., both particle inertia and Brownian motion are neglected. In the absence of particle inertia and Brownian motion, Robinson [25] has shown that particle concentration is constant along particle trajectories if: (1) the flow is incompressible and (2) the external forces acting on the particle are all divergence free. For the infinite parallel-plate geometry with constant-property flow, the flow is clearly incompressible and the second condition is met for the gravitational and Coulombic electric particle forces (which are each constant between the plates).
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3.7.3 Particles entering through the showerhead For this case, collection efficiency is defined as the fraction of particles entering the inter-plate region through the showerhead (between r ¼ 0 and RW) that deposit on the wafer. These particles are presumed to originate upstream of the showerhead and are assumed to be evenly distributed across the showerhead. Particle acceleration through the showerhead will be considered in Section 3.8.1. The present Lagrangian formulation accounts for the coupling between particle inertia and external forces in determining particle transport in the inter-plate region. The calculation of a collection efficiency with a Lagrangian technique requires the determination of the critical radius, Rcrit, which is the starting radial position (at the showerhead) of a particle that follows a trajectory that leads it to deposit at the edge of the wafer, RW (see Figure 3.7). All particles starting closer to the centerline will deposit on the wafer, while those starting farther out will exit the reactor. For a uniform concentration across the showerhead, the collection efficiency, h, can be written as h¼
Rcrit RW
2 ¼
2 Ri Rf
Eq. (3-47)
In general, the critical trajectory must be found by a trial-and-error method. The second equality of Eq. (3-47) is a simplification that only applies under our quasi-1-D approximation. In this case, all the factors that influence particle deposition (e.g., axial fluid velocity profile, the particle initial velocity, and particle axial drift velocity) are independent of radial position; thus, the question of whether a particle will hit CL R crit
rp•• RW
Figure 3.7 Critical trajectory. Diagram of a critical trajectory for a particle which starts at the showerhead at radial position Rcrit and deposits at the wafer edge RW.
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the wafer must not depend on its initial radial position, Ri (although the radial position at which the particle hits the wafer, Rf, will depend on Ri). It can be shown for our quasi-1-D case that the ratio Ri/Rf is independent of initial radial position. Thus, efficiency in the Lagrangian framework is calculated by starting the particle at a particular radial position (Ri ¼ 1) and calculating its trajectory to determine the radial position of contact with the wafer;9 the efficiency is then (Ri/Rf)2 ¼ (1/Rf)2 as given in Eq. (3-47). The total number of particles depositing on the wafer is the product of efficiency times the total flux of particles entering through the showerhead.
3.7.3.1 External force limit For the case where external forces control particle deposition (neglecting inertia, interception, and diffusion), Rader et al. [26, 27] used a Lagrangian analysis to obtain the following expression for deposition efficiency in isothermal, quasi-1-D parallel-plate flows: 2 jV tp j Rcrit 2 Ri ¼ ¼ t h¼ jV p j þ U0 RW Rf
V tp £ 0
Eq. (3-48)
where Vpt is the z-component of the net particle drift velocity (the resultant of all external forces in the axial direction).10 For net drift velocities greater than zero (net external force pushing particles away from the wafer), no particle deposition on the wafer is predicted (although it will be shown later that particle inertia or diffusion can cause deposition even in this case). Equation (3-48) provides a lower bound for particle deposition, as inertial and diffusional effects can only increase deposition from what is predicted. Interestingly, as the particle net drift velocity is typically much smaller than the fluid entrance velocity, Eq. (3-48) predicts that (in the absence of inertia and diffusion) the particles which land on the wafer originate from near the reactor centerline.
9
In the event that the particle axial velocity becomes zero, or begins to move away from the wafer, then the trajectory calculation is terminated and the efficiency is set to zero. 10 When inertia is neglected, the particles enter the reactor with the mean gas velocity so that Vpo ¼ U0. Also, note that U0 is the magnitude of the face velocity, and so is positive.
220
FUNDAMENTALS
Equation (3-48) is independent of the flow field (consider that the flow Reynolds number does not appear) that can be more easily understood by applying Robinson’s [25] result (as discussed above). Neglecting diffusion and inertia, the concentration over the lower plate must equal the inlet concentration, n0. The rate at which particles deposit on the lower plate becomes jV tp jno pR 2W , while the rate at which particles enter through the showerhead is ðjV tp j þ Uo Þno pR 2W . Taking the ratio of these expressions gives the same efficiency as Eq. (3-48) (see also [28]). Similar results, including Eq. (3-48), were found by Ramarao and Tien [29] for plane-stagnation flow. Interception effects were neglected in Eq. (3-48), which implies that a particle is collected only when its center of mass reaches the wafer surface. A better assumption is that particle collection occurs when the particle comes within one particle radius (rp ¼ dp/2) of the wafer surface.11 The derivation of Eq. (3-48) can be easily modified to include interception, with the following result: h¼
Rcrit RW
2 ¼
2 jV tp j þ juðz ¼ rp Þj Ri ¼ jV tp j þ Uo Rf
V tp £ juðz ¼ rp Þj Eq. (3-49)
Note that particle collection is now expected in the absence of external forces (or even for weak repulsive forces); the physical interpretation is that collection occurs when the flow brings the particle within one particle radius of the wall. The inclusion of interception also has the effect that Eq. (3-49) [unlike Eq. (3-48)] depends on the flow field through the term u(z ¼ rp). Because the gas velocity one particle radius away from the wafer is typically vanishingly small, interception effects are generally neglected in the following discussion, and Eq. (3-48) is used.
3.7.4 Particle traps/in situ nucleation Another source of wafer contamination is from particles that start somewhere between the plates, and are subsequently transported to the wafer. One example is particles generated in situ by nucleation. A second example is particles that are originally trapped between the plates during 11
The inclusion of particle interception effects is somewhat overkill, as we have neglected wafer surface roughness/structure which is likely characterized by dimensions similar to particle sizes.
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a plasma process, which are subsequently released at plasma extinction. While the plasma is on, contaminant particles generally accumulate in specific regions of the radio frequency (RF) discharge. Roth et al. [30] first used laser light scattering to observe that particles accumulate near the bulk plasma-sheath boundary in these discharges. Sommerer et al. [31] and Barnes et al. [32] first proposed that particle transport in the discharge is dominated by two forces: electrostatic and viscous ion drag. The electrostatic force accelerates negatively charged particles toward the center of electropositive plasmas, while viscous ion drag accelerates particles in the direction of net ion flux (generally toward plasma boundaries). Particle ‘‘traps’’ occur in regions where the sum of forces acting on the particle vanishes. In many cases these traps are approximately planar and parallel to the plates [33]; a schematic of a planar trap is shown in Figure 3.8, where the particles are uniformly distributed at a distance h above the lower plate. Only planar traps are considered in this work, although a variety of other trap structures (rings, domes, etc.) are well known in the literature. For any trap structure more complicated than an infinite plane the problem becomes inherently 2-D, which is beyond the scope of the present analysis. At the end of the process step, the discharge is extinguished and the plasma-induced forces responsible for particle trapping are assumed to dissipate rapidly (compared to particle transport times) in the afterglow. In this work, we assume that the charged particles are rapidly neutralized after the plasma extinction and can therefore be treated as neutral particles as experimentally observed by Jellum et al. [34], CL
Particle Trap R crit h
rp•• RW
Figure 3.8 Trap schematic. Diagram of particles in a planar trap located at a distance h from the lower plate; a critical trajectory is also shown for a particle which starts at radial position Rcrit and deposits at the wafer edge RW.
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FUNDAMENTALS
Shiratani et al. [35], and Yeon et al. [36].12 Under the assumption of rapid neutralization, the particles are released from the traps and can deposit on the wafer as a result of external forces, inertia, or Brownian motion (diffusion). To analyze the extent of deposition both the Lagrangian and Eulerian formulations have been used. Although the physical interpretation of efficiency (fraction of particles starting in the trap that end up on the wafer) is the same for both approaches, the methods of calculating the efficiency are quite different.
3.7.4.1 Efficiency for the Lagrangian formulation In the Lagrangian formulation, Brownian motion is neglected and calculation of particle trajectories is determined from the coupling between particle inertia and external forces. Consequently, the determination of a collection efficiency reduces to the determination of a critical trajectory just as defined in Eq. (3-47) of the previous section, except that the particle starting position is now at axial position h and the particle initial velocity is assumed to be zero. As before, it can be shown for our quasi-1-D case that the ratio Ri/Rf is independent of initial radial position within the trap. Thus, efficiency in the Lagrangian framework is calculated by starting the particle at a particular radial position (Ri ¼ 1) in the trap (z ¼ h) and calculating its trajectory to determine the radial position of contact with the wafer; the efficiency is then calculated by Eq. (3-47).
3.7.4.2 Efficiency for the Eulerian formulation For small particles and/or at low pressure, the effects of Brownian motion on particle transport must be considered. Brownian motion results from random variations in the force exerted on the particle by background-gas molecular bombardment, and gives rise to particle diffusion along concentration gradients. Also, Brownian motion implies that particle trajectories are no longer deterministic; that is, identical particles started at the same initial location with the same initial conditions will not follow the same path through the reactor. In this case, an Eulerian formulation of particle transport is used, in which the particles 12
However, a study by Collins et al. [37] suggests that some particles might retain a few residual charges (positive or negative) in the afterglow.
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are treated as a continuum or cloud and the particle concentration field is calculated (inertia is neglected). Particle deposition is determined in terms of a particle flux at the wafer’s surface, J0 (#/cm2/s), which is calculated from the surface concentration gradient (where particle interception is neglected): dn Eq. (3-50) Jo ¼ D dz z¼0 where n is the particle concentration and D is the particle diffusion coefficient. Note that a general expression for particle flux would include both a diffusional term, given by Eq. (3-50), and a drift-velocity term, given by nV~tp . In Eq. (3-50) only the diffusional term is shown because, under our assumption that particle concentration vanishes at surfaces, the drift-velocity contribution must also vanish at the susceptor. Thus, even when external forces are controlling deposition, a thin boundary layer must exist near the susceptor wherein the concentration drops from the free-stream value to zero at the susceptor’s surface. The particle collection efficiency is then calculated as the ratio of particle flux to the wafer divided by the particle source term (number of particles being released from the trap). Equation (3-50) can be extended to account for particle interception by evaluating the concentration derivative at rp (instead of zero): dn Eq. (3-51) Jo ¼ D dz z¼rp
3.7.4.3 External force limit As in the previous section, an analytical result can be derived for deposition efficiency in the limiting case where external forces control particle deposition (particle inertia, interception, and diffusion are all neglected): 2 jV tp j Rcrit 2 Ri ¼ ¼ t h¼ RW Rf jV p j þ juðz ¼ hÞj
V tp £ 0
Eq. (3-52)
which is the same as Eq. (3-48) except that the gas axial velocity at the trap location replaces the mean gas velocity in the denominator. For net drift velocities greater than zero (net external force pushing particles away from the wafer), no particle deposition on the wafer is predicted.
224
FUNDAMENTALS
Equation (3-52) provides a lower bound for particle deposition, as inertial and diffusional effects can only increase deposition from what is predicted. As expected, the collection efficiency tends toward unity as the particle trap moves closer to the lower plate (h0) because the axial gas velocity must approach zero at the plate surface. For particles which ultimately deposit on the wafer, Equation (3-52) also can be used to determine the radial position on the wafer at which particles are collected, Rf, based on starting position r ¼ Ri and z ¼ h. As discussed in the previous section, particles which deposit on the wafer are those which start nearest to the reactor centerline. It should be noted that both the Eulerian and Lagrangian collection efficiencies defined above must tend to Eq. (3-52) in the limit when particle diffusion, inertia, and interception effects are all negligible. Equation (3-52) can be extended to include particle interception as in the previous section: h¼
2 jV tp j þ juðz ¼ rp Þj t Rcrit 2 Ri ¼ ¼ V £0 jV tp j þ juðz ¼ hÞj p RW Rf
Eq. (3-53)
As before, particle collection is now predicted in the absence of (or for weak) external forces, and is seen to depend on the flow field through flow velocity terms in both the numerator and denominator. Both the Eulerian and Lagrangian collection efficiencies defined above must tend to Eq. (3-53) in the limit where particle diffusion and inertial effects are negligible.
3.7.5 Diffusion-enhanced deposition from traps or in situ nucleation One difference between these two particle–source scenarios is that the source term resulting from nucleation is continuous, while the source term for a plasma-trap release is a transient event characterized by the number of particles in the trap at the time of release. In either case, the particles of interest are likely to be quite small and chamber pressures may be low, so that the effect of particle Brownian motion must be considered. Although these very small particles are not currently considered to reduce yield, the trend towards smaller feature sizes on integrated circuits is continually reducing the size of a killer defect. Thus, the industry will inevitably be faced with the need to understand the role of diffusion in particle transport and deposition.
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The analysis of this section closely follows the previous work of Peters et al. [20] who investigated the diffusive deposition of particles onto disks in an infinite stagnation point flow (such as for a wafer exposed to the downward flow in a clean room). In their work, Peters and coworkers assume axisymmetric viscous stagnation point flow, while in this work an analytical asymptotic result for flow between two axisymmetric infinite parallel plates is used. Peters et al. also used different particle concentration boundary conditions than in this work: particle concentration was assumed to be zero at the disk and to approach a constant infinitely far away from it. Here, the two plates are considered perfectly absorbing (vanishing particle concentration), and a planar particle source is assumed to be located somewhere between them.
3.7.5.1 Problem definition We assume the geometry shown in Figure 3.9: axisymmetric flow between two infinite, parallel plates (a showerhead and a susceptor) separated by a distance S. The effect of jetting out of the showerhead holes is neglected, so that the flow is assumed to be uniformly distributed across the bottom of the showerhead with velocity, U0. The flow is assumed to be isothermal (constant gas properties), steady, laminar, incompressible, and viscous such that the quasi-1-D analytical result [Eq. (3-46)] can be used. As discussed, Eq. (3-46) is reasonably accurate for flow Reynolds numbers less than about four based on comparison to more accurate numerical finite-element simulations. The particles are assumed to enter the domain at a steady volumetric rate L (#/cm3/second) from a planar source located a distance h from CL SHOWERHEAD −Uo Particle Trap Λ
S z
h r
SUSCEPTOR
Figure 3.9 Geometry. Diagram of parallel, infinite-plate geometry with particles in a planar trap located at a distance h from the lower plate.
226
FUNDAMENTALS
the susceptor. Although this description adequately applies to a continuous source such as particle nucleation, it is not immediately obvious that a steady-state analysis is applicable to the transient case where a finite number of particles are simultaneously released from a trap at time t ¼ 0. Analysis of the governing equations reveals that the particle collection efficiencies from the steady-state and transient problems are in fact the same under the following conditions: (1) steady flow field, (2) infinite parallel-plate (1-D) domain, (3) radially uniform distribution of initial particle positions for the transient problem, and (4) radially uniform particle source for the steady-state problem. To confirm this contention, particle transport calculations using the present steady-state Eulerian approach have been compared with the Brownian dynamics simulations (BDS) of Choi et al. [38]. Choi and coworkers solved the Langevin equation directly using a massively parallel numerical Lagrangian particle tracking model which included a fluctuating Brownian force; transport calculations were presented for particles that were initially distributed in planar traps in a parallel-plate geometry similar to that assumed here. The BDS method is inherently transient in nature, in that a large number of particles were initially distributed uniformly throughout the trap, and their trajectories followed in time until the particles either deposited on a plate or left the calculation domain. For comparison with the present approach, Brownian dynamics simulations were performed with the analytical velocity field given by Eq. (3-46). As expected, BDS results for particle collection efficiency were in excellent agreement with the steadystate Eulerian formulation presented here. Thus, the analytical result for particle collection efficiency given below applies equally well for a steadystate particle planar source as for the case of a cloud of particles released from a planar trap.
3.7.5.2 Solution of the Eulerian particle transport equation Neglecting particle inertia, the Eulerian expression for particle concentration, n (#/cm3), is Eq. (3-33) which is reproduced here: qn þ UHn ¼ HDHnHðV tp nÞ þ L qt
Eq. (3-54)
where D (cm2/second) is the Stokes–Einstein particle diffusion coefficient, L (#/cm3/second) is the particle source term, and is the net drift velocity vector. Consistent with our flow assumptions, the concentration field is assumed to be steady and one-dimensional (depending only axial
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position). Also, for isothermal flow, the diffusion coefficient and particle drift velocity are constant. With these assumptions and simplifications, Eq. (3-33) may be rewritten as u
dn d 2n dn ¼ D 2 V tp þ L dz dz dz
Eq. (3-55)
In Eq. (3-55), V tp is the z-component of the net drift velocity vector and u is the axial velocity field given by Eq. (3-46). For boundary conditions, the assumption of perfectly absorbing walls is made which implies that the particle concentration is zero at both the upper and lower plates, i.e. n(z ¼ 0) ¼ n(z ¼ S) ¼ 0.13 Note that by assuming an absorbing surface at the showerhead we are neglecting the showerhead holes, but this is reasonable as the holes typically account for only a few per cent of the total showerhead surface. For this analysis, the particle source is assumed to be infinitely thin so that L ¼ Lh dðzhÞ
Eq. (3-56)
where Lh (#/cm2/second) is a constant area source term and d (cm1) is the Dirac delta function. Although the following derivation also could be followed for a finite-thickness source term, the resulting analytical expression for particle collection efficiency would be much more complicated than that given below. To nondimensionalize Eq. (3-55), the appropriate characteristic length and velocity scales are S and U0, respectively. A characteristic particle concentration, n0, can be defined based on the particle source strength and gas inlet velocity: n0 ¼
Lh U0
Eq. (3-57)
Using these definitions, Eq. (3-55) becomes: u~
d~ n 1 d2 n~ ~ t d~ n ~ V p þ dð~ ¼ z hÞ d~ z Pe d~ d~ z z2
Eq. (3-58)
where n~ ¼ n=n0 , u~ ¼ u=Uo , z~ ¼ z=S, V~ tp ¼ V tp =U0 , Pe¼SU0/D, and h~ ¼ h=S. As discussed above, the solution for the dimensionless 13
Deposition by interception, due to the finite size of the particle, is neglected. To account for interception requires that the boundary conditions be given as n(z ¼ rp) ¼ n(S rp) ¼ 0 where rp is the particle radius.
228
FUNDAMENTALS
~ concentration is completely determined by the dimensionless groups Pe, h, t ~ V p , and Re (which enters implicitly as u~ depends on Reynolds number). After defining a dimensionless concentration gradient d~ n G~ ¼ d~ z
Eq. (3-59)
equation (3-58) can be rewritten as dG~ ~ z hÞ Peð~ u þ V~ tp ÞG~ ¼ Pe dð~ d~ z
Eq. (3-60)
The solution to Eq. (3-60) is G~ ¼ G~ 0 expðAÞexpðAÞ
Zz~
~ Pedð~ z hÞexpðAÞd~ z
Eq. (3-61)
0
where
1 4 3 Re 1 8 7 9 4 13 3 t ~ Að~ z Þ ¼ Pe z~ ~ z þ z þ z~ z~ þ V p z~ z~ ~ 2 70 4 2 3
Eq. (3-62)
and G~ o is the dimensionless concentration gradient at the lower plate, z~ ¼ 0. Note that G~ o is frequently referred to as the Sherwood number, Sh z ¼ 0Þ ¼ (e.g., [20]). To determine G~ o , apply the boundary conditions ð~ n~ð~ z ¼ 1Þ ¼ 0 after integrating Eq. (3-59): Z1
d~ n d~ z¼ d~ z
0
Z1
Z1 d~ n¼0¼ 0
~ z Gd~
Eq. (3-63)
0
Solving Eq. (3-63) for G~ o gives
Eq. (3-64)
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3.7.5.3 Particle collection efficiency The particle collection efficiency is found as the ratio of particle flux to the lower plate divided by the total number of particles entering the reactor: dn DLh d~ n Aw D j dz z¼0 SU0 d~ z z~¼0 G~ 0 Eq. (3-65) ¼ ¼ h¼ RS Lh Pe Aw Lh dðzhÞdz 0
where Aw is the area in the r–u plane. Thus, an analytical result for the particle collection efficiency is given by Eqs. (3-64) and (3-65)—although the solution requires numerical quadrature. The dependence of the col~ V~ t , and Pe, is lection efficiency on the four dimensionless groups, Re, h, p clearly shown in Eqs. (3-64) and (3-65). For comparison to previous work in the literature, the particle collection efficiency defined by Eq. (3-65) can also be expressed as the ratio of the Sherwood to Peclet numbers, h ¼ Sh/Pe. The use of collection efficiency as the dimensionless number characterizing the deposition process is preferred to the Sherwood number for this application for two reasons: (1) determination of the collection efficiency is also straightforward for Lagrangian formulations to be applied to showerhead-enhanced inertial deposition in which critical trajectories can be calculated and (2) efficiency is a commonly accepted concept within the semiconductor industry (e.g., yield). In practical terms, an efficiency of unity indicates that all particles in the chamber are depositing on the wafer, while an efficiency of zero indicates that no particles are depositing on the wafer.
3.7.5.4 Particle flux The particle deposition rate on the wafer is found as the product of collection efficiency times the number of particles released from the trap (or generated by nucleation): J0 ¼ D
dn DLh d~ n G~ 0 ¼ Lh h ¼ jz~¼0 ¼ Lh Pe dz SU0 d~ z
Eq. (3-66).
When the nature of the source term Lh is not known, the best strategy for reducing the number of defects on a wafer is to choose conditions that inhibit particle transport to the wafer, i.e., minimize the collection
230
FUNDAMENTALS
efficiency. One potential weakness of this strategy is if process conditions selected to reduce the collection efficiency result in a corresponding increase in the particle generation rate; this possibility is certainly of concern for particle nucleation.
3.7.6 Nondimensional results This section presents calculations of particle collection efficiency using numerical quadrature of Eqs. (3-64) and (3-65) based on a fourth-order Runge–Kutta technique with automatic error control. Both local and global error control parameters can be set, and convergence tests showed that the resulting integrals were unchanged in the fifth place when these parameters were set to 1010. Efficiency is found to be a function of four ~ V~ t , and Pe (a fifth—the interception dimensionless parameters: Re, h, p parameter dp/S—is neglected in this work). Calculations of particle collection efficiency versus Peclet number are shown in Figure 3.10 for creeping flow (Re ¼ 0) for three attractive forces (characterized by V~ tp ¼ 0:1; 0:5; and1:0), for no external force (V~ tp ¼ 0), and for three repulsive forces (V~ tp ¼ 0:1; 0:5; and1:0). Plots are shown for three different trap heights, where the particles are trapped: (a) near the wafer (h/S ¼ 0.1), (b) midway between the wafer and showerhead (h/S ¼ 0.5), and (c) near the showerhead (h/S ¼ 0.9).
3.7.6.1 Efficiency at intermediate Peclet numbers Although the small- and large-Pe asymptotic limits for the collection efficiency are well described by analytical expressions, the shape of the collection efficiency curves for intermediate Peclet numbers can be quite complex and requires the full numerical integration of Eqs. (3-64) and (3-65). For example, while the efficiency-curve transition between the small- and large-Pe asymptotic limits is generally monotonic (e.g., Figure 3.10a for V~ tp > 0 or Figure 3.10c for V~ tp < 0:5), in some cases there may be a local minimum (e.g., Figure 3.10a for V~ tp ¼ 0:1) or maximum (e.g., Figure 3.10c for V~ tp ¼ 0:1). The exact shape of the efficiency ~ V~ t , and curve depends on the magnitudes of the three parameters, h, p Pe, and although the interaction among them can be complex, a few simple observations can be made. First, moving the particle trap away ~ always tends to lower the collection from the wafer (i.e., increasing h) efficiency. Although this effect is most notable for low or intermediate
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–1 –0.5
EFFICIENCY
0.8 –0.1
h˜ = 0.1 0.6
Re = 0
0.4
V˜ pt = 1.0
0.5
0.1
0
0.2 0
(b)
.01
.1
1
10
100
104
103
104
103
104
1.0
h˜ = 0.5
0.8
V˜ pt = –1.0
Re = 0 EFFICIENCY
103
0.6 –0.5
0.4 1.
0 .5
0
0.2
–0.1
0. 1
0
0
(c)
.01
1
10
100
1.0 0.8
EFFICIENCY
0.1
h˜ = 0.9 Re = 0
0.6
V˜ pt = –1.0
0.4
–0.5
0.2 0
–0.1 1
.01
0.1
1
0.5
0
0.1
10 Pe
100
Figure 3.10 Efficiency vs. Pe for various deposition velocities. Figures show calculated efficiencies for particles starting in traps at: (a) h/S ¼ 0.1, (b) h/S ¼ 0.5, and (c) h/S ¼ 0.9.
Pe values where diffusional effects are strong, it is also true for large Pe values where deposition is controlled by external forces. The latter ~ claim is supported by noting that gas velocity at the trap location, u~ðhÞ, increases with increasing distance from the wafer so that collection
232
FUNDAMENTALS
efficiency decreases. Trap manipulation can be accomplished in practice under some conditions. For example, in plasma processing, the trap location is determined by process parameters such as pressure, rf (radio frequency) power, and flow rate; while these parameters may be fixed during etching by process requirements, they could be adjusted to manipulate the particle trap location just prior to plasma extinction. Similarly, trap position when particle nucleation is present could be controlled by pressure, wall temperature, flow rates, or chemistry selections. Second, reducing the dimensionless attractive external force or increasing the dimensionless repulsive force always lowers the collection efficiency. This trend is clearly evident in Figure 3.10 for intermediate and large Peclet numbers, although the benefit becomes less significant at low Pe where diffusion dominates deposition. It is interesting to note that for attractive forces such as gravity (wafer facing up) or thermophoresis (wafer cooler than the surrounding gas), the dimensionless drift velocity increases as pressure is decreased (for constant U0). In this case, the tendency toward processing at lower pressures ultimately must lead to an increase in the fraction of particles which end up on the wafer. If a process recipe is selected that maintains the wafer warmer than its surroundings, however, the drift velocity resulting from this repulsive external force will increase with decreasing operating pressure (for constant U0) and thereby reduce the fraction of particles depositing on the wafer. To explore the effect of Reynolds number on collection efficiency, calculations were made for Reynolds numbers of 0 and 8 using the analytical approximation for the flow field given in Eq. (3-46);14 the results are shown in Figure 3.11. As shown, even this relatively large variation in Re (spanning the Re range of the majority of low pressure commercial tools) produces only modest variations in the collection efficiency. Reynolds number effects are most apparent in the large-Pe limit for attractive forces. This effect can be quantified by noting that: (1) the large-Pe effi~ ciency limit of Eq. (3-52) depends on gas velocity at the trap location, u~ðhÞ, ~ and (2) the value of u~ðhÞ changes from 0.5 at Re ¼ 0 to a value of 0.625 ~ associated with Re being increased at Re ¼ 8. This 25% increase in u~ðhÞ from 0 to 8 leads to an approximately 25% decrease in collection efficiency ~ As V~ t is increased to a u ðhÞj. for a weak attractive force, i.e. jV~ tp j<<j~ p ~ magnitude comparable to u~ðhÞ, this effect diminishes; for example, for V~ tp ¼ 1 the efficiency for Re ¼ 8 is only 8% less than for Re ¼ 0. 14 Note that Re ¼ 8 is beyond the range over which the analytical approximation was found to be accurate, but the analytical result is used here beyond its range to qualitatively investigate any Reynolds number dependencies.
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1.0 h˜ = 0.5
EFFICIENCY
0.8
Re = 0 Re = 8 V˜pt = –1.0
0.6 –0.5
0.4
–0.1
1.0
0.2
0.1
1
10 Pe
0.1
0.5
0 .01
0
100
103
104
Figure 3.11 Efficiency vs. Pe for various deposition velocities. Figures show calculated efficiencies for Re ¼ 0 and 2 (h/S ¼ 0.5).
For small Peclet numbers, the effect of Reynolds number vanishes for all values of the external force. In this case, particle transport by diffusion dominates convective transport, so that the collection efficiency is decoupled from the details of the flow field. Figure 3.11 also shows that Reynolds effects are negligible in the presence of repulsive external forces; although this conclusion is true in an absolute sense, Reynolds number effects do become important in a relative sense for larger Peclet numbers where the collection efficiency becomes small. For example, for V~ tp ¼ 1:0 and a Pe ¼ 15, the collection efficiency for Re ¼ 8 (h ¼ 3.18 · 103) is approximately 50% larger than that for Re ¼ 0 (h ¼ 2.11 · 103). While such differences may not be detectable at low particle concentrations, the difference in the number of particles depositing on the wafer may become quite large when particle concentrations are high—such as is typical of systems in which particle nucleation is occurring.
3.7.7 Dimensional results This section presents several example calculations of collection efficiency in dimensional terms when gravity and diffusion act simultaneously. The solution scheme described in the previous section is
234
FUNDAMENTALS
again used here, except that the dimensional inputs are first converted into the required nondimensional groups before the numerical integrations are performed. The particle diameter replaces the Peclet number as the independent variable in all of the following. All of the examples assume a 200 mm diameter with a showerhead-to-wafer gap of 2.54 cm. For these calculations, a baseline process is taken as argon flowing at a mass flow rate of 1000 sccm (standard cubic centimeters per minute) at a pressure of 1 torr and temperature of 300 K. Constant gas properties are assumed (isothermal flow) along with a particle density of 1 g/cm3. The Reynolds number for these conditions is 0.984, which indicates viscous dominated flow and is well inside the range for which the analytical flow field expression can be used. In the following examples, trap height, pressure, flow rate, and pressure are individually varied about the baseline value. Note that these parameters may not be independent; for example, trap height may depend on both pressure and gas flow rate. Finally, the section concludes with a demonstration of the reduction in deposition that can be obtained by introducing a force that opposes deposition, such as heating the wafer relative to the showerhead to take advantage of thermophoretic protection.
3.7.7.1 Trap height effects Plots of calculated particle collection efficiency as a function of particle size are shown in Figure 3.12 for dimensionless trap heights of 0.1, 0.3, 0.5, 0.7, and 0.9. All of the curves exhibit a minimum near 0.1 mm, with increasing efficiency for both smaller and larger sizes. This shape has commonly been reported in previous deposition studies: for example, see Figure 3 of [39] which shows the net stagnation-point drift velocity based on additivity of convective-diffusion, electrostatic, and gravitational velocities. In Figure 3.12, the increase in efficiency below 0.1 mm is associated with increasing diffusional deposition, while the increase in efficiency above 0.1 mm is associated with increasing gravitational deposition. Note that in the present geometry the diffusional branch does not increase without bound, but instead asymptotically approaches ~ As seen in Figure 3.12, however, this the highly diffusive limit h!1h. limit is not quite achieved even for particles as small as 0.001 mm. As expected based on the previous discussion in nondimensional terms, the trapping height plays a key role in net particle deposition. Clearly, it is always advantageous to manipulate the particle trap to a location as far from the wafer as possible. It is clear from Figure 3.12 that as the size of
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EFFICIENCY
1
10-1
10-2
h˜ = 0.1
ρp= 1. g/cc 1000 sccm Argon S=2.54 cm T=300 K P=1 torr
10-3 .001
0.3 0.5 0.7 0.9 0.01
0.1
1
dp (µm)
Figure 3.12 Efficiency vs. particle diameter and trap position (isothermal case). Collection efficiencies for particle transport over a 200 mm wafer including gravitational settling and diffusion for dimensionless trap locations of 0.1, 0.3, 0.5, 0.7 and 0.9 (S ¼ 2.54 cm, Q ¼ 1000 sccm argon, P ¼ 1 torr, T ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3).
IC-killing particles shrinks below 0.1 mm that particle collection efficiencies will climb as a result of increased particle diffusion.
3.7.7.2 Pressure effects Plots of calculated particle collection efficiency as a function of particle size are shown in Figure 3.13 for reactor pressures of 1, 10 100, and 760 torr. For these calculations the mass flow rate is held constant at the baseline value of 1000 sccm, and the trap height is assumed to be 1.27 cm which is exactly half-way between the wafer and showerhead. As before, all of the curves show the characteristic ‘‘U’’ shape resulting from the combination of deposition from convective-diffusion and gravitational settling. It is evident, however, that the diffusional branch of the efficiency curves is independent of pressure for this example. This result is explained by considering that the Peclet number (which along with geometry completely specifies the convective-diffusive problem) depends on the ratio of inlet gas velocity to the particle diffusion coefficient, and that both of these quantities are inversely proportional to pressure at a constant mass flow rate. The pressure dependence of the
236
FUNDAMENTALS
10-1
0t or r
ρp= 1. g/cc 1000 sccm Argon S=2.54 cm h=1.27 cm T=300 K
76
EFFICIENCY
1
00
1
10-2
rr
to
10
rr
to
<
10-3 .001
0.01
dp (µm)
0.1
1
Figure 3.13 Efficiency vs. particle diameter and pressure (isothermal case). Collection efficiencies for particle transport over a 200 mm wafer including gravitational settling and diffusion for reactor pressures of 1, 10, 100, and 760 torr (S ¼ 2.54 cm, Q ¼ 1000 sccm argon, h ¼ 1.27 cm, T ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3).
diffusion coefficient is evident in the free molecule limit given in Eq. (3-36), which applies at low pressures and for small particle size. The velocity used in scaling the problem, U0, is the lineal gas velocity at the reactor pressure, and for a presumed constant mass flow rate this also must scale inversely proportional to pressure. Thus, the collection efficiency resulting from particle diffusion is nearly independent of pressure for a fixed gas mass flow rate. The branch of the efficiency curve resulting from gravitational settling is also seen to be independent of pressure below 10 torr. This result is explained by considering the limiting expression for external- force domi~ is ~ and V~ t . The term u~ðhÞ nated deposition, which depends only on u~ðhÞ p independent of pressure as it depends only on trap position and Reynolds number (see Eq. (3-46)), and as at constant mass flow rate the Reynolds number is independent of pressure. In the free molecule limit given by Eq. (3-28), the gravitational drift velocity, V~ p varies inversely with pressure so that its ratio to the inlet velocity, V~ tp , must also be independent of pressure. Thus, all of the terms describing the collection efficiency are independent of pressure in the particle free molecule limit. As pressure increases above 10 torr and for particles larger than 1 mm, however, the free molecule limit for the settling velocity no longer applies and the full expression of Eq. (3-26) must be used. As the particle mean free path decreases, the inverse pressure dependence of the dimensional
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settling velocity diminishes, until the continuum regime limit Eq. (3-27) is reached which is independent of pressure. As V tp becomes independent of pressure, V~ tp becomes proportional to pressure, resulting in the marked increase in collection efficiency with pressure as seen in Figure 3.13 for larger particles and at higher pressures.
3.7.7.3 Mass flow rate effects Plots of calculated particle collection efficiency as a function of particle size are shown in Figure 3.14 for argon mass flow rates of 10, 100, and 1000 sccm. For these calculations the reactor pressure is held constant at the baseline value of 1 torr, and the trap height is assumed to be 1.27 cm (half-way between the wafer and showerhead). As before, all of the curves show the characteristic ‘‘U’’ shape resulting from the combination of deposition from convective-diffusion and gravitational settling. These results show that the collection efficiency is a strong function of gas mass flow rate except for very small particle sizes, for which diffusion dominates and all curves must tend toward the same limit. Note that the point at which the diffusion-dominated limit is achieved varies with mass flow rate: for the lowest flow rate of 10 sccm the limit (h ¼ 0.5) is reached 100
EFFICIENCY
10 sccm 10-1 100 sccm
10-2
10-3 .001
= 1. g/cc Argon S=2.54 cm h=1.27 cm T=300 K P=1 torr p
1000 sccm
0.01
0.1
1
dp ( m)
Figure 3.14 Efficiency vs. particle diameter and flow rate (isothermal case). Collection efficiencies for particle transport over a 200 mm wafer including gravitational settling and diffusion for gas mass flow rates of 10, 100, and 1000 sccm argon (S ¼ 2.54 cm, Q ¼ 1000 sccm argon, P ¼ 1 torr, T ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3).
238
FUNDAMENTALS
for particles less than about 0.01 mm, while at the highest flow rate of 1000 sccm the collection efficiency is still below the limit for 0.001 mm. Thus, a significant reduction in particle collection efficiency can be achieved by increasing the mass flow rate at constant pressure. The effect of mass flow rate on the actual number of particles depositing on the wafer is less obvious. For example, consider the case in which the mass flow rate is increased from 100 to 1000 sccm. Although the collection efficiency drops by approximately a factor of 10, the flow increases by a factor of 10, so that if the number of particles entering the domain scales with flow rate, then the total number of particles depositing on the wafer should be about the same for the two flow rates. If, however, the number of particles present is independent of the flow rate, then increased flow rates should reduce the number of particles on the wafer. For calculations where pressure is fixed, it should be noted that the Reynolds number increases proportionately with mass flow. However, even at the highest flow rate considered, 1000 sccm, the Reynolds number is less than one and the analytical flow approximation is excellent.
3.7.7.4 Effect of thermophoresis This section explores the role of thermophoresis in determining particle collection efficiency. For these calculations the showerhead temperature has been held constant at 300 K, and the wafer temperature varied to produce a temperature gradient that drives thermophoretic deposition. To accommodate our assumption of constant properties, only small temperature differences are considered. Plots of calculated particle collection efficiency as a function of particle size are shown in Figure 3.15 for wafer temperatures of 280, 290, 300, 310, and 320 K. The baseline conditions described above are used for all of these calculations: reactor pressure of 100 mtorr, argon mass flow rate of 1000 sccm, wafer-to-showerhead gap of 2.54 cm, and the trap height is assumed to be 1.27 cm. A particle of density 1 g/cm3 was assumed, and the ratio of the gas to particle thermal conductivity was taken as 0.02 to approximate a fused silica particle. As before, all of the curves show the characteristic ‘‘U’’ shape resulting from the combination of deposition from convective-diffusion and external forces, where the net external forces contain contributions from both gravitational and thermophoretic forces. The minimum collection efficiency for the case of thermophoretic protection (wafer hotter than showerhead) becomes vanishingly small and so is not shown; note that even for thermophoretic protection the
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1
EFFICIENCY
10-1
Twafer = 280 K 290 K
-2
10
300 K
10-3
p = 1. g/cc 1000 sccm Argon S=2.54 cm h=1.27 cm P=100 mtorr
10-4 .001
0.01
310 K 320 K
0.1 d p ( m)
310 K 320 K
1
10
Figure 3.15 Efficiency vs. particle diameter and wafer temperature. Collection efficiencies for particle transport, including gravity, thermophoresis and diffusion for wafer temperatures of 280, 290, 300, 310, and 320 K (200 mm wafer, 1000 sccm argon, S ¼ 2.54 cm, h ¼ 1.27, P ¼ 100 mtorr, Tshowerhead ¼ 300 K, and particle density ¼ 1 g/cm3).
collection efficiency never reaches absolute zero as there always is some contribution from diffusion/convection. A key result of these calculations is that even modest temperature differences can lead to dramatic changes in collection efficiency. For example, deposition is nearly eliminated in the 0.1–1.0 mm range when the wafer is kept only 10–20 C warmer than the showerhead. On the other hand, the collection efficiency increases by an order of magnitude when the wafer temperature is decreased 10 C as compared to the isothermal case. In addition, when the wafer temperature is kept below the showerhead temperature, the depth of the collection efficiency minimum at about 0.1 mm becomes shallower; this results from the fact that the thermophoretic drift velocity is nearly independent of particle diameter as indicated by Eqs. (3-30) and (3-31). These calculations clearly demonstrate the importance of keeping the wafer warmer than its surroundings at all times.
3.7.8 Summary: diffusion-enhanced deposition This section explored particle deposition resulting from external forces and Brownian motion in a parallel-plate geometry characteristic of a
240
FUNDAMENTALS
wide range of semiconductor process tools. The need to properly account for diffusion-enhanced particle deposition becomes increasingly important as the semiconductor industry moves toward smaller feature sizes and becomes concerned with smaller-sized particles. Particle transport was modeled using the Eulerian approach of Section 3.6, so that the continuum convective-diffusion equation was solved for particle flux. One strength of the Eulerian formulation is in predicting particle transport resulting from the combination of applied external forces (including the fluid-drag force) and the chaotic effect of particle Brownian motion (i.e., particle diffusion), although the current implementation neglected particle inertia. Furthermore, particles were assumed to originate in a planar trap located between the plates, and only transport in the interplate region was considered (showerhead acceleration was neglected). Flow between infinite parallel plates was assumed as described by the quasi-1-D creeping flow approximation, where the showerhead was treated as a porous plate. The key result of the analysis of this section was the derivation of expressions for the particle collection efficiency—which is the fraction of trapped particles which end up on the wafer. An analytical, integral expression was derived that gives the particle collection efficiency as a ~ V~ t , and Pe (a fifth— function of four dimensionless parameters: Re, h, p the interception parameter dp/S—was neglected). The first parameter, the Reynolds number, completely specifies the flow field under the present assumptions. The second parameter, the dimensionless trap height, h~ ¼ h=S, specifies the position of the particle source term. The influence of external forces enters through the third parameter, the dimensionless particle drift velocity, V~ tp ¼ V tp =U0 , which is defined as the z-component of the net drift velocity. The fourth parameter is the particle Peclet number, Pe ¼ SU0/D, which is a measure of the relative importance of particle Brownian motion. In the free molecular limit the Peclet number is proportional to diameter squared, so that Pe1/2 can be thought of as a dimensionless particle size. Numerical quadrature of Eqs. (3-64) and (3-65) using a fourth-order Runge–Kutta technique was used to calculate particle collection efficiency in terms of the controlling dimensionless parameters. Initial calculations showed the numerical results to be in good agreement with the various analytical limits, providing confidence in the current implementation. In general, the highly diffusive limit was approached for Peclet numbers less than about 0.1, while the nondiffusing limit was essentially reached for Peclet numbers larger than 102 or 103 depending on the strength of the external force and the initial particle trapping position.
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For intermediate Peclet numbers, the shapes of the collection efficiency curves were often found to be complex; for example, some conditions gave efficiency curves which showed local minima or maxima. Despite this complexity, a few simple observations were made: moving the par~ always lowered the ticle trap away from the wafer (i.e., increasing h) collection efficiency, as did reducing the attractive external force or increasing the repulsive force. Finally, calculations made for Reynolds numbers of 0 and 8 showed only modest variations in particle collection efficiency, suggesting that this parameter plays only a minor role over the range likely to be encountered in realistic processing environments. Example calculations of collection efficiency were presented in dimensional terms for one representative set of process conditions (200 mm wafer, showerhead-to-wafer gap of 2.54 cm, mass flow rate of 1000 sccm argon, 1 torr, 300 K). In all cases, the efficiency curves exhibited a minimum near 0.1 mm, with increasing efficiency for both smaller and larger sizes. Trapping height was found to play a key role in deposition, and in all cases it was advantageous to manipulate the particle trap to a location as far from the wafer as possible. Trap manipulation can be accomplished in practice under some conditions. For example, in plasma processing, the trap location is determined by process parameters such as pressure, rf power, and flow rate; while these parameters may be fixed during etching by process requirements, they could be adjusted to manipulate the particle trap location just prior to plasma extinction. Similarly, trap position when particle nucleation is present could be controlled by pressure, wall temperature, flow rates, or chemistry selections. At constant mass flow rate, collection efficiency was found to be independent of pressure for the low pressures and small particle sizes of interest. At constant pressure, collection efficiency was found to decrease significantly with increasing mass flow rate. Thus, from a particle transport point of view, reduction of particle-on-wafer counts could be obtained by increasing the mass flow rate in a process, assuming particle concentration varies inversely with mass flow rate rather than remaining independent. Another key result was that even modest temperature differences can lead to dramatic changes in collection efficiency due to the thermophoretic force. For example, deposition is nearly eliminated when the wafer is kept only 10–20 C warmer than the showerhead. On the other hand, the collection efficiency increases by an order of magnitude when the wafer temperature is decreased 10 C below the showerhead temperature. Caution is suggested in implementing any of these strategy as the effect on the particle source term is not known.
242
3.8
FUNDAMENTALS
Inertia-Enhanced Deposition
The use of a showerhead restricts the area available to the flow inside the showerhead; consequently, the velocity of the gas inside the holes is much larger than the face velocity in the gap below. Particles originating upstream of the showerhead and suspended in the flow can be dramatically accelerated while passing through the showerhead, so that, at the exit of the showerhead, particle velocities much larger than the fluid face velocity are possible. Depending on conditions, particle acceleration by the showerhead can lead to inertia-enhanced particle deposition on the wafer below. Thus, a complete description of particle deposition on a wafer in a parallel-plate reactor must include a description of particle transport through the showerhead as well as an analysis of particle transport in the inter-plate region. This section explores the role of inertia-enhanced deposition using the Lagrangian particle transport formulation given in Section 3.3. The strength of the Lagrangian formulation is in predicting particle transport resulting from the combination of applied external forces and particle inertia; the current implementation does not account for particle diffusion. The problem is separated into two domains in which particle and fluid transport are determined:(1) within a showerhead-hole and (2) between the showerhead and susceptor.
3.8.1 Particle transport in the showerhead holes Particles are assumed to be evenly distributed across the showerhead hole inlet and to enter with zero radial velocity and with an initial axial velocity equal to the face velocity U0. The particle will immediately see a fluid velocity Ujet(r), and will either be accelerated or deaccelerated by fluid drag depending on the magnitude of Ujet. Because of inertia, however, the particle will require a finite time to respond: in particular, the particle will accelerate to Ujet only if the showerhead hole is sufficiently long or the particle sufficiently small. In practice, the particle velocity at the exit of the showerhead, Vpo, will fall somewhere between U0 and Ujet; depending on the relative magnitudes of these two velocities, the showerhead thickness, and the particle relaxation time t. Assuming fully developed flow at the inlet and neglecting lift forces, the particle will remain at its initial radial position while in the tube; consequently, the axial fluid velocity driving the particle through the tube will also remain constant during the traverse. For plug flow, all
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particles will be accelerated by the same fluid velocity, U jet , independent of radial starting position. For fully developed parabolic flow, the local fluid velocity for each particle will depend on its starting position; particles near the wall will be slowed by drag, while particles near the centerline will be significantly accelerated. For parabolic flow, the assumption that the particles are evenly distributed (i.e., that the particle flux is constant) across the tube inlet is based on the assumption that the fluid entrance length is so short that particles do not have time to migrate radially as the flow is developing.15 The problem of a particle of given initial velocity experiencing a stepfunction change in the local fluid velocity is a classic problem. Although the problem could be solved in dimensional form, it is convenient for matching with the second part of this analysis if we solve the nondimensionalized particle equations of motion, Eqs. (3-19) and (3-20). As stated previously, we choose the mean chamber axial velocity U0 as the characteristic velocity and the inter-plate spacing S as the characteristic length scale. External forces are assumed negligible compared to the large drag forces encountered in the showerhead holes. Given a particle of Stokes number St entering the hole with initial velocity U0, and an axially constant fluid velocity Ujet(r), Eqs. (3-19) and (3-20) can be solved analytically for the particle velocity at the showerhead exit, z ¼ L: L Ujet Ujet t~ 1 eSt 1 ¼ t~ þ St U0 U0 S ~t Vpo Ujet Ujet ¼ 1 eSt U0 U0 U0
Eq. (3-67)
Eq. (3-68)
The solution procedure is as follows: (1) calculate Ujet/U0, L/S, and St from process and particle parameters, (2) solve Eq. (3-67) for the dimensionless time t~, and (3) use t~ in Eq. (3-68) to solve for the dimensionless particle velocity at the showerhead exit. Equation (3-67) must be solved iteratively; for this purpose we use a Newton root-finding technique. Some complexity has been added to Eqs. (3-67) and (3-68) by our use of one characteristic length and one characteristic velocity for both the showerhead and parallel-plate domains. An interesting result is found if 15
An alternate assumption is that the particles follow streamlines, in which case the particle concentration is constant across the tube inlet so that the local flux of particles through the tube depends on radial position.
244
FUNDAMENTALS
L and Ujet (natural choices for characterizing transport through the showerhead) are substituted for S and U0 as the characteristic length and velocity. With the appropriate redefinitions of the nondimensional terms, a set of equations similar to Eqs. (3-19) and (6.20) can be derived that depend on the jet Stokes number, which is related to our earlier definition by: Stjet ¼
tUjet Ujet S ¼ St L U0 L
Eq. (3-69)
Using the same assumptions and initial conditions as above, we can derive a set of equations analogous to Eqs. (3-67) and (3-68) that are independent of L/S, i.e. Vpo/Ujet ¼ f(Ujet/U0, Stjet). In addition, the functional dependence on the velocity ratio Ujet/U0 is very weak (entering only as a result of the assumption that the initial particle velocity is U0), and vanishes for the limiting case where Ujet/U0 >> 1 (which includes the case where the particle initial velocity is zero). In this limiting case, the ratio of the showerhead-exit velocity of the particle to Ujet depends only on the jet Stokes number. This result suggests plotting the results of Eqs. (3-67) and (3-68) as Vpo/Ujet against Stjet—such as shown in Figure 3.16. As can be seen, the dimensionless particle velocity at the exit of the showerhead, Vpo/Ujet, is reasonably insensitive to the velocity ratio when Ujet/U0 > 10.
Vpo / Ujet = (Vpo /Uo)(Uo /Ujet )
1.0
0.8 0.6
Ujet /Uo = 2
0.4 5 10
0.2
50,100 0.0
0
20
40 60 Stjet = St (Ujet /Uo)(S/L)
80
100
Figure 3.16 Acceleration of particles through the showerhead. Dimensionless velocity of particles exiting showerhead tubes, Vpo/Ujet, as a function of jet Stokes number, Stjet, for a range of velocity ratios (Ujet/U0 ¼ 2, 5, 10, 50, and 100).
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Thus, the analysis of particle transport in the showerhead domain is complete: given the three inputs U jet =U0 , L/S, and St (and particle initial radial position to determine Ujet(r) for parabolic flow), we can calculate the dimensionless velocity Vpo/U0 at which the particle exits the showerhead. Interestingly, both the mean velocity ratio and the length ratio depend only on reactor geometry; process conditions such as temperature, pressure, or flow rate enter only through the Stokes number. Thus, for a given Stokes number, the extent of particle acceleration in the showerhead is entirely determined by hardware and is thus a characteristic of a specific tool design. Finally, in moving to the calculation of particle trajectories between the plates, the sign of the particle velocity Vpo/ Ujet must be switched to account for the different coordinate systems used in the two domains (see Figure 3.5b and the inset).
3.8.2 Particle transport between parallel plates In this section, a Lagrangian formulation is used to calculate particle trajectories in the inter-plate region using both numerical FIDAP and analytical solutions of the flow field. Under the present assumptions, four dimensionless parameters uniquely determine particle transport in the inter-plate region: Re, St, Vpt/U0, and Vpo/U0 (a fifth—the interception parameter dp/S— is neglected in this section). The first parameter, the Reynolds number, completely specifies the flow field for the infinite parallel-plate geometry—as demonstrated in the analytical low-Re approximation to the flow field given in Eq (3-46). For a finite-plate geometry, the aspect ratio is also needed to specify the flow. The second parameter, the particle Stokes number, is used in this work as a dimensionless particle diameter—as suggested by the free molecule limit Eq. (3-23). The influence of external forces enters through the third parameter, the dimensionless particle drift velocity, which parameterizes the forces via the z-component of the net drift velocity, Vpt. The fourth parameter, the dimensionless particle velocity at the showerhead exit, is determined by the strength of the showerhead acceleration effect as described in Section 3.8.1. Initially, however, Vpo/U0 will be taken as an independent variable; later, we discuss the coupling of the showerhead and parallel-plate domains. The effect of the these dimensionless parameters is shown in Figure 3.17, where particle collection efficiency is plotted against Stokes number for Re ¼ 8. For Figure 3.17a, an initial dimensionless particle velocity Vpo/U0 ¼ 1 is assumed (no particle showerhead acceleration), while in
246
FUNDAMENTALS 1.0
a)
Re = 8 Vpo /Uo = -1
EFFICIENCY
0.8
0.6 Vpt /Uo = -0.5
0.4
0.2
0
-0.1 0 0.1
-0.01 .01
.1
St
1.0
1
10
1.0
b)
EFFICIENCY
0.8
Re = 8 Vpo /Uo = -100
0.6
0.4
Vpt /Uo = -0.5
0.2 -0.1 0 .001
-0.01
0 .01
1.0 .02
St
Figure 3.17 Efficiency vs. Stokes number for various deposition velocities for Re ¼ 8. Solid lines are calculated using an analytical flow field and a Runga–Kutta integrator, while the symbols are calculated using numerical flow solutions and the FIDAP particle tracking post-processing routines. (a) Particle dimensionless initial velocity of 1 and (b) particle dimensionless initial velocity of 100.
Figure 3.17b the initial velocity is taken as -100 (substantial showerhead acceleration characteristic of commercial reactors). In each plot the influence of external forces is explored by varying the drift velocity: curves for Vpt/U0 ¼ 0.5, 0.1, 0.01, 0, 0.1, and 1.0 are shown. Negative values of the drift velocity correspond to an external force
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directed toward the wafer (attractive, enhancing deposition), while positive values correspond to an external force directed away from the wafer (repulsive, inhibiting deposition). Several important features of these plots will now be explored. First, inertial effects lead to particle deposition even in the absence of external forces as shown by the curves for Vpt/U0 ¼ 0 in Figure 3.17. In this case there is a critical Stokes number, Stcrit, below which no deposition occurs. At Stcrit there is a sharp jump in efficiency, which then increases toward unity with increasing St. The jump is steeper, higher (approaching unit collection efficiency) and occurs for a much smaller Stcrit in the case with substantial showerhead acceleration than when the particles enter with the fluid face velocity. This effect is discussed in greater detail below. As seen in Figure 3.17, particle inertia can also lead to deposition even when an external force is pushing particles away (Vpt/U0 > 0). The extent of external force ‘‘protection’’ is significantly reduced for large initial velocities: compare the Vpo/U0 ¼ 0 and 1 curves in Figure 3.17a and b. Second, when an external force is directed toward the wafer (Vpt/U0 < 0), particle deposition occurs at all values of the Stokes number. In the small-St limit (negligible particle inertia), the collection efficiency should tend to Eq. (3-48) for external forces that can be described by a potential; this trend is clearly evident in Figure 3.17. For example, for Vpt/U0 ¼ 0.5, Eq. (3.48) predicts an efficiency of 1/3 which is the observed asymptote of the appropriate curves in Figure 3.17a and b. The presence of an attractive external force smooths the shape of the efficiency curves for large attractive forces; however, when the magnitude of the attractive force is small (e.g., Vpt/U0 ¼ 0.1), the efficiency still exhibits a sharp increase in the neighborhood of Stcrit (from the no-force case). The rise in efficiency near Stcrit is much steeper for high initial particle velocities. Finally, in the large-St limit, the collection efficiency must approach unity for all cases. That is, for large enough Stokes numbers, particle inertia leads to straight trajectories and complete deposition independent of the details of the flow field, the external forces, or particle initial velocity (assuming it is not zero). This limit is approached in all of the calculations shown in Figure 3.17.
3.8.2.1 Asymptotic limit of critical Stokes number An interesting result is suggested by Figure 3.17b for the case of no external force: as the particle initial velocity becomes large, the collection
248
FUNDAMENTALS
efficiency tends toward a step function which jumps from zero to unity at a critical Stokes value equal to the inverse of the dimensionless initial particle velocity. To confirm this result, a series of calculations were made to explore the dependence of the critical Stokes number on initial particle velocity in the absence of an external force. These results are shown in Figure 3.18, where Stcrit is plotted as a function of Vpo/U0 for fluid Reynolds numbers of 0, 4, and 8. For a given value of Vpo/U0, particles with St < Stcrit (below the line) will exit the reactor, while particles with St > Stcrit (above the line) will impact the reactor. The effect of Reynolds number is negligible for large values of Vpo/U0; in fact, for Vpo/U0 > 10 the three Re curves approach the same asymptotic limit. For large values of Vpo/U0 particle inertia dominates deposition and the details of the flow field become unimportant. Inspection of the large initial-velocity asymptotic limit reveals the following relationship: Stcrit !
Uo Vpo
Eq. (3-70)
A simple explanation of this limit is readily illustrated by rearranging Eq. (3-70) to give StcritVpo/U0 ¼ t Vpo/S ¼ 1, which states that impaction
10 Re 0 4 8
t
Vp /Uo = 1 1 Stcrit
COLLECTED t Vp /Uo =
0
0.1 NOT COLLECTED
0.01 .1
1
10
100
Vpo /Uo Figure 3.18 Crtical Stokes number vs. particle dimensionless inlet velocity. Values of the critical Stokes number were calculated using the analytical approximation to the flow field for Reynolds numbers of 0, 4, and 8. One set of curves applies for no external force (Vpt/U0 ¼ 0), the other set applies for a strong force resisting deposition (Vpt/U0 ¼ 1).
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occurs when the particle stopping distance based on its initial velocity Vpo equals the showerhead-to-wafer gap.16 Figure 3.18 also shows the variation of the critical Stokes number when a large external force opposing deposition is applied (Vpt/U0 ¼ 1). Although the value of Stcrit is greatly increased for small Vpo/U0 (compared to the case with no external force acting), all curves approach the same asymptote —Eq. (3-70)—in the limit of very large initial particle velocity. The Stcrit value for a large external force was found to be 4% higher than without an external force for Vpo/U0 ¼ 100. As noted above, the influence of Reynolds number on Stcrit is greatly reduced when a repulsive force is acting. Thus, for no or repulsive external forces, a great simplification results for large values of the initial particle velocity (say for Vpo/U0 > 100): the collection efficiency can be closely approximated by a step function (from zero to unity) at a critical Stokes number calculated by Eq. (370). When an attractive force is present, the concept of a critical Stokes number breaks down, as there is some deposition at all Stokes numbers. Even in this case, however, a sharp increase in efficiency near Stcrit is still seen (such as shown in Figure 3.17b).
3.8.3 Coupled transport—nondimensional results In this section, showerhead-enhanced inertial deposition is explored by coupling the transport of particles through the showerhead and in the inter-plate region. The procedure is as follows: (1) for given values of Ujet/ U0, L/S, and St, calculate the dimensionless velocity of the particle exiting the showerhead, Vpo/U0, using Eqs. (3-67) and (3-68); and then (2) using Vpo/U0 as the initial particle velocity, and the parameters Re, St, and Vpt/ U0, integrate the particle trajectory between the plates to determine the particle collection efficiency. Thus, the coupled particle transport problem (for an infinite parallel-plate geometry and under the present assumptions) is completely specified by five independent dimensionless parameters (note that Vpo/U0 is dependent). Efficiency results from these coupled calculations should look qualitatively like those shown in Figure 3.17, although some variations are expected as the initial particle velocity
16
A further implication of Eq. (3.70) is that for large values of Vpo/U0 a more appropriate choice for the characteristic velocity in defining particle Stokes number would have been Vpo.
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is no longer fixed but depends on the degree of particle acceleration through the showerhead. It is valuable at this point to clarify the use of the jet to face-velocity parameter Ujet/U0, which is the local fluid velocity that a particle experiences while passing through a showerhead hole. For the assumption of plug flow through the showerhead, Ujet =U0 ¼ U jet =Uo ¼ Ashowerhead =SAjet where U jet is the mean velocity in the tube. In the plug-flow case, Ujet/U0 must always be larger than unity and is constant across each showerhead tube cross-section. In commercial reactors, values of U jet =U0 are seldom less than twenty, and can range up to several hundred. The other limit considered in this work is parabolic flow through the showerhead holes. In this case, Ujet/U0 is function of both the area ratio and the radial starting position of the particle in the showerhead tube. For example, a particle starting on the tube centerline would experience a fluid velocity twice the mean, so that Ujet ðr ¼ 0Þ=U0 ¼ 2U jet =Uo . Because the fluid velocity must vanish at the tube wall, jet to face-velocity ratios less than one are possible for the parabolic case for particles starting near the wall. In the following, results are parameterized with the most general form Ujet/U0.
3.8.3.1 Critical Stokes numbers One set of coupled efficiency calculations is shown in Figure 3.19, which plots efficiency versus Stokes number for jet to face-velocity ratios of 0.1, 1, 10, 100, and 1000. For these calculations, the showerhead thickness was assumed equal to the plate gap (L/S ¼ 1) for the case of Re ¼ 0 and no external forces acting (Vpt/U0 ¼ 0). The critical Stokes number (the smallest St for which collection occurs) is found to decrease with increasing values of Ujet/U0. This result is not surprising: as Ujet/U0 increases the particle velocity at the showerhead exit (Vpo/ U0) must also increase, and we have shown in Section 3.8.2 that increasing values of Vpo/U0 lead to smaller values for Stcrit (see Figure 3.18). In particular, we have shown in the limit of large Vpo/U0 that Stcrit U0/!Vpo. It is interesting to note that, for coupled transport, the large Ujet/U0 limit of Stcrit is not U0 /Ujet, but a slightly higher value (e.g., for Ujet/U0 ¼ 100, Stcrit ¼ 0.01237). This difference is explained by the fact that, because of inertia, the particle cannot accelerate to the jet velocity before exiting the showerhead (i.e., Vpo/U0 Ujet/U0); consequently, a larger Stokes number is required to initiate deposition.
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1.0
EFFICIENCY
0.8
0.6
Ujet /Uo= 1000
100
10
1
0.1
0.4
Re = 0 L/S = 1 Vpt /Uo = 0
0.2
0
10-4
10-3
10-2
St
10-1
100
101
Figure 3.19 Effect of jet to face–velocity ratio. Efficiency vs. Stokes number for Ujet/U0 ¼ 1, 10, 100, and 1000 including coupling between showerhead and inter-plate transport (for this calculation L/S ¼ 1, Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 107).
In the slow-jet limit, say Ujet/U0 < 1, the critical Stokes number becomes less sensitive to the particle inlet velocity, although the shapes of the efficiency curves can be quite different (e.g., compare the curves for Ujet/U0 ¼ 0.1 and 1). Here, the details of the efficiency curve result from a complicated interplay among the parameters. Overall, reducing the value of Ujet /U0 (more and/or larger showerhead holes) increases Stcrit—with the favorable result of increasing the minimum size for which inertial effects lead to particle deposition on the wafer. The showerhead thickness also plays a role in determining the magnitude of the critical Stokes number. The effect of showerhead thickness is presented in Figure 3.20, in which collection efficiency is plotted against St for L/S ¼0.1, 0.5, 1 and 2 (for Ujet/U0 ¼ 100, Re ¼ 0, and Vpt/U0 ¼ 0). For large L/S values, there is sufficient time in the showerhead for the particle to accelerate to the jet velocity (Vpo/U0 Ujet/ U0), which by Eq. (3-70) gives the asymptotic limit StcritU0/Ujet. As seen in Figure 3.20, this limit is approached for L/S > 2. For very thin showerheads, the particles spend only a short time in the showerhead, and will exit the showerhead with a velocity much less than the jet velocity. In this case, larger Stokes numbers are needed to initiate deposition—as seen in Figure 3.20 for the curves with L/S ¼ 0.1 and 0.5. Based on these results, Stcrit can be increased (and inertial deposition reduced) by reducing the dimensionless showerhead thickness L/S.
252
FUNDAMENTALS 1.0
EFFICIENCY
0.8
0.6 L/S =2 1
0.5
0.1
0.4 Ujet /Uo = 100 Re = 0 Vp t /Uo = 0
0.2
0
0.01
0.1 St
Figure 3.20 Effect of showerhead thickness. Efficiency vs. Stokes number for L/S ¼ 0.1, 0.5, 1, and 2 including coupling between showerhead and interplate transport (for this calculation Ujet/U0 ¼ 100, Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 107).
3.8.3.2 Grand design curves If the effect of a repulsive force is neglected, then the value of Stcrit (for a given flow field) is determined solely by the values of Ujet/U0 and L/S. Interestingly, both of these parameters are geometrical in nature. The geometric interpretation of L/S is obvious (the ratio of showerhead thickness to inter-plate gap), while that for Ujet/U0 requires some explanation. Under the assumption of plug flow within the showerhead holes, it has already been shown that Ujet =U0 ¼ U jet =Uo ¼ Ashowerhead =SAjet where U jet is the mean velocity in the tube. Thus, in the plug-flow limit the velocity ratio is completely specified by the number and size of the showerhead holes and by the diameter of the showerhead—purely geometric properties of the showerhead. Under the assumption of parabolic flow, the radial starting position of the particle within the showerhead hole must also be considered, but this is another geometrical parameter. Thus, for a specific flow field and neglecting external forces, the critical Stokes number is uniquely specified by chamber and showerhead geometry (and possibly an assumed particle starting position), and is independent of process parameters (e.g., gas temperature, pressure, or flow rate). This simplification leads to the idea of the grand design curves, which give critical Stokes number as a function of the velocity ratio Ujet/U0 for
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various dimensionless showerhead thicknesses L/S. An example of a grand design curve over a wide range of these two parameters is shown in Figure 3.21 for Re ¼ 0 and Vpt/U0 ¼ 0. The qualitative trends are consistent with earlier discussion: the critical Stokes number decreases with increasing values of Ujet/U0 and L/S. The curves for all values of L/S intersect at Ujet/U0 ¼ 1, which corresponds to the case for which the particle enters (and exits) the showerhead at the same velocity. Variations in Stcrit with L/S become small for dimensionless showerhead thicknesses larger than about two; in this case, the particle has had sufficient time to accelerate to near the gas velocity, so that making the showerhead longer has little effect. For velocity ratios less than one, the critical Stokes number is essentially independent of velocity ratio and the dimensionless showerhead thickness. For large velocity ratios, the curves in Figure 3.21 for different L/S values become parallel with a slope of unity— suggesting that in this limit Stcrit becomes proportional to U0/Ujet. As shown, the value of Ujet/U0 at which this asymptotic limit is reached depends on L/S: for thick showerheads the linear limit is achieved at much smaller velocity ratios than for thin showerheads. For design applications, the grand design curves are used with the parameters Ujet/U0 and L/S to find the critical Stokes number for the proposed reactor geometry. To minimize particle deposition on the wafer, it is desirable to choose parameters that give as large a critical 1
Stcrit
Re = 0 Vp t / Uo = 0
0.1
0.01
L/S 0.05 0.1 0.2 0.5 1.0 2.0 5.0
1
10 Ujet / Uo
100
Figure 3.21 Grand design curve for estimating the critical Stokes number based on showerhead parameters (for this calculation Re ¼ 0, Vpt/U0 ¼ 0, and rp/S ¼ 1 · 107).
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Stokes number as possible, as increasing Stcrit increases the minimum size at which inertial deposition begins. Based on Figure 3.21, larger values of Stcrit are obtained by decreasing Ujet/U0 (use more and/or larger showerhead holes) or by decreasing L/S (use a thin showerhead or a large inter-plate gap). Introducing a force that opposes deposition (such as by heating the wafer relative to the showerhead) will always help, but as discussed above, the effect is fairly small under realistic conditions. Once Stcrit has been determined, the corresponding particle critical size, dp,crit, can be found from Eq. (3-21). Note that although the critical Stokes number depends only on geometric parameters, the critical particle diameter depends on geometric, process, and particle parameters. Thus, particle density and gas pressure, temperature, type, and flow rate all play a role in determining dp,crit. The effects of process parameters on showerhead-enhanced inertial deposition are discussed in a later section.
3.8.3.3 External forces Although particle deposition only occurs for St > Stcrit for repulsive or zero external forces, inertial deposition will always take place when the net external forces are attractive. To demonstrate this behavior, particle collection efficiencies calculated using fully coupled particle transport (i.e., including showerhead acceleration) are shown for various values of the external force in Figure 3.22 (for Re ¼ 0, Ujet/U0 ¼ 100, L/S ¼ 1). The results are very similar to those in Figure 3.17b, which gives efficiency for a fixed particle inlet velocity (Vpo/U0 ¼ 100) instead of the present case where the showerhead exit velocity is calculated based on showerhead parameters.17 The large and small Stokes limits are the same: for small St inertial effects vanish and the efficiency must tend to Eq. (3-48), while for large St inertia dominates and efficiency must tend to unity. At intermediate values of St there are some differences. For example, it is seen that the critical Stokes number for the coupled analysis is slightly larger than for the case where Vpo/U0 is held constant; as discussed above, for a finite-length showerhead the particle velocity at the showerhead exit must be slightly less that Ujet/U0, so that a larger Stokes number is needed to initiate inertial deposition. Note that the case of constant Vpt/U0 (i.e., Vpt/U0 is independent of particle size or Note that although Re ¼ 8 in Figure 3.10b and Re ¼ 0 in Figure 3.22, Reynolds number effects are small. 17
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1.0
EFFICIENCY
0.8
Re=0 L / S=1 Ujet / Uo =100
0.6
0.4
Vpt / Uo = -0.5
0.2 -0.1 0
-0.01 0
.001
0.01
1.0 0.02
St
Figure 3.22 Efficiency vs. Stokes number for various deposition velocities. Collection efficiencies for fully coupled particle transport for Vpt/U0 values of 0.5. 0.1, 0, and 1 (for this calculation L/S ¼ 1, Re ¼ 0, Ujet/U0 ¼ 100, and rp/S ¼ 1 · 107).
Stokes number) corresponds to the physically meaningful situation in which a thermophoretic force is acting (as the thermophoretic drift velocity is independent of particle diameter). For other external forces—such as gravity—the net drift velocity will not be a constant but will vary with particle diameter (and hence with St).
3.8.3.4 Parabolic profile For fully developed parabolic flow in the showerhead hole, the gas velocity varies with radial position within the hole as given by Eq. (3-45); in this case the local velocity experienced by a particle in a showerhead hole depends on its radial starting position and the mean velocityU jet [as given by Eq. (3-44)]. For example, a particle starting on the hole centerline will experience the highest local gas velocity (2U jet ), while ones starting near the hole wall will experience much lower velocities. As the amount of acceleration the particle experiences within the showerhead depends on the local gas velocity, the particle collection efficiency must vary with particle radial position within the showerhead hole. Thus, the calculation of the net collection efficiency for the parabolic flow case requires integrating the local efficiency radially across the showerhead hole. Assuming that the particles are uniformly distributed
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across the showerhead hole (i.e., that the flux of particles across the tube cross-section is constant), the net efficiency is: 2 hnet ðStÞ ¼ 2 Rjet
R Zjet
h½Ujet ðrÞ; Strdr
Eq (3-71)
0
The numerical integration of Eq. (3-71) is computationally expensive, as each evaluation of the integrand h[ Ujet(r), St] requires a coupled calculation of the particle acceleration through the showerhead [with local gas velocity Ujet(r)] along with the corresponding numerical integration of the particle trajectory between the two plates. The integration of Eq. (3-71) is further complicated by the fact that, in some cases, efficiency can change significantly with small changes in St or Ujet(r). In the present work, an adaptive Gauss integration scheme with automatic error control has been used to evaluate Eq. (3-71). An example of a net efficiency curve for a parabolic velocity profile is shown in Figure 3.23 for the case where there is no external force (Re ¼ 0, U jet =Uo ¼ 100, L/S ¼ 1, and Vpt/U0 ¼ 0). For comparison, efficiency curves are also shown for plug flow (where all the particles experience the mean velocity) and for the hypothetical case where all of the particles 1.0
EFFIC IENCY
0.8
Re=0 L / S=1 Ujet / Uo =100 Vp t / Uo =0 Parabolic Profile
0.6
0.4
Centerline Velocity Mean Velocity
0.2
0
.001
0.01 St
0.1
Figure 3.23 Efficiency vs. Stokes number for parabolic showerhead profile (no external force). Collection efficiencies for fully coupled particle transport for particles experiencing the showerhead hole centerline and mean velocities (plug flow assumption), and integrated over the parabolic velocity profile in the showerhead holes in the absence of external forces (L/S ¼ 1, Re ¼ 0, U jet/U0 ¼ 100, and rp/S ¼ 1 · 107).
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experience the centerline velocity (essentially a plug flow moving at twice the mean velocity). These three curves show three interesting effects. First, the critical Stokes number for the centerline case is approximately one half that for the plug flow case; this result is explained by the fact that the critical Stokes number is inversely proportional to jet velocity in the limit of large values of Ujet/U0 (i.e., doubling the local showerhead gas velocity halves Stcrit).18 Second, the efficiency curve for the parabolic case approaches unity much slower than either of the plug flow curves. This is expected, as particles located near the tube wall experience very low local velocities; for some region very close to the wall, particles actually deaccelerate while passing through the showerhead. Note that although this slow approach to complete collection is favorable from a defect reduction point of view, it is not of practical significance because in this large Stokes regime the majority of particles entrained in the flow would still be deposited. Third, the critical Stokes number for the parabolic case is the same as for the centerline case. The smallest particles deposited are those experiencing the highest velocity in the showerhead hole; thus, for parabolic flow inertia-enhanced deposition begins with those particles moving along the showerhead-hole centerline. The slope of the parabolic case is not as steep as for the centerline case because few particles are contained in the small-area region near the centerline, whereas in the centerline case we have assumed all of the particles are moving at the centerline velocity. The centerline case therefore serves as a limit of the smallest Stokes value for which inertial-enhancement to deposition becomes important in parabolic flow. In fact, the centerline case serves as a lower limit for all laminar flow conditions in the tubes, since even for developing flow the maximum velocity in the tube will always be less than 2U jet . Thus, the most conservative practice for predicting the effects of inertia-enhanced deposition in real reactors is to use Ujet =Uo ¼ 2U jet =Uo as the characteristic velocity ratio in the grand design curves. The present results show that, for parabolic flow in the showerhead, the best practice for determining net efficiency is to perform the full integration of Equation (6.71). However, since this calculation can be computationally expensive, the following approximations are suggested: for attractive external forces (say Vpt/U0 < 0.01) use the mean velocity approximation, otherwise (say Vpt/U0 > 0) use the more conservative centerline approximation. 18
The critical Stokes number becomes less dependent on the velocity ratio for small Ujet/U0.
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3.8.4 Coupled transport—dimensional results The two approaches to reduce inertia-enhanced particle deposition are:19 (1) design equipment with as large a value of Stcrit as possible and (2) select process conditions that give as high a value of dp,crit as possible. Based on our previous analysis, the only three ways to increase Stcrit is to design for minimum U jet =U0 and/or L/S, and to apply an external force that opposes deposition. To minimizeU jet =U0 , very porous showerhead designs are needed to reduce the constriction of the flow (decrease the area ratio given by Eq. (3-44) by either increasing the number or the size of holes). The ratio L/S can be reduced by reducing the showerhead thickness or by increasing the showerhead-to-wafer gap. Intuitively, a short showerhead thickness reduces the time available to accelerate the particle, and a large showerhead-to-wafer gap provides the particle more opportunity to slow down. Finally, an opposing external force could be used to inhibit inertial deposition such as by keeping the wafer warmer than the showerhead to take advantage of thermophoresis but remembering that the opposing force typically had a fairly weak effect on reducing inertia-enhanced deposition. Once a hardware design is fixed, Stcrit is fixed, but it is still possible to minimize inertial deposition by selecting process conditions that give as high a value of dp,crit as possible. Based on the free molecule definition of Stokes number in Eq. (3-23), we can see that low face velocities U0 and large showerhead-to-wafer gaps S are preferred. Mean gas velocities can be reduced by reducing mass flow rates (at constant pressure) or by operating at higher pressures (for a fixed mass flow rate). As seen in Eq. (3-23), operating at higher pressures also directly increases dp,crit. Thus, for a constant mass flow rate, a twofold increase in pressure produces a fourfold increase in dp,crit (one factor of two directly from the pressure reduction, and an additional factor of two from lowering the face velocity).20 Recall that Eq. (3-23) strictly applies to particles in the free molecular limit (small sizes and/or low pressures) which is a reasonable 19
It is impossible to eliminate inertial effects, as one can always imagine a particle large enough so that it will impact. 20 For higher pressures and/or larger particle diameters the quadratic relationship between pressure and critical diameter fails as the free-molecule expression for Stokes number given by Eq. (3.23) becomes inaccurate. In the continuum limit the particle relaxation time becomes independent of pressure and proportional to diameter squared, so that a fourfold pressure increase would result in a twofold increase in dp,crit. Thus, the influence of pressure on dp,crit is most pronounced in the free-molecule regime.
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assumption for the pressure and particle size regimes in typical semiconductor manufacturing reactors. An example of particle collection efficiency as a function of particle size is shown in Figure 3.24 for a hypothetical 200 mm (diameter) reactor characterized by: an argon flow rate of 1000 sccm (standard cubic centimeters per minute) through a showerhead 2.54 cm thick with 1000 holes of diameter 0.0635 cm with a showerhead-to-wafer gap of 2.54 cm. The flow is assumed isothermal and a particle density of 1 g/cm3 is used. These reasonable physical parameters give the dimensionless quantities L/S ¼ 1, U jet =U0 ¼ 99:2 and Re ¼ 0.984; the dimensionless drift velocity varies with size according to the expression for gravitational settling velocity—Eq. (3-26). Efficiency curves are shown for reactor pressures (i.e., pressure between the two plates) of 0.5, 1.0, 2.0, and 10. torr. For pressures less than 2 torr, inertial-enhancement to deposition is clearly evident by the abrupt jump in efficiency from nearly zero to unity in the vicinity of a critical size. As seen, this critical size is a strong function of pressure, with an approximately fourfold decrease in the critical size for a twofold decrease in chamber pressure. For chamber pressures above about 10 torr inertial effects no longer contribute to deposition; the increase in efficiency for increasing particle size seen in 1.0
EFFICIENCY
0.8
ρp = 1. g/cc 1000 sccm Argon L / S =1 T=300K
0.6 0.5 torr
1.0
2.0
0.4
10.
0.2
0
0.1
1 dp (µm)
10
Figure 3.24 Efficiency vs. particle diameter and pressure (isothermal case). Collection efficiencies for fully coupled particle transport assuming plug flow through the showerhead hole for reactor pressures of 0.5, 1.0, 2.0, and 1 torr (L/S ¼ 2.54 cm, Ujet/U0 ¼ 99.2, Q ¼ 1000 sccm argon, T ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3).
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Figure 3.24 for the P ¼ 10 torr case results because the gravitational drift velocity increases with size. The same reactor geometry and process conditions have been used to calculate the effect of thermophoresis on collection efficiency as shown in Figure 3.25. The showerhead temperature has been held constant at 300 K while the wafer (lower plate) temperature is made colder (280 K), isothermal (300 K), or hotter (320 K). Fairly modest temperature differences have been used in accordance with our isothermal (constant gas properties) assumption for flow calculations, but that small temperature differences are allowed to drive particle thermophoresis. The isothermal case shows that, for small particle sizes, deposition decreases with decreasing size because the gravitational drift velocity is decreasing. When the wafer temperature is less than the showerhead temperature, thermophoresis acts to increase deposition compared to the isothermal case. Although the differences become small for sizes larger than dp,crit (about 1.5 mm), the thermophoretic contribution is clear in the smallparticle limit where the efficiency approaches a constant.21 Heating the 1.0 ρp = 1. g/cc
EFFICI ENCY
0.8
0.6
1000 sccm argon P = 1 torr L/S = 1 Tshowerhead = 300K
0.4
Twafer 280K 300K 320K
0.2
0 0.1
1 dp (µm)
10
Figure 3.25 Efficiency vs. particle diameter and wafer temperature (with thermophoresis). Collection efficiencies for fully coupled particle transport assuming plug flow through the showerhead hole for wafer temperatures of 280, 300, and 320 K (L/S ¼ 2.54 cm, Ujet/U0 ¼ 99.2, Q ¼ 1000 sccm argon, P ¼ 1 torr, Tshowerhead ¼ 300 K, Re ¼ 0.98, and particle density ¼ 1 g/cm3). 21
Since the thermophoretic drift velocity is independent of particle diameter (Eq. (331)) while the settling velocity is proportional to diameter, for small particles thermophoretic deposition dominates and the efficiency becomes constant.
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wafer relative to the showerhead eliminates all small-particle deposition as the thermophoretic resistive force overwhelms the attractive gravitational force. The critical diameter at which inertial effects dominate is shifted to a slightly larger size than for the isothermal case, although the shift is fairly small since the effect of an external force on Stcrit is fairly weak. By using thermophoretic protection and by designing a reactor with a sufficiently large dp,crit particle deposition can be mitigated over the particle size range of interest. The two previous examples highlight two important points: (1) that inertia-enhanced deposition becomes dramatically more important at low pressure and (2) that thermophoretic protection coupled with careful control of inertial effects can significantly reduce particle deposition. Dimensional calculations could also be used to demonstrate all of the effects reported in Section 3.8.3, however, because of the wide variability in reactor geometry and particle and process parameters, only these two examples are presented.
3.9
Chapter Summary and Practical Guidelines
This chapter reviewed the basic phenomena controlling particle transport and the underlying general equations with an emphasis on conditions encountered in semiconductor process tools (i.e., subatmospheric pressures and submicron particles). The discussion included expressions for the following particle forces: fluid drag, gravity, thermophoresis, and electrophoresis. The concepts of particle drift velocity and stopping distance were introduced, and issues of continuum vs. free molecular particle transport were outlined. Particle concentrations were assumed to be low enough to allow a dilute approximation, for which the coupling between the fluid and particle phases is one-way. In this case, the fluid/ thermal transport equations can be solved either analytically or numerically neglecting the particle phase; the resulting velocity and temperature fields were then used as input for the particle transport calculations. Isothermal flow was assumed, although small temperature differences were allowed to drive particle thermophoresis; both analytical and numerical solutions of the flow field representative of a parallel plate geometry were presented. Particle collection efficiency was defined as the fraction of particles present in the inter-plate region of the reactor that deposit on the wafer. Particles were presumed to either enter the reactor through the showerhead (uniformly spread between r ¼ 0 and RW), or to originate in a plane parallel to the wafer. The latter case corresponds to
262
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particles being released from a plasma trap upon plasma extinction or being formed in a nucleation process; in this case, the particles are initially assumed to be uniformly spread radially between r ¼ 0 and RW at some distance h from the wafer. Analytical expressions for collection efficiency were presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Particle transport in the parallel-plate geometry was predicted using both the Lagrangian approach (where individual particle trajectories are calculated) and the Eulerian approach (where the particles are modeled as a cloud). The Eulerian formulation yielded an analytical, integral description of particle deposition for the case where the flow field between the plates can be approximated analytically. The strength of the Eulerian formulation is in predicting particle transport resulting from the combination of applied external forces (including the fluid drag force) and the chaotic effect of particle Brownian motion (i.e., particle diffusion), although the current implementation cannot account for particle inertia. In particular, the Eulerian formulation cannot accommodate particle acceleration effects within the showerhead, and is therefore restricted to particle transport in the inter-plate region. The need to properly account for diffusion-enhanced particle deposition becomes increasingly important as the semiconductor industry moves toward smaller feature sizes and becomes concerned with smaller-sized particles. Based on the Eulerian analysis, the following guidelines are intended to help tool operators and designers reduce particle deposition when diffusional effects are important: Keep traps as far from the wafer as possible. Take advantage of repulsive forces, such as thermophoretic protection gained by keeping the wafer warmer than the showerhead. Reduce attractive forces. For a specific pressure, use as high a mass flow rate as possible. The strength of the Lagrangian formulation is in predicting particle transport resulting from the combination of applied external forces and particle inertia, although the current implementation cannot account for particle diffusion. It is the Lagrangian formulation, that can properly account for inertia-enhanced deposition resulting from particle acceleration in the showerhead. The problem was treated in two steps, in which both particle and fluid transport were determined: (1) within a
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showerhead- hole and (2) between the showerhead and the susceptor. For fluid and particle transport in the showerhead, approximate analytical expressions were derived based on a few assumptions. The output of this first step was the particle velocity at the exit of the showerhead, as a function of showerhead geometry, flow rate, and gas and particle properties. The particle showerhead-exit velocity was next used as an initial condition required for particle transport between the plates. The output of the second step was a prediction of particle collection efficiency by the susceptor (wafer), as a function of showerhead-exit particle velocity, the plate separation, flow rate, and gas and particle properties. Based on the Lagrangian analysis, two approaches were identified to help tool operators and designers reduce particle deposition when inertial effects are important: (1) design equipment with as large a value of Stcrit as possible and (2) select process conditions that give as high a value of dp,crit as possible. Based on this analysis, Stcrit is determined primarily by reactor and showerhead geometry. Only three methods were identified for increasing Stcrit: Decrease the showerhead velocity ratio U jet =U0 by increasing the number of holes and/or enlarging the size of the showerhead holes. Decrease the showerhead thickness ratio L/S by making the showerhead very thin or the inter-plate gap large. Apply an external force that opposes particle deposition (such as keeping the wafer warmer than the adjacent gas). Given a specific hardware design (and corresponding Stcrit), inertial deposition can be reduced by selecting process conditions that give as high a value of dp,crit as possible. Based on the free molecule limit of Stokes number, the following general guidelines are offered to increase the critical diameter (for a given Stcrit):
Increase the gap between the showerhead and wafer Use low mass flowrates Raise chamber pressure Use a high molecular weight gas
The previous recommendations specifically pertain to reducing particle deposition given an assumed dominant deposition mechanism; note that one set of guidelines (e.g., for inertia) may conflict with those intended to reduce deposition by other mechanisms (e.g., gravity or diffusion).
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In order to reduce particle deposition in real tools, it is up to equipment designers/operators to first identify the dominant deposition mechanism so that an effective improvement strategy can be identified. Note that the guidelines given above are not intended to replace detailed calculations (using the proper analysis with the actual process conditions), but to provide the user with a general feel for inherently-clean practices. In addition, equipment designers should be aware that while these recommendations should improve particle performance, the effect of any changes on process performance must also be investigated.
References 1. M. D. Allen and O. G. Raabe, ‘‘Re-evaluation of Millikan’s Oil Drop Data for the Motion of Small Particles in Air,’’ J. Aerosol Sci. 6, 537 (1982). 2. R. P. Donovan, T. Yamamoto, R. Periasamy and A. C. Clayton, ‘‘Mechanisms of Particle Transport in Process Equipment,’’ J. Electrochem. Soc. 140, 2917 (1993). 3. D. J. Rader and A. S. Geller, ‘‘Particle Transport Modeling in Semiconductor Process Environments,’’ Plasma Sources Sci. Technol. 3, 426 (1994). 4. W. C. Hinds, ‘‘Aerosol Technology,’’ John Wiley, New York (1982). 5. S. K. Friedlander, ‘‘Smoke, Dust and Haze,’’ John Wiley, New York (1977). 6. R. Turton and O. Levenspiel, ‘‘A Short Note on the Drag Correlation for Spheres,’’ Powder Technol. 47, 83 (1986). 7. E. Cunningham, ‘‘On the Velocity of Steady Fall of Spherical Particles through Fluid Medium,’’ Proc. R. Soc. A 83, 357 (1910). 8. M. Knudsen and S. Weber, ‘‘Luftwiderstand gegen die langsame Bewegung kleiner Kugeln,’’ Annalen der Physik 341, 981 (1911). 9. Y. Ishida, ‘‘Determination of Viscosities and of the Stokes-Millikan Law Constant by the Oil Drop Method,’’ Phys. Rev. 21, 550 (1923). 10. D. J. Rader, ‘‘Momentum Slip Correction Factor for Small Particles in Nine Common Gases,’’ J. Aerosol Sci. 21, 161 (1990). 11. R. A. Millikan, ‘‘The General Law of Fall of a Small Spherical Body through a Gas, and its Bearing upon the Nature of Molecular Reflection from Surfaces,’’ Phys. Rev. 22, 1 (1923). 12. J. M. Eglin, ‘‘The Coefficients of Viscosity and Slip of Carbon Dioxide by the Oil Drop Method and the Law of Motion of an Oil Drop in Carbon Dioxide, Oxygen, and Helium at Low Pressure,’’ Phys. Rev. 22, 161 (1923). 13. N. A. Fuchs, ‘‘The Mechanics of Aerosols,’’ Dover Publications, New York (1964). 14. R. Clift, J. R. Grace and M. E. Weber, ‘‘Bubbles, Drops, and Particles,’’ Academic Press, New York (1978). 15. C. B. Henderson, ‘‘Drag Coefficients of Spheres in Continuum and Rarefied Flows,’’ AIAA J. 14, 707 (1976). 16. P. S. Epstein, ‘‘On the Resistance Experienced by Spheres in Their Motion Through Gases,’’ Phys. Rev. 23, 710 (1924).
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17. L. Talbot, R. K. Cheng, R. W. Schefer and D. R. Willis, ‘‘Thermophoresis of Particles in a Heated Boundary Layer,’’ J. Fluid Mech. 101, 737 (1980). 18. G. K. Batchelor and C. Shen, ‘‘Thermophoretic Deposition of Particles in Gas Flowing over Cold Surfaces,’’ J. Colloid Interface Sci. 107, 21 (1985). 19. L. Waldmann and K. H. Schmitt, ‘‘Thermophoresis and Diffusiophoresis of Aerosols,’’ Chapter VI in Aerosol Science, C. N. Davies (Ed.), Academic Press, New York (1966). 20. M. H. Peters, D. W. Cooper and R. J. Miller, ‘‘The Effects of Electrostatic And Inertial Forces on the Diffusive Deposition of Small Particles onto Large Disks: Viscous Axisymmetric Stagnation Point Flow Approximations,’’ J. Aerosol Sci. 20, 123 (1989). 21. D. J. Rader and A. S. Geller, ‘‘Showerhead-Enhanced Inertial Particle Deposition in Parallel-Plate Reactors,’’ Aerosol Sci. Technol. 28, 105 (1998). 22. R. B. Bird, W. E. Stewart and E. N. Lightfoot, ‘‘Transport Phenomena,’’ John Wiley, New York (1960). 23. R. M. Terril and J. P. Cornish, ‘‘Radial Flow of a Viscous, Incompressible Fluid Between Two Stationary, Uniformly Porous Discs,’’ J. Appl. Math. Phys. (ZAMP) 24, 676 (1973). 24. C. Houtman, D. B. Graves and K. F. Jensen, ‘‘CVD in Stagnation Point Flow: An Evaluation of the Classical 1D Treatment,’’ J. Electrochem. Soc. 133, 961 (1986). 25. A. Robinson, ‘‘On the Motion of Small Particles in a Potential Field of Flow,’’ Comm. Pure Appl. Math. 9, 69 (1956). 26. D. J. Rader, A. S. Geller, S. J. Choi and M. J. Kushner, ‘‘Application of Numerical Models to Predict Particle Contamination in Semiconductor Process Environments,’’ in Proc. IES 40th Tech. Mtg., pp. 308–315, Institute of Environmental Sciences and Technology, Rolling Meadows, IL (1994). 27. D. J. Rader, A. S. Geller, S. J. Choi and M. J. Kushner, ‘‘Particle Transport in Plasma Reactors,’’ in Proc. Microcontamination 94 Conference, pp. 39–48, Sematech, San Jose, CA (1994). 28. D. W. Cooper, R. J. Miller, J. J. Wu and M. H. Peters, ‘‘Deposition of Submicron Aerosol Particles During Integrated Circuit Manufacturing: Theory,’’ Part. Sci. Technol. 8, 209 (1990). 29. B. V. Ramarao and C. Tien, ‘‘Aerosol Deposition in Two-Dimensional Laminar Stagnation Flow,’’ J. Aerosol Sci. 20, 775 (1989). 30. R. M. Roth, K. G. Sears, G. D. Stein and G. Wong, ‘‘Spatial Dependence of Particle Light Scattering in an RF Silane Discharge,’’ Appl. Phys. Lett. 46, 253 (1985). 31. T. J. Sommerer, M. S. Barnes, J. H. Keller, M. J. McCaughey and M. J. Kushner, ‘‘Monte Carlo-Fluid Hybrid Model of the Accumulation of Dust Particles at Sheath Edges in Radio-Frequency Discharges,’’ Appl. Phys. Lett. 59, 638 (1991). 32. M. S. Barnes, J. H. Keller, J. C. Forster, J. A. O’Neill and D. K. Coultas, ‘‘Transport of Dust Particles in Glow-Discharge Plasmas,’’ Phys. Rev. Lett. 68, 313 (1992). 33. S. J. Choi, P. L. G. Ventzek, R. J. Hoekstra and M. J. Kushner, ‘‘Spatial Distributions of Dust Particles in Plasmas Generated by Capacitively Coupled Radio Frequency Discharges,’’ Plasma Sources Sci. Technol. 3, 418 (1994).
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34. G. M. Jellum, J. E. Daugherty and D. B. Graves, ‘‘Particle Thermophoresis in Low Pressure Glow Discharges,’’ J. Appl. Phys. 69, 6923 (1991). 35. M. Shiratani, S. Matsuo and Y. Watanabe, ‘‘In Situ Observation of Particle Behavior in RF Silane Plasmas,’’ Jpn. J. Appl. Phys. 30, 1887 (1991). 36. C.-K. Yeon, J.-H. Kim and K.-W. Whang, ‘‘Dynamics of Particulates in the Afterglow of a Radio Frequency Excited Plasma,’’ J. Vac. Sci. Technol. A 13, 927 1995). 37. J. Kang, R. N. Carlile, J. F. O’Hanlon and S. M. Collins, ‘‘Mapping of Radio Frequency Plasma Potential Throughout a Particle Trapping Region using an Emissive Probe,’’ J. Vac. Sci. Technol. A 14, 639 (1996). 38. S. J. Choi, D. J. Rader and A. S. Geller, ‘‘Massively Parallel Simulations of Brownian Dynamics Particle Transport in Low Pressure Parallel-Plate Reactors,’’ J. Vac. Sci. Technol. A 14, 660 (1996). 39. D. W. Cooper, M. H. Peters and R. J. Miller, ‘‘Predicted Deposition of Submicrometer Particles due to Diffusion and Electrostatics in Viscous Axisymmetric Stagnation-Point Flow,’’ Aerosol Sci. Technol. 11, 133 (1989).
4 Relevance of Particle Transport in Surface Deposition and Cleaning Chao-Hsin Lin Environmental Control Systems, Boeing Commercial Airplanes Group, Seattle, WA, USA Chao Zhu Departmental of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ, USA
4.1
Introduction
Through numerous natural phenomena as well as human activities, we have ample experience about foreign objects in various fluid media and their interactions. To name a few that occur naturally are sandstorms, precipitation, cloud formation, and botanical reproduction. In our daily economic life activities, such as pest control through spraying, dust collection, mining and manufacturing processes, and transportation and pollution control are just a tiny fraction of examples that involve interaction of droplets, vapors, particles, and bubbles with various fluid media. Physically speaking, we live in a world of tremendous systems of fluid–particle interactions, as first delineated by Soo in 1965 [1]. Researches on this subject and its related phenomena have progressed significantly since the second half of the last century [2–4]. In this chapter, we are focusing primarily on the recent progress in gas-particle flows, in general, and their relevance to fine particle surface deposition/cleaning, in particular. The characteristics of gas-particle flows vary widely with respect to the geometric and material properties of the particle [4]. In solid fuel combustion, pneumatic conveying, fluidization, gas-particle separation, particle deposition on semiconductor wafers [5], and other processes, gas-particle flows are commonly witnessed. Likewise, gas-particle flows play important roles in various natural phenomena such as dry
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deposition of particulate matters on natural surfaces [6], dispersion of natural allergens, volcanic ashes, cosmic dusts, etc. Surface contamination due to the presence of fine particles has caused enormous yield loss and degradation of reliability in microelectronics manufacturing [7] and material processing [8], damages in agricultural and forestry products [9] and art works [10]. In general, deposition of atmospheric contaminants onto solid surfaces is a dynamic process. This process is carried out in three steps as follows: (1) particles are transported aerodynamically to the proximity of the boundary layer surrounding the solid surfaces, (2) particles are transported within the boundary layer and toward the gas– solid interfaces, and (3) particles come physically in contact with the solid surfaces [11]. In this chapter, descriptions of the important mechanisms that are involved in this process are provided. In Section 4.2, particle transport in gas-particle flows related to surface deposition is described. At the particle–solid interfaces, the primary adhesion mechanisms are also detailed and discussed in Section 4.2. Subsequently, Section 4.3 presents the various mechanisms of the aerodynamic and boundary layer transport of particles. The relevance of the particle transport theories is given. In Sections 4.4–4.6, three mechanisms, namely thermophoresis, electrostatics and dielectrophoresis, and their implications in particle deposition are delineated. Section 4.7 is devoted to a unique particle deposition problem, namely abrasive erosion and its relevance in surface cleaning. The recent progress in numerical and experimental studies on particle transport phenomena described in the aforementioned sections is summarized.
4.2
Particle–solid Surface Interactions
For understanding the various phenomena involved in surface contamination by particles to developing means for monitoring and removing the contaminants, it is necessary to learn and apply the mechanics of gasparticle flows. Fuchs [12] and Friedlander [13], in their widely cited books, have compiled and provided the most up-to-date knowledge on the motion of aerosols (i.e. solid or liquid particles) in natural or manmade environments in the 1960s and 1970s, respectively. Hinds summarized further progress in aerosol technology in his well-received textbook [14]. Most recently, Fan and Zhu have given a thorough description of the basic principles and fundamental phenomena associated with gas–solid flows [4]. In this chapter, from the application perspectives of surface
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deposition and cleaning, we focus our discussion on the important mechanisms involved in the context of gas-particle flows. For more rigorous theoretical derivations, the readers are encouraged to refer to the references cited in this chapter. When a solid particle physically contacts either another solid particle or a solid surface, the forces between these solid objects are primarily attractive in nature and result in adhesion of particles to each other or to the solid surface. The finer the size of the particles, the adhesion forces involved become more significant and particles become more difficult to remove [15]. Particle agglomeration due to adhesion could change the particle size distribution and other physical properties in the gas–solid system. Consequently, this effect would alter the effectiveness of particle removal. From the perspectives of surface deposition of particles, the most affected industry is the manufacturing of microelectronics [16]. Therefore, the entire clean room technology was mostly built with the aim of controlling the deposition of fine particles to reduce yield losses during the manufacturing of integrated circuits. After a physical contact between particles and a solid surface is established, it is considered that van der Waals and electrostatic forces are the predominant attractive forces between the adhering particles. Other interfacial forces such as liquid bridges, double-layer repulsion and chemical bonds may play important roles under specific circumstances [15, 16]. Penney and Klingler [17] have reported that, by measuring the contact potential differences of adjoining dust particles, the combination of van der Waals and electrostatic forces is normally an order of magnitude greater than the adhesion force by mechanical means. Figure 4.1 shows a schematic of adhesion by the van der Waals forces. For a spherical particle depositing on a planar surface, the resulting van der Waals forces
3
1 dp
Z0
2
Figure 4.1 van der Waals interaction: sphere-planar surface [15].
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are expressed as FvdW ¼ A
dp z 20
Eq. (4-1)
where FvdW is the van der Waals forces, A is the Hamaker constant, dp is the particle diameter, and z0 is the clearance between the particle and the surface [14, 16]. For the same configuration, as shown in Figure 4.1, the difference in the work functions of the two materials results in a contact potential, fc, between the particle and the surface. The force due to the electrostatic double-layer is given [15] as Fe ¼ pe0
dp f2c 2 z0
Eq. (4-2)
where Fe is the force due to the electrostatic double-layer and e0 is the dielectric constant of vacuum. With the common presence of humidity in the environment, it is not unusual to have some moisture adsorbed on the surface of most materials. At the interface where two different materials contact, a liquid bridge (or film) forms and results in an attractive force due to the surface tension of the liquid, as shown in Figure 4.2. For an ambient relative humidity above 90%, this attractive force is given as Fs ¼ 2pgdp
Eq. (4-3)
where Fs is the adhesion force due to the surface tension, g, of the liquid bridge. The major adhesion forces mentioned above are all proportional to the particle diameter, dp. In contrast, to remove the particle by mechanical means, we need to employ either a centrifugal force that is proportional to dp3 or an air current force that is proportional to dp2. Therefore, much greater force is needed to remove deposited micrometer and sub-micrometer particles. Based on measurements of hard materials
Particle
Flat surface Figure 4.2 Adhesion force due to a liquid film.
Liquid
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and clean surfaces at 298 K, an empirical formula for the overall adhesion force, Fad, is given as [14]: Fad ffi150dp ½0:5 þ 0:0045ð%RHÞ
Eq. (4-4)
For spherical particles of unit density, a comparison among the adhesion force, calculated using Eq. (4-4), and the corresponding gravitational and aerodynamic drag forces is made in Table 4.1. This example illustrates the significance of adhesion force and the difficulty in dislodging the deposited particles from the surface, especially for fine particles. Even though we can calculate the primary mechanisms of particle–solid surface adhesion based on the equations above, in reality, however, the distance of separation, z0, is not measurable and an assumed range from 0.4 to 1.0 nm is used. Therefore, this introduces a certain degree of uncertainty into both the measured and predicted data. In addition, approximations are made to define the roughness and asperities of the adhering bodies, as illustrated in Figure 4.3. Further research to improve the accuracy of adhesion forces, experimentally and computationally, is rightly justified. Numerous ways, dry and wet, have been proposed and investigated to remove particles from surfaces. To reduce contamination, researchers and practitioners, though not always in agreement, prefer dry approaches, as reported by Cooper et al. [7] and Ranade [16]. It is known that blowing dry air or nitrogen jet is not effective to remove particles smaller than 10 mm in diameter. Cooper et al. [7] applied an electric field between an electrostatic film cleaner and the particle-deposited product to remove particles by electrostatic force, as shown in Figure 4.4. Their success was not universal with respect to all the particles they had tested, as Table 4.1 Comparison of Adhesion, Gravity, and Air Current Forces on Spherical Unit-density Particles [14]
Diameter (mm) 0.1 1.0 10 100 a
Adhesiona 108 107 106 105
Calculated by Eq. (4-4) for 50% RH.
Force (N) Gravity Air Current (at 1 m/s) 5 5 5 5
· · · ·
1018 1015 1012 109
2 · 1010 2 · 109 3 · 108 6 · 107
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dp
(a)
dp
(b)
Figure 4.3 Effect of surface roughness on particle deposition [15]. (a) Asperities smaller than particle size. (b) Asperities larger than particle size.
Take-up roller DC Power Supply
Film, particles
Conductive roller
Product Ground Plate
Figure 4.4 Schematic diagram of the electrostatic film cleaner [7].
summarized in Table 4.2 [7]. Ranade [16] reviewed many removal schemes and processes, both dry and wet, and no preferred technique was recommended due to the complexity involved in the phenomena of surface deposition of particles.
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Table 4.2 Summary of Measured Removal Efficiencies, Using an Electrostatic Film Cleaner [7]
Particle Diameter (mm)
Particle Type
Film Used
Removal Field Voltage Efficiency (%) (MV/cm) (kV)
Conductive surfaces—smooth (specular) Metal film 1.1 Latex Polyimide >46–98 0.5 Latex Polyimide >95 Polyimide >95 0.3 SiO2 Silicon wafer 6 Ni Laminate 80–100 Laminate >95 2 SiO2 Laminate >80 0.5 SiO2 Conductive surfaces—patterned or rough Semiconductor chips post-metallization 2–5 Ni Laminate 60–90 Laminate >50 2 SiO2 Insulator surfaces—smooth (specular) SiO2 (0.5 mm) silicon wafer 2–5 Ni Laminate 98 Laminate 97 2 SiO2 1 Latex Laminate 60 Ceramic substrate Laminate 96–100 12 SiO2 6 Ni Laminate 96–100 Glass plate. 1.5 mm thick 6 Ni Laminate 93 Laminate 2 SiO2 Laminate 0.5 SiO2 Insulator surfaces—patterned or rough Multilayer ceramic with metal pads Laminate 97 12 SiO2 6 Ni Laminate 95–99
4.3
2.8 7.0 8.4
– – –
– – –
4 6 6
– –
14 14
– – –
4 3 3
– –
10 10
– – –
8 8 8
– –
3–4 3–4
Dry Deposition
Dry deposition of particulate matter on natural systems such as vegetated canopies and natural water bodies has been studies for several decades [6, 9, 11]. For a wide variety of biotic and natural surfaces, Sehmel gave a detailed review of published dry particle and gas deposition
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velocities that ranged over three and four orders of magnitude, respectively [6]. The factors that may affect dry deposition of particles and gas species are summarized in Table 4.3 [6]. The mechanisms for dry deposition could be inertial impaction [18–22], interception [23, 24], diffusion [5, 25–27], sedimentation [5, 25, 26], and electrostatic precipitation and thermophoresis [28]. For surface deposition of particles in many industrial processes, inertial impaction and interception are the dominant forces encountered in particle deposition on filters, work benches and in particle sampling of high purity gases for semiconductor manufacture. On the other hand, for finer particles (such as micrometer and sub-micrometer particles), Brownian diffusion emerges as one of the primary mechanisms for deposition of particles on surfaces. Conventionally, to study particle deposition on a surface, many researchers favor a rotating disk in a stagnation flow setting [8, 23]. Ramarao and Tien [23] proposed a procedure to study the combined effect of inertial impaction, sedimentation and interception on particle deposition in a two-dimensional stagnation flow field. For particle size ranges from 1 to 100 mm in diameter, they found that the deposition flux, J, was greater by taking the boundary layer effect (denoted as JBL) into account than by excluding it (denoted as JID). A correction factor, F = JID/ JBL, for the effect of the boundary layer on particle deposition under a range of the flow field constant, a, is obtained, as shown in Figure 4.5. Thus, a laminar flow is usually maintained in microelectronics manufacturing in cleanrooms. Usually finer particles whose diameter ranges between 0.01 and 10 mm are deposited on semiconductor wafers and diffusion is known to be the predominant deposition mechanism. By using the analogy with heat and mass transfer, Liu and Ahn [5] deduced the particle deposition velocity for three laminar flow settings typically used in the manufacturing environment for semiconductor wafers, as shown in Figure 4.6. For a horizontal wafer in a vertical airflow configuration, as shown in Figure 4.6(a), the mass transfer is given as Sh=1:08Sc1=3 Re1=2
Eq. (4-5)
Sh0 ¼ 0:834Sc1=3 Re1=2
Eq. (4-6)
and
where Sh = KDw/D is the mean Sherwood number, K is the mass transfer coefficient, Dw is the wafer diameter, D = kTC/(3pmdp) is the diffusion coefficient, k is the Boltzmann constant, T is the absolute
ZHU
(Continued)
AND
Inversion layer
Electrostatic effects —Attraction —Repulsion Gravitational settling Hygroscopicity
Canopy structure —Area density —Bark —Bole —Leaves —Porosity —Reproductive structure —Soils —Stem —Type
Senescence
Biotic surfaces Canopy growth —Dormant —Expanding
Adhesion
Surface Variables
SURFACE DEPOSITION, LIN
Friction velocity
Flow separation —Above canopy —Below canopy
Diffusion, effect of —Canopy —Diurnal variation —Fetch
Diffusion —Brownian —Eddy equal to (a) Particle (b) Momentum (c) Heat —Effect of canopy on diffusiophoresis Partial pressure in equilibrium with surface solubility
Diffusion —Brownian —Eddy
Diameter Density
Chemical activity
Gases
Agglomeration
Particles
Deposition Material
IN
Atmospheric stability
Aerodynamic roughness —Mass transfer (a) Particles (b) Gases —Heat transfer —Momentum transfer
Micrometeorology Variables
Table 4.3 Some Factors that Influence Dry Deposition of Particles [6]
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Momentum Physical properties Re-suspension Shape Size
Seasonal variation
Solar radiation
Surface heating
Temperature
Terrain —Uniform —Non-uniform
Zero-plane displacements —Mass transfer (a) Particles (b) Gases —Heat transfer —Momentum transfer
Turbulence
Interception
Relative humidity
Thermophoresis
Solubility
Impaction
Particles
Gases
Deposition Material
Pollutant concentration
Micrometeorology Variables
Table 4.3 Some Factors that Influence Dry Deposition of Particles [6] (cont’d)
Water
Prior deposition loading
Pollutant penetration and distribution in canopy
Non-biotic surfaces pH effects on —Reaction —Solubility
Leaf-vegetation —Boundary layer —Change at high winds —Flutter —Stomatal resistant
Electrostatic properties
Surface Variables
276 FUNDAMENTALS
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1 α=0.1 α=1 α=5 α=10
F = JID/JBL
0.9
0.8
0.7 1
10 Particle diameter (mm),dp
100
Figure 4.5 Flux correction factor, F, as a function of particle diameter for various values of a, flow field constant [23].
temperature, C is the Cunningham slip correction factor, m is the molecular viscosity of the fluid, Sc = n/D is the Schmidt number, Re = UDw/ n is the Reynolds number, U is the airflow velocity, and n is the kinematic viscosity. In Eqs. (4-5) and (4-6), the symbol Sh denotes the mean Sherwood number based on the mean mass transfer coefficient, K, for the entire wafer; and Sh0 denotes the Sherwood number at the stagnation point. Note the definition of K = j/N, where j is the particle deposition flux in number of particles per unit surface area of the wafer per unit time and N is the number concentration of particles in the free stream. Therefore, K is also the deposition velocity of the particles. For the airflow configuration depicted in Figure 4.6(a), the overall deposition velocity, V, becomes V ¼ K þ rp gCd 2p =18m
Eq. (4-7)
where the second term on the right-hand side of the equation is the sedimentation velocity, rp is the material density of the particles, and g is the gravitational acceleration.
278
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(a)
(b)
(c)
Figure 4.6 Schematic diagram showing three types of airflow in semiconductor manufacturing [5]. (a) A horizontal wafer in a vertical laminar flow cleanroom. (b) A horizontal wafer in a horizontal-flow clean hood. (c) Vertical wafers in a wafer carrier.
For a horizontal wafer in a horizontal airflow configuration, as illustrated in Figure 4.6(b), the mean and the local mass transfers are given in Eqs. (4-8) and (4-9) and expressed as Shx ¼ 0:664Sc1=3 Re1=2 x
Eq. (4-8)
Shx ¼ 0:332Sc1=3 Rex1=2
Eq. (4-9)
and
where Shx ¼ Kx=D, Shx = Kx/D and Rex = Ux/n are all based on the distance, x, measured from the leading edge of the wafer and the air
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velocity, U. By performing an integration of K over the entire surface area of the wafer, we have 1=2
ShD ¼ 0:739Sc1=3 ReD
Eq. (4-10)
where ShD ¼ KDw =D, ShD = KDw/D and ReD = UDw/n are all based on the wafer diameter, Dw. As shown in Figure 4.6(c), the third configuration is an array of vertical wafers in a wafer carrier. The mean mass transfer coefficient, K, is given by K ¼ ð2h=pRw ÞUfd
Eq. (4-11)
where h is the half width of the channel formed by two neighboring wafers, Rw is the radius of the wafers, U is the mean air velocity in the channel, and fd is the fractional particle deposition and is expressed as fd ¼ 97:27V0:6654
Eq. (4-12)
where V = DDw/h2U is a dimensionless parameter. For the first configuration, as shown in Figure 4.6(a), Liu and Ahn’s prediction on particle deposition velocity was in good agreement with the measured data reported by Pui, Ye and Liu using ammonium fluorescein aerosols [26], as depicted in Figure 4.7.
Deposition Velocity, cm/s
1.0000
Theoretical [5] Experimental
0.1000
0.0100
0.0010
0.0001 0.01
0.1 1 Particle Diameter, mm
10
Figure 4.7 Comparison of the final deposition data from the theory of Liu and Ahn [5] with experimental data of [26] for 3.8-cm diameter wafer and for a free stream velocity of 20 cm/s.
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By taking convection, diffusion, sedimentation, electrical forces, and thermophoresis into account, a numerical simulation of particle deposition on a typical semiconductor wafer in a cleanroom using two different modeling approaches was reported by Peterson et al. [28]. The predicted particle deposition velocity and flux showed a good agreement between the two approaches (i.e. a boundary layer approach and a full numerical simulation) they had adopted. For particle sizes between 0.02 and 0.7 mm at a surface temperature of 330 K, they found that the effect of thermophoresis could be effectively utilized to prevent such particles from depositing on a surface [28].
4.4 Thermophoresis and Its Relevance in Surface Cleaning The phenomenon of particle repulsion from hot surfaces was first observed in the 1880s. However, the theoretical interpretation of the mechanism is still far from complete due to the complexity of the physical processes involved and the new findings obtained recently [12, 29–34]. The radiometric forces acting on particles due either to a temperature gradient in the gas medium or to non-uniform radiation cause this phenomenon. The radiometric motion of particles by temperature gradient is called thermophoresis while the motion of particles by non-uniform radiation is called photophoresis [2, 12, 35, 36]. If, instead a concentration exists and causes particle movement, this phenomenon is then called diffusophoresis [37, 38]. Thermophoresis has been studied by numerous researchers to understand its effect on particle deposition on a cold surface [10, 39, 40], or on particle removal from a heated surface, or in a thermal precipitator [14, 41, 42]. In the air, for spherical particles ranging between 0.05 and 1 mm in diameter, the corresponding Schmidt numbers, Sc = n/D, are from 6 · 103 to 5 · 105. Therefore, Brownian diffusion is negligible and the predominant mechanisms for the movement of the aforementioned particles are convection and thermophoresis [39]. For an airborne particle much smaller than the mean free path of air molecule, l (l = 0.065 mm at 298 K and 1 atm), the particle motion is in the so-called freemolecular regime where the Knudsen number Kn = l/dp 1. The calculation of the thermophoretic force in this regime has long been acknowledged to be in good agreement with experimental data [30]. However, due to the boundary layer effect and other complexities, the theoretical development of the thermophoresis in the transition regime
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(Kn 1) and the slip-flow regime (Kn < 1) is still evolving. The available formulas for these two regimes should be considered as tentative. Talbot et al. [29] have proposed an expression to calculate the thermophoretic velocity applicable to all Knudsen numbers. This formula has been received quite favorably by other researchers [10, 39] and is given as n vt ¼ K T T
Eq. (4-13)
and K ¼ 2Cs
ðkg =kp þ Ct l=Rp Þ½1 þ ðl=Rp Þð1:2 þ 0:41e0:88Rp =l Þ ð1 þ 3Cm l=Rp Þð1 þ 2kg =kp þ 2Ct l=Rp Þ Eq. (4-14)
where K is the thermophoretic coefficient, T is the ambient absolute temperature of the gas and T is the temperature gradient, Cs = 1.147, Cm = 1.146, Ct = 2.2, kg is the thermal conductivity of the surrounding gas, and kp is the thermal conductivity of the particle. For various kg/kp ratios, K in Eq. (4-14) is plotted against l/Rp as shown in Figure 4.8 [39]. Adjacent to a heated planar surface, within the laminar boundary layer, 0.7 0.6
Kg/Kp=0.5
0.5 0.4 0.2
K 0.3
0.1
0.2
0.05 0.1 0.01 0 0.001
0.01
0.1
1
10
λ/Rp
Figure 4.8 Values of the thermophoretic coefficient K for a spherical particle of radius a according to the expression in Eq. (4-14). l is the mean free path of gas molecules and kg/kp is the ratio of the thermal conductivity of the gas to that of the particle [39].
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a particle-free zone about one half of the boundary-layer thickness was reported by Talbot et al. [29]. However, as particles may rotate in the boundary layer under certain conditions, Chomiak and Gupta [43] and Batchelor [44] argued that the effect of thermophoresis on particle removal might not be as conspicuous as predicted from Eqs. (4-13) and (4-14). As reported in Chomiak and Gupta [43], in a laminar boundary layer, thermophoretic force would not affect the particle if its radius, Rp, is 0
11=2 18nD k =k Re x1=4 Tp g p A Rp >@ 2l 1 U¥ þ aRp 1þl =Rp
Eq. (4-15)
where DTp is the thermal diffusivity of the particle material, a is the accommodation coefficient, l* = {(2lCp/Cv)/[Pr(Cp/Cv+1)]} is the heat conduction mean free path, Cp and Cv are the specific heats of the gas at constant pressure and volume, respectively, Pr is the Prandtl number, Rex is the Reynolds number of the flow depending on the distance from the leading edge, and U¥ is the gas velocity outside of the boundary layer. Likewise, in a turbulent boundary layer, the critical particle size is given as 0 11=2 202:7nD k =k Re0:1 Tp g pA x R p >@ 2l 1 U ¥ þ aRp 1þl =Rp
Eq. (4-16)
While applying thermophoresis as a cleaning mechanism to remove deposited particles in a naturally convective airflow, as observed in most Table 4.4 Temperature Gradient and Thermophoretic Velocity [33]
Particle
MgO <20 mm> SiO2 <20 mm>
Temperature Gradient T (K/mm)
Thermophoretic Velocity Predicted Using the Theory in [29] vt (mm/s)
16 45 22 80
0.042 0.13 0.20 0.86
Thermophoretic velocity measured in [33] vt (mm/s) 0.22 0.67 0.58 3.00
– – – –
0.021 0.097 0.017 0.094
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Table 4.5 The Measured Temperature Gradient and Thermophoretic Effect
Particles Material Diameter (mm) SiO2 SiO2
1.0 2.7
SiO2 SiO2 PMMA
10 30 5.0
PMMA
12
PMMA
30
Temperature Gradient T (K/mm)
Particle Velocity Measured in [34] vt (mm/s)
40.0 22.0 80 40.0a 40.0 40.0 31.4 49.5 40.0a 31.4 42.0 40.0a 31.4 49.5 40.0a
1.68 0.58 3.00 1.03 0.69 0.53 0.55 1.14 0.80 0.40 0.73 0.66 0.35 0.78 0.53
a
These values are obtained by interpolation using two preceding data values.
cleanroom operations, the conditions indicated in Eqs. (4-15) and (4-16) are rarely encountered, as reported by Nazaroff et al. [10, 45]. Experimental investigations on thermophoresis have been reported by a number of researchers. Like the corresponding theoretical development in the transition and slip-flow regimes mentioned above, the complexity of the phenomenon has limited the quantity and quality of the experimental data available for model validation. The greatest hindrance to obtain reliable measured data in thermophoresis studies is the interference of natural convection generated also by a temperature gradient in normal gravity [33, 34]. By conducting thermophoresis experiments in a microgravity environment, Toda et al. produced some interesting data as listed in Tables 4.4 and 4.5 [33, 34]. The comparison between the thermophoretic velocity measured by Toda et al. [33, 34] and the predictions using Eq. (4-17), derived by Talbot et al. [29], for Kn < 1, vt ¼ 2Cs n
ðkg =kp þ Ct l=Rp Þ T ð1 þ 2Cm l=Rp Þð1 þ 2kg =kp þ 2Ct l=Rp Þ T
Eq. (4-17)
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Figure 4.9 The relation between the diameter and velocity of the SiO2 particles (T = 40 K/mm). Solid line: measured in [34]. Dotted line: predicted values based on the Brock equation in [29, 30].
Figure 4.10 The relation between the diameter and velocity of the PMMA particles (T = 40 K/mm). Solid line: measured in [34]. Dotted line: predicted values based on the Brock equation in [29, 30].
is shown in Figures 4.9 and 4.10 [29, 30, 33, 34]. As shown in Figure 4.9, Eq. (4-17) has substantially under-predicted the thermophoretic velocity for the SiO2 particles (size ranging from 1 to 30 mm). For the polymethyl methacrylate (PMMA) particles (size ranging from 5 to 30 mm), under-predictions of thermophoretic velocity exist for dp < 25 mm particles and a slight over-prediction for dp = 30 mm particles, as shown in Figure 4.10. The above discrepancies indicated the importance of
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gravity effect. Hence the existing theories on thermophoresis could be biased due to the fact that they were deduced from experimental data in the presence of gravity.
4.5 Electrostatic Force and Its Relevance in Surface Cleaning As shown in Figure 4.4, an artificial electrostatic field was created to remove particles deposited on microelectronics products [7, 46, 47]. On the other hand, similar to the thermophoretic effect, the electrostatic force is another mechanism that would affect particle deposition on surfaces [48–50]. Electrostatic phenomena have been observed since the early period of human civilization, but electrostatic force had not been quantified until the discovery of the Coulomb’s law that laid the foundation for the science of electrostatics two centuries ago. Even though a primitive electrostatic device for cleaning polluted air was built in 1885, it was never developed to the stage suitable for commercialization [51]. Electrostatic precipitators have been widely used to collect fine particles such as fly ashes from coal-fired furnaces or reactors. Another example of the application of the effect of electrostatic precipitation is the electrostatic air cleaners for household use. Particles may acquire charges through surface contact, collection of atmospheric electricity, ionization, and similar phenomena [52]. For a conductive particle, the acquisition of charge on its surface is almost instantaneous. The total charge on the surface of a particle, q, is given as q ¼ e0 p3 d 2p E=6
Eq. (4-18)
where e0 is the dielectric constant of vacuum and E is the electric field strength. For particles with different electrical charges, it was theoretically shown that for dissimilar particles their agglomeration rates were enhanced with increasing surface charge and particle size polydispersity [53]. To remove conductive spherical particles adhered to a conductive surface, the force required to overcome the adhesion force, Fe, is expressed as [46, 47]: Fe ¼ 1:37pe0 E 2 d 2p
Eq. (4-19)
For several simple configurations such as parallel plate, tubular, and wire–plate geometry, the electric field distribution could be obtained
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Figure 4.11 Particle sizes for which the electrostatic force just equals that of adhesion or of gravitation (lines). The legends shown on the lower left corner on this plot indicate the type of the particle used. ‘‘’’ are the Ni particles. ‘‘^’’ are the SiO2 glass particles. ‘‘&’’ are the polystyrene latex particles [46].
either by measurement or by solving the governing equation of electrical potential distribution numerically. Figure 4.11 illustrates the relative strength of adhesion, gravitational and electrostatic forces with respect to various particle sizes. To remove particles of various sizes and chemical compositions, the required electric fields are listed in Table 4.6 [46].
4.6 Dielectrophoresis and Its Relevance in Surface Cleaning When a neutral particle of dielectric material is placed in an electric field, the particle becomes polarized and behaves like an electric dipole. If the electric field is not uniform, the force exerted on the particle is not balanced and results in the movement of the particle. This phenomenon is called dielectrophoresis [54–56]. In the natural environment, most of the particles are not spherical in shape. Therefore, the effect of particle shape plays an important role in the deposition
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Table 4.6 Electric Fields Needed to Remove Particles of the Indicated Size and Composition [46]
Particle Material
Diameter (mm)
Glass
34–35a 9–15
SiO2 Nickel
0.52 60–75 8–10 5–8 3–5 1–3
Polystyrene
10
d
1.1
Field (kV/cm) Needed to Remove the Percentage of Particles Indicated 5% 50% 95% 27 20 29 22 20 >525 10 18 <0 27 12 29 46 600b 41 70 >550e
72 55 69 72 88
116 91 109 123 156
21 87 77 100 78 159 137
32 155 163 174 144 289 227
600c 243 367
446 644
The symbol > means a higher field is needed to remove 5%. a Data from 11 runs, taken after 60 minutes on fully charged particles. b Two of 35 removed. c 23 of 43 removed. d Only 25 particles total, both runs; not likely fully charged. e One of 109 removed; not likely fully charged.
of non-spherical particles. For instance, much effort has been invested to study the deposition of fibers along the human respiratory tract [56]. It is imperative to sort out particles by their specific aspect ratio or by length for the applications mentioned above. For a conductive fiber with an aspect ratio, b = L/dp, its dielectrophoretic velocity is given by Lipowicz and Yeh [56] as v = limb!¥
Km e0 2 ln 2b 0:5 L E2 24m ln 2b 1
Eq. (4-20)
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FUNDAMENTALS
where v is the dielectrophoretic velocity, Km is the dielectric constant of the electrically insulating medium, L is the length of the fiber, and E is the strength of the electric field. As indicated in Eq. (4-20), v is proportional to the square of the length of the fiber. Therefore, dielectrophoresis is a more effective fiber classifier than electrophoresis, as recommended by Lipowicz and Yeh [56]. In the presence of a strong electric field, to avoid the interference by electrophoresis, it is necessary to use either uncharged particles or use an alternating (AC) electric field to fully utilize the effect of dielectrophoresis [55, 56].
4.7 Abrasive Erosion and Its Relevance in Surface Cleaning Solid particle erosion or abrasive blasting erosion refers to the general mechanical degradation or wear of a solid material subjected to a jet stream of abrasive particles impinging on its surface. Examples of the application of abrasive erosion can be found in abrasive cleaning of metal surfaces for coating [58] and for stress corrosion cracking investigation [59], in chemical mechanical polishing [60], and in abrasive drilling and cutting by water jet [61, 62]. However, in many other applications, abrasive erosion causes sever surface damage, which is, of course, not desired. Abrasive erosion damage has been extensively reported, such as in rocket motor tail nozzle [63], on helicopter rotors and gas turbine blades [64], and in pipeline systems for pneumatic or hydraulic transportation of solids [4, 65]. In this section, some recent developments on fundamental mechanisms of solid particle erosion, including abrasive erosion by a single particle impact and erosion by multiple impacts of a solid particle stream, as well as parametric effects on the abrasive erosion rate are discussed. When a solid particle impinges on a material surface, it may skid and/ or rotate on the surface and at the same time create an indentation (ductile materials) or crater (brittle materials). With successive impacts of particles on the same location, this indentation causes material removal due to the repeated plastic deformation and the skidding of sharp-edged hard particles over a surface of relatively low hardness. When the impact velocity is lower than the critical impact velocity, the particle does not skid but rotate, resulting in no cutting damage but only plastic fatigue damage. When the impact velocity is higher than
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n
Ω′ Vt V′n θ Vn
V′ V′t
V G r
t
β C
Figure 4.12 Schematic diagram of surface impact of an abrasive particle.
the critical velocity, the solid particle will skid on the surface, creating a crater, and then rotate on the surface, as shown in Figure 4.12. The critical impact velocity, Vc, can be estimated based on a rolling/sliding contact mechanism [66], as: Vc ¼
K þ cos bðcos b f sin bÞ f ðK þ sin bÞ cos b
kl d sy qffiffiffiffiffiffiffiffi ffi 10E sin u 1=5 m ke V n ð1 þ eÞ p 2ppr s Eq. (4-21)
where u is the impact angle, b is the contact angle, Vn is the normal component of impact velocity, p is the yield pressure, rs is the equivalent radius of a solid particle, d is the maximum crater diameter, m is the particle mass, ke and kl are material property related constants, f is the friction coefficient, E is elasticity or Young’s modulus, sy is the yield stress, e is the rebounding coefficient, and K is the shape factor of particle. The friction coefficient was further estimated by Yabuki and Matsumura [66] and given as: p 2 1 d3 0 rffiffiffiffiffiffiffiffiffiffiffiffi p d sþ p m ke 1=5 8 12 rs · þ V f¼ 2 2pprs 2 n mð1 þ eÞVn
Eq. (4-22)
where p0 is the average pressure required to displace the soft material from the front of the particle and s is the shear strength of the soft material.
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FUNDAMENTALS
The rebounding coefficient was calculated by Tabor [67] using a normal impact model and is given by 104 e¼
m
!1=8
p5 43 35 2r3s
1 n2p 1 n2s þ Ep Es
!2 p5=8
Vn
3 V 2n Vn02 8
3=8
Eq. (4-23) where e is the restitution coefficient (or rebounding coefficient), n is the Poisson’s ratio, V n0 is the normal component of rebounding velocity. The most important issue in abrasive erosion is the erosion rate. The volume of material, Q, removed by a single abrasive impact was given by Finnie [68] and is expressed as: 8 mV2 6 > > sin2u sinu < rck k Q¼ 2 > mV k > : ðcosuÞ2 rck 6
k 6 k tan u > 6
tan u £
Eq. (4-24)
where c and k are the ratio of length to depth of the scratch formed and the ratio of vertical to horizontal force components, respectively, r is the energy required to remove a unit volume of material from the body. Winter and Hutchings [69] further identified two mechanisms for volume removal, namely, ploughing and cutting. Ploughing occurs when a particle rolls over, instead of sliding along the surface, which causes the cutting edge of the particle to penetrate deeply into the material surface instead of performing a scooping action. The total volume removed by an abrasive impact comes from two contributions: the ploughing loss [65], QP ¼
0:5m ðVsin u kÞ2 O
Eq. (4-25)
m 2 2 ðV cos u V2r Þ 2f
Eq. (4-26)
and the cutting loss [70], QC ¼
where O and f are the energies required to remove a unit volume of material from the body by ploughing and cutting, respectively, k is a material property related constant, and Vr is the particle rebounding velocity.
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Despite a relatively clear understanding of abrasive erosion by a single particle impingement, the current knowledge on abrasive erosion by a jet stream of abrasive particles is still inadequate to provide predictive and reliable information on the erosion rate for a given engineering design or application. This lack of knowledge has resulted from insufficient information in three interrelated areas: (1) definition of erosion resistance as an objective material property; (2) establishment of the quantitative relationship among erosion rate, erosion resistance, and environmental parameters; and (3) the determination of these environmental parameters for a given application. So far most studies on erosion rate are reported in terms of the material loss curves or loss rates for particular types of materials of interest. The erosion rate is defined as the ratio of mass loss to mass of erodent particle, which is a dimensionless quantity. There have been many attempts to correlate the erosion rates measured for different materials with one or more established mechanical properties of these materials [71–73]. A theoretical dynamic analysis of a new laboratory technique was recently proposed by Talia et al. [74] for investigating the abrasive erosion mechanisms of brittle, ductile and semi-ductile materials. As shown in Figure 4.13, the solid material samples are mounted on a rotating disk, which are air-blasted by abrasive particles. This measurement system is easy to individually investigate the effects of abrasive impact angle, impact velocity components (normal and tangential), and abrasive material properties. Typical effect of the impact angle on erosion rate is shown in Figure 4.14, in which a nonlinear relationship between erosion rate and impact angle is seen. In addition, the erosion loss appears to be undetectable at small impact angles, which indicates that a minimum angle is required for material removal. Typical effect of impact velocity on erosion rate is illustrated in
Figure 4.13 Experimental system for study of particle erosion mechanism [74].
292
FUNDAMENTALS
Figure 4.14 Example of effect of impact angle on erosion rate [74].
Figure 4.15, in which the erosion rate of different materials representing ductile, brittle and semi-ductile at various impact velocities but with the same impact angle are presented. The apparent linear relationships between the erosion rate and normal impact velocity in a semi-logarithm scale indicate certain similarities of the materials tested.
4.8
Summary
Particle deposition problems are vital challenges to the practitioners in the industries dealing with contaminant removal and surface cleaning. In many manufacturing and processing environments, such as that for producing semiconductors and integrated circuits, substantial amounts of time and efforts are devoted to tackle the ubiquitous problems of particle deposition. Multiple mechanisms are involved in the deposition of particles on various surfaces encountered in industrial processes. In this chapter, the most common and influencing mechanisms of particle deposition are described. The physical aspects of the effect due to dry deposition, thermophoresis, electrostatic force and dielectrophoresis on particle deposition on surfaces are delineated and emphasized to
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Figure 4.15 Example of effect of normal impact particle velocity on erosion rate [74].
strengthen their relevance in contaminant removal and surface cleaning. The applicable range of a specific theory and related caveats when applied to an industrial setting are also provided throughout this chapter. For an in-depth understanding of each of the mechanisms involved in particle deposition, the references cited in this chapter should serve as further reading material and guide to the specific knowledge as well. Surface cleaning by mechanical means can be achieved by abrasive erosion from impingement of fine and hard particles on the surface to be cleaned. The effectiveness of abrasive erosion depends on impact velocity, impact angle, and materials involved. The available empirical correlations are typically application oriented, namely, they are valid for specific applications and within a narrow range of parametric conditions. One particular difficulty in model generalization of abrasive erosion for practical applications is the low predictability of particle behaviors in turbulent jets and boundary layer flows over rugged (eroded) surfaces. Theories with a much wider applicability and a deeper scientific basis are yet to be developed.
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63. J. H. Neilson and A. Gilchrist, ‘‘Erosion by a Stream of Solid Particles,’’ Wear 11, 111 (1968). 64. W. A. Hibbert, ‘‘Helicopter Trials over Sand and Sea: Helicopter Rotor Blade and Engine Erosion by Sand and Seawater,’’ J. R. Aeronaut. Soc. 69, 769 (1965). 65. J. G. A. Bitter, ‘‘A Study of Erosion Phenomena,’’ Wear 6,169 (1963). 66. A. Yabuki and M. Matsumura, ‘‘Theoretical Equation of the Critical Impact Velocity in Solid Particles Impact Erosion,’’ Wear 233–235, 476 (1999). 67. D. Tabor, The Hardness of Metals, p.129, Clarendon Press (1951). 68. I. Finnie, ‘‘Erosion of Surfaces by Solid Particles,’’ Wear 3, 87 (1960). 69. R. E. Winter and I. M. Hutchings, ‘‘Solid Particle Erosion Studies Using Single Angular Particles,’’ Wear 29, 181 (1974). 70. A. Magnee, ‘‘Generalised Law of Erosion: Application to Various Alloys and Intermetalics,’’ Wear 181–183, 550 (1995). 71. Y. Ballout, J. A. Mathis and J. E. Talia, ‘‘Solid Particle Erosion Mechanism in Glass,’’ Wear 196, 263 (1996). 72. Y. Iwai, T. Honda, H. Yamada, T. Matsubara, M. Larsson and S. Hogmark, ‘‘Evaluation of Wear Resistance of Thin Hard Coatings by a New Solid Particle Impact Test,’’ Wear 251, 861 (2001). 73. K. L. Rutherford, R. I. Trezona, A. C. Ramamurthy and I. M. Hutchings, ‘‘The Abrasive and Erosive Wear of Polymeric Paint Films,’’ Wear 203–204, 325 (1997). 74. M. Talia, H. Lankarani and J. E. Talia, ‘‘New Experimental Technique for the Study and Analysis of Solid Particle Erosion Mechanisms,’’ Wear 225–229, 1070 (1999).
5
Tribological Implication of Particles Koji Kato
Department of Mechanical Engineering, College of Engineering, Nihon University, Koriyama City, Japan
5.1
Introduction
When two solid surfaces are brought into contact and are followed by separation or sliding, wear particles are generated at the contact interface and they behave as contaminants for the contact surfaces and surroundings. These particles are generated by the mechanisms of adhesive, abrasive, plastic flow, fatigue, corrosive, diffusive, and melting wear, some of which take place at the same time in the contact region [1, 2]. The size of a wear particle ranges from the scale of nm to that of mm, and the microstructure of the particle material is very different from that of the original surface material in general. Both dry and wet contact systems generate wear particles of this character. Wear particles and the mechanisms of their generation are described in this chapter from this view point.
5.2 The Micro-Site for Generation of Wear Particles Any solid surface is not ideally smooth from a microscopic view point. The cleaved surface of mica sheet is rough at the scale of a silicon atom. The well polished silicon wafer surface of single crystalline structure is still rough at the scale of nanometer. The surfaces of standard glass mirrors, optical lenses, and fine diamond tips of manipulators have surface asperities whose height ranges from about 10 to about 100 nm. The surfaces of machine elements and devices made of metals, ceramics or
R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 299–327 ª 2008 William Andrew, Inc.
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plastics have surface asperities whose height ranges from about 0.1 to about 100 mm. Figure 5.1 shows an example of surface asperities observed with the AFM (atomic force microscope) on the mirror surface of a silicon wafer. A cross section of a flat surface as shown in Figure 5.1 is schematically shown in Figure 5.2, where asperities distribute along the center line of z = 0 at various heights in the direction of z-axis and the probability density of the asperity height at the level z is given by the function f(z). By introducing this function f(z) for describing the height distribution of asperities, the number n(d) of asperities in contact against an ideally flat surface at the height of z = d in Figure 5.2 is given by the following equation: Z¥ fðzÞdz
nðdÞ ¼ hA0
Eq. (5-1)
d
Figure 5.1 An AFM image of surface asperities on a polished silicon wafer.
Figure 5.2 A schematic model of height distribution of asperities along the center line and a function f(z) showing the distribution of probability density of contact of asperities at the level z.
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where h is the density of asperities on the nominally flat surface, A0 is the nominal surface area, and f(z) is generally given by the Gaussian. The value of h varies depending on the level of surface finish and a certain finishing method does not always give its specific value. Briefly speaking, the value of h may be supposed to vary in the range from 102 per mm2 to 104 per mm2. Therefore, when a flat surface has the nominal or apparent surface area of 10 · 10 mm2 for contact, the total number of asperities for the consideration of real contact between asperities is supposed to vary from 104 to 106. Among these asperities, the relatively higher asperities contact first and the contact level of z = d shown in Figure 5.2 is determined so as to give the necessary size of the real contact area to support the applied load. If two asperities are assumed to have the semi-spherical tip shape with the radii of R1 and R2, a model of initiation of sliding between them is schematically shown in Figure 5.3, where W is the normal load, F is the friction force for initiating sliding, and A is the real contact area. The mean contact pressure p and the shear strength si at the contact interface are given by p = W=A
Eq. (5-2)
si = F=A
Eq. (5-3)
When two asperities are in contact with perfectly elastic deformation only, the contact area A is theoretically given by Hertz [3] as follows: 3 WR 2=3 A=p 4 E
Eq. (5-4)
Figure 5.3 A schematic model of contact of two spherical asperities. R1, R2: radius of asperity; E1, E2: Young’s modulus; n1, n2: Poisson’s ratio; W: normal load; F: friction force; A: real contact area; p: mean contact pressure; si : shear strength of the contact interface.
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where 1/R = 1/R1 + 1/R2; 1/E = (1 n12 )/E1 + (1 n22 )/E2; E1, E2 are Young’s modulus; n1, n2: Poisson’s ratio. When a single asperity is in contact with perfectly plastic deformation only, the contact area A is experimentally given by McFarlane and Tabor [4] as follows: pffiffiffi W= ak A = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eq. (5-5) 1ðsi =kÞ2 where a is the experimental constant of 3.3–25, k is the shear strength of the material of the asperity in plastic deformation, and si is the shear strength of the contact interface. By comparing Eqs. (5-4) and (5-5), it is clear that the contact area A is independent of the shear strength si in elastic contact, but it strongly depends on the value of si in plastic contact, where si is close to zero in ideally lubricated condition and is close to k in high vacuum with uncontaminated surfaces of ductile material. It is obvious that the smallest pffiffiffi value of A is given by W= ak. The value of a changes with the ductility of the asperity material and the shape of contact [5]. Friction between two asperities given in Figure 5.3 is generated at the contact interface of the area A given by Eqs. (5-4) or (5-5), and the friction coefficient m defined as the ratio of the friction force F against the load W is given by Eqs. (5-2) and (5-3) as follows: m = F=W = si =p
Eq. (5-6)
From these analyses of micro-mechanisms of contact and friction, it is confirmed that the wear particles are generated at the contact interface of surface asperities whose size is determined by Eq. (5-4) or (5-5), and it depends on the shear strength si of the contact interface in plastic contact. Micro-contacts of this mechanism distribute at the apparent large contact interface as shown in Figure 5.2 and generate a large number of wear particles from them in contact and separation or sliding.
5.3
Wear Modes and Particles
5.3.1 Adhesive transfer of atoms in contact and separation When two uncontaminated solid surfaces are in contact, surface atoms on both surfaces form atomic bonds as they are in the bulk, and the
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substrates on both sides of the contact interface are deformed elastically or plastically. In many practical cases, the microstructure of the solid has micro-defects such as vacancies, voids, inclusions, dislocations, and grain boundaries. Therefore, the strain in the contact region is not perfectly removed microscopically by unloading even when the apparent strain is within the elastic limit. When two uncontaminated solid surfaces are in contact, surface atoms on both surfaces form atomic bonds by their original nature. In the process of unloading, there is no reason for separation to occur only at the contact interface. The contact region around the contact interface also has a strain distribution. As a result, fracture in separation of two surfaces can take place at a new site different from the initial contact interface. This means that some atoms are transferred to the mating contact surface. In the contact and separation between a clean spherical pin tip of tungsten and a clean flat surface of gold in high vacuum, the transfer of atoms of gold to the surface of tungsten was experimentally observed by field ion micrographs [6]. In the contact and separation between a tip of nickel and a flat surface of gold, the mutual adhesive transfer of atoms of gold and nickel was shown theoretically by molecular dynamics simulation [7].
5.3.2 Adhesive transfer of flake-like particles in sliding contact Macroscopic sliding occurs at the contact interface without fracture in its vicinity when the contact surfaces are well contaminated or lubricated and the shear strength si of the contact interface is relatively much smaller than the shear strength k of the contact material. The generation of wear particles from the contact surfaces does not happen in such a situation. Relative displacement at the contact interfaces is expected to take place between atoms or molecules of contaminants or lubricating materials. However, contaminants or lubricants at the contact interface are partially removed from there by sliding in practice because of the nonuniformity of the atomic structure in the surface layer and that of the surface roughness. As a result, atomic bonds are partially formed in such parts in the contact interface where contaminants or lubricants are removed. The distributions of contact stresses of shear and tension or compression become complex at the nanometer scale, which introduces cracking in
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the subsurface and generates adhesive transfer of particles of bulk material to the mating surface. Figure 5.4 shows three modes of crack initiation and propagation caused by the strong adhesion at the contact interface [8]. In Figure 5.4(a), a fragment is generated as an adhesive wear particle in sliding by having a crack in the lower body at the exit side of the contact and another crack in the upper body at the entry side of the contact. When each crack reaches the front free surface, a fragment is formed as a mixture of materials of the upper and the lower bodies. It is generally rolled up in the following sliding [9]. In Figure 5.4(b), a crack is introduced in the lower body at the entry side of the contact and it propagates to the contact interface by generating the adhesive transfer of a thin fragment from the lower body to the upper surface. In Figure 5.4 (c), a crack is introduced in the lower body at the exit side of the contact and it propagates to the free surface on the other side by generating the adhesive transfer of a thick fragment from the lower body to the upper surface. These three modes of generation of adhesive transfer of a fragment can take place at any scale from nanometer to micrometer. Figure 5.5 shows the cluster of thin flake-like fragments which are transferred by the mode of Figure 5.4(b) from the mating surface by adhesion. The thickness of each fragment ranges from about 0.1 to about 1.0 mm [8].
Figure 5.4 The modes of crack initiation and propagation for the adhesive transfer of a particle. (a) Curving of the adhesive contact interface and crack initiation and propagation on entry and exit sides of contact. (b) Strong adhesion at the contact interface and crack initiation and propagation at the exit side of contact. (c) Strong adhesion at the contact interface and crack initiation and propagation at the entry side of contact.
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Figure 5.5 Adhesive wear particles of SUS 304 stainless steel transferred from the mating surface by one pass of sliding [8].
5.3.3 Micro-cutting and generation of fine feather-like particles in abrasive sliding When the upper asperity is relatively harder and has a certain amount of indentation on the relatively softer and flatter surface, a fine featherlike particle is generated by the mechanism of micro-cutting. The shear strength si of the contact interface must be low enough to have continuous relative movement at the contact interface without adhesion between two surfaces. The fine feather-like particle detaches from the surface when a crack is introduced at its neck. The mechanism of this micro-cutting is the continuous plastic flow of the material in the subsurface of the lower body along the surface of the harder upper body. This mechanism can take place even at the nanometer scale on the surfaces of metals and ceramics. Figure 5.7 shows a cluster of fine feather-like particles of silicon formed by this mechanism at the tip of diamond by one pass of sliding on a silicon wafer [10]. When the shear strength si at the contact interface is relatively large because of partial adhesion and when the amount of indentation of the upper spherical asperity is relatively small, a fine feather-like particle described in Figure 5.6(a) is not formed, but a wedge-like particle is formed as described in Figure 5.6(b). The wedge is detached from the surface when it is hit by surface irregularities during the following sliding motion.
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Figure 5.6 The modes of plastic deformation and particle generation in abrasive sliding. (a) Fine feather-like particle generation. Sliding takes place between the spherical asperity and the particle. (b) Wedge generation. Sliding takes place at the bottom of the wedge as a result of adhesion between the wedge and the spherical asperity. (c) Ploughing with a small amount of plastic deformation on the flat surface without generating a free particle. An accumulated plastic deformation by repeated sliding contact generates a filmy wear particle by the mechanism of plastic flow wear or low cycle fatigue wear.
When the indentation of the upper spherical asperity is relatively small and the shear strength si is also small, the surface layer of the lower flat is slightly deformed plastically, but a free particle is not generated by a single pass of sliding as shown in Figure 5.6(c). The accumulation of plastic deformation by the repeated contact of sliding is necessary to generate a free particle from the flat surface by the mechanism of plastic flow or low cycle fatigue. The regimes of these three modes of wear are theoretically described in Figure 5.8 by the degree of penetration Dp and the normalized shear strength f as follows: 1=2 hðdepth of indentationÞ pHv 1=2 pHv 2 Dp = R 1 =R 2W 2W aðradius of contact areaÞ Eq. (5-7)
f=
si ðshear strength of the contact interfaceÞ kðshear strength of the grooved materialÞ
Eq. (5-8)
where R is the radius of asperity tip, W is the normal load, and Hv is the hardness of the grooved material. It is experimentally well confirmed that Figure 5.8 predicts each wear mode very well [11].
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(a)
(b)
Figure 5.7 A cluster of fine feather-like particles of silicon formed by the abrasive cutting of a diamond pin. Small abrasive asperities on the surface of the tip are invisible [10]. (a) 2 mm sliding and (b) 20 mm sliding.
5.3.4 Surface plastic flow and thin filmy wear particle generation by repeated contacts When a ductile asperity is repeatedly rubbed by a relatively harder flat surface in plastic contact with low shear strength si at the contact interface, the surface layer of the asperity flows plastically and generates a thin filmy particle which is smeared out of the interface as shown in Figure 5.9 (a). Figure 5.10 shows one thin filmy particle generated from steel in oil by this mechanism after 8 · 103 cycles [12].
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Figure 5.8 Abrasive wear mode diagram [11].
Figure 5.9 The modes of plastic flow and generation of thin filmy wear particles in the repeated sliding contact with the relatively low shear strength si at the interface. (a) A thin filmy wear particle is squeezed out from the surface layer to the sliding direction by the repeated unidirectional shear under compression (upper figure). (b) Thin filmy wear particles are squeezed out from the surface layer to the vertical direction against the sliding direction by the repeated compression (lower figure). ˜ Denotes the sliding direction of the upper surface which is perpendicular to the paper surface.
A similar mechanism operates, as shown in Figure 5.9(b), on a flat surface of a ductile material when a relatively harder spherical asperity slides repeatedly on the same groove formed by the plastic deformation of the flat surface. Thin filmy particles are formed on both sides of the groove as a result of accumulated plastic strain in the repeated contact.
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Figure 5.10 A thin filmy wear particle of steel generated at a ridge after 8 · 103 cycles of sliding contact against a steel flat pin in oil [12].The arrow indicates the sliding direction of the counter surface.
5.3.5 Crack initiation and propagation in the subsurface of contact and generation of a flake-like particle by repeated contact When an asperity repeatedly slides over the same interface in elastic– plastic contact, a crack is generated at the local region of plastic yield and it propagates within the subsurface until it reaches the surface and generates a thin flake-like particle by the mechanism of fatigue as shown in Figure 5.11. In Figure 5.12, a very thin flake-like particle is delaminated by the low cycle fatigue mechanism from the surface of CNx coating, which has hardness around 25 GPa, after repeated sliding contact of a diamond pin under the light load in the mN range [13].
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Figure 5.11 The mode of crack initiation and propagation for the generation of a flake-like particle by the mechanism of fatigue fracture. (a)
(b)
(c)
Figure 5.12 AFM images of delamination of thin flake-like particles from the CNx coating by the repeated sliding contact of a diamond pin of 15 nm radius under the load of 14 mN [13]. (a) A wavy pattern of wear scar after 18 cycles of sliding, (b) sudden surface delamination after 19 cycles, and (c) whole image of the wear scar after 19 cycles.
Wear particles of similar type can be generated from metals, ceramics, and plastics. Depending on the amount of the contact load and the contact geometry, the thickness of the flake-like particle ranges from the order of nanometer to that of micrometer.
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5.3.6 Tribo-oxidation and generation of particles of oxides by repeated contacts in air and water In the case of sliding contact of steel elements in air without lubrication, contact surfaces are quickly oxidized by friction and the oxide film of iron grows on the rubbed surface. The iron oxide delaminates from the surface by itself at a certain thickness and forms free particles. The growth of oxide film is not simply a function of temperature at the interface, which is raised by frictional heat, but a function of tribological activation of oxidation through the deformation and fracture of surface materials and the successive mechanical removal of oxides by friction. A wear model based on this understanding of oxidative wear gives an expression of wear coefficient K as follows [14]: K=
wear volume=sliding distance = dA expðQ=Rq T Þ=j2 r2 v Eq. (5-9) load=hardness
where j is the critical thickness of oxide for self delamination, d is the contact length, v is the sliding speed, A is the Arrhenius constant, Q is the activation energy, Rq is the gas constant, T is the temperature, and r is the density of the oxide. Tribological activation of oxidation is well observed in rolling contact of silicon nitride Si3N4 which is known as an inert ceramic. Figure 5.13(a) shows fine and transparent fragments of SiO2 on the surface of a Si3N4
(a)
(b)
Figure 5.13 Optical images of fine and transparent wear particles of Si3N4 generated in pure rolling contact in air. Particles are SiO2 [15]. (a) Particles on the roller surface of Si3N4 after 106 rolling cycles. (b) One transparent wear particle of SiO2.
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roller generated after 106 rolling cycles in air, and Figure 5.13(b) shows the collection of these fragments as oxidative wear particles [15]. In the pure rolling contact for the observation of Figure 5.13, frictional heat generation is negligibly small at the contact interface and the microscopic contact pressure at asperities is close to the hardness value of Si3N4 which is around 20 GPa. In this contact condition, the oxidation of Si3N4 was enhanced at the contact interface in air at room temperature. When a Si3N4 pin slides against a Si3N4 disk in water, Si3N4 reacts with oxygen and water as follows, Si3 N4 þ 6H2 O ! 3SiO2 þ 4NH3 SiO2 þ 2H2 O ! SiðOHÞ4
Eq. (5-10) Eq. (5-11)
where SiO2 dissolves into water by forming the structure of Si(OH)4 [16, 17]. When the content of Si(OH)4 in water is over the saturation point, SiO2 precipitates as fine particles from the solution. Figure 5.14(a) shows the thin films of SiO2 growth by friction in water at 40 C. Figure 5.14(b) shows fine needles of SiO2 formed by friction of Si3N4 against itself in water at 20 C, and Figure 5.14(c) shows fine particles of SiO2 precipitated from the solution of Si(OH)4 formed by wear of Si3N4 in water.
5.3.7 Wear particles generated in sliding of steels in oil with additives When steel surfaces slide against each other under the condition of boundary lubrication with a base oil (hexadecane), which contains antiwear additives such as zinc dialkyl-dithiophosphate (ZDDP) or metatricresyl phosphate (TCP), wear particles of various sizes are generated as shown in Table 5.1 [19] and Tables 5.2 and 5.3 [20]. Table 5.1 shows that many wear particles have a thickness of about 100 nm and size in the range of 1000–5000 nm. Small particles of thickness of about 5–10 nm are also included. Table 5.2 shows that the typical size of small particles (debris) ranges from 10 to 300 nm and the typical size of large particles ranges from 500 to 2000 nm depending on the type of the additive. The thickness of the particles has a range smaller than 500 nm.
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Figure 5.14 Wear particles formed on the surface of Si3N4 by the self-mated sliding in water [18]. (a) Thin films of SiO2 on the surface of Si3N4 grown by friction against itself at 40 C. (b) Fine needle-like particles rolled up from SiO2 film on the surface of Si3N4 by friction against itself at 20 C. (c) Fine particles precipitated from the water containing Si(OH)4 generated by wear of Si3N4.
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Table 5.1 Mean Sizes of Particles [19]
Nature of Interfacial Material
h/h*
d/d*
1000–5000 ffi 5000 100
1 1 ffi 101
102 102 103
3000 500 >5000
1 1 1
105 2 · 103 2 · 102 2 · 103
Mean Size (nm) h
Without additives Delaminated plates 100 Chips 500–1000 Particles 100 With antiwear additives Particles 5–10 Rolls ffi 100 Lumps ffi 100 Films ffi 100
d
h: height; d: lateral mean size; h*: interfacial thickness; d*: Hertzian diameter (approximately 1.5 · 105 nm).
Table 5.2 Shape and Size of Wear Particles Generated in Boundary Lubrication [20]
Film on Scar
Second ZDDP TCP Amine phosphate Amine monothiophosphate S/P Thiocarbamate Base oil
Typical Large Debris (mm)
Thick 0.5 mm 3 · 2 (composite) Thick 0.2 mm 0.5 (few, composite) Thin* 0.5 (composite) Thin 0.5 (flakes) Thin Thin Thin
0.5 (composite) gel 2 (composite)
Typical Small Debris (nm) 50 120 300 200 80 30 10
Table 5.3 shows that carbon, oxygen, and phosphorous are highly contained in the wear particles although they are generated by friction between steels. It means wear particles are formed from the chemical reaction products of steel, oil, additives and oxygen.
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Table 5.3 Chemical Composition of Wear Particles and Wear Surfaces [20]
Sample On ball (5 minutes)
Analyses
Location
C
O
P
Fe
Scar 11 42 Film on scar 6 52 Auger Debris ahead 31 44 of scar SEM/EDX 63 24
10 15 8
34 24 17
2
1.3
Auger
Gold extraction replica (6.5 minutes) Carbon adhesive replica (6.5 minutes) Centrifuge (30 minutes) SEM/EDX Filter (60 minutes) SEM/EDX
86 12 0.7 0.5 75 22 1 0.1
5.4 Wear Rate and Number of Generated Wear Particles The wear rate ws is generally defined as the wear volume V divided by the load W and the sliding distance L as follows: ws = V=WL
Eq. (5-12)
It is called specific wear volume or specific wear amount, and has the dimension of mm3/Nm for the convenience of engineering usage. When a non-dimensional coefficient is preferred to describe the wear rate, the wear coefficient K is introduced by the following definition: K=
V=L W=Hv
Eq. (5-13)
where Hv is the hardness of wearing material and W/Hv is an estimation of the real contact area in plastic contact. Hv has the dimension of N/m2, so K is non-dimensional. The value of Hv is of the order of 1 GPa for metallic materials and 10 GPa for ceramics. Therefore, the value of ws expressed by the unit of nm3/Nm ranges within a value that is about ten times smaller than the value for K. The value of wear coefficient K of metals in self-mated sliding in air varies of the order from 103 to 102 as shown in Table 5.4 [21]. The value of K of AISI 52100 steel in self-mated sliding is of the order of 102 in dry argon and it is reduced down to the order of 1010 by the condition of lubrication as shown in Table 5.5 [22].
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Table 5.4 Wear Coefficient K in Self-mated Sliding of AISI 52100 Steel [21]
Environment Dry argon Dry air Cyclohexane Paraffinic oil Paraffinic oil + TCP Engine oil
Wear Coefficient (K) 1.0 · 102 1.0 · 103 8.4 · 106 3.2 · 107 3.3 · 109 2.0 · 1010
TCP: Meta-tricresylphosphate.
Table 5.5 Wear coefficient K in self-mated sliding of pure metals in air [22]
Materials Combination Silver/silver Cadmium/cadmium Copper/copper Platinum/platinum Zinc/zinc
Wear Coefficient (K) 4.0 5.7 1.1 1.3 5.3
· · · · ·
103 103 102 102 102
Figure 5.15 shows the distribution of the specific wear volume ws and the friction coefficient m observed with Al2O3, ZrO2 and SiC in self-mated sliding in air where ws varies from 109 to 102 mm3/Nm depending on the load and velocity. The similar distribution of ws is confirmed with Si3N4/ Si3N4, SiC/SiC, PSZ/PSZ (partially stabilized zirconia) and Al2O3/Al2O3 [24]. If the self-mated sliding of Si3N4 and SiC is carried out in water, the specific wear amount ws changes from 106 to 108 mm3/Nm by the repetition of friction cycle [25]. Figure 5.16 shows a comparison of the specific wear amount of three kinds of materials: cermets, ceramics, and metals. Here ws of ceramics and cermets varies in the range from 107 to 105 mm3/Nm and that of the metals varies in the range from 104 to 103 mm3/Nm [26]. By considering all these observations shown in Tables 5.4 and 5.5 and in Figures 5.15 and 5.16, the value of ws can be supposed to vary in a wide range from 1010 to 102 mm3/Nm depending on the contact material, load, velocity, environment, and lubricant. Only when lubrication is very
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Figure 5.15 Specific wear amount ws and friction coefficient m observed with self-mated sliding of Al2O3, ZnO2, and SiC in air without lubrication [23].
Figure 5.16 The specific wear amount ws of ceramics, cermets and metals, where the ceramics are original ones and metals are binders for cermets. Observations are made under the same load and velocity in air with self-mated materials [23].
well applied and the contact surfaces are well separated by a lubricant film, a specific wear volume smaller than 1010 mm3/Nm can be expected. If we suppose that all wear particles have the same size and shape of a thin rectangular plate, which has the thickness t, the width l, and the
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length l, the volume DV of one wear particle is described by DV = tl2
Eq. (5-14)
By introducing the total number N of the wear particles for the wear volume V, V is described by V = Ntl2
Eq. (5-15)
It is generally observed by experiments that t/l 1/10. By introducing this experimental relationship into Eq. (5-15), V=
N 3 l 10
Eq. (5-16)
By introducing Eq. (5-16) into Eq. (5-12), the total number N of wear particles under the load W and after the sliding distance L is described by N 10 = 3 ws WL l
Eq. (5-17)
If we assume the value of l = 104 mm and ws = 106 mm3/Nm, Eq. (5-17) gives the following value: N = 107 ð1=NmÞ WL
Eq. (5-18)
This value given by the brief calculation shows that very large number of wear particles are generated even when the wear rate is acceptably small for practice. For more exact prediction of the number of wear particles generated at a certain wear rate, the distribution of particle size must be more precisely understood. It is easy to understand that the total number of wear particles generated under the unit load and unit sliding distance must be much larger than the value of Eq. (5-18) when wear particles in the size range of nm are counted for the calculation.
5.5
The Size Distribution of Wear Particles
In sliding of a spherical pin against a flat surface, wear particles are generated by different wear mechanisms working at the same time,
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although one or two dominant wear mechanisms can be expected. Therefore, the size of a wear particle is obtained on all particles by measuring its largest aspect length with a particle counter as a characteristic parameter without regard to the mode of wear for the generation of each particle. Figure 5.17 shows the inversely set friction apparatus for producing wear particles by sliding of a pin against a rotary disk from which wear particles drop on the surface of silicon wafer by gravity in the SEM with the vacuum of 9 · 103 Pa [27]. Figure 5.18 shows the number n of wear particles generated from a disk of stainless steel for each cycle of disk rotation and sliding against a pin of WC or diamond. Wear particles of the size in the range from 0.25 to 10 mm are observed in the figure [28]. In the case of sliding against a diamond pin, the particle number n reaches a maximum value in the fourth friction cycle and it becomes smaller as the friction cycle is increased up to ten cycles. But in the case of sliding against a WC pin, the particle number n varies rather randomly for each friction cycle from the first to the tenth cycle. The total number of wear particles generated in ten friction cycles is larger for the WC pin than for the diamond pin. Some experimental relationships between the number of
Figure 5.17 Friction apparatus of pin on disk which is inversely set in the SEM and has a silicon wafer of 500 diameter for receiving wear particles dropped from the contact by gravity in the vacuum of 9 · 103 Pa [27].
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Figure 5.18 The number n of wear particles generated from a stainless steel disk in its each cycle of rotation for 10 cycles sliding against a pin of WC or diamond [28].
wear particles n and the friction conditions in the abrasive sliding tests by the apparatus shown in Figure 5.17 are obtained as follows: For diamond pin/SUS 304 stainless steel disk n = 6:0 · 102 D2:3 p
Eq. (5-19)
For sapphire pin/SUS 304 stainless steel disk n = 9:8 · 104 D2:3 p
Eq. (5-20)
For WC pin/SUS 304 stainless steel disk n = 1:1 · 104 D1:2 p
Eq. (5-21)
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where n is the total number of wear particles of stainless steel generated in the sliding of 1 m and Dp is the parameter defined by Eq. (5-7). The differences among these three equations are caused by the different shear strength of si at the contact interface. Diamond has the smallest value of si and WC has the largest value of si among the three materials of the pin [28]. Figure 5.19 shows the effects of pin material, pin tip radius and normal load on the mean size d of wear particles. The load does not seem to have strong effect on the mean size d, but the material and tip radius of the pin show much stronger effect on d. Diamond is the material that generates smaller wear particles and WC generates larger wear particles [29]. For more exact analysis of the distribution of the size of wear particles, the description of the style of Figure 5.20 is useful, where f(d) is a function to give the probability density of the size d. Figure 5.20 is observed with WC pin/SUS304 stainless steel disk for the different pin tip radius and normal load. The number of wear particles for sliding of 1 m is given for n in the figure. As is observed in the figure, the value of f(d) increases in the range below 1.0 mm. The particles smaller than 0.25 mm are not observed in the figure because of the limit of resolution of the particle counter used for counting. If the particles smaller than 0.25 mm could be counted down to the size in nm scale, an enormously
Figure 5.19 The mean size d of wear particles generated from the SUS 304 stainless steel disk sliding against a pin made of sapphire or SiC. The value of d is obtained for the different combinations of pin material, pin tip radius and load [29].
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Figure 5.20 The probability density f(d) of the size d of wear particles observed on particles generated from the SUS 304 stainless steel disk sliding against a WC pin in vacuum of 9 · 103 Pa. The number of wear particles is shown by n in the figure [29].
large number of wear particles would be counted and a value of f(d) much higher than 100 might be observed in the range below 0.25 mm. Equations (5-19)–(5-21) must be changed for such high-resolution particle counting.
5.6
Concluding Remarks
5.6.1 Solid wear particles The representative wear mechanisms of solids (metals, ceramics, and hard coatings) and characteristics of wear particles were explained in this chapter by introducing wear models and experimental observations in vacuum, air, water, and oil. In order to give better understanding about the microscopic contact points between surface asperities where wear particles are generated, the mechanisms of contact and friction were briefly introduced before
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explaining the wear mechanisms and the size and distribution of wear particles. The mechanisms of generation of wear particles introduced in this chapter are applicable to particles in the size range from nm to mm. Experimental observations of wear particles in the range of 1–10 nm are not yet well made. However, the wear models confirmed in the range of mm may be applied to wear at the nm scale, because the usefulness of the traditional contact mechanics based on the continuum theory is very well confirmed in the theoretical analysis with the molecular dynamics simulations [30, 31].
5.6.2 Gas molecules by wear In the unlubricated sliding of diamond against hard materials in air, a high temperature is generated at the contact region as the result of frictional heating and diamond is worn by oxidation generating carbon dioxide CO2 [32]. If silicon nitride Si3N4 is rubbed in air, it is oxidized and NH3 gas is generated together with silicon oxide (SiO2) as shown in Eq. (5-10) [17, 18]. These gases CO2 and NH3 are contaminants on a molecular scale for various clean surfaces. These kinds of gas molecules generated by wear were not explained in this chapter, because there are very few published reports and these are insufficient to provide useful information from the viewpoint of contamination sources.
5.6.3 Triboemission of electrons, ions, photons, and particles Electrons, ions, photons, and particles, which are charged negatively or positively, are emitted from the contact region during friction [33]. The amount of their emission increases with load and sliding velocity. Tribo-microplasma is generated near the contact region and it introduces unique tribo-chemical reactions [33, 34]. Figure 5.21 shows the total image, UV image and IR image observed from the side of the contact through the sapphire disk [35]. Figure 5.22 shows the images observed from the bottom of contact through the sapphire disk [35]. The plasma observed in these figures enhances the chemical reaction at the contact region. The resultant chemical reaction products work as contaminants in some cases. However, practically useful explanations from the viewpoint of contamination are not considered in this chapter at the present time,
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Figure 5.21 The images of tribo-microplasma observed from the side of sliding contact between a spherical diamond pin and a sapphire disk [35]. (a) Total side image. The arrow for V denotes the sliding direction of lower disk. The arrow for F denotes the loading direction at the center of contact. (b) UV image. (c) IR image.
Figure 5.22 The images of tribo-microplasma observed from the bottom of sliding contact between a spherical diamond pin and a sapphire disk. The rings O in the image denote observed contact area [35]. (a) Total image. The arrow for V denotes the sliding direction of lower disk. (b) UV image. (c) IR image.
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because this tribo-plasma was found very recently [35, 36]. Further research from the viewpoint of contamination and cleaning is planned in the future.
Acknowledgment This author would like to express his appreciation to Mr. Boyko Stoimenov and Mr. Kosuke Ito in the Laboratory of Tribology at Tohoku University for their considerable help in preparing materials for this chapter.
References 1. K. Kato, ‘‘Classification of Wear Mechanisms/Models,’’ Proc. Inst. Mech. Engrs., J. Eng. Tribol. 216, 349 (2002). 2. K. Kato, ‘‘Wear Mechanisms,’’ in New Directions in Tribology, I. Hutchings (Ed.), pp. 39–56, Mechanical Engineering Publications, London (1997). € 3. H. Hertz, ‘‘Uber die Ber€ uhrung fester elastischer Ko¨rper (On the contact of elastic solids),’’ J. reine und angewandte Mathematik 92, 156–171 (1882) [For English translation see ‘‘Miscellaneous Papers by H. Hertz,’’ D. E. Jones and G. A. Schott (Eds.), Macmillan, London (1896)]. 4. J. S. McFarlane and D. Tabor, ‘‘Relation between Friction and Adhesion,’’ Proc. Roy. Soc. London, Series A 202, 244 (1950). 5. T. Kayaba and K. Kato, ‘‘Experimental Analysis of Junction Growth with a Junction Model,’’ Wear 51, 105 (1978). 6. D. Buckley, ‘‘Surface Effects in Adhesion, Friction, Wear and Lubrication,’’ in Tribology Series, Volume 5, pp. 253–254, Elsevier, London (1981). 7. U. Landman, W. Luedtke, N. Burnham and R. Colton, ‘‘Atomistic Mechanisms and Dynamics of Adhesion, Nanoindentation and Fracture,’’ Science 248, 454 (1990). 8. T. Kayaba and K. Kato, ‘‘The Adhesive Transfer of the Slip-Tongue and the Wedge,’’ ASLE Trans. 24, 164 (1981). 9. J. A. Greenwood and D. Tabor, ‘‘The Properties of Model Friction Junctions,’’ Proc. Conf. on Lubrication and Wear, Inst. Mech. Engs. 314 (1957). 10. J. G. Xu and K. Kato, ‘‘Microwear Mechanisms of Silicon Sliding Against Diamond in Water Vapor,’’ STLE Tribology Transactions 39, 621 (1996). 11. K. Hokkirigawa and K. Kato, ‘‘An Experimental and Theoretical Investigation of Ploughing, Cutting, and Wedge Formation during Abrasive Wear,’’ Tribology International 21, 151 (1988). 12. T. Akagaki and K. Kato, ‘‘Plastic Flow Process of Surface Layer in Flow Wear Under Boundary Lubricated Conditions’’, Wear 117, 179 (1987). 13. K. Kato, H. Koide and N. Umehara, ‘‘Micro-Wear Mechanisms of Thin Hard Coatings Sliding Against Diamond Tip of AFM,’’ Advances in Information Storage Systems 8, 289 (1998).
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14. T. F. J. Quinn, in Proc. Int. Conf. on Tribology-Friction, Lubrication and Wear Fifty Years On, Inst. Mech. Engrs. Conf. Series 1987-5, 253 (1987). 15. M. Akazawa, K. Kato and K. Umeya, ‘‘Wear Properties of Silicon Nitride in Rolling Contact,’’ Wear 110, 285 (1986). 16. T. E. Fischer and H. Tomizawa, ‘‘Interaction of Tribochemistry and Microfracture in the Friction and Wear of Silicon Nitride,’’ Wear 105, 29 (1985). 17. T. Saito, Y. Imada and F. Honda, ‘‘An Analytical Observation of the Tribochemical Reaction of Silicon Nitride Sliding with Low Friction in Aqueous Solutions,’’ Wear 205, 153 (1997). 18. J. Xu, K. Kato and T. Hirayama, ‘‘The Transition of Wear Mode during the Running-in Process of Silicon Nitride Sliding in Water,’’ Wear 205, 55 (1997). 19. J. M. Georges, ‘‘Colloidal Behavior of Films in Boundary Lubrication,’’ in Microscopic Aspects of Adhesion and Lubrication, J. M. Georges (Ed.), pp. 729–761, Elsevier, New York (1982). 20. J. Sheasby, T. Canghlim, S. Terranova and A.Cohen, ‘‘An Examination ofAdditive Debris to Give Insight into Boundary Lubrication,’’ in The Third Body Concept, D. Dowson , C. M. Taylor, T. H. C. Childs, G. Dalmaz, Y. Berthier, L. Flamand, J.-M. Georges and A. A. Lubrecht (Eds.), pp. 685–693, Elsevier, New York (1996). 21. R. S. Fein, ‘‘AWN-A Proposed Qualitative Measure of Wear Protects,’’ Lub. Engr. 31, 581 (1975). 22. J. F. Archard, ‘‘Contact and Rubbing of Flat Surfaces,’’ J. Appl. Phys. 24, 981 (1953). 23. K. Adachi, K. Kato and N. Chen, ‘‘Wear Map of Ceramics,’’ Wear 103–204, 291 (1997). 24. P. Gautier and K. Kato, ‘‘Wear Mechanism of Silicon Nitride, Partially Stabilized Zirconia and Alumina in Unlubricated Sliding Against Steel,’’ Wear 162–164, 305 (1993). 25. M. Chen, K. Kato and K. Adachi, ‘‘Friction and Wear of Self-Mated SiC And Si3N4 Sliding in Water,’’ Wear 250, 246 (2001). 26. Y. Tsuya and S. Ishii, ‘‘Wear Characteristics of Ceramics and Cermets,’’ J. Jap. Soc. Tribol. 35, 384 (1989). 27. M. Mizumoto and K. Kato, ‘‘The Principal Characteristics of Wear Particles Generation Observed By SEM-Tribosystem,’’ in Proc. Japan Int. Tribol. Conf., Nagoya, pp. 899–904 (1990). 28. M. Mizumoto and K. Kato, ‘‘Mechanism of Abrasive Particle Generation (Part 2): The Number of Wear Particles,’’ J. Jap. Soc. Tribol. 38, 87 (1993). 29. M. Mizumoto and K. Kato, ‘‘Size Distribution and Number of Wear Particles Generated by the Abrasive Sliding of a Model Asperity in the SEM-Tribosystem,’’ in Proceedings of the 18th Leeds–Lyon Symposium on Tribology ‘‘Wear Particles: From the Cradle to the Grave,’’ M. Godet, D. Dowson, C. M. Taylor, T. H. C. Childs and G. Dalmaz (Eds.), Elsevier, London (1992). 30. U. Landman, W. D. Luedtke and E. Ringer, ‘‘Molecular Dynamics Simulations of Adhesive Contact Formation and Friction,’’ in Fundamentals of Friction: Macroscopic and Microscopic Processes, L. Singer and H. M. Pollock (Eds.), pp. 463–510, Springer, Berlin (1991). 31. K. Kato, ‘‘Nanoscale Analyses of Wear Mechanisms,’’ in Nanotribology: Critical Assessment and Research Needs, S. M. Hsu and Z. C. Ying (Eds.), pp. 45–54, Kluwer Academic Publishers, Boston (2003).
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32. D. Tabor and J. E. Field, ‘‘Friction of Diamond,’’ in The Properties of Natural and Synthetic Diamond, J. E. Field (Ed.), pp. 549–571, Academic Press, London (1992). 33. K. Nakayama and H. Hashimoto, ‘‘Triboemission of Charged Particles and Photons from Wearing Ceramic Surfaces in Various Gases,’’ Tribol. Trans. 35, 643 (1992). 34. K. Nakayama and H. Hashimoto, ‘‘Effect of Surrounding Gas Pressure on Triboemission of Charged Particles and Photons from Wearing Ceramic Surfaces,’’ Tribol. Trans. 38, 35 (1995). 35. K. Nakayama and R. A. Nevshupa, ‘‘Plasma Generation in a Gap of Sliding Contact,’’ J. Phys. D. Appl. Phys. 35, L53 (2002). 36. K. Nakayama and R. A. Nevshupa, ‘‘Characteristics and Pattern of Plasma Generated at Sliding Contact,’’ J. Tribol. 125, 780 (2003).
6 Airborne Molecular Contamination: Contamination on Substrates and the Environment in Semiconductors and Other Industries Taketoshi Fujimoto, Kikuo Takeda, and Tatsuo Nonaka Sumika Chemical Analysis Service Ltd., Osaka, Japan
6.1
Introduction
A Japanese book to systematically describe airborne molecular contaminants (AMCs) from various viewpoints, such as primary sources, analytical methods to determine their concentrations on surfaces, in the air, and at the source, monitoring methods, chemical properties, detrimental mechanisms, and removal methods, was published 10 years ago [1]. This is one of the few books that systematically describe AMCs and their effects. In the present chapter, the authors intend to focus on the activities that have occurred since the book was published 10 years ago. At that time, there were only a very small number of people in Japan who understood what AMCs were. In the past 10 years, the number of reports on AMCs has increased considerably and outstanding progress has been made in various fields. Studies to establish principles to systematically describe relevant phenomena, as well as to formulate equations by means of modeling, are also increasing. The authors believe that the study of AMCs is entering a new paradigm. In 2001, a cleanroom was planned to be installed at the National Institute for Environmental Studies for the study of endocrine disruptors (Environmental Hormones). It had been previously doubted that many AMCs, including ester phthalates, exhibited the effects of an endocrine disruptor. In order to evaluate an endocrine disruptor, it is necessary to conduct the evaluation of the AMCs in an ultra cleanroom. All the knowledge and technology described in this chapter were used and considered to construct a cleanroom to evaluate potential endocrine actions. R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 329474 ª 2008 William Andrew, Inc.
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After construction of the cleanroom was completed, the quantification of AMCs that have a dramatic effect on endocrine actions, including ester phthalates, resulted in concentrations below ng/m3 levels. This result is evidence to support the usefulness and validity of our research into clean technology as a countermeasure to mitigate AMCs in cleanroom environments. The technology to reduce AMCs in cleanrooms was demonstrated to be possible. From this point onwards, the subject of clean technology has shifted to cost-effective and efficient countermeasures to mitigate AMCs.
6.1.1 Background Scientific personnel and research and development activities to study airborne molecular contaminants (AMCs) are increasing these days. Ten years ago reports on particle removal filters such as HEPA (high efficiency particulate air) and ULPA (ultra low penetration air) constituted the majority of the activities in the air cleanliness field. This trend has drastically changed over the past 10 years. AMCs have become a major topic in the study of cleanliness in cleanroom air and on Si wafer surface. The trends in the study of AMCs in Japan over the past 510 years are summarized below by quoting the proportion of papers reported at the Annual Technical Meeting on Air Cleaning and Contamination Control held by the Japan Air Cleaning Association (JACA). 1. Total presentation papers: about 100. 2. The papers on AMCs account for 65%. 3. Adding the papers on dwellings (sick house syndrome, indoor facilities, including hospitals, and bio-cleanrooms) of 15%, the papers on AMCs account for over 80%. 4. The papers on analytical methods for AMCs in the air, AMCs on Si wafer surface and outgassing account for 30%. 5. The papers on removal methods for AMCs account for 20%. Recently, reports on other removal methods than chemical filtration, such as use of UV (ultraviolet)/ photoelectron radiation, UV radiation/catalyst, and TiO2 catalysts, have been increasing. 6. The papers that report new contaminant sources are not exhausted, but the number of papers reporting on new contaminants (even including those in indoor air environment) is decreasing. For example, dioctylphthalate
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(DOP; synonym: bis (2-ethylhexyl) phthalate) is often detected, and it is very frequently reported as a cause of deleterious effects. The DOP concentration calculated based on the currently available data from all DOP sources is still only half of the DOP concentration actually measured in the air. This means the material balance has not yet been correctly calculated. 7. Air cleanliness in a wider range of places, such as art and other museums and large computer rooms in banks, as well as bio-cleanrooms and indoor dwellings, is now being studied. 8. Studies to establish generic models and equations by interpreting various phenomena and data are increasing to 20%. Some of these quantitative equations feature outstanding compatibility with actual data, universality and usefulness. They help analyze and interpret large amounts of data appropriately. It has been reported recently that a cleanroom with high cleanliness has been developed in which phthalate and phosphate concentrations are as low as 10 ng/m3 or lower. These reports indicate that actual cleanliness is getting closer to a target cleanliness level. It is not impossible to improve cleanliness by one or two orders of magnitude to achieve the ultimate target in the future. These trends indicate that the study of AMCs has been regarded as a target theme in Japan, and that the study of AMCs is moving through the following evolutionary stages, namely from frontier technology and know-how to science (a new paradigm). 1. Know-how for countermeasures against deleterious effects 2. Developments in analytical chemistry methods for qualification and quantification. 3. Establishment of database and reports on phenomenological mechanisms and findings. 4. Models and equations that have a wide-range versatility and applicability. 5. Science. The present authors feel that the study of AMCs is in the transition period from Stage 3 to 4. Therefore, this chapter needs to not only generally introduce frontier technology reports, but also to describe the laws and
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chemistry to summarize the behavior of AMCs which will then be applied to a wide range of industrial and environmental chemistry. To comprehensively describe here new technologies and to systematically explain them are intrinsically contradictory to each other. It was difficult to avoid some issues. There are a number of literature references and there is some overlap when systematically introducing theories, interpretations and data. It is very much expected that a more systematic book on science and technology of AMCs will be published in the near future. In the meanwhile, the authors expect the readers to keep in mind that this chapter describes a situation which is premature as science and that therefore it describes a precursor of the science of AMCs. Guides and primers on AMCs include SEMATECH Technology Transfer Report [2], as well as published papers [35] and proceedings of recent SEMICON Europe conferences [6]. Guides and primers published in Japan regarding AMCs include the 1997 AMC book [1], plenary lectures at the Japan Aerosol Society [79], the special issue of JACA [10], Realize Inc. Seminar [11] and review papers [12, 14]. For basic information on the analytical methods for AMCs, the papers of Fabry [1315], Kaiser [16] and Miki [17] are informative. Trends in standardization of the analytical methods will be discussed in Section 6.5.6.2.
6.1.2 Changes in semiconductor integration The semiconductor industry has been growing by increasing the density of semiconductor devices [2]. Currently, the industry is exploring technologies to fabricate 256M bit DRAM (dynamic random access memory) with 0.15 mm geometry on 300 mm wafers. As the density of semiconductor devices increases, higher cleanliness levels must be achieved on the Si wafer surface [18]. Accordingly, the air in the manufacturing environment is also required to achieve higher cleanliness levels. Also, in cleanrooms used by other advanced industries, such as magnetic disk drives [1922] and liquid crystal display [23], as well as the brewery and biotechnology industries, contamination caused by AMCs and by particles becomes an issue that must be overcome [24].
6.1.3 Changes in target contaminant One of the biggest contributors to advancing semiconductor manufacturing technology was cleanliness improvement in the manufacturing
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environment. In the 1980s, particles were regarded as a major contaminant. Particle contamination was successfully controlled by development of cleanrooms equipped with HEPA and ULPA filters and even SULPA (super ultra low penetration air) filters. To manufacture 1M bit DRAM, the cleanliness of the manufacturing environment must be controlled at ISO (International Standards Organization) Class 3 for particles of 0.5 mm or larger. Currently, the highest cleanliness of a cleanroom in ISO Class 3 is 0.1 mm, i.e. no more than 1000 particles of 0.1 mm size in one cubic meter. Particle contamination has the following features. Particle contamination can be detected by means of electron microscopic examination. Particle contamination physically affects devices, e.g. defective interconnect and particle adhesion. Particle contamination can be overcome (cleanliness in terms of particle can be increased) by improving the filter performance. In the 1990s, the detrimental effects caused by contaminants other than particles started to be reported, characterized by the following features. These contaminants were too small to be detected by means of electron microscopic examination. Some chemical reactions contribute to these effects. The behavior and detrimental effects of each contaminant are different and, therefore, a unique mitigation solution must be developed for each contaminant. It was gradually realized that these new contamination effects were attributable to AMCs.
6.2
Definitions, Types and Sources of AMCs
6.2.1 Definition of ‘‘Airborne Molecular Contamination’’ For the purpose of this chapter, the following definition will be used in order to make it easier to describe the complex issues related to AMCs.
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‘‘Contamination mainly comes from airborne molecular contaminants which are unable to be removed with particle filters such as HEPA and ULPA.’’ In order to explore the mechanisms of AMC contamination and their potential solutions, it is necessary to investigate not only AMCs in a narrow classification, but also metal vapor and mist which may not exist in the air in a gaseous phase. At present, measures are being taken against not only AMCs, but also other contamination caused by chemical reaction of metals and contaminants. The International Technology Roadmap for Semiconductors (ITRS) Roadmap (1999, 2001, and 2004) [18] sets a requirement on the cleanliness of a Si wafer surface and the air in the manufacturing environment by specifying not only classical contaminants which are in a gaseous phase at room temperature, but also metals which are referred to as AMCs. In other words, the ITRS Roadmap uses the term AMCs to refer to all contaminants that degrade air cleanliness and that cannot be removed with particle filters such as HEPA and ULPA filters. Airborne Molecular Contamination, the title of this chapter, is comparable to particle contamination. The most common film contamination occurs when organic impurities which are in a gaseous phase in the air adhere to the Si wafer surface to form a contaminant film on the surface. In order to come up with comprehensive understanding and practical solutions, however, it is necessary to interpret the airborne molecular contamination more extensively including the following cases. 1. Airborne Molecular Contamination includes inorganic compounds and metal organic compounds as well as organic compounds, such as hydrogen fluoride, boron trifluoride, ammonia, cyclosiloxane, and tributyl phosphate. Recently it has also included metal contaminants. 2. Airborne Molecular Contamination is much more limited in concentration than molecular layer contamination. What typically causes problems is not contamination that covers the entire surface of a Si wafer, glass or a hard disk, but a local contaminant island with thickness of less than 1/100 or 1/1000 of a molecular layer. In other words, it is usually not a ‘‘film’’ of contaminants. 3. Airborne Molecular Contamination is detected as particle on Si substrate (Si wafer), while it does not exist as a
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particle in the air. Rather, it is generated from gaseous contaminant sources. For example: Hydrochloric acid in the air corrodes Al interconnect, eventually generating corrosion products such as aluminum oxide. Ammonia in the air gets adsorbed onto a Si wafer surface. It then reacts with sulfur dioxide gas in the air to generate ammonia sulfate which is eventually detected as an impurity. Cyclosiloxanes adhering to a glass surface react with UV radiation used in subsequent lithography process, and consequently through photochemical reaction (decomposition), SiO2 particles are generated on the glass surface. Phosphorus oxide solidified on SiO2 layer absorbs NH3 and moisture in the air. By repeating the fusionprecipitation process, compounds are generated whose moisture and NH3 concentrations are in equilibrium with these concentrations in the air. During this process, isolated spots and/or continuous lines are formed, which may be incorrectly identified as particle contamination. 4. Airborne Molecular Contamination may degrade the underlying surface. For example: When the perfluoro oil lubricant layer of ten plus angstroms thick on the disk surface in a HDD (hard disk drive) gets contaminated with siloxane or alcohol, the head crash phenomenon occurs in too many localized areas to determine which areas are precisely contaminated [19, 20, 25]. It is hypothesized that the impurities change the conformation of the perfluoro oil lubricant which is present not as a film but as multiple molecular layers on the surface. Three dimensionally, fluorine and oxygen are no longer randomly distributed, exhibiting self-insoluble tendency which is often observed in paint technology. In this case, AMCs affect film conformation on HDD substrate surface. Since ammonia and amines react with protons on the surface of photoresist used in the lithography process, protons on the surface decrease in number. As a result, the lithography process does not proceed satisfactorily,
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FUNDAMENTALS and photoresist residues remain like T-shaped bridges on the surface. This is referred to as the T-top phenomenon. Hexamethyldisilazane (HMDS) which is used to change intrinsically hydrophilic Si wafer surface to lipophilic surface so as to enhance photoresist adhesion, as well as trimethylsilanol which is a derivative generated when HMDS reacts with moisture in the air, adhere to the glass surface to generate lipophilic spots. Discoloration takes place when pigments selectively adhere to these lipophilic spots. Boron compounds and ester phosphate adhere to the Si wafer surface and diffuse into the Si wafer during subsequent manufacturing processes to change the dopant doses.
What is common to the above degradation mechanisms is that these effects are caused not by film-type contamination, but by contaminants in cleanroom air which cannot be removed with particle removal filters. Therefore, this chapter uses the term airborne molecular contamination when comparing it to contamination by a particle. As a generic term that refers to all contaminants that cannot be removed with particle removal filters, however, this chapter uses AMCs similarly to its usage in SEMATECH Technology Transfer No. 95052812A-TR [2]. Contamination generated on Si wafer due to these AMCs will be referred to as film contamination. This chapter uses the term AMC contamination when the contamination is attributed to AMCs even if the contaminants are of particulate shape.
6.2.2 Examples of AMC-induced problems in the manufacturing process Below is a list of AMCs and the problems caused by them in the device manufacturing process [1, 2642]. Boron compounds: shift of threshold voltage and drop of driving voltage. SOX: interconnect corrosion. NH3 and amines: lithography pattern defect and T-top phenomenon.
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HMDS (hexamethyldisilizane): fogged glass and lens. LMCS (low molecular weight polycyclodimethylsiloxane): fogged glass and lens. DOP (dioctylphthalate): dielectric breakdown voltage failure of gate oxide. TCEP (trichloroethyl phosphate): shift of threshold voltage. Sources of these contaminants are mainly non-natural compounds, including construction materials of the cleanroom and chemicals used in the manufacturing process. Usually AMC concentrations are lower in outdoor air than in cleanroom air. In a sense, AMC contamination can be regarded as a contamination side effect which is induced by using the cleanroom to suppress particle contamination.
6.2.3 Nature of AMC-induced effects The deleterious effects induced by AMCs are quite different from those induced by particles. AMC concentration in a cleanroom does not show a visible day-to-day fluctuation. It is a gradual drift from a month to another. By setting manufacturing conditions at current AMC contamination levels, therefore, it is possible to maintain the manufacturing yield to some extent. In these cases, AMC contamination may not be recognized. In observing that the appropriate manufacturing conditions are different between cleanrooms, engineers often recognize for the first time that the differences are attributed to the difference in chemical contamination level in cleanrooms. In order to work out solutions to eliminate the deleterious effects of different contaminants, it is necessary to study each individual chemical contaminant in terms of source, generation mechanism, state in the air, mechanism to adhere to a clean surface, mechanism to cause these effects, and physical and chemical characteristics. One of the major sources of AMCs contamination is construction material of the cleanroom. Therefore, it is important to select appropriate materials prior to start of
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FUNDAMENTALS cleanroom construction. Even if cleanliness of the cleanroom is found to be inadequate, it is not easy to replace construction materials after cleanroom construction is completed as cleanroom operation needs to be suspended for a long time. AMC contamination can be significantly decreased by replacing common construction materials with low outgassing cleanroom construction materials. The required AMC concentration is extremely low of the order of ng/m3 order. This concentration is far lower than the chemical concentration that affects the human body. It is only very hazardous toxic gases (sarin, soman, nickel carbonyl, etc.) that are found to be dangerous at ppt (parts per trillion) or ng/m3 level. There are few formal (and practical) analytical methods reported for these concentration levels. The environmental regulations in Japan [43] use the unit of microgram/m3 for all contaminants except dioxin. AMC contamination in semiconductor wafer fabs having no odor is hardly sensed by people working there. When a water droplet of 10 ml is deposited on a substrate such as clean glass or a Si wafer that was exposed to cleanroom air, the surface of the substrate gradually changes from hydrophilic to hydrophobic due to AMCs in the air deposited on the surface. The change in the contact angle of the water droplet as a function of exposure time is one of the few phenomena, other than analytical results, that provide evidence of AMC contamination. A practical chemical filter capable of removing AMCs to maintain cleanliness of less than the order of mg/m3 for a long time is still under development. A chemical filter to selectively remove certain target low-concentration molecules is harder to develop than a particle removal filter, and it also requires chemical consideration. The removal efficiency of a particle filter is 99.9999%, while that of an AMC chemical filter is around 99%. Chemical filters for AMC contamination feature low efficiency and short lifetime and they are costly. When the manufacturing process is affected by particle contamination, such a solution as filter replacement (upgrade to more advanced particle removal filter) is effective. In the case of AMC contamination, however, installing a chemical filter is not
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necessarily the best solution as AMCs vary a lot in type. Although the performance of chemical filters has increased remarkably, it is necessary to improve it further technically and economically. Improvement of chemical filters requires research and development of trace-amount analysis. Some chemical filters feature removal efficiency of 99.99% in removing high-concentration AMCs. This level of chemical filter performance, however, is not sufficient to solve the problems of low-concentration AMCs. What is critical in maintaining cleanliness of the cleanroom air in the semiconductor industry is the ultimate AMC concentration at the downstream location of the chemical filter. Section 6.5.3 describes a case where the removal efficiency of a chemical filter is different between highconcentration AMC environment and an extremely low-concentration AMC environment due to the difference in adsorption mechanism of the chemical filter for NH3 removal in which oxides of phosphorus have been impregnated in the filter as an adsorbing center. When multiple types of AMCs coexist, it is necessary to consider the fruit-basket phenomenon described in Section 6.4.3.4.4. AMC contamination must be fully understood in terms of source, behavior in the air, contamination mechanism on substrates such as Si wafer, and the mechanisms that can cause problems. Based on this understanding, it is then necessary to develop appropriate mitigation solutions. The objectives of this chapter are (1) to describe the development of qualitative and quantitative analyses for various AMCs for different sources such as air, substrates and cleanroom construction materials, (2) to study the behavior of AMCs by using established analytical methods, and (3) to describe solutions that have been worked out based on personal investigation.
6.2.4 Classification of airborne molecular contaminants The International Technology Roadmap for Semiconductors (ITRS) 1999 classifies AMCs into five groups of acids, bases, condensables, dopants and metals, and specifies the required AMC concentration in the air for each group as shown in Table 6.1 [18]. The required AMC concentration on a Si wafer is defined in Tables 6.2 and 6.3.
Wafer environmental control Particles Critical particle size (nm) Particles of critical size (/m3) AMCs (ppt M) Lithography—Bases (as amine, amide, or NH3) Gate—metals (as Cu, E = 2 · 105) Gate—organics (as MW > 250, E = 1 · 103) Organics (as CH2) (*: Cn = 18) Salicidation contact—acids Salicidation contact—bases Dopants P or B
Year Technology Node
90 10 1000 0.3 170 3000 10 32 <10
1000 0.3 200 3600 10 40 <10
2000
90 12
1999 180 nm
2400 10 24 <10
130
0.25
750
75 8
2001
1800 10 20 <10
100
0.2
750
65 5
2002 130 nm
1620 10 16 <10
90
0.2
750
60 4
2003
1440 10 12 <10
80
0.15
750
55 3
2004
1260 10 10 <10
70
0.1
750
50 2
2005 100 nm
Table 6.1 ITRS Roadmap Defect Prevention and Elimination Technology Requirements [18]
<0.07
<0.07
1260 10 4 <10
900 10 <4 <10
50
<750
<750
70
25 1.00E + 00
2011 50 nm
35 1
2008 70 nm
<900 10 <4 <10
<50
<0.07
<750
18 1
2014 35 nm
340 FUNDAMENTALS
1999 180 nm
2000
2001
2002 130 nm
2003
2004
2005 100 nm
2008 70 nm
2011 50 nm
2014 35 nm
DRAM 1/2 PITCH 180 165 150 130 120 110 100 70 50 35 (nm) Wafer diameter 200 300 300 300 300 300 300 300 300 450 (mm) ‡90 ‡82.5 ‡75 ‡65 ‡60 ‡55 ‡50 ‡35 ‡25 ‡17.5 Particle: Front surface particle size (nm) latex sphere equivalent Particles (cm2) £0.13 £0.12 £0.12 £0.14 £0.13 £0.12 £0.10 £0.10 £0.10 £0.10 Particles £38 £84 £80 £95 £89 £84 £72 £73 £72 £165 (number/wafer) £1.8 · 1010 £1.4 · 1010 £1.2 · 1010 £8.8 · 109 £6.8 · 109 £5.8 · 109 £4.9 · 109 £4.2 · 109 £3.6 · 109 £3.4 · 109 Metal: Critical surface metals (atoms/cm2) Silicon-on-insulator wafer Si final 30200 30200 30200 30200 30200 20100 20100 20100 20100 20100 device layer thickness (nm) (tolerance – 5%)
Year Technology Node
Table 6.2 ITRS Roadmap Starting Materials Technology Requirements [18]
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1999 180 nm
2000
2001
2002 130 nm
2003
2004
2005 100 nm
2008 70 nm
2011 50 nm
2014 35 nm
DRAM 1/2 PITCH 180 165 150 130 120 110 100 70 50 35 (nm) Wafer diameter 200 300 300 300 300 300 300 300 300 450 (mm) Front end of line Particle size (nm) 90 82.5 75 65 60 55 50 35 25 18 £9 · 109 £7 · 109 £6 · 109 £4.4 · 109 £3.4 · 109 £2.9 · 109 £2.5 · 109 £2.1 · 109 £1.8 · 109 £1.7 · 109 Critical surface metals (atoms/cm2) Organics/polymers 7.3 · 1013 6.6 · 1013 6.0 · 1013 5.3 · 1013 4.9 · 1013 4.5 · 1013 4.1 · 1013 2.8 · 1013 2.0 · 1013 1.4 · 1013 (C atoms/cm2)
Technology Node
Year
Table 6.3 ITRS Roadmap Surface Preparation Technology Requirements [18]
342 FUNDAMENTALS
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6.2.4.1 SEMATECH technology transfer report No. 95052812A-TR SEMATECH Technology Transfer Report No. 9505212A-TR [2] published in 1995 focused on chemical characteristics of four groups of AMCs: molecular acids (MA), molecular bases (MB), molecular condensables (MC), and molecular dopants (MD). Table 6.4 shows a summary of this classification. Condensables are those compounds whose boiling point is higher than room temperature and which are detected on substrate such as Si wafer. Water is excluded from the group of condensables according to the definition in the report. Many of organic impurities which often cause problems fall in this group. Shiramizu and Kitajima [44] reported 0.2 ng/cm2 of DOP on silicon wafer surface degrades the surface properties, leading to harmful effects of lowering TDDB (time-dependent dielectric breakdown). Dopants are defined as compounds of boron, phosphorus, or others, which affect the electrical characteristics of Si wafer. The required cleanliness level for the AMCs is set at 1/100 of the minimum concentration of the compound reported to have caused problems.
6.2.4.2 International technology roadmap for semiconductor (ITRS) 1999 Table 6.1 from ITRS 1999 includes metals as part of AMCs to be controlled in the manufacturing environment for the 130 nm technology node in 2002. Table 6.4 Projected AMC Limits for the 0.25 mm Process SEMATECH Technology Transfer No. 95052812A-TR [2]
Process Step
Pre-gate oxidation Salicidation Contact formation DUV Lithography
Max. MA MB Residence (ppt M) (ppt M) Time (h) 4 1 24 2
13,000 180 5 10,000
MC (ppt M)
MD (ppt M)
13,000 1000 (0.06*) 0.1 13,000 35,000 1000 13,000 2000 100,000 1000 100,000 10,000
*Calculated by Shiramizu and Kitajima based on Japanese data [44]. MA: molecular acids; MB: molecular bases; MC: molecular condensables; MD: molecular dopants; DUV: deep ultraviolet.
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The 130 nm device production is to be implemented in the manufacturing environment that contains various AMCs with trace concentration at mg/m3, ng/m3, and/or pg/m3 levels. These concentration levels are much lower than those stipulated in work environment codes and environmental regulations. Compounds with this level of concentration have no odor. The concentration of pg/m3 is used when discussing dioxin in the air. Similar classification is included in STRJ 1999 published by the Semiconductor Technology Roadmap Committee in Japan (STRJ) [45]. This classification is appropriate for the semiconductor industry to control cleanliness, identify contaminant sources, explore the mechanisms of contamination problems, and work out mitigation solutions. Some researchers suggest that a classification using organic groups and inorganic groups is appropriate for other industries and research areas. The present chapter refers to the most common ITRS 1999 classification when describing leading-edge cleanliness research.
6.3
Analysis Methods
Unlike particle contamination, AMC contamination requires a number of enabling technologies such as trace analysis, material characterization, and study of chemical reaction mechanisms. For AMCs in the air, however, very few technologies have been reported; a method to simultaneously analyze AMCs of several tens of micrograms per cubic meter is the only one that has been reported [46]. A major obstacle to developing an innovative AMC analysis technology is that the blank test value usually becomes high when a large volume of sample is taken in which a number of chemicals coexist, resulting in large noise in the analytical signal. Ohmi and Miki [47] analyzed specific metal ions at a level mg/m3 order in air. They took a large volume of ultra pure water exposed to cleanroom air, concentrated it to a few mL, and analyzed the concentrated solution with ICP-AES (inductively coupled plasma— atomic emission spectrometry)/ICP-MS (inductively coupled plasma mass spectroscopy). They also took precautions to prevent contamination during each handling step. They suggested the possibility that contaminant analysis of lower concentration in air can be performed when the blank value or its variation is low and is controlled [4749]. It has now become possible to study AMCs by examining accurate analysis results obtained with trace analysis. As cutting edge trace analysis and local surface analysis need to be fully utilized for this purpose, it is recommended the reader refer to the introductory guides of these
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analysis methods [13, 5055]. For metal analysis on silicon wafer surface, chemical analysis and instrumental analysis methods have been described [5659]. The remainder of this section discusses analysis methods required for the study of AMC in the following order. 1. Methods to analyze chemical contaminants of the order of ng/m2 adhering to Si wafer and glass substrate surfaces, including qualification/quantification by instrument and/ or surface analysis quantification. 2. Methods to analyze chemical contaminants at mg/m3 or ng/ m3 levels in the air. 3. Outgassing evaluation methods for cleanroom construction materials and plastics which constitute the main sources for generation of AMCs.
6.3.1 Substrate surface analysis 6.3.1.1 Quantitative analysis Quantitative analysis of contaminants on a substrate surface often uses solvent cleaning method and wafer thermal desorption gas chromatography/mass spectrometry (WTD-GC/MS). To analyze specific local surface areas with contaminants or defects rather than the entire surface, local surface analysis methods such as time-of-flight secondary ion mass spectrometry (TOF-SIMS), X-ray photoelectron spectroscopy (XPS), and Fourier transform infrared spectroscopy (FT-IR) are applied.
6.3.1.1.1 Solvent washing method The substrate surface is cleaned with an appropriate solvent to dissolve the contaminants on the surface in the solvent. The composition of the solvent is adjusted to prepare a final sample solution. The sample solution is analyzed with ICP-MS, ion chromatography (IC), CE, CE/ MS (capillary electrophoresis/mass spectrometry) or GC/MS [54, 5768]. Recently, Iikawa and Momoji [64, 68] reported a CE/MS method for cation and anion analysis in the wafer cleaned solution, which is rapid and accurate, and provides a lower determination limit in routine analysis. The results from CE/MS analysis for ammonia and amines are shown in Table 6.5 and Figure 6.1.
346
FUNDAMENTALS
Table 6.5 Amine and Ammonia Concentration (mg/m3) in Air in Various Cleanrooms
Compound
C/R-1
C/R-2
R-1
NH4+ Methylamine Amine-a* Amine-b* Amine-c* Total Amines
1.4 0.03 0.06 0.05 0.02 0.13
3.5 <0.01 0.07 0.08 0.04 0.17
1.4 <0.01 1.5 0.06 <0.01 1.5
*Calculated using a tetramethylammonium standard working curve.
Figure 6.1 Electropherogram of the air in cleanroom C/R-1 (in Table 6.5) by (a) CE (upper figure) and (b) CE/MS (lower figure).
It is critical to select the most appropriate solvent for a target contaminant. Several solvents are proposed which feature high purity, dissolve contaminants effectively, can be applied to a wide range of contaminants, are easy to be concentrated, and are resistant to spectral
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interferences. It is necessary to select the most appropriate solvent for each target contaminant as these solvents have their merits and demerits. This method is further segmented by the solvation method, including solvent vapor cleaning method, solvent droplet extraction method, and the like [6777].
6.3.1.1.2 Wafer thermal desorption—gas chromatography/ mass spectrometry (WTD-GC/MS) In this method, a sample is heated in a cell and the gas evaporated from the sample is introduced into GC/MS to measure the concentration. There are two types of WTD-GC/MS. Static headspace—gas chromatography—mass spectrometry (SHS-GC/MS) in which the gas emitted from the cell is introduced directly into the GC/MS. Dynamic headspace—gas chromatography—mass spectrometry (DHS-GC/MS) has an adsorption tube to collect the gas. The gas collected in the tube is then concentrated. The adsorption tube is heated again to regenerate the gas and an appropriate carrier gas is added prior to introduction into the GC/MS. The solvent cleaning method is highly accurate, but it may not meet a target determination limit in some cases. DHS-GC/MS is suitable for trace analysis as it features high sensitivity. Figure 6.2 shows the GC/MS chromatograms for DHS and SHS outgassing tests. The identification limit appears to be governed by whether it is possible to prevent inclusion of the gas evaporated from the back surface of the substrate and to collect the gas evaporated only from front surface of the substrate. This method is often used to analyze a Si wafer surface that has been exposed to the air for an extended period. The witness plate method is one of the methods used to measure particulate contamination in the air. A Si wafer or a glass substrate is exposed to cleanroom air for a given period of time and the particle count on its surface is measured. WTD-GC/MS is analogous to the witness plate method for analysis of AMCs for the following reasons. For some organic compounds, the lowest determination limit measured with WTD-GC/MS is lower than that measured with the air analysis described below. Very useful
348
FUNDAMENTALS
Figure 6.2 GC/MS chromatograms of a polypropylene sheet sample from (a) dynamic headspace outgassing tests and (b) static headspace outgassing tests.
information can be obtained with the database of the sticking probability which is the relationship between AMC concentration in air and on silicon wafer surface exposed for 24 hours. Sticking probability is discussed later in Section 6.4.3.4. What is generally required is information on a target AMC to contaminate a Si wafer surface in the manufacturing process. When the cleanroom is located far away from the analytical laboratory, it is easier to transport a Si wafer exposed to cleanroom air than to transport sampled cleanroom air.
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Figure 6.3 shows a schematic diagram of WTD-GC/MS system. Recently, Ishiwari et al. have reported on the use of a small Si plate exposure method that is rapid and convenient [69, 71]. However, the common plastic wafer carrier is not appropriate to transport Si wafers exposed to cleanroom air because the plastic carrier also seriously contaminates the wafer with AMCs. For instance, in order to measure cleanliness levels at 0.001 ng/cm2, it is essential to select a container which maintains the blank value on a 300 mm Si wafer below 1 ng. An all-aluminum carrier has been developed as a single or multiple wafer carrier that is free from AMC generation. Figures 6.4 and 6.5 show the carriers for one wafer and for 26 wafers, respectively. A large database is available on the data taken through the analytical procedure combining the all-aluminum carrier and WTD-GC/MS [78].
Figure 6.3 Schematic of the setup for wafer thermal desorption GC/MS (WTD-GC/MS).
Figure 6.4 Example of a single sample wafer carrier made of aluminum.
350
FUNDAMENTALS
Figure 6.5 Example of a multiple sample wafer carrier made of aluminum.
6.3.1.2 Surface (instrumental) analysis X-ray micro-analysis (XMA), total refection X-ray fluorescence (TRXRF), and XPS are available methods to analyze inorganic compounds such as NH3, NOx, and SOx. For the analysis of organic compounds, TOF-SIMS, FT-IR, ion mobility spectrometry (IMS), and thermal desorption spectrometry/atmospheric pressure ionization mass spectrometry (TDS-API-MS) are available [2529, 54, 5658, 7988]. Recently, Beckhoff et al. [56] reported metal analysis by TXRF and NEXAFS with Synchrotron Orbital Ray (SOR) in the BESSY II accelerator which indicates improvement of the determination limit. It suggests the possibility of achieving lower a determination limit for the low-Z elements, such as C, O, N, Mg, Na, and Al. The SOR of BESSY II has an absolute detection limit of 0.31.3 pg, corresponding to approximately 2 · 107 to 1 · 108 atoms/cm2. Wang et al. [57] reported the determination limit for metal analysis 3.6 · 104 atoms/cm2 can be attained ‘‘theoretically’’ with synchrotron radiation total reflection X-ray fluorescence (SRTXRF) using a preconcentration process such as vapor phase decomposition (VPD). They discussed the actual determination limit of each contaminant by controlling the contaminant concentration of DI water and chemicals. Figures 6.66.8 show the concentration of AMCs measured with TOFSIMS and XPS on the same Si wafer. In-depth AMC profiles are different among these methods although the same sample was measured.
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Figure 6.6 Typical spectra from TOF-SIMS analysis of a wafer surface.
Figure 6.7 TOF-SIMS spectra of a wafer surface exposed to cleanroom environment.
When AMCs adhering to glass that cause hazing were analyzed, siloxanes, CN, CNO, NO2 and NO3 were detected with TOF-SIMS, while CNHx, CONH, NO2, NO3, and NH+4 were detected with XPS. Based on consideration of the spectra from the two methods and the behavior of AMCs in a vacuum tool, it is suggested that NH4NO3, NH4NO2, and similar compounds were possibly generated.
352
FUNDAMENTALS
Figure 6.8 XPS spectra analysis of a wafer surface exposed to cleanroom environment.
6.3.2 Air analysis For the analysis of AMCs, several reports have been presented [21, 8996]. JACA standard No. 35A-2003 (revised version of No. 35-2000) has been published by the Japan Air Cleaning Association (JACA) [90]. Figure 6.9 outlines the sampling and analysis methods for AMCs. A sample is taken in a solid form with collection-with-filter method, or it is taken as gas sample with an impinger or an adsorption tube. The sample is concentrated and its composition is adjusted before it is evaluated with trace analysis methods such as ICP-MS, ion chromatography, and GC/MS. The analysis method for each analyte category defined by SEMATECH will be discussed below.
6.3.2.1 Acids [8084] SO2, NO, NO2, HCl, Cl2 and HF are acids gases that are often detected. They are mainly collected with the absorption-to-solution method using an impinger and are subsequently analyzed with ion chromatography. Figure 6.10 shows the absorption-to-solution sampling system and Figure 6.11 shows typical chromatograms from IC analysis. Two different absorption solutions were tested: ultra pure water and/ or ultra pure water spiked with H2O2. Table 6.6 compares the results of the analysis of each solution. When the H2O2 concentration is high,
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Figure 6.9 Outline of the different sampling and analysis methods for AMCs.
it appears that NO decreases and NO2 increases. However, NOx, the sum of NO and NO2, remains unchanged. Cl2 features low saturated solubility in ultra pure water. When 0.1% H2O2 is spiked to ultra pure water, however, Cl2 recovery goes up sufficiently due to enhancement of the dissolution rate and the saturated solubility (or because Cl2 is converted not to ClO but to Cl). Tables 6.7 and 6.8 show results from various cleanroom air analyses.
6.3.2.2. Bases: ammonia (NH3) and amines Ammonia is derived from outdoor air as well as air inside the cleanroom. Just like acids, ammonia together with several amines are collected with the absorption-to-solution method and analyzed with ion chromatography.
354
FUNDAMENTALS
Figure 6.10 Schematic of the absorption-to-solution sampling system.
Figure 6.12 shows the typical ion chromatogram. Amines are analyzed, like organic compounds described below, with GC/MS.
6.3.2.3 Condensables: organic compounds Organic compounds are mainly analyzed with GC/MS. Organic compounds in cleanroom air are collected with activated carbon, TENAX and other adsorbents [9092]. After going through pretreatment such as concentration, they are analyzed with GC/MS. Organic compounds are identified and quantified from the obtained peaks and their intensities. To evaluate overall contaminant distribution, total ion monitoring
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Figure 6.11 Ion chromatograms of a standard solution with known concentration (a) 5 ng/ml and b) 10 ng/ml.
Table 6.6 IC Analysis Results of Room Air in Various Absorbing Solutions
AIR Sample
Absorption Solution
Room A H2O H 2O H 2O Room B H2O H 2O H 2O
Cr
Anions (ng/m3) NO2 NO3 Total NOx SO43
1000 13,000 900 18,000 + 0.01% H2O2 1100 12,000 1900 18,000 + 0.1% H2O2 1200 8000 6200 17,000 17 220 20 240 + 0.01% H2O2 18 210.00 30 240 + 0.1% H2O2 12 140 110 250
1,900 3300 3500 34 59 63
(TIM) should be used to detect abnormal compounds which do not exist under normal conditions. Quantification of regular contaminants which always exist is carried out in Selective Ion Monitoring (SIM) mode to obtain precise information. Table 6.9 shows the ion mass numbers used for determination of various AMCs in SIM mode. By reducing the variation and carefully controlling the blank value, it is possible to perform routine analysis at a level of 0.01 mg/m3. To control the accuracy and reliability, it is important to arrange multiple adsorption
356
FUNDAMENTALS
Table 6.7 Results of IC Analysis of Various Air Samples
Sample Air Location Outdoor Cleanroom A Cleanroom B Cleanroom C Cleanroom D Cleanroom E Analysis laboratory
Cr
NO2
76 670 90 20 <10 <10 105
9 <5 <5 6 <5 <5 10
Anions (ng/m3) NO3 SO42 900 580 660 150 <5 <35 1100
8070 3560 1890 2420 5 1300 11,200
PO43 <10 <10 <10 600 <10 1300 20
Table 6.8 Results of IC Analysis of Cleanroom Air for Various Processes
Cleanroom Process Process Process Process
A B C D
F
Cl
<10 <10 <10 4000
160 570 150 1100
Anions (ng/m3) NO3 SO42 18,000 10,000 3000 3000
12,000 20,000 56,000 24,000
PO43 <10 <10 <10 3000
Figure 6.12 Ion chromatograms of ammonia and amines from cleanroom air in an absorption solution.
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Table 6.9 Mass Numbers for Analytical Ions for Different Compounds for the SIM Method of GC/MS
Compound Hexamethylcyclotrisiloxane (D3) Octamethylcyclotetrasiloxane (D4) Decamethylcyclopentasiloxane (D5) Dodecamethylcyclohexasiloxane (D6) Dibutylphthalate (DBP) Di-(2-ethylhexyl) phthalate (DOP) Tributylphosphate (TBP) Tri-(2-chloroethyl) phosphate (TCEP)
Analytical Ions (m/z) Quantification Identification 207 281 73 73 149 149 99 249
96 265 267 429 167 155 83
tubes in series and compare the ratio of recovery between the first tube and the second tube and the recovery ratio between the second tube and the third tube. Figure 6.13 shows a typical adsorption tube. Figure 6.14 shows a TIM chromatogram. Table 6.10 shows the results of identification of 50 plus peaks of compounds that are often detected with GC/MS. The identification was based on fragmentation with synthetic standard samples, as well as published data [93]. Taking DOP as an example, Figures 6.15 and 6.16 show mass spectra of a standard sample and the calibration curve in SIM mode, respectively. For gases generated from urethane sheet, it is possible to identify not only each peak but also groups of peaks. Organic compounds, which are detected as regular contaminants and are likely to adhere to a Si wafer surface and likely cause problems in a manufacturing environment, are discussed below.
6.3.2.3.1 Siloxanes The monomers of siloxanes are HMDS mentioned previously. Their dimers are hexamethyldisiloxanes, which are rarely observed compared with other siloxanes. The primary siloxanes in cleanroom air that can cause problems are the cyclosiloxanes (Dn) at the trimer (D3) and above, where n represents the number of polymerization of (CH3)2(SiO)n. Most commonly reported polymerization numbers include n = 3, 4, 5, 6, and 12. HMDS is a reagent in the silicon fabrication process. Cyclosiloxanes mainly come from silicone sealants.
358
FUNDAMENTALS
Figure 6.13 Typical adsorbent tube.
Figure 6.14 Total ion chromatogram of cleanroom air.
6.3.2.3.2 Ester phthalates Di-(2-ethyl hexyl) phthalates or DOP are typical phthalates. Other compounds that are often detected are dibutyl phthalates (DBP) and diethyl phthalates (DEP). When AMCs on Si wafer surface are analyzed with WTD-GC/MS, 2-ethyl hexanol (2-EH) and phthalic anhydride are detected in addition to DOP. It appears that these compounds exist in the air besides DOP. Therefore, chemical filters have reportedly been developed to capture them. However, these AMCs are almost never detected when a Si wafer is cleaned with a solvent and the solvent is analyzed. Instead, DOP
Tetrachloromethane 2,3-Dimethylpentane 1-Methoxy-2-propanol 2-Hexanone Toluene Acetic acid, 2-methylpropyl Ethylbenzene Xylene Xylene 2,4,6-Trimethyldecane 2-Butoxyethanol 2-Ethoxyethylacetate 2,6-Dimethyloctane 4-Propylheptane Propylbenzene
Compound
93.5 84.7 87 86.8 89.7 94.2 93.2 92.3 91.2 88.5 81.6 91.3 90.1 91.8
Reliability*
Toluene Toluene Toluene Toluene STD Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene
Calculation Method
<1 <1 18 <1 221 2 72 121 39 12 7 2 1 2 2
<1 1 5 1 89 <1 25 36 11 5 2 <1 <1 <1 1
<3 <3 <3 2 48 3 5 5 <3 4 <3 <3 <3 <3 <3
Ambient air
Concentration (mg/m3) Cleanroom air A B
Table 6.10 Results of Analysis of Condensable Compounds in Cleanroom Air
ET AL.
(Continued)
C A A, C A A, C A, C A, C A, C C C C C C
A
Origin**
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1-Ethyl-3-methylbenzene 1,3,5-Trimethylbenzene 2,6-Dimethyloctane 1-Ethyl-3-methylbenzene 1-Ethyl-3-methylbenzene Decane Octamethylcyclotetrasiloxane (D4) 1,3,5-Trimethylbenzene 2,3-Dimethylnonane 2-Ethyl-1-hexanol 1,2-Diethoxybenzene 1-Methylpropylbenzene 1,2-Diethylbenzene 1-Ethyl-3,5-dimethylbenzene 1-Methylpropylbenzene
Compound
96.3 93.7 89.9 95.9 94.7 90.9 92.2 86.5 88.8 86.5 91.5 91.1 93.3 71.8
Reliability*
Toluene Toluene Toluene Toluene Toluene Toluene STD Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene
Calculation Method
19 9 3 4 23 26 0.5 7 3 8 10 11 6 16 3
7 4 1 2 9 10 0.2 2 2 2 4 3 4 7 2
Cleanroom air A B
11 <3 <3 <3 5 12 <3 <3 <3 <3 <3 <3 <3 <3 <3
Ambient air
Concentration (mg/m3)
Table 6.10 Results of Analysis of Condensable Compounds in Cleanroom Air (cont’d)
A, C C C C A, C A, C C C C C C C C C C
Origin**
360 FUNDAMENTALS
1-Ethyl-2,4-dimethylbenzene 2-Ethyl-1,3-dimethylbenzene 6-Ethyl-2-methyldecane 1,2,3,4-Tetramethylbenzene 1,2,3,4-Tetramethylbenzene Decamethylcyclopentasiloxane (D5) Pentadecane Dodecamethylcyclohexasiloxane (D6) Propanoic acid, 2-methyl-, 2,2-dimethyl-1(2-hydroxy-1-) Butanoic acid, 1-methylpropylester 2-Methyltetradecane 3-Isopropoxy-1,1,1,7,7, 7-hexamethyl-3,5,5Cyclohexane, 1,1-methylene(oxy)bis1,1,3,4-Tetrachloro-2,2,3,4, 4-hexafluorobutane Bis(2-ethylhexyl)phthalate Trimethylsilanol 2-Propanol 2-Methyl-1-propanol 1-Butanol Ethanol, 2-methoxy, acetate Cyclohexanone
Toluene Toluene Toluene Toluene Toluene STD Toluene STD Toluene Toluene Toluene Toluene Toluene Toluene Toluene STD Toluene Toluene Toluene Toluene Toluene
93.8 93.1 93 92 91.2 91.3 91.8 79.5 92.1 67.5 77.5 67.6 78.4 83.1 85.8 85.1 80.6 85.1
3 <1 <1 <1 <1 <1 1 1 <1
<1 2 <1 4 4 3 <1
<1 <1 4
<1 2 5 2 <1
7 10 12 1 4 0.4 <1 1.8 <1
17 24 26 6 10 2.3 2 9.1 <1
ET AL.
(Continued)
C C C C C C C
C A
<3 5 3 <3 <3 <3 <3 <3 <3
C C C
C C C C C C C C C
<3 <3 <3
<3 <3 6 <3 <3 <3 <3 <3 <3
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STD Toluene Toluene Toluene
78.3
Calculation Method
86.5 86.7
Reliability*
96 <1 <1 <1
5 <1 <1 <1
Cleanroom air A B
<3
<3 <3 <3
Ambient air
Concentration (mg/m3)
*Reliability: acquired mass spectrum compared with standard mass spectrum from library data base. **Origin: A = ambient air; C = cleanroom air.
2-Butanone oxime Phosphoric acid, trimethyl ester Benzenemethanol, alpha, alpha-dimethyl1-(2-Butoxyethoxy)ethanol
Compound
Table 6.10 Results of Analysis of Condensable Compounds in Cleanroom Air (cont’d)
C
C C
Origin**
362 FUNDAMENTALS
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Figure 6.15 Mass spectrum of di (2-ethylhexyl) phthalate.
Figure 6.16 Calibration curve for di (2-ethylhexyl) phthalate.
accounts for the majority in this analysis. Figure 6.17 shows the results of GC/MS analyzing the same sample to compare the two analysis methods. These two compounds (2-EH and phthalic anhydride) are the pyrolysates of DOP. Therefore, it is necessary to closely evaluate the measured
364
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Figure 6.17 Total ion chromatogram for (a) solvent extraction GC/MS and (b) thermal desorption GC/MS.
data and the conditions of each cleanroom to decide whether or not a chemical filter must be used [21, 75].
6.3.2.3.3 Ester phosphates Ester phosphates including tributyl phosphates (TBP) are used as fire retardant sand plasticizers. TBP, triethyl phosphate (TEP), tris(2-chloroethyl) phosphate (TCEP), tris(1-chloro-2-propyl) phosphate (TCPP), tricresyl phosphate (TCrP) and similar compounds are often detected.
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The above-mentioned organic compounds, namely siloxanes, phthalates, and phosphates, are present in large volume. They are almost always detected in cleanroom air and are often detected on Si wafer surface [21, 75, 9195]. These compounds represent the primary significant condensables (organic compounds) that contribute to contamination. They need to be quantified in order to be reported, together with bases such as NH3, HMDS and BF3, in the routine analysis of cleanroom air and Si wafer surface. In addition, gases generated from urethane resin and butylated hydroxytoluene (BHT; 2,6-di-tert-butyl-p-cresol) are often detected in cleanroom air and on Si wafer surface. They are significant secondary condensables that constantly require close monitoring and control. For the primary and secondary significant condensables, it is critical to know whether or not their concentrations are within the control limits. For the other condensables, the fact that they are detected often constitutes critical information. By comparing the information with relevant historic data, this information will tell us whether they have been detected before and how they behave. Anomalous peaks detected in the TIM mode of GC/MS are subject to mass spectra analysis (fragmentation) in which comparison with reference materials and search of available databases are performed to identify their molecular structures.
6.3.2.4 Dopants: boron, phosphorus, and metals Dopants are primarily analyzed by combination of the absorption-tosolution method and ICP-MS (or FL-AAS, flame atomic absorption spectroscopy). The detection limits for boron and phosphorus are 0.1 and 20 ng/m3, respectively [90]. Similar to boron, the metals are sampled into solution and analyzed with ICP-MS. Both boron and metals might be released into the air not in a form of AMC but in the form of particle. In order to distinguish gaseous AMCs from particles, two sampling methods, namely the absorption-to-solution method and the collectionwith-filter method, are adopted. The absorption-to-solution method collects both AMCs and particles. An outline of the method is shown in Figure 6.18, while the impinger is shown in Figure 6.19. On the other hand, the collection-with-filter method selectively collects particles only. The apparatus is shown schematically in Figure 6.20 and the filter is shown in Figure 6.21. Comparison of the two sets of data provides information on the volume of gaseous contaminants. The correlation
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FUNDAMENTALS
Figure 6.18 Absorption-to-solution sampling system used for dopants.
map for such a comparison is shown in Figure 6.22. Figure 6.23 shows the algorithms used to analyze the data from the absorption-to-solution method with ICP-MS analysis and to calculate the concentration of contaminants in the air. Section 6.4.1.4 presents specific data and examples of the analyses. Imai et al. [96] report a series of analysis of organic ester phosphates by GC/MS and total phosphorus high resolution ICPMS (sector/double focus type), which has the capability for organic and inorganic phosphorus analysis after with microwave acid digestion. High recovery of phosphorous compounds has been achieved (Table 6.11). The mass spectra are shown in Figure 6.24 for low and high resolution analysis. Like condensables, organo-phosphates are also analyzed with GC/MS.
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Figure 6.19 Schematic diagram of an impinger for the absorption-to-solution sampling system used for dopants.
Tables 6.12 and 6.13 show the lowest determination limit of the above analysis methods for AMCs in air and on Si wafer surface. API-MS and IMS also provide useful information.
6.3.3 Outgassing evaluation method for construction materials The most important consideration in order to achieve a clean manufacturing environment and a clean surface is the technology for selecting proper construction materials.
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Figure 6.20 Typical collection-with-filter sampling system.
The outgassing method is used as a screening method for construction materials. It measures the volume of AMC gases generated from a sample [25, 97108]. This method is designed in an attempt to improve sensitivity and throughput. Gas generated from a heated sample is introduced to an adsorption tube in which the gas is cooled down to be collected in a collection tube. The collection tube is then heated to release the gas and the carrier gas transports the gas to GC/MS. Figure 6.25 is a schematic diagram of the method. This method is primarily applied to organic compounds (condensables, dopants including phosphorus compounds, and bases including amino compounds). For analysis of acids and bases, this method is combined with other methods such as ICP-MS, IC and CE [5359].
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Figure 6.21 Filter and filter holder for the collection-with-filter sampling system.
Figure 6.22 Schematic model of the analysis results for gas and for solid by the absorption-to-solution and the collection-with-filter sampling systems.
369
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Figure 6.23 Outline of the analysis procedure for absorption-to-solution ICP-MS method.
Table 6.11 Recovery of Organophosphate Compounds by Microwave Acid Digestion for High Resolution ICP-MS
Compound Triethylphosphate (TEP) Tri-(2-chloroethyl) phosphate (TCEP) Tributylphosphate (TBP) Triphenylphosphate (TPP) Tritolylphosphate (TCP)
Recovery (%) 107 83 95 93 71
6.3.3.1 IEST WG 031 [25, 99] 6.3.3.1.1 Screening test method In the Institute of Environmental Sciences and Technology (IEST) WG031 document it is required to perform rough screening of multiple
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Figure 6.24 Mass spectra of P+ at (a) low resolution (upper figure) and (b) high resolution (lower figure).
types of samples. A screening test is described in which small samples are rapidly heated to 150 C to release all the gases from the samples and the gases are measured. From the results of the screening test, the samples that generate large volume of gases are rejected as candidate cleanroom construction materials.
6.3.3.1.2 Engineering test method The samples selected with the screening test method as favorable candidates for cleanroom construction materials are then closely analyzed
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Table 6.12 Determination Limit for AMCs on a Si Wafer Surface
Contaminants Non-metallic Compounds Siloxanes D3, D4, D5 D6 D7, D8 D12 Phthalates Diethylphthalate (DEP) Dibutylphthalate (DBP) Di(2-ethylhexyl)phthalate (DOP) Phosphates Triethylphosphate (TEP) Tributylphosphate (TBP) Triphenylphosphate (TPP) Tricholoroethylphosphatae (TCEP) Tricresylphosphate (TCrP) Butylhydroxytoluene (BHT) Dibutyl adipate (DBA) Di(2-ethylhexyl)adipate (DOA) Metals B Na Al K Ca Cr Mn Fe Co Ni Cu Zn Mo Sn Pt Au Ta W
Determination Limit for Method 300 mm Wafer WTD-GC/MS pg/cm2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 atoms/cm2 3.00E 7.00E 7.00E 6.00E 4.00E 8.00E 3.00E 5.00E 3.00E 3.00E 3.00E 1.00E 2.00E 3.00E 1.00E 1.00E 1.00E 1.00E
+ 09 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08 + 08
HF washing ICP-MS
Li, Be, B, Na, Mg, Al, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, Cd, Sb, Ba, Pb P B Na, Mg, Al, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, Cd, Pb
Metals
Inorganic ions NH4+ F Cl I NO3 PO43 SO42
(High sensitivity)
Contaminants
Type
0.05 0.05 0.05 0.05 0.05 0.1 0.05
2 0.1 0.01
ng/m3 ng/m3 ng/m3
mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3
1
Solution absorption
Cycone sampling
Solution absorption
Determination Limit Sampling
ng/m3
Unit
Table 6.13 Determination Limit for AMCs in Air
Nox IC
IC
ICP-MS ICP-MS ICP-MS
ICP-MS
(Continued)
Analysis Method
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Organics and condensables
(High sensitivity)
Type
5 5 5 20 5 0.1 0.1 0.5 0.1 0.1 0.1 0.1 0.05 0.05 0.1 0.1
ng/m3 ng/m3 ng/m3 ng/m3 ng/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3
F Cl NO3 PO43 SO42 Formic acid
Acetic acid Oxalic acid Methylamine Dimethylamine Trimethylamine TMAH Ethanoholamine Cyclohexylamine 2-Amino-2-methyl propanaol TMSiOH
20
ng/m3
NH4+
Column absorption
Solution absorption
Solution absorption
Determination Limit Sampling
Unit
Contaminants
Table 6.13 Determination Limit for AMCs in Air (cont’d)
GC/MS
IC
IC with conc.
Analysis Method
374 FUNDAMENTALS
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3
*The determination limit for high sensitivity analysis is <0.01 mg/m3.
M2 D3 (hexamethylcyclo siloxane) D4 D5 D6 D7 D8 DBP DOP* Total condensables Qualitative analysis TENAX TENAX
GC/MS MS library
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Figure 6.25 Schematic of the outgassing apparatus for the dynamic headspace screening test.
with an engineering test method. This method looks at larger samples and measures gas generation at room temperature. It has been proposed to combine the screening test method and the engineering test method, and the proposal is currently being deliberated [25]. The proposed method should be capable of rapidly analyzing a large number of samples. However, since some polymers start decomposing below 150 C, it is important to note that the state of the interface between the sample surface and the atmosphere may be changed. In addition, at temperatures above 100 C the coexisting moisture in the air may also vary between moisture, liquid water and steam. These conditions are significantly different from those at room temperature. It has also been discussed that engineering test data cannot be directly derived from screening test data, and that the engineering test needs to be standardized.
6.3.3.2 JACA 34-1999 [100103] JACA 34-1999 specifies five outgassing measurement methods for different applications as described below, including a screening step and quantitative estimation of gas volume. The methods are shown schematically in Figures 6.266.30.
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Figure 6.26 JACA sampling system for air in a test chamber.
Figure 6.27 Examples of JACA outgassing systems using (a) a microchamber (upper figure) and (b) a small chamber (lower figure).
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Figure 6.28 Example of an outgassing system for a one-sided surface.
Figure 6.29 Schematic of the JACA outgassing engineering test system.
Figure 6.30 Outgassing apparatus for the substrate surface adsorption/thermal desertion method (JACA method 4).
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6.3.3.2.1 Static headspace method A sample is confined for a while in a sealed container. The gas concentration in the air inside the container is to be measured after concentration in the air is in equilibrium with that on the sample surface.
6.3.3.2.2 Dynamic headspace: screening test method Three samples, (a) a small disk-shaped sample, (b) a large plateshaped sample, and (c) a combined sample, are heated under conditions which trigger evaporation at an equilibrium state between gases and the sample surface. Gases generated at several arbitrary temperatures are collected in adsorption tubes to be concentrated. These adsorption tubes are then heated to generate AMCs, and volume of the generated AMCs is measured.
6.3.3.2.3 Dynamic headspace: engineering test method The ambient conditions of target cleanroom are reflected in the test conditions when setting the humidity and the temperature of the test environment. Gases generated under the test environment are measured. A formula is applied to the measurement data to estimate the volume of gases generated under different temperature conditions.
6.3.3.2.4 Substrate surface absorption: thermal desorption test method A sample and a Si wafer are confined in a sealed container for a known time period. AMC gases generated by heating the substrates are then analyzed and the AMC concentration on the Si wafer surface is measured. This method is practical and is often used to measure gases generated from a Si wafer carrier and assembly in a mini-environment. This method is also referred to as a witness plate method for outgassing. In principle, this method follows the same procedure as the analysis of contamination level on Si wafer. Figure 6.30 shows this method schematically. Figure 6.31 shows a flowchart of the four outgassing methods described above for creating a low-contamination wafer carrier. To begin with, small samples are analyzed with the dynamic headspace screening test. The samples with low gas generation are selected with
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Figure 6.31 Flowchart for creation of a low-contamination wafer carrier.
the dynamic headspace screening test. After that, large-sized plate-shaped samples and assemblies are selected as favorable candidates for construction materials with the screening test and the engineering test in order to achieve high quality manufacturing process environment. In order to demonstrate the integrity of a Si wafer storage container and the mini-environment, the Si wafer is confined in them and the inside air is measured with the substrate surface absorption thermal desorption test method [102108]. In order to evaluate a mini-environment in a cleanroom located far away from the analytical laboratory, a carrier not subject to contamination from transportation is extremely useful such as the all-aluminum carrier described in Section 6.3.1.1.2 [78].
6.3.3.2.5 Onsite measuring method This method is useful to identify gas generation sources in a constructed cleanroom and to find out which portions of cleanroom should be
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replaced and to quantify the improvements. A sampling device is designed to make a sampling point a closed chamber. The sampling device is mounted on the wall, floor, ceiling and/or other areas to collect ambient air. The collected air is introduced into a collection tube, and AMCs in the tube are analyzed. There are two different methods: a double-tube chamber method, and a method to confine and collect ambient air [109111]. There have been several papers published that evaluate the two methods in terms of cycle time, ease of use, calculation of gas generation per unit time and unit area, estimation of contamination contribution, sampling from ceilings, and the effect of substitution with low outgassing plates. Figures 6.32 and 6.33 show schematic diagrams for these outgassing evaluation methods. Section 6.4.3.3 compares the IEST and JACA methods and also discusses the outgassing phenomenon in more detail. For any outgassing evaluation method, it is critical to make measurements at appropriate
Figure 6.32 Example of an on-site system for outgassing evaluation.
Figure 6.33 Example of the JACA chamber for on-site outgassing evaluation.
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FUNDAMENTALS
temperatures between room temperature and 150 C that do not induce thermal decomposition of the sample, or glass transformation, or hydrothermal reaction on the sample surface. For plastics, in particular, special consideration should be given to chlorinated polymers and silicone polymers. Ion mobility spectroscopy has a high sensitivity for AMCs. Various reports have been presented on outgassing evaluation and Si wafer contamination analysis. It has been proposed in SEMI E46-95 for application to mini-environments [112116].
6.4. Nature of Airborne Molecular Contamination and Its Effects In this section, the sources and properties of contaminants and contamination mechanisms on substrate surfaces will be discussed.
6.4.1 Investigation of the properties of AMCs Cleanroom air discussed in this section takes in about 5% of fresh outdoor air which is treated with preliminary filtration for particle removal. Relative humidity of the fresh outdoor air is adjusted at 4050%. The outdoor air is introduced from the ceiling of the cleanroom through filters at an average flow rate of 40 cm/second in a form of laminar flow. The remaining 95% of cleanroom air is circulated air. The ratio is expressed as a function of the with air age. Therefore, the cleanroom air is susceptible to the effects of AMCs generated inside the cleanroom. Figures 6.34 and 6.35 show schematic diagrams of the design, construction, materials used, and the air flow in a typical cleanroom.
6.4.1.1 Effects of rinsing the outdoor air In those areas where inexpensive water is available in large volume (e.g. some areas in Asia), fresh outdoor air is often rinsed in a washer before being introduced into the cleanroom. With respect to air cleanliness, the rinsing process is often found to be effective in removing AMCs from outdoor air. In particular, this process is effective in removing acid gases and NH3 [89, 12130]. Outdoor air in the vicinity of farmland and rice paddies, which is considered clean, contains NH3. Outdoor air in the
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Figure 6.34 Example of the plan view and a section A-A of a typical cleanroom.
Figure 6.35 Flow of air in a typical cleanroom.
vicinity of factories contains SOx and NOx, and the air near roads contains NOx, oxidants, and hydrocarbons. The air rinsing process is considered effective in removing these contaminants. Although this process is effective in removing SOx, it is less effective in removing
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carbonyl sulfide (COS) and other AMCs which are difficult to absorb in water. It is essential to standardize a method to sample and quantify NH3 present as mist that is appropriate to the operating environment in order to measure how much NH3 is removed by rinsing the air. Some acids and bases are introduced into the cleanroom together with outdoor air, while some of them are generated in the cleanroom and mixed with circulated air. Condensables and dopants are mainly generated in the cleanroom and mixed in the circulated air. The remainder of this section discusses these sources and describe the behavior of various AMCs. Several publications report on AMC contamination on Si wafer surface, while increasing numbers of papers report on AMC contamination on the surface of glass, optical lenses, LCD and HDD, and their prevention and control.
6.4.1.2 Acids Acid contaminants include HF, HCl, Cl2, NOx species (NO is present in minor amounts in the cleanroom) and SOx (SO3 can be present in minor amounts in the cleanroom). They are mainly brought in together with outdoor air, while acid gases are sometimes generated in manufacturing process. Acids tend to induce problems such as corrosion, and they can lead to the formation of abnormal particles on substrates and wirings.
6.4.1.3 Bases Bases include NH3, amino alcohol, N-methyl pyrollidone and tetramethyl ammonium hydroxide (TMAH). Some amines are used as rust inhibitors for industrial water.
6.4.1.3.1 NH3 As noted earlier, it is essential to standardize a method to sample and quantify NH3 present as mist that is appropriate to the operating environment in order to measure how much NH3 is removed by rinsing the air. When NH3 is precipitated as salt, the surface may form a haze or develop other unacceptable features [60, 131].
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6.4.1.3.2 HMDS Among amines, hexamethyldisilazane (HMDS), in particular, is found to cause contamination problems. HMDS is one of the primary sources of ammonia, and it is by itself an amine and an organic compound. HMDS is used in the lithography process to treat the surface of a Si wafer (silane coupling agent). HMDS, reacting (silane coupling reaction) with the surface of metals and ceramics, forms hydrophilic trimethylsilanol (TMSiOH) on the surface. This makes it easier to coat a Si wafer surface with photoresist. 2fSiOHg þ ðCH3 Þ3 SiNHSiðCH3 Þ3 ¼ 2fSiOHSiðCH3 Þ3 g þ NH3 HMDS also reacts with moisture in the air and gradually converts to NH3 and methyl silanol. ðCH3 Þ3 SiNHSiðCH3 Þ3 þ H2 O ¼ 2ðCH3 Þ3 SiOH þ NH3 Therefore, HMDS must be considered as one of the primary sources of NH3. When excessive HMDS exists in the cleanroom air, it will induce unwanted reactions with the surface of a Si wafer or a glass substrate to form a trimethylsiloxy bond (this is not adhesion but surface reaction), which results in persistent organic contamination. NH3 and TMSiOH show a strong correlation in some cases, while they do not show any correlation at all in other cases. Figure 6.36 shows the relationship between NH3 and TMSiOH. HMDS generates NH3 which induces particle generation and the Ttop phenomenon on chemically amplified photoresist. Also HMDS forms the (CH3)3SiO-group on Si wafer surface and on glass surface which changes these surfaces to lipophilic and indirectly facilitates formation of a surface susceptible to adhesion of organic impurities. The organic compounds adhering to the surface tend to decompose, causing particle generation or problems in the film deposition process. Specifically, they may cause abnormal colors, haze and clouding on glass which adversely affects the optical properties and the display function. When a glass surface is irradiated with light such as UV radiation, the (CH3)3SiOgroup is decomposed due to photoreaction and precipitates SiO2. The SiO2 precipitates may make the glass cloudy, generate particles, or cause other problems on the glass surface.
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Figure 6.36 Scattering map of the relationship between NH3 gas and TMSiOH based on analysis of cleanroom air contaminated by these compounds.
6.4.1.3.3 Amino alcohol Amines or amino alcohol are sometimes spiked in the water for rinsing and humidification as rust inhibitor. Since they are bases, they may also induce particle generation and T-top phenomenon. Amines used in the lithography process, such as TMAH and N-methyl pyrollidone, are detected in the air or on a Si wafer. They may induce Ttop phenomenon and degrade the color uniformity of the display. There are many other sources. Concrete used for buildings (especially when a building is newly constructed) constitutes a major source of NH3 generation [8].
6.4.1.4 Condensables: siloxanes, phthalates, phosphates and other organic compounds Table 6.14 shows the results of analysis for organic compounds in outdoor air. There are a few compounds to which the definition of condensables applies [48, 49, 132]. Outdoor air contains few condensables, while circulated air contains condensables in large volume. This means
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Table 6.14 Results of Analysis of Organic Compounds in Outdoor Air
Compound
Furon 113 Acetone Methyl acetate n-Hexane Methyl ethyl ketone (MEK) Ethyl acetate Chloroform 1,1,1-Trichloroethane Carbon tetrachloride 1,2-Dichloro ethane Benzene Trichloroethylene 1,2-Dichloro propane Methyl isobutyl ketone Toluene Butyl acetate Tetrachloroethylene Chlorobenzene m,p-Xylene o-Xylene
Analysis Results mg/m3 <0.1 2.3 <0.07 8.6 0.72 2.0 4.0 0.1 0.1 1.6 2.8 <0.08 <0.09 0.3 16.0 0.4 0.3 0.8 0.6 0.5
Determination Limit mg/m3
ppb vol
0.1 0.3 0.07 0.2 0.01 0.004 0.008 0.02 0.006 0.009 0.04 0.08 0.09 0.06 0.4 0.004 0.002 0.02 0.06 0.04
0.01 0.1 0.02 0.05 0.003 0.001 0.002 0.004 0.001 0.002 0.01 0.02 0.02 0.01 0.1 0.001 <0.001 0.005 0.014 0.008
Total hydrocarbons: 1.72 ppm vol. Unsaturated hydrocarbons: 0.046 ppm C (ethylene: 560 ppm). Non-methane hydrocarbons: 0.49 ppm C.
many of the condensables are generated in the cleanroom. Toluene, BHT, alkyl benzene, and condensables generated from urethane resin are often detected. Many of them are artificially synthesized. Construction materials of a cleanroom constitute the main sources for generation of condensables. From the viewpoint of ultraclean technology, however, it is necessary to mention other minor sources as well. For example, human expiration, shoes, and garments of the operators are also sources of condensables [74]. Equipment such as the air conditioning system and process tools also generate condensables. Sealants, lubricants and paints used in the equipment are often found to have detrimental effects [1].
388
FUNDAMENTALS
Figure 6.37 shows GC/MS spectra of AMCs in outdoor air and AMCs in cleanroom air [11, 133136]. Cleanroom air, shown on the bottom chart, is found to contain more AMCs than outdoor air (upper chart) in terms of both type and volume. Figure 6.38 shows TIM mode GC/MS chart of cleanroom air and that from a Si wafer surface exposed to the cleanroom air for 24 hours. It is clearly evident that several condensables among those found in cleanroom air are selectively deposited on Si wafer surface in large amounts. Table 6.15 compares the contaminants in the atmosphere and on Si wafer surface exposed in the atmosphere. The main contaminants in the column ‘‘Shiramizu and Kitajima [44]’’ are ester phthalates, while ester phosphates are the primary contaminants in the column ‘‘Camenzind and Kumar [21].’’ Condensables generated from urethane and BHT are
Figure 6.37 Comparison of GC/MS charts from (a) outside air and (b) cleanroom air (magnified 4· in sensitivity).
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Figure 6.38 Total ion chromatograms of organic contaminants from (a) cleanroom air and (b) thermal desorption gas from Si wafer surface exposed for 24 hours to cleanroom air.
scarcely detected on the Si wafer surface. BHT is not only used as an antioxidant for polymers, but it is also spiked in various industrial materials. It is sometimes used in hair cosmetics. Of the various contaminants above, three contaminants are always detected in air and on silicon wafer surface that can cause contamination problems in the manufacturing processes. These contaminants, cyclosiloxanes, ester phthalates, and ester phosphates, are discussed below in greater detail.
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Table 6.15 Relationship Between the Concentration of AMCs in Air, on a Si Wafer Surface, and After Outgassing Test [21, 44]
Item
Camenzind and Kumar [21]
Shiramizu and Kitajima [44]
Required Level: Defect Level · 1/100 Outgassing test Air Si wafer surface Problems Sticking probability Exposure time
531 ppmW 0.2 ppmw
(5.3 ppmW)
900 ng/m3 (0.34 ng/m3) 9 ng/m3 13 ng/m3 (0.005 ng/m3) (0.13 ng/m3)
5.7 ng/m3 0.2 ng/cm2
Yes [1/200]
No [1/200]
Not expected [1/200]
Yes [1/100]
24 hours
24 hours
24 hours
24 hours
The schematic relationship between contaminant concentration on Si wafer surface and the exposure time for various cleanroom contaminants is shown in Figure 6.39. When a Si wafer is exposed in a closed atmosphere, where the volume of air supplied is limited, such as a minienvironment (FOUP, Silicon wafer carrier), the relationship between the amount of AMC contamination on the Si wafer surface and the exposure time is shown in Figure 6.40.
6.4.1.4.1 Siloxanes Silicone polymers constitute a major source of siloxanes. Silicone polymer is used in the sealant between the filter and the ceiling and as a sealant between wall boards. It is used for various applications to seal hard boards as well as soft tubes [137]. During the polymerization process, silicone polymer is easily mixed with a polymerization initiator and the monomer used as raw material. The D12 monomer featuring the lowest vapor pressure is more likely to remain in silicone than other monomers during the monomer removal step. The D12 (or D6) monomer released from silicone, therefore, is preferentially detected in cleanroom air immediately after completion of cleanroom construction. The amount of D12 detected in cleanroom
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Figure 6.39 Schematic diagram of AMCs on a silicon surface exposed to cleanroom air in representative time (1hour/24 hours) and representative state (horizontally set against vertical laminar flow of cleanroom air).
Figure 6.40 Typical representation of the concentration of surface contamination as a function of exposure time.
air gradually decreases as it is governed by amount of D12 (or D6) remaining in silicone [94]. The trend in reduction of D6, like other general organic AMCs, follows the coupled exponential model equation of Tamura et al. [138]. In this silicone polymer, the polymerization initiator
392
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that functions to cut the SiO bond in the cyclosiloxane monomer remains in the polymer. This remaining catalyst starts to become active in severing SiO bonds some time after completion of cleanroom construction, which triggers the generation of cyclosiloxanes such as D3 and D4. In fact, it has been reported that more D3 and D4 cyclosiloxanes are detected in cleanroom air when they are measured one year or several years after cleanroom construction than when they are measured immediately after completion of construction [11, 94, 139141]. Cyclosiloxanes are adsorbed on the Si wafer surface and the glass surface which makes the surfaces lipophyllic. The lipophyllic surfaces are susceptible to adhesion of organic compounds, which will induce various contamination problems in the manufacturing process. Organic compounds adhering to the surfaces are decomposed by light or heat, which may lead to particle generation on the surfaces. In order to obtain good information on this type of phenomena, it is critical to combine the results of cleanroom air analysis, Si wafer analysis and surface analysis data.
6.4.1.4.2 Ester phthalates Ester phthalates are mainly used as plasticizers for polymers. They are also used as additives in the polymerization and formulation processes and as additives to paints and adhesive agents. This is because ester phthalates feature high boiling point and high viscosity, they are chemically stable, and they have an organicinorganic ratio to affect solvent characteristics. There are few inexpensive substitutes. Ester phthalates are also used as standard for measuring open pore sizes for verification of particle removal filter performance. Most commonly, the compounds detected on Si wafer include DBP, DOP, (DEP), dicyclohexyl phthalate (DCHP), di(n-octyl) phthalate (DOP), didecyl phthalate (DDP), and dinonyl phthalate (DNP). Among these phthalates, DOP is always detected in cleanroom air and it is reported to induce problems. There are a number of published papers on DOP since it is used frequently [44, 93]. Since DOP has a high boiling point, its evaporation heat is high and its sticking tendency is also high. DOP remains persistently in the fruit-basket phenomenon. In other words, DOP adheres to the Si wafer by replacing phosphates and other organic compounds on the wafer surface, as shown in Figure 6.41 for DOP and TCEP. Since DOP has a high boiling point, its evaporation temperature and the thermal decomposition temperature of its CC aliphatic bond are close each other. Thermal decomposition takes place prior to evaporation
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Figure 6.41 Change in concentration of DOP and TCEP on Si wafer surface as a function of time on exposure to cleanroom air (17 days).
and DOP has a long aliphatic chain. The radicals formed when the DOP CC chain is thermally decomposed form new aryl rings and generate carbonaceous materials [1, 26]. Ester phthalates adhering to a Si wafer are heated in subsequent manufacturing process steps and are partially carbonized to remain on Si wafer surface as the so-called carbonaceous materials. In turn, they react with neighboring atoms such as Si and C, and develop various defects that reduce the electric breakdown voltage of SiO2 [28]. Figure 6.42 shows the model for the thermal decomposition of DOP. By choosing a suitable atmosphere and the temperature conditions, it is possible to remove ester phthalates from Si wafer surface by forming highly evaporable and combustible carbonaceous materials [142]. As described above, ester phthalates persistently remain on Si wafer surface and are likely to induce contamination problems. The degree of this persistency is revealed through comparison of data for different condensables and is referred to semi-quantitatively as ‘‘staying tendency.’’ [21] This is discussed in more detail in Sections 6.4.3.4.4 and 6.4.3.4.5.
6.4.1.4.3 Ester phosphates Ester phosphates are mainly generated from cleanroom construction materials. Phosphates are often used as anti fire retardants that are added to HEPA gel such as sealant, foam and other construction materials. They are also used as plasticizers or stabilizers. Phosphates such as TEP, TBP, TCrP, TCEP, and TCPP are often detected in cleanroom air.
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Figure 6.42 Schematic representation of the vaporization and thermal decomposition of DOP at (a) room temperature, (b) 200350 C, (c) 450600 C, and (d) 800 C.
Phosphates are next to phthalates with respect to the boiling point, fruit-basket phenomenon, sticking probability, staying tendency, and thermal stability without evaporation. Like phthalates, phosphates cause those troubles that are common for organic compounds with high boiling points. They are more readily detected than other AMCs. Phosphates feature higher staying tendency than phthalates since they contain other hetero atoms than C, H, and O. As has been reported in
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some cases, phosphates form acid points to induce formation of defects and precipitates on the surface. It has also been reported that phosphorus atoms exhibit undesirable behavior as a dopant. For TCPP, Camenzind and Kumar [21] and Shiramizu and Kitajima [44] reported the relationship between the threshold level that causes problems and data on outgassing amount, concentration in the air, and concentration on Si wafer surface. By considering the data in a pair-wise manner together with the calculated sticking probability of TCPP, the required cleanliness level for problem-free operations has been defined (Table 6.15). The ‘‘C-O-P’’ ester bond of ester phosphate undergoes thermal decomposition when heated to temperatures of 200 C or higher. Under these conditions, phosphoric acid will remain on the surface of the substrate, although the ester structure is no longer preserved. This thermal action, which is difficult to eliminate, is shown in Figure 6.43. This phenomenon can be avoided by choosing a suitable atmosphere and heating temperature.
6.4.1.4.4 Dopants: boron and phosphorus compounds What is unique about dopant contamination is that the effect on device physics is not proportional to the concentration of the contaminant. Usually boron and phosphorus are doped in Si wafers. Dopant contamination on Si wafer will enhance or neutralize the previously present dopant in the Si wafer. This is why the effect of dopant contamination is not linearly proportional to the dopant concentration in the air, or on the time of exposure to dopant contamination.
6.4.1.4.4.1 Sources of boron generation This section discusses what the analysis data indicate about sources of boron released to cleanroom air in the semiconductor manufacturing process. Boron is generated in the form of BF3 gas, together with SiF4 and PF6 from the borophosphosilicate glass (BPSG)* passivation film during the HF etching process [143, 144]. In some cases, boron is derived from source gases for the *BPSG is an unstable glass. Pyrex1 glass is the so-called ‘‘boro-phospho-silicate glass,’’ but it contains Al which makes it stable with good properties as laboratory glassware. It is quite different from BPSG in its stability, melting point and other characteristics. The melting point of BPSG glass is controlled by boron and/or phosphorus concentration to give a low-temperature product to make glass fiber for HEPA filters.
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Figure 6.43 Schematic representation of the vaporization and decomposition phenomenon for ester phosphate at (a) room temperature, (b) 200350 C, (c) SiO2 < 10 nm, and (d) 800 C.
passivation film including B2H6, R3B, PH3 and R3P (‘‘R’’ represents an alkyl group or an alkoxy group in general, including CH3, C2H5, and C2H5O). A major contaminant that is most commonly generated is BF3. Published reports suggest that BF3 is generated when hydrogen fluoride gas used in semiconductor manufacturing process in a cleanroom is mixed into recycled air and it comes into contact with the HEPA filter material consisting of borosilicate glass fiber [145, 146]. Table 6.16 shows the results of analysis of boron and other metals in an absorbing solution in which cleanroom air containing AMCs was absorbed. Analysis of
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Table 6.16 Comparison of Analysis Results Obtained with Various Absorption Solutions
Absorption Solution
Run
Pure water
1 2 1 2 1 2
3% HCl 3% HNO3
B
Metal (ng/m3) Na Al Zn
Fe
37 39 45 43 43 45
140 150 150 160 150 160
3 5 22 24 23 23
4 6 16 18 20 18
33 31 34 30 33 31
different metals is possible by using an acid absorbing solution spiked with nitric acid. Table 6.17 shows the results of analysis of boron sampled from the air at different locations by means of the absorption-to-solution method and the collection-with-filter method. The results of both methods are similar and indicate the presence of boron compounds as particles, which are often observed in outdoor air. The boron concentration measured with the absorption-to-solution method is higher than that measured with the collection-with-filter method because some boron exists in a gaseous form. This is the case for cleanroom air. Table 6.18 shows boron concentration measured upstream and downstream of a HEPA filter and a chemical filter. Boron in gaseous form increases downstream of the HEPA filter and decreases downstream of the chemical filter. Particulate boron in outdoor air decreases downstream of the HEPA filter. Boron in gaseous form in cleanroom air decreases downstream of the HEPA filter. Boron in gaseous form in cleanroom air, however, does not show an increase downstream when the HEPA filter is made from polymers which contain no boron. Figure 6.44 compares data from the absorption-to-solution method and those from the collectionwith-filter method. BF2+ (m/e = 48 and 49) in cleanroom air can be detected with API-MS [146]. Table 6.19 shows that the boron concentration in the air increases when the air contains alcohol [147] or moisture [148]. The existence of boron is not in the form of B2F6 due to corrosion of the glass with HF, rather it is present as B(OH)3. The mechanism is the reaction of moisture or alcohol with B2O3 crystallized from BPSG as described below.
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Table 6.17 Boron Concentration in Air at Various Locations
Sample
Outdoor air
Cleanroom
Boron (ng/m3)
Site*
A B C D E F G H I J K L M
Solution Method
Filter Method
3 6 9 11 22 25 32 35 130 155 30 180 290
3 5 9 10 20 23 31 30 125 160 3 8 40
Difference** 0 1 0 1 2 5 1 5 4 5 27 172 250
Conc. Ratio: Gaseous Boron to Total Boron 0.00 0.15 0.00 0.10 0.10 0.10 0.30 0.10 0.04 0.00 0.90 0.96 0.86
*A: Mountain valley; B: Field; C: Pasture; D: Town-1; E: Town-2; F: Town-3; G: Traffic; H: Plant; I: Seaside; J: Seaside; K: After HEPA filter-1; L: After HEPA filter-2; M: After HEPA filter-3. **Difference in boron concentration between the solution absorption method and the filter collection method.
According to the solidliquid phase diagram of the SiO2B2O3P2O5 system (Figure 6.45) presented by Kern et al. [143, 144] and Hummel et al. [149, 150], the boron, phosphorus, and silica glass is unstable in the region of very low-phosphorous composition where B2O3 is highly likely to be precipitated. This so-called ‘‘Vidrid’’ phenomenon is induced depending on the glass fiber manufacturing conditions [1]. It has been speculated that moisture or alcohol triggers evaporation of B2O3 precipitated on the surface into the air. The form of the contaminant generated in the air is different, depending on whether the HEPA filter fiber is uniformly glassy, or B2O3 precipitation takes place locally. Countermeasures for these effects need to be correspondingly different. Among the boron compounds, BH3, organic boron compounds, BF3, BCl3 and B(OH)3 are expected to be detected. These compounds have higher vapor pressure
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Table 6.18 Boron Concentration in Air Before and After HEPA Filtration and Chemical Filters
Air Outdoor air Inlet air to cleanroom (95% recycled air + 5% outside air) Inlet air to cleanroom (95% recycled air + 5% outside air)
Sampling Point Before HEPA filter After HEPA filter Before HEPA filter After HEPA filter Before chemical filter After chemical filter
Boron (ng/m3) Room A Room B 136 5 5 30
32 1 5 11
30 <1
11 <1
Figure 6.44 Scattering map of the analysis results for boron concentration from the solution absorption method compared with the filter collection method.
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Table 6.19 Boron Concentration in Air Containing Moisture and Alcohol at Various Locations
Air
Sampling Point
Outdoor air Glass Glass Glass Glass
HEPA HEPA HEPA HEPA
Boron (ng/m3) Room A Room B
filter* filter* filter* filter*
32 35 136 155
1 5 5 1
Inlet air to Glass HEPA filter* cleanroom Glass HEPA filter* Glass HEPA filter* Glass HEPA filter* Polypropylene HEPA filter
5 5 10 3 3
30 11 91 15 3
5
1
11 32
<1 <1
Inlet air to Chemical filter** cleanroom Chemical filter** Chemical filter**
Remarks
HF: 300 ng/m3 HF: 300 ng/m3 Alcohol: >500 ng/m3 Alcohol: >500 ng/m3 (no boron source)
*B2O3: 8%. **Active charcoal filter.
Figure 6.45 Diagram of the SiO2B2O3P2O5 ternary system.
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in air than the metal, oxides and salts and they are highly likely to be present in the air. As noted earlier, boron in cleanroom air adheres to the Si wafer surface and affects the electrical characteristics such as the threshold voltage of devices [1]. How the boron contamination described above is investigated and analyzed will help in the study of other metal AMCs in the future.
6.4.1.4.4.2 Sources of phosphorus generation Chemicals used in the patterning process and BPSG glass used for film deposition contain phosphorus compounds in large amounts. Therefore, in these process steps, PH3 and (RO)3PO are sometimes detected as contaminants. They are often generated from phosphates which were described in Section 6.4.1.4.3. Phosphorus compounds are often used as flame retardants in construction materials and as plasticizers. Phosphorous is particularly used in urethane paint, HEPA gel and foam [93]. Recently, another type of fire retardant sealant is being used that does not use ester phosphate [151, 152].
6.4.1.4.5 Other contaminants Gases of organic metals, metal hydrides, metal halides and metal hydroxides have higher vapor pressure than other compounds. They are sometimes detected as AMCs in air and they have a tendency to adhere to and react with the surface to develop defects or to generate particles.
6.4.2 Examples of problems caused by AMC contamination This section presents some examples of problems that are often attributed to AMC contamination [1, 44]. Si wafer: particles, failure in lithography, TDDB failure, surface roughness, and poor thickness reproducibility. LCD: surface roughness, abnormal color, blurring of color, and discoloration [22, 23, 120, 137, 153, 154]. HDD: head crash [24, 25].
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The remainder of Section 6.4.2 will discuss what problems occur frequently, what contaminants cause serious problems, and what effects can lead to misinterpretation of analysis data.
6.4.2.1 General The adhesion of AMCs to a substrate surface generally results in some changes to the manufacturing process. It is necessary to consider AMC reactions such as evaporation and partial carbonization of AMCs, as well as the primary process reactions of the manufacturing process. Usually the reactions of AMCs are negligible in comparison with the primary process reaction. In some cases, however, these three reactions become competitive with each other, or they may be consecutive reactions in which all AMCs are evaporated before film deposition starts. Both the competitive reactions and the consecutive reactions will increase intraand inter-lot variation.
6.4.2.2 Effects of ammonia Figures 6.6 and 6.7 showed XPS and TOF-SIMS spectra from a Si wafer surface on which particles of ammonium salts were detected [77, 85, 86]. Although siloxanes, phosphates, sulfites, and sulfates were detected by TOF-SIMS which can acquire information from the top surface, NH4+, NO3, CNH, and other N1S spectra were detected by XPS which can acquire information from a surface layer thickness of greater than 10 A˚. Based on this data, amines and NH3 adhere first to the surface, followed by organic compounds and acidic gases to form foreign substance particles. NH3 not only constitutes a primary cause of contamination, but it also may induce adhesion of other AMCs and generation of particles to indirectly cause further problems. NH3 not only generates particles of inorganic salts and organic salts, but it also reacts with the proton in optically amplified photoresist. This reaction consumes H+ to make the top surface less photosensitive, causing the problem associated with the T-top phenomenon. This phenomenon, however, can be caused by other nitrogen compounds such as amines and amino alcohols. In some cases, problems may occur though the NH3 monitor detects no excursion. Or in other cases, no problems are found even though the NH3 monitor detects an excursion. It is critical to fully understand the measurement mechanism of the NH3 monitor and mechanism of troubles to take place.
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6.4.2.3 Effects of siloxanes The surface of optical glass and lenses often forms a haze when siloxanes adhering to the surface are converted to SiO2 due to photoreaction with UV radiation which then crystallizes on the surface. As noted previously, the primary sources of siloxanes are cyclosiloxanes derived from silicone polymer (oligomer) in construction materials. HMDS used in the lithography process is also a siloxane.
6.4.2.4 Effects of HMDS The characteristics of HMDS have been discussed in Section 6.4.1.3. In the air, HMDS is decomposed with moisture into NH3 and trimethylsilanol (TMSiOH). The NH3 monitor will indicate high values when the air is contaminated by HMDS. TMSiOH makes glass cloudy. Analysis of TMSiOH can reveal the relationship between air cleanliness and glass clouding [1]. What makes data interpretation complex is the fact that another contaminant cyclosiloxane that also makes glass cloudy. Since cyclosiloxanes are generated from construction materials, their concentrations hardly show a rapid change in a cleanroom. In some cases, however, cyclosiloxanes concentrations in a cleanroom are significantly different from those in another cleanroom. In order to make effective use of alarm information and take appropriate actions, it is critical to understand the functions of the contaminant monitor and the chemistry of clouding.
6.4.3 Chemistry of AMCs Theoretical and experimental investigations on the chemistry of AMCs are discussed in this section.
6.4.3.1 Monolayer and sub-monolayer contamination By measuring the concentration of contaminants adhering to a Si wafer surface, several authors were able to obtain actual data to draw a monolayer adsorption curve (Figure 6.39). Figure 6.46 shows the variation of contaminant concentration on Si wafer, glass, and an aluminum plate as a function of time. This data confirms that a so-called ‘‘fruit-basket phenomenon’’ takes place as the amount of adsorbed contaminants
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Figure 6.46 Relationship between exposure time and DOP concentration on a silicon wafer, glass substrate, and an aluminum surface.
gets close to the theoretical amount of monolayer coverage and the remaining ‘‘sites’’ decrease in number. The fruit-basket phenomenon occurs when organic compounds with lower boiling points rapidly adsorb on the wafer surfaces at first, but they tend to be gradually replaced by organic compounds with much higher boiling points. This phenomenon has a great impact on the reliability of a method to evaluate cleanroom construction materials. A construction material and a Si wafer are confined in a container together for a given period of time, after which the Si wafer is heated to evaluate the gases evaporated from its surface. This phenomenon was found to be useful for developing a new chemical filter to trap a specific contaminant [1]. There are two major models to calculate the concentration of monolayer contaminants. 1. Calculation of silicon substrate from density, molecular (atomic) weight and Avogadro’s number. The surface concentration of Si atoms on Si wafer is calculated by
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using values of density, atomic weight and Avogadro’s number. The calculated concentration is then replaced with the surface concentration of contaminants (Figures 6.47 and 6.48). When a metal is a contaminant, no significant difference is found even if the concentration is calculated with this method because of the DulongPetit law between atomic weight and density. Only the alkali metals deviate slightly from this model. When this model is applied to a monolayer of organic contaminants, DOP is 27 carbon atoms/cm2 when Si atoms and carbon atoms on Si wafer are assumed to be in a 1:1 ratio. 2. LangmuiBlodgett thin layer model for organic compounds. The model described above is inappropriate for many of the organic contaminants since their specific gravity is around 1. The second model that is used to calculate monolayer concentration of organic compounds is developed based on the LangmuirBlodgett thin layer model [155]. Figure 6.49 shows schematically the calculation
Figure 6.47 Calculation of monolayer surface coverage in different units.
405
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Figure 6.48 Model of monolayer surface coverage for the case of substitution of a carbon atom for a silicon atom.
Figure 6.49 Model of monolayer surface coverage for the Langmuir-Blodgett thin film model of organic compounds.
method Si and organic contaminants are slightly different with respect to the number and distribution of the atoms per unit surface area. When calculating the concentration by using specific gravity, molecular weight (to be converted
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Figure 6.50 Concentration of contaminants per unit surface area for various metals and organic compounds.
to carbon-atom-equivalent) and Avogadro’s number and ignoring the distribution of Si atoms on the surface, the concentration of phthalates turns out to be 1.3E14 DOP molecules/cm2, 88.2 DOP ng/cm2 and 65 C ng/cm2. The measured values of surface contaminant concentration that reach a constant value with exposure time are always in the range of 60100 ng/cm2 (Figure 6.49). Figure 6.50 compares the concentration on the surface per unit surface area for several metals and organic compounds.
407
408
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6.4.3.2 ClausiusClapeyron relation A new method based on ClausiusClapeyron equation has been developed to evaluate the amount of gases generated during heating. The new method is highly reproducible and accurately represents real situation. Figure 6.51 shows chromatogram data on gas evolution from a
Figure 6.51 GC/MS chromatograms of gas from a polypropylene sheet sample at (a) 60 C, (b) 80 C, (c) 100 C, and (d) 120 C (outgassing time: 1 hour. Gas flow rate: 300 ml/min).
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polypropylene sheet. The amount of gases generated as a function of temperature is shown in Figure 6.52. The ClausiusClapeyron equation considers vaporization of organic compounds, including polymer, the glass transition temperature Tg, and the effect of moisture or steam (>100 C). It has been shown that the amount of gases generated can be estimated at any arbitrary temperature when the ClapeyronClausius equation is applicable and the gas generation mechanism is constant within the region where linearity is observed, and that the slope is almost the same as that of the vapor pressuretemperature curve for each compound. Figure 6.53 shows the applicable form of the equation. It has been found for many contaminants that the amounts of gas generated at 150, 120, 100, and 80 C are multiples of the amount of gas generated at room temperature. Figure 6.54 compares the amount of outgassing of polypropylene at room temperature estimated from the measured amount at elevated temperature, and the measured outgassing concentration at room temperature. Since the amount of outgassing from a contaminant depends significantly on its vapor pressure, this new method is found to be effective in measuring those contaminants that are lie between the contaminants
Figure 6.52 Relationship between the logarithm of the concentration in mm/g of outgassing contaminants and the reciprocal outgassing temperature in degrees K.
410
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Figure 6.53 Representation of the ClausiusClapeyron equation (p = pressure of the phase; T = absolute temperature; DH = molar enthalpy of the phase transition; DV = difference in the molar volumes of the two phases 1 and 2; c = integration constant; R = gas constant).
Figure 6.54 Outgassing amount from a polypropylene sample at room temperature: comparison of the measured value (circles) with the calculated value (square symbol).
which can decrease in amount in a day and those which scarcely decrease even after three years [11, 133]. Figure 6.55 shows the vapor pressure of organic compounds as a function of reciprocal absolute temperature. The outgassing data from polypropylene measured with the JACA 34-1999 method [100] have been included in this figure. The temperature dependence of the amount of gas evolved is in good agreement with the vapor pressure dependence [103, 155157].
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Figure 6.55 Vapor pressure of relevant organic compounds as a function of reciprocal temperature together with data on outgassing amounts (ng/g) from polypropylene.
6.4.3.3 Outgassing phenomenon: two-phase exponential model of vaporization and diffusion of contminants All the JACA methods [100] emphasize taking measurements under those conditions which enable evaporation to take place at an equilibrium state between the gas and the surface. A linear relation can be found between the measured amounts and reciprocal of the temperature that triggers surface vaporization and gas release (1/T). By using this linear
412
FUNDAMENTALS
relation, it is possible to estimate the amount of gas generated at any arbitrary temperature [94, 158, 159]. The same sample was repeatedly measured with this method to verify its reproducibility. The method is found to be highly reproducible. Also, since this method takes measurements in an equilibrium state between the gas and the surface, the measured values are truly represent the real physical situation. The two methods described in Section 6.3.3 will be discussed here. The IEST dynamic headspace screening test method [25, 99] is capable of evaporating all AMCs in a sample and measure them promptly. In other words, the IEST method features high throughput. Therefore, this method is effective when it is necessary to select candidate materials from a large number of materials. The JACA methods enable us to use a measured value at a certain temperature as a reference basis to estimate the amount of gas evaporated within a unit time at an arbitrary temperature. For example, compared with amount of gas generated at room temperature, the amount of gas generated is 900 times greater at 150 C, 200 times greater at 120 C, 140 times greater at 100 C, and 65 times greater at 80 C. Takeda et al. [103] have proposed a method to calculate the amount of gas evaporated at room temperature (ng/m2hour) by using a nomogram (Figure 6.56), based on measurement data and measurement conditions such as temperature, heating time and surface area of the sample. They reported that the calculated values are in good agreement with measured values. The sample in the IEST method is a very small pin type with a comparatively large surface. The temperature elevation is rapid. The evaporation of the contaminant from the sample surface is the rate-determining step. Diffusion from the interior to the surface of the sample is not a ratedetermining step. All contaminants on the sample surface are quickly evaporated. On the other hand, the JACA methods enable evaporation to take place at a gassurface equilibrium state where contaminants transfer from the interior to the surface of the sample which is the rate-determining step. Tamura et al. [125, 160] reported reaction rate equations for the two methods by applying the two-phase exponential model of Chang and Krebs [161]. They assumed two reaction rate steps, evaporation from the surface and diffusion to the surface, and formulated a model using a two-phase exponential equation. They reported that the results from this model are in a good agreement with the measured values. This report clearly defines the positions of the IEST and JACA methods. The measurement data by the JACA methods enable us to estimate
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Figure 6.56 Nomogram for prediction of the outgassing rate of organic AMC compounds.
the amount of gas evaporated within a unit time, to calculate the amount of gas evaporated over time, and to calculate the AMC concentration in the air at 7 days later [106, 160, 162]. To ascertain the relationship between the two models above, it is instructive to consider a hybrid model. By modifying the sample size and shape, and selecting the proper heating conditions, a hybrid model has been developed and experimental data have been obtained to validate the model. The data show both reaction steps surface, evaporation and diffusion to the surface, contribute to the rate-determining step. Using this
414
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data, both evaporation and diffusion rates can be estimated and compared with each other.
6.4.3.4 Sticking probability, sticking coefficient, and staying tendency The authors present the actual contamination level in a cleanroom which was regularly measured over several years from start of cleanroom operation. This section also describes the relationship of AMC concentrations at the contamination source, in the air and on Si wafer surface, and their relationship to the problems caused in the manufacturing process. Figure 6.57 shows TIM mode chromatography data for contaminants at different exposure times. The variation of chemical filter performance over a period of several years is discussed in Section 6.5.3.
6.4.3.4.1 Sticking probability [163] Sticking probability as an indicator of susceptibility to contamination was found to be useful to represent the relationship between AMC concentration in the air and that on Si wafer surface which was exposed to the air [164, 165]. Suzuki and Maki’s equation [163] used for particle contamination can be applied and the sticking probability can be calculated only from the data obtained. Qualitatively, the sticking probability shows the relative intensity of AMC-to-substrate surface adhesion. Table 6.20 shows the calculation results. Figure 6.58 shows relationship between AMCs concentration in cleanroom air and that on Si wafer which was exposed to the cleanroom air for 24 hours. Sticking probability is particularly useful when discussing how easily AMCs adhere to substrate surface and how AMCs relate to the fruitbasket phenomenon, compared with particles in cleanroom air. The sticking probability of a particle is 1/400, while the sticking capability of DOP and of phosphate is 1/100 and 1/200, respectively [133]. Figure 6.59 shows DOP concentration in the air on the horizontal axis and that on Si wafer surface on the vertical axis for different exposure time and sticking probability. This figure demonstrates that it is possible to predict the concentration of AMCs on silicon wafer surface in air for a given exposure time. It is also possible to predict the required cleanliness level for air and the exposure conditions to maintain the substrate surface
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Figure 6.57 Total ion chromatograms of the surface contaminants on a Si wafer exposed in cleanroom air.
cleanliness level required for each condition. Figure 6.60 shows the levels for DOP and siloxanes. Momoji et al. [65] reported the sticking probability of acidic and basic contaminants on the surface of a Si wafer using Ion Chromatography and Capillary Electrophoresis Mass Spectrometry. The data are shown in Table 6.21 and Figure 6.61.
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Table 6.20 Sticking Probabilities for Various Contaminants
Contaminant Di(2-ethyl hexyl) phthalate Trichloro ethyl phosphate Cyclosiloxanes Aromatic hydrocarbons
Sticking Probability 0.010000 0.005000 0.002500 0.000017
Figure 6.58 Relationship of the concentration of contaminants between air and a Si wafer surface (calculated for 24 hours exposure).
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Figure 6.59 Concentration of DOP on a Si wafer surface (ng/cm2) and in air (ng/m3) for varying exposure times and different sticking probabilities.
6.4.3.4.2 Sticking coefficient A recent model of the sticking coefficient uses the gas diffusion coefficient in its formulation [165, 166]. This model should be useful for quantitative prediction in a sealed space with no air flow where diffusion is the rate-determining step. At present, this model is often applied to a minienvironment which is totally different from a cleanroom environment in terms of the rate and patterns of air flow. The sticking probability is the basis for a contaminant model dominated by the flow rate of the air such as particles, while sticking coefficient is the basis for a model of contaminants dominated by gas diffusion. Namiki et al. [166168] have developed a model to integrate these two parameters. Using the model, they calculated the migration rate, average migration distance per unit time, and the deposition rate of gaseous molecules and particles, as shown in Figure 6.62. Three regions, namely a turbulent region, turbulent boundary layer, and a viscous bottom layer, are identified to express the adsorption and the desorption mechanisms on the surface. This model is in good agreement with actual data.
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Figure 6.60 Relationship between the concentration of organic compounds in cleanroom air and on Si wafer surface necessary to maintain a specified cleanliness level on 1 hour exposure.
Table 6.21 The Sticking Probability of Ionic Species on a Si Wafer
Species
Sticking Probability Condition 1 (without amine) Condition 2 (with amine)
Cl NO3 SO42 NH4+ Alkanol amine
6 · 105 6 · 105 3 · 105 3 · 105 does not exist in air
3 · 103 4 · 104 <107 no sticking 5 · 103
By considering the interaction with water molecules in the air, Kagi et al. [168, 169] have obtained the desorption coefficient of DOP from the values measured with API-MS, and calculated the amount of adsorbed DOP. They reported that their calculated results are in good agreement with the measured values. Figure 6.63 compares the calculated DOP concentration with the measured DOP concentration on Si wafer surface.
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Figure 6.61 Relationship between exposure time and concentration of ionic species on the front surface of a Si wafer for (a) exposure time from 0 to 100 hours (upper figure) and (b) exposure time from 0 to 480 hours (lower figure).
Using this numerical model, Tamura et al. [138] reported that an explanation using sticking probability would be more applicable to those cases where the rate of air flow was high since the flow rate affects the amount of AMCs adsorbed on the surface. In addition to the above, Ishiwari et al. [6971], Godo et al. [170173], Habuka et al. [174], and Buegler et al. [98] reported numerical expressions to express the relationship between AMC concentrations in air and on Si wafer surface. In many cases, the adsorption of AMCs onto the substrate was explained by the van der Waals adsorption mechanism.
420
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Figure 6.62 Migration velocity and average migration length for unit time and deposition rate for particles and gaseous molecular contaminants.
Godo et al. [170173] have attempted to explain the adsorption mechanism using a molecular structure model. However, Bent [175] has reported that there is an interaction between the substrate surface and compounds, such as ester phthalates, which have ‘‘the conjugated double bond’’ in the chemical structure. The CH stretching vibration is different between the monolayer and the multilayer of butadiene on the surface of a silicon wafer. (The stretching vibration of CH: 3080 cm1 at the multilayer comes to be 2994 cm1 at the monolayer). The analysis method is ‘‘Multieflection FT-IR’’ which Nishiyama and Ohmi have reported [84]. The results of FT-IR have been reported for many years on the interaction between the metal and the compounds including a ‘‘conjugated double bond’’ in the
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Figure 6.63 Comparison of the calculated concentration with the measured values for DOP concentration on a Si wafer surface according to the Kagi model [168, 169].
chemical structure. The interaction between acrylonitrile and alkyl aluminum/titanium chloride was reported by Yasui et al. [176], and the interaction between methyl methacrylate, methacryonitrile and LiALH4 was reported by Fujimoto et al. [177]. (The stretching vibration of the triple bond of C:N of methacrylonitrile: C:N; 2230 cm1 in solvent becomes 2267 cm1 as adduct with LiAlBuEt3. The stretching vibration of the double bond of C=O of methyl methacrylate: C=O, 1724 cm1 becomes 1732 cm1 as adduct with LiAlH4). These discoveries contributed to the high tactility polymer consumption. When considering a mechanism for AMC adsorption onto the surface of the substrate, it should be taken into consideration that there is a chemical interaction between two non-transition metals, which have no d-orbital electrons, and the organic compounds, which have a conjugate double bond. The shift in stretching vibration of CH, C=O and C:N, which were reported in the results from FT-IR analysis, is thought to be a demonstration of the interaction phenomena between two metal atoms and a conjugated double bond. Consideration of this interaction was described by Buriak [178], Cypryk and Apeloig [179], and Schwarz and Hamers [180]. Schwarz and Hamers reported that there was a shift to 1985 cm1 in the C:N stretching vibration on the surface of a silicon wafer, while a stretching vibration of 2230 cm1 was detected in a liquid medium.
422
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In addition, the mechanism and bonding configuration between two Si atoms and acrylonitrile was also considered. The research into AMC adsorption onto the surface of a substrate has progressed since both physical adsorption, according to van der Waals adsorption mechanism, and chemical adsorption, are taken into account. It is expected that the model of interaction between the substrate surface and the AMCs will become more accurate as the research progresses into the areas of adsorption probability, staying tendency, fruit-basket phenomenon, and other interactions.
6.4.3.4.3 Staying tendency The concept of staying tendency has been proposed [25] to express the relationship between concentration of AMCs on Si wafer surface immediately after exposure in air, and the amount of residual AMCs (not evaporated) on Si wafer surface which is converted to carbonaceous materials after thermal treatment. As noted previously, the carbonaceous material can cause problems in the subsequent manufacturing process.
6.4.3.4.4 Fruit-basket phenomenon Hayashi et al. have reported on the fruit-basket phenomenon [181, 182]. It is also referred to as ‘‘musical seat games’’ phenomenon. This is the phenomenon where AMCs previously adhering to Si wafer are replaced by those which reach the Si surface later but are much more adhesive. Organic compounds with lower boiling points rapidly adsorb on the wafer surfaces at first, but they tend to be gradually replaced by much higher boiling points organic compounds. Figure 6.64 illustrates the fruitbasket phenomenon. The lower diagram shows a model based on the assumption that each AMC adheres separately. In reality, however, multiple AMCs coexist as shown in the upper diagram, and the most adhesive AMCs will ultimately adhere to the Si surface. As shown in Figures 6.41 and 6.65, the adhering ester phosphates are progressively replaced with ester phthalates [133]. For the first 24 hours, ester phosphates, just like DOP, increase in proportion to time on Si wafer. The amount of ester phosphates exceeds 5 mg/cm2 after 24 hours (Figure 6.41). At this stage, 510% of the ‘‘available seats’’ are occupied if it is assumed that the maximum amount of ester phosphates that adhere is 60100 mg/cm2. As the number of vacant seats becomes smaller, the fruit-basket phenomenon starts to take place.
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Figure 6.64 Schematic model of the fruit-basket phenomenon. (a) Co-exists as multiple contaminants. (b) Exists as single contaminant.
Ester phosphates begin to gradually decrease after showing the maximum concentration value after one or two day exposure. When multiple AMCs coexist, the fruit-basket phenomenon takes place. Ester phthalates follow a similar S-shaped curve, and other AMCs reach peak values once and then keep decreasing. Wafer thermal desorption GC/MS (WTD-GC/MS) is a method to measure the concentration of AMCs on Si wafer exposed to cleanroom air for the purpose of evaluating AMC concentration in cleanroom air. When this method is used, it is necessary to select the exposure condition (time) to allow the concentration of AMCs on the Si wafer to increase proportionally with time. For the case shown in Figure 6.64, the
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Figure 6.65 Change in concentration of DOP and TCEP on a Si wafer surface as a function of exposure time (24 hours) to cleanroom air.
concentration of ester phosphates decreases due to the fruit-basket phenomenon since the amount of DOP exceeds 15 ng/cm2. Thus, in this case, the concentration of ester phosphates on Si wafer measured within the first 24 hours must be used. As shown in this figure, the fruit-basket phenomenon takes place when the amount of DOP exceeds 15 ng/cm2. In other words, the fruit-basket phenomenon does not take place when the amount of DOP is less than 1 ng/cm2. As has been reported, the DOP concentration on Si wafer reaches a constant value with time at a concentration is 60100 DOP ng/cm2 which is assumed to be a monolayer. If it is assumed that a monolayer of DOP is 100 DOP ng/cm2, the fruitbasket phenomenon starts when 1/100 of the total available seats are occupied by DOP.
6.4.3.4.5 Carbonization phenomenon The present authors have investigated the carbonization behavior of contaminants and the methods to prevent problems by evaluating the thermal behavior of DOP. A measurement method was developed to observe the thermal behavior of DOP in a reducing/oxidizing environment. The new measurement method has enabled us to reveal various phenomena and their mechanisms which has contributed to the resolution of problems and to the improvement of the cleanliness of the manufacturing environment [1, 88, 183]. DOP is often detected especially on Si wafer surface exposed to cleanroom air in which numerous organic compounds exist. DOP also draws
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attention as it causes device problems such as the reduction of electric breakdown voltage of oxides. Hence, the thermal behavior of DOP was studied in comparison with that of ester phosphates and siloxanes both of which feature high sticking probability. Evaporation is a common phenomenon which takes place primarily when organic compounds are heated. If it were only evaporation that occurred when DOP was heated, DOP would be removed easily. In reality, however, DOP-induced problems are always observed. Based on this fact, it has been hypothesized that the heating process triggers not only DOP evaporation, but also other phenomena such as DOP carbonization [184, 185]. Changes in the thermal behavior of organic compounds were examined by means of thermogravimetry (TG) and differential thermal analysis (endotherm/exotherm calorimetry) (DTA). The behavior of various organic compounds in air flow and in nitrogen gas flow was investigated by thermogravimetry (TG) and differential thermal analysis (DTA). Figures 6.666.68 show the measurement results and Table 6.22 summarizes these results. All contaminants except DOP and TBP in the air keep absorbing heat until they reach temperatures where there is no mass, indicating that these contaminants are evaporated. Like other organic compounds, DOP absorbs heat in nitrogen gas flow. In air, however, DOP generates heat, which indicates that DOP burns. For TBP in the air, a precise observation of its DTA curve reveals that the heat generation curves overlaps with the evaporation curve. The DOP weight is totally eliminated in air at a temperature of 300 C or higher. However, it appears that DOP thermal decomposition might be taking place around 200 C and that TBP also tends to be thermally decomposed to some extent [1]. These phenomena are helpful when performing contaminant analysis and investigating contaminant behavior by interpreting relevant measurement data. Those organic compounds with high sticking probability adhere to the Si wafer surface, and they go through various thermal treatments in the subsequent manufacturing process steps. Investigation of their vapor pressure suggests that evaporation is the primary reaction when they are heated: they are evaporated and released from the Si wafer surface. When temperature is increased rapidly, however, thermal decomposition and oxidation in the air, as well as primary evaporation reaction, may take place. It is speculated that due to these secondary reactions, organic compounds are partially carbonized and remain on the Si wafer surface. Measurement data taken by means of the TG and DTA are very useful to assess the staying tendency of each organic compound [25].
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Figure 6.66 Thermogravimetry and differential thermal analysis data of DOP for (a) N2 (upper figure) and (b) air (lower figure).
6.4.3.5 Investigation of contamination based on the ‘‘Organic Conceptual Diagram’’ [186189] This section describes the application of the Organic Conceptual Diagram to AMCs in cleanroom air. In the semiconductor manufacturing process, there are problems induced by AMCs which adhere to the surface of substrates such as a Si wafer and glass. There is a wide range of relevant
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Figure 6.67 Thermogravimetry and differential thermal analysis data for TBP in (a) N2 (upper figure) and (b) air (lower figure).
contaminants, including acids and bases and organic compounds. In order to sort these numerous AMCs, the Organic Conceptual Diagram can be applied [172175]. Figure 6.69 shows the diagram for AMCs. The key features are highlighted below. Basic contaminants react with protons of photoresist to interfere with optical amplification, which triggers T-top
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Figure 6.68 Thermogravimetry and differential thermal analysis data for cyclosiloxane tetramer (D4) in (a) N2 (upper figure) and (b) air (lower figure).
phenomenon due to lack of photosensitization. These basic contaminants are located in the strong inorganic region of the diagram. Ester phosphates and ester phthalates adhere to Si wafer surface, and are partially carbonized on heating to generate defects in oxides which result in degradation of the electric breakdown voltage. Both ester phosphates and ester phthalates are located in the strong organic region above
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Table 6.22 Results of TG and DTA for Various Contaminants
Compound
Temperature ( C) for 99.5% Weight Loss
Atmosphere N2
Air
DOP TBP
Endothermic Endothermic
OMCTS
Endothermic
Exothermic Endothermic and exothermic Endothermic
378 282 172
the sensitization limit line. Cyclosiloxanes, after adhering to Si wafer, are sensitized with UV and photolyzed allowing silicon dioxide to be precipitated which hazes or clouds the lens and mirror. The cyclosiloxanes are located just between the organic region and the inorganic region. Some relationships are also observed between the type of problems and the location of AMCs on the diagram. The surface of a Si wafer of SiH type, after being treated with HF is extremely organic and water-repellant. On this type of surface, located very close to and almost parallel with the organic axis, ester phthalates do not adhere so much. Native oxides are found to contain both organic and inorganic portion as determined by contact angle measurements of a water droplet. This is probably because a variety of surfaces including inorganic oxides, Si substrates, and organic SiH films coexist. Ester phthalates, cyclosiloxanes, acid contaminants, and base contaminants are found to adhere to the surface with these native oxides. The Organic Conceptual Diagram is very effective in exploring appropriate synthetic high molecular weight dyes. Similarly, the relationship between contact angle of a water droplet and the Organic Conceptual Diagram of AMCs can be more clearly defined as more data are accumulated. When a new contaminant is detected, by locating it on the Organic Conceptual Diagram, its behavior could be described by similarity with AMCs of known behavior located nearby on the diagram. DTA curves indicate that both heat absorption due to evaporation and heat generation due to thermal decomposition
Figure 6.69 The organic conceptual diagram for AMCs.
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Figure 6.70 Schematic representation of sticking probability and staying tendency on the organic conceptual diagram for AMCs.
take place when AMCs are heated in an inert gas atmosphere. It is expected that the staying tendency of residues after carbonization of organic compounds can also be estimated when contours are drawn from available data. An example of a schematic diagram is shown in Figure 6.70 to define the sticking probability and the staying tendency by means of the contours on the Organic Conceptual Diagram. The Organic Conceptual Diagram is useful when investigating compounds which are suspected to cause troubles. Specifically, the Diagram is informative when estimating the mechanism and the likelihood of a potential problem and when determining the priority of experiments. Recently, high-performance personal computers have become available to present the nth-order figure and easily obtain a map along a desired cross section plane, for example, the distribution of u on the xz plane at certain x and y values from a (x, y, z, u) tetra-dimension figure. It becomes possible to make more effective use of The Organic Conceptual Diagram. Compared with the Organic Conceptual Diagram, quantitative structure activity relationship (QSAR), one of the
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FUNDAMENTALS computer-based quantitative chemistry techniques, still has a limited database. In addition, it uses hydrogen bound as an important calculation factor. Therefore, at present the Organic Conceptual Diagram, which has a large experimental database, is more useful to the study of AMCs.
6.5 Examples of Application of Knowledge and Technology This section discusses the sources and excursion of AMCs and countermeasures against contamination.
6.5.1 Excursion of AMCs 6.5.1.1 Data analysis Problems cannot be solved merely by revealing the state of contamination on a substrate surface. It is necessary to identify the contaminant sources from upstream cleanroom air, outdoor air, and cleanroom construction materials (building materials, tools installed in the cleanroom, paint, cleanroom garments, shoes, people, chemicals, and water). It is very common to identify contaminant sources by combining and comparing different data taken from these potential sources. So far a database of more than 100,000 contaminants has been built. Still, a new contaminant source is added to the database from time to time, though it is less frequent than before.
6.5.1.2 Investigation of contaminant sources in cleanroom Methods have been established to identify contaminant sources in an operating cleanroom [110, 190, 191]. Figure 6.71 shows a method for easily sampling contaminants from ceilings, walls, and any other locations within a cleanroom [191]. Using this sampling method, Itoh et al. [191] have shown that the AMC concentration in the cleanroom was significantly reduced by identifying the major contaminant source in the walls of a cleanroom and substituting it with a low outgassing material (Figure 6.72).
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Figure 6.71 Schematic of the outgassing methods for evaluating a cleanroom surface after construction by (a) field outgassing method and (b) laboratory outgassing method.
Figure 6.72 Relationship between the amount of total organic compounds in cleanroom air and the period after construction for (a) an ordinary cleanroom and (b) an improved (wall substituted) cleanroom.
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Figure 6.73 shows a double cylinder sampling system [110, 190]. By using this system, taking measurements and applying a modeling equation, it is possible to estimate the variation of AMC concentration in the air. Figure 6.74 shows the variation of AMC concentration in cleanroom over several years after construction of the cleanroom was completed. Immediately after completion of construction, the concentration of AMCs showed a considerable drop on a daily basis. A few months of operation after construction, the AMC concentration declined slowly. It has been suggested that evaporation of the AMCs adhering to the surface are a major driving force for the decrease in concentration immediately following construction, and that diffusion and transfer of AMCs to the surface of the materials is the major driving force several months after construction. In other words, two behaviors of AMCs, namely evaporation from surface and diffusion from the interior to the surface for replenishment, are relevant. This is very similar to the phenomenon of the outgassing evaluation method. Fujii et al. [166, 192, 193] reported that the data obtained by measuring samples taken with the double pipe sampling system are in a good agreement with
Figure 6.73 Schematic diagram of the double-cylinder chamber test method.
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Figure 6.74 Schematic model of the concentration or organic contaminants in cleanroom air as a function of time after completion of construction.
theoretical values expressed with a double exponential equation based on the assumption of two reaction steps, namely evaporation from surface and diffusion to the surface. It is possible to estimate the concentration at a few months or at several years later.
6.5.2 Selection of construction materials with fewer AMC contaminant sources Kobayashi et al. [194, 195] reported in 1996 that they had succeeded in constructing a cleanroom with very high cleanliness since they had selected low-outgassing cleanroom construction materials using the outgassing test method. Since then the application of this method has become common and many of the newly constructed cleanrooms feature very high cleanliness. This method has also been applied to minienvironments [104, 105]. Recently, published evaluation reports for mini-environments have been increasing [124, 125, 193, 196199]. Also, it has now become possible to fabricate Si wafer carriers with low concentration of contaminants by selecting low-outgassing plastics.
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The number of published reports related to newly detected contaminants has recently tapered off, while published reports on emission sources are still increasing [124, 125, 193, 198209]. Section 6.3.3 discussed this issue in detail. Section 6.5.6.4 describes how the low levels of AMCs have been achieved in a cleanroom.
6.5.3 Chemical filter for air cleaning 6.5.3.1 Change of total organic concentration with time Figure 6.75 shows the concentration of total organic compounds in cleanroom air as a function of the years of cleanroom operation. As can be seen, with only an ULPA filter and no chemical filter, the total organic concentration decreased rapidly in the first 6 months of cleanroom operation, though the initial concentration was about as high as 800 mg/m3. Since then, the total organic concentration has been maintained constant at about 100 mg/m3 for 3 years. The total organic concentration in outdoor air was about 10 mg/m3. At the start of cleanroom operation and after one month of operation, the total organic concentration measured at the chemical filter and at the ULPA filter was far lower than that measured under ULPA filter alone with no chemical filter installed. After 6 months operation, the total
Figure 6.75 Time-dependent fluctuation of the concentration of organic AMCs in cleanroom air during the 3 years since the start of operation.
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organic concentration was found to gradually increase. After 2 years of operation, the total organic concentration measured at the chemical filter was almost the same as that measured under the ULPA filter.
6.5.3.2 Change of siloxanes concentration in cleanroom air A variety of organic compounds are detected in cleanroom air. Among these organic compounds, siloxanes are known to be gases derived from silicone sealant. Silicone sealant is used in large quantities in cleanrooms. At the start of cleanroom operation, gases derived from monomer low molecular weight cyclosiloxanes contained in the sealant are generated in very large amounts. When the polymerization catalyst (initiator) added during silicone polymer production remains in the sealant, it is suggested that the catalyst gradually decomposes the polymer to generate low molecular weight siloxanes which constitute a major contaminant source. The degradation products mainly include octamethylcyclotrisiloxane (D3) which is a trimer of cyclosiloxane, and decamethylcyclotetrasiloxane (D4) which is a tetramer of cyclosiloxane. The low molecular weight siloxanes detected as degradation products are released for a relatively long time. For siloxanes (cyclic trimer to hexamer), Figure 6.76 shows the change in their contamination levels and their concentrations measured under chemical filters as a function of time of cleanroom operation, and Figure 6.77 shows changes in their
Figure 6.76 Effect of chemical filter on the time-dependent changes in the concentration of siloxanes in cleanroom air.
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concentrations measured under ULPA filters. Clearly, the concentration of siloxanes remains at a certain level for years though it initially shows a gradual decrease. Table 6.23 shows the total organic concentration as well as concentration of specific siloxanes such as cyclosiloxanes (D3 to D6), as well as the phthalates DBP and DOP, measured under ULPA filters and chemical filters after three years of cleanroom operation. The total organic concentrations measured under the two types of filters are found to be of the same order. This indicates that the removal efficiency of the chemical filter for total hydrocarbons is relatively low. With respect to the concentration of low molecular weight cyclosiloxanes, however, the removal efficiency of the chemical filter is still observed after 3 years of
Figure 6.77 Time-dependent change in concentration of siloxanes in cleanroom air during the 3 years since the start of operation with ULPA filtration only.
Table 6.23 Air Contaminant Concentration After the ULPA Filter and After Chemical Filter Combination After 3 years of Cleanroom Operation
Analyte Total organic compounds DOP DBP Siloxanes (D3D6)
Standard ULPA Filter (mg/m3)
Chemical Filter + ULPA Filter (mg/m3)
140 0.15 0.03 0.12
95 0.02 <0.01 0.04
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operation in reducing the concentration of siloxanes to less than a 10th of the value with a standard ULPA filter [133].
6.5.3.3 Effect of chemical filter For total organic concentration, removal efficiency of chemical filter declines gradually over time and is very limited after three years of cleanroom operation. For ester phthalates and cyclosiloxanes, such as DOP and DBP which cause serious problems in semiconductor manufacturing process, the concentrations measured under chemical filter are lower by about one order of magnitude than the concentrations measured under a standard ULPA filter. This suggests that a chemical filter still maintains its removal capacity after three years of use. A standard evaluation method for chemical filters has been published [139, 208213]. The principle of the evaluation method is shown in Figure 6.78 [213].
6.5.3.4 Published reports on removal mechanisms Several reports have been published that describe chemical filters to remove trace AMCs [94, 214216]. Recently, reports on removal mechanisms have also been published. Sometimes NH4H2PO4 is detected as a solid on Si wafer surface. In ambient conditions at a temperature of 23 C, relative humidity (RH) of 40% and NH3 concentration of 10 ng/m3, NH4H2PO4 is a stable compound with respect to its equilibrium vapor pressure. It is assumed that
Silicon wafer
5e+7
Below ULPA filter
4e+7 3e+7 2e+7 1e+7
ULPA
0 5.0
Air flow
5e+7
Chemical filter 2
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
Below chemical filter
4e+7 3e+7 2e+7 1e+7 0 5.0
Chemical filter 1
5e+7
10.0
Below fan unit
4e+7 3e+7
Cleanroom air
Fan unit
2e+7 1e+7 0 5.0
10.0
Figure 6.78 Standard evaluation method for a chemical filter.
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(NH4)2HPO4 and (NH4)3PO4 exist in equilibrium when NH3 concentration in the air is much higher [217, 218]. Chemical filters for NH3 are sometimes impregnated with P2O5 which serves as an absorption site. The chemical state of ammonium phosphate salts which are in equilibrium at 40% RH and ammonia in air are (NH4) H2PO4 at 10 ng/m3 and (NH4)3PO4 at 1000 ng/m3, respectively. In other words, the chemical state of active sites is a function of the equilibrium concentration in air. The rate of removal efficiency (%) was calculated by using the ratio between NH3 concentration measured downstream of the filter and that measured upstream of the filter in an experiment performed in an atmosphere in which NH3 concentration is so high (much higher than 10 ng/m3) that it is in equilibrium with (NH4)3PO4 downstream of the filter. It is necessary to check whether the same rate is obtained when NH3 concentration in ambience is so low (10 ng/m3) that its ultimate concentration becomes equilibrium with NH4H2PO4. It should be noted that the form of the stable compound in an equilibrium state depends on NH3 concentration downstream of the filter. It is necessary to analyze the data obtained from experiments which employ NH3 concentration close to the actual operating condition. The common logic employed in chemical filter evaluation is as follows: ‘‘The experimental data are obtained to indicate that NH3 concentration of 1 mg/m3 measured upstream of the filter is reduced to 1 mg/m3 downstream of the filter. The removal efficiency is 99.9%. Therefore, this filter is capable of reducing NH3 concentration from 10 mg/m3 at its upstream location to 10 ng/m3 at its downstream location.’’ In this type of experiment, the concentration of a target AMC is measured in an environment where the AMC exists by itself at high concentration. In reality, however, various types of AMCs coexist in the environment and the concentration of the target AMCs is relatively low. The adsorption equilibrium state of AMCs at low concentration may be different from that of AMCs at high concentration. Also, the fruit-basket phenomenon may take place among various coexisting AMCs. The removal efficiency obtained in experiments where the target AMC exists at high concentration cannot necessarily be applied as is to low concentration AMCs. It is not necessarily correct to refer only to removal efficiency obtained in experiments to decide whether the cleanliness requirement (20 ppt in ITRS 2002, 10 ppt in 2010) is achievable. In other words, researchers need to look at AMC concentration measured in experiments in which the ambient AMC concentration is close to the AMC concentration in actual cleanroom air.
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6.5.3.5 Other issues Activities to standardize chemical filter evaluation methods are under way [12], and some of them are reported in JACA. In the future, it will be important to focus on the following aspects. Critical evaluation parameters (BET, micropores, absorption rate, removal efficiency of high-concentration contaminant and the like) for chemical filters to remove water and high-concentration odors Macropores (200500 A˚) for diffusion and AMC concentration downstream of the filter to evaluate catalytic carriers (surfactants) Recent reports suggest that a ceramic filter is effective in removing some AMCs, including phthalates, phosphates, and siloxanes [219221]. When the ultimate concentration required in the filter after removal of AMCs is very low, the fruit-basket phenomenon is expected to take place in the filter. Once this phenomenon occurs, it becomes necessary, in the case of adsorption and desorption of high molecular weight AMCs, to consider a model in which diffusion is a rate-determining step as in the case of catalytic chemistry. Not only parameters relating to adsorption, such as BET, surface area, and micropores, but also the number of macropores which determine ease of diffusion and migration must be evaluated. For a ceramic filter, it should be technically advantageous if it is designed to allow the macropore diameter and the number of pores to be changed appropriately, as well as to allow the quality of adsorbing points to be selected and adjusted.
6.5.4 Removal from the substrate surface (carbon chemistry) 6.5.4.1 Cleaning technology using UV photoelectron with catalyst Fujii et al. [222227] have reported methods to decompose organic compounds by means of UV photoelectrons, UV and catalyst sources, or other similar excitation sources. Some of these methods have been introduced into actual manufacturing process [228231]. A silicon wafer
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carrier equipped with this removal system has been reported [232, 233]. This removal system combined with other methods has been successfully applied to the manufacturing process and to mini-environments [234]. While the target contaminant decomposes by UV photoelectron/ catalysis, the detection and structural analysis of the secondary contaminants which cause the secondary reactions to occur are reported. While certain compound combinations are cleaved, there is the possibility that these rejoin to generate another compound. Not all carbon compounds decompose to form CO2. Some of these include the following: aliphatic CC bond with a binding energy of 83 kcal/mol; C=C bond which has a higher binding energy; and aryl C=C bond which constitutes a benzene ring. From now onwards, further research will be to investigate which bond combinations decompose easily [235]. Table 6.24 shows the binding energies of the CC, CN, CH and CO bonds for several carbon compounds.
Table 6.24 Bond energies for cleavage of various carbon bonds
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6.5.4.2 Other cleaning technology It has been reported that organic compounds are reduced by means of catalysts. There are several reports on organic compound decomposition by means of ceramic catalyst, decomposition on TiO2-plated surface, and non-thermal equilibrium plasma [236240].
6.5.5 Monitoring systems NH3: A method has been proposed to absorb NH3 into aqueous solution with a double-pipe wetted-wall technique and to quantify the NH3 with ion chromatography. A multiple-point sampling technique has been commercialized. In 2001, more than 100 systems were in actual use in Japanese semiconductor fabs. Methods with a determination limit of 20 ng/m3 have become common [241243]. STRJ 1999 [45] calls for in-line monitoring systems to feature the following sensitivity: 800 ng/m3 for NH3, 80 ng/m3 for amines and 214 ng/m3 for organic compounds. The above-mentioned NH3 monitoring system meets this requirement. NOX: Monitoring systems employing chemical-luminescence and absorbance techniques are commercialized [244, 245]. IMS: IMS is used to monitor specific organic compounds. The basic principles of IMS are described by Budde and Holzapfel [5153, 246]. Illuzzi and Landoni have applied IMS to monitoring AMCs in an actual fab cleanroom [247, 248]. SAW: Bower [249] has proposed the use of SAW to mainly monitor condensables. Recently, applications of SAW to AMC monitoring in actual cleanrooms are increasing [250253]. Figure 6.79 shows a typical SAW signal as a function of exposure time.
Figure 6.79 Typical result of SAW sensor monitoring showing the SAW mass as a function of exposure time.
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API-MS: Several authors have proposed the use of API-MS for monitoring AMCs [254257].
6.5.6 Recent developments Recent developments in AMC technology are discussed in this section.
6.5.6.1 Cleanliness requirements for Si wafer 6.5.6.1.1 Cleanliness The cleanliness requirements for Si wafer are shown in Tables 6.1 and 6.2 taken from the ITRS Roadmapy [18]. Table 6.2 indicates that the cleanliness required in 2002 is 5.3 · 1013 C atoms/cm2. For a monolayer model, this cleanliness level is equivalent to 2.5 ng/cm2. For a 300-mm Si wafer, cleanliness of less than 1750 ng must be achieved.
6.5.6.1.2 Analysis To analyze this level of cleanliness, analytical methods need to quantify a level of 100 ng to one order of magnitude lower than the required level. For a witness plate Si wafer of 1 cm · 3 cm, however, it is necessary to analyze on the order of 1 ng (0.3 ng/cm2). The STRJ Roadmap [45] requires a measurement method that has a detection limit for organic compounds on Si wafer surface of 1.4 E atoms/ cm2 (7 pg/cm2) in 2002. It is possible to quantify sub-nanogram level
y Each table of the cleanliness requirement in the 1999 edition of ITRS is compared to the corresponding table of the 2001 edition of ITRS.
Roadmap Overall roadmap Starting material roadmap Surface preparation technology roadmap Defect prevention and technology Requirement (wafer environment control)
ITRS 1999
ITRS 2001
Over all Table 32 Table 33 Table 80
Over all Table 49 Table 50 Table 95
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contamination on a 300 mm Si wafer by controlling blank values at a low level. Cleanliness of 1 ng on a 300 mm Si wafer is equivalent to 1.5 pg/cm2, which meets the required determination limit.
6.5.6.1.3 Required cleanliness The approach to establish a required cleanliness level described by Kinkead et al. in SEMATECH No. 95052812ATR [2] is that ‘‘a cleanliness level is to be 1/100 of the minimum concentration (in the air/on Si wafer surface) that was reported to cause detrimental effects.’’ In accordance with this approach, the required cleanliness level of either DOP or TCPP should be 0.02 and 0.13 ng/cm2 on Si wafer surface, respectively. The determination limit of the conventional analytical methods for 200 mm wafer is 0.003 ng/cm2. This level of cleanliness can be evaluated if a wafer is used as a sample.
6.5.6.1.4 Air Table 6.25 lists the cleanliness levels from the ITRS roadmaps for 1997 and 1999. From 2002 to 2011, the required levels of cleanliness for AMCs such as metals, organics and bases will be gradually lowered, while those for acids and dopants will remain unchanged.
6.5.6.2 Trends in standardization 6.5.6.2.1 Representation of cleanliness SEMI F 21-1102 [258] designates the classification of AMCs. For each type of AMC, the class designation specifies the maximum allowable concentration of that contaminant for the cleanroom to meet the requirements for that specific designation. The concentration is in parts per trillion (ppt) calculated on a molar basis. Both ITRS [18] and SEMATECH Technology Transfer No. 95052812A-TR [2] have adopted this representation. JACA No.35A-2003 [90] has adopted ng/ m3. For cleanliness, exponential values expressed with g/m3 have been adopted. Table 6.15 shows the JACA cleanliness levels. The ISO Technical Committee 209 is also working on standardization of AMCs.
1997 Edition Critical particle size (nm) Particles > critical size (nm) AMC’s (ppt M) Lithography—Bases (as amine) Gate—Metals (as Cu, E = 2 · 105) Gate—Organics (as MW ‡ 250, E = 1 · 103) Salicidation contact—Acids (as Cl, E = 1 · 105) Salicidation contact—Bases (as Na+, E = 1 · 106)
1994 Edition VOC (mg/m3) (ca. ppbM) Ionics (mg/m3) THC (ppb) Metals (ppb)
Year Technology Node
100 1 10 0.1 90 12 1000 0.3 200
10 40
125 27 1000 0.7 300
10 80
30 0.3 3 0.03
30
10
200
0.3
1000
75 8
10 0.01 1 0.01
20
10
100
0.2
1000
65 5
10
10
100
0.1
1000
50 2
1995 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2008 350 250 180 130 100 70 nm nm nm nm nm nm
Table 6.25 AMCs in the ITRS Roadmap for 1994, 1997, and 1999 [18]
4
10
70
<4
10
50
<0.07
1000
1.0 · 103 0.07
25 1
2011 2012 2014 50 35 nm nm
35 1
2009
446 FUNDAMENTALS
1999 Edition Critical particle size (nm) Particles > critical size (nm) AMC’s (ppt M) Lithography—Bases (as amine) Gate—Metals (as Cu, E = 2 · 105) Gate—Organics (as MW ‡ 250, E = 1 · 103) Gate—Organics (as CH2) Salicidation contact—Acids (as Cl, E = 1 · 105) Salicidation contact—Bases (as Na+, E = 1 · 106) Dopants P or B 0.2
0.3 170
0.3 200
90
0.2
750
60 4
80
0.15
750
55 3
70
0.1
750
50 2
32 <10
40 <10
<10
24 <10
20 <10
16 <10
12 <10
10
3600 3000 2400 1800 1620 1440 1260 10 10 10 10 10 10 10
130
100
750
1000 1000 750 0.25
65 5
90 10
75 8
90 12
<0.07
<0.07
<10
4
1260 10
<10
<4
<4 <10
<900 10
<50
<0.07
<750
18 1
900 10
50
<750
<750
70
25 1
35 1
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6.5.6.2.2 Analytical methods Si wafer surface: JACA [73], ASTMz [259], and other organizations have published analytical methods for inorganic and organic compounds. Air: JACA has established the analytical methods [73, 90]. ISO Technical Committee 209 WG8 is also working on standardization of the methods. Outgassing evaluation. SEMI [116, 259261], IEST [99], JACA [100], and ECMA [262] have published standards on analytical methods.
6.5.6.3 New analytical techniques IMS-GC/MS [263] and EmporeTM disk in column GC/MS [264267] are drawing attention as methods to analyze trace AMCs. Methods to analyze phthalates and phosphates at sub-ng/m3 in the air have been reported. GC/MS is becoming popular for analysis and investigation of the properties of low-concentration acids and bases [6365].
6.5.6.4 Achieving cleanroom cleanliness at low AMCs level (DOP 0.1 ng/m3) This chapter has described the experience and the technology utilized in order to reduce AMCs for experimental investigation of endocrine disruptors in the cleanroom constructed at the National Institute for Environmental Studies in Japan. After construction of the cleanroom was completed using low AMC content materials, the AMC concentration of the cleanroom air was evaluated. The amount of DOP and DBP was found to be below 0.1 and 0.8 ng/m3, respectively. These results satisfy the present demand for an environment for the experimental investigations of endocrine disruptors and also for the manufacture of semiconductors. Our approach for improving cleanroom environments was proven to be suitable, as shown by the results in Table 6.26.
z
This standard was withdrawn in 2003 and transferred to SEMI.
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Table 6.26 Results of AMC Concentration in for a Cleanroom Constructed from Low AMC-containing Materials
Compound D3 D4 D5 D6 DBP DOP TBP TCEP TCPP
6.6
Measured Value (mg/m3)
Determination Limit (mg/m3)
0.2 <0.1 <0.1 <0.1 0.8 <0.1 <0.1 <0.1 <0.1
0.2 0.1 0.1 0.1 0.3 0.1 0.1 0.1 0.1
Future Directions
6.6.1 Technology for cleanliness of AMCs Technology developments for AMCs will be focused in two primary directions. One direction is in the area of ultraclean technology, while the focus of the other direction will be on ‘‘clean enough.’’ At the frontier of technology development, new technologies will be developed to further reduce AMCs. At present, cleanrooms with phosphates and phthalates of <10 ng/m3 are available. Cleanliness will be further improved. One of the highlights is reduction of AMCs concentration in minienvironments, including Si wafer carrier. On the other hand, it is also important to define and maintain an appropriate level of air cleanliness, depending on the purpose of the cleanroom and the manufacturing process, by considering the type of products, substrate exposure time to the air, and AMC removal methods.
6.6.2 Advances in analytical methods Qualification: Due to improvement in instrumental analysis, the mechanisms of AMC adhesion and decomposition
450
FUNDAMENTALS will be identified. It will also be to identify the mechanism of surface adsorption of AMCs and how AMCs cause contamination problems. It is also expected that the mechanism of organic compound carbonization on substrate surface will be defined. Quantification: It will become possible to determine AMCs at a level of pg/m3 in the air and at a level of pg/cm2 on Si wafer surface.
There are a few standardized ultra-microchemical analysis methods for contaminants of the order of nanogram or picogram in the air. (Only a few methods are standardized to determine trace contaminants in water and for electronic grade chemicals and trace acids in water at water storage source locations.) This is partly because inter-laboratory variation is significant for trace analysis and partly because very few laboratories are capable of analyzing analytes of extremely low concentration without contaminating or losing them. We can learn from the experience of pictogram level dioxin analysis when standardizing analysis of cleanroom air, since accuracy control and standardization are significantly more advanced in the dioxin analysis field [268]. It is essential in dioxin analysis to specify exactly the determination limits of the procedure, the analytical method, and the instrument, as well as the blank value, surrogate reference materials, control chart, check interval, and follow exactly what is specified, otherwise satisfactory inter laboratory reproducibility for the pico-level analysis cannot be achieved. The lower the concentration of dioxin gets, the more difficult it becomes to obtain mutually reliable data. Standardization and development of standards have just begun based on repeated crosschecks and accuracy control studies in the international arena. These experiences in dioxin analysis will set a good example to those who are engaged in cleanroom air analysis. Control methods for analysis of electronic grade ultrapure water and chemicals are important and difficult. For analysis of the air, there are more factors to induce errors that affect reliability. Not only those who analyze cleanroom air and Si wafer surface but also those who receive and study measurement data will learn a lot from the experiences in dioxin analysis on how to maintain reliability and how to control accuracy of the measurement and data. These analytical activities are quite different from instrumental analysis in which instrument performance governs the determination limit.
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Figure 6.80 Schematic model for calculating the determination limit, the calculation limit, and the blank value for analysis of AMCs.
Specifically, these analytical activities fall in the wet chemical analysis category which requires a lot of pre-treatments such as sampling, condensation and preparation. It is essential to handle analytes without losing or contaminating them and to keep blank values as low as possible. This is the detection limit of the third type, according to Kaiser [16] a model ‘‘to measure weight of captain (analyte) on a boat (blank value)’’. Figure 6.80 illustrates this model. Here is a case where it is not the blank value itself, rather its variation that affects the detection limit.
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FUNDAMENTALS
6.6.3 Application of air cleanliness technology to various fields The technologies to control AMCs in cleanroom air will be increasingly deployed in various fields. Below are some examples that illustrate how the technologies to achieve air cleanliness are being applied to other fields than the semiconductor industry. The methods to analyze AMCs in cleanroom air are also being applied to trace contaminant analysis in the environment conservation field.
6.6.3.1 Sick house syndrome A variety of compounds can trigger sick house syndrome in indoor dwellings. The guidelines specify DBP of <220 mg/m3 (December 2000) and DEHP of <1200 mg/m3 (July 2001) [269]. In the future, a method will be required to quantify compounds of the ng/m3 order. Fujimoto et al. have reported the vapor pressure estimation method for AMCs at room temperature [162].
6.6.3.2 Endocrine disrupters Phthalates, DBP in particular, are strong estrogenic chemicals. As endocrine disrupters, their trace analysis for environmental samples including air and water will become increasingly important. Figure 6.81 shows the Organic Conceptual Diagram for estrogenic endocrine disrupters. Estrogen (No. 1) and DBP (No. 15) are found to be located very close to each other [188].
6.6.3.3 Cleanliness of experiment and analysis environments Cleanliness of cleanroom in terms of ester phthalate contamination is very critical in reducing and maintaining blank values, not only in the experiments but also in the analysis of experimental results. It is found that the blank value may be affected by the environment for drying and storage of the vessel and apparatus, as well as by the atmosphere for sampling, reduction and condensation. So-called ‘‘once-through draft’’
Figure 6.81 The organic conceptual diagram for endocrine disruptor materials.
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measures have been reported that perform analysis in outdoor air atmosphere and that take in (and not recycle) fresh outdoor air [188, 202, 270273].
6.6.3.4 Other applications Biology: In bio-cleanrooms, siloxanes and phosphates will become problematic. In museums, art museums and large-scale PC rooms, specific compounds such as acids, bases and organics will need to be better controlled. In cleanrooms, testing rooms, and laboratories of other industries than the semiconductor industry, it will be necessary to give consideration to cleaning, storage and transportation of containers for trace analysis and to control the background level of AMCs. It will be essential to establish theories, models and equations in moving from technology to science. The know-how for interpreting and handling a phenomenon within a limited range will be replaced by universal and generic models, theories or equations. Detailed discussion about the proper cleanliness level for a specific contaminant in various manufacturing processes will be consequential in making further advances in measurement and evaluation methods. This is expected to reveal the mechanisms of various phenomena, including the fruit-basket phenomenon, diffusion from the interior to the surface of a solid material, adsorption/desorption on the substrate surface, and carbonization of organic compounds.
6.6.4 Contribution of the analyst/chemist to troubleshooting Problems in leading-edge technologies are sometimes solved by the inspiration of production experts. It is also common that these problems are often solved by a group effort. A cross-functional team meets to identify potential factors and to work out various actions that are combined to tackle all the potential factors. This type of approach has often been taken to actually solve a number of problems. This approach has
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often proven to be effective in promptly and efficiently taking appropriate actions, but sometimes this approach does not work. When the same problem recurs, it is unclear which actions taken before were effective. When the nature of this problem is slightly different from that of the previous problem, the measures designed precisely for the previous problem do not work at all this time. There is a concern in these cases that the past experiences of problem-solving are not at all helpful and that new solutions need to be worked out from square one. On the other hand, the approach to collect measurement data and to chemically analyze them requires time and labor, and it is not efficient. This approach, however, enables us to accumulate data, conduct and brainstorm technical discussions, and to establish common rules and practices. This approach helps us to deal with a wide range of variables. Specialists in ultra-microanalysis, chemists, and experts in troubleshooting in semiconductor fabs described above have extensive experience to successfully take the latter approach. In many cases, we have realized that ‘‘chemist sense’’ has more to contribute to breakthrough ultra clean technology than an analyst. These people helped us a lot in preparing this chapter.
6.7
Summary of the Chapter
The analytical methods for AMCs have been presented. The main analysis for AMCs are (a) on Silicon wafer surface, (b) in the cleanroom environment, and (c) outgassing amounts from raw materials for cleanroom construction materials, such as sealants, plastics, and so on. The analytical methods consist of quantification of inorganic compounds, organic compounds, and identification of abnormal results with local/ surface analysis. The investigation of AMCs has been discussed based on the analytical results, including the source of the contaminants and how AMCs cause contamination problems. This discussion also leads to the methods for preventing contamination and to mitigation solutions. The sticking probability map is useful for selecting target AMCs which have high sticking probability, found usually in cleanroom atmosphere and on Silicon wafer surface, and induce trouble in fab and product quality. Various other interesting findings from the analytical data have been observed and investigated.
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Acknowledgments The present authors would like to emphasize that solving AMCinduced contamination problems requires people who (a) are experts in trace analysis, (b) are capable of interpreting data to explore chemistry, (c) understand well how semiconductor devices are made, and (d) have extensive experience in successful problem solving. Some overseas physicists are still convinced that having high-sensitivity analysis systems is sufficient. The authors have had a number of repeated fruitful discussions about AMCs with Dr. Mark Camenzind and Dr. Marjorie K. Balazs of Air Liquide Balazs, Dr. Klaus J. Budde of Siemens AG, and Dr. Laszlo Fabry of Wacker Siltronic AG. These discussions have enabled us to complete this chapter. The above researchers are also authorities on AMCs who have published clear and in-depth primers on AMCs. The AMC research described here has been greatly facilitated by a number of stimulating meetings with Professor Tadahiro Ohmi and other Ultra Clean Technology members, the Standardization Committee (chaired by Professor Susumu Yoshizawa) of the Japan Air Cleaning Association organized by Professor Shuji Fujii, Enhanced Clean Technology working group of the Japan Association of Aerosol Science and Technology organized by Professor Toshiaki Nishioka, and the Clean Technology Study Group organized by Professor Shuji Fujii in Tokyo Institute of Technology. Ultra microanalysis methods have been developed based on our repeated discussions with Professor Taketoshi Nakahara at Osaka Prefecture University. The authors would like to extend their heartfelt gratitude to them.
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7 Aspects of Particle Adhesion and Removal David J. Quesnel Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA Donald S. Rimai Eastman Kodak Company, Rochester, NY, USA David M. Schaefer Department of Physics, Towson University, Towson, MD, USA
7.1
Introduction
The adhesion of particles to surfaces is of immense technological importance. Moreover, as applications of microminiaturization advance, the importance of understanding the factors that control particle adhesion, deposition, and removal becomes more significant. This becomes quite clear when one thinks about such topics as fabrication of microelectromechanical systems (MEMS), uses and properties of buckyballs and nanotubes, formation of nanoclusters, etc. In some sense, even the definition of ‘‘particle’’ has perhaps changed to include agglomerates of a few atoms or molecules. The roles of particle adhesion in everyday life range from the quite esoteric to the mundane. For example, we merely have to think of the plethora of products in our own homes that are designed solely for the purpose of removing and collecting dust. Familiar items such as vacuum cleaners and mops, to sophisticated dust collection systems, including electrostatic air cleaning and HEPA filtration, depend on particle adhesion to function properly. New products on the market range from microfiber cloths that take advantage of van der Waals interactions
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to disposable tribocharging cloths that take advantage of electrostatic processes to capture dust without solvents. The expanding knowledge base of particle adhesion is improving our day-to-day quality of life. On the other hand, anyone who suffers from seasonal allergic reactions knows the consequences of the adhesion of pollen particles to mucous membranes. To illustrate the range of importance of particle adhesion, let us consider a few diverse examples. The most familiar, of course, is the problem of dust in homes. This has spurred a myriad of products and services, some of which were mentioned in the preceding paragraph, including manufacturing and sales of products such as vacuum cleaners and their components (including filters), chemicals to facilitate dusting of furniture, air duct cleaning services, etc. Add to this list the products sold to remove particulate contamination from dishes and other eating utensils (we have all had to scrub our pots and pans), and one sees that there is a major industry that thrives on controlling particulate contamination in the daily lives of average people. Particle adhesion has a direct bearing on public health. We are sure that, by this time, most people are aware of the effects of particles of tobacco smoke, asbestos, and coal dust adhering to lung tissue. Indeed, the effects of particulate inclusion and adhesion in biological systems are an active area of research today [1–3]. One can readily extend the biological connection to particle adhesion by considering cells to be sophisticated particles. Following this path, researchers such as Moss and Anderson [4] and Love and Forsten [5] have related cancer metastasis to particle adhesion. They recognized that metastasis is controlled by a cell detaching from a substrate comprising other cells of the primary cancer site and migrating through the organism until it adheres to a substrate comprising the cells of what will become a secondary site. In related research, Attenborough and Kendall [6] have proposed that the adhesion of erythrocytes is responsible for the formation of blood clots. Other examples of the importance of particle adhesion in the biological and pharmaceutical areas abound. Particle adhesion has become increasingly important in the fabrication of micro and nano- devices such as MEMS and microoptoelectromechanical (MOEMS) devices, as well as semiconductor chip fabrication. As the size scale of such devices has decreased, the tolerance for the presence of smaller and smaller particulate contaminants has decreased. Moreover, the ability to clean such surfaces has become more complicated. This is due, in part, to the increasing difficulty encountered in removing such particles without damaging the surface and, in part,
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because the use of previously favored cleaning materials such as Freon has become illegal due to environmental concerns. The reader is referred to the series of books edited by Mittal [7] for a more in-depth discussion of this topic. There are many other examples of the commercial importance of particle adhesion. Air contamination control has led to the development of electrostatic air and HEPA filters that are commonly used today. To avoid hydrocarbon emissions, automobile manufacturers, among others, are exploring the use of dry paint particles in place of traditional painting techniques. Grinding and polishing, and the related problem of wear, are associated with the formation of particles due to contact and subsequent separation of surfaces. Sintered part fabrication relies on the ability of particles to cohere strongly enough to avoid fracturing. And the list goes on. The importance of particle adhesion is not simply a case of devising particles that stick to substrates, such as the example of dry paint, or removing particles from unwanted areas, such as in semiconductor device fabrication. In some instances it is necessary to have particles adhere to and release from the same substrate during a process. An example of this is electrophotography, as commonly practiced with copiers and laser printers. In the electrophotographic process, an electrostatic latent image is formed on a photoconducting member by first uniformly charging that member and then image-wise exposing it using, for example, a laser scanner. The latent image is developed into a visible image by depositing electrically charged plastic particles comprising a pigment. These particles are commonly referred to as toner. Despite the fact that these particles are highly charged with the same polarity, they must both cohere and adhere to the photoconductor if a usable image is to be produced, throughout the rest of the electrophotographic cycle. The image is next transported through the printer to a place where it is transferred to paper upon application of an electrostatic field. Again, the image must be detached from one substrate and adhered to another while maintaining cohesion between the toner particles. It is important that most of the toner transfers at this point. However, it is also important that the toner should not detach from the photoconductor prior to reaching the point of actual transfer. The image-bearing paper must now be sent to a fuser, where the toner is heated to a temperature above its glass transition temperature Tg and subjected to pressure. This alters the area of contact between toner particles and between the toner particles and the paper, thereby permanently fixing the image. The photoconductor is then cleaned to remove
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residual toner, generally using a scraper blade or a rotating brush, so that it is ready for the process to start again. It should be clear that cohesion, adhesion, and abhesion (the opposite of adhesion) must be carefully controlled throughout this process if an electrophotographic device is to produce usable images. This article describes the forces, interactions, and factors that control the adhesion and cohesion of particles. It also discusses how the adhesion of particles to surfaces is commonly determined.
7.2 Interactions Giving Rise to Particle Adhesion Particles adhere to surfaces because of both the existence of attractive forces between the particles and the substrates and the mechanical responses of these materials to these attractive forces. Specifically, the interactions between a particle and a contacting substrate cause stresses in both materials. These stresses cause the materials to deform and it is the combination of the deformation and the strength of the interactions that determines how strongly a particle is bonded to a substrate. This and the subsequent sections present the general physics of these interactions, enhancing the engineer’s ability to understand and solve technical problems. A more in-depth treatment of particle adhesion is given elsewhere [8]. Forces of nature are generally categorized as one of four types: strong interactions, weak interactions, electromagnetic interactions, and gravitational interactions. Which of these are important in a given instance depends on the size of the particles and the separations between the particles or between the particles and the substrates. Consider, for example, the realm of the high-energy physicist. His is a world of baryons and leptons, where the size scales of both the particles and their separation distances are less than 104s. At this range, the dominant forces are generally the strong and weak interactions, although gravity can play a significant role at very short distances such as those encountered when subatomic particles undergo gravitational collapse, as occurs in a black hole. For the size scales of interest in this discussion, theses interactions are negligible and will not be considered further. For the case of macroscopic particles, gravitational forces become quite significant. Let us consider, for example, the case of a spherical particle of radius R and mass density r at the surface of the earth. The gravitational
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force Fg acting on such a particle is given by 4 Fg ¼ p r R3 g 3
Eq. (7-1)
where g is the acceleration due to gravity and equals 9.8 m/s2. For a particle with a radius of 5 mm and a density r = 1 g/cm3, the gravitational force, Fg, is 5 · 1012N. While this force is quite small for this particle, its dependence on the cube of the radius implies that this force will increase rapidly with increasing particle size. The effect of gravity is shown in Figure 7.1. Finally, let us consider the role of electromagnetic interactions in particle adhesion. To do so, however, requires that we further subdivide these interactions into magnetic, electrostatic, and electrodynamic interactions. Furthermore, let us first consider the role of magnetic interactions. Magnetic interactions are important for certain classes of materials that are of technological importance today, ranging from magnaflux devices used to detect cracks to magnetic recording materials to magnetic carrier
Figure 7.1 The gravitational, electrostatic, and van der Waals forces acting on a particle in contact with a substrate. Note how van der Waals interactions dominate for small particles, whereas gravity is the dominant force for large particles and electrostatic forces dominate for intermediate-size particles.
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used in electrophotographic engines to charge and transport the toner particles. Unfortunately, there has not been much research in the area of the adhesion of magnetic particles and this remains a rich field for enterprising scientists and engineers to explore. Let us now turn our attention to electrostatic interactions. Electrostatics comprise those areas in which a net transfer of charge has occurred (although not necessarily between the contacting bodies), leaving at least one of the materials possessing an electric charge, and those materials in which there has been a net displacement of charge without a transfer, thereby leaving no net charge (or monopole) but with a dipole and/or other multipole moment. This set of interactions includes particles that have a net charge through triboelectric interactions [9], as well adhesion through surface chemistry [10] be it ionic, covalent [11], metallic [12], or Lewis acid–base interactions [13]. For the most part, the chemical interactions giving rise to particle adhesion are more limited than those giving rise to adhesion in general. The world we live in is dirty. An exposed surface chemically reacts with oxygen or other atoms very rapidly. Moreover, air-borne organics rapidly coat any exposed surface. In short, there are only a relatively few instances, such as lunar dust [14] or nanoclusters formed in ultrahigh vacuum on clean substrate surfaces in which chemical mechanisms play a role in adhesion. Although interactions leading to particle contamination in space may be of practical importance, such a discussion would be divergent from the main themes of this paper and book and, therefore, should be left to a separate paper. Similarly, a discussion of the adhesion of particles with permanent dipole moments, such as electrets, would be of more limited interest than this paper would allow and the interested reader is referred elsewhere [15] for a more in-depth discussion. Therefore, the present discussion will focus on the effect of electric charge on the adhesion of particles. Most particles have an electric charge q. This can be caused through triboelectrification [16–18] or upon the initial formation of the particle through a process known as fractoemission [19]. The presence of a charge on a particle can generate an attractive force to a substrate by polarizing the substrate. This can occur whether the substrate is a conductor or an insulator. As an example, consider the case of a uniformly charged dielectric (insulating) spherical particle of radius R in contact with an electrically conducting, grounded substrate. Because it is conducting and grounded, the potential V must be zero everywhere within the substrate. This can only occur if the substrate is polarized in such a way as to be equivalent to a charge, equal in magnitude but opposite in polarity located
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a distance, R, within the substrate. The presence of this equivalent charge allows the force of attraction to be calculated using the so-called method of images [20, 21]. Once it is recognized that the charge distribution within the substrate is equivalent to the presence of an image charge, the attractive electrostatic force FE between the particle and the substrate can be calculated from the Coulomb force law. Accordingly, FE ¼
1 q 2 4pe0 2R
Eq. (7-2)
where e0 is the permittivity of free space, 8.85 · 1012 C2/(N-m2), and the factor of 2 in the denominator occurs because the separation distance from the center of the particle to the image charge is twice the radius of the particle. If, as commonly occurs, the charge on the particle is due to triboelectrification, it is plausible to assume that, after multiple contacts, the charge is proportional to the surface area of the particle. Accordingly, under this circumstance, q ¼ 4pR 2 s
Eq. (7-3)
where s is the surface charge density. Upon substituting Eq. (7-3) into Eq. (7-2), one finds that FE ¼
ps 2 R 2 e0
Eq. (7-4)
The variation of the electrostatic contribution to the detachment force with the square of the particle charge is shown in Figure 7.2. The effect of particle size on the electrostatic force is shown in Figure 7.1. Upon comparing Eqs. (7-1) and (7-4), it is obvious that, while both Fg and FE, increase with particle radius, Fg does so at a faster rate than does FE. Conversely, as the particle radius decreases, both forces tend toward zero. However, Fg vanishes at a faster rate than does FE. This implies that there should be some crossover diameter below which the electrostatic forces dominate and above which the gravitational forces are dominant. The crossover radius Rg-E is given by Rg-E ¼
3 s2 4 r ge0
Eq. (7-5)
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Figure 7.2 The effect of electric charge on the detachment force of a spherical polyester particle to an organic photoconductor. The photoconductor had been coated with a monolayer of zinc stearate to reduce van der Waals interactions (from Ref. [22]).
Assuming that r = 103 kg/m3 and s = 2 · 105 C/m2, which are the values typical of electrophotographic toners, the crossover between Fg and FE is at 0.003 m. This point is shown in Figure 7.1. Whereas there is not much that can be done to alter Fg other than to increase the mass density of the particle or incline the substrate so that only a fraction of the gravitational force is normal to the substrate, FE can be significantly altered. Most notably, two effects can significantly impact FE. The first effect is a variation in the surface charge density over the surface of the particle. Such a variation can concentrate charge within a localized region. The presence of such a variation, or charged patch, would bring the image charge closer to the particle, thereby increasing the attractive force. This model has been proposed by Hays [9]. How much such a charge variation can affect the attractive force remains an issue of debate in the literature [22]. It is the opinion of the present authors that such variations would not account for more than, perhaps, a small increase in the adhesion force, based on the cited Ref. [22]. However, the present authors do acknowledge that this issue is still being investigated.
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The second effect arises from the tendency of the dielectric particle to polarize in an electric field, as discussed by Fowlkes and Robinson [23]. Even though the particle in question is electrically insulating, it has a nonzero dielectric constant. Such a constant is the measure of the ability of the positive and negative charges to separate, or become polarized, in the presence of an electric field. For a conductor, the dielectric constant is infinite, as no field can exist within the conductor. The dielectric constant for most insulators (materials such as TiO2 and BaTiO3 are notable exceptions) is 3. In effect, the charge on the particle induces an image charge within the substrate. The image charge then polarizes the particle, inducing a dipole. Each pole of the dipole then induces its own image charge within the substrate. These image charges now induce a quadrupole within the substrate. In effect, one gets an infinite, slowly converging series of multipole attractive interactions. As of this time, there are no experimental data supporting the Fowlkes and Robinson model, but that should not be construed to say that the model is necessarily incorrect. The model does, however, have several limitations. First, it assumed that a Gaussian surface could be constructed around the particle. This is not the case for irregular particles or particles that have deformed as a result of adhesion-induced stresses. Moreover, the multipole contributions to the attractive force all depend on the difference between the dielectric constants of the particle and the substrate. However, for most materials, this difference is close to zero, suggesting that polarization effects may not be significant. This would be different, of course, if the particle were close to, but detached from, the substrate. In that case, because of the intervening medium (air), the attractive force between the detached particle and substrate would be greater than that between the attached particle and the substrate. One could readily imagine a scenario in which sufficient force is applied to the particle to detach it. Immediately upon detachment, the attractive force undergoes a stepwise increase, upon which the particle again attaches to the substrate. However, since the detachment force is still present, the particle immediately detaches. This process would repeat ad infinitum. Obviously, further work in needed to validate the multipole model. Finally, the reader should be reminded that the present discussion has been, for the most part, limited to the electrostatic attraction between a dielectric particle and a conducting substrate. The problem of a dielectric particle to a dielectric substrate has not yet been solved. However, insofar as contact charging [24] and polarization can cause electrostatic forces between the particle and substrate, electrostatic forces do play a role here too.
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Finally, let us now focus on electrodynamic forces. These differ from electrostatic forces as there is a time varying component to the fields giving rise to these forces. Of the set of electrodynamic forces, adhesion arises principally from three distinct interactions that, taken together, are termed ‘‘van der Waals forces’’ [8, 25]. There are three distinct types of interactions that make up van der Waals forces. The first occurs between freely rotating permanent dipoles (Keesom interactions) aligning. The second occurs when a freely rotating permanent dipole induces and aligns with an instantaneous dipole in a neighboring molecule (Debye interactions). The third arises when an instantaneous dipole forms in one molecule and induces an instantaneous dipole in a neighboring molecule (London or dispersion forces). In each case, the interaction potential falls as the inverse of the separation distance between the molecules to the sixth power. Of these three types of interactions, the dominant contribution to van der Waals interactions generally arises from dispersion forces. This is partially due to energetics concerns, as discussed in Refs. [8, 25], and partially due to the fact that, in solids, the dipoles are constrained and are not freely rotating. Upon integrating the interaction potentials over all molecules, one could determine the net interaction potential between a spherical particle and a planar substrate. Then by integrating over the distance needed to bring the particle from infinity into contact with the substrate, the force of attraction can be determined. This is discussed in more detail elsewhere [8]. Upon performing such integrations, the force of attraction due to van der Waals interactions FVdW is calculated as FVdW ¼
AR 6z 20
Eq. (7-6)
Here, A, often referred to as the Hamaker coefficient [26], is typically of the order of 1019 J and z0 refers to the separation distance between the surface of the particle and that of the substrate and is typically of the order of 4 s. The latter is based on the interatomic spacings of van der Waals bonded solids such as argon. Using these parameters, the dependence of the van der Waals forces on the size of the particle is shown by the straight line in Figure 7.1. It should be noted that, in contrast to either the electrostatic or the gravitational forces, van der Waals forces are relatively short range, decreasing as the square of the inverse of the separation distance. In practical terms, this means that, once a particle is detached from a surface, the van der Waals interactions can be ignored.
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As with both gravitational and electrostatic forces, van der Waals forces increase with the radius of the particle. However, FVdW increases only linearly with the particle radius. Conversely, all three forces tend toward zero with decreasing particle radius, but van der Waals forces vanish at a slower rate than do either electrostatic or gravitational forces. As was the case with the other two types of forces, there is a crossover radius RVdW-E, below which the van der Waals forces should be the dominant force and above which the electrostatic or the gravitational forces should dominate. RVdW-E can be readily calculated by equating Eqs. (7-4) and (7-6). Upon doing so, one finds RVdW-E ¼
Ae0 6p ðz0 sÞ2
Eq. (7-7)
Assuming that A = 1019 J, s = 2 · 105 C/m2, e0 = 8.85 · 1012 C /(Nm2), and z0 = 4 · 1010 m, one finds that RVdW-E = 0.0007 m. However, just as the electrostatic forces can vary, depending on specific charge distribution and dielectric constant, so can the van der Waals attraction. For example, consider the case of a metallic substrate or particle. As discussed, the largest contribution to van der Waals interactions comes from London forces. As these depend on the polarizability of the materials, one would expect metals to have a higher surface energy than do semiconductors and semiconductors to have higher surface energies than do electrical insulators. Indeed, as discussed by Krupp [27] this is the case. Experiments by Pashley and Tabor [28] showed that the adhesion between a clean tungsten tip and a nickel substrate is very high. Here, the term ‘‘clean’’ implies that the tip and substrate were both prepared and cleaned in an ultra-high vacuum. The real world, however, is far from clean. Metals rapidly become oxidized and this should reduce adhesion due to the reduced polarizability of the oxide layer compared to the clean metal surface. In the same paper, Pashley and Tabor also reported that as little as two monolayers of oxide on the nickel surface reduced adhesion by a factor of three. Additional oxidation should further decrease adhesion. Oxidation is not the only the method by which adhesion can be altered. The atmosphere is full of organic molecules that rapidly coat any exposed surface, further reducing adhesion. Yet, another factor that can influence the van der Waals contribution to adhesion is surface roughness. As discussed previously, the range of van der Waals forces is rather short—typically not more than a few nanometers [29]. As a 2
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result, the presence of a few asperities on the surface of, say, the particle can effectively separate the bulk of the particle from the substrate. Under this scenario, the radius of the particle would no longer control the force of adhesion. Rather, the force of adhesion would depend on the radius of the asperities times the number of asperities in contact with the substrate. This approach is still too simplistic because not all asperities are the same size, nor do they touch with the same pressure. As discussed by Fuller and Tabor [30], the contacts between asperities and a smooth substrate are broken sequentially, with the smallest asperity contacts breaking first. Essentially, the asperity contacts unzip sequentially from the surface. As a result, there is a factor by which the force needed to detach a single particle from a substrate is divided in order to properly represent the detachment force for a multiple contact system. Measurements by Schaefer et al. [31] suggest that the net detachment force is about 1/15 of what one would expect simply based on breaking the bonds to all asperities simultaneously. Particle roughness is commonly introduced to toner particles by coating the particles with silica clusters having diameters of 50 nm. As shown in Figure 7.3, the force needed to detach 8.6 mm diameter toner
Figure 7.3 The effect of the concentration of silica on the surface of 8.6 mm diameter toner particles on the force needed to detach these particles from an organic photoconductor. The silica particles serve as asperities, thereby creating a roughened surface on the toner (from Ref. [32]).
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particles from an organic photoconductor decreases monotonically with silica concentration [32]. Finally, one might think that asperities can both reduce and increase adhesion, depending on the size and frequency of the asperities on both the substrate and the particle. The argument for reducing adhesion has just been presented. However, it is conceivable that, if the asperities on both bodies can nestle together, adhesion would actually be increased. In a practical sense, however, this never happens. The asperities would have to perfectly mesh together to get an increase in adhesion. This would require that the amplitude and periodicity of the asperities on both bodies be exactly equal, as even small divergences would cause a mismatch. This does not normally occur. As a result, the presence of asperities always decreases the force needed to detach a particle from a substrate.
7.3
Mechanics of Particle Adhesion
Thus far, the types of interactions that give rise to particle adhesion have been presented. However, as mentioned earlier in this paper, both the interactions and the mechanical responses of the materials to the stresses generated by these interactions determine how strongly a particle is bonded to a surface. Accordingly, we will now turn our attention to discussing the adhesion theories that relate the interactions to the mechanical properties of the materials. The present day understanding of particle adhesion is based on the theory proposed by Johnson et al. [33]. This theory, generally referred to as the JKR theory, is based on small elastic deformation contact mechanics. It does not allow for any long-range interactions. It assumes that the total energy of the system, which must be at a minimum at equilibrium, is composed of three distinct terms. The first term is the mechanically stored energy, which is simply generated by applying a load P to the particle, thereby creating a displacement of the centers of the contacting materials. The second term is the elastically stored energy that is generated when the materials are deformed. The final contribution to the total energy US comes from the surface energy and is given by US ¼ wA p a2
Eq. (7-8)
where a represents the radius of contact and wA is the thermodynamic work of adhesion and is related to the surface energies g P and gS
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of the particle and substrate, respectively, and their interfacial energy gP-S by wA ¼ g P þ gS g P-S
Eq. (7-9)
As discussed in Ref. [8], the work of adhesion can be directly related to the van der Waals interactions. After some manipulation, it is found that h i1=2 R 2 a= P+3wA pR+ 6wA pRP þ ð3wA pRÞ K 3
Eq. (7-10)
where K¼
4 3 pðkP þ kS Þ
Eq. (7-11)
and kPðSÞ ¼
1 n 2PðSÞ pEPðSÞ
Eq. (7-12)
where the letters P and S denote the particle and substrate, respectively and n refers to the Poisson ratio and E denotes the Young’s modulus. Equation (7-10) is generally referred to as the JKR equation. Although presented in terms of a particle adhering to a substrate, it is equally applicable to interparticle cohesion simply by replacing the particle radius with a reduced radius. In the absence of surface forces, such as those arising from van der Waals interactions, wA = 0 and Eq. (7-10) reduces to a3 ¼
RP K
Eq. (7-13)
which the reader may recognize as the Hertz equation for an elastic indenter. On the other hand, in the absence of any applied force, Eq. (7-10) reduces to a¼
6 p wA K
1=3 R2=3
Eq. (7-14)
Equation (7-14) implies that there is a finite contact between the particle and the substrate simply due to adhesion.
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The JKR theory also allows the force needed to separate a particle from the substrate to be determined. Specifically, Eq. (7-10) predicts the actual contact radius as a function of the applied and adhesional forces. As such, the solutions to Eq. (7-10) must be real. Now, consider the case where one is attempting to detach a particle. This is accomplished by applying a sufficiently large negative force to the particle. However, it is important that the radicand in Eq. (7-10) does not become negative, as this would predict a complex, rather than real, contact radius, which is a physical impossibility. As a result, detachment occurs when a force Pdetach is applied such that 3 Pdetach ¼ wA pR 2
Eq. (7-15)
It should also be noted that according to the JKR theory, it is not necessary for the contact radius to vanish as P approaches Pdetach. Rather, detachment occurs at a finite contact radius that is 63% of the equilibrium contact radius in the absence of an external load. Finally, it should be noted that according to the JKR theory, the force needed to detach the particle from the substrate is independent of the Young’s modulus of either material. The independence of the detachment force on Young’s modulus may seem to go against intuition. We all know, for example, that the adhesive on tape is sticky and the principal reason for its stickiness is the low value of the modulus. However, in order to resolve this apparent paradox, one must remember that particles generally are not atomically smooth. Rather, they have asperities. As the asperities deform or penetrate more deeply into a substrate, as would occur naturally as the Young’s modulus of either material decreases, the force needed to effect detachment would increase. This is discussed by Gady et al. [34]. As previously discussed, the JKR model only allows for forces to be present within the actual area of contact. Because of the short range of van der Waals forces, this approximation is valid when the dominant mode of interactions arises from surface forces. Gravitational forces also do not pose any problem, as the gravitational attraction between even relatively large particles and substrates is small, and one only needs to be concerned with the earth’s gravitational field. However, contributions to particle adhesion caused by electrostatics can be significant. Let us now consider the case where the particle is attracted and attached to the substrate by both electrostatic and van der Waals forces. The electrostatic forces are clearly long-range and, therefore, cannot be
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simply assumed to vanish once contact between the particle and substrate has been broken. Rather, a formal treatment of this problem would require that the fundamental treatment of particle adhesion by the JKR theory be reexamined, with the energy required to bring a charged particle from infinity to the substrate added to the other three contributions. This has not yet been done. However, as shown by Rimai and coworkers [35, 36] the contributions to particle adhesion resulting from van der Waals and electrostatic interactions can be deconfounded by measuring the detachment force as a function of the square of the particle charge. The y-axis intercept, corresponding to q = 0, approximates the van der Waals contribution to the force and the difference between the measured force and the van der Waals contribution gives the electrostatic component. An alternative theory of particle adhesion was proposed by Derjaguin et al. [37] and is generally referred to as the DMT theory. This theory, rather than being energy based as is the JKR model, uses a force balance approach and assumes that the shape of the contact region was Hertzian. As a result of the differing assumptions, for a given size contact radius, the DMT theory predicts a work of adhesion that is approximately six times greater and a removal force that is 1/3 greater than that predicted by the JKR model [38]. This discrepancy was apparently resolved by Muller et al. [39], who showed that the JKR model was valid for systems comprising lower Young’s moduli and larger particles, whereas the DMT model was valid for more rigid systems and smaller particles. It is the view of the present authors that, in practical terms, the JKR model reasonably describes particle adhesion for just about any size particle if one of the materials is elastomeric. Moreover, the present authors further believe that, for most cases, one need not be concerned with the DMT model, which would be expected to be valid for submicrometer particles on harder substrates. This is because, for such materials, the deformations would generally be plastic rather than elastic, as will be discussed presently. That adhesion forces between a particle and a substrate could induce plastic flow was first proposed by Krupp [27]. Subsequently, Maugis and Pollock (MP) [40] extended the JKR theory to allow for total plasticity. They found that the contact radius was related to the yield strength Y of the lower-strength material by P þ 2p wA R ¼ 3p a2 Y
Eq. (7-16)
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In the absence of any applied load, Eq. (7-16) reduces to a¼
2wA 1=2 R 3Y
Eq. (7-17)
The difference in the power-law dependence of the contact radius on particle radius for the JKR and MP theories gives an easy method of distinguishing elastic and plastic deformations. If plastic deformations are to occur, the adhesion-induced stresses must exceed Y. As discussed elsewhere [8], the average surface force-induced pressure pm between a spherical particle and a substrate is given by pm ¼
2 wA z0
Eq. (7-18)
For most materials, the calculated pressures are comparable in magnitude to the Young’s modulus, implying that adhesion-induced strains are quite large. In fact, certain materials such as elastomers would be capable of supporting such strains without yielding. More rigid materials should yield at such large strains. Indeed, Bowen et al. [41] reported that the adhesion-induced deformations between micrometer-size sodalime glass particles and a silicon substrate were plastic rather than elastic. Calculation of the detachment force in the case of plastic deformations is not as straight-forward as it is for elastically deformed materials. Certainly, negative values for P can be substituted directly into Eq. (7-16). As there are no solutions that would cause complex solutions for a, as is the case with the JKR theory, one could simply infer that detachment occurs when a vanishes. This would be correct when the deformations remain plastic even as the size of the negative load is increased, corresponding to decreasing strains in the materials. This is often referred to as ductile fracture. However, as the magnitude of P increases, upon application of a negative load, the total stress decreases. Often, the stress can decrease to the point where the deformations are elastic. The detachment force would then have to be determined by the JKR or DMT criteria, depending on whichever theory is applicable under the particular circumstances. This problem has not yet been fully solved. The act of deforming plastically is not instantaneous. Rather, over time, the size of the contact area would increase until some equilibrium is established. As the size of the contact increases, the tenacity with which
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the particle is bonded to the substrate should also increase. This effect was observed by Krishnan et al. [42], who determined the contact radius and detachment force as a function of time for submicrometer polystyrene latex spheres on a silicon substrate. They found that the adhesion-induced contact area increased logarithmically with time. Corresponding to that increase, the force needed to separate the particle from the substrate also increased logarithmically, with the same time constant. These results suggest that if one wishes to remove particles from a surface, one should clean that surface as soon after the particles are deposited as possible.
7.4
Factors Affecting Particle Adhesion
As previously discussed in this chapter, the two dominant forces that affect adhesion arise from electrostatic and van der Waals interactions. van der Waals interactions, being relatively short range, can be reduced by adding asperities to particles, as is commonly done by coating the surface of electrophotographic toners with silica [43]. Other agents that coat the substrate, such as zinc stearate or Teflon [44], also reduce the detachment forces. Representative data showing the effects of such coatings on the detachment force of polystyrene particles from a polyester substrate is shown in Figure 7.4. While there is some debate as to the mechanisms by which these occur, there is evidence that these materials reduce the van der Waals interactions without altering the electrostatics [36]. Obviously, altering one or both sets of interactions by physically changing the properties of the materials would alter the radius at which a given interaction is dominant. Similarly, the distance from a substrate is important. Electrostatic air filters work because of the long-range nature of the electrostatic forces. Relative differences in the position of the contacting materials in the triboelectric series, along with the number of times the two materials contact each other, also affect the detachment force [45]. Finally, some discussion about the effects of relative humidity (RH) on particle adhesion is in order. Water can affect particle adhesion in two ways. First, it can alter the surface resistivity, thereby altering surface charge distributions and possibly affecting the formation of multipoles [46]. Moreover, there could be capillary condensation around the particle-substrate interface. As shown by Zimon [47], the presence of capillary condensation would be expected to dominate over van der Waals forces. It is perhaps surprising, therefore, that experiments have found that the detachment forces appear to be independent of RH up to about 70% RH. At higher humidity, adhesion does seem to increase rapidly
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Figure 7.4 The force needed to detach polystyrene spheres, as a function of particle diameter, from a bare (solid circles) polyester substrate, as well as one that had been coated with a thin layer of silicone (open circles), Teflon (solid triangles), and zinc stearate (open triangles) (from Ref. [44]).
with RH [47, 48]. The reasons that humidity does not seem to play a larger role at intermediate values of humidity are not presently known. Figure 7.5 shows the effect of RH on the adhesion of polystyrene latex spheres to a silicon substrate [48].
7.5 Methods of Measuring the Adhesion of Particles to Substrates Although a detailed discussion of the techniques used to determine the adhesion of particles to substrates is beyond the scope of this chapter and is, in fact, given elsewhere [8], this chapter would not be complete if some discussion were not presented. The reader is referred to Ref. [8] for a more complete discussion of this topic, along with the appropriate references. As should be clear following the discussion of the JKR theory, the forces that attract the particle to the surface and the force that must be applied to remove that particle are not the same. Rather, because of the mechanical responses of the materials to the stresses, the detachment force must be determined from energetics considerations, rather than
494
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Figure 7.5 The effect of relative humidity on the adhesion of polystyrene latex spheres on a silicon wafer (from Ref. [48]).
by simply assuming that detachment occurs when the forces of attraction are balanced by the applied forces. In fact, because the force-balance assumption does not take into account the work done when the materials deform in response to the adhesion-induced stresses, it is simply incorrect. With this in mind, one needs to define just what one means by the term ‘‘particle adhesion.’’ Specifically, it is necessary to distinguish between the attractive forces that bring a particle to a surface in the first place and the magnitude of the force needed to detach the particle from the surface. Both have applications and are important, but they clearly are not equal. With this in mind, let us first look at some techniques that allow one to measure the detachment force. Perhaps the most commonly used technique to measure the force needed to separate a particle from a substrate is centrifugation. Here, the particles are deposited onto a substrate and the number of particles on that substrate is determined initially and as a function of centrifuge speed. This technique works well for particle having radii between 3–5 and 50–100 mm, depending on both the particle and substrate properties. This technique requires the use of an ultracentrifuge and needs to be run under low (13.33 Pa or 102 Torr) vacuum. There are several concerns that need to be addressed when using this technique. First, it is important
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that the centrifuge be capable of detaching most of the particles from the substrate. Because of the theta (step) function response of the number of particles on the substrate as a function of the centripetal acceleration, one simply cannot extrapolate from small particle removal percentages in order to estimate the detachment force. It is important to use the point where 50% of the particles are removed. Using higher or lower values skews ones results toward the statistical outliers rather than the mean detachment force. Centrifugation is a time consuming method, generally requiring several hours to produce a complete set of measurements. Since plastic flow is often occurring, it is important to conduct the measurements in as short a period as possible. A rule of thumb is to perform all measurements the same day the particles are deposited, unless one wishes to know the effect of time on adhesion. Even then, each set of measurements should be completed in as short a period of time as possible. Finally, the rotational speeds at which the centrifuge is run should be randomized to eliminate systematic increase in the measured adhesion. An advantage of the centrifugation technique is that good statistics can be readily obtained. The principal advantage of centrifugation is the ability to get good statistics, especially when the measurements are combined with analytical tools that allow particle counting, as well as particle size and shape distribution and other characteristics. Moreover, this technique is relatively simple and there are few, if any, interactions between the applied and attractive forces, such as may be encountered using electrostatic measurement techniques. Determination of the detachment force via the application of an electrostatic field is another commonly used technique. In general, the particles are deposited on an electrode that forms part of a parallel plate capacitor having a controlled spacing. This method has several advantages and disadvantages compared to centrifugation. The size range of particles that can be evaluated with this technique is comparable to that of centrifugation. Good statistics can be obtained. In some instances, electrostatic detachment provides a closer simulation to the process of interest than does centrifugation. An example of this is the electrophotographic transfer process. Measurements can be made in shorter periods of time, in some cases, than is possible with centrifugation [44]. In addition, measurements can be made in a variety of atmospheres. There are four principal disadvantages to this technique. First, only electrically conducting substrates can be used. Second, the forces that can be applied are often lower than in centrifugation. Third, the application of an electric field can interact with the adhesion of the
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particle by polarizing the particle. Fourth, the charge on the particle must be known and well controlled. Busnaina et al. [49] have pioneered a technique that allows the detachment force of particles in the tenths of a micrometer diameter range to be determined. This technique involves rotating the substrate bearing the particles while impinging a fluid stream. Using standard equations from hydrodynamics, the detachment force can be determined. The principal advantage of this technique is that it allows detachment forces to be determined for particles that are too small for centrifugation or electrostatic techniques. It also allows good statistics to be obtained. Its principal disadvantage is that it introduces a fluid, which, in turn, can alter the attractive forces. Schaefer et al. [31] were able to measure detachment forces for particles that had radii in the range of 5 mm by attaching the particles to atomic force microscope (AFM) cantilevers. After allowing the particle to contact the substrate, the cantilever was moved away from the substrate until particle-substrate detachment occurred. The detachment force was determined from the degree of bending of the cantilever. This technique requires relatively sophisticated equipment and skilled operators. It also allows the detachment force to be determined for only one particle at a time. This greatly limits the ability to use statistical techniques. The orientation of the particle is also fixed, so the point of the particle contacting the substrate may not be representative of the entire particle. On the other hand, this technique allows known loads that increase the deformation to be applied to the particle. It can be run in a variety of atmospheres, including vacuum. The time of contact can be varied from seconds to minutes, allowing some time variation, and also allowing exploration of short-time effects. It also allows a precise mapping of the adhesion properties of the substrate and allows the local adhesional properties to be correlated precisely with particle and substrate roughness, Young’s modulus variations, and other particle characteristics. Finally, this technique allows the contribution of triboelectric interactions to be directly determined. DeMejo et al. [50] did not measure the detachment force directly. Rather, they determined the adhesion-induced contact radius as a function of particle radius. From those data, they were able to determine the work of adhesion and then infer a detachment force using Eq. (7-15). The principal advantage of this technique is that the particle and substrate are in equilibrium. This is not the case for methods where the particle is actually removed. On the other hand, one may be interested in a dynamic removal force that simulates a specific process.
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Finally, Gady et al. [29] developed several AFM-based methods that allow the attractive force between a particle and a substrate to be determined. Gady et al. determined the attractive force between the particle and the substrate as a function of displacement by measuring the deflection of the AFM cantilever at separation distances greater than that where the jump-to-contact occurs. They also determined the force gradient as a function of displacement by measuring the resonance frequency of the cantilever. Using these independent measurements, they were able to determine both the electrostatic and van der Waals contributions to the attractive force at a given separation.
7.6
Conclusions
Much understanding of particle adhesion has been gained over the past few decades. This knowledge has increased our understanding of the science behind adhesion, in general, and allows engineers to more readily control processes that involve particle adhesion phenomena. There are, however, a number of questions that need to be answered. Understanding the factors that contribute to the adhesion of particles to surfaces is extremely important in areas such as cleaning and contamination control, with the specific means employed to control contamination and clean surfaces depending on the application. For example, in semiconductor fabrication, relatively few particles having diameters less than one micrometer and adhering to the surface of silicon wafers by van der Waals forces can adversely affect the production of integrated circuits. In this instance, the size of the contaminants would preclude the use of devices such as blade cleaners or brushes. However, the number of devices fabricated per unit time is sufficiently low as to allow the jetting of CO2 snow particles to clean the surface. At the other extreme of removing particles from a surface is the waiter using a blade to remove crumbs from a dinner table prior to the patrons ordering coffee and dessert. In this example, the particles are sufficiently large so that gravitational forces are the dominant interaction. Here, the waiter uses the blade to sweep the particles into a small dustpan or similar device. Dusting furniture or cleaning electronic devices or electrical equipment are examples where van der Waals, electrostatic, and gravitational forces are all significant. The effect of gravitational forces is evident by the fact that dust predominantly settles on the top surface of furniture. On the other hand, if that piece of furniture were to be turned upside down, the
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dust would not fall off. Here, damp dust cloths, so-called ‘‘tack cloths’’ comprising an agent that makes the cloth sticky, various sprays and liquids are commonly used to reduce electrostatic forces and increase the adhesion of the particle to the cloth to effect cleaning. Various sprays, waxes, and other fluids are also used to reduce the adhesion to the furniture and electronic devices. Electrophotographic devices such as laser printers, especially those operating in commercial establishments, also have demanding cleaning requirements. Toner particles are typically 8 mm in diameter and are highly charged. They are attracted to an image-wise electrically charged photoreceptor during a process called ‘‘development.’’ After development, the image is transferred to paper by pressing the paper against the photoreceptor and applying an electric field to attract the toner particles to the paper. In an electrophotographic engine, residual toner left on the photoreceptor after transfer as well as paper fibers and paper filler, such as submicrometer particles of calcium carbonate, must be removed. While more particles can be left on the photoreceptor after cleaning in electrophotographic engines compared to semiconductor device fabrication tools, a far greater number of particles must be removed at a much higher process speed and cover a much larger area than that encountered in the semiconductor industry. Here, van der Waals and electrostatic forces are dominant and cleaning often employs corona chargers to control the electrostatic forces, electrically conducting fur brushes, blades, and similar devices. It should be apparent from the above discussion that the choice of the means of cleaning must consider the particle-substrate interactions as well as the process speeds. Particle adhesion has also become an increasingly important subject in seemingly unrelated phenomena ranging from the mechanisms by which pressure sensitive adhesives work to how individual cancers metastasize. In modern times, when specialization is the norm, one must always keep his/her eyes on the larger picture, even as one strives to make progress in his/her own area.
References 1. L. C. Carter, J. M. Carter, P. A. Nickerson, J. R. Wright and R. E. Baier, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai and L. H. Sharpe (Eds.), pp. 52–78, Taylor and Francis, New York (2001).
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2. B. Baier, E. Axelson, A. Meyer, L. Carter, D. Kaplan, G. Picciolo and S. Jahan, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai, and L. H. Sharpe (Eds.), pp. 79–102, Taylor and Francis, New York (2001). 3. R. Baier, A. Meyer, D. Glaves-Rapp, E. Axelson, R. Forsberg, M. Kozak and P. Nickerson, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai and L. H. Sharpe (Eds.), pp. 103–124, Taylor and Francis, New York (2001). 4. M. A. Moss and K. W. Anderson, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai and L. H. Sharpe (Eds.), pp. 19–40, Taylor and Francis, New York (2001). 5. B. J. Love and K. E. Forsten, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai and L. H. Sharpe (Eds.), pp. 1–18, Taylor and Francis, New York (2001). 6. F. R. Attenborough and K. Kendall, In Particle Adhesion: Applications and Advances, D. J. Quesnel, D. S. Rimai and L. H. Sharpe (Eds.), pp. 41–52, Taylor and Francis, New York (2001). 7. K. L. Mittal (Ed.), Particles on Surfaces: Detection, Adhesion, and Removal, Vols. 1–3, Plenum Press, New York (1986–1990); also, K. L. Mittal (Ed.), Particles on Surfaces: Detection, Adhesion, and Removal, Marcel Dekker, New York (1994), K. L. Mittal (Ed.), Particles on Surfaces 5 & 6: Detection, Adhesion, and Removal, VSP, Utrecht, The Netherlands (1999), K. L. Mittal (Ed.), Particles on Surfaces 7: Detection, Adhesion, and Removal, VSP, Utrecht, The Netherlands (2002), K. L. Mittal (Ed.), Particles on Surfaces 8: Detection, Adhesion, and Removal, VSP, Utrecht, The Netherlands (2003), and K. L. Mittal (Ed.), Particles on Surfaces 9: Detection, Adhesion, and Removal, VSP, Utrecht, The Netherlands (2006). 8. D. S. Rimai and D. J. Quesnel, Fundamentals of Particle Adhesion, Global Press, Srbija (2001). Presently available through the Adhesion Society, Blacksburg, VA, USA. 9. D. A. Hays, In Fundamentals of Adhesion, L.-H. Lee (Ed.), pp. 249–278, Plenum, New York (1991). 10. L.-H. Lee, In Fundamentals of Adhesion, L.-H. Lee (Ed.), pp. 1–86, Plenum, New York (1991). 11. J. D. Miller and H. Ishida, In Fundamentals of Adhesion, L.-H. Lee (Ed.), pp. 291–324, Plenum, New York (1991). 12. A. Banerjea, J. Ferrante and J. R. Smith, In Fundamentals of Adhesion, L.-H. Lee (Ed.), pp. 325–348, Plenum, New York (1991). 13. L.-H. Lee, In Fundamentals of Adhesion, L.-H. Lee (Ed.), pp. 349–362, Plenum, New York (1991). 14. L.-H. Lee, In Fundamentals of Adhesion and Interfaces, D. S. Rimai, L. P. DeMejo and K. L. Mittal (Eds.), pp. 73–94, VSP, Utrecht, The Netherlands (1995). 15. T. B. Jones, Electromechanics of Particles, Cambridge University Press, Cambridge, UK (1995). 16. R. G. Horn, D. T. Smith and A. Grabbe, Nature 366, 442 (1993). 17. R. G. Horn and D. T. Smith, Science 256, 362 (1992). 18. D. T. Smith, J. Electrostatics 26, 291 (1991).
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19. J. T. Dickinson, L. C. Jensen, S. Lee, L. Scudiero and S. C. Langford, In Fundamentals of Adhesion and Interfaces, D. S. Rimai, L. P. DeMejo and K. L. Mittal (Eds.), pp. 179–204, VSP, Utrecht, The Netherlands (1995). 20. W. R. Smythe, Static and Dynamic Electricity, 3rd Edition, Hemisphere Publishing, New York (1989). 21. P. Lorrain and D. Corson, Electromagnetic Fields and Waves, 2nd Edition, Freeman Press, San Francisco, CA, USA (1970). 22. See, for example, D. S. Rimai, M. Ezenyilimba, W. K. Goebel, S. Cormier and D. J. Quesnel, J. Imaging Sci. Technol. 46, 200 (2002) and the references cited therein. 23. W. Y. Fowlkes and K. S. Robinson, In Particles on Surfaces 1: Detection, Adhesion, and Removal, K. L. Mittal (Ed.), pp. 143–155, Plenum, New York (1988). 24. B. Gady, D. Schleef, R. Reifenberger and D. S. Rimai, In Fundamentals of Adhesion and Interfaces, L. P. DeMejo, D. S. Rimai and L. H. Sharpe (Eds.), pp. 291–306, Gordon and Breach, Amsterdam, The Netherlands (1999). 25. J. Israelachvili, Intermolecular and Surface Forces, Academic Press, San Diego, CA, USA (1992). 26. H. C. Hamaker, Physica 4, 1058 (1937). 27. H. Krupp, Adv. Colloid Interface Sci. 1, 111 (1967). 28. M. D. Pashley and D. Tabor, Vacuum 31, 619 (1981). 29. B. Gady, R. Reifenberger, D. S. Rimai and L. P. DeMejo, Langmuir 13, 2533 (1997). 30. K. N. G. Fuller and D. Tabor, Proc. R. Soc. Lond. Ser. A 345, 327 (1975). 31. D. M. Schaefer, M. Carpenter, B. Gady, R. Reifenberger, L. P. DeMejo and D. S. Rimai, J. Adhesion Sci. Technol. 9, 1049 (1995). 32. D. S. Rimai, P. Alexandrovich and D. J. Quesnel, J. Imaging Sci. Technol. 47, 1 (2003). 33. K. L. Johnson, K. Kendall and A. D. Roberts, Proc. R. Soc. Lond. Ser. A 324, 301 (1971). 34. B. Gady, R. Reifenberger, D. M. Schaefer, R. C. Bowen, D. S. Rimai, L. P. DeMejo and W. Vreeland, In Fundamentals of Adhesion and Interfaces, L. P. DeMejo, D. S. Rimai and L. H. Sharpe (Eds.), pp. 19–36, Gordon and Breach, Amsterdam, The Netherlands (1999). 35. D. S. Rimai and D. J. Quesnel, J. Adhesion 78, 413 (2002). 36. D. S. Rimai, M. Ezenyilimba, W. K. Goebel, S. Cormier and D. J. Quesnel, J. Imaging. Sci. Technol. 46, 200 (2002). 37. B. V. Derjaguin, V. M. Muller and Yu. P. Toporov, J. Colloid Interface Sci. 53, 314 (1975). 38. D. Tabor, J. Colloid Interface Sci. 58, 378 (1977). 39. V. M. Muller, V. S. Yushchenko and B. V. Derjaguin, J. Colloid Interface Sci. 77, 91 (1980). 40. D. Maugis and H. M. Pollock, Acta. Metall. 32, 1323 (1967). 41. R. C. Bowen, L. P. DeMejo and D. S. Rimai, J. Adhes. 51, 201 (1995). 42. S. Krishnan, A. A. Busnaina, D. S. Rimai and L. P. DeMejo, J. Adhes. Sci. Technol. 8, 1357 (1994). 43. B. Gady, D. J. Quesnel, D. S. Rimai, S. Leone and P. Alexandrovich, J. Imaging Sci. Technol. 43, 288 (1999).
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44. D. S. Rimai, D. J. Quesnel, L. P. DeMejo and M. T. Regan, J. Imaging Sci. Technol. 45, 179 (2001). 45. B. Gady, R. Reifenberger, D. S. Rimai and L. P. DeMejo, Langmuir 13, 2533 (1997). 46. T. N. Tombs, In Advances in Particle Adhesion, D. S. Rimai and L. H. Sharpe (Eds.), pp. 15–25, Gordon and Breach, Amsterdam, The Netherlands (1996). 47. A. D. Zimon, Adhesion of Dust and Powder, 2nd Edition, Consultants Bureau, New York (1982). 48. A. A. Busnaina and T. Elsawy, In Proc. 21st Annual Meeting of the Adhesion Society, R. A. Dickie (Ed.), pp. 315–317, Adhesion Society, Blacksburg, VA, USA (1998). 49. A. Busnaina, J. Taylor and I. Kashkoush, J. Adhes. Sci. Technol. 7, 441 (1993). 50. L. P. DeMejo, D. S. Rimai and R. C. Bowen, J. Adhes. Sci. Technol. 5, 959 (1991).
8 Relevance of Electrostatic Discharge Controls to Particle Contamination in Cleanroom Environments Larry Levit and Arnold Steinman MKS, Ion Systems, Alameda, CA, USA
8.1
Introduction
Contaminant particles are produced inside a high quality cleanroom by personnel, production equipment and processes, and materials transfer in and out of the cleanroom. Unfortunately, all of these particle sources are usually close to the product. If surfaces are also charged, electrostatic attraction (ESA) tends to attract and adhere particles to the surface that would otherwise remain airborne in the cleanroom laminar air flow. Sub-micrometer-sized particles cause defects in semiconductor production similarly to the visual defects from dust particles on a photographic negative. With the trend increasing toward smaller feature sizes in semiconductor devices, the size of the ‘‘killer’’ particles also decreases. Smaller particles are more easily attracted and more difficult to remove because of the static charge on surfaces and because the adhesion force per unit area increases as the particle size decreases. Static charge also causes other production problems since the uncontrolled transfer of static charge can damage product directly. This is an electrostatic discharge (ESD) event that typically occurs in 1–10 nanoseconds. One result of this rapid transfer of energy is local heating, sufficient to melt the silicon or metallization of the semiconductor device and cause device failure. Electrostatic discharge events are typically in the frequency range of 100 MHz–2 GHz, which is the same frequency range as the microprocessors that control the operations of most semiconductor production equipment.
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ESD events generate electromagnetic interference (EMI) that can cause a variety of equipment malfunctions from simple stoppage to erratic robotic operations that destroy products. Since EMI propagates through both radiation and conduction, an ESD event in one piece of equipment may affect the operation of other nearby equipment, making the source of the problem difficult to locate. This chapter focuses on the problems of static charge in cleanroom environments as related to particle contamination and the methods to control static charging.
8.2 Electrostatic Charge Problems in Cleanrooms The relationship between electrostatic charge and contamination control in high-technology cleanrooms is a strong one, representing a significant source of particle deposition on charged objects within the cleanroom. The rate of ESA of small particles to charged objects has been calculated for a controlled environment [1] and particle deposition data recorded in cleanroom environments have been found to be consistent with the calculation [2, 3]. Several studies involved employing a high-voltage (HV) power supply to bias one wafer to a voltage of at least 2 kV while another was electrically connected to ground. In one of the studies [3], 200 mm wafers were exposed to the environment in an isolated part of an ISO Class 3 cleanroom. Human traffic through the area was eliminated by cordoning off the area where the exposure was done. In order to assure that a statistically valid sample was acquired, an exposure time of 6 weeks was employed. The wafers were scanned using a Tencor Surfscan with a particle size threshold of 0.2 mm. The Surfscan results are shown in Figure 8.1. While the numbers of particles observed on the two wafers are not representative of real world contamination levels for semiconductor processing, the ratio of the number of particles on the neutral wafer (3,389) compared to the number of particles on the wafer at a voltage of 2000 V (22,764) is accurate. In this case, the ratio is 6.7:1. The calculation of electrostatically driven contamination sums the components of the deposition velocity due to each deposition mechanism. Deposition velocity, loosely defined, is the rate at which particles move toward the surface of the object due to the forces on the particle. Particles deposit on wafers, flat panel displays, disk drive components, and equipment surfaces due to gravity, diffusion, and other forces.
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Figure 8.1 Comparison of particle contamination on a charged (a) and a neutral (b) silicon wafer.
HEPA filtration attempts to keep particles out of the cleanroom, and laminar airflow is designed to minimize the sedimentation rate of contaminating particles by entraining them in the air flow. Even though a cleanroom is maintained at a high level of cleanliness, particles are still generated within the cleanroom due to personnel, equipment motion, and processes. The forces on the particle are aerodynamic (viscous drag), gravitational, diffusion, and electrostatic in nature. The gravitational forces decrease as the size (mass) of the particle decreases. Similarly, the magnitude of the viscous drag on the particle also is smaller for small particle sizes. In contrast, the magnitude of the diffusional forces is greater for smaller particles because the greater efficiency of momentum transfer to particles that are closer in mass to the gas atoms that strike them. Calculation [1] shows that the force of ESA exceeds the other physical forces for the conditions normally present in a cleanroom. The conditions include surface voltages of several thousands of Volts and particles in the micrometer to sub-micrometer range. The calculation assumed that the particles in the air were neutral on the average but had a distribution of charges with a width which was monotonically related to the total number of electrons on the particle. Thus, larger particles have the possibility of more charge on them and can experience greater electrostatic forces but also are more massive. Thus, the deposition velocity due to electrostatic forces exhibits a maximum for a specific size. Theoretically, increased particle deposition due to electrostatic forces will occur at any voltage, but at field strengths of 200 V/cm or more, the effects are significant and easy to measure. Field strengths of 4000 V/cm or more are not uncommon in cleanrooms.
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Figure 8.2 illustrates some of the forces that act to attract particles to a surface [4]. For small particles (0.01–1.0 mm in size), electrostatic forces are the primary cause of increased particle deposition. What size of particle is to be expected in a modern high-technology cleanroom? Figure 8.3 gives some insight into the size range to expect. The figure shows that the nature of a HEPA filter is to stop virtually all particles that are incident upon it, but that the efficiency of the filter is lowest in the near sub-micrometer range (0.1–0.2 mm). In this size range and with the forces shown in Figure 8.2, it is expected that the major contributor to contamination at 500 V/cm is ESA. How significant are the calculations and the measurements discussed above? Is ESA a significant factor in high-technology manufacturing? In a typical cleanroom used in high-technology manufacturing which has no electrostatic charge control program, insulators in a room (e.g., reticles, wafers with oxide coating, and disk drive media) typically achieve voltage levels of 5–20 kV. Thus, based upon the data presented above, the majority of the contamination is electrostatically driven. Often this major factor goes unnoticed because the cleanliness levels are so good in the cleanroom. In sub-ISO Class 3 cleanrooms, the number of ‘‘particle adders’’ (particles-per-wafer-pass or PWP) in a typical modern process
Figure 8.2 Deposition velocity as a function of particle diameter for the principal forces acting on a particle.
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Figure 8.3 Filter efficiency as a function of particle size for two different filter configurations (courtesy of Camfil-Farr Corporation, Riverdale, NJ, USA).
can be as low as 0.1 mm (>75 nm). Over the course of processing many layers of the product this can be 2–20 particles, still a very small number. If the average static charge level in the process is only 500 V owing to the fact that there is static control in some parts of the process delivered by the process tool manufacturer, the part of the contamination contributed by ESA would be quite low (0.25–10 particles). In a process with such low-contamination levels, it is very difficult to devise a method for measuring the contribution due to one particular source. Nonetheless, the economic impact of removing this contamination source is profound. For example, we assume only one of the static-attracted particles causes a die loss on 10 semiconductor wafers. If there were 100 dies on the wafer this would represent a yield loss of 0.1%. If the wafer fab produced 500,000 wafers per year, this would be a loss of 50,000 dies per year. With good dies selling for up to US$500 each, this is a significant loss. In reality, static-attracted particles cause greater losses than used in this example. Electrostatic attraction and its effect on contamination control is not the only negative effect of static charge. As mentioned earlier, static charge is responsible for ESD due to the discharge from one object to another. Such a discharge can cause physical damage to a product which experiences such a discharge owing to either electrical overstress or due to damage caused by the energy deposit of the discharge (spark). ESD is particularly important in the case of disk drive assembly (manual handling of magnetoresistive (MR) heads) and in photolithography
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(damage to the reticle caused either by charge on the reticle, or by induced discharges caused by electric fields from other charged objects in the proximate environment). Most recently, semiconductor wafers with the smallest feature sizes (£0.15 mm) have exhibited gate oxide punch-through due to processing steps that are known to cause high charging such as cleaning and certain wet processing steps. The remaining problem caused by ESD is robotic malfunction. When a metal-to-metal discharge takes place, the frequency content of the discharge is extremely high (multiple GHz). The discharge dissipates much of its energy in the form of EMI transients which are within the bandpass of microprocessors controlling the robots. Occasionally (daily to weekly), such a discharge can cause the microprocessor to execute meaningless or invalid instructions. When this happens, the robot will either stop and display a difficult-to-interpret error message or, worse, exhibit some strange behavior like bumping into a wall or trying to insert a wafer into an incorrect location. Most often this behavior is assumed to be a software bug. While this may be the case, the problem can also be the result of EMI transients generated by ESD. Electrostatic charge control in cleanrooms must prevent product damage, equipment malfunctions, and ESA caused by charge accumulation.
8.3
Static Charge Generation
Whenever two dissimilar surfaces placed in close contact are separated, one surface loses electrons and becomes positively charged, while the other surface gains electrons and becomes negatively charged. This is known as triboelectric charging. Any material (solid or liquid) may be charged triboelectrically by friction, separation of materials, or fluid flow. The magnitude of the charge will be affected by the surface condition, area of contact, speed of separation or rubbing, and the humidity. Whether the material remains charged depends on its conductivity and the availability of a path for the charge to flow to ground. If charge is allowed to accumulate on a material, it may attract and bond particles to its surface. The principle of triboelectric charging is related to the work function of each material. This is defined as the energy required to remove an electron from the surface of the material. Since the work function is related to the electronic energy levels of the material, the work function of each material is unique. Thus, any time two materials are placed in contact with each other, electrons are transferred from one material to the other.
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The amount of transfer is dependent upon the nature of the surfaces and the nature of the contact. Smooth surfaces with a significant amount of contact pressure and relative motion (sliding) result in a greater amount of charge transfer. When the materials are separated, the capacitance between them decreases and the potential difference (voltage) between them increases. Thus, the mechanism of triboelectric charging results from contact of dissimilar materials and separation of the materials afterward. The environment of a cleanroom lends itself to increased levels of tribocharging and decreased dissipation of the charge from the surface of insulators as compared with charge levels on insulators in a conventional room. For example, any contamination that exists on the surface of an insulator provides a discharge path to ground for the charge. In a cleanroom, all objects are wiped down to eliminate this discharge mechanism. Studies [5] have also shown the relationship between humidity and tribocharging. In any location, the humidity will achieve an equilibrium between water vapor in the air and on the surface of each material. At lower humidity [35–45% relative humidity (RH)], the equilibrium condition dictates that less water vapor will be present on the surface of the material. This water vapor modulates the work function of the material, shifting the value between the work function of the material and the work function of water. Thus, materials in a low humidity environment exhibit more triboelectric charging than those that are in a higher humidity environment. Since cleanrooms are maintained at low humidity, more charging is observed in the cleanroom than in a conventional room. Static charge is also generated by induction. Static charge on an object can create or ‘‘induce’’ opposite polarity charges on the surface of another object by causing the positive and negative charges on the object to separate. As with charge generated triboelectrically, the induced charges can attract particles and contact with ground can result in damaging ESD events and EMI [3]. An example of contamination resulting from induction is when a wafer is stored in a highly charged container such as a front opening unified pod (FOUP) assumed to be negatively charged for discussion purposes. If wafers without an oxide coating are held in an inner support structure which is conducting (as is the case with a FOUP) and connected to ground, the charge on the wafer support structure will separate and the negative charge will be displaced from the wafers to the support structure and from there to ground. When the container is removed from the ground structure, the wafers will be charged positively and present a contamination issue.
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Insulators Versus Conductors
All materials can be characterized as either electrical conductors or as electrical insulators. A conductor is a material through which an electrical current can pass, while an insulator is a material through which an electrical current cannot pass. There is a good deal of variation in the electrical properties of conductors (electrical resistivity) that allows electrical conductors to be further classified as conductors (good conductors) and as dissipative (poor conductors), but both are differentiated from insulators by their ability to sustain an electrical current. Electrical resistivity is a measure of the voltage that must be applied to cause a unit current to flow through a cubic sample of a material 1 meter on a side. Surface resitivity is a similar parameter corresponding to current passing along the surface of a material rather than through a bulk sample. It is defined in terms of the voltage required to pass a unit current through a square sample of the material. Bulk resistivity is measured in units of W-m or W-cm and the surface resistivity (relating to currents passing along the surface of a sample) is measure in W/square. The range of values of resistivities for different classes of materials is shown in Table 8.1. Conductive materials [6] are defined as those having a surface resistivity <1 · 105 W/sq or a volume resistivity <1 · 104 W-cm. With a low electrical resistance, electrons flow easily across the surface or through the bulk of these materials. Charges go to ground or to another conductive object that the material contacts. Metals like copper and aluminum have exceptionally low resistivities on the order of 10 8 W-cm, making them extremely good conductors of electricity. Dissipative materials [7] have a surface resistivity equal to or >1 · 105 W/sq but <1 · 1012 W/sq, or a volume resistivity equal to or >1 · 104 W-cm but <1 · 1011 W-cm. For these materials, the charges flow to ground more slowly and in a somewhat more controlled manner than with conductive materials. Dissipative materials are used for ESD control because they discharge so slowly that they often do not cause ESD damage to microstructures that are manufactured in high technology cleanrooms. Insulative materials [8] are defined as those materials with a surface resistivity >1 · 1012 W/sq or a volume resistivity >1 · 1011 W-cm.
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Table 8.1 The Resitivity of Different Classes of Materials
Material Type
Surface Resistivity (/sq)
Volume Resistivity (-cm)
Conductive Dissipative Electrostatic shielding Insulative
<1 · 105 ‡1 · 105, <1 · 1012 <1 · 104 ‡1 · 1012
<1 · 104 ‡1 · 104, <1 · 1011 <1 · 103 ‡1 · 1011
Because of the incredible variation (>1015) in the resistivity of materials, it is clear that the ability of an insulator to dissipate surface charge is so poor that it can be ignored. For a typical 30 · 30 cm2 object located 1 cm from a ground plane, the capacitance of the object is 10 10 Farads, so that the characteristic time to discharge will be given by the product of its resistance and its capacitance [9]. For a conductor, this corresponds to a time of 1 second. For a fairly good insulator (>1013 W/sq), this corresponds to >1,000 seconds. For extremely good insulators like quartz, Teflon or SiO2, the material can be assumed to NEVER discharge. Thus, in a cleanroom where high levels of charge are developed on such surfaces, they will build up to extremely high levels over a period of days. Grounding one of these extremely good insulators accomplishes nothing and the charge remains on the surface. The small amount of humidity present in the cleanroom would only shorten the discharge time to hundreds of hours. Grounding of conducting or dissipative materials is an important first step in cleanroom static charge control, but it is of no help in dealing with insulators. Details of how to ground the materials, utilization of dissipative materials, selection of insulators that have similar work functions to the materials that they contact (called tribo-matching), and techniques for dealing with static charge developed on insulators is the discipline called electrostatic management.
8.5
Cleanroom Electrostatic Management
A variety of methods have been developed to deal with static charge. The basic methods are grounding of all facility components (walls, floors, work benches, and equipment), appropriate use of conductive and static dissipative materials, and local or room ionization to control static charge
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on insulators. In addition to these basic methods, education of cleanroom personnel in the practice of static control, as well as auditing for compliance with the static control program, are also essential to the success of the program. Modern cleanroom environments make extensive use of grounding with conductive and static dissipative materials to control electrostatic charge. Grounding prevents the storage of static charge on materials that are connected to ground. If a conductive or static dissipative material does become charged, connecting it to ground will remove this stored charge. To be effective in controlling static charge, conductive and static dissipative materials must be provided with a reliable path for the static charge to flow to ground. The success of any grounding method depends on the integrity of the ground path. In critical applications, ground path monitoring and periodic verification may be important aspects of a static control program. By creating the ground path, the static charge on equipment, materials and personnel, can be rapidly and harmlessly neutralized. Ground connections should exist for most accessible surfaces of production equipment. It is particularly important to assure grounding of these surfaces within 30 cm of the static sensitive product. Care should also be taken with moving parts of equipment. A ground connection that exists when a robot handler is stationary may be lost when the robot is in motion. Flexible grounding connections are advisable rather than relying on conductive lubricants. Static dissipative materials are used in the construction of cleanrooms and mini-environments to reduce the accumulation of static charge. Walls and floors of a cleanroom and panels of a mini-environment may be constructed from these materials. Static dissipative materials should be selected over conductive materials in order to slow down the charge removal process and prevent a damaging ESD event. They may be used for parts of equipment that come into contact with a sensitive product. Tweezers used in disk drive assembly and dissipative work surfaces used for reticle inspection stations are two examples of locations where dissipative materials are the best material choice. In contrast to metal tweezers, metal work surfaces, or insulative minienvironment walls, the cost of the dissipative material is higher, but often the payback in terms of decreased amount of ESD damage makes the dissipative materials a good investment. Static dissipative packaging materials are also used to shield the product from static charge buildup or ESD damage as it is transported between process steps in the cleanroom.
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When an object takes on a given amount of charge and then discharges to a sensitive product, the discharge can occur at different rates depending upon the resistivity of the material. A metal-to-metal discharge typically occurs in a sub-nanosecond interval, whereas a discharge of a dissipative material to a metal object or a dissipative-to-dissipative discharge can take multiple microseconds to occur. The slower discharge necessarily will have a lower peak current than the faster discharge of the same amount of charge. Due to the small size of modern electronics (submicrometer MR heads or deep sub-micrometer semiconductor feature sizes), the time required to dissipate heat from the structure is extremely short [10], on the order of nanoseconds. Thus, a discharge time from a dissipative object can be orders of magnitude longer and not cause damage, whereas the same discharge from a conductor is often lethal to the product. While it is important to employ static dissipative materials to minimize the peak current in a discharge, use of dissipative materials does not assure that the product itself will not charge. It will also be important to verify that the materials are cleanroom compatible and do not present a contamination hazard. Particularly with construction materials used in cleanrooms, static dissipative properties may be sacrificed to achieve other features like dimensional stability, low outgassing, or low cost. Grounding methods and static dissipative materials are also used to assure that charge does not accumulate or transfer from personnel to sensitive products or equipment. A variety of personnel grounding methods are employed using garments, booties, gloves, static dissipative flooring, and wrist or heel straps. For successful static charge control, all of these methods must be monitored and verified periodically. Unfortunately, cleanrooms must also use many materials that are insulators, such as Teflon, various plastics, and quartz. Very often the insulating materials are an essential part of the product itself. It is not possible to remove the electrostatic charge on insulators by connecting them to ground. Most insulators are easily charged, retain their charge for long periods of time, and are often close to or part of the product. Teflon and quartz wafer carriers, oxide coated wafers, epoxy IC packages, insulated component leads, and glass hard disk media are examples of insulators present in the cleanroom. The requirements of cleanrooms preclude the use of carbon particles or chemical additives to insulating materials to make them static dissipative. Antistatic sprays and solutions can create a contamination problem. Humidity control was proposed in the past as a static control method, but it has been shown to be expensive and ineffective.
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Neutralizing static charge on insulators and isolated conductors has become a necessity for achieving high product yields in cleanrooms. With few other methods available, this will often require the use of some type of air ionization. Using only the highly filtered cleanroom air, ionizers create clouds of both positive and negative air ions to neutralize static charges wherever they may exist in the cleanroom environment.
8.6
Air Ionization for Static Charge Control
Air is a rather good insulator so any static charge that develops on a clean surface of a good insulator will remain on that surface indefinitely. Air ionizers are used to decrease the electrical resisitivity of the air through the addition of ions which act as charge carriers. Air consists primarily of nitrogen, oxygen, carbon dioxide, and other trace gases. Air ions are gas molecules in air that have either lost or gained an electron. Air ionizers are used to introduce ionization into the atmosphere and have an effect similar to that of a lightning storm on the environment. Ions occur naturally in the air, but in a cleanroom the HEPA (high efficiency particulate air) and ULPA (ultra low penetration air) filters serve to eliminate the ions from the air. Positive and negative air ions are present in normal outside air, resulting primarily from radioactive decay of materials in the soil (such as uranium) and gases in the air (such as radon). But most air ions are stripped out of cleanroom air by HEPA filtration. This makes the air in the cleanroom very insulative and encourages the generation of static charge. Air ionizers restore and increase the level of air ions in the filtered cleanroom air. When the ionized air comes in contact with a charged insulating surface, the charged surface attracts air ions of the opposite polarity. As a result, the static charge on the insulator is neutralized. Air ions of both polarities are required for neutralization because both polarities of static charge are created in the cleanroom. This is shown in Figure 8.4. There are three methods that are commonly used to make air ions for charge control. These methods are corona, photoelectric, and radioisotope ionizations. While ions created by these methods are identical, generally each method has its own application. The tradeoffs involve issues of cleanliness level, ion distribution requirements, shielding, voltage balance (precision) level, and government regulations. Each type will be discussed below.
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Figure 8.4 Neutralizing surface charges with bipolar air ionization.
8.6.1 Corona ionization The most common method used to create air ions in cleanrooms is corona ionization. In corona ionization, a very high electric field is created by applying HV to one or more sharp emitter points. This technique involves the use of HV (5–20 kV). The voltage is applied to a set of sharp points and an intense electric field is established very near (100 mm) the points. This field accelerates free electrons to sufficiently high energy to allow them to ionize molecules that they collide with. When the voltage on the point is positive, positive ions are repelled into the environment; when the point is negative, negative ions are delivered to the environment. The basic principle of corona ionization for positive and negative polarities is shown in Figure 8.5. Corona ionizers can be made using AC or DC voltages. Each has an advantage. Both will be described below.
8.6.1.1 AC ionizer An AC ionizer uses a step up transformer to create the HV bias (–7 kV) required to make ions (Figure 8.6). The transformer creates both positive and negative voltage swings, so AC ionizers do not require any form of adjustment to work. The simplicity of an AC ionizer makes it the lowest cost method in most ionizer applications. Since an ionizer produces positive and negative ions in sequence from the same emitter point(s), these ions are separated in time by half of the period of the AC
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Figure 8.5 Principle of corona ionization.
Figure 8.6 Schematic diagram of an AC-type ionizer.
power line (i.e., 1/100 or 1/120 seconds). This means that the waves of positive and negative ions are rather close to each other, making loss through recombination a large factor. AC ionizers typically utilize fast airflow velocity to minimize recombination. This is not always desirable in a cleanroom environment. Increased emitter point current to offset recombination also increases contamination and limits an AC ionizer to ISO Class 5 cleanrooms or above. Since the transformer secondary is well isolated from ground, the current drawn from the emitter point(s) during the positive and negative voltage excursions of the emitter (corresponding to positive and negative excursions of the AC power line) should be equal. Experience shows that the actual offset voltage as measured with a Charged Plate Monitor (CPM) is typically <10 V [11]. Unfortunately, it has also been shown,
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that a CPM is not capable of accurately recording voltage excursions faster than 1 Hz [12]. Although the instrument has the bandwidth to track such signals, its plate cannot slew fast enough to follow signals that vary at 50–60 Hz. In contrast, the small size of objects like an MR head make them capable of tracking the voltage excursions driven by the time varying electric fields from an AC ionizer. The actual voltage excursions on these objects may be significantly greater than the balance voltage measured by the CPM. Thus, for small objects with extreme voltage sensitivity, such as an MR head, AC ionizers are not recommended.
8.6.1.2 DC ionizer A DC ionizer employs a HV power supply to create the necessary voltage. DC ionizers use separate emitter points connected the positive and negative DC HV power supplies to generate the ions. In order to provide equal numbers of positive and negative ions from separate sources, DC ionizers need some form of control to maintain this balance. For the demanding requirements of electrostatic management of production lines where GMR (giant MR) heads are handled, the control must be active feedback to account for variations in the environment and for any wear that occurs over the life of the ionizer. A schematic diagram of a DC type ionizer is shown in Figure 8.7. Because of the greater sophistication and control systems needed for DC ionizers, the
Figure 8.7 Schematic diagram of a DC ionizer.
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DC ionizing systems are more expensive to manufacture. Owing to the fact that the positive and negative emitters are well separated from each other, recombination is a lesser effect and the DC ionizer can sometimes utilize lower air flow velocity to deliver the ions to the location where the ionization is required. Because of their lower recombination rates as compared with AC ionizers, DC ionizers are used in more contamination critical applications. In fact, for ISO Class 3 cleanroom operation, many DC ionizers perform effectively to the required Class 3 cleanliness level and are only limited by the turbulence and particulation issues of the fan and its motor. DC ionizers are used in ISO Class 3 cleanroom applications. In this ultraclean application, fan driven ionization cannot be used. In this case, the laminar air flow of the cleanroom is used for distribution of the ions throughout the room. DC ionizers used to provide ionization within a mini-environment or a process tool are called bars and provide a small aerodynamic cross-section to the laminar air flow. They contain one or more pairs of emitter points to produce the ionization. Pulsed DC ionizers represent an alternate type of DC ionizer in an ISO Class 3 cleanroom, most commonly in the form of a ceiling-mounted ion emitter. An array of ceiling emitters is mounted to the ceiling of the cleanroom, typically at 1.2–1.8 m centers, and the laminar air flow from the HEPA filters distributes the ionization throughout the entire room. Normally the ionizers are operated in a mode called pulsed DC. This is very much like the steady state DC mode described above, but the two polarities are turned on one at a time with ‘‘on’’ times of 1–10 seconds (Figure 8.8). Pulsed DC provides even less recombination than steady state DC because the voltage is switched, maximizing the separation between the two polarities of ions. As a tradeoff, objects in the room
Figure 8.8 Schematic diagram of a pulsed DC ionizer.
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swing through voltage levels of –50 to –150 V. This makes this method of ionization unacceptable for the most sensitive products such as MR heads, but ideal for applications where such sensitivity is not an issue and high levels of charge must be eliminated in a large work area.
8.6.2 Photoelectric ionization A photoelectric ionizer utilizes extreme UV to soft X-ray photons to create ions. When the energy of a photon exceeds the ionization potential of the medium it traverses, the photon can create an ion by collision with an atom. This is called the photoelectric effect [13]. The most common method of photoelectric ionization involves the use of very soft X-rays. These are X-rays in the range of 5–10 keV, in contrast with medical or dental X-rays which are in the range of 125–175 keV. The lower energy makes them suitable for use as an ion source because the air is rather opaque to photons in this energy range. In contrast, medical X-rays must be chosen to be capable of traversing a human body with reasonable efficiency and, as such, have an attenuation length in air of hundreds of meters. Thus, medical X-rays are not suitable for creating ionization in a localized volume such as inside a process tool. In contrast, most of the X-rays in the 5–10 keV energy range are absorbed in 1 meter of air as shown in Figure 8.9 [14]. A soft X-ray source has a 100% efficiency for creating an ion within about 1.5 m for each photon it emits. As such, it is capable of mediating very high levels of static
Figure 8.9 Transmission factor of photons through 50 cm of air at 1 atmosphere.
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charge. Although the device can be shielded by a few meters of air, it is regulated by governments in the countries it is used in. These regulations require licensing and also specify shielding requirements. While neither the licensing (in the USA by the FDA) nor the safety requirements are very difficult to manage, it does represent an extra step that is necessary for the use of this technology.
8.6.3 Radioisotope ionization The alpha ionization method involves the use of ionizing radiation to make ions. While several forms of ionizing radiation sources are available, only a (alpha) radioactive sources are used for static control. The other radioactive sources have much longer penetration ranges and require shielding in impractical amounts. Most commonly, Po-210 is employed as the radioactive source because of its properties as an a emitter. It produces a particles with a range of only 3.8 cm in air and 0.02 mm in aluminum [15], so that virtually none of the a particles is emitted from the ionizing blower used at a work station, either through the air or through the chassis of the a source. Thus, a sources of this sort are regarded as harmless by government regulatory organizations in virtually every country. The other aspect of Po-210 that makes it an ideal choice is that it decays to Pb-206 which is a naturally occurring stable isotope. Unlike Po-210, many other sources decay into isotopes that may be active as well. The reason that the range of a particles is so short is that they move much more slowly than any other natural radioactive source and thus, couple their energy much more efficiently to the air molecules, resulting in ionization. This makes an alpha type ionizer particularly efficient at creating ions; thus, it provides fast discharge times. The greatest advantage of an alpha ionizer is that it does not employ HV to create the ions and thus, it does not emit electric fields, either AC or DC. Thus, a ionizers should have a balance voltage of zero, an important attribute in applications that involve very small and ESD sensitive products. This technology is crucial to the manufacture of disk drives with MR or GMR heads; as heads become smaller, it will be even more necessary to their manufacture. The main disadvantages of the alpha ionizer systems are that personnel have a health concern about radioactive sources in their work environment. This disadvantage can be overcome with education of personnel. In addition, the device also requires some government paperwork for
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tracking and regulation of the radioactive material, and the sources must be replaced annually. This is not a financial issue but rather a logistical issue as the cost of replacement is comparable to the cost of maintenance required only of corona ionizers.
8.6.4 Measuring ionizer performance Because the majority of ionizers use corona to generate ions, the ionizers involve HV. With HV come high electric fields. These fields are responsible for making the ions, but they also drive the voltage on objects around them to a non-zero voltage. While the voltage is most often much lower than the voltages caused by a static charge, it can be problematic nonetheless. For this reason, one of the parameters which must be measured to benchmark ionizer performance is the balance voltage. Loosely speaking, balance voltage is a measure of how accurately the positive and negative voltages of the ionizer can be set equal. A CPM [11] is an instrument which is used to measure the performance of an ionizer. It includes a 15 · 15 cm2 (6 · 6 in2) plate isolated from ground and with a capacitance of 20 pF as the voltage sensor. The balance voltage is the voltage to which the ionizer drives the plate. In addition, a CPM is used to measure the discharge time which is defined as the time to drive the plate from 1000 to 100 V.
8.7
Air Ionizer Applications
Static charge can cause problems anywhere in the cleanroom environment. To control these problems ionizers are used in a variety of configurations. Applications can involve cleanrooms which operate in the ISO Class 4 and 5 levels and are mostly involved with manual assembly. This is common, for example, for disk drive and flat panel assemblies. In contrast, disk drive media, flat panel cell and semiconductor front end cleanrooms are most often characterized by high levels of automation and typically require cleanliness levels at ISO Class 3 or better. These two scenarios require very different ionization solutions. Each of these situations will be discussed below. The most common method used in ISO Class 3 ballroom-style cleanrooms is room air ionization. Ionizers are mounted at or near the filtered cleanroom ceiling and the laminar air flow is ionized as it passes the ionizer emitter points. The advantage of this type of system is that it
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controls static charge on any surface that is exposed to the room air flow. Corona ionizers are mounted in the ceiling to provide global coverage of the insulators moving through the room. These ionizers are either bars which hang from the ceiling, or they are ceiling emitters mounted to the ceiling (and incorporating rods to stand off the emitter points from the ceiling). The distance that the emitter points are stood off from the ceiling is typically 30–100 cm. The purpose of this distance is to separate the sources of the ions from the grounded elements of the ceiling. If the ionizer emitters were flush mounted to the ceiling, all of the ions would be drawn to the grounded ceiling elements and none of the ions would be borne in the laminar air flow, providing electrostatic control for the insulators in the room. A typical room system will provide global coverage with discharge times (90% reduction in charge levels) in the range of 20–120 seconds. High ceilings and low air flow velocities represent the upper level and 2.4 m (8 feet) ceilings with 0.5 m/seconds (100 feet per minute air flow) provide the fastest discharge times. Many cleanrooms today employ mini-environments for protection of the product from contamination. This configuration involves keeping silicon wafers in clean enclosures [standard mechanical interface (SMIFs) for wafers or reticles and front opening universal pods (FOUPs) for 300 mm wafers] as they are transferred from process tool to process tool. The individual tools are also fully enclosed to block contamination from the room. While this strategy blocks the contamination from contacting the product, it also blocks the ionization from contacting the products. Ions recombine as they pass through a HEPA filter, so room systems do not provide any electrostatic protection of objects within the process tools. To provide protection within the process tools, ion bars are mounted within the mini-environments as shown in Figure 8.10. The bar, most typically a pulsed DC corona bar, should be mounted below the HEPA filter, if possible. To minimize offset voltages, the bar should be located at least 30 cm from the product. For applications requiring closer mounting, steady state DC bars should be used. If the direct HEPA location is infeasible (due to mounting particulars or due to a metal structure in the path of the air flow), a location should be chosen which is not immediately adjacent to a grounded metal structure, if possible. Care should be taken to select a location such that the air flow direction will carry the ions toward the object to be protected since the ions are not efficiently drawn against the wind electrostatically for more than a few centimeters (Figure 8.11). The question often arises as to whether room ionization is necessary in a mini-environment cleanroom. In fact, from a contamination standpoint, most of the electrostatically driven particle deposition occurs in the
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Figure 8.10 Ionizer applications in an ISO Class 3 cleanroom.
Figure 8.11 Utilizing ambient air flow to drive ions to the product to be protected.
mini-environments and in the carriers. The electric fields from objects outside of the carriers penetrate the carriers and add to the electric fields inside. As the carrier moves through the room or as charged objects in the room move past the carrier, the fields cause contamination within the
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carrier to move, representing a secondary contamination issue. Also, charged objects within the room, but external to the mini-environments, can drive a discharge from one object to another. While this does not affect the contamination control of the product directly, it does generate EMI in the room and can easily cause irrational performance by the robotics. For these two reasons, many people choose to install ionization both within the mini-environments and also in the cleanroom itself.
8.7.1 Discharge in process tools Severe discharge requirements in process tools involving high levels of charge may employ the photoelectric ionizer, particularly in environments where it is possible to mount an ionization bar at a distance of 30 cm or greater from the product or in applications involving high levels of charge. Practically, this means either >20,000 V or highly capacitive objects. Cleaning processes tend to produce high charge levels. Also, processes that place flat products (like wafers or plates) on a flat surface, and then raise them up a significant distance when the processing is complete, are candidates for high charging. In order to use the photoelectric ionizer, it is necessary to have an enclosure which serves as a complete shield against the photons. A rather thin shield is adequate (5 mm of plastic or 750 mm of aluminum), but it is necessary to assure that there are no hairline cracks in the structure, such as doorways without an overlapping seal, as these can present a way for the photons to escape. In addition to the shielding requirement, there is a second requirement for a physical knife switch that shuts down the ionizer when the door is open. If these requirements are followed, it is very straightforward to get an FDA (United States Food and Drug Administration) X-ray cabinet license for this type of ionizer. While this small amount of paperwork is not required for a corona ionizer, there are applications of the sort mentioned above where this type of ionizer is the only solution which will provide protection for the process. The other ionizer type which is used in tight confined spaces, or where static charge levels can be quite high, is the alpha ionizer. An alpha ionizer involves no HV so it has a balance voltage of zero, and it can be used with the most static sensitive products such as MR or GMR heads. An alpha ionizer requires air flow to deliver the ionization to the item to be protected, so it needs either a blower (discussed below) or it needs to be placed in a laminar flow field. However, it can be operated very close to the product with no significant effects. Since the range of Po-210
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a particles in air is 3.8 cm, placing the ionizer within a distance of 5 cm of the charge source is perfectly acceptable. Again, at short distances an alpha ionizer is capable of dealing with extremely high charge levels. It requires minimal licensing, but, in practice, it does cause concern to manufacturing workers who do not understand it and it does require training by the RSD (radioactive source disposal) team on site.
8.7.2 Flow benches and work surfaces For clean laminar flow benches and other work surfaces in applications involving manual assembly such as in the disk drive industry, faster discharge times (5–20 seconds) are required to account for the rate of charging by objects being handled by operating personnel. In addition, the requirement for laminar air flow is not as great in this environment. Therefore, the ionization solution used for these applications involves forced air ionizers or ionizers with integral blowers. Most often, the ionizers are simply mounted on the table top and directed toward where the work is being done. While this can deal with most issues of static control, there are several practical issues that come into play in this environment. When objects are placed on a table top, they can block the airflow and, as such, render the ionizer useless as a static control device. Also, many operators find the air flow from the ionizer unpleasant due to the fact that the air makes them cold and causes their eyes to dry out. As a result, operators will occasionally turn off the ionizer when no one is watching, thus eliminating the protection that the ionizer provides. The alternative to a table top ionizer is the use of an overhead ionizer. This is a better solution, although the cost is somewhat higher than a table top blower. An overhead blower ionizer is mounted above the work surface and blows air in the same direction as the laminar air flow (Figure 8.12). Since it is mounted above the work surface rather than on it, it is impossible to place objects on the work surface and block the air flow from reaching the product it is designed to protect. In addition, experience shows that this configuration eliminates the possibility of air flow into the operators’ eyes by directing it downward rather than horizontally and thus eliminates the habit of turning off the ionizer. The overhead ionizer typically achieves discharge times in the 5–15 seconds range, thus providing the ability to protect sensitive products that are being handled in a manual assembly area. Alpha ionizers are commonly used in overhead blowers. They provide fast discharge times similar to corona ionizers but also feature
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Figure 8.12 Directing the air flow downward to avoid blowing in the eyes of an operator.
zero-balance voltage. This type of ionizer is used almost exclusively in operations that involve handling of critically sensitive MR and GMR heads.
8.8
Conclusions
Reduction of product defects to levels acceptable in high quality, worldclass cleanroom manufacturing requires continuing attention to static charge control. Uncontrolled, static charge is responsible for increasing the number of particle-related defects, damaging products and equipment by ESD, and interfering with factory automation. As factory profitability increasingly depends on both high yields and high product throughput, minimizing or eliminating static-related problems in cleanrooms has become a necessity.
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Static charge control begins with the grounding of personnel, equipment, and any materials that come close to static sensitive products. Insulating materials should be removed, whenever possible, and replaced with static dissipative equivalent materials. When insulators must be used to satisfy other process requirements, ionizers are used to neutralize static charge on the insulators. It should be remembered that insulators are very often a part of the product itself and cannot be eliminated. Air ionization is one of the few methods available for controlling static charge in high-quality cleanroom environments. In some cases it is the only method that can be used. Ionizers can reduce the number of contamination and ESD-related defects occurring in mini-environments and production equipment as well.
References 1. R. P. Donavan (Ed.), Particle Control for Semiconductor Manufacturing, pp. 325–339, Marcel Dekker, NY (1990). 2. D. W. Cooper, J. J. Wu and R. W. Miller, ‘‘Deposition of Submicron Aerosol Particles During Integrated Circuit Manufacturing,’’ Proceedings 9th ICCCS Symposium, Los Angeles, CA (1988). See also Part. Sci. Technol. 8, 209 (1990) and J. Environ. Sci. 32, 27 (1989). 3. L. B. Levit, T. M. Hanley and F. Curran, ‘‘In 300 mm Contamination Control, Watch Out for Electrostatic Attraction,’’ Solid State Technology (June 2000). 4. A. Steinman, ‘‘Static Charge-The Invisible Contaminant,’’ Cleanroom Management Forum, Microcontamination (October 1992). 5. L. B. Levit and W. Guan, ‘‘Effects of Static Charge on Contamination Control in Semiconductor Manufacturing,’’ Proceedings SEMICON China, Shanghai, p. 381 (April 2000). 6. ESD-ADV 1.0-2004, ‘‘Glossary of Terms,’’ ESD Association, Rome, NY (2004). 7. ANSI/ESD S541-2003, ‘‘Packaging Material for ESD Sensitive Items’’, ESD Association, Rome, NY (2003). 8. ESD TR20.2-2000, ‘‘ESD Handbook, ESD Association, Rome, NY (2000). 9. D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, John Wiley, New York (1996). 10. L. B. Levit and A. Wallash, ‘‘Measurement of the Effects of Ionizer Imbalance and Proximity to Ground in MR Head Manufacturing,’’ Proceedings EOS/ESD Symposium, EOS-20, pp. 375–382, ESD Association, Rome, NY (1998). See also J. Electrostatics 47, 305 (1999). 11. ANSI ESD STM3.1:2000, ‘‘Ionization,’’ ESD Association, Rome, NY (2000). 12. C. E. Newberg, ‘‘Analysis of the Electrical Field Effects of AC and DC Ionization Systems for MR Head Manufacturing,’’ Proceedings EOS/ESD Symposium, EOS-21, pp. 319–328, ESD Association, Rome, NY (1999). € 13. A. Einstein, ‘‘Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,’’ Annalen der Physik 17, 149 (1905).
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14. Lawrence Berkley National Laboratory Computing Resource at http://cindy.lbl. gov/optical_constants/gastrn2.html. 15. W. P. Trower, ‘‘High Energy Particle Data. Range, Energy and dE/dx Plots of Charged Particles in Matter,’’ Lawrence Radiation Laboratory UCRL-2426, Volume II, University of California, Berkeley, CA (1966 revision).
PART II CHARACTERIZATION OF SURFACE CONTAMINANTS
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Electron Microscopy Techniques for Imaging and Analysis of Nanoparticles Zhong Lin Wang1 and Jean L. Lee2 1
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA 2
Nano-SciTech, Norcross, GA, USA
9.1
Scanning Electron Microscopy
9.1.1 Instrumentation Scanning electron microscopy (SEM) is probably the most common technique for analysis of particles. A modern SEM can furnish a resolution of 1 nm, relatively simple image interpretation, and large depth of focus, making it possible to directly image the three-dimensional structure of nanomaterials. SEM is a versatile tool that provides not only the morphological information of particles, but also chemical and in some cases crystallographic information. An SEM is composed of an electron gun that provides an electron probe with high intensity, a condenser lens system that generates a small probe size, an objective lens for imaging, electron probe scanning coils, and a detector system for receiving images and spectra. The electron beam is formed by accelerating electrons generated from a filament set in a cathode held at a slightly negative or ground potential toward an anode whose potential is selectable. The cathode, filament, and anode are collectively referred to as the electron gun; the type, mode of operation, and cost of the filament depend on the brightness desired, its lifetime, and the vacuum level achievable in the electron gun chamber. The brightness b is
R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 529–584 ª 2008 William Andrew, Inc.
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defined as the current density per solid angle and can be calculated as b¼
4I ðpdc a0 Þ2
Eq. (9-1)
where I is the beam current, dc is the diameter of the beam at its crossover between the cathode and the anode, and a0 is the divergence semiangle of the beam as it emerges from crossover. Tungsten hairpin filaments which operate by thermionic emission (i.e. filament heating) are the least expensive and can tolerate a relatively high pressure (105 Torr), but they also produce relatively low brightness (5 · 104 A/cm2ster) over a life time of 100 hours. LaB6 thermionic filaments have a typical lifetime of several hundred hours and are able to produce a higher brightness electron beam (5 · 105 A/cm2-ster) than tungsten thermionic filaments because of their lower work function, but they are also more expensive and require an electron gun vacuum of about 106 Torr. Field emission sources can produce a brightness about two to three orders of magnitude greater than a LaB6 filament and if handled with care can have a lifetime that exceeds that of LaB6 filaments, but they are expensive and require a vacuum that is at least in the low 109 Torr range. However, if very high spatial resolution is a must, a field emission source is recommended because the electron tunneling that occurs through the few atoms at its sharp tip can produce an effective electron source size that is 1 nm in diameter, which is considerably smaller than that of any of the thermionic electron sources. Moreover, the energy distribution of electrons generated by a field emission source is usually smaller than that of thermionic sources, which contributes to the production of a smaller source size by reducing the effect of condenser lens chromatic aberration. Selection of the operating voltage and current depends on the nature of the sample and the information desired. Most modern SEMs can be run using an operating voltage in the range 100 V–30 kV. For small particles, usually an accelerating voltage of 10 kV or less is used since higher accelerating voltages have larger electron penetration depths into the sample and correspondingly larger electron probe interaction volumes with the sample. Electron lenses are basically circular coils of wire whose axis coincides with the optic axis of the electron microscope. Application of a potential across the coil of wire produces a current in the coil; this in turn induces a magnetic field that has a significant component parallel to the optic axis. In addition, the objective lens contains a pole piece that serves to
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concentrate the magnetic field inside the lens. The pole piece has a gap, which will produce a fringing magnetic field with a small radial compo~ that is the sum of the largely axial magnetic nent. The magnetic field B field produced by the current in the lens and the fringing field produced by the pole piece. Therefore, any electron in the beam that strays from the optic axis experiences a Lorentz force F L that causes it to spiral toward the optic axis: ! FL ¼ qð v · BÞ
Eq. (9-2)
where q is the elementary charge and v is the velocity of the electron. Electron lens design is complicated by the precision needed for a very small beam diameter and the addition of pole pieces, apertures, analytical detectors, etc. which break the symmetry of the simple circular wire coil design and introduce lens aberrations. Electron microscopes with smaller values of key aberration coefficients such as spherical aberration Cs and chromatic aberration Cc are preferred for work requiring high spatial resolution, but microscope cost also tends to scale inversely with the magnitudes of Cs and Cc. Because Cs and Cc are set by the microscope manufacturer and often cannot be corrected by the operator, we will not delve into further details on electron lens design and electron optics effects on lens aberrations. As its name implies, the function of the condenser lens and aperture is to demagnify or condense the beam diameter produced by the electron source. Beam spatial coherency is affected by the choice of condenser aperture size, with a smaller aperture producing a more coherent beam (i.e. a more point-like source). While greater spatial coherency of the incident beam is desirable in imaging specimens requiring very high resolution, it is done so at the cost of some signal intensity loss from using a smaller condenser aperture. The objective lens focuses the incident beam onto the sample surface; it is also where final correction of some beam aberrations (such as astigmatism) takes place. The distance over which the sample surface can be moved along the optic axis without degrading image resolution is called the depth of field, and the choice of objective aperture size affects the depth of field (Figure 9.1). In general, a smaller aperture produces a greater depth of field, but one must take into consideration that the image magnification M inversely affects the depth of field such that Depth of field ¼
d Ma
Eq. (9-3)
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Figure 9.1 Schematic diagram showing the depth of field in scanning electron microscopy.
where d is the lateral resolution of the image and a is the objective aperture semi-angle. In the case of imaging small particles where it is necessary to operate at or near the limit of the probe size dmin, the optimum objective aperture semi-angle aopt should be used, resulting in Depth of field at the instrument resolution ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 Cs d 2min M
Eq. (9-4)
The working distance (i.e. the distance between the bottom of the final objective lens and the sample surface) may be adjusted slightly to achieve aopt, but substantial changes in working distance may result in deviation away from the minimum probe size [1]. Finally, as with all electron microscopes, vibration isolation and shielding from stray electromagnetic fields are critical if high spatial resolution is desired. Most electron microscopes are located on the lowest floor of a building away from vibration sources like elevators to reduce vibration problems. Commercially available vibration isolation solutions such as vibration isolation feet or vibration isolation platforms can be used satisfactorily with an electron microscope to help decouple it from vibrations transmitted through the floor. Some electron microscope facilities take the additional step of physically isolating the rooms in which high-resolution
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instruments are located by constructing those rooms on a foundation that is separate from the rest of the building. This may be necessary if the building is susceptible to low-frequency vibration from nearby sources such as railroad tracks, a truck route, or heavy construction. Microscope operators should also take care to eliminate high-frequency vibration sources (such as talking, touching the microscope, noise from nearby pumps, etc.) when taking high-resolution images. Strong fields generated by nearby pieces of equipment can produce beam instabilities and undesirable beam deflections in an electron microscope; shielding the exterior of the microscope column with a sheet of m metal may be effective in stabilizing the beam. If stray fields continue to be problematic, more drastic measures such as isolating the microscope in its own shielded room and providing the microscope with its own electrical ground may be helpful.
9.1.1.1 Environmental scanning electron microscope The recent development of the environmental scanning electron microscope (ESEM) addresses the need to examine specimens under conditions as close as possible to their ‘‘natural’’ conditions, with a minimum of sample preparation. This includes the ability to image moist samples, which requires the ESEM to operate at relatively high pressures (up to 50 Torr) using gases such as water vapor, nitrogen, argon, or carbon dioxide. The electron gun and most of the column of the ESEM are designed as for a conventional SEM, but in order to sustain such high pressures in the ESEM specimen chamber a series of apertures is used in the column of the ESEM just above the specimen chamber. Each aperture is designed to sustain a pressure difference of about 2–3 orders of magnitude that helps to minimize the scattering of electrons from the incident beam until the beam encounters the gas molecules in the specimen chamber. Collision of the incident electrons with the gas molecules causes beam spreading and therefore some degradation in the spatial resolution of ESEM images. However, the gas molecules also act as a secondary electron (SE) amplifier where SEs emitted from the sample ionize gas molecules and electrons released by the ionized gas molecules, can cause additional gas molecules to become ionized. These electrons are ultimately collected by a positively biased gaseous SE detector. The remaining positively charged gas ions in the specimen chamber help to neutralize any specimen charging that might occur, making the ESEM a useful tool for studying electrically insulating samples.
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The spatial resolution of ESEM images is largely limited by the scattering experienced by the incident electrons when they collide with gas molecules in the specimen chamber. A spatial resolution of 5 nm may be achieved when operating the ESEM at the upper end of its pressure capabilities, with the resolution improving as the specimen chamber pressure decreases.
9.1.2 Signals produced by the SEM 9.1.2.1 Imaging 9.1.2.1.1 Backscattered electron imaging and secondary electron imaging For imaging SEM specimens, two main types of electrons emitted by the specimen are often used: backscattered electrons (BSEs) and SEs (Figure 9.2). In the case of imaging nanoscale materials, the choice of whether to use BSE or SE imaging depends mainly on the sample’s topography sensitivity, composition sensitivity, and the orientation of the sample’s small dimension (i.e. depth or lateral) with respect to the incident beam. Backscattered electrons are relatively energetic electrons and are generated when incident probe electrons undergo elastic scattering by atoms in the sample through a total angle greater than 90 . A BSE can be generated from a single scattering event or from multiple scattering events, and the volume within the sample from which BSEs are produced generally increases with increasing accelerating voltage. Because BSE yield depends on the atomic number of the atom causing the backscattering, BSE images are sensitive to the elemental make-up of the sample. Secondary electrons are conventionally regarded as having energies <50 eV and therefore the SEs that are detected are typically generated within a few nanometers of the sample surface. As such, SE images are sensitive to sample topography as well as surface chemical composition and surface electrical characteristics. SEs can be produced as the consequence of either single or multiple scattering events (i.e. produced directly from scattered incident electrons or produced from BSEs); the latter implies that the lateral extent from which SEs can be generated may be quite large. The fact that SEs can be emitted either from the region covered by the incident electron probe and/or from an extended region as by-products of BSEs points to an important consideration in high-resolution imaging in the SEM: the image resolution depends not only on the incident probe diameter but also on the region of the specimen that is affected by the
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Figure 9.2 Schematic diagram showing the signals produced in beam–specimen interaction in scanning electron microscopy. SE I are secondary electrons produced from a single scattering event such as direct interaction between the incident electron beam and the sample. SE II are secondary electrons that are produced from a multiple scattering event such as from BSEs.
incident beam (either directly or indirectly), known as the beam–specimen interaction volume. The size and lateral extent of the interaction volumes that produce BSEs and SEs depend not only on the energy of the incident beam, but also the stopping power of the atoms contained in the sample. The interaction volume can be relatively large in polymer specimens, for example, because of the low atomic number of the target atoms. In BSE imaging, secondary factors that can affect the interaction volume include specimen thickness along the beam direction and specimen tilt with respect to the incident beam. The depth in the sample from which BSEs are emitted depends on the incident energy of the electron probe and the composition of the sample; greater amounts of high atomic
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number elements in a dense specimen provide more stopping power to the electron beam. The depth resolution of BSEs emitted by the sample can be improved by limiting the sample thickness and by tilting the sample so that incident electrons enter the specimen at a glancing angle with reduced depth penetration. The lateral extent from which BSEs are produced depends on the electron probe incident energy and the sample tilt with respect to the incident beam, with lower incident electron energies and normal incidence producing a smaller lateral region for BSE production. These secondary factors of sample thickness along the incident beam direction and sample tilt tend not to have as great an impact in SE imaging. The SE interaction volume is in particular not strongly dependent on sample tilt; using a large sample tilt degrades the lateral spatial resolution of SE images because it results in a greater area of the sample surface intercepting the SE interaction volume and therefore a larger area from which SEs are emitted. Given these factors affecting the interaction volume, the imaging of small particles is typically carried out using SE imaging with a low operating voltage (5 keV or less) to minimize the size of the interaction volume and to reduce the number of BSEs that might give rise to SEs [1]. Since BSEs and SEs have different energies and are produced via different mechanisms, diverse information can be extracted by taking both a BSE image and a SE image from the same location of a sample. For example, unlike SEs, BSE production is strongly dependent on atomic number and therefore bright areas in a BSE image can reveal regions where higher concentrations of high atomic number elements reside. SE images are strongly influenced by specimen topography as well as any electric or magnetic fields that are present at or near the area of interest on the sample. Use of a low operating voltage and low current for the incident beam is advantageous in the case where the specimen is insulating, as these beam conditions help reduce specimen charging. Low operating voltage and low current are also recommended for samples that are beam-sensitive. In this case, tasks such as focusing and stigmating should be carried out not directly on the area of interest but in an adjacent, similar area; when the focus and astigmatism are set the specimen can be quickly moved to the area of interest for image recording. Use of a cooling sample holder may help reduce beam damage. A key trade-off in the case of beam-sensitive samples is that of incident electron dose received by the sample vs. the image signal-to-noise ratio. Some experimentation may be necessary to find the right combination of incident beam current and image scan speed that produces an acceptable image. If the sample is not susceptible to drift, several images of a given
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sample area taken at a high scan speed can be averaged together to improve the image signal-to-noise ratio. A detector that is commonly used for sensing BSE and SE signals is the Everhart–Thornley detector, which basically consists of a scintillator surrounded by a Faraday cage attached to a light pipe and a photomultiplier. The scintillator converts the electron signal into light, and it is held at a potential of about +10 kV in order to attract electrons emitted from the specimen and to impart them with enough energy so that a sufficiently strong light signal can be produced when the electrons strike the scintillator. The light emitted by the scintillator is then guided by the light pipe to the photomultiplier, which amplifies the light signal for processing. By adjusting the bias on the Faraday cage, one can select whether BSEs or SEs enter the detector. Application of a small positive bias of a few hundred V to the Faraday cage serves to attract both BSEs and SEs to the detector. The magnitude of this bias is large enough so that the detector can attract some SEs that may originate outside of the direct line of vision between the detector and the specimen. By changing the bias on the Faraday cage to 50 V, SEs can be repelled by the detector without substantially altering the number of BSEs that enter the detector. The BSEs that do enter the detector when the Faraday cage is negatively biased in this way are from regions of the specimen that fall within the line of sight of the detector. Therefore this can give rise to a ‘‘directional’’ appearance and ‘‘shadows’’ in SEM images formed using only BSEs, whereas sample features in SEM images that include SEs may look as if they are more uniformly illuminated. Because of this directional effect on BSE collection, the Everhart–Thornley detector is generally used in SE imaging. For BSE imaging in the SEM, solid state detectors consisting of a pair electrodes attached to opposite sides of a semiconductor p–n junction and a current amplifier are frequently used. As an energetic BSE strikes the electrode on the entry face of the detector, it creates a number of electron– hole pairs in the semiconductor that is directly proportional to its energy. The intrinsic electric field of the p–n junction helps to separate the electrons and the holes that are created, and the electrons are swept toward the current amplifier. The relatively low energies of SEs are not sufficient to create significant quantities of electron–hole pairs and therefore SEs are not influential in images obtained using a solid state detector. The active area of a solid state detector typically covers a large radius and a large range of polar angles with respect to the optic axis, which helps to reduce the directional effects produced by the Everhart–Thornley detector in BSE imaging.
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Figure 9.3 shows an SEM image recorded from gold particles deposited on an alumina substrate using a template provided by a photonic crystal. The periodically arranged Au nanoparticles serve as the catalyst for growing nanorods/nanowires [2]. Figure 9.4 shows the SEM image of the ZnO nanorods grown from the gold nanoparticles. The spatial distribution of the nanorods is determined by the distribution of the Au catalyst [3].
Figure 9.3 SE image of gold particles deposited on an alumina substrate using a template provided by a photonic crystal.
Figure 9.4 SE image of ZnO nanorods grown from gold nanoparticles.
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9.1.2.1.2 Low-voltage imaging Low voltage, high-resolution SEM is an effective technique for imaging specimens that are sensitive to electron radiation. Low-voltage SEM has attracted a great deal of attention in recent years because of its application in polymers, biology, and materials science. The resolution of low-voltage SEM is primarily limited by chromatic aberration. If the energy spread of the electron emission source is DE, the incident beam energy is E0 and the chromatic aberration coefficient is Cc, the probe size limited by this effect is given by dc ¼ a
DE Cc E0
Eq. (9-5)
where a is the beam convergence angle. The resolution of an SEM at 200 V can be as high as 2.5 nm, which is capable of resolving many nanoscale defects. A low operating voltage (<5 kV) is also desirable in the case where the sample is an electrical insulator and application of a conductive coating to the sample is undesirable. In a low accelerating voltage regime, it is possible to achieve conditions where the electron emission from the sample exceeds the incident electrons from the electron beam, thereby preventing sample charging [4].
9.1.2.2 Composition analysis 9.1.2.2.1 X-rays There are a number of outputs that result from the interaction of incident probe electrons in the SEM with the atoms and electrons in the sample. Signals that are collected and amplified from these outputs are often the basis for obtaining analytical information about the sample. X-rays are among the outputs emitted from the sample, and they are commonly used to determine the composition of the sample. X-rays can be produced when an energetic incident electron knocks out a core electron of an atom in the sample. This puts the atom in an excited state, and in order to achieve a state that is more energetically stable an electron from an outer electron shell of the atom will reduce its energy by occupying the core electron vacancy. The amount of energy reduction experienced by the atom is then equal to the difference between the energy levels of the outer shell and the core shell where the vacancy occurred, and
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following energy conservation principles an X-ray having this amount of energy is emitted. Because the energy difference between different electron shells is characteristic for each element, analysis of the energies of X-rays generated by the sample offers information about the composition of the sample. The energies of the emitted X-rays are usually on the order of a few keV, which means that both incident probe electrons and sufficiently energetic BSEs can give rise to X-ray production. This implies that the volume in the sample from which X-rays are emitted can be relatively large in comparison to the probe diameter; this volume tends to increase with increasing incident electron energy and decreasing sample density. The volume from which X-rays are produced from a sample in SEM is frequently larger than the probe dimensions, making chemical analysis of small particles in the SEM quite challenging. One problem associated with chemical analysis of small particles is the extraneous signal associated with material other than the particles themselves (e.g. the signal from a supporting substrate). If the approximate composition of the particles is known, a substrate material that does not have any of the elements contained in the particles and that is stable under an electron beam should be used; the signal from the substrate is then easily identified and removed from chemical analysis. Lowering the operating voltage also helps to reduce the volume in the specimen from which X-rays are produced. If the composition of the small particles is unknown, a first step for composition analysis using the SEM is to deposit the particles onto a transmission electron microscope grid covered with a thin carbon film. This film consists mostly of carbon and is usually thin enough so as not to make a significant contribution to the X-ray data. The energies of emitted X-rays are usually analyzed by at least one of two ways: wavelength dispersive spectrometry (WDS) or energy dispersive spectrometry (EDS). In a WDS spectrometer, X-rays emitted by the sample strike an analyzing crystal with known interplanar spacing dhkl. By choosing an analyzing crystal with an appropriate dhkl, the Bragg relation nl ¼ 2dhkl sin u;
n a positive integer
Eq. (9-6)
can be satisfied by rotating the analyzing crystal so that X-rays with wavelength l strike the {hkl} planes of the crystal at the Bragg angle uB. Therefore, X-rays with energy E are diffracted by the analyzing crystal into an amplifier and counter, where the energy E of the X-ray is related to its wavelength l at typical SEM accelerating voltages (i.e. where
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relativistic effects are negligible) by E¼
h2 2me l2
Eq. (9-7)
where h is the Planck’s constant and me is the rest mass of the electron. The diffracted X-ray signal is amplified when it enters a proportional counting tube, which contains a biased wire and is typically filled with an inert gas. When the gas atoms absorb the incoming X-rays, they become excited and emit photoelectrons that are attracted to the biased wire. As they photoelectrons proceed toward the biased wire, they can scatter elastically with electrons in other gas atoms it encounters along the way to produce a thousand-fold or greater amplification in signal. This structure of the WDS detector highlights its key strength as well as a drawback: good signal-to-noise and resolution can be achieved using WDS, but signal production using Bragg diffraction from a crystal analyzer implies that WDS is able to detect only one characteristic X-ray peak at any given time, making a search for multiple elements in a sample using WDS potentially very time consuming. The EDS is also commonly used to analyze X-rays emitted by a sample in the SEM. Here, the X-ray enters the EDS spectrometer through a very thin window made of low atomic number material. The thickness and composition of this window may absorb low-energy X-rays and therefore determine the lower limit on the atomic number of the elements that can be detected by the spectrometer. The X-ray then strikes a detector consisting of a reverse biased, lithium-doped silicon p–i–n junction (p-type, intrinsic, n-type), creating electron–hole pairs in the intrinsic region of the junction. Since it takes about 3.8 eV to create an electron–hole pair, the number of electron–hole pairs created is proportional to the X-ray energy. The reverse bias applied to this junction helps to separate the electrons and the holes that are created, and the electrons are swept toward the current amplifier. The detector is kept cool with liquid nitrogen to prevent the lithium from diffusing away from the intrinsic region of the junction and to reduce noise. EDS is favored in the analysis of X-rays emitted by SEM samples largely because it can detect the characteristic X-ray peaks of many elements simultaneously, but WDS may be more useful in cases where high resolution of X-ray energies is required and/or very low atomic number elements need to be detected. In analyzing the composition of nanostructures, it may be difficult to obtain sufficient signal from the sample. If the sample is stable under the
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electron beam and contamination is not an issue, a long data acquisition time may be necessary for an acceptable X-ray spectrum. Otherwise, the data can be improved by adding together the X-ray spectra from compositionally identical nanostructures to effectively create a single X-ray spectrum whose intensity and acquisition time is equal to the sum of the signals and acquisition times of the component spectra. When performing quantitative analysis of SEM X-ray data, it is best to have X-ray data from a standard specimen for comparison. However, this is often not possible in the case of new materials development. Care must be exercised in the analysis of X-ray spectra, as there are some elements that share similar characteristic X-ray energies, and in quantitative analysis of X-ray spectra the relative intensities of the X-ray peaks of elements do not necessarily correspond to the relative amounts of those elements present in the sample. Common sample-based corrections that need to be taken into account are atomic number (Z) effects, absorption (A) effects, and fluorescence (F) effects; these three factors are collectively referred to as the ZAF correction. The atomic number factor takes into consideration the increased probability that interaction with an incident electron will produce BSEs rather than X-rays, and that the electron stopping power (which in inversely proportional to the density of the sample) decreases with increasing Z. Absorption accounts for the increased probability that an X-ray emerging from an atom may be absorbed by another atom in the sample as its path length inside the sample increases; this depends largely upon the incident electron energy and the specimen tilt with respect to the X-ray detector. In the phenomenon of fluorescence, X-rays with sufficient energy can cause emission of characteristic X-rays from a nearby atom through the same excitation—relaxation process by which an incident electron produces X-rays from the specimen. In addition, there are detector-based corrections that need to be taken into account in X-ray spectrum analysis. An example of a detector-based correction is the type and thickness of the X-ray detector window and any ice build-up on the X-ray detector window that can cause absorption of lower energy X-rays. Another correction is the accounting of extraneous X-ray peaks in the spectrum resulting from sufficiently energetic X-rays entering the detector and causing the fluorescence of characteristic X-rays from a detector component, such as from the gas in the proportional counting tube (in WDS) or from the silicon in the p–i–n junction (in EDS). This detector-based fluorescence peak is often accompanied by an escape peak whose energy is equal to the difference between the energy of the X-ray entering the detector and the energy of the detector-based fluorescence peak. Multiple X-rays that enter the detector within the time resolution of the detector’s pulse processor may be processed as a false
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single X-ray called a sum peak whose energy is equal to the sum of the energies of the contributing X-rays. User-induced factors can also complicate the interpretation of X-ray spectra. Contamination of the sample through improper handling or storage can give rise to peaks in the X-ray spectrum from the contaminant material (usually hydrocarbons). If the sample is able to tolerate it, vacuum baking or ion milling may help remove surface contamination prior to examination in the SEM. Use of a cold finger in the SEM can help reduce the effects of contamination by providing a surface that is colder than the sample where contaminant molecules can condense.
9.1.2.2.2 Auger electrons When an atom in the specimen relaxes from the excitation caused by an incident electron producing an inner shell vacancy, it can emit excess energy in one of several forms. In the previous section we described the consequences when this excess energy is released in the form of an X-ray photon. However, this excess energy need not always be emitted in the form of an X-ray photon; through a similar de-excitation process an atom can also emit an electron known as an Auger electron that is also characteristic of each element and of the electron shells involved in the relaxation process. An atom cannot emit both a photon and an Auger electron when it relaxes from a given outer shell electron filling a particular inner shell vacancy. While Auger electron spectroscopy (AES) is not commonly used with the SEM, it may be advantageous to use the Auger electron signal in cases where the X-ray yield is known to be low (such as in low atomic number elements). Probably the main reason why AES is not often used is because Auger electrons are typically generated from within 10 s of the specimen surface. For accurate AES analysis, this necessitates ultra-high vacuum (UHV) conditions in SEM and very careful sample preparation and handling to avoid the formation of unwanted surface layers on the sample. Like SEs, Auger electrons are generated very close to the specimen surface and hence the factors that limit SE image resolution also apply in determining the lateral resolution of Auger electron spectra.
9.2 High-resolution Transmission Electron Microscopy High-resolution transmission electron microscopy is the most powerful technique for direct imaging of atoms in nanoparticles. A conventional
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TEM usually has an image resolution of better than 0.2 nm and is very capable of resolving atomic scale structures of nanoparticles. The most important development in recent years is the integration of HRTEM imaging with high spatial resolution chemical analysis. By forming a nanometer size electron probe, as small as 0.2 nm, TEM is unique in identifying and quantifying the chemical and electronic structures of individual nanoparticles using electron energy-loss spectroscopy (EELS) and EDS. This is the high-spatial resolution spectroscopy.
9.2.1 Main components of a transmission electron microscope Both the TEM and the SEM share the same electron gun design (Section 9.1.1). A schematic of a TEM is illustrated in Figure 9.5. Most modern TEM electron guns use either a LaB6 filament or a field emission filament to obtain the desired brightness. The condenser lens also serves
Figure 9.5 Schematic optical diagram of a transmission electron microscope.
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the same function in both the SEM and the TEM and therefore TEM condenser lenses are designed in the same way as SEM condenser lenses. In addition to focusing the incident beam onto the specimen surface, the objective lens [and the intermediate lens(es)] in a TEM also provides some magnification. The magnification ability of an objective lens is determined in part by a pole piece situated within the objective lens, where the pole piece provides an additional magnetic field concentrated near the specimen. The specimen is usually placed within the objective lens during TEM study, and the relative position of the specimen and the objective aperture gives rise to different imaging modes that can be used in the TEM. Specifically, the incident electron beam passes through the specimen before reaching the objective aperture, which means that the objective aperture can be used to select the electrons scattered by the specimen used in forming an image. If the objective aperture is positioned to include the incident beam that is unscattered by the thin TEM sample, the resulting image is known as a bright field (BF) image. If the objective aperture excludes the unscattered portion of the incident beam, the resulting image is called a dark field (DF) image. By including the unscattered portion of the incident beam, one of the primary contrast mechanisms in BF images is mass thickness contrast. Contrast mechanisms that are important in DF images include diffraction contrast and contrast due to defects and/or deviation from crystallinity in the sample. An electron detector (usually in the form of a phosphor screen, a CCD camera, or electron-sensitive film) is placed in the image plane for viewing the resulting image or scattering pattern. A selected area diffraction (SAD) aperture and a projector lens located between the objective lens and the image plane are used for viewing diffraction patterns. With the TEM operating in a normal BF or DF imaging mode, the size of the SAD aperture is chosen if diffraction pattern information is desired only from a specific location on the specimen. When the TEM is switched to diffraction mode, electrons that have been scattered through the same angle by the sample are focused to a point in the back focal plane of the TEM, and the projector lens serves to project an image of the back focal plane onto the image plane of the TEM to create a viewable diffraction pattern. The formation of a diffraction pattern on the image plane is typically accompanied by the use of a relatively large objective aperture and a reduction in strength in the intermediate lens(es). Analytical equipment such as an EDS detector or and electron energyloss spectroscopy (EELS) can also be found on some TEMs.
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9.2.2 The physics for atomic resolution lattice imaging 9.2.2.1 Phase contrast imaging Images in TEM are usually dominated by three types of contrast. First, diffraction contrast [5], which is produced due to a local distortion in the orientation of the crystal (by dislocations, for example), so that the diffracted intensity of the incident electron beam is perturbed, leads to contrast observed in bright-field image. The nanocrystals (NC) oriented with their low-index zone-axis parallel or nearly parallel to the incident beam direction usually exhibit dark contrast in the BF image that is formed by selecting the central transmitted beam. Since the diffraction intensities of the Bragg reflected beams are strongly related to the crystal orientations, this type of image is ideally suited for imaging defects and dislocations. For NC, most of the grains are defect-free in volume, while a high density of defects are localized at the surface or grain boundary. Thus, diffraction contrast can be useful for capturing strain distribution in NC whose sizes are larger than 15 nm. For smaller size NC, since the resolution of diffraction contrast is in the order of 1–2 nm, its application is limited. Phase contrast is produced by the phase modulation of the incident electron wave that transmits through a crystal potential [5], which is the dominant mechanism for high-resolution imaging. This type of contrast is sensitive to the atom distribution in the specimen and it is the basis of highresolution TEM. To illustrate the physics of phase contrast, we consider the modulation of a crystal potential to the electron wavelength. To show the phase contrast imaging, we use a very thin sample [Figure 9.6(a)], and consider the phase shift to the electron wave after transmission. When the electron goes through a crystal potential field, its kinetic energy is perturbed by the variation of the potential field, resulting in a phase shift with respect to the electron wave that travels in a space free of potential field. For a specimen of thickness d, the phase shift f is approximately Zd f sVp ðbÞ ¼ s
dzVðrÞ
Eq. (9-8)
0
where s ¼ p=lU0 , (x, y) are the lateral coordinates perpendicular to the incident beam direction, U0 is the acceleration voltage, and Vp(x, y) the thickness-projected potential of the sample. Therefore, from the phase
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point of view, the electron wave is modulated by a phase factor Cðx; yÞ ¼ exp½isVp ðx; yÞ
Eq. (9-9)
This is known to be the phase object approximation (POA), in which the sample acts as a phase grating filter, and its atomic distribution projected along the beam direction is directly captured in the electron phase [Figure 9.6(b)]. If the incident beam travels along a low-index zone-axis, the variation of Vp (b) across atom rows is a sharp function because an atom can be approximated by a narrow potential well and its width is on the order of 0.2–0.3 s. This sharp phase variation is the basis of phase contrast, is fundamental in atomic-resolution imaging in TEM. Finally, in mass-thickness or atomic number produced contrast, atoms with different atomic numbers exhibit different powers of scattering. If the
Figure 9.6 Abbe’s theory of image formation in a one-lens transmission electron microscope.
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image is formed by collecting the electrons scattered to high-angles, the image contrast would be sensitive to the average atomic number along the beam direction. This type of contrast is less useful for analysis of nanoparticles.
9.2.2.2 Image formation As introduced above, phase contrast is fundamental in high-resolution imaging. We now introduce the image formation process that is about the information transfer of the electron phase through the optical system in TEM. Image formation in TEM is analogous to that in an optical microscope [6]. For easy illustration, a TEM is simplified into a single lens microscope, as shown in Figure 9.6, in which only a single objective lens is considered for imaging and the intermediate lenses and projection lenses are omitted. This is because the resolution of the TEM is mainly determined by the objective lens. The entrance surface of a thin foil specimen is illuminated by a parallel or nearly parallel electron beam. The electron beam is diffracted by the lattice planes of the crystal, forming the diffracted beams which are propagating along different directions. The electron–specimen interaction results in phase and amplitude changes in the electron wave that are determined by quantum mechanical diffraction theory. For a thin specimen and high-energy electrons, the transmitted wave function Y(x, y) at the exit face of the specimen can be assumed to be composed of a forward-scattered wave. The propagation through the objective lens is the main source of nonlinear information transfer in TEM. The diffracted beams will be focused in the back-focal plane, where an objective aperture could be applied. An ideal thin lens brings the parallel transmitted waves to a focus in the back focal plane. Waves leaving the specimen in the same direction (or angle u with the optic axis) are brought together at a point on the back focal plane, forming a diffraction pattern. The electrons scattered to angle u experience a phase shift introduced by the chromatic and spherical aberrations of the lens, and this phase shift is a function of the scattering angle, thus, the diffraction amplitude at the back-focal plane is modified by c0 ðuÞ ¼ cðuÞ exp½ixðuÞ
Eq. (9-10)
where c (u) is the Fourier transform of the wave C(r) at the exit face of the specimen, u is the reciprocal space vector that is related to the scattering angle by u = 2 sin u/l, and x(u) is determined by the spherical aberration
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coefficient Cs of the objective lens and the lens defocus Df xðuÞ ¼
p Cs l3 u4 pDf lu2 2
Eq. (9-11)
where l is the electron wavelength. The exp[ix(u)] represents the distortion of the wave by the non-linear information transfer characteristic of the optical system. The chromatic aberration arises from the change in focal length as a result in energy fluctuation of the incident electron beam. The spherical aberration is due to the dependence of the focal length on the electron scattering angle u. From simple optics, a change in focal length changes the phase of the electron beam. Thus, the aberration and defocus of the lens modulate the phases of the Bragg beams scattered to different angles. In the electron diffraction plane, there are many beams that have been scattered by the sample and they carry the phase and amplitude information from the sample. The electron image is the result of interference among the beams scattered to different angles, and this interference pattern is affected by the phase modulation introduced by the aberrations of the objective lens. The image is calculated according to Iðx; yÞ ¼ jCðx; yÞ tobj ðx; yÞj2
Eq. (9-12)
where indicates a convolution calculation of (x, y), tobj (x, y) is the inverse Fourier transform of the phase function exp[ix(u)]. The convolution of the lens transfer function introduces the non-linear information transfer characteristics of the objective lens, leading to complexity in image interpretation. It is apparent that the phase information is contained in the image, and the problem is how to interpret the image.
9.2.2.3 Image interpretation of very thin samples Image interpretation is very important in TEM. In a HRTEM image, one usually wonders if the atoms are in darker or brighter contrast. To answer this question, we adopt the weak scattering object approximation (WPOA), which assumes that the scattering power of the sample is so weak so that the phase modulation is small. If the specimen is so thin that the projected potential satisfies jsVp ðx; yÞj<<1; from Eq. (9-9), the phase grating function is approximated by Cðx; yÞ1 þ isVp ðx; yÞ
Eq. (9-13)
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From Eq. (9-12) and ignoring the s2 term, the image intensity is calculated by Iðx; yÞ1 2sVp ðx; yÞts ðx; yÞ
Eq. (9-14)
where ts ðx; yÞ ¼ Im½tobj ðx; yÞ: The second term in Eq. (9-14) is the interference result of the central transmitted beam with the Bragg reflected beams. Any phase modulation introduced by the lens would result in contrast variation in the observed image. To reveal the true atomic scale structure of the sample, the experimental condition has to be chosen in such a way that the ts(x, y) function is a sharp peak function and it can be approximated by a delta function. It has been found that by choosing the defocus to be D f ¼ ½4=3Cs l1=2 , which is known as the Scherzer defocus, ts(x, y) is approximated to be a negative Gaussian-like function with a small oscillating tail. Thus, the image contrast using the WPOA is directly related to the two-dimensional thicknessprojected potential of the crystal, and the image reflects the projected structure of the crystal and the atoms show dark contrast. This is the basis of structure analysis using high-resolution TEM. On the other hand, the contrast of the atom rows is determined by the sign and real space distribution of ts(x, y). Therefore, the image contrast in HRTEM is critically affected by the defocus value. A change in defocus could lead to contrast reversal, which makes it difficult to match the observed image directly with the projection of atom rows in the crystal. This is one of the reasons that image simulation is a key step in quantitative analysis of HRTEM images. It must be pointed out that the WPOA is probably the simplest model for illustrating the physics in image formation, but it is not valid for a general case because the sample is usually thicker than we would like it to be. Quantitative analysis of high-resolution TEM image requires numerical calculations using full dynamic theory for electron scattering.
9.2.2.4 Dynamic theory and image simulation In practice, interaction between the incident electron and the specimen is rather complex and multiple scattering is inevitable. We usually need to use rigorous dynamic theory for image simulation. Here we introduce the fundamentals of image simulation. Image simulation needs to include two important processes: the dynamic multiple scattering of the electron in the crystal and the information transfer of the objective lens system. The dynamic diffraction process is to solve the Schro¨dinger equation under given boundary conditions. There are several approaches for performing
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Figure 9.7 (a) A schematic diagram showing the physical approach of the multislice theory for image and diffraction pattern calculations in TEM. (b) Transmission of electron wave through a thin crystal slice. (c) An approximate treatment of the wave transmission through a thin slice.
dynamic calculations [6], among which the multislice theory [7] and the Bloch wave theory are the most frequently used ones. For a finite size crystal containing defects and surfaces, the multislice theory is most adequate for numerical calculations. The multislice many-beam dynamic diffraction theory was first developed based on the physical optics approach. The crystal is cut into many slices of equal thickness Dz normal to the direction of the incident beam (Figure 9.7). When the slice thickness tends to be very small the scattering of each slice can be approximated as a phase object, the transmission of the electron wave through each slice can be considered separately if the backscattering effect is negligible, which means that the calculation can be made slice-by-slice. The defect and 3D crystal shape can be easily accounted for in this approach. The transmission of the electron wave through a slice can be considered as a two step process—the phase modulation of the wave by the projected atomic potential within the slice and the propagation of the modulated wave in ‘‘vacuum’’ for a distance Dz along the beam direction before striking the next crystal slice. The wave function before and after transmitting a crystal slice is correlated by Cðx; y; z þ DzÞ ¼ ½Cðx; y; zÞQðx; y; z þ DzÞPðx; y; DzÞ Eq. (9-15) where the phase grating function of the slice is zþDz Z
Qðx; y; z þ DzÞ ¼ exp½is
dz Vðb; zÞ z
Eq. (9-16a)
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which is given to account for the phase modulation introduced by the thin crystal slice. The propagation function is Pðb; DzÞ ¼
expðpiKjbj2 =DzÞ ilDz
Eq. (9-16b)
which represents the Fresnel propagation of the electron for a distance Dz in vacuum. The most important characteristic of this equation is that no assumption was made regarding the arrangement of atoms in the slices, so that the theory can be applied to calculation of the electron scattering in crystals containing defects and dislocations. This is the most powerful approach for NC. The next step is the information transfer through the objective lens system. By taking a Fourier transform of the exit wave function, the diffraction amplitude is multiplied by the lens transfer function exp(ix) E(u), where the defocus is a variable. The defocus value of the objective lens and the specimen thickness are two important parameters which can be adjusted to match the calculated images with the observed ones. Figure 9.8 shows systematic simulations of a decahedral Au particle in different orientations. The particle shape can only be easily identified if
Figure 9.8 Simulated images for a decahedral Au particle at various orientations and at foci of (A) Df = 42 nm and (B) Df = 70 nm. The Fourier transform of the image is also displayed (Courtesy of Drs. Ascencio and M. Jose-Yacaman).
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the image is recorded along the five-fold axis. The group A and group B images were calculated for two different defoci, exhibiting contrast reversal from dark atoms to bright atoms. In practice, with consideration of the effects from the carbon substrate, it is difficult to identify the particle shape if the particle orientation is off the five-fold axis.
9.3
Shapes of Nanocrystals
9.3.1 Polyhedral shapes Nanocrystals exhibiting distinctly different properties from bulk are mainly due to their large portions of surface atoms, and the size effect and possibly the shape effect as well. Since different energy exhibited by different crystallographic planes, a nanoparticle constituting a finite number of atoms is bounded by some lower energy crystal planes, thus it has a specific geometrical shape. Surface energies associated with different crystallographic planes are usually different. Take facecentered cubic structured metal as an example: a general sequence may hold for surface energy of, g{111} < g{100} < g{110}. Facets tend to form on the particle surface to increase the portion of the low-index planes. Therefore, for particles smaller than 10–20 nm, the surface is a polyhedron. Figure 9.9(a) shows a group of cubo-octahedral shapes as a function of the ratio, R, of the growth rate of the h100i to that of the h111i [8]. The fastest growth direction in a cube is h111i, the longest direction in the octahedron is the h100i diagonal, and the longest direction in the cubooctahedron (R = 0.87) is the h110i direction. The particles with 0.87 < R < 1.73 have {100} and {111} facets, which are named the truncated octahedral (TO). The other group of particles has a fixed (111) base with exposed {111} and {100} facets [Figure 9.9(b)]. An increase in the area ratio of {111} to {100} results in the evolution of particle shapes from a trianglebased pyramid to a tetrahedron. Imaging of facets and atoms on the facets of NC relies on the profile imaging technique. If a particle is oriented along a low-index zone axis, the distribution of atoms on the surface can be imaged in profile, and the surface structure is directly seen with the full resolution power of a TEM [9]. This is a powerful technique for direct imaging of the projected shapes of nanoparticles particularly when the particle size is small. With consideration of the symmetry in particle shapes, HRTEM can be used to determine the 3D shape of small particles although the image
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Figure 9.9 (a) Geometrical shapes of cubo-octahedral nanocrystals as a function of the ratio, R, of the growth rate along the h100i to that of the h111i. (b) Evolution in shapes of a series of (111) based nanoparticles as the ratio of {111} to {100} increases. The beginning particle is bounded by three {100} facets and a (111) base, while the final one is a {111} bounded tetrahedron. (c) Geometrical shapes of multiply twinned decahedral and icosahedral particles.
is a 2D projection of a 3D object. It usually requires at least two images recorded from different orientations to define the particle shape. We now take Co particles as an example to show the experimental details for particle shape determination [10]. Cobalt NC prepared from solution phase reduction of cobalt chloride in the presence of stabilizing agents has been determined by X-ray diffraction to exhibit the b-Mn structure (e-Co phase, space group P4132) [11] with a cubic unit cell of 20 atoms and 6.30 s on a side. Figure 9.10 shows an electron diffraction pattern recorded from a Co NC assembly. This diffraction pattern is consistent with the X-ray diffraction data reported previously with the most intense diffraction peaks appearing as {221}, {310}, and {311}. The three rings were enclosed by the objective aperture of the HRTEM, thus the atomic-scale lattice images are dominated by the interference among the three beams and the central transmitted {000} beam. The two-dimensionally projected shape of the Co nanocrystal is easily seen in the HRTEM images shown in Figure 9.11. From X-ray diffraction studies of the Co NC assembly, it is known that the (221) and (310) planes diffraction, but the interpretation of the image has to consider the structure of the e-Co phase. From the electron diffraction pattern, the dominant diffraction that will contribute to the images will be the {221} and
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Figure 9.10 Electron diffraction pattern recorded from the as-synthesized Co nanocrystals, which matches well to the intensities and indices for the b-Mn structure.
{310} reflections with the central transmitted beam. By matching the interplanar distances and plane-to-plane angles through the Fourier transform of the images, the NC facets can be directly linked to the {221} and {310} planes. The (221) and (310) reflection rings are almost inseparable in the electron diffraction pattern, but the angles among them are critical in identifying the facets. From the images shown in Figure 9.11 (a, b), where the electron beam is parallel to [62 1], the NCs are partially enclosed by the –(2 1 2), –(122), and (1 30) facets. When the electron beam is parallel to [001] [Figure 9.11(c)], the (3 10) and (1 30) facets are imaged edge-on. Along the [120] direction [Figure 9.11(d)], the (2 12) and (2 1 2) facets are imaged edge-on. These HRTEM images recorded from three different NC orientations are used to reconstruct the NC 3D shapes. Figure 9.12(a) shows a polyhedral model of the nanocrystal enclosed by –(2 1 2), –(122), –(1 30), –(310), –(2 12), and –(1 2 2) facets [11]. The structure can be simply constructed from a square based rod defined by the –(1 3 0) and –(310) facets, which is cut by the (2 1 2), (122), (2 12), and (1 2 2) facets at the top and by the (2 1 2), (122), (2 1 2), and (12 2) facets at the bottom. The projected shapes of the polyhedron along [62 5], [120], and [001] are given in Figure 9.12(b–d), respectively. These projections match well with the NC shapes observed in the images displayed in Figure 9.12. Using the model described here, the local orientation order in the self-assembly of Co NC has been successfully interpreted.
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Figure 9.11 Typical HRTEM images of the Co nanocrystals oriented along (a, b) [62 5], (c) [001] and (d) [120], showing the {221} and {310} facets. The inserts are the Fourier transforms of the corresponding images.
9.3.2 Twining structure and stacking faults Twining is one of the most common planar defects in NC, and it is frequently observed for fcc structured metallic NC possibly because it lowers the energy of the entire system. Twining is the result of two subgrains by sharing a common crystallographic plane, thus, the structure of one subgrain is the mirror reflection of the other by the twin plane. Figure 9.13(a) gives a HRTEM image of an FePt NC, showing the presence of a twin. Stacking faults are typical planar defects. Stacking faults are produced by a distortion to the stacking sequence of atom planes. The (111) plane stacking sequence of a fcc structure follows A–B–C–A–B–C–A–B–C–. If the stacking sequence is changed to A–B–C–A–B–A–B–C–, a stacking fault is created. Figure 9.13(b) shows an Au particle that contains twins and stacking faults near the twins. It is known that NC usually contains strain but no dislocation. Twins and stacking faults are probably created due the high strain energy in the volume.
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Figure 9.12 (a) Three-dimensional polyhedral shape of the Co nanocrystals constructed using the information provided by HRTEM images. (b–d) The projected shapes of the polyhedral model along [62 5], [120], and [001], respectively. (e, f) Monolayer close-packing of the polyhedra oriented in [62 5] and [120], respectively.
9.3.3 Multiply twinned particles—decahedron and icosahedron The two most typical examples of multiple twinned particles (MTP) are decahedra and icosahedra [12]. Starting from an fcc structured
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Figure 9.13 HRTEM images of (a) FePt and (b) Au nanocrystals having twin (T) and stacking fault (S) structures. The nanocrystals are oriented along [110] and the twin plane and stacking fault are parallel to the direction of the electron beam.
tetrahedron, a decahedron is assembled from five tetrahedra sharing an edge [Figure 9.14(a)]. If the observation direction is along the five-fold axis and in an ideal situation, each tetrahedron shares an angle of 70.5 , meaning that five of them can only occupy a total of 352.6 , leaving a 7.4 gap. Therefore, strain must be introduced in the particle to fill the gap. An icosahedron is assembled using 20 tetrahedra via sharing an apex [Figure 14(b, c)]. The icosahedral and decahedral particles are the most extensively studied twinned NC [13]. The easiest orientation for identifying the MTPs is along the five-fold symmetry axis. Figure 9.15(a) shows a TEM image recorded from a FePt nanoparticle that is made of five twinned sub-particles. The Fourier transform of the image clearly indicates the five-fold pattern.
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Figure 9.14 Atomic models of (a) decahedral, (b), and (c) icosahedral nanocrystals.
Figure 9.15 TEM images of decahedral FePt nanocrystals when the incident electron beam is parallel or nearly parallel to the fivefold symmetry axis. The strain field introduced by the five-fold twins is apparent in (a). (b) A Fourier transform of the image shown in (a) clearly reveals the fivefold symmetry.
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Nanodiffraction
Electron diffraction is a powerful tool for materials research ever since the invention of TEM. A popular experimental set up for electron diffraction is the so called selected area diffraction (SAD). Using parallel illumination, the area of interest is selected by placing an aperture in the image plane of the objective lens. Because of the physical size of the aperture, the lens aberration, and diffraction, the practical selected area by the aperture is limited to micrometer level. For conventional materials with a grain size of 10–100 mm, the diffraction pattern is a spot pattern. However, for nanostructured materials with a grain size of, say 20 nm, the diffraction pattern by the SAD method becomes a ring pattern (also called powder pattern) because so many grains are included in the aperture. Such a ring pattern contains rich information about the structure of the specimen and can be used to identify uniquely a known phase [14]. However, it is occasionally necessary to obtain spot pattern from a single grain of nanometer dimension for applications such as determination of crystal orientation, crystal structure of modulated phase, and epitaxy. This is the nanodiffraction technique, e.g. electron diffraction from a nanosized area of a specimen.
9.4.1 Optics for nanodiffraction Unlike SAD, nanodiffraction is realized by focusing the electron beam on the specimen. The experimental set up for nanodiffraction is schematically shown in Figure 9.16(b), in comparison with SAD in Figure 9.16(a). The area contributing to diffraction is controlled by the probe size. Since the probe size can be as small as 0.2 nm, nanodiffraction can therefore be readily achieved from an area smaller than the size of the unit cell.
Figure 9.16 Schematic illustration of the experimental setup for (a) SAD and (b) nanodiffraction.
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When the probe is focused, a minimum probe size can be obtained. The diffraction spots in the diffraction pattern are disks instead of sharp spots. The diameter of the disk is defined by the semi-convergence angle of the electron beam. This could cause overlapping of spots if the unit cell is large.
9.4.2 Experimental procedure to obtain a nanodiffraction pattern The procedure for carrying out nanodiffraction is outlined below [15]. 1. Choose a proper probe size: a probe size smaller than half of the grain size under study is preferred. The smaller the probe size, the less chance there is to encounter a defect. However, if the probe is too small, the diffraction pattern would be too dark to be seen. Another point that needs to be mentioned is that the probe size must be a few times larger than the unit cell in order to preserve the symmetry of the crystal in the diffraction pattern. 2. Align the high voltage center and current center. Both are important for obtaining a good probe. 3. Correct astigmatism of the condenser lens in image mode by making the electron beam circular. 4. Correct astigmatism of the objective lens. This can be done using a larger spot size. This alignment ensures that a minimum spot size can be obtained. 5. Focus the image. This is done by setting the objective current at a desired value through adjusting the z control (the vertical translation of the specimen). Fine focus is done by adjusting the objective current. 6. Find the zone axis. Going through the above procedure will generate a good probe. Now going to the diffraction mode will generate a diffraction pattern. Although tilting can still be used to find the proper zone axis, large angle tilting is limited by the size of the grain and can cause overlapping with adjacent grains. Therefore, finding the zone axis is done by alternately probing a grain while watching the diffraction pattern and making appropriate adjustments to specimen position and orientation until a grain with the desired zone axis is found.
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7. Expose the film. A shorter exposure time of 1–2 seconds is preferred. This can be done by using a smaller camera length. The trick to taking good quality nanodiffraction patterns is to reduce the beam illumination time on the crystal under examination. A nanoprobe placed on crystals can cause very fast contamination. The contaminants are light elements such as carbon. The clear diffraction pattern can disappear in a few seconds. The contamination can come from poor vacuum or from the specimen surface. Using a cold specimen stage is an effective way to reduce specimen contamination. The contaminant atoms can be ‘‘frozen’’ at the specimen surface. Heating the specimen to 273 K (100 C) is also occasionally helpful to eliminate contaminants from the specimen surface.
9.5 Scanning Transmission Electron Microscopy A dedicated scanning transmission electron microscope (STEM) is related to the TEM via the principle of reciprocity in optics: given an imaging system consisting of a source, a series of lenses and apertures, and a detector, the same image can be obtained by interchanging the positions of the source and the detector (Figure 9.17). (The term ‘‘dedicated’’ is used to differentiate between an electron microscope designed primarily to be used as a STEM from a TEM with a STEM mode.) In a TEM, the electron source is typically regarded as a point source, which corresponds to a point detector or a ‘‘point image’’ in a STEM. Therefore, in order to create a 2D image in a STEM, it is necessary to scan the beam across the specimen. The advantage of using a dedicated STEM in nanoscale studies of materials lies in the very small probe that is formed by the gun lens— condenser lens—objective lens/aperture combination and the high brightness of the electron source.
9.5.1 Instrumentation Because the STEM and TEM are related by the principle of reciprocity, many of the lenses and apertures used in TEM retain their positions relative to the specimen, although in the STEM they may serve a different function (see Figure 9.17). One key difference is the scan coils located prior to the beam’s entry into the objective lens in STEM that is used for
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Figure 9.17 Schematic diagram showing the relationship between STEM and TEM. The sequence of lenses and apertures traversed by an electron in a TEM is shown on the left-hand side of the diagram, reading downward. An electron in a STEM sees the sequence of lenses and apertures indicated on the right-hand side, reading upward (note that some STEMs do not have post-specimen lenses). The optic axis is shown as a vertical line in the center of the diagram.
rastering the beam across the specimen. The small beam diameter produced in STEM necessitates a high brightness electron source for sufficient signal. Field emission sources such as crystalline tungsten tips are frequently used. Another major difference between a dedicated STEM and a TEM lies in the electron detectors (and therefore imaging modes) that are typically used. In a TEM, the objective aperture determines whether a BF or DF image is acquired and usually the same detector is used for acquiring both types of images. This implies that BF and DF images cannot be
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obtained simultaneously in TEM. In a typical dedicated STEM, however, there are separate BF and annular DF (ADF) detectors (Figure 9.18). This allows for the simultaneous acquisition of BF and ADF images from the specimen with each image containing different information about the specimen. Spectrometers and detectors for analytical work (e.g. EDS and EELS) can also be integrated into a dedicated STEM in a manner similar to that used in conventional TEM microanalysis.
9.5.2 Imaging modes Both BF and DF imaging modes similar to that in TEM are available in STEM. Electrons that are unscattered by the specimen or are scattered through a small angle (a few mrad) by the specimen can pass through the hole in the center of the ADF detector and proceed on to the BF detector. A collector aperture located ahead of the BF detector serves a purpose analogous to the objective aperture in TEM by limiting the angular spread of the electrons contributing to the BF image. The hole in the ADF detector itself can also be used as a collector aperture for BF imaging. On-axis ‘‘conventional’’ DF images can be obtained from the BF detector in STEM by using a post-specimen set of coils (Grigson coils) to deflect the 000 beam away from the optic axis and scan the desired scattered beams onto the BF detector. The position of the objective aperture prior to the beam’s entry into the specimen and the separation of the BF and ADF detectors in a STEM also gives rise to a different method of obtaining DF images than that used in TEM. In TEM, the specimen is located between the electron source and the objective aperture, and one of the primary functions of the objective aperture is to exclude the 000 beam while selecting the desired diffracted beam(s) to be used in creating a conventional DF image. However, in STEM, the objective aperture is located between the electron source and the specimen, and it plays a key role in determining the size of the probe incident upon the specimen. The ADF detector typically receives electrons that have undergone large angle scattering (50–200 mrad) from the specimen; a plot of the probe position on the specimen vs. the intensity that is read from this detector is the ADF image. Unlike TEM DF images that are usually formed using a small sector of reciprocal space, ADF images incorporate electrons scattered by the specimen into a cone covering the entire 360 polar angle range and a range of azimuthal angle that depends on the angular extent and location
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Figure 9.18 Schematic diagram showing a typical dedicated analytical STEM. Dotted arrows show examples of electron trajectories in the STEM.
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of the detector. A mask can be placed over part of the ADF detector to obtain the desired azimuthal angle range. Electrons scattered into the region intercepted by the ADF detector include atomic number-sensitive scattering from the specimen, specimen defects, strain, phonons, and intensity from Laue zones. Thus a complete interpretation of ADF images takes into account these effects. The physical separation of the BF and ADF detectors leads to another advantageous feature of STEM: BF and ADF images can be obtained simultaneously from a sample. This feature is extremely useful in cases where information from BF and ADF imaging is required from exactly the same location on the specimen, which is often the case in nanoscale studies of materials. Moreover, complementary information can often be obtained from the simultaneous BF and ADF images of a specimen. For example, ADF images tend to be more sensitive to differences in atomic number and less prone to thickness-dependent contrast reversal than BF images. Because diffraction effects are significant in ADF images, a BF/ ADF image pair can reveal specimen features such as small amorphous regions. Therefore, BF/ADF image pairs allow for a wealth of information to be extracted from a sample.
9.5.3 Composition-sensitive imaging Two of the most common analytical techniques available on STEMs and TEMs are EELS and EDS; both of these methods are able to produce composition maps of specimens using STEM. In a STEM, an EEL spectrometer is located on the optic axis between the ADF detector and the BF detector. Incident electrons scattered by electrons in the specimen can undergo a characteristic energy loss that is derived from the difference between the binding energies associated with different shells in a given element. The scattered electrons are discriminated according to their energy loss by a bending magnet in the EEL spectrometer that acts on the electrons in a manner analogous to the way a prism acts on light. Electrons having a desired value of energy loss can be directed into the EEL spectrometer through the application of an offset voltage or by changing the current in the spectrometer magnet. The energy resolution of the EELS spectrum is determined by the width of the spectrometer slit and/or by the properties of the detector (such as in the case where a CCD detector is used). By selecting the appropriate value of energy loss and energy resolution, electrons having an energy loss characteristic of particular element are received
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by the detector and an image can be formed by plotting the intensity of the EELS signal as a function of probe position on the sample. This type of image is called an energy filtered image, where areas of high intensity on the image correspond to relatively large concentrations of the particular element. Quantitative composition interpretation of an energy filtered image depends on knowledge of the scattering crosssection of the relevant EELS edge, the sample thickness, and the energy resolution. STEMs equipped with EDS and the appropriate software are also capable of producing composition maps. Using a strategy similar to energy filtered imaging, software designed to produce EDS composition maps plot the intensity of a characteristic X-ray peak as a function of probe position to map out the concentration of a specific element in a sample. A phenomenon called coherent bremsstrahlung is a type of channeling that can occur when electrons in the incident beam enter a crystalline sample. Depending on the incident electron energy and the incident angle, electrons can interact with the periodic structure of the sample to produce spurious X-rays peaks in the EDS spectrum [16]. Because the diameter of the STEM probe is on the order of interatomic spacing, the probe may channel between columns of atoms in a crystalline sample if the sample is oriented in an appropriate manner with respect to the electron beam. A method called ALCHEMI [17] takes advantage of the orientation dependence of an atom’s ability to become ionized in a crystalline sample. Since characteristic X-rays are often emitted when an ionized atom seeks to lower its energy, the intensity of a given characteristic X-ray peak is expected to vary as a function of sample orientation. Therefore, ALCHEMI represents another way in which X-rays can be used to give localized composition information about a sample.
9.5.4 Nanoscale microanalysis As mentioned earlier, the orientation of crystalline samples in STEM can be an important factor in acquiring nanoscale analytical information using a technique such as ALCHEMI. Because STEM and TEM examine samples in projection, it is often also beneficial to use very thin samples for STEM or TEM to avoid any ‘‘overlap’’ effects that can occur when one nanoparticle is located directly above another nanoparticle along the beam direction. Moreover, thinner specimens reduce the likelihood of multiple scattering events and subsequently the beam broadening that can diminish analysis spatial resolution.
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Given this preference for thin samples, EELS-based analytical methods tend to be favored over EDS-based analytical methods for studies of nanomaterials. Among the reasons for this are: (1) the generation of electrons with characteristic energy loss is more efficient than the generation of characteristic X-rays and (2) the interpretation of EELS data is considerably simplified when the sample thickness is less than the mean free path of the incident electron in the sample [18]. Nevertheless, the availability of more than one analytical method on an electron microscope can be very useful for discerning composition information from samples that contain elements whose characteristic edges overlap in a given analytical method or where detection of certain elements is difficult or impossible. An example of this is the inability of EDS to detect elements having atomic number Z < 5; EELS is able to detect these elements as long as they are present in the specimen in sufficient quantities.
9.6
In-situ TEM and Nanomeasurements
The presence of a large percentage of surface atoms in nanomaterials results in surface dominated phenomena. The large mobility of the surface atoms and the faceted shapes of the NC that are not formed under thermodynamic equilibrium conditions could have very interesting physical, chemical and electronic structures of fundamental interests and technological importance. TEM is an ideal tool for tracing the in-situ behavior of NC induced by temperature and/or externally applied fields. The in-situ experiments can be carried out on the same nanocrystal over a large range of temperature, giving the possibility of examining the temperature induced shape transformation, structural evolution, melting and surface phenomena. This section focuses on the several types of in-situ TEM techniques for probing the unique properties of NC.
9.6.1 Thermodynamic properties of nanocrystals The thermodynamic properties of NC depend strongly on not only the crystal size but also their shapes [19]. The thermodynamic properties of Au nanorods are an example. A series of in-situ TEM images recorded for the same specimen region as the temperature was increased continuously from room temperature to 923 K show the formation process of Au nanoparticles on the carbon support in Figure 9.19(a–h). The nucleation started at 473 K as shown in Figure 9.19(b) and it was only observed by
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TEM at 488 K shown in Figure 9.19(c). It is clear that as the temperature reached 433 K the structure of the micelles around the rods was found to collapse in solution and no visible change was observed in the morphology of the nanorods. At T = 488 K [Figure 9.19(c)], small nuclei of gold nanoparticles began to form on the surface of the carbon substrate. A small increase in temperature to 493 K [Figure 9.19(d)] resulted in a rapid growth of these small particles on the carbon substrate. Further increase in temperature to 513 K led to the growth of the particles, and the stable particle size was reached at T = 600 K. At T > 513 K, the widths of the nanorods increased significantly, while their lengths remained the same [compare the rod marked by an arrow in Figure 9.19(a, e, h)]. This is due to surface melting that induces shape transformation, so that the thickness of the nanorods decreased when placed onto the substrate as a ‘‘liquidlike’’ material. It is noticed that the density of the particles in the regions adjacent to the Au rods is approximately the same as the particles in the regions without rods. We propose that the formation of small Au nanoparticles in Figure 9.19 (d–h) is the result of surface sublimation from gold nanorods as well as the gold atoms contained in the solution deposited onto the carbon substrate. The sublimation of gold atoms from the surface is supported by following observation. Shown in Figure 9.20 is a series of TEM images recorded from the same area in which the shrinkage of a particle indicated by an arrowhead is visible. Such a drastic reduction in size could be the result of surface sublimation, and more interestingly, this phenomenon occurs at a relatively low temperature. A model can be proposed to understand the observed phenomena. The initial rapid growth of the Au particles is due to the contribution of the diffusion of atoms on the substrate surface. This process is assumed to follow the hit- and -stick model and is directly related to the intersection length of the particle with the substrate surface. On the other hand, the atoms on the surface of the Au particles can sublime, and their sublimation rate is directly proportional to the exposed surface area of the particle. Accordingly, for a spherical particle of radius r, partially embedded in the substrate as shown in Figure 9.21(c), the net growth of the number of atoms (nr) in the particle is given by: dnr ¼ ð2pr sin uÞN0 kd 4pr2 ars ks dt
Eq. (9-17)
where u is the angle that specifies the degree of contact of the particle with the substrate; kd is the diffusion rate constant of the atoms adsorbed
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Figure 9.19 (a–f) show the result of the sublimation, condensation, and diffusion of gold atoms from gold nanorods. A series of in-situ TEM images recorded for the same specimen region as the temperature was increased continuously from room temperature to 923 K, showing the formation process of Au small nanoparticles on the carbon support. The nucleation started at 473 K and it was only clearly observed by the TEM at 488 K shown in (b). At T > 513 K, the widths of the nanorods increased significantly, while their lengths remained the same (compare the rod marked by an arrow in (a), (e), and (f)). This is due to the surface melting which induces shape transformation, so that the thickness of the nanorods decreased when placed onto the substrate as a ‘‘liquid-like’’ material (note an increase in the width does not necessarily mean an increase in the volume).
on the substrate; N0 is the steady state concentration of the Au atoms on the surface; a is a factor representing the fraction of the exposed surface area; rs is the surface density of the particle; and ks is the sublimation rate constant. The direct condensation of Au atoms onto the particle surface can be accounted for by a proper choice of the a factor. Initially, the diffusion term is dominant, resulting in a rapid growth of the particle. As the particle grows in size, the sublimation term increases because of the r2 term. When the two terms are equal, a steady state is reached (dnr/dt = 0), achieving a maximum radius (rmax) at this temperature, which is given by rmax ¼
N0 kd sin u 2ars ks
Eq. (9-18)
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Figure 9.20 In-situ TEM images recorded as a function of time at 498 K (225 C), showing the shrinking of an Au particle indicated by an arrowhead at such a low temperature, indicating surface sublimation and diffusion. (a) t = 0; (b) t = 1.5 min; (c) t = 3.5 min; (d) t = 16 min.
Using the relation nr = 4/3 ar3r0, where r0 is the volume density of Au atoms, and the boundary condition r = 0 at t = 0, the solution of Eq. (9-17) relating r to t is given by:
rmax rmax ln r ¼ ½ars ks =r0 t rmax r
Eq. (9-19)
The kinetics of Au particle growth was determined using in-situ TEM at 498 K, as soon as the newly formed particles were observed in TEM. From the kinetic curve given in Figure 9.22(a), the particles seem to experience a rapid growth in the first 500 seconds, and then the size reached a constant value. By setting the left-hand side of Eq. (9-19) equal to Y and using the
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Figure 9.21 (a) The dependence of the steady state particle radii (rmax) formed at different specimen temperatures for particles located at different distances from the Au rods (diamond shapes are for the closest to the rod and triangles are for the furthest away). The size of the particles located closest to the rod (50 nm) drops sharply at 650 K. Considering the specimen drift at higher temperature and the effect of carbon substrate on the image contrast, the newly formed particles were seen in TEM only when their sizes were larger than 2 nm. ^, +, and r represent the particles at distances of 50, 100, and 200 nm, respectively, from the gold nanorods. (b) The ln(rmax) versus 1/T plot in the low-temperature range, the slopes of which gives the difference between the activation energy of diffusion and the sublimation energy Q of the gold atoms. (c) A sketch showing the growth process of the small gold cluster on the TEM substrate. Growth kinetics of the small particles at a constant temperature of T = 498 K.
experimental data in Figure 9.22(a), the plot of Y versus time can be used to calculate the activation energy Q for sublimation of gold atoms, which is Q = 1.39 – 0.01 eV. The crystallographic shape of the Au nanorods has been investigated using HRTEM to understand why the gold atoms can sublimate at lower temperature. The nanorods have been found to exhibit the unstable {110} facets (Figure 9.23), in addition to the {100} and {111} facets present in the spheres [20]. For the face-centered Au NC, the surface energy follows a relationship of gf110g > gf100g > gf111g. The presence of a significant percentage of gold atoms on the {110} surface suggests that the nanorod is relatively thermodynamically unstable. The {111} and {100} faceted
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Figure 9.22 (a) Shows the particle radii as a function of time. (b) Shows a comparison of the theoretically calculated Y versus time curves according to Eq. (9.19) with the experimentally observed data points. From the slopes of the lines, the sublimation energy Q is calculated.
Au spheres have lower surface energy. Thus, their atoms may not sublime at relatively low temperatures. Therefore, the sublimation of Au atoms from the nanorods at lower temperatures is due to the shape of the nanorods, which has unstable {110} surfaces. Study of shape-controlled NC has a great interest from a catalysis viewpoint. Platinum nanoparticles with a high percentage of cubic-, tetrahedral-, and octahedral-like shapes, respectively, have been synthesized by changing the ratio of the concentration of polymer capping material (polyacrylate) to that of Pt2+ being reduced by H2 from K2PtCl4 at room temperature [21]. The polymer acts not only as the passivative protection layer of the NC, but it is also the key factor in controlling their shapes [22, 23]. The growth mechanism of the shape controlled Pt NC is attributed to a kinetic process in which most of the nuclei are tetrahedral, while a shape transformation from tetrahedral to cubic occurs as the particles grow [24]. The in-situ behavior of the Pt NC has also been studied by TEM [25]. The surface capping polymer was removed by annealing the specimen to a temperature of 453–523 K (180–250 C), while the particle shape showed no change up to 623 K (350 C). In a temperature range of 623– 723 K (350–450 C), a small truncation occurred in the particle shape
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Figure 9.23 HRTEM image showing the {110} and {100} facets of the Au nanorods. The electron beam is parallel to [110].
but no major shape transformation. The particle shape experienced a dramatic transformation into a spherical-like shape when the temperature was higher than 773 K (500 C); the macroscopic surface melting occurred at 873 K (600 C), much lower than the melting point of bulk Pt (2046 K or 1773 C).
9.7 Electron Energy-loss Spectroscopy of Nanoparticles Chemical microanalysis is an important field in TEM. Under the impact of an incident electron beam, the electrons bounded to the atoms in the specimen may be excited either to a free electron state or to an unoccupied energy level with a higher energy. The quantum transitions associated
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with these excitations will emit photons (or X-rays) and electrons such as SEs, Auger electrons, and ionized electrons. These inelastic scattering signals are the fingerprints of the elements that can provide quantitative chemical and electronic structural information.
9.7.1 Quantitative nanoanalysis Energy dispersive X-ray spectroscopy [1] and EELS [18] in TEM have been demonstrated as powerful techniques for performing microanalysis and for studying the electronic structure of materials. Atomic inner shell excitations are often seen in EELS spectra due to a process in which an atom-bound electron is excited from an inner shell state to a valence state accompanied by incident electron energy loss and momentum transfer. This is a localized inelastic scattering process, which occurs only when the incident electrons are propagating in the crystal. Figure 9.24 shows an EELS spectrum acquired from a superconducting compound La0.5Sr0.5CoO3, where the ionization edges of O K, Co–L, and La–M are present in the displayed energy-loss range. Since the innershell energy levels are the unique features of the element, the intensities of the ionization edges can be used effectively to analyze the chemistry of the specimen.
Figure 9.24 An EELS spectrum acquired from La0.5Sr0.5CoO3 showing the application of EELS for quantitative chemical analysis.
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After subtracting the background, integration is performed to the ionization edge for an energy window of width D that takes into account the threshold energy. Thus, the intensity of oscillation at the near edge region is flattened, and the integrated intensity is dominated by the properties of single atoms. This type of information is most useful in material analysis and the integrated intensity is given by IA ðDÞ I0 ðDÞsA ðD; bÞnA d
Eq. (9-20)
where I0(D) is the integrated intensity of the low-loss region including the zero-loss peak for an energy window D; sA(D, b) is the energy and angular integrated ionization cross-section. In imaging mode, b is mainly determined by the size of the objective aperture or the upper cut-off angle depending on which is smaller. In diffraction mode, the b angle is determined not only by the size of the EELS entrance aperture and the camera length but also by the beam convergence. In general, the width of the energy window is required to be more than 50 eV to ensure the validity of Eq. (9-20), and D = 100 eV is an optimum choice. If the ionization edges of two elements are observed in the same spectrum, the chemical composition of the specimen is nA IA ðDÞsB ðD; bÞ ¼ nB IB ðDÞsA ðD; bÞ
Eq. (9-21)
This is the most powerful application of EELS because the spatial resolution is almost entirely determined by the size of the electron probe. The key quantity in this analysis is the ionization cross-section. For elements with atomic numbers smaller than 14, the K edge ionization cross-section can be calculated using the SIGMAK program [18], in which the atomic wave function is approximated by a single-electron hydrogen-like model. The ionization cross-section for elements with 13 < Z < 28 can be calculated using the SIGMAL program [19]. For a general case, the ionization cross-section may need to be measured experimentally using a standard specimen with known chemical composition.
9.7.2 Near edge fine structure and bonding in transition metal oxides The energy-loss near edge structure (ELNES) is sensitive to the crystal structure. This is a unique characteristic of EELS and in some cases it can serve as a ‘‘fingerprint’’ to identify a compound. In EELS, the L ionization
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edges of transition-metal and rare-earth elements usually display sharp peaks at the near edge region (Figure 9.25), which are known as white lines. For transition metals with unoccupied 3d states, the transition of an electron from 2p state to 3d levels leads to the formation of white lines. The L3 and L2 lines are the transitions from 2p3/2 to 3d3/23d5/2 and from 2p1/2 to 3d3/2, respectively, and their intensities are related to the unoccupied states in the 3d bands. Numerous EELS experiments have shown that a change in valence state of cations introduces a dramatic change in the ratio of the white lines, leading to the possibility of identifying the occupation number of the 3d orbital using EELS. EELS analysis of the valence state is carried out in reference to the spectra acquired from standard specimens with known cation valence states. Since the intensity ratio of L3/L2 is sensitive to the valence state of the corresponding element, if a series of EELS spectra are acquired from several standard specimens with known valence states, an empirical plot of these data serves as the reference for determining the valence state of the element present in a new compound [26–29]. The L3/L2 ratios for a few standard Co compounds are plotted in Figure 9.26(a). EELS spectra of Co-L2,3 ionization edges were acquired from CoSi2 (with Co4+), Co3O4 (with Co2.67+), CoCO3 (with Co2+) and CoSO4 (with Co2+). This is the basis of our experimental approach for measuring the valence states of Co or Mn in a new material. Determining the crystal structure of nanoparticles is a challenge particularly when the particles are smaller than 5 nm. The intensity maxima observed in the X-ray or electron diffraction patterns of such small
Figure 9.25 EELS spectrum acquired from cobalt oxide showing the Co-L3 and Co-L3 white lines. The five windows pasted in the Co-L edge are to be used for extracting the image formed by the ratio of white lines.
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Figure 9.26 Plots of the intensity ratios of L3/L2 calculated from the spectra acquired from (a) Co compounds and (b) Mn compounds as a function of the cation valence. A nominal fit of the experimental data is shown by a solid curve.
particles are broadened due to the crystal shape factor, and greatly reduce the accuracy of structure refinement. The quality of the high-resolution TEM images of the particles is degraded because of the strong effect from the substrate. This difficulty arose in our recent study of CoO NC whose shape is dominated by tetrahedra of sizes smaller than 5 nm [30].
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Figure 9.27 Comparison of EELS spectra of Co-L2 and Co-L3 ionization edges acquired from Co3O4 and CoO standard specimens and the synthesized nanocrystals, proving that the valence state of Co is 2+ in the nanocrystals. The full width at half maximum of the white lines for the Co3O4 and CoO standards is wider than that for the nanocrystals due to size effect.
Electron diffraction indicates the crystal has an fcc-type cubic structure. The synthesized NC are likely to be CoO. EELS is used to measure the valence state of Co. Figure 9.27 shows a comparison of the spectra acquired from Co3O4 and CoO standard specimens and the synthesized NC. The relative intensity of the Co-L2 to Co-L3 for the NC is almost identical to that for CoO standard, while the Co-L2 line of Co3O4 is significantly higher, indicating that the Co valence in the NC is 2+, confirming the CoO structure of the NC.
9.8 Energy Dispersive X-ray Microanalysis (EDS) X-rays emitted from atoms represent the characteristics of the elements and their intensity distribution represents the thickness-projected atom
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Figure 9.28 EDS spectrum acquired from a specimen of CdSe nanosaws. The copper signal came from the TEM grid.
densities in the specimen. This is the basis for EDS which has played an important role in microanalysis, particularly for heavier elements. EDS is a key tool for identifying the chemical composition of a specimen. A modern TEM is capable of producing a fine electron probe of smaller than 2 nm, allowing direct identification of the local composition of an individual nanocrystal. Shown in Figure 9.28 is an EDS spectrum acquired from a sample of CdSe nanosaws [31], from which the chemical composition of the nanosaw structures is determined.
9.9
Summary
There are several important developing directions in TEM-related techniques, including but not limited to (1) moving toward 0.1 nm image resolution using image processing or Cs corrector, (2) electron holography, (3) energy-filtered electron imaging and diffraction, (4) quantitative electron diffraction and imaging, (5) high-energy-resolution spectroscopy, (6) angstrom probe microscopy and spectroscopy, (7) environmental and in-situ microscopy, (8) in-situ nanoscale property measurements, and (9) analysis of real devices. Transmission electron microscopy and associated techniques are powerful tools for characterization of nanophase materials. This chapter mainly introduced high-resolution imaging in TEM and some newly developed techniques, such as electron energy filtering. High-spatial resolution analysis is vitally important for solving many of the practical problems of nanomaterials. Spectroscopy analysis of solid state effects and valence states mapping are new directions of quantitative microscopy.
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In-situ TEM is anticipated to be important for characterizing and measuring the properties of individual nanoparticles, from which the structure–property relationship can be clearly registered to a specific nanoparticle/structure. An emphasis has been placed on new developments in TEM for in-situ nanomeasurements of the mechanical and electrical properties of individual nanostructures, aiming to correlate the measured properties with the nanostructure. This is a new direction in TEM and it is important for characterizing nanophase materials. Therefore, TEM is truly a versatile tool not only for crystallographic and chemical structure analysis, but also a powerful approach for nanomeasurements.
References 1. J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, A. D. Romig, Jr., C. E. Lyman, C. Fiori and E. Lifshin, Scanning Electron Microscopy and X-ray Microanalysis, 3rd Edition, Kluwer Academic/Plenum Publishers, New York (2003). 2. Z. W. Pan, Z. R. Dai and Z. L. Wang, ‘‘Nanobelts of Semiconducting Oxides,’’ Science 291, 1947 (2001). 3. X. D. Wang, C. J. Summers and Z. L. Wang, ‘‘Large-Scale Hexagonal-Patterned Growth of Aligned ZnO Nanorods for Nano-Optoelectronics and Nanosensor Arrays,’’ Nano Lett. 3, 423 (2004). 4. C. W. Oatley, The Scanning Electron Microscope, Cambridge University Press, Cambridge, UK (1972). 5. J. M. Cowley, in High Resolution Transmission Electron Microscopy and Associated Techniques, P. Buseck, J. M. Cowley and L. Eyring (Eds.), Oxford University Press, Oxford, UK (1988). 6. Z. L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and Imaging, Plenum Press, NY (1995). 7. J. M. Cowley and A. F. Moodie, ‘‘The Scattering of Electrons by Atoms and Crystals. I. A New Theoretical Approach,’’ Acta Crystallogr. 10, 609 (1957). 8. Z. L. Wang, ‘‘Transmission Electron Microscopy of Shape-Controlled Nanocrystals and Their Assemblies (Invited review article),’’ J. Phys. Chem. B 104, 1153 (2000). 9. D. J. Smith and L. D. Marks, ‘‘Direct Lattice Imaging of Small Metal Particles,’’ Phil. Mag. A 44, 735 (1981). 10. Z. L. Wang, Z. R. Dai and S. Sun, ‘‘Polyhedral Shapes of Cobalt Nanocrystals and Their Effect on Ordered Nanocrystal Assembly,’’ Adv. Mater. 12, 1944 (2000). 11. D. Dinega and M. G. Bawendi, ‘‘A Solution-Phase Chemical Approach to a New Crystal Structure of Cobalt,’’ Angew. Chem. Int. Edit. 38, 1788 (1999). 12. S. Ino, ‘‘Epitaxial Growth of Metals on Rocksalt Faces Cleaved in Vacuum. II. Orientation and Structure of Gold Particles Formed in Ultrahigh Vacuum,’’ J. Phys. Soc. Jpn. 21, 346 (1966). 13. L. D. Marks, ‘‘Experimental Studies of Small Particle Structures,’’ Rep. Prog. Phys. 57, 603 (1994).
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14. Y. Liu, R. A. Thomas, S. S. Malhotra, Z. S. Shan, S. H. Liou and D. J. Sellmyer, ‘‘Phase Formation and Magnetic Properties of Co-Rare Earth Magnetic Films,’’ J. Appl. Phys. 83, 6244 (1998). 15. Z. L. Wang, Z. Zhang and Y. Liu, ‘‘Transmission Electron Microscopy and Spectroscopy,’’ in Nanophase and Nanostructured Materials—Characterization, Volume II, pp. 29–97, Z. L. Wang, Y. Liu and Z. Zhang (Eds.), Kluwer Academic/Plenum Publishers, NY (2001). 16. J. C. H. Spence and G. Reese, ‘‘Pendellosung Radiation and Coherent Bremsstrahlung,’’ Acta Crystallogr. A42, 577 (1986). 17. J. C. H. Spence and J. Taftø, ‘‘ALCHEMI: A New Technique for Locating Atoms in Small Crystals,’’ J. Microsc. 130, 147 (1983). 18. R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, 2nd Edition, Plenum Press, NY (1996). 19. M. Mohamed, Z. L. Wang and M. A. El-Sayed, ‘‘Temperature-Dependent SizeControlled Nucleation and Growth of Gold Nanospheres,’’ J. Phys. Chem. A 103, 10255 (1999). 20. Z. L. Wang, R. P. Gao, B. Nikoobakht and M. A. El-Sayed, ‘‘Surface Reconstruction of the Unstable 110 Surface in Gold Nanorods,’’ J. Phys. Chem. B 104, 5417 (2000). 21. T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein and M. A. El-Sayed, ‘‘ShapeControlled Synthesis of Colloidal Platinum Nanoparticles,’’ Science 28, 1924 (1996). 22. R. L. Whetten, J. T. Khoury, M. M. Alvarez, S. Murthy, I. Vezmar, Z. L. Wang, C. C. Cleveland, W. D. Luedtke and U. Landman, ‘‘Nanocrystal Gold Molecules,’’ Adv. Mater. 8, 428 (1996). 23. Z. L. Wang, ‘‘Structural Analysis of Self-Assembling Nanocrystal Superlattices,’’ Adv. Mater. 10, 13 (1998). 24. J. M. Petroski, Z. L. Wang, T. C. Green and M. A. El-Sayed, ‘‘Kinetically Controlled Growth and Shape Formation Mechanism of Platinum Nanoparticles,’’ J. Phys. Chem. B 102, 3316 (1998). 25. Z. L. Wang, J. Petroski, T. Green and M. A. El-Sayed, ‘‘Shape Transformation and Melting of Cubic and Tetrahedral Platinum Nanocrystals,’’ J. Phys. Chem. B 102, 6145 (1998). 26. H. Kurata and C. Colliex, ‘‘Electron-energy-loss Core-edge Structures in Manganese Oxides,’’ Phys. Rev. B 48, 2102 (1993). 27. D. H. Pearson, C. C. Ahn and B. Fultz, ‘‘White Lines and D-electron Occupation for the 3d and 4d Transition Metals,’’ Phys. Rev. B 47, 8471 (1993). 28. Z. L. Wang, J. Bentley and N. D. Evans, ‘‘Valence State Mapping of Cobalt and Manganese Using Near-Edge Fine Structures,’’ Micron 31, 355 (2000). 29. Z. L. Wang, J. S. Yin and Y. D. Jiang, ‘‘EELS Analysis of Cation Valence States and Oxygen Vacancies in Magnetic Oxides,’’ Micron 31, 580 (2000). 30. J. S. Yin and Z. L. Wang, ‘‘Ordered Self-Assembling of Tetrahedral Oxide Nanocrystals,’’ Phys. Rev. Lett. 79, 2573 (1997). 31. C. Ma, Y. Ding, D. Moore, X. D. Wang and Z. L. Wang, ‘‘Single-Crystal CdSe Nanosaws,’’ J. Am. Chem. Soc. 126, 709 (2004). See also Nature 427, 497 (2004).
10 Surface Analysis Methods for Contaminant Identification David A. Cole Evans Analytical Group LLC, East Windsor, NJ, USA Lei Zhang DuPont Central Research and Development, Wilmington, DE, USA
10.1 Introduction Contamination in the broadest sense affects nearly all manufacturing industries. As such, it is virtually impossible to present a detailed review of all analytical methods used for contaminant identification. However if one takes as a subset of contaminants, namely only those at surfaces, the task is considerably simplified. As industries push for detection of submonolayer films and sub-micrometer particles, the number of generally applicable surface analysis methods becomes quite limited. Four methods were selected for inclusion in this overview: Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), time-of-flight secondary ion mass spectrometry (TOF-SIMS), and low-energy ion scattering (LEIS). These methods in combination are fully capable of examining sub-monolayer films and sub-micrometer particles, and are readily available through numerous industrial, academic, and national laboratories. As will be demonstrated, each method is best suited for specific contaminant studies. Judicious selection of a particular method requires knowledge of substrate and contaminant properties, such as size, shape, morphology, composition, volatility, concentration, and history. The selection process often begins with inspection by optical or electron microscopy to estimate whether the contamination is due to a surface film or particles. In addition to this, one must decide whether the study should provide qualitative or quantitative results and what specific type of R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 585–652 ª 2008 William Andrew, Inc.
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information is required, e.g. elemental composition, chemical bonding, or exact compound identification. The answers to these questions will generally limit the choice to one or two methods. Additional criteria for method selection include: detection limit, sampling depth, imaging, and depth profiling. These properties are summarized for the four methods in Table 10.1. For a detailed description of the basis for these properties, see the individual sections on basic principles. For a detailed description of how these techniques have been employed to study contaminants on contemporary products, see the individual sections on applications.
10.2 Auger Electron Spectroscopy (AES) 10.2.1 Background of AES Auger electron spectroscopy is one of a handful of techniques routinely used for surface analysis. It has reached this position because it can quantitatively detect all elements except hydrogen and helium, in the outer 10 nm of a sample. The technique is based on the fact that when a core electron is removed from an atom, the core electron vacancy can be filled by an electron from an outer (lower energy) shell with the consequent emission from the atom of a second outer shell electron. The ‘‘Auger process’’ and the ‘‘Auger’’ electron are named after Pierre Auger who reported the phenomenon in 1925 [1]. However, not until 1953 was it shown that Auger electrons, produced by bombarding a solid with electrons, could be used for surface analysis [2]. Then in 1968 the first practical Auger electron detection scheme was reported [3, 4]. This set the stage for explosive development of the technique in the 1970s and 1980s and more modest growth in the past 15 years.
10.2.2 Basic principles of AES To understand how AES can be used to study contaminants on surfaces, one needs to examine the Auger process more closely. For demonstration purposes consider a piece of household aluminum foil. The bulk of the foil is metallic aluminum, however the outermost surface consists of organic contaminants such as rolling oils, and a native aluminum oxide layer that always forms when metallic aluminum is exposed to air. When a high energy electron beam bombards this sample, core electrons are removed from atoms of all types within a depth of around 1 mm.
AES
Imaging Depth Profiling Major Limitations
Only with standards
Yes, standards not required 100 mm diameter
1 monolayer 1 · 109 to 5 · 1015 atom/cm2 Yes, rapid Yes, in principle Yes, rapid Yes Electron beam damage. Poor sensitivity for low Charging of mass atoms. Poor insulating samples. resolution between high mass atoms.
5–25 monolayers 0.1–1.0 at.%
Molecular weight, chemical bonding, and elemental
Elemental
2 mm diameter for organic analysis, 50 nm diameter for inorganic analysis 1–3 monolayers 1 ppma, 1 · 108 atom/cm2 Yes, rapid Yes, rapid Ion yields vary by orders of magnitude. Standards needed for quantitative analysis.
Any solid
TOF-SIMS
Any solid
LEIS
Yes Yes Relatively large analysis area. Analysis is often time consuming.
5–25 monolayers 0.01–1.0 at.%
Yes, best with standards 10 mm diameter
Chemical bonding, oxidation state, and elemental
Any solid
XPS
AND
Sampling Depth Detection Limit
Conducting or semiconducting solids. Insulators are very difficult Information Elemental. Oxidation state or chemical bonding in select cases Quantitative Analysis Yes, best with standards Minimum Analysis Size 10 nm diameter
Material
Method
Table 10.1 Overview of Selected Properties for Four Surface Analytical Methods
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For aluminum atoms the core electron is the K or 1s shell, having energy, Ex (see Figure 10.1). Ionization leaves the atom in an excited state from which it can partially relax by filling the core vacancy with an electron from an outer shell, in this case the L2,3 or 2p, having energy, Ey. The energy difference between the K and L2,3 shells, Ex Ey, is transferred to a second electron say from the L2,3 shell, with initial energy Ez, thereby causing it to be ejected from the atom. The kinetic energy of the emitted electron, EA is the transferred energy, Ex Ey, minus the initial energy of the emitted electron, Ez, i.e. EA ¼ Ex Ey Ez
Eq. (10-1)
Because the energies of each shell are specific to the atom, the kinetic energy of the emitted electron is also specific to the atom from which it originated. Hence an Auger spectrum will have at least one peak for every atom having at least three electrons. Hydrogen and helium having less than three electrons cannot undergo the Auger process. Auger electrons are typically referred to by the letters of the shells involved in the Auger process, i.e. Al KL2,3L2,3 in the example above. After this Auger process the atom is left in a doubly ionized state with two missing L-shell electrons. These vacancies can be filled by electrons from the valence band with transference of energy to other valence electrons, Auger Electron
EKLL
EVAC=0 Ef
Φ Incident Beam
3/2
2p 1/2
L3 L2
2s
L1
1s
K
Figure 10.1 Schematic diagram of the Auger electron emission process. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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which are ejected from the atom. This creates a second peak in the spectrum due to Al L2,3VV electrons. Clearly as the number of electrons in an atom increases, so will the number of peaks in an Auger spectrum. Fundamentally an Auger spectrum thus consists of a plot of the number of electrons emitted vs. electron kinetic energy. In this plot there will be one or more peaks for every type of atom in the sampling volume. Typically, AES refers only to spectra generated by bombardment of the solid with high-energy electrons. However, it is important to note that the Auger process will take place whenever a core vacancy is generated. Hence ‘‘Auger’’ electrons are generated when a sample is irradiated with X-rays as in XPS also known as Electron Spectroscopy for Chemical Analysis (ESCA) or in some cases when irradiated with ions such as when carrying out sputter depth profiling. Since AES relies on measuring the kinetic energy of electrons emitted from the atom, the electrons must actually be emitted not only from the atom but also from the solid itself. This has a profound effect on the sampling depth in AES. In a typical AES measurement the primary electron beam would have an energy of 3–20 keV. The high energy of the primary electrons causes Auger electrons to be generated at depths up to 1 mm. As these electrons travel through the sample they undergo inelastic collisions which reduce their kinetic energies. Since the degree of energy loss is not quantized, inelastically scattered electrons appear as part of the loss tail at the low energy side of the Auger peak. Only those electrons that exit the solid without experiencing inelastic collisions contribute to the main body of the Auger peak. Inelastic collisions are random chance events and as such the inelastic mean free path, l, is defined as the distance electrons travel after which 27% will have lost energy and 63% will still have their initial energy. To a first approximation, the inelastic mean free path has been found to be roughly proportional to the square root of the kinetic energy of the electrons and typically ranges between 0.5 and 2.5 nm for kinetic energies of 100–2000 eV, respectively. For the Al L2,3VV electrons in our example, which have an energy of 50 eV, 63% will have come from the 1l (0.5 nm), 95% come from 3l (1.5 nm), and 99% come from 5l (2.5 nm). In contrast, for Al KL2,3L2,3 electrons having energies of 1380 eV, 63% come from 2 nm, 95% come from 6 nm, and 99% come from 10 nm. Clearly AES is extremely surface sensitive. Unfortunately, inelastic scattering introduces one of the more confusing issues in AES, namely sampling depth. In fact, there is no single AES sampling depth; it depends on the atom of interest, the specific electron monitored, and how one defines ‘‘sampling,’’ i.e. 63, 95, and 99% of the signal, or some other ‘‘definition.’’
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With an understanding of sampling depth, it is an almost trivial task to understand AES sampling volumes. AES uses high-energy primary electron sources similar to those found in scanning electron microscopes. These electron beams are very easy to steer to discrete locations on a surface or to raster across a surface. Thus, changing the size and shape of the sampling volume is a simple task. For instance, if the primary beam is focused to a fine point, say 10 nm in diameter, the sampling volume would take the shape of an exceedingly small sphere roughly 10 nm in diameter. Alternatively, if the primary electron beam were rastered over an area, say 100 · 100 mm2, the sampling volume would take the shape of a very thin square box. This wide range of sampling volumes is ideally suited for analysis of contaminants such as films and sub-micrometer particles. The use of high-energy electrons to create core vacancies dictates that Auger spectra can be obtained from conductors and semiconductors, and also from insulating films less than a few micrometers thick on conducting substrates. Bulk insulators are exceedingly difficult, if not impossible, to analyze by AES. The technique of coating insulating samples with conducting layers, as is often done prior to energy dispersive spectroscopy (EDS) analysis, generally does not work in AES due to the shallow sampling depth. A side benefit of using high-energy electrons is that most AES instruments are capable of secondary electron imaging. Some commercial systems are capable of additional imaging methods such as backscattered electron and absorbed current imaging. Thus, the location and morphology of surface features, including contaminants, can be documented prior to elemental analysis by AES. From the description so far one can see that AES can identify the presence of all elements except H and He in the first few atomic layers. That in itself would be useful, but AES is also a quantitative technique. The traditional method of quantifying elements is through the use of peak-to-peak heights in the first-derivative spectrum. The reasons for using first-derivative spectra will be discussed later in this section. One peak each is chosen for each of the elements present. Barring spectral interferences, this is generally the most intense peak for that element. The peak-to-peak heights are then normalized by dividing by the elemental sensitivity factor. The normalized values are then expressed as a percent of the total with the units being atom percent. Commercial instruments come with tables of sensitivity factors that can be used for unknown materials, such as in contamination studies, with an accuracy of 50–80%. Quantitative accuracy of >95% requires calculation of sensitivity factors specific to a given material.
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Moreover, this material must be of constant composition within the sampling volume. There are six dominant factors affecting sensitivity factors. These are: (1) the probability of forming the initial vacancy, (2) the probability that the initial vacancy will be filled by an outer shell electron, (3) the probability that the filling of the core vacancy will cause emission of an Auger electron, (4) the magnitude of inelastic scattering in the solid, (5) the detection efficiency of the spectrometer, and (6) peak shape. Factor 1, the probability of forming the initial vacancy, is controlled by the energy of the primary electron beam. It has been shown that the maximum production of vacancies requires a primary energy 3–6 times the energy of the core shell. Thus for the Al LVV peak, where the energy of the L shell is less than 0.1 keV, the highest sensitivity beam energy would be <1 keV. Conversely, for the Al KLL peak, where the energy of the K shell is around 2 keV, the highest sensitivity beam energy would be 5–10 keV. Factors 2, 4, and 6 are controlled by the composition of the solid but vary only slightly with composition. To a first approximation, they are assumed to be constant. Factor 5, the detection efficiency of the spectrometer, is fixed by the instrument design. And finally, factor 3, the probability that the filling of the core vacancy will cause emission of an Auger electron, is a fundamental property of the atom and is, therefore, constant. Although the probability that filling of the core vacancy will cause emission of an Auger electron is constant, it is worth investigating in greater detail. There are actually two competing processes for returning the atom to its initial state: emission of an Auger electron and emission of a characteristic X-ray, i.e. X-ray fluorescence. Since two pathways exist, the probability of Auger electron emission is unity minus the probability of X-ray emission. Auger emission is the highly favored process for filling core vacancies having energies less than about 2 keV. Thus, Auger emission is the dominant process for K-shell vacancies of boron through arsenic. K-shell vacancies in elements heavier than arsenic relax primarily via X-ray emission. Although this sounds like AES would be insensitive to heavy elements, in fact other highly probable Auger emissions exist for vacancies from other shells, i.e. L, M, and N. Fortunately, one can select peaks for all elements in which the Auger emission to X-ray emission ratio is >0.9. Because of this, AES typically is well suited for analysis of unknown materials, particularly those suspected of containing light elements such as boron through sodium. The discussion above has alluded to the fact that Auger spectra can be plotted as the number of emitted electrons, N(E), vs. electron kinetic energy, E, or as a first derivative dN(E)/dE vs. E. Actually there are
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many ways to display the data. The most common methods are not based on properties intrinsic to Auger electrons but on the large number of background electrons. At low energies, <300 eV, the background level of electrons emitted from a solid is dominated by low-energy secondary electrons, often called ‘‘true’’ secondary electrons. At higher energies, the background is dominated by high-energy secondary electrons and, to a much lesser degree, by Auger loss tails. Superimposed on this background are the Auger electrons of interest, yielding a plot of N(E) vs. kinetic energy, E, see Figure 10.2(a). By taking the first derivative of this, one can remove much of the influence of the high-energy secondary electron background, see Figure 10.2(b). However, the low energy secondary electrons still disproportionately affect the low energy region. To overcome this, one can multiply the number of electrons by
(a)
1000
(b) 0
800
C KLL -200 dN(E)/dE
N (E)
600
400
Al KLL
O KLL
-400
200
Al KLL
O KLL
-600 -800 Al LMM 0
-1000 0
500
1000
1500
2000
0
500
Kinetic Energy (eV)
(c)
(d)
1.4x105
d(E.N(E))/dE
Al KLL O KLL
1.0x105 4
6.0x104 4.0x104
C KLL
8.0x10
AL LMM
E.N(E)
1500
2000
60000 40000
1.2x105
2.0x104
1000
Kinetic Energy (eV)
20000 0
C KLL
-20000 Al LMM
-40000 -60000
0
500
1000
1500
Kinetic Energy (eV)
2000
Al KLL
O KLL
-80000 0
500
1000
1500
2000
Kinetic Energy (eV)
Figure 10.2 AES spectra of aluminum foil with signal intensity displayed as (a) the number of emitted electrons, (b) the first derivative of the number of emitted electrons, (c) the electron’s kinetic energy times the number of emitted electrons, and (d) the first derivative of the electron’s kinetic energy times the number of emitted electrons. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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any function that increases with electron kinetic energy, e.g. the electron kinetic energy itself. This yields the E N(E) vs. E plot as shown in Figure 10.2(c). The first derivative of this, d(E N(E))/dE vs. E, removes most of the secondary electron influence on the spectrum leaving sharp Auger electron peaks [Figure 10.2(d)]. The last figure is in fact the historic way Auger spectra have been displayed since dE N(E)/dE vs. E is the nominal output of many older detection schemes. In this form quantitative analysis is performed, as stated earlier, from the peakto-peak height for a given electron emission. The first derivative form, dE N(E)/dE vs. E, has the advantage of easy comparison with historic spectra, easy identification of low intensity Auger peaks, and little user intervention needed for quantitative analysis. In contrast, the underivatized form, E N(E) vs. E, has the advantage of better signal-tonoise, better definition of peak shape, and the potential for more accurate quantitative analysis. For most studies of unknown materials and thin film contaminants, the first derivative form is sufficient. However, for sub-micrometer particle analysis, the underivatized form is gaining popularity due the better signal-to-noise. This is particularly true when qualitative particle screening is required rather than quantitative analysis.
10.2.3 AES instrumentation All Auger spectrometers consist of a vacuum chamber operated at a pressure less than 108 torr housing a high energy electron source and an electron energy analyzer, often co-axial to each other, see Figure 10.3. Other common features are sample introduction and manipulation hardware, a secondary electron detector for obtaining secondary electron images, and inert gas ion guns for sample cleaning and depth profiling. Cooling and heating stages are useful for preservation of volatile components and sample modification, respectively. Current commercial instruments permit computer control of most components. Computer control of the high-energy electron source simplifies analysis at a given point on the sample such as an individual particle, or a specific area such as a film. Combined control of the source and detector permits acquisition of elemental (or in special cases, chemical) images and line-scans, i.e. a display of peak intensity vs. location on the sample. Of particular importance is the ability to digitally store spectral data for subsequent analysis such as quantification, curve fitting, factor analysis, and principal component analysis.
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Ion pump
Source translator FE source Source lens Isolation valve Multi-channel detector Objective aperture CMA outer cylinder Objective lens Sample
Figure 10.3 Schematic diagram of an AES chamber. (Source: Physical Electronics Inc., Chanhassen, MN. Reprinted with permission.)
10.2.4 Applications of AES for characterizing surface contaminants An ideal contaminant identification tool would provide elemental composition, chemical bonding, and exact compound identification of organic, inorganic, and metallic compounds of any size and any phase—solid, liquid, or gas. Unfortunately, such a tool does not exist. However, AES fulfills many of these requirements. If we momentarily limit contaminants to those existing on surfaces, then the task at hand would be to analyze particles and films, though not necessarily continuous films. Since particles and films can be very small in one or more dimensions, a surface sensitive method would be useful. Auger electrons by the fact that they have low energies must come from a depth no greater than 10 nm. Moreover, all elements except for hydrogen and helium yield Auger electrons and the number of electrons emitted for each element is directly proportional to the atomic concentration of that element. Hence, AES is a quantitative surface analysis method. In most cases Auger peak energies are sufficient for identifying the element from which the electron originates, but not the chemical- or oxidation-state of that atom. Therefore, compound identification by AES is deduced from the relative abundance
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of elements detected. For example, if a particle was found to contain only boron and nitrogen in roughly equal concentrations, it would be safe to describe the particle as boron nitride. Of course, when many elements are detected at the same location, compound identification is more difficult. Because AES uses a high-energy electron beam as the probe, it is limited to analysis of conducting and semi-conducting surfaces, or to insulating films and particles on conducting or semi-conducting substrates. Note, a common restriction for insulating films and particles is that at least one dimension should be less than a few micrometers. The use of an electron beam probe has the additional benefit that the sample can be viewed by secondary electron microscopy. This permits the operator to inspect and document surface morphology, and to perform analysis on discrete features such as individual particles. When secondary electron contrast is insufficient to locate the desired feature, one can perform survey analysis from an area encompassing the suspected contaminant and then map the detected elements. Auger maps are two-dimensional pseudo-color images showing the intensity of a given emitted electron as a function of X,Y location on the surface. If the elemental composition of the contaminant differs significantly from the substrate, one or more maps should clearly identify its location. Selected area analysis can then be used to evaluate the contaminant in detail. For complex assemblies of contaminants this sequence of steps may need to be iterated several times. If the contaminant of interest is not on the outer surface, then the overlying material must be removed. In the simplest case this is done by fracturing the sample, thereby exposing contaminants at the fracture face. This method is quite useful when studying adhesion failure, weld failure, and fatigue cracking. If sample fracturing does not reveal the contaminant, then the overlying material must be removed by chemical or mechanical means. Chemical etching is most useful when the etch process stops near but not actually at the contaminant since the process tends to deposit its own contaminants on the sample. The overlying material remaining after chemical etching is then removed by ion beam milling. Mechanical removal can be done in two ways: cutting and polishing, and ion beam milling. Cutting and polishing is acceptable for particles >1 mm in diameter and contaminant films >1 mm thick. Since this is a rather small subset of typical contaminants, it is not widely performed. Conversely, ion beam milling is exceedingly common. The most common ion beam milling method uses an inert gas ion gun to remove material. By cycling between AES data acquisition and ion milling, a plot of concentration vs. sputter time can be generated. Figure 10.4 shows a typical
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100 90 Al° Atomic Concentration (%)
80 70 60 O 50 40
Al+3
30 20 10 0
C Al° 0
20
40 60 Sputter Depth (Å )
80
100
Figure 10.4 AES depth profile of aluminum foil with a 0.3 nm thick organic layer and a 2.5 nm thick native oxide layer. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
depth profile of household aluminum foil that has two contaminant layers, an outer organic layer 0.3 nm thick and a native oxide roughly 2.5 nm thick. If the sputter rate of the material is known, the plot is displayed as concentration vs. sputter depth. A depth profile plot, therefore, shows the location, thickness, and composition of a contaminant layer. For buried particles, ion milling is often used solely to remove the overlayer at which time the exposed particle is analyzed as if it were a surface feature. Some of the newer Auger systems incorporate a focused ion beam (FIB) source for ion milling. These sources operate at very high current and very small beam diameters allowing one to selectively ion mill trenches that bisect buried particles. As one might expect AES is widely used by the metallurgical community [5]. The ability to detect unknown elements at sub-monolayer coverage with high spatial resolution is vital to the study of interfacial failure. This includes adhesion failure in composites and adhesive joints, and fatigue failure of metals and alloys. In each case, segregation of contaminants at the interface produces a weak layer in which failure propagates. In contamination-induced adhesion failure in composites and adhesive joints, contamination often arises from improper cleaning of the metal substrate
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prior to bonding. In fatigue failure of metals and alloys, the contaminants are generally present when the material is cast. An exception to this is the weld failure where contaminants both within and on the surface of the material can cause failure. Moreover, the contaminant can be introduced during the welding. For example, Al–Li alloy 2195 is a light-weight, high fracture-toughness alloy slated to replace much of the Al–Cu alloy 2219 in the Super Light Weight Tank (SLWT) of NASA’s Space Shuttle. AES investigations of test welds indicated that weld integrity was directly related to the amount of aluminum oxide at the grain boundaries at the weld site [6]. The presence of lithium increased the oxidation kinetics of the alloy such that low concentrations of oxygen in the shielding gas cause thin oxide film growth not seen in lithium-free alloys (see Figure 10.5). Surface contamination of finished metal products is also an area of great interest. The most common detrimental result of such contamination
(a)
dN/dE
x2
C KLL
Al KLL
Al LMM
dN/dE
(b)
Al LMM Al KLL O KLL 0
200
400
600
800
1000 1200 1400
Kinetic Energy (eV)
Figure 10.5 AES spectra of fracture surfaces from (a) a typical weld in Al–Cu alloy 2219 and (b) a repair weld in Al–Li alloy 2195. Note that both samples were vacuum fractured at 1 · 109 torr. (Adapted from reference [6]. Reprinted with permission.)
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is corrosion. Although one might have expected AES to have been used long ago in corrosion studies, it has in fact been routinely employed only in the past 15 years [5]. The complexity of corrosion processes and the desire to monitor chemical states rather than elemental identification has slowed the adoption of AES in this field. Nonetheless, AES is often used to study surface contaminants on metals. For example, blemishes in the cosmetic appearance of metal surfaces are often caused by surface contaminants. In other instances, surface contamination can directly affect the end-use properties. This is certainly the case for orthopaedic implants. Many studies have been done to determine appropriate surface chemistry for biocompatibility. In such studies one should remember to include real-world issues such as sterilization. For example, a study of titanium implants sterilized by three different methods found considerable differences in particulate contamination and oxide growth [7]. Higher levels of contamination and oxide growth correlated with decreased cell attachment and spreading in assay studies which may pose serious biological concerns. Thus although the alloy composition and manufacturing process could produce an implant with excellent biocompatibility, it would be to no avail if improperly sterilized. The ability to characterize sub-micrometer features and particles makes AES quite useful to the disk drive industry [8]. The semi-conductor and microelectronics industries also rely on AES for contaminant analysis. Most studies fall into two categories: process development or failure analysis. Many processes can and have been improved with the information provided by AES. Plasma etching is an excellent example. Plasma etching is an inherently dirty process because etch products either deposit on or attack chamber walls and hardware. By studying the composition of particles deposited on wafers during plasma etching, such as is shown in Figure 10.6 [9], one can determine their production mechanisms and thereby adjust process conditions and hardware as needed to minimize their production [9, 10]. Whereas process development can be done in a controlled fashion, failure analysis is, by definition, uncontrolled. Contamination is often suspected when failure is related to adhesion, such as delamination of a multilayer metal stack or wire debonding. Delaminated metal stacks can be examined by depth profiling down to the failure layer, or more optimally by analyzing the two mating faces after delamination. Although the latter method results in slight surface contamination during sample preparation, it is often the preferred method. Wire debonding resulting from organic contamination or corrosion of the bond pad is easily studied by a combination of surface analysis for contaminant identification and depth profiling for contaminant thickness [11].
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(b)
S Si
Al Si
C Ti
O N+Ti 200 600 1000 1400 1800 Kinetic Energy (eV) (d)
(c)
Ti Si C N Al Ti
200
Si Al O 600 1000 1400 Kinetic Energy (eV)
1800
Si
C Ti Ti Si 200
O
Si
600 1000 1400 1800 Kinetic Energy (eV)
Figure 10.6 (a) SEM micrograph of a Ti/Al composite particle found on a silicon wafer after W etch back (WEB) processing and AES spectra of (b) a titanium-rich region, (c) an aluminum-rich region, and (d) the wafer substrate. (Adapted from reference [9]. Reprinted with permission.)
Auger electron spectroscopy is often used to evaluate the efficacy of a cleaning process and to measure consequential substrate damage. All high surface free energy materials are contaminated with airborne organic contaminants and most often with native oxide films. Since these contaminants often interfere with device operation, they must be removed during production. This is particularly true in the semi-conductor industry. Different materials (Ge, AlN, GaN, InAs, etc.) may require different cleaning methods. However, in each of these cases AES can be used to monitor cleaning efficacy [12–14]. Care must be taken to assure that the substrate is not damaged during the cleaning process. AES analysis of several laser cleaned substrates showed that organic contaminants could be removed without surface damage [15, 16], but removal of the native oxide from silicon caused permanent surface damage [17]. Other cleaning
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methods such as Ar+ bombardment [18] and Ar/H2 plasma treatment [19] can clean surfaces but may damage the cleaned surface or cause collateral damage to adjacent components.
10.2.5 Recent developments and future directions of AES As with many mature analytical techniques, recent advances in AES have been evolutionary rather than revolutionary. The three most important advances have been in speed and ease of analysis, analytical beam size, and sample handling. Much of the improvements in speed have been made possible by advances in electronics, multi-channel detectors, computers, and software. Faster electronics has the obvious effect of reduced dead time, and multi-channel detectors permit parallel electron detection. Faster and more powerful computers have made it much easier to operate Auger spectrometers. However, the largest impact from improved software and computing power has been in data analysis. Software features such as curve fitting, factor analysis, and principal component analysis, particularly when combined with underivatized spectra, E N(E) vs. E, permit extraction of much more chemical information from AES spectra. For the highest degree of chemical information, the use of an electrostatic hemispherical analyzer is recommended. Auger electron spectroscopy has always been an excellent tool for particle analysis due to the ability to confine the analysis to the particle and not the substrate upon which it resides. Particle analysis has been greatly improved by the incorporation of Schottky field-emission electronsources. These sources can be operated at extremely narrow beam diameters and at high beam currents, permitting AES analysis of features as small as 10 nm. However, this ability comes with a price, specifically the difficulty in preventing contamination of the sample with extraneous particles and in locating nanometer-sized particles. A solution to these problems has been found in the semi-conductor industry [20]. Extraneous particles come from two sources: sample preparation such as cleaving the wafer to a suitable analytical size, and sample handling. Design of instruments capable of handling whole 200 and 300 mm wafers under clean room conditions eliminates particle generation during sample preparation and handling. Stand-alone optical defect detection (ODD) tools based on laser light scattering can be used to map and count particles on whole wafers. However, to date, ODD tools have not been incorporated into Auger spectrometers. Rather than requiring the operator to hunt for particles,
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a daunting task if one is looking for 10 nm particles, automated stage navigation is available using imported files from ODD tools. While the operator must still make the final selection of the analysis location, the particle of interest is typically in the field of view of the Auger spectrometer. An additional advancement of significant importance is improvements in ion guns. This has been a two-pronged approach. Low-energy highcurrent ion guns provide improved depth resolution while minimizing the loss of chemical information from the sputtered layer. Combined, these permit more accurate identification of layer composition and thickness. The second approach is to incorporate FIB sources into the spectrometer chamber. FIB sources operate at very high current and very small beam diameters allowing one to selectively ion mill stair-stepped trenches. This greatly reduces the time and effort required to expose buried particles or layers for subsequent AES analysis. If past history predicts future advances, one should expect soon to see instruments that are faster [21] and offer greater ease of use for chemical analysis, not simply elemental analysis. Moreover, instruments tailored to specific industrial concerns will continue to be developed. This will most likely include industry-specific sample handling hardware as well as multitool analytical chambers.
10.3 X-ray Photoelectron Spectroscopy (XPS) 10.3.1 Background of XPS The evolution of XPS as a surface analytical method parallels AES in many ways. Both trace their foundation to turn-of-the-century studies of the properties of the atom. The photoelectric effect in which electrons are spontaneously emitted from a material upon illumination by X-rays was discovered by Hertz in 1887 [22]. Eighteen years later Einstein described the basic equation of XPS that related the kinetic energy of the electron to the binding energy of the electron and the X-ray source energy [23]. In the 1920s the understanding of XPS progressed rapidly and it was shown that XPS spectra contained not only photoelectrons but also Auger electrons. It was not until the late 1940s that Steinhardt and Serfass envisioned XPS as an analytical tool for investigating surface chemistry [24]. Siegbahn and co-workers followed this lead and observed chemical shifts of core-level binding energies [25–28], which was the basis of XPS for years to come. Siegbahn also coined the acronym ESCA to emphasize the fact that XPS
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spectra contained both photoelectrons and Auger electrons. To this day, the terms XPS and ESCA are used synonymously by practitioners even though it causes some confusion among lay users.
10.3.2 Basic principles of XPS X-ray photoelectron spectroscopy is based on the detection of electrons emitted from a surface under illumination with X-rays [5, 29]. A schematic diagram of the photoelectron emission process is shown in Figure 10.7. If the X-ray source is mono-energetic, having an energy of hn, the kinetic energy, EK, of the emitted electrons will be related to the binding energy of the electron EB by the following equation: EK ¼ hn EB F
Eq. (10-2)
In this equation F is a small correction term used to account for the combined work function of the sample and the spectrometer. Note that electrons are emitted only if the X-ray source energy hn is greater than the electron binding energy and instrument work function, EB + F. Thus by measuring the kinetic energy of the emitted electron one can calculate the binding energy of that electron, i.e. the energy needed to strip the electron from the atom. Electron binding energies are characteristic not only of the atoms from which the electrons originate but the chemical state or EK
EVAC=0 Ef
Φ
3/2 1/2
2p
x-ray, hν 2s
1s
Figure 10.7 Schematic diagram of photoelectron emission. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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oxidation state of the atom [30, 31]. Except for hydrogen and helium, all elements in the periodic table are readily detected by XPS. Hydrogen and helium are undetectable due to their very low X-ray cross-sections. Thus XPS, at a minimum, is a qualitative elemental and chemical analysis method. Electron binding energies are fundamental properties of the atom. Conversely, electron kinetic energies are not since they vary with the X-ray source energy. Thus in XPS, electron energies are reported exclusively in terms of binding energies. An XPS spectrum is, therefore, a plot of the number of emitted electrons vs. electron binding energy. One or more photoelectron peaks will be present in the spectrum for each type of atom in the sampling volume. Photoelectrons are generally classified as being either core electrons or valence electrons. The vast majority of photoelectrons are core electrons, which are used to determine elemental composition and chemical states (oxidation states). Valence electrons are of lower intensity but are extremely valuable for fingerprint identification of compound. Photoemission of an electron from a core shell of energy Ex creates a core hole, thereby putting the atom in an excited state. Relaxation begins with the core vacancy being filled by an electron from an outer shell of energy, Ey. The energy difference between the core and outer shells, Ex Ey, is dissipated by photon emission, i.e. X-ray fluorescence, or by electron emission from a shell of energy Ez, i.e. Auger electron emission. The kinetic energy of the emitted Auger electron, EAuger is the transferred energy, Ex Ey, minus the emitted electron’s initial energy, Ez, i.e. EA ¼ E x Ey Ez
Eq. (10-3)
Because the energies of each shell are specific to the atom, the kinetic energy of the emitted Auger electron is also specific to the atom from which it originated. An XPS spectrometer cannot directly differentiate between photoelectrons and Auger electrons and since XPS spectra are displayed in terms of binding energies, the same mathematical conversion is performed on both electrons, i.e. EB ¼ hn Ek F
Eq. (10-4)
even though the conversion has no meaning for Auger electrons. Since the kinetic energy of an Auger electron is a constant value dependent solely on the energies of the electrons involved in the Auger cascade, the ‘‘binding energy’’ of an Auger electron changes with X-ray source energy.
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Thus a simple way to indirectly differentiate between photoelectrons and Auger electrons is to acquire spectra using two X-ray sources of different energies. If the binding energy of the peak remains constant, the peak is due to photoelectrons. If the binding energy of the peak changes, the peak is due to Auger electrons. For a more detailed description of Auger electron generation see the section on basic principles of AES. The very simple XPS spectrum of polyethylene, [CH2]n, a polymer containing only carbon and hydrogen, is shown in Figure 10.8. Since hydrogen is not detected, the XPS spectrum consists of peaks due to carbon. A carbon atom has six electrons. The two 1s electrons in the K shell are considered to be core electrons and emission of these electrons creates the carbon 1s or ‘‘C 1s’’ peak. Since polyethylene contains only one type of carbon a single C 1s peak is present. The two 2s and two 2p electrons in the L shell are considered to be valence electrons and generate a series of peaks between 0 and 25 eV. The shape of the valence band region is largely controlled by the band structure of the material. Since band structures are not easily estimated, the valence band region is often used as a fingerprint region with comparisons made to reference spectra from pure materials. Valence band spectra are particularly useful for differentiating organic compounds [32]. In addition to photoelectrons, the XPS spectrum contains carbon Auger electrons (C KLL) produced when L shell electrons fill the K shell vacancy.
1200
-Valence Band
-C KLL Auger
XPS Intensity (a.u.)
C 1s
1000
800
600
400
200
0
Binding Energy (eV)
Figure 10.8 XPS survey spectrum of polyethylene (PE). (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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As stated earlier, when a compound contains multiple elements one or more peaks will be present for each element, hence XPS can be used for qualitative analysis. Perhaps of more importance is the fact that photoelectron peak intensities are directly related to elemental concentration, hence XPS can be used for quantitative analysis. Theoretically, the intensity of the photoelectrons Ii, is proportional to the X-ray flux f, the photoelectric cross-section si for the corresponding electronic shell, the inelastic mean free path li of the photoelectron, the analysis area A, the density ni of atom i in the analysis volume, an angular asymmetry factor L based on the geometry of the spectrometer, the transmission function of the spectrometer T, and the detection efficiency D [5]. Thus the measured intensities Ii can, in principle, be related to atom density by ni
I fsi li ALTD
Eq. (10-5)
This method is not used because it is difficult to perform and has large experimental errors. In practice, an empirical method is used to calculate relative elemental concentration. By defining elemental sensitivity factors as Si = fsiliALTD, the density Eq. (10-5) can be rewritten as ni
Ii Si
Eq. (10-6)
Note that Si is different for each element and is dependent on instrument conditions, but is, to a first approximation, independent of chemical composition and state. The general expression for calculating elemental concentrations expressed in atom percent is given by Ii =Si Ci ¼ 100 · X Ii =Si
Eq. (10-7)
i
Because this equation uses intensity ratios one need not know the absolute magnitude of each peak, but only the relative peak intensities. Most commercial instrument manufactures provide tables of sensitivity factors derived from pure compounds or photoelectron cross-sections, allowing straightforward calculation of relative elemental concentrations. Quantitative analysis is readily illustrated by examining the XPS spectrum of poly(ethylene terephthalate) (PET), a polymer containing two ester O–C=O functional groups –[O(O=C)R(C=O)OR1]n–, where R is
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-C 1s
-O 1s 1200
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-Valence Band
-O KLL Auger
-C KLL Auger
XPS Intensity (a.u.)
C6H4 and R1 is C2H4. Each monomer of PET contains 10 carbon, 4 oxygen, and 8 hydrogen atoms giving rise to the survey spectrum shown in Figure 10.9. By measuring the intensities of one peak for each element, i.e. the C 1s and O 1s peaks, and using the appropriate sensitivity factors, the atomic concentrations can be calculated from Eq. (10-7). In this sample the analyzed volume contained 71.4 at.% carbon and 28.6 at.% oxygen. Because the sample was pure and the sensitivity factors were accurate, the measured concentrations exactly matched the theoretical values for this material. Quantitative analysis of chemical bonds can also be achieved if the bonds generate distinct peaks in the spectrum. As shown in Figure 10.10(a) the oxygen 1s spectrum of PET contains two components, O–C at 533 eV and O=C at 532 eV. As shown in Figure 10.10(b) the carbon 1s spectrum contains three components, C–(C, H) at 285 eV due to the aromatic ring, C–O at 286 eV and O–C=O at 288.5 eV. The intensity of each component is directly related to the concentration of atoms having the specified bond [32]. In this sample the two components of the oxygen spectrum have relative intensities of 1.1:1.0, in excellent agreement with the theoretical ratio of 1:1. Moreover, the three components of the carbon spectrum have relative intensities of 1.1:1.0:3.0, also in excellent agreement with the theoretical ratio of 1:1:3. In XPS, detection of electrons requires that the electrons exit the material. As the electron travels through the solid toward the surface it can
800
600
400
200
0
Binding Energy (eV)
Figure 10.9 XPS survey spectrum of poly(ethylene terephthalate) (PET). (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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-C=O
-C-O
XPS Intensity (a.u.)
(a)
544 542 540 538 536 534 532 530 528 526
Binding Energy (eV)
298
296
294
292
290
-C-O
-O-C=O
-C-(C,H)
XPS Intensity (a.u.)
(b)
288
286
284
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Binding Energy (eV)
Figure 10.10 High-resolution spectra of poly(ethylene terephthalate) (PET) showing the (a) oxygen 1s and (b) carbon 1s regions. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
undergo elastic or inelastic scattering. Only those electrons that undergo elastic scattering exit the solid with their initial kinetic energy and hence contribute to the photoelectron peaks. Electrons that undergo inelastic scattering form energy loss tails and the background continuum. Inelastic collisions are random chance events and as such the inelastic mean free path, l, is defined as the distance electrons travel after which 27% will have lost energy and 63% will still have their initial energy. For electrons with kinetic energies >50 eV this distance has been found to be roughly proportional to the square root of the kinetic energies of the electrons (see Figure 10.11). The probability that elastically scattered electrons can
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Figure 10.11 Inelastic mean free path l vs. the emitted electron energy for elements. (Source: M. P. Seah and W. A. Dench, Surface Interface Anal., 1, 2 (1979). Reprinted with permission.)
reach the surface and are detected decreases exponentially with distance, d, into the material and is given by Id ¼ I 0 ½1 eðd=l sin uÞ
Eq. (10-8)
where u is the take-off angle, i.e. the angle between the sample plane and the entrance to the electron analyzer. This means that there is no single XPS sampling depth since it depends on the probability of electron scattering, the electron take-off angle, and the inelastic mean free path which varies with electron energy. For example, 63% of all electrons in a particular photoelectron peak originate from a depth of l sin u. Conversely, 95 and 99% of these electrons come from depths of 3l sin u and 5l sin u, respectively. Hence, the sampling depth can be based on detecting 63, 95, 99% or any portion of the elastically scattered electrons. It is important to note that sampling depth can be varied by changing the take-off angle, u. At a take-off angle of 90 , the depth from which 63% of all detected electrons originate is l sin(90 ) or l. At grazing take-off angle of 10 , the sampling depth drops to l sin(10 ) or 0.17l. For carbon
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electrons in polymers, l is 3 nm, hence the 63% sampling depths are 3 nm and 0.5 nm at take-off angles of 90 and 10 , respectively. This makes XPS an extremely surface sensitive technique. By changing the take-off angle, and consequently the sampling depth, one can obtain non-destructive depth profiles from the outermost surface to 10 nm [33]. Moreover, if the contamination layer is thin (<10 nm), one can also estimate the thickness [34]. When contaminant layers are thicker than 10 nm, nondestructive profiling is not possible. In these cases destructive depth profiling methods are needed. Destructive depth profiling can be performed by a variety of mechanical and chemical means. The most popular method is ion beam etching wherein the surface is first etched with an ion beam, such as Ar+, and the freshly exposed surface is then analyzed. This sequence of steps is repeated until the desired sputter depth is reached. A depth profile plot thus presents the intensity or concentration of the measured peak vs. sputter time, or if the sputter rate is known, vs. sputter depth. The consequences of ion beam sputtering warrant further discussion to prevent erroneous interpretation of profile data. When a high-energy incident ion strikes a surface, the energy of the incident ion is dissipated by the surface atoms, resulting in bond breaking and ejection of material from the surface. For typical ion beam voltages of <5 kV the damaged layer is a few nanometers thick. For some materials such as silicon and aluminum oxides the damaged layer has the same elemental and chemical composition as the undamaged material. Unfortunately, this is often not the case and ion sputtering results in two artifacts: preferential sputtering and ion beam damage. As the name implies, preferential sputtering results in elements being sputtered at different rates. This causes a change in the elemental composition within the damaged layer. For example, when Ta2O5 was ion sputtered using 3 keV Ar+ ions, the Ta:O ratio changed from 2:5 (Ta2O5) to 2.3:1 (Ta2.3O). Since oxygen is removed at a faster rate than tantalum, tantalum sub-oxides are formed. This classic example illustrates that when ion sputtering is performed one cannot rely on the intensity and location of XPS peaks to be representative of the unsputtered material. Rather, the extent of preferential sputtering must be investigated for each material. From these control studies one can calculate sensitivity factors appropriate for sputtered materials. Although one can often correct for the effect of preferential sputtering on peak intensities, the effects of ion beam damage are more problematic. Even in the absence of preferential sputtering, ion beam damage causes bond breaking and consequential creation of new bonds. Thus chemical bonding information is often lost. For example, ion sputtering of PET results in preferential
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sputtering of oxygen. Consequently, the remaining carbon atoms recombine to form a material resembling an organic char. Unlike with preferential sputtering, once chemical information is lost it cannot be retrieved. Thus when chemical information from the sub-surface region is required one must minimize the thickness of the ion beam damaged layer. To some extent this can be accomplished by lowering the ion beam energy and the incident angle, and by using polyatomic ion beams [35] such as SF5+ or C60+. All of the examples presented about have demonstrated the use of XPS for organic compound analysis. This is rightly so since XPS is one of the few techniques that provides organic compound identification. However, XPS is also widely used for analysis of inorganic materials. Since changes in the chemical environments of atoms cause a shift in binding energy of the electrons, one can identify different oxidation states. In general, the binding energies of the core electrons increase with increasing oxidation of the element. For most metals XPS can easily distinguish between the metallic and oxide states. For example, the titanium 2p3/2 peak in metallic titanium is found at 453.8 eV whereas in titanium dioxide it is at 458.5 eV. In some instances XPS can even distinguish between different oxidation states. For example the 3d5/2 peak of niobium is at 202 eV for Nb , 204 eV for NbO, 206 eV for NbO2, and 207.6 eV for Nb2O5. However, for some elements chemical shifts due to differences in oxidation states are of the same magnitude as the shifts due to differences in chemical states. For example, the 2p3/2 binding energies of iron as Fe2+ and Fe3+ are 709.6 and 711 eV in FeO and Fe2O3, but are 710.6 and 711.3 eV for FeCl2 and FeCl3. For electronegative elements the binding energies of the core electrons decrease with increasing reduction of the element. For instance, reduction of S to S2 causes a decrease in the electron binding energy from 164.1 to 161–162 eV. This downward shift upon reduction is observed for fluorine, chlorine, bromine, iodine, oxygen, phosphorus, sulfur, arsenic, and selenium. Occasionally spectra contain loss features such as plasmons, phonons, and p ! p* peaks or relaxation related features such as shake-up and shake-off peaks [5]. These peaks appear on the high binding energy side of the core level peak and can provide clues to chemical states. Although the origins of these peaks are complex and not easily predicted, their presence or absence can be used to identify oxidation states of many elements such as aluminum, silicon, magnesium, cobalt, nickel, copper, lanthanum, and cerium. Take for instance, when oxides or stains are formed on metallic copper, the existence of strong shake-up peaks indicates the formation of Cu+2 (e.g. CuO and CuSO4). While the lack of shake-up features implies that the surface is Cu0 or Cu+1 (e.g. Cu2O).
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For some elements chemical shifts are small and satellites features are absent. In these cases the only means left for deducing chemical information is by examining the position of Auger peaks [36, 37]. This is most often done by calculating the ‘‘Auger parameter,’’ a, (actually the modified Auger parameter), a ¼ EB ðiÞ þ EK ðjklÞ
Eq. (10-9)
where EB(i) is the binding energy of the photoelectron i and EK(jkl) is the kinetic energy of the Auger electron jkl. The Auger parameter is often used to identify chemical composition and oxidation states in fluorine, sodium, silicon, copper, zinc, arsenic, silver, cadmium, indium, tellurium, and lead. For example, the binding energies of Cu0 and Cu+1 are nearly the same, 932.5 eV. However, these two species are readily distinguished since their Auger parameters are 1851.2 and 1849.4 eV, respectively.
10.3.3 XPS instrumentation The typical components in an XPS system include an ultra-high vacuum (UHV) chamber, one or more X-ray sources, an energy analyzer, a multi-axis sample stage, an imaging device, a sample neutralizer, an ion gun, and one or more computers for data acquisition, storage, and manipulation. A simplified schematic of an XPS system is shown in Figure 10.12. Common polychromatic X-ray sources generate aluminum X-rays, e.g. the Al Ka1, 2 doublet of energy 1486.6 eV with a 0.85 eV line width, or magnesium X-rays, e.g. the Mg Ka1, 2 doublet of energy 1253.6 eV with a 0.7 eV line width. To improve spectral resolution a monochromator is often used to select Al Ka1 singlet, thereby reducing the source width to 0.35 eV. Moreover, monochromatic X-ray sources greatly reduce or eliminate damage caused by heat, electrons, and Bremsstrahlung radiation generated by polychromatic X-ray sources. The most common analyzer is a concentric hemispherical analyzer (CHA). This analyzer has good absolute energy resolution and can be operated at a fixed energy resolution independent of electron energy. A multi-axis sample stage facilitates sample positioning and allows analysis at different sampling depths by varying the electron take-off angle. Cooling and heating stages are useful for preservation of volatile components and thermal sample modifications, respectively. Specific analysis areas are routinely determined from optical and X-ray induced secondary electron images or from XPS elemental and chemical maps. Unless specimen neutralizers are used, insulating samples
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x-ray source
retarding grid
e-
sample
concentric hemispherical analyzer
detector
Figure 10.12 Schematic diagram of an XPS system. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
can develop positive surface charges during XPS analysis, which cause distortion and shifting of peaks. Thus most spectrometers are equipped with sample neutralizers such as electron flood guns, or low energy ion guns, or polychromatic X-ray sources. Most XPS spectrometers can acquire a variety of data types. The most common are survey spectra, high resolution spectra, and depth profiles. In these modes the analysis area is generally dictated by the X-ray source illumination area or by transfer lenses and apertures. Survey spectra are acquired in a mode whereby energy resolution is sacrificed in order to improve detection limits. Moreover, as the name implies, data are acquired over all binding energies so as to survey all elements. Quantitative precision is generally lower when data are acquired in survey mode. Conversely, high resolution spectra are acquired in a mode whereby detection limit is sacrificed in order to improve energy resolution. High resolution spectra typically encompass specific energy windows of interest rather than all energies. These spectra are used for high precision quantitative analysis and chemical bonding studies. Depth profiling is typically performed by interlacing ion beam sputtering with high resolution data acquisition. Elemental and chemical mapping are available on current commercial instruments. Mapping is performed by four methods: sample translation, rastering the transfer lens, rastering the X-ray source, or direct imaging
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onto a multi-channel detector. In each mode the result is a pseudo-color image showing the intensity of a selected peak as a function of X,Y location on the surface. Direct imaging has the advantage of rapid image acquisition, whereas transfer lens and X-ray source rastering assures that subsequent selected area analysis is in perfect spatial alignment with the imaged area. Sample translation is the slowest method but permits mapping of very large areas.
10.3.4 Applications of XPS for characterizing surface contaminants The need to monitor and control contaminants spans almost every manufacturing industry. XPS has been widely used for cleaning and contamination studies in diverse industries such as aerospace, automotive, biomedical, chemical, catalysis, electronic equipment, medical device, packaging, paint, paper, pharmaceutical, plastics, polymer, printing, and semi-conductor. Surface contaminants can be categorized into two major groups, organic and inorganic materials. Common organic contaminants include lubricants, oils, waxes, greases, mold-release agents, anti-oxidants, plasticizers, surfactants, and adventitious airborne compounds. Common inorganic contaminants include metals, compounds, adsorbed cations or anions, corrosion products, and oxides. When one considers the number of common contaminants along with the number of potential substrates from just the few industries highlighted above it becomes obvious that a detailed comprehensive review is impossible. Examples included in the following discussions highlight routine uses of XPS to study (1) surface composition, (2) adhesion failure, (3) corrosion, and (4) cleaning methods. XPS is uniquely suited to these studies because it can examine contaminants that are solids or low volatility liquids on both conductive and insulating substrates. Within these bounds the primary limitations of the method are in detection limits and minimum analysis area. The minimum detectable level for most elements is a fraction of a monolayer or a bulk concentration of 0.05–0.5 at.%. The current state-of-the-art minimum analysis area is 10 mm in diameter. It should be no surprise that man-made materials are often contaminated since contamination can take place at all phases of a product’s life cycle. Polymers and plastics are generally either very clean or they contain significant concentrations of surface contaminants. Most of these ‘‘contaminants’’ are either foreign compounds found only at the surface or additives that have migrated to and concentrated at the surface. While the
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latter might not fit a strict definition of a contaminant, they are included here since they often have similar detrimental effects on product performance. Many compounds can be identified by elemental and chemical analysis using core electron spectra. For example, by examining the positions and intensities of the silicon 2p and oxygen 1s peaks it is easy to detect and quantify poly(dimethylsiloxane), –[O–Si(CH3)2]n–, contamination on polyolefin film surfaces. Conversely, polyolefin contamination by fatty acid amides such as behenamide, H(CH2)21CONH2, or erucamide, H(CH2)8CH=CH(CH2)11CONH2, common slip agents added to aid processing, is more difficult to identify since most of the atoms of these compounds are part of the olefin chain. Using the core electron spectra, only the amide end group, CONH2, distinguishes it from the substrate. However, if the polyolefin is polypropylene, then the valence band spectrum can be used for identification since the pendent methyl groups of polypropylene produce a valence band spectrum distinctly different from the unbranched tail of a fatty acid amide. For example, upon heating an oriented polypropylene (OPP) film that contained myristamide H (CH2)13CONH2, 4 hours at 65 C, the fatty acid amide bloomed to the surface. Quite different from the valence band spectrum produced by the branched carbon of the as-received OPP film [see Figure 10.13(a)], the valence band spectrum of the heated OPP film [Figure 10.13(b)] resembled to that produced by the unbranched tail of pure myristamide [Figure 10.13(c)]. In fact valence band spectra are useful in determining the structure of many additives [38]. In many ways assessing contaminants on inorganic materials is easier since the contaminants often contain foreign elements not found in the pure material. Since XPS can detect all elements except hydrogen and helium, it is well suited for these studies. Most inorganic compounds have high surface free energies and become coated with adventitious airborne organic compounds. Thus carbon is almost always detected on inorganic materials. Moreover, exposure to air and moisture often leads to surface oxidation. For instance, two commercially available high purity silver halide powders, AgF and AgF2, were examined by XPS [39]. Even after brief sputtering with 1 keV He+ to reduce surface contaminants, the surfaces still contained carbon and oxygen in various organic forms, silver oxides, and perhaps even CHF and CFO(OH) like species. Clearly these surfaces were not pure AgF and AgF2. This illustrates the general principle that one should never simply assume that surface and bulk compositions of inorganic compounds are the same. There are times when a particular processing step is needed, however the method by which it is accomplished drastically changes
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XPS intensity (a.u.)
(a)
XPS intensity (a.u.)
(b)
XPS intensity (a.u.)
(c)
35
30
25
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10
5
0
Binding Energy (eV)
Figure 10.13 Valence band spectra of oriented polypropylene containing myristamide (a) as-received and (b) after heating for 4 hours at 65 C and (c) of pure myristamide. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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surface composition. For example, orthopaedic implants must be sterilized prior to insertion into the body. While the efficacy of autoclaving for killing pathogens is known, it is less well known that the method often deposits surface contaminants. It has been shown that steam autoclaved titanium surfaces contain high levels of oxygen and nitrogen containing organic compounds and a variety of inorganic contaminants [40]. Conversely, ultraviolet or g-irradiation produces much cleaner surfaces [40]. In some materials, surfaces initially appear clean only to have contamination develop with time. For instance, migration of bulk contaminants along grain boundaries of electroplated metals can take place, particularly if the sample experiences elevated temperatures. This phenomenon was reported recently for electrolytically gilded silver [41]. After 8 months of indoor storage, red spots of gold chloride were observed. Contamination also can take place during use of a product. This is quite true for catalytic materials such as automotive exhaust converters. In one simulation study, contaminants such as phosphorus, lead, zinc, and calcium were found to deactivate the catalyst [42]. The main sources of these contaminants were believed to be lubricant additives. XPS has been used to investigate adhesion failure for many years [43]. Studies have found that many adhesion failures are caused by contaminants at interfaces. Among all the materials that can cause adhesion failure, poly(dimethylsiloxane) (PDMS) is probably the most ubiquitous, being used as mold release agents, lubricants, surfactants, anti-foaming agents, and plasticizers. There are literally thousands of materials containing PDMS and it is not easy to avoid exposure to them. Unfortunately, low molecular weight fractions can cover bonding surfaces, either through direct contact with a PDMS source or through surface segregation and migration. For example, PDMS mold release agents can concentrate in molds if too much release is used or if the molds are improperly cleaned. Parts produced in such molds can have silicone layers from a few nanometers to several tens of nanometers thick. Attempts to join these components either through adhesive or thermal bonding often result in weak adhesive joints or total adhesion failure. In one case where molded polypropylene was bonded to steel with an ethylcyanoacrylate adhesive, complete adhesion failure was observed. As shown in Figure 10.14(a), the XPS spectrum taken from the steel side of the failure was a mixture of adhesive and silicone, whereas the spectrum taken from the polypropylene side of the failure was nearly pure silicone [Figure 10.14(b)]. Even seemingly clean environments can, with time, become contaminated with PDMS even though no source is apparent. For example, it was observed that a clean room table, on which the fiber-reinforced composite plies were
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288
286
284 282 280
-Si 2s -Si 2p
-N 1s
-O KLL
290
-C-(C,H,Si)
-C-O,C-N
-O-C=O 292
-C KLL
XPS Intensity (a.u.)
C 1s
-C 1s
-O 1s
(a)
1200
1000
800
600
400
200
0
Binding Energy (eV) -O 1s
(b)
-C 1s
-Silicone
1200
96
-O KLL
-Si 2s -Si 2p
110 108 106 104 102 100 98
-C KLL
XPS Intensity (a.u.)
Si 2p
1000
800
600
400
200
0
Binding Energy (eV)
Figure 10.14 XPS spectra from (a) the steel side and (b) the polypropylene side of a failed polypropylene-ethylcyanoacrylate-steel adhesive joint. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
handled, was contaminated with PDMS [44]. Transfer of PDMS from the contaminated table top to the composite plies resulted in poor composite adhesion. Silicones can even come from products designed to prevent contamination such as disposable gloves [45]. The surfaces of disposable vinyl gloves are quite often covered with plasticizers such as PDMS. Although these gloves are used ostensibly to prevent sample contamination, they can in fact act as a source.
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XPS is equally useful for investigating adhesion failure caused by other organic and polymeric materials. Low molecular weight fluorocarbons were observed to migrate in a plasma reactor used to deposit multilayer films for corrosion protection of aluminum alloys [46]. In this process trimethylsilane (TMS) and hexafluoroethane were sequentially deposited by a cathodic DC plasma. It was found that this process produced weakly adhered films. Poor adhesion was traced to fluorocarbon migration from the chamber walls to the sample during evacuation of the chamber. However, if an oxygen plasma cleaning step was introduced to clean the alloy before deposition of the TMS film, strongly adherent films were produced. Unfortunately, this process converted the fluorocarbon layer to a fluoride containing oxide layer which was considered detrimental to corrosion resistance. Another typical example where adhesion failure was traced to a prior processing step was the failure of gold plated nickel contacts in ceramic packages [47]. In this study a 20 nm thick carbon layer was found on a freshly failed contact. The XPS carbon 1s spectrum obtained from the contact matched that of a wax used in a process step prior to plating. Since the root cause of failure was wax buildup, adhesion was restored by more frequent changing of the cleaning solutions. XPS is often used to study corrosion since the technique provides elemental and chemical information. Many metals and alloys have passive oxide layers that limit corrosion. For example, bronzes were found to have a protective surface layer of lead oxide. However, when this layer was destroyed, such as by exposure to a moist SO2 environment, copper oxide and copper sulfite were formed [48]. Similarly when copper nickel alloys were exposed to synthetic sweat, e.g. to mimic contact of earrings, jewelry and watches with skin, copper (I) oxide and chloride were formed on high copper alloys [49]. Conversely, on high nickel alloys, copper (II) hydroxychloride, nickel hydroxide, and nickel oxide were formed. Corrosion of ferrous alloys has also been extensively analyzed, once again due to the ability of XPS to determine chemical states. Moreover, depth profiling by ion beam sputtering was often used during these experiments to measure the in-depth composition and the thickness of the corrosion layers. In one study of iron–aluminum intermetallics exposed to traces of H2S at 600 C, the scale formed consisted of three layers: an outermost organic layer, a mixed layer of FeS and Al2O3, and a bottom layer of Al2O3 [50]. In another study, chemical state depth profiling was obtained for an electropolished stainless steel surface, see Figure 10.15. The outermost surface contained an organic layer that was less than a monolayer thick. Both Cr+x and Fe+x oxides were detected with Fe+x being concentrated at the outer surface. The approximate thicknesses of the Cr+x and Fe+x layers
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Atomic Concentration (%)
90 Fe°
80 70 60
O
50 Cr+x
40
Fe+x
30 20
C Cr°
10 0 0
10
20
30
40
50
60
70
Sputter Depth (Å)
Figure 10.15 Chemical depth profile of an electropolished stainless steel sample. Note that sputter depth is based on the sputter rate of SiO2. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
were 2 and 0.9 nm, respectively, assuming that this material sputtered at the same rate as SiO2. Corrosion not only results in cosmetic blemishes and surface damage but can cause poor adhesion. This is particularly important in the microelectronics industry. For example, good adhesion of gold ball bonds to bond pads is vital since it is first external link allowing information to travel from the IC device to board level components. In one study ball bond failure was traced to a reactive ion etching step performed after the pad was formed [51]. Since bond pad production is not the last step in device fabrication, one must bear in mind the effect of subsequent processing step on bond pad cleanliness. Although production methods can be selected to minimize surface contamination, often the resulting surface requires additional cleaning processes. Because the matrix of contaminants, cleaning methods, and substrates can be large, it is imperative to examine the efficacy of the method chosen for a given substrate. For many systems this is performed easily by XPS. Not only does the method permit quantitative evaluation of contaminant removal, but it can also verify that the substrate composition has not been altered and that new contaminants were not introduced during the cleaning process. A gentle method for removing organic compounds from inorganic surfaces is simply to heat the material.
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For example, heating NiP/Al or hard disk glass substrates to 400 C removes nearly all of the carbon contamination [52]. Care must be taken, however, to assure the substrate is not damaged or modified by thermal exposure. In fact, surface segregation of mobile elements took place at temperatures as low as 300 and 350 C for the glass and NiP/Al substrates, respectively. Thus only a portion of the organic contaminants could be removed without sample damage. Wet chemical cleaning methods have also been studied by XPS. When stripping photoresist from aluminum, silicon, and silicon dioxide surfaces it is desirable to remove all traces of photoresist while leaving the substrates unaffected. Low molecular weight alcohols, e.g. isopropanol, were demonstrated to remove photoresist and produced surfaces with organic contamination levels similar to the RCA cleaning method [53]. The process appears, however, to leave a residual adhesion promoter layer that was applied prior to the photoresist. Dry cleaning methods such as oxygen-containing plasmas are well known to remove organic residues from surfaces [54] but the cleaned surfaces are typically oxidized [55]. While this would not be a problem for silicon dioxide surfaces, the growth of oxides on aluminum substrates such as bond pads is undesirable since it impairs wire bonding. Plasmas such as Ar/H2 have been shown to remove the surface oxide from bond pads but the process may also damage adjacent passivation layers [19]. Clearly the conditions under which plasma cleaning is performed must be carefully monitored and controlled. The cleaning examples presented above demonstrate that it is difficult to select a cleaning method that is both effective and harmless to the substrate. However, that is not to say that it cannot be done. In the case of indium tin oxide (ITO) substrates used in organic light-emitting diodes, the goal was to remove organic compounds that raised the turn-on voltage and lowered brightness. For this system, cleaning under ultraviolet light in conjunction with ozone gas, i.e. UV/O3 treatment, was found to significantly reduce organic contamination [56, 57] while having no apparent effect on the chemical composition of the ITO substrate [56].
10.3.5 Recent developments and future directions of XPS The four most important areas in which XPS has progressed over the past few years include analysis speed, minimum analysis area, imaging, and depth profiling. Analysis speed and sample throughput continue to
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climb due to advances in electronics, multi-channel detectors, computers, and software. Improvements in electronics and detectors have increased data acquisition rates. In addition, advances in software have allowed rapid identification and quantification of surface elements often with little or no user intervention. Moreover, computer controlled automation permits rapid sample positioning for both routine and complex multi-sample analyses. Large sample platens are often used to facilitate automated analysis of multiple samples or multiple areas on a large sample. The largest platen that is commercially available is designed specifically to hold 300 mm diameter silicon wafers. Small area XPS analysis is one of the major areas that has experienced improvements in recent years. Two approaches are available for decreasing analysis areas: use of microprobe [58] X-ray sources, and a combination of apertures and input lenses [59]. The microprobe method uses a focused electron beam that strikes the X-ray anode surface to generate X-rays. The X-rays are refocused onto the analysis area by a crystal monochromator. The most recent microprobe system has a minimum analysis area of 10 mm diameter. The aperture method uses a broad Xray source to generate photoelectrons from a large area of the sample. Apertures and input lenses are used to define the analysis area. With this scheme, the smallest area that has been achieved is 12–15 mm diameter. XPS imaging is another area that has advanced significantly in last few years. The two methods presently used for producing XPS images or maps are microprobe imaging [60] and parallel imaging [59, 61]. In microprobe imaging, images are generated either by scanning a focused X-ray probe beam across the analysis area, or moving the analysis area under the probe beam. The spatial resolution of microprobe imaging is defined by the X-ray spot size, and is on the order of 10 mm. In parallel imaging, either a polychromatic or a monochromatic X-ray beam is used. Images are simultaneously collected from the entire analysis area utilizing a two-dimensional array detector. The best spatial resolution in this mode is currently 2–3 mm. Finally, the need for high depth resolution and fast depth profiling has spurred advances in ion gun design. The introduction of low-energy highcurrent ion guns provides improved depth resolution during profiling while minimizing artifacts from the sputter damaged layer. Moreover, finely FIB are now available that can be used to sputter small areas or to reduce the sputtering time when depth profiling. Given the vast number of industries in which XPS analysis is employed it is not surprising that instrument manufacturers are being pulled in
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many directions. Fortunately, many of the latest improvements are applicable to a large majority of users. One can expect future instruments to offer greater ease of use, smaller analysis areas, faster acquisition times, and chemical depth profiling.
10.4 Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) 10.4.1 Background of TOF-SIMS Time-of-Flight Secondary Ion Mass Spectrometry is one of the few techniques that can provide specific compound identification of molecules on a surface. Conceptually TOF-SIMS is rather simple: bombardment of a surface by high-energy ions causes emission of secondary ions, which are mass analyzed by measuring the time required for the ions to fly from the sample to the detector. The difficulty, however, is in the details, i.e. producing a well defined short-duration primary ion pulse and accurately measuring the secondary ion flight time. Much of the early development of TOF-SIMS was carried out by Professor Benninghoven and his team at the University of M€ unster in Germany [62]. It was not until the early 1980s that TOF-SIMS was developed into a viable analytical method. Although acceptance of the technique was initially slow, it has evolved into a standard tool for identifying organic and inorganic contaminants on surfaces. The compound specificity of TOF-SIMS clearly differentiates it from other chemically sensitive surface analysis methods such as XPS also known as ESCA.
10.4.2 Basic principles of TOF-SIMS The generic class of SIMS methods is based on measuring charged species emitted from a surface due to bombardment by high-energy ions. Specifically, when a primary ion strikes the surface of a solid its kinetic energy is dissipated by the solid through collisional cascades within the near-surface region. The end result is that the primary ion is buried below the surface, bonds near the impact site are broken, and atoms, molecular fragments, and molecules are ejected from the top 1–3 atomic layers. Most of the ejected species have no net charge. However, a small fraction of these species will be either positively or negatively charged. Only these charged species (ions) are detected by the mass spectrometer,
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hence the term ‘‘SIMS.’’ If the primary ion dose is below 1012 ions/cm2 the probability that two primary ions will strike the same location (on the atomic scale) is low and the measurement is said to have been performed in the static mode. That is, the surface is unchanged, or static during the measurement. Thus nearly all ions emitted from the sample originate from virgin, unsputtered material, and hence are characteristic of the original surface. If the primary ion dose greatly exceeds 1012 ions/ cm2, there is a significant probability that the emitted ions will arise from a previously sputtered area, and thus are not representative of the virgin surface. In this case the measurement is said to have been performed in the dynamic mode. Dynamic SIMS provides elemental composition typically as a function of sputter depth. Unfortunately, it does not provide the chemical information, as does static SIMS. For a review of dynamic SIMS see [63]. Dynamic SIMS is preferred when one needs to determine the in-depth concentration of contaminants. Remember, however, that dynamic SIMS provides only elemental analysis. Conversely, static SIMS is usually preferred for identification of surface contaminants. This is particularly true when chemical information is needed such as for organic compound identification. There are three types of static SIMS instruments differing in the mode of ion separation and detection: magnetic-sector, quadrupole, and time-of-flight spectrometers. Magnetic-sector spectrometers can provide excellent detection limits and high mass resolution. They are limited, however, in mass range, generally <300 amu, and scan speed. Quadrupole spectrometers have the advantage of high scan speed, mass range up to 1,000 amu, ease of use, and adaptability to hybrid systems. The primary limitation of quadrupole systems is poor mass resolution, resulting in the inability to distinguish between ions of the same nominal mass. Time-ofFlight spectrometers have high mass range (up to several thousand amu), high mass resolution (>10,000 m/Dm above 100 amu), and rapid data acquisition. The main disadvantage of TOF-SIMS is the low current of the primary ion beam resulting in very slow depth profiling. In general, TOF-SIMS is the preferred method for static SIMS. In a time-of-flight spectrometer ions of charge q, typically –1, are subjected to an extraction field, Ve, of several thousand volts, imparting each ion with a fixed kinetic energy, Ek. Kinetic energy is given by Ek = qVe which is also equal to 1/2 mv2, where m is the mass of the ion and v is the velocity of the ion. Since Ek is constant for all ions, the velocity of each ion is inversely proportional to its mass. Lighter ions reach higher velocities in the extraction field. Hence for a given flight path length, l, the flight time, t, is shorter for lighter ions, t = l/v. Heavier ions have lower velocities and
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travel more slowly. Thus, the mass of any ion having unit charge can be determined from the flight time, m ¼ 2qVe t2 =l2
Eq. (10-10)
In practice Ve, t, and l are not explicitly known so mass spectra are internally calibrated from ions of known masses such as CH3+, C2H3+, OH, C2H, etc. An important feature of TOF-SIMS is that a complete mass spectrum is obtained from each primary ion pulse. Moreover, a higher mass resolution can be obtained by using longer flight tubes. This description has omitted two important items, namely, that the primary ions must be produced in packets and that the generation time of each packet should be as short as possible. This is necessary because the spread in generation time, Dt, directly affects mass resolution (Dm)1/2. The spectrometer described above generates a plot of ion counts vs. mass/ charge. Since the vast majority of all ions have a charge of –1, mass/charge and mass are almost synonymous terms. Figure 10.16 shows a typical mass spectrum. This figure shows the negative ion spectrum of a mixture of the antibiotic Tobramycin sulfate and Simplex-P bone cement, which itself is a mixture of poly(methyl methacrylate) (PMMA) and BaSO4. Note that ions can be positively or negatively charged but only one polarity is present in a given spectrum. Thus for complete characterization of a material one must
Counts (0.19 amu/bin)
O-
C4H5O2-
1.5E+7
HSO4-
CH-
1.0E+7
OHSO3C8H13O2-
5.0E+6 C2H- CH O3 0
C9H13O4-
x150
0
50
100
150
100 m/z
150
Figure 10.16 TOF-SIMS negative ion spectrum of a mixture of the antibiotic Tobramycin sulfate and Simplex-P bone cement, which itself is a mixture of poly (methyl methacrylate) (PMMA) and BaSO4. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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obtain both positive ion and negative ion spectra. In addition to spectral analysis, TOF-SIMS is routinely used for ion imaging. Ion images or maps are two-dimensional pseudo-color images showing the intensity of a given emitted ion, or sum of ions, as a function of X,Y location on the surface. Figure 10.17 shows the distribution of PMMA, BaSO4, and Tobramycin sulfate in a cross-sectioned sample of a bone cement/antibiotic mixture. This specimen was taken from residual material in an injection nozzle used during a hip replacement surgery. The ions used to image PMMA, BaSO4, and Tobramycin sulfate were C4H5O2 (85 m/z), SO3 (80 m/z), and HSO4 (97 m/z). Microprobe imaging uses a finely focused probe beam that is rastered over the desired analysis area. Hence, the primary beam size dictates image resolution. State-of-the-art resolution in microprobe mode is 50 nm diameter. Spectra of organic surfaces can contain literally thousands of peaks. Yet the time required to reach the static limit can be a few minutes or less in small areas. This means that the analyst may not have sufficient time to acquire preliminary spectra necessary for defining ion images without exceeding the static limit. This is particularly true if the sample is both small and unique. In these instances the ability to store all of the raw data is vitally important. Remember that each primary ion pulse generates a complete mass spectrum. Thus a raw file is a sequence of 104–105 individual spectra. Also included in the raw file are specifications for the raster pattern from which the X–Y location of each spectrum can be determined. From this file the analyst can create any desired ion image or display complete mass spectra from any pixel area. The value of this becomes apparent when one inspects spectra of heterogeneous surfaces. Consider a
(a) total negative ions
100µm
(b) SO3-
(c) HSO4-
100µm
100µm
Figure 10.17 Negative ion images showing (a) the general uniformity of the crosssectioned bone cement sample and the distributions of (b) SO3 characteristic of BaSO4 and (c) HSO4 characteristic of Tobramycin sulfate. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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failed hard disk that contained a series of micrometer-sized defects that were visible in optical images of the disk. TOF-SIMS raw data were acquired from an area encompassing the defects. The defects were easily located in the total ion image, see Figure 10.18(a). By filtering the data, positive ion spectra from the defects [circled areas in Figure 10.18(b)] and an adjacent defect-free region [boxed area in Figure 10.18(b)] were generated, see Figure 10.19. Images of intense ions found in the defect-free and defect regions clearly highlight the locations of the hydrocarbon droplets in Figure 10.18(c, d), respectively. The spectrum from the defect-free area was in excellent agreement with perfluoroether lubricant AM2001, whereas the defect spectrum matched that of a grease used in the drive. The ultimate quest in TOF-SIMS is to devise a method for quantitative chemical analysis. In order to perform quantitative analysis one must know or be able to predict a material’s ion yield, i.e. the number of (b)
(a)
10µm
10µm (c)
(d)
10µm
10µm
Figure 10.18 TOF-SIMS positive ion images of defects on a (40 mm)2 hard disk surface: (a) total ion image, (b) circled and boxed areas indicating region-ofinterest boundaries for defect and control spectra, respectively, (c) image of intense ions (12, 31, 47, and 50 m/z) in the defect-free region, and (d) image of intense ions (27, 41, 55, 113, 127, 371, 483, and 497 m/z) in the defect regions. (Source: Physical Electronics Inc., Chanhassen, MN. Reprinted with permission.)
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12 119 31
100 47
50
50
0
69
m/z
100
150
(b)
483
357 350
497
469
371
400
450
500
m/z Figure 10.19 Positive TOF-SIMS spectra of (a) the defect-free region and (b) the defect regions on a hard disk surface. (Source: Physical Electronics Inc., Chanhassen, MN. Reprinted with permission.)
ions formed per incident ion. This is a daunting task since ion yields can vary by several orders of magnitude. Elements with high ionization potentials, such as sodium, tend to more readily form positive ions, whereas those with high electron affinities, such as fluorine, tend to form negative ions. The same theory holds for organic compounds but one must also consider the degree of charge stabilization. For these reasons an aliphatic compound, such as polyethylene, has a positive ion yield many times lower than that of an aromatic ester such as poly(ethylene terephthalate). In addition, the matrix from which a compound is ionized can affect ion yields and fragmentation patterns of organic molecules. For example, the presence of sodium ions or silver ions or even organic acids can increase positive ion yields while decreasing fragmentation of organic molecules. For these reasons, many TOF-SIMS studies are purely qualitative. When used with caution, relative ion intensity, such as contaminant ion vs. substrate ion, can provide semi-quantitative analysis, i.e. rank ordering. Truly quantitative analysis is possible if the contaminants and substrate are well defined and control samples of known contaminant concentration can be made. Metal contamination on silicon wafers is one such system.
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10.4.3 TOF-SIMS instrumentation A typical TOF-SIMS spectrometer consists of a vacuum chamber operated at a pressure lower than 109 torr, a pulsed ion gun, extraction and focusing optics, a flight tube, and a detector. Many different ion guns are available such as Ga+, In+, Ar+, O2+, Cs+, SF5+, Aux+, Bix2+, and C60+. The two liquid metal ion guns, Ga+ and In+, are easily operated to give high mass resolution (short pulse length) for spectral analysis or high spatial resolution (narrow beam diameter) for microprobe imaging. Gas guns such as Ar+ and O2+ are robust and easy to use for large area and/or direct imaging analysis. Cs+, a surface ionization source, is also used for large area and/or direct imaging analysis and as an auxiliary gun for high depthresolution profiling. Polyatomic ion guns such as SF5+, Aux+, Bix2+, and C60+ are used to enhance ion yields of organic compounds while minimizing fragmentation [64, 65], as is clearly demonstrated by comparing the spectra of polystyrene obtained with Ga+ and C60+ primary ion beams [65] (see Figure 10.20). Flight tubes are of two distinct designs, reflectron [66] and TRIFTTM [67] as shown in Figure 10.21, and are generally up to
600k
50 40 C60+
Intensity (Counts)
400k
30 20 10
200k
0 1200 1500 1800 2100
0 15k
10
Ga+
10k
5
5k
0 1200 1500 1800 2100
0
0
100
200
300 m/z
400
500
600
Figure 10.20 Positive TOF-SIMS spectra of poly(styrene) using 10-keV C60+ or Ga+ ions. Dose (ions): C60+, 4.05 · 108; Ga+, 4.3 · 108. The inset spectra clearly demonstrate that C60+ ions produce much higher ion yields for high mass ions. (Source: Ref. [65]. Reprinted with permission.)
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Ion Mirror
Detector Transport Optics
Ion Gun
Extractor Sample Electrostatic Analyzer
Electron Flood Gun
Electrostatic Analyzer
Electron Flood Gun
SED
Post Spectrometer Blanking Plates
Energy Slit
Sample
High Mass Blanker
Angular Filter
Electrostatic Analyzer
Detector Ion Gun Figure 10.21 Schematic diagram of (a) a reflection TOF-SIMS system and (b) a €nster, Germany, TRIFTTM TOF-SIMS system. (Source: (a) ION-TOF GmbH, Mu and (b) Physical Electronics Inc., Chanhassen, MN. Reprinted with permission.)
two meters long. Other typical components are a computer for instrument control and data acquisition and storage, an electron neutralizer for charge compensation of insulating samples, and a multi-axis sample stage. Cooling and heating stages are useful for preservation of volatile components and sample modification, respectively.
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10.4.4 Applications of TOF-SIMS for characterizing surface contaminants Identification of contaminants is easiest if the analytical technique can quantitatively detect all elements in the periodic table and all functional groups of organic compounds, or better yet entire molecules, while confining the analytical volume solely to the contaminant. In general TOFSIMS fulfills these requirements; however it is often limited to qualitative and semi-quantitative analysis. The shallow sampling depth of the method, 1–3 atomic layers, means that the sampling volume is well defined. When combined with the ability of ion images to display graphically the location of contaminants with a lateral resolution down to 50 nm, it becomes quite clear that TOF-SIMS is an excellent contaminant identification tool. It is important to note that any material—organic, inorganic, or metallic—can be analyzed as long as it is vacuum compatible. This generally restricts analysis to solid or low volatility liquid contaminants on solid substrates. In many industrial products one wishes to monitor surface contaminants. For example, inspection of raw materials often reveals that bulk contaminant levels can be very low while surface contaminant level can be high. If the material has a low surface area, bulk analytical methods may fail to detect surface contaminants. Moreover, many contaminants and low molecular weight molecules preferentially migrate to the outer surface. For example, analysis of starch grains revealed lipids (fats) and other contaminants on the surface [68]. Low surface free energy molecules such as silicones, fatty acids, lipids and their derivatives often migrate to the outer surface of solids since by doing so the surface free energy of the solid is decreased. Low molecular weight molecules such as these are readily identified by TOF-SIMS since the entire molecule is usually removed from the surface intact. This is illustrated in Figure 10.22 were the fatty acid esters butyl palmitate and butyl stearate were found on the outer surface of a molded polypropylene container. In other industrial products one might wish to know the efficacy of different cleaning methods or the effect of processing on surface cleanliness. This is particularly true for orthopaedic and dental implants where contamination can lead to infection or premature failure of the implant. Studies with these materials are often performed with model contaminants such as bovine serum albumin or benign bacterial spores to mimic blood or pathogenic contamination, respectively [69]. In these studies molecular fragments are used as markers since the contaminants are too large to be liberated intact.
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Ion Counts (arbitrary units)
[bp+H]+ [bs+H]+ [bp-C4H9O]+ x10 200 0
50
100
150
200
[bs-C4H9O]+ 250 250
300 300
350
m/z
Figure 10.22 Positive TOF-SIMS spectrum of a molded polypropylene container showing contamination by fatty acid esters [butyl palmitate+H]+ at 313 m/z and [butyl stearate+H]+ at 341 m/z. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
TOF-SIMS is not limited to analysis of contaminated surfaces. It can also be used to study ‘‘pure’’ contaminants such as those found in dust and air pollution. In a study of 2.5 mm particles from Salt Lake City air pollution [70] the high spatial resolution of TOF-SIMS permitted analysis of individual particles. The high mass resolution and detection sensitivity of the method enabled trace metals analysis as well as organic compound identification. Surface contaminants can lead to destruction of the surface, e.g. corrosion, or to changes in the properties of the sample, e.g. haze formation [71]. In both cases it is important to be able to detect contaminants of all chemical compositions and of varying size. Contaminants also change the chemical properties of surfaces thereby impacting adhesion and wettability. Poor adhesion and wettability often results in adhesion failure [72], coating defects [73], and poor print quality [74]. Contaminants can be introduced to the surface from the environment or they can originate within the material and migrate to the surface [73]. For example, in one study of paint defects in polycarbonate automotive parts, Irgafos 168 and fatty acid esters of pentaerythritol were identified in the defects (see Figure 10.23). While Irgafos 168, an antioxidant added to the polycarbonate, apparently surface segregated, the source of the fatty acid esters was uncertain since it is commonly used as a plasticizer (i.e. an internal source) as well as a release agent (i.e. an external source). TOF-SIMS is widely used to study adhesion failures since many of the contaminants causing adhesion loss are low molecular weight and readily ionized. The most ubiquitous contaminant that
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Figure 10.23 Positive TOF-SIMS spectrum of a painted polycarbonate automotive part taken inside a coating defect showing contamination by Irgafos 168 and pentaerythritol fatty acid esters. (Source: Ref. [73]. Reprinted with permission.)
causes adhesion failure is poly(dimethylsiloxane) (PDMS), which is found in many materials such as anti-foaming agents, cosmetics, hydraulic fluids, lubricants, and release agents. This material has a very high ion yield, and thus the detection limit is generally well below 1% of a monolayer. High mass resolution and mass range, and small analysis areas are useful for all types of surface analysis. However, TOF-SIMS affords a unique capability for failure analysis, i.e. retrospective analysis. Many failures are one of a kind or at least rare such that the analyst is often
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forced to study a single sample. The ability to perform retrospective data analysis, i.e. off-line processing of raw data streams, greatly simplifies this task. The analyst need not worry about confining the analysis to the failure area but rather must simply verify that the analysis area includes the failure area and that the appropriate trade-off between mass resolution and spatial resolution has been made. After the raw data are acquired, the analyst can extract from the data ion images to highlight contaminants and mass spectra to ascertain their chemical composition such as are shown in Figures 10.18 and 10.19. This is particularly important when the analysis area is small as is often the case in the hard disk [8] and semiconductor [75] industries. As stated earlier, TOF-SIMS is often limited to qualitative or semiquantitative analysis. The primary cause of this limitation is the difficulty in producing standards of known contaminant concentrations on well characterized substrates. One would also like to have alternative analytical methods to corroborate the TOF-SIMS results. One system that meets these requirements is the quantitative surface metals analysis of silicon wafers. Surface metals are routinely studied in-situ by Total Reflection X-ray Fluorescence (TXRF), or in solution by Vapor Phase Decomposition Inductively Coupled Plasma Mass Spectroscopy (VPD-ICPMS) or Vapor Phase Decomposition Atomic Absorption Spectroscopy (VPDAAS) [29]. Were it not for the several potential advantages of TOF-SIMS the methods of choice would remain TXRF, VPD-ICPMS, and VPDAAS. Whereas TXRF cannot detect hydrogen through fluorine, TOFSIMS can examine all elements in the periodic table, with equal or better sensitivity [76–78]. VPD-ICPMS and VPD-AAS can also examine all elements, however unlike TOF-SIMS they are difficult methods to perform accurately, they cannot differentiate between particulate and plated contaminants, and they do not provide lateral distributions [77, 78]. Moreover, TOF-SIMS offers analysis of both inorganic and organic contaminants [79–81]. Several methods have been developed to generate surface metal calibration standards. The simplest method is to spin coat a solution containing the desired contaminants onto a clean silicon wafer [82]. Unfortunately it is difficult to control the level of contamination and to produce a uniform coverage of metals. A more elegant method is to ion implant metals through a removable layer with the energy of the implant selected to place the peak of the implant at the interface between the removable layer and the substrate [83, 84]. Once the sacrificial layer is removed, the sample surface contains a known concentration of the implanted species. Contaminant concentration can be easily changed
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by varying the implant dose. Advantages of this method are the high precision and accuracy of the implant concentration and uniformity across the wafer. The disadvantage is the time and expense in preparing the standards and the need for many different standards. A third method, sputter deposition, has been demonstrated for GaAs wafers [85]. In this method single element or multi-element targets are sputtered to produce sub-monolayer concentrations of the target elements. As robust protocols for quantification of surface metals contamination by TOF-SIMS are developed, this technique will gain favor as the method of choice. As one would expect, TOF-SIMS also has been used to verify the efficacy of new cleaning methods. For example, it has been used to study the effect of ozone based cleaning processes for the removal of organic contaminants from silicon wafers [86]. One prerequisite for studying cleaning efficiency is depositing organic contaminants in a reproducible and quantitative way. Although several methods have been investigated, wet chemical exposure was found to produce the best results [86]. Other studies have used the high sensitivity of TOF-SIMS for organic compounds to verify that cleaning solution additives such as chelating agents did not deposit on wafers during cleaning [87].
10.4.5 Recent developments and future directions of TOF-SIMS Being a relatively new analytical technique, advances in TOF-SIMS instruments are still proceeding rapidly. The wide utility of the method means that manufacturers are being pulled in many directions at the same time. Many recent advances have been driven by the semiconductor industry’s need to analyze low concentrations of surface contaminants, primarily surface metals. Tools are now available for analyzing whole 200 and 300 mm wafers. Automation of sample positioning is possible from optical images of the sample or from off-line ODD maps. Advances in both extremes of analysis area now permit the analyst to examine regions as large as (1 mm)2, and as small as 50 nm in diameter. With time, the early limitation of the lack of organic compound reference spectra is slowly being addressed. Current commercial libraries contain several hundred compounds. Still, this is in stark contrast with the profuse reference spectra for other mass spectroscopic methods. Hopefully TOF-SIMS analysts will continue to share reference spectra for the benefit of the entire community. Organic analysis will benefit from larger
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libraries, as well as from better spectral analysis software. Although expert systems for compound identification are many years away, incremental steps should be taken to ease the burden of examining the thousands of peaks in a typical spectrum. And finally there is the ultimate quest to devise a method for routine quantitative analysis by TOF-SIMS. This quest will require the concerted efforts of analysts, theoreticians, and software engineers, with considerable financial support.
10.5 Low-energy Ion Scattering (LEIS) 10.5.1 Background of LEIS Low-energy ion scattering (LEIS), also known as ion scattering spectroscopy (ISS), was first developed in the early seventies by D. P. Smith for use for elemental identification [88]. Since then, it has been used to study the composition and structural properties of the first atomic layer of a sample surface [89]. This technique, based on elastic scattering of atomic ions incident on the surfaces, is one of the four major surface analysis methods including SIMS, AES, and XPS. In contrast to AES and XPS, and somewhat similar to static-SIMS, LEIS only observes the first atomic layer. Its major advantages over other techniques are its extreme surface sensitivity and minimal matrix effects. Because of its rather low spectral resolution between adjacent high mass elements and poor sensitivity to low-mass elements, LEIS is less used compared to the other three techniques. However, the technique is quite useful for quantitative analysis of the outermost surface layer.
10.5.2 Basic principles of LEIS Low-energy ion scattering is a surface analytical technique based on the measurement of backscattered ions during ion-surface collisions [90]. The most commonly used ion is 4He+. When low energy ions bombard a surface, some of the ions are elastically scattered from the surface and, consequently, impart some of their kinetic energy to surface atoms. This process is described by a simple two-body elastic collision between an incident ion and target atom and can be modeled as simple hard-sphere or billiard-ball collisions [91–93]. If the incident ions are monoenergetic, having initial kinetic energy Ei, the kinetic energy Ef of the scattered ions can be derived from the energy and momentum conservation laws
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and expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 m2 sin2 u 6cos u þ 6 m1 Ef ¼ 6 6 m2 4 1þ m1 2
32 7 7 7 Ei 7 5
Eq. (10-11)
Here m1 and m2 are the masses of the incident ions and surface atoms, respectively, and u is the known scattering angle (u ‡ 90 ). A schematic of the LEIS process is shown in Figure 10.24. Mass m2 of the target atom must be greater than m1 of the incident ion in order to have backscattering. There are no backscattered ions from hydrogen atoms because the mass of the hydrogen target atom will never exceed that of the probe ions. In Eq. (10-11), Ei, m1, and u are fixed. By measuring the kinetic energy Ef of the scattered ions, one can calculate mass m2 of the surface target atom. Thus the kinetic energies of the scattered ions are characteristic of surface atoms. A typical LEIS spectrum is a plot of the number of scattered ions vs. their kinetic energies. A typical LEIS spectrum from a polycrystalline nickel surface [88] is shown in Figure 10.25. This surface was contaminated by an adsorbed hydrocarbon or CO, possibly in combination with a surface oxide. When 4He+ probe ions (m1 = 4) bombarded this area, at scattering angle u of 90 , the scattered ion peaks appeared at kinetic energies of 0.87Ei, 0.6Ei, and 0.5Ei. Thus according to Eq. (10-11), these three peaks corresponded to the scattering from nickel, oxygen He+, Ef(S)
He+, Ei
He+, Ef(A)
He+, Ei
A: Adsorbed atoms S: Substrate atoms
θ
θ: Scattering angle
Figure 10.24 Schematic of low energy ion scattering using He+ probe ions. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
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Figure 10.25 Plot of scattered ion intensity vs. scattered ion energy ratio (Ei /Eo) for 1500 eV 4He+ from polycrystalline Ni contaminated with C and O. (Source: Ref. [88]. Reprinted with permission.)
and carbon surface atoms, respectively. Moreover, this result demonstrates that the ion will retain most of its energy if it is scattered from a heavier atom (like nickel in this example). However, an ion scattered from a lighter atom (such as carbon) will lose most of its energy. Therefore, the LEIS energy spectrum is, in a sense, a mass spectrum. The kinetic energies of the peaks identify each elemental species on the surface. Moreover, peak heights or peak areas can be used to determine surface elemental concentrations [93]. The extreme surface sensitivity of LEIS results from the high neutralization probability of the He+ ions [94–96]. As a consequence, only 103 to 104 of the primary ions will survive the collision and finally reach the detector. The scattered ions originating from deeper than the first atomic layer have a high probability of being neutralized and are not detectable. This makes LEIS unique in studying the surface composition of the first atomic layer. A systematic investigation of metal/metal oxide systems using LEIS clearly illustrates its capability of distinguishing a monolayer of adsorbed atoms from those present in clusters [97–99]. If a surface is completely covered by a monolayer of adsorbed atoms as shown in Figure 10.26(a), only the ions scattered from the adsorbate are
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(a) adsorbates as a monolayer
(b) adsorbates as clusters
Figure 10.26 Schematic diagram of adsorbed atoms as a (a) monolayer vs. (b) clusters. (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
measured and the substrate intensity is completely attenuated. However, if the same amount of adsorbate forms clusters [Figure 10.26(b)], a fraction of the substrate will remain exposed, and ions scattered from both the adsorbate and substrate will be detected. As stated earlier, a LEIS spectrum is essentially a mass spectrum. Each peak represents an element in the surface layer. Of equal importance is the fact that peak intensities can be used to determine elemental concentrations, therefore LEIS can be used for quantitative analysis. Strictly speaking, since one measures atoms from the first atomic layer, LEIS can detect only areal densities rather than volume concentrations as in AES and XPS. The intensity of the ions scattered from atom i into angle u can be described as [100] Ii ¼ Io si Pþ i RTni
Eq. (10-12)
where Io is incident ion current, si is the differential scattering crosssection for scattering from element i, Pi+ is the ion survival probability, R is a factor that accounts for surface roughness related to the shadowing and blocking effects, T is the transmission function of the spectrometer, and ni is the number of surface atoms i per unit area. Thus the areal density ni can, in principle, be determined from the measured intensity Ii by ni ¼
Ii Io si Pþ i RT
Eq. (10-13)
It should be noted that direct quantification is possible only if all the parameters on the right-hand side of Eq. (10-13) are known. However, this method is not generally used because parameters, such as Pi+ and R, are poorly known and result in large experimental errors.
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In practice, quantitative analysis of surface elemental concentration is based on calibration against standard compounds. Equation (10-12) can be rewritten as Ii ¼ Io Si ci
Eq. (10-14)
where Si is the elemental sensitivity factor relative to a standard1 and ci is the relative surface concentration of element i. Therefore, the relative surface concentration, i.e. surface coverage of element i, can be obtained as ci ¼
Ii Io Si
Eq. (10-15)
It has been found that Si generally does not depend on the chemical environment of an atom in the surface (i.e. there are little or no matrix effects). This makes it relatively simple to perform quantitative analysis in LEIS. Relative sensitivity factors Si have been measured from pure compounds by different laboratories through round robin experiments, which allow straightforward calculation of relative elemental concentrations. Furthermore, it has been noted that Si increases monotonically with atomic mass [89]. Because of this simple relationship, it is possible to use the peak intensity as a direct quantitative measurement of the elemental concentration. Theoretically, LEIS can be used to detect all elements having atomic mass greater than that of the incident ions. Its ability to resolve the masses of different atoms depends on the energy spread of the incident ions, the mass ratio m2/m1 between the target atoms and incident ions, and the scattering angle u. The optimum mass resolution can be obtained by choosing the mass ratio m2/m1 to be close to unity, as shown in Figure 10.27 [30]. Moreover, a large scattering angle also gives good mass resolution. For low mass atoms, LEIS has good mass resolution but poor sensitivity with minimum detection levels of a few atom %. For higher mass atoms, this technique has very good sensitivity but poor element specificity. For example, LEIS can be used to detect ppm levels of gold, but it is extremely difficult to resolve adjacent high mass atoms, such as Au–Pt, or even Cu– Zn, Fe–Co, K–Ca, etc. The elemental specificity for high mass atoms can be improved by using higher-mass probe ions (Ne+, Ar+, Kr+, and Xe+). 1
For one case in a round robin experiment performed on a set of representative polycrystalline, metallic samples at five different laboratories, Cu was used as a standard [100].
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Resolving power (m2/∆m2)
m2/m1=1.625 100
4 16.25
10
50
1
0.1 0
30
60
90
120
150
180
Scattering angle (θ) (degree)
Figure 10.27 Mass resolving power vs. the scattering angle for different mass ratios of m2/m1 (plot reproduced according to Eq. (4.13) in Ref. [30]). (Source: Evans Analytical Group, Sunnyvale, CA. Reprinted with permission.)
10.5.3 LEIS instrumentation The basic elements for LEIS experiments are an ultrahigh vacuum chamber, an ion gun, and an energy analyzer. This technique is often designed as an add-on technique to supplement XPS and AES. A differentially pumped ion gun is used to generate positive ions with low energies, typically from 500 eV to 5 keV. The most commonly used ion sources are the noble gas ions He+, Ne+, and Ar+, or the alkali metal ions Li+, Na+, and K+. In most instances the spatial resolution of LEIS is limited by the size of the ion beam. The same energy analyzers as used for XPS and AES, i.e. cylindrical mirror or CHAs, can also be used for LEIS. Only the analyzer polarity needs to be changed because the ions are positively charged. Large scattering angles are needed in most LEIS experiments (for example, they range from 130 to 170 ) in order to obtain maximum resolving power. When using conventional LEIS instrumentation, the probe ions often cause damage to the sample surface. Ion-induced damage includes the sputtering of atoms from the surface and breaking of surface chemical bonds. To circumvent this problem, Brongersma and coworkers designed a parallel detection analyzer to maximize data collection while minimizing
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Figure 10.28 Schematic diagram of toroidal electrostatic analyzer with a positionsensitive detector. (Source: Ref. [89]. Reprinted with permission.)
analysis time [101]. As shown in Figure 10.28, a double-toroidal electrostatic analyzer is used for imaging the energy distribution onto a detector [101]. A specially designed position-sensitive detector allows simultaneous detection of energies from 100 channels and has sensitivity about 1000 times that of conventional LEIS measurements. This increased detection efficiency allows one to use very low ion beam current, therefore beam damage is significantly reduced.
10.5.4 Applications of LEIS for characterizing surface contaminants In many applications, surface contaminants are concentrated at the first atomic layer of a surface. The end result is that the elemental concentration of the outermost surface will be significantly different from that in deeper layers. Since LEIS is unique in studying elemental compositions of the first atomic layer due to its extreme surface sensitivity, it is well suited for these studies. A particular strength of the method is the ability to perform quantitative analysis of the outermost surface layer. The early applications of LEIS included the detection of surface contaminants on pure conductive materials, particularly on metal and alloy surfaces. Because these materials have high surface free energies, adventitious carbon contamination is almost always present. Moreover, exposure to air and moisture often causes the formation of metal oxides and hydroxides on the surface. Since LEIS can easily distinguish low mass elements such
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as carbon and oxygen from high mass transition metals, it is well suited for studying this type of samples. As is shown in Figure 10.25, LEIS unambiguously identified carbon and oxygen on a polycrystalline nickel surface contaminated with adsorbed hydrocarbon or CO, possibly in combination with a surface oxide. In addition, recent LEIS studies of aluminum foils [102] further demonstrate its ability to identify surface impurities on metal surfaces. As displayed in Figure 10.29(a) [102], the LEIS spectrum taken from an as-received hot-rolled aluminum foil indicates that the outermost surface was contaminated by carbon, oxygen, and chlorine. Aluminum was not detected in this spectrum, which implied that aluminum lay beneath the organic layer. LEIS is also used to evaluate the efficiency of surface cleaning methods. Since surface contaminants often interfere with product operation and
Figure 10.29 LEIS spectra taken from the hot-rolled Al foil using 1 keV He+ after (a) insertion into the UHV chamber, (b) a 12-hour exposure to the H-atom flux, and (c) 4-hour of sputtering with 2 keV Ne+. (Source: Ref. [102]. Reprinted with permission.)
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even cause product failures, they need to be removed during processing. In the study of hot-rolled aluminum foil it was found that a 12-hour exposure of the surface to a flux of hydrogen atoms removed the carbon and oxygen contamination, as shown in Figure 10.29, spectrum b. Subsequent Ne+ sputtering for 4 hours removed almost all the remaining surface contaminants and left a clean aluminum surface as shown in Figure 10.29, spectrum c. Similarly, an air-exposed polycrystalline Ni/Cr alloy was studied by LEIS [103]. The outermost surface of the as-received Ni/Cr alloy not only contained nickel, but also had oxygen, carbon, and sodium impurities. Following a 12-hour exposure to a hydrogen atom flux and a subsequent 15-minute Ar+ sputtering, a clean alloy surface with only a small amount of oxygen was obtained [103]. In practice, for these nearsurface contaminants, not only can LEIS provide quantitative evaluation of the surface cleanliness, but it can verify that new contaminants were not introduced during the cleaning process. For instance, thermal heating is a gentle method to remove organic compounds from inorganic surfaces, but can cause substrate modification and damage. One example was given by studying Au–Ni alloys [104]. After heat treatment at 250 C, molybdenum impurities were found to segregate to the surface. In this particular case the use of a Ne+ probe rather than the more conventional He+ probe is beneficial since it permits complete separation of molybdenum and gold (see Figure 10.30) [104]. The study of corrosion on finished metals is of great interest. Corrosion not only results in cosmetic blemishes and surface damage but can cause adhesion failure. Sometimes, even fractional monolayer contamination by elements such as chlorine and sulfur can initiate corrosion. The application of LEIS to monitor outermost surface contaminants has been extremely helpful in providing critical information for device manufacture [105]. Examples have included the detection of surface contaminants on copper [105], steel [106], and electrical contacts [89]. Depth profiling by ion beam sputtering was also utilized during these experiments to measure the in-depth composition and thickness of the contaminants. As in SIMS, AES, and XPS, the etching capability of ion beams allows depth profiling measurement in LEIS. Either a single ion beam is used for both etching and LEIS analysis, or dual ion beams are used with one for etching and the other for LEIS analysis. A depth profile plot in LEIS represents areal density at each sputter depth vs. sputter time. If the sputter rate is known, a depth profile can be converted to elemental concentration vs. sputter depth [105, 106]. The study of surface contaminants and segregation on polymer surfaces is another area that has generated considerable interest recently. As indicated previously, the LEIS system designed by Brongersma and coworkers
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Figure 10.30 LEIS spectra using He+ and Ne+ ions from Ni–Au alloy contaminated by Mo. Note the increased mass resolution obtained by choosing the heavier primary ions (Ne+). (Source: Ref. [104]. Reprinted with permission.)
makes it possible to study polymers without causing noticeable beam damage to the surface [101]. LEIS is particularly useful for studying surface segregation, when often a monolayer or less of surface contaminants are present. A good demonstration of its unique capability can be seen by studying poly(3-hexylthiophene) (P3HT) films [107]. In this example, LEIS was used to investigate P3HT films that had 2% siloxane monomers in the bulk. The topmost surface was found to be silicone enriched due to the segregation of siloxane towards the outermost surface. It contained 25–100% siloxane (depending on the preparation method) by referencing to a pure poly(dimethylsiloxane) (PDMS). In addition, sputter profiling was also performed on these samples to determine the siloxane chain orientation. LEIS depth profile results indicated that the methyl groups of the siloxane were preferentially situated on the outermost surface of P3HT and partially screened oxygen atoms that were below the methyl groups. Furthermore, by comparing the measured and calculated LEIS intensities of surface carbon, oxygen and sulfur at different surface siloxane coverage, it was concluded that the structure of the siloxane on P3HT
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Figure 10.31 LEIS spectrum from a poly(phenylene vinylene) (PPV) semiconducting polymer using 3 keV 3He+ ions. Note that the strong silicon peak shows that the surface is heavily contaminated by siloxane. (Adapted from Ref. [99]. Reprinted with permission.)
resembled that of a PDMS film. Another study examined the outermost surface of a poly(phenylene vinylene) (PPV) semi-conducting polymer in a polymer light emitting diode (PLED) [99]. A strong silicon peak was observed in the LEIS spectrum and indicated that the surface was heavily contaminated by silicone, as displayed in Figure 10.31 [99]. This silicone contamination was caused by the surface segregation of silicone from the bulk PPV layer.
10.5.5 Recent developments and future directions of LEIS In comparison with other surface analysis techniques, LEIS has its merits as well as disadvantages. As has been demonstrated, it is conceptually simple, quantitative, and extremely surface sensitive. However, this technique has relatively poor elemental specificity for materials consisting of elements with similar masses. Furthermore, in studying polymer surfaces, the probe ions often cause damage to the surface. This is particularly true for older instruments. Therefore, its applications have been limited compared to other surface analysis techniques. Fortunately, progress has been made since the 90s, and now it is possible to analyze samples without causing significant damage to the surface. This is particularly important when studying polymer surfaces.
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Based on its past applications, the future trends of LEIS will be focused on improvements in sensitivity, mass resolution, and analysis time. As it becomes more widely recognized that the composition of the first atomic layer is critical in a product performance, LEIS will likely become a more common technique in routine surface analysis. One hopes that commercially available systems that offer higher performance and ease of use will be available in the near future.
10.6 Summary When selecting a method for surface contaminant analysis one must consider factors such as the size, shape, morphology, composition, volatility, concentration, and history of both the substrate and the contaminant. In addition one must decide whether the study should provide qualitative or quantitative results and what specific type of information is required, e.g. elemental composition or chemical bonding or exact compound identification. AES, XPS, TOF-SIMS, and LEIS are four classical surface analysis methods, each capable of quantitative analysis of sub-monolayer contaminants. These methods differ significantly in applicability for particle analysis. LEIS and XPS require particles of 100 and 10 mm diameters, respectively. In contrast sub-micrometer particle analysis requires the use of TOF-SIMS or AES with AES having the smallest analysis size of 10 nm diameter. Whenever elemental analysis is insufficient for contaminant identification, XPS and TOF-SIMS are the methods of choice. This is particularly true for analysis of organic materials. Often the choice between XPS and TOF-SIMS can be made based on whether the contaminant is a complete unknown for which XPS excels or whether a specific contaminant needs to be identified for which TOF-SIMS excels. Minimum detection limit is often a deciding factor in method selection. LEIS and AES generally have limited sensitivity with XPS being only slightly more sensitive. On the other hand, TOF-SIMS has extremely low detection limits for all elements and many organic molecules, particularly those having molecular weights between 100 and 500 amu. In many instances the choice of analysis method is not immediately obvious. It is then helpful to consult Table 10.1 to rank the suitability of these methods. Given the complexity of manufacturing processes and the often uncontrolled history of industrially relevant samples, one is forced frequently to employ multiple analytical methods.
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11 Ionic Contamination and Analytical Techniques for Ionic Contaminants Beverly Newton Rohnert Park, CA, USA
11.1 What is an Ion? An ion is described as an atom or group of atoms that has either lost one or more electrons making it positively charged (a cation), or gained one or more electrons making it negatively charged (an anion). Some common examples of cations are ammonia (NH3+), sodium (Na+) and copper (Cu2+), some common examples of anions are chloride (Cl ) and fluoride (F ). The gain or loss of electrons has an enormous impact on the chemical and physical properties of the atom. Sodium metal bursts into flame when it comes in contact with water. Chlorine atoms instantly combine to form Cl2 molecules, which are so reactive that entire communities are evacuated when trains carrying chlorine gas derail. However, when positively charged Na+ and negatively charged Cl ions combine, they are so unreactive that we safely take them into our bodies whenever we salt our food. The sources of ionic contamination are varied. In general, the contamination can be classified as coming from the processes, people and objects that come in contact with manufactured product. Ionic contamination includes ions in chemicals, ions deposited during handling, ions from the air, ions from cleaning products and equipment, and ions from packaging materials. Devices such as printed circuit boards, semiconductor wafers, microelectromechanical systems (MEMS), data storage components, medical devices, automotive and aerospace electronics, and flat panel displays are the most susceptible to ionic contamination as they have electronic circuitry which in the presence of ions and moisture can develop conductance
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paths resulting in a variety of electronic failure modes. These failure modes can degrade the performance of the device or cause the device to fail completely. Because ions are everywhere in our environment, industry has had to go to great lengths to remove ionic contamination from the manufacturing processes for electronic components. Chemicals and water that come in contact with the devices are passed through expensive membranes to remove ions, people involved in the manufacturing process are required to wear cleanroom garments from head to toe, the air that surrounds the device as it is being manufactured is filtered to remove ions and final packaging is specially designed so as not to contribute to ionic contamination.
11.2 Sources and Effects of Ionic Contamination in Electronics Manufacturing Classical chemical, electrochemical, and galvanic corrosion processes, induced or assisted by ionic contamination, particularly in the presence of adsorbed moisture, have often been found to cause degradation of electronic equipment and devices in a wide variety of ways [1]. Figure 11.1 shows ion-induced contamination on a printed circuit board. Potentially corrosive ions found on printed circuit boards and electronic devices include: Bromide—commonly found in solder masks. Sulfate—comes from a variety of materials such as oils and release agents. Chloride—commonly found in fluxes. Organic acids such as adipic or succinic acid—found in fluxes. Typically, the higher the concentration of corrosive ions on a particular assembly, the higher the risk of electrochemical failure. In the manufacture of printed circuit boards, solder fluxes are one of the most common sources of ionic contaminants which contribute to circuit failure. Solder flux is used to improve wettability (reduce surface tension) and to remove oxides, sulfides and tarnishes from metals, or connections to be joined by solder. This is done so that a clean active surface is exposed to the molten solder to promote better solder adherence.
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Figure 11.1 Ion-induced contamination on a printed circuit board.
Pure rosin, activated rosin, and water soluble fluxes are the commonly used fluxes. If rosin residues are not removed, then ionic contaminants from the flux can become trapped in and around the electronic device that is being soldered. Water soluble fluxes use a wetting agent instead of rosin to reduce surface tension and to promote improved soldering. They also use the same acid activators as the activated rosin fluxes only in higher concentration. Water soluble fluxes are inherently more corrosive and all residues must be completely removed with water. Another source of ionic contamination is from the fluxes that are contained within the core of the solder. The type of flux within the solder can be determined by a code found on the solder container. An ‘‘R’’ code means the flux is non-activated rosin; ‘‘RMA’’ is a Mildly Activated flux; ‘‘RA’’ is Activated; ‘‘RSA’’ is Super-Activated having approximately twice the activity as RA; ‘‘OA’’ is organic-acid filled. There is also an ‘‘IA’’ inorganic-acid filled flux, but this flux should not be used in electronic applications as it is highly corrosive. In the presence of moisture, salts from fingerprints may dissolve into sodium and chloride ions which are highly mobile and may contribute to metallic migration, dendrites and current leakage or otherwise degrade
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circuit operation. Therefore, it is especially important that the cleaning process remove fingerprints in any electronic circuitry that is densely packed and operates in a high humidity environment. Last but not least, the water used in the cleaning process can be a major source of ionic contamination. Cleaning processes for electronic boards and components should only use DI water; unfortunately, some manufacturers still use tap water containing high levels of ions.
11.3 How Does Corrosion Begin? All water will conduct electricity to some degree. The conductivity is determined by the number of ions present in the water, which serve as the mobile charge carriers. Therefore, the conductivity of water is a strong function of its ionic content. The presence of even minute quantities of water soluble ions can drastically reduce the resistivity of moisture films which form on the surface of a material. If this material serves as an insulator between two conductors of an electrochemical circuit, the result is a significant increase in the reaction rate. This is the reason why thorough cleaning of electronic components and assemblies is essential to their long term reliability. Not all residues produce the same drop in resistivity. The most damaging are ionic compounds which are highly soluble in water (such as halides) [2].
11.4 Sources and Effects of Ionic Contamination for Semiconductor and MEMS Manufacturing The manufacture of semiconductors and MEMS has much in common. Unlike most printed circuit board manufacture, the processes for semiconductor and MEMS are performed in cleanrooms with higher levels of contamination control in effect. However, even with these precautions, ionic contamination can still creep into the processes. Figure 11.2 shows the results of ionic contamination of aluminum interconnect lines by chloride ion during manufacturing. Production processes such as plating (metallization), chemical mechanical polishing (CMP), etch, and photolithography all use purified chemicals. These chemicals even if purchased as ‘‘ultra-pure’’ can be
11: IONIC CONTAMINATION, NEWTON 6HCl +
2Al
AlCl3 + 3H2O
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Figure 11.2 Chloride ion contamination of aluminum interconnect lines during manufacturing.
contaminated with ions during transport to the fab or even during delivery within the fab. Outgassing from materials such as building materials, solvents, chemicals, epoxies, adhesives, tapes, cleaners, foams, rubbers, lubricants, oils, paints, coatings, sealant, and composite materials can also be a source of ions such as NH4+ (from ammonia) or chloride (from hydrochloric acid). Molecular migration is the process by which contaminants, for example HCl, become airborne and find their way onto surfaces of the wafers. Sources of such contamination are any material that comes near the product or which can produce a low level volatile that can migrate long distances [3]. The adverse effect of airborne molecular contamination, such as ammonia, on the control of critical dimensions of sub-0.5-mm linewidths is well understood in the semiconductor industry. As device dimensions continue to shrink, this phenomenon and its effects on defect density and product yield have become an increasingly important concern [4]. For the lithography process, the most noteworthy examples of ionic contaminants are organic amines and ammonia in parts-per-billion concentrations, which poison chemically amplified deep-ultraviolet (DUV) photoresists [5, 6]. Other researchers have reported that when a chemically amplified photoresist was exposed to as low as 8 ppb of ammonia for
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10 minutes, there was a 20% change in linewidth [7]. Unlike i-line photoresist, chemically amplified DUV resist forms an acid during the exposure step. Acid loss at the resist/air interface can then cause capping on the resist profile. Such a loss may be caused by a reaction with a base adsorbed from the air into the resist film or by acid evaporation during post-exposure bake [8]. If a material outgases ammonia the acid in the resist film can be neutralized. In extreme cases, the result is complete insolubility of the film in the developer, leaving only the latent image on the wafer [9]. Another form of ‘‘poisoning’’ of the semiconductor wafer can be with ionic borate (B(OH)4 ). The impact of boron poisoning of semiconductor wafers from part per billion levels of borate in water has been studied and it was concluded that the presence of boron on the surface of the wafers might cause poor N–P junctions, causing a lower production yield [10]. Haze on semiconductor wafers is defined as non-localized light scattering resulting from surface topography or from dense concentrations of surface or near-surface imperfections. Some types of wafer haze are caused by the reaction of ammonia with some anions (SO42 , Cl , F ) [11].
11.5 Ionic Contamination of Data Storage Products Data storage products such as disk drive components are susceptible to ionic contamination. Micro-contamination and subsequent corrosion of the recording head is of particular concern. The heads are composed of nickel/iron alloys that are particularly susceptible to corrosive attack by ions such as chloride, sulfate, and sodium. As in semiconductor processing, the source of the ions may be materials that are used during fabrication, from water used for cleaning, or from coatings that are used on the disk surface. Figures 11.3 and 11.4 show a non-corroded disk head versus a corroded one. Several studies have been completed on the analysis of ionic contamination on failed disk drive components [12].
11.6 Ionic Contamination of Cleanroom and Packaging Materials Ionic contamination can also be found on the materials that come in contact with the product as it is being manufactured and packaged.
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Figure 11.3 Uncorroded head of a hard disk drive.
Figure 11.4 Severely corroded head of a hard disk drive.
The manufacturing consumables such as gloves, wipes and brushes and final packaging can transfer contamination to the product through touch and outgassing and need to be examined for contamination in the same way as the final product [13]. A recent study of stored semiconductor wafers indicated that timedependent haze can be caused by humidity inside wafer packaging and by organic or ionic contamination on the wafer surface that exceeds typical levels [14].
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11.7 Analytical Techniques A traditional method of cleanliness verification that has been used in many industries is visual inspection. This includes assessments such as the ‘‘white glove’’ and ‘‘water break’’ tests. This approach may be all that is required for sheet metal and other non-critical cleaning applications, as long as the limitations are understood. For applications that relate to electronics, semiconductors, aerospace, and medical devices where highprecision cleaning is required, instrumental methods are a must. There are a number of less sensitive methods for the analysis of ionic contamination. Methods such as the water drop test, also called the contact angle test, SIR (Surface Insulation Resistance), the ROSE (Resistivity of Solvent Extract) test, and NVR (Non-Volatile Residue) are all examples of less sensitive tests for ionic contamination that do not give definitive information on the precise ionic species present on the surface being tested. Therefore, these techniques will not be covered in this chapter. For more information on these types of test techniques, the Institute of Environmental Sciences and Technology (IEST) and Association Connecting Electronics Industries (IPC) organizations have standards documentation that is helpful. Some of the instrumental methods described in this chapter are used to analyze particles. This chapter will focus on their use for the analysis of ions.
11.8 Selection Criteria The choice of instrumentation used to measure cleanliness depends on the degree of precision needed. In many cases, to obtain the most complete analysis possible, multiple forms of analysis should be used. For example, ion chromatography can provide information on a variety of ions including some metals but for a comprehensive analysis of metals, graphite furnace AA (atomic absorption) or ICP/MS (inductively coupled plasma/mass spectrometry) would be preferable. Another consideration is the extent of quality control required. Is the analytical method to be used as a screening technique or as a failure analysis technique? This is an important differentiation criterion since many precision analytical techniques are not designed for production screening needs. Also, as part of the analytical process, it will be necessary to analyze standards, controls, and duplicate samples. Data accuracy and precision should be established to the level dictated by the project objectives.
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The level of cleaning obtained by a given process is determined at the substrate surface after all cleaning and drying procedures have been completed. For critical cleaning applications, this is generally done via instrumental methods. Some instruments directly measure the surface contamination while others use indirect measurements where the contaminant is first extracted into a medium such as water and then analyzed.
11.9 Instrumentation Selection Table 11.1 lists the common types of instrumentation used to analyze surfaces for ionic contamination. Below is a short synopsis of each technique along with some relevant contamination evaluation examples.
11.9.1 Ultraviolet photoelectric emission In many cases ultraviolet (UV) light can be used to determine the surface cleanliness. In these cases, the contaminants being sought will ‘‘fluoresce’’ in the presence of UV light. Fluorescence occurs when the energy from UV light is absorbed by a contaminant and ‘‘excites’’ the electrons in that contaminant to a higher electronic state. The electrons are not stable in this state of higher energy and subsequently will go through a ‘‘relaxation’’ process. During this relaxation, the absorbed energy is released in the form of a photon (this is the ‘‘glow’’ seen in fluorescence). Fluorescence can provide a visual indication of where contamination remains on a surface. The intensity of the radiation can also be measured which indicates the degree of contamination on a surface. This form of analysis is useful for locating contamination, but it will not identify the species.
11.9.2 Phase imaging Phase imaging is a surface-mapping technique that utilizes an oscillating probe brought into contact with a surface. The amplitude of the oscillations (signal) varies with changes in the surface topography. Surfaces are illustrated as light and dark areas. This technique can locate areas of surface contamination, which stand out as topographically distinct.
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Table 11.1 Overview of Surface Analysis Instrumentation for Ionic Contamination
Instrument Ultraviolet photoelectric emission Phase imaging
Direct or Indirect Method
Sensitivity
Direct
Surface contamination
–
Direct
Surface contamination Elemental analysis
–
Energy dispersive X-ray spectroscopy
Direct
GFAA ICP/MS Optically stimulated electron emission Secondary ion mass spectroscopy Auger electron spectroscopy X-ray photoelectron spectroscopy
Indirect Indirect Direct Direct Direct Direct
Total reflection Direct X-ray fluorescence Ion chromatography Indirect
Capillary electrophoresis
Typical Applications
Indirect
Surface metals Surface metals Surface contamination Contamination profiling Elemental surface analysis Surface analysis of organic and inorganic molecules Surface contamination Surface extractable or leachable ions Surface extractable or leachable ions
0.1–1 at%
ppt ppt – ppm-ppb 0.1–1 at% –
What is Detected? Excited electrons – Secondary and backscattered electrons and X-rays Metal ions Metal ions Reflected electrons Secondary ions Auger electrons Photoelectrons
109–1010 atoms/cm2 ppb-ppt
X-rays from excited atoms Most anions and cations
ppb
Most anions and cations
11.9.3 Energy dispersive X-ray spectroscopy (EDS/EDX) Energy dispersive X-ray spectroscopy (EDS) is a chemical microanalysis technique performed in conjunction with a scanning electron microscope (SEM). The technique utilizes X-rays that are emitted from the
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sample during bombardment by the electron beam to characterize the elemental composition of the analyzed volume. Features or phases as small as about 1 mm can be analyzed. EDS works by using an electron microscope to focus an electron beam to interact with the atoms in a sample. As the electron beam displaces electrons in the sample, a detector converts the electrons scattered by the electron beam into a microscopic image. This also causes the generation of characteristic X-rays. In order to return the atom to its normal state, an electron from an outer atomic shell drops into the vacancy in the inner shell. This drop results in the loss of a specific amount of energy, namely, the difference in energy between the vacant shell and the shell contributing the electron. This energy is given up in the form of electromagnetic radiation X-rays. Since energy levels in all elements are characteristic to that element, X-rays are generated. The accumulation of energy counts creates a spectrum representing the analysis of the sample. Therefore, while the electron microscope produces an image of the sample topography, energy dispersive X-ray microanalysis tells the microscopist what elements are present in the sample. An interference that has been observed with the use of EDS is that it cannot detect fluoride in the presence of iron because there is an overlap of the Fe (iron) and F signals. It is also not particularly sensitive for nitrogen or chloride ions [11]. Figure 11.5 shows an EDS spectrum of a corroded disk drive head, showing cation and anion attack, with elemental signals at O, P, S and Cl, as well as at Na, K and Si.
11.9.4 Graphite furnace atomic absorption (GFAA) Graphite furnace atomic absorption (GFAA) spectroscopy is a highly sensitive spectroscopic technique that is used to identify and quantify the total amount of inorganic ions (positive and negative) present on a surface. This technique provides excellent detection limits for measuring concentrations of metals in aqueous and solid samples. The analysis is made by passing light of a specific wavelength through the atomic vapor of an element of interest, and measurement is made of the attenuation of the intensity of the light as a result of absorption. Samples to be analyzed by AA are vaporized or atomized by the graphite furnace. The graphite furnace is an electrothermal atomizer system that can produce temperatures as high as 3000 C. The heated graphite furnace provides the thermal energy to break chemical bonds within the sample and produce free ground-state atoms. Ground-state atoms then are
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Figure 11.5 EDS spectrum of the corroded head of a disk drive showing cation and anion attack.
capable of absorbing energy, in the form of light, and are elevated to an excited state. The amount of light energy absorbed increases with the concentration of the selected element. GFAA has been used primarily for analysis of low concentrations of metals in samples of water. The more sophisticated GFAAs have a number of lamps and therefore are capable of simultaneous and automatic determinations for more than one element. The GFAA technique is subject to certain interferences. The composition of the sample matrix typically has the largest effect on the results of the analysis. Chemical interferences occur when the atoms are not completely free or in their ground state. Spectral interferences occur when atomic or molecular species other than the element being analyzed absorb energy at the wavelength of interest. Ionization interferences occur when the furnace causes complete removal of electrons from an atom. Detection limits are very low with GFAA analyses, usually 10–100 times lower than the detection limits for analyses by flame AA or ICP for the same element.
11.9.5 Inductively coupled plasma/mass spectrometry (ICP/MS) ICP-MS is a fast, precise and accurate multi-element analytical technique for the determination of trace elements (<0.1 wt.%) in liquid and
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solid samples. In ICP-MS, elemental abundances or isotopic ratios are determined by the mass spectrometry (MS) of ions generated in an inductively coupled argon plasma. An ICP-Mass Spectrometer consists of a sample injection system, inductively coupled plasma, plasma sampling interface, mass analyzer, detector, and computer. In ICP-MS, elemental abundances or isotopic ratios are determined by the mass spectrometric detection of ions generated in an inductively coupled argon plasma. Using a stream of argon carrier gas, liquid or solid sample material is introduced into an inductively coupled argon plasma which serves as a source of positively charged analyte ions. The ions are extracted from the environment of the plasma into a high-vacuum enclosure via an interface region containing two apertures. Focused by an ion lens system, analyte isotopes are separated according to their mass/charge ratio by a mass spectrometer and detected and measured by a detector.
11.9.6 Optically stimulated electron emission (OSEE) Optically stimulated electron emission (OSEE) works according to the theory that when high energy UV light is directed to a surface, electrons will be emitted, and that reflected ‘‘current’’ can be measured. A clean surface will give the highest return current, so any drop in current will represent contamination. This method is good for detecting low levels of contamination (both ionic and nonionic), but it can only detect contamination, it cannot identify different species. Mandle [15] describes the use of optically stimulated electron emission (OSEE) to measure the effectiveness of magnetic disk cleaning processes. In this method, the cleaned surface is irradiated in air with short wavelength ultraviolet energy; electrons are collected across an air gap and measured.
11.9.7 Secondary ion mass spectroscopy (SIMS) Secondary ion mass spectroscopy (SIMS) is used for the composition analysis of surfaces. An energized primary ion beam (Ar+, Cs+, N2+, or O2+) is directed at the surface, resulting in the ejection of surface atoms as secondary ions. This process is known as ‘‘sputtering.’’ This spectroscopy
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technique can identify elements, but does not identify bonding characteristics as would ESCA. SIMS can detect both positive and negative ions. The typical sampling depth ranges from 2 to 6 s. SIMS is sensitive to all elements and their isotopes and can be used to quantify part-per-billion levels in semiconductors.
11.9.8 Auger electron spectroscopy (AES) Auger (pronounced ‘‘oh-jay’’) electron spectroscopy (AES) is used for determining which atoms are present on a surface. Electrons are directed toward the surface resulting in the ionization of surface atoms by removal of an electron from the inner shell of the atom. The atom now becomes ‘‘excited’’ and must release energy to return to its original state. This is done by transferring the extra energy to an electron that can leave the atom. This electron is known as the auger electron. The energy of the auger electron is unique to each particular atom. AES is a destructive analysis but is useful in looking for concentrated areas of contamination. It can also be used quantitatively. The typical sampling depth for AES is 20–50 s. AES is used in the semiconductor field for corrosion and failure analyses, and thin-film analyses. Disk drive monitoring methods such as Auger Electron Spectroscopy (AES) are described by Brar and Narayan [16]. These methods, when applied appropriately, can detect contamination/handling damage.
11.9.9 X-ray photoelectron spectroscopy/electron spectroscopy for chemical analysis (XPS/ESCA) XPS/ESCA is a spectrophotometric technique where X-ray bombardment of the surface results in emission of an electron from a given atom. Knowing the energy of the X-ray and measuring the energy of the emitted electron can determine the binding energy of the electron. Peaks represent the various oxidation states that are associated with each energy level. XPS methods reveal chemical structure, bonding, and oxidation state. XPS methods are more commonly used than AES methods. They have the benefit of revealing chemical structure, bonding, and oxidation state. XPS is considered nondestructive. Figure 11.6 shows the elemental analysis of wafer discoloration [17].
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Figure 11.6 XPS/ESCA identification of wafer discoloration.
11.9.10 Total reflection X-ray fluorescence (TXRF) X-rays are radiated onto the surface causing the atoms to reach a momentary excited state. After atoms return to normal state, a specified X-ray is generated which becomes the means for measuring the amount and kind of atoms present, this in turn enables to determine the degree of contamination on the surface of the wafer. The technique is sensitive to very dilute quantities of material, but it does require very flat samples. This technique is particularly adapted to analysis of contamination on semiconductor wafers. Figure 11.7 shows the use of TXRF to measure cleaning efficacy [17].
11.9.11 Ion chromatography (IC) Ion chromatography separates, identifies, and quantifies ions. The sample is typically a water matrix containing ions of interest but can also be a chemical matrix such as isopropanol. The sample is injected into the system and combined with an eluent stream that carries the sample to the analytical column. The analytical column separates the ions of interest in the sample within the stream of the eluent. The eluent then sweeps the ions into the suppressor device, which electrolytically transforms the eluent into pure water, leaving just the ions of interest in pure water.
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Figure 11.7 TXRP analysis to measure the cleaning efficacy of a semiconductor wafer.
These ions are then passed downstream to the conductivity detector. The detector detects the ions based on their conductivity relative to the water eluent. The suppressor removes all of the interfering ions allowing for part per billion and part per trillion sensitivity at the detector. Figure 11.8 is a diagram of an ion chromatography system. The technique of ion chromatography is uniquely qualified for troubleshooting the root cause of failures due to ionic contamination on printed circuit boards, semiconductor wafers, disk drive components, medical devices and general electronics components. Ion chromatography can provide information on the chemical nature of the ionic residue causing the failure. The output of the ion chromatograph is called a ‘‘chromatogram’’ and gives the identity and quantity of each ion found in a sample of a rinse extract of the device of interest. Figure 11.9 shows a chromatogram of a rinse extract of a semiconductor wafer. Ion chromatography provides the unique capability of identifying the individual ions for a given contamination issue. Since the source for chloride contamination can be much different than the source for organic
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Figure 11.8 Ion chromatography system configuration.
acid contamination it is important to know which ions the manufacturer is dealing with in order to understand and correct the root cause of the problem. The capability to identify and quantify individual ions makes ion chromatography a valuable troubleshooting tool for process contamination issues and process monitoring programs. In addition to being the most economical analytical technique for monitoring multiple ions, ion chromatography also provides the ability to distinguish between noncorrosive and corrosive ions. Furthermore, in addition to liquid samples, ion chromatography can also be set up to analyze ions in cleanroom air as a source of contamination (Figure 11.10). A number of studies have been published to show the use of ion chromatography to troubleshoot reliability issues with electronic products. One of the best sources of case study information for electronics applications can be found on the web site for Contamination Studies Laboratory (CSL) at www.residues.com. CSL regularly publishes case studies showing the hazards of ionic contamination to electronic device reliability on their web site and in each issue of Circuits Assembly magazine. A good explanation of how ion chromatography has been used to identify sources of conductive anodic filament (CAF) failures can be found in a study completed by Ready et al. and presented at the Materials Research Society Symposium in 1998 [18].
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Plat and Leo [19] reported that IC with FTIR detection was superior to other surface analysis techniques for determining ionic NO2 and NO3 species involved in the corrosion of gold plated copper wires. Shive et al. [14] reported the use of ion chromatography for ions on wafers showing time-dependent haze due to packaging issues. Yang et al. [20] reported the use of ion chromatography for analysis of corroded aluminum interconnect lines on wafer surfaces due to chlorine contamination.
11.9.12 Capillary ion electrophoresis (CIE) Ion analysis by Capillary Ion Electrophoresis uses different separation mechanisms and instrumentation compared to ion chromatography. Because of this, ion chromatography principles cannot be used to explain the performance of capillary electrophoresis. The CIE is a separations technology for the analysis of inorganic and organic ions in aqueous solutions. CIE is a free zone capillary electrophoresis technique designed for the analysis of low molecular weight inorganic anions, organic acids, alkali and alkaline earth cations, and amines. In CIE, ions are separated based upon their differences in ion mobility in the carrier electrolyte when an electric field is applied through the capillary. Mobility is related to the ratio of ion charge to hydrated size in solution. CIE is characterized by fast separations, generally less than 7 minutes, with high resolving power, approaching 500,000 theoretical plates. The instrumentation is simple with few moving components compared to ion chromatography (IC). CIA also gives selectivity different than IC without the need for gradient elution. In CIE, charged electrical species migrate when dissolved, or suspended, in an electrolyte through which an electric current is passed. Cations migrate toward the negatively charged electrode (cathode) and anions migrate toward the positively charged electrode (anode). Neutral solutes are not attracted to either electrode. The use of CIE for analysis of metals and ions on the surfaces of bare semiconductor wafers has been reported in the literature [21].
11.10 Summary For optimal analysis of ionic contamination, use of only one instrumental technique may not be enough. This is due to the interferences that
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may affect a certain technique and the variability of the contamination itself. Most labs will use more than one technique to assure that the identification and quantification of the contaminant is correct. Many of the instrumental techniques describe here have evolved into specialized hardware and technology such as Field Emission Auger Electron Spectroscopy (FE AES). With increasing requirements for lower and lower ionic contamination levels on electronic, medical, semiconductor and data storage devices, these new cleanliness verification technologies will become more widely adopted.
References 1. J. D. Sinclair, ‘‘Corrosion of Electronics. The Role of Ionic Substances,’’ J. Electrochem. Soc. 135, 89C (1988). 2. D. Pinsky and N. Carl Miller, ‘‘Corrosion Failures on Assembled Electronic Modules,’’ www.reliabilityanalysislab.com (2006). 3. D. Kinkead, M. Joffe, J. Higley and O. Kishkovich, ‘‘Forecast of Airborne Molecular Contamination Limits for the 0.25 Micron High Performance Logic Process,’’ SEMATECH Technical Report, Technology Transfer # 95052812A-TR (May 1995). 4. Z. Lin and A. F. VanNatter, ‘‘Using CD SEM To Evaluate Material Compatibility with DUV Photoresists,’’ Micro (February 1999). 5. S. A. MacDonald, N. J. Clecak, H. R. Wendt, C. G. Willson, C. D. Snyder, C. J. Knors, N. B. Deyoe, J. G. Maltabes, J. R. Morrow, A. E. McGuire and S. J. Holmes, ‘‘Airborne Chemical Contamination of a Chemically Amplified Resist,’’ in Proc. Advances in Resist Technology and Processing VIII, SPIE Vol. 1466, H. Ito (Ed.), pp. 1–12, SPIE, Bellingham, WA (1991). 6. J. C. Vigil, M. W. Barrick and T. H. Grafe, ‘‘Contamination Control for Processing DUV Chemically Amplified Photoresists,’’ in Proc. Advances in Resist Technology and Processing XII, SPIE Volume 2438, R. D. Allen (Ed.), pp. 626–643, SPIE, Bellingham, WA (1995). 7. Y. Kawai, A. Otaka, A. Tanaka and T. Matsuda, ‘‘The Effect of an Organic Base in a Chemically Amplified Resist on Patterning Characteristics Using KrF Lithography,’’ in Digest of Papers from MicroProcess ’94, the Seventh MicroProcess Conference, pp. 202–203 (1994). See also Jpn. J. App. Phys. 33, 7023 (1994). 8. S. A. MacDonald, W. D. Hinsberg, H. R. Wendt, N. J. Clecak and C. G. Wilson, ‘‘Airborne Chemical Contamination of a Chemically Amplified Resist. 1. Identification of Problem,’’ Chem. Mater. 5, 348 (1993). 9. A. Toxen, ‘‘Controlling Contamination Levels in Hard Disk Drives,’’ A2C2, pp. 13–16 (September 1998). 10. P. B. Mee, M. J. Smallen and D. J. Vickers, ‘‘Management of Disk Drive Component Microcontamination,’’ IDEMA Insight, 10 21 (March/April 1997). 11. J. Thompson, T. Promanuwat, A. Siriraks and S. Heberling, ‘‘Development of Microextraction for Ion Chromatographic Measurements on Thin Film Sliders for Hard Disk Drives,’’ IDEMA Insight, pp. 24–29 (May/June 1999).
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12. S. Lin, and S. Graves, ‘‘Comparing the Molecular Contamination Contribution of Clean Packaging Films’’, Micro, pp. 95–105 (October 1998). 13. K. Bahten and D. McMullen, ‘‘Material Purity, Handling and Installation Advances in Mechanical Brush Scrubbing Applications,’’ Proc. SPWCC (Semiconductor Pure Water and Chemicals Conference) (March 1999). Available at www. spwcc.com/conference.htm. 14. L. W. Shive, R. Blank and K. Lamb, ‘‘Investigating the Formation of Time Dependent Haze on Stored Wafers,’’ Micro (March 2001). 15. J. B. Mandle, ‘‘Measuring the Effectiveness of Magnetic Disk Cleaning and Cleaning Processes,’’ Report J. B. Mandle and Associates (September 1990). Available at www.photoemission.com/downloads/jmandle20001.pdf. 16. A. S. Brar and P. B. Narayan, ‘‘Disk Drive Program: Surface Analysis Program Aims for Zero Defects,’’ Microelectronics Manufacturing & Testing, pp. 73–74 (May 1989). 17. Evans Analytical Group web site www.eaglabs.com (2006). 18. W. J. Ready, B. A. Smith, L. J. Turbini and S. R. Stock, ‘‘Analysis of Catastrophic Field Failures due to Conductive Anodic Filament CAF Formation,’’ Proc. Mater. Res. Soc. Symp. 515, 45 (1998). 19. M. Plat and J. De Leo, ‘‘Application of Ion Chromatography to Failure Analysis of Electronics Packaging,’’ J. Chromatography 546, 347 (1991). 20. D. Yang, C. Lee, Y. Y. Yang, E. Kaiser, S. Heberling and B. Newton, ‘‘Combating Chlorine Corrosion through Ion Chromatography,’’ Precision Cleaning, pp. 17–23 (May 1998). 21. T. Ehmann, L. Fabry, J. Moreland, J. Hage and M. Serwe, ‘‘Ion Chromatography and Capillary Electrophoresis in Large-Scale Manufacturing of Semiconductor Silicon,’’ Semiconductor FABTECH, 12th Edition 12, 71 (2000).
12 Relevance of Colorimetric Interferometry for Thin Surface Film Contaminants Michel Querry and Philippe Vergne LaMCoS UMR CNRS/INSA, Lyon, France ome ^ Jer Molimard Centre SMS, Ecole Nationale Superieure des Mines (de Saint Etienne), Saint Etienne, France
12.1 Introduction The specific application of interferometry addressed in this chapter concerns the measurement of the thickness of films fabricated from various materials and, by the nature of the optical method employed, this necessarily requires them to be transparent. This optical transparency can be either an intrinsic material property, or it can be the consequence of a low-sample thickness, which often confers a limited absorption. The aim of this chapter is to show the interesting effects that can arise from using two techniques that have different origins, and have been developed from different initial objectives: interferometry, which is a technique that generates visual information that is related to the sample thickness, and colorimetry, which is a quantitative procedure. This chapter is necessarily brief concerning theoretical approaches, with a comprehensive reference to appropriate sources given in the bibliography. The experimental method presented in Section 12.4 of this chapter results from studies carried out on the lubrication of contacts between solid bodies occurring in mechanical mechanisms, such as ball bearings and gears. Alternative techniques to interferometry can involve the use of many different resources. For example, in the field of optoelectronics, solid film thickness (often of oxides) is measured using techniques derived from
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ellipsometry. There is also the capacitance variation method that has particular use in surface force devices [1]. Some attempts have been carried out to use spectroscopic techniques involving different physical phenomena, such as fluorescence or the Raman effect. Theoretically, the emitted light intensity is proportional to the quantity of matter excited by the incident radiation, and therefore, to its thickness. In the same manner, luminous absorption can be used to determine the thickness of a film contaminating the surface of a transparent solid. In addition to the difficulties arising from the determination of an optimal excitation wavelength (UV or blue light for fluorescence, UV to IR for the Raman effect, and generally IR for absorption) and from signal saturation imposing the need for calibration (fluorescence), the main limitation of spectroscopic techniques is their low sensitivity. The measurement time needed to determine the thickness of a very thin layer can be significant (up to several tens of minutes), prohibiting any real time application and wide area analysis at the local scale. A bibliographical review of these techniques has been carried out by Molimard [2].
12.2 Interferometry 12.2.1 Elementary phenomena An electric field and a magnetic field, which can both be written using the following generic form, characterize a monochromatic wave resulting from a light source. 2p j ¼ Jcos ðntnrÞC l
Eq. (12-1)
From the above equation, we can recognize the expression for a traveling wave, variable in time (t) and in space (x), having wavelength l. In this equation, n is the wave velocity and c represents a phase change. When two luminous rays resulting from the same wave train meet, the electromagnetic fields of each wave train are added together. One then speaks about ‘‘interference’’ having occurred. Current optical detectors [e.g., the human eye, photographic emulsions, and charge coupled device (CCD) arrays] do not recognize the amplitude, J, but the intensity, I, which is the square of the amplitude. If the two rays present an optical path difference, d, the intensity takes the form
12: COLORIMETRIC INTERFEROMETRY, QUERRY ET AL. pffiffiffiffiffiffiffiffi 2pd I ¼ I1 þ I2 þ 2 I1 I2 cos l
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We note that the resulting intensity is different from the sum of the intensities of each ray, and varies between two extreme values pffiffiffiffiffiffiffiffi Imin ¼ I1 þ I2 2 I1 I2
Eq. (12-3)
pffiffiffiffiffiffiffiffi I1 I2
Eq. (12-4)
Imax ¼ I1 þ I2 þ 2
The visibility (or the contrast), given by (Imax Imin)/(Imax þ Imin), is maximum if the intensities of each wave are equal, that is I1 ¼ I2. However, wave trains have a very short lifetime (around 109 seconds). Their amplitudes change over this interval of time, and each wave train has neither the same phase, the same amplitude, nor the same frequency as the preceding wave train, and therefore, two rays stemming from two different wave trains cannot interfere. To observe interference fringes, it is necessary that the two rays arise from the same wave train, which means that they must come from the same place at the same time and thus be in-phase. This condition is met if one can divide a beam into two rays, which can be achieved, for instance, by crossing an optical interface characterized by a change in optical index and reflectivity. According to the diagrams presented in Figure 12.1, two extreme cases arise. 1. If the reflection coefficient at the external interface, R, is very small, this is the basic case arising for two-wave interferometry. 2. If the reflection coefficient at the external interface, R, is large, then the configuration is that encountered in multiple-wave interferometry as seen, for example, in the FabryPerot interferometer. In the colorimetric interferometry technique, the interference conditions are situated between the two extreme cases described above. Newton’s well-known experiment on using white light interferometry, which will be described later on, is an example of this type. Film thickness measurement was one of the first developments in this area. The relation between the film thickness, h, and the intensity of the emergent beam, I, implicitly introduces the optical path difference between
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large R
small R
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Figure 12.1 Interference fringes obtained by reflection.
two consecutive interfering rays, d. The total output intensity is then written as pffiffiffiffiffiffiffiffi 4pnh I ¼ I1 þ I2 þ 2 I1 I2 cos f l
Eq. (12-5)
where under normal incidence, d ¼ 2nh. In addition, we note that the reflection at the interface between the substrate and the film introduces a phase shift, j, that modifies the interference conditions. The intensity varies periodically according to h. With monochromatic light, any variation in h results in a successive occurrence of intensity maxima and minima. The observation under these conditions of a contaminating film of non-uniform thickness shows alternating dark and clear fringes, thus revealing the interface topography. The experimental techniques of monochromatic interferometry, and the associated theoretical aspects will not be discussed here. The periodic character of this variation leads to the concept of interference order: several film thicknesses, corresponding to various optical paths whose differences are multiples of the same wavelength, can lead to the same emergent intensity. Finally, three new constraints need to be added to implement interferometry: we require a knowledge of the phase shift, j, and the refractive index, n, which are both material parameters and play a role at the optical level, and we need to determine the interference orders that directly result from the measurement method.
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Adopting white light interferometry, as has been practiced since the Newton’s rings experiment in 1704 can solve these difficulties.
12.2.2 White light interferometry White light results from the superposition of an infinite number of monochromatic waves of different wavelengths. When white light is applied to the optical assembly shown in Figure 12.1, superposition of the interference rings results as described above. However, in this case the interference covers the entire visible spectrum with intensities varying according to the wavelength. In addition to intensity variations observed with monochromatic light, white light interferometry results in the appearance of different colors arising from the selective extinction of some components of the spectrum. These colors, which play a significant role in optics, are grouped under the name of Newton’s color scale, and evoke the colors of the rainbow. They are approximately repeated when the interference order changes. However, when the difference in the optical path increases, their periodic character lessens and the fringe color becomes less and less identifiable, because there is simultaneous extinction in several parts of the spectrum. Under ideal reflecting conditions, beyond the third order, the colors are primarily pink and green, and beyond the tenth order, the identification is illusory. Nevertheless, white light interferometry makes it possible to lessen the ambiguity of the response of a monochromatic interferometric system, thanks to its pseudo periodic nature. The principal difficulty in its current application lies in color recognition. The human eye is particularly dependent on the operator, in addition to being sensitive to many disturbing parameters. Moreover, compared with the use of monochromatic light, this technique is of interest because it decreases the measurable minimal thickness. The limit for white light is around 50 nm, whereas it is difficult to reach values below a quarter of the wavelength used in monochromatic lighting, and the limit is typically about 130 nm. The developments suggested hereafter consist of automating the color recognition, making this function systematic and independent of the user. This goal is reached thanks to a colorimetric method associated with image analysis techniques. However, this improvement in the above method does not solve the need for knowing the phase shift, j, and the refractive index, n. A global calibration using the same optical system allows us to take into account these last two parameters.
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The remaining point to be addressed is the need to obtain the minimum measurable thickness using the above technique to cover a range as broad as possible, and one that is as representative as possible of the expected range of contaminant thickness. The use of a ‘‘spacer layer’’ was first introduced in lubrication by Westlake and Cameron [3]. The spacer layer allows us to extend the capability of white light interferometry to include very thin film thickness. It is generally composed of silica, a material chosen for its refractive index rather than having a value matching that of the material under analysis. The use of a spacer layer in lubrication applications implies that the external surface of the contaminant film must be in close contact with the surface of an optical component coated with silica. Thus, in the treatment of interferograms, one can shift classical thickness domains toward very low values by subtracting the thickness of the silica layer. The first-order fringes appear tightened, and their chromatic differences are more pronounced. This allows for a more precise thickness determination that can be obtained for films composed of few molecular layers.
12.3 Colorimetry 12.3.1 Definition of the problem After having discussed the use of white light interferometry to measure the thickness of thin layers present at the surface of a substrate, it is advisable to ask questions surrounding fringe perception, and consequently, the problem of color identification. Indeed the new difficulty to be solved is, ‘‘How do we switch from a feeling resulting from a visual observation to a quantitative representation?’’ Visual perception is a complex phenomenon, which varies from one individual to another, and it is governed by physiological parameters. The retina contains three different types of retinal cones, and each one recognizes one part of the visible spectrum. The cones have maximum sensitivity centered in the green part of the visible spectrum, at a wavelength of 555 nm. Color recognition and its quantification constitute a common concern in a large number of scientific and technical fields, with a variety of aims. A few examples are mentioned below to illustrate this diversity. 1. In the field of chemical analysis, Prasad et al. [4] have provided a detailed account of color specifications for the
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evaluation of color changes for acid–base and complexometric indicators. Tl aczal a and Bartecki [5] have used trichromatic colorimetry to determine the color of inorganic pigment mixtures. Their results suggest that this method can be applied to improve the analysis of coloring compounds. Color is used as a factor in assessing the quality of many agricultural and food products, and for this objective, Zhang et al. [6] have proposed a system that can simulate human vision in color recognition. In an application closer to the purpose of this chapter (contaminant evaluation), Wienhold et al. [7] and Wienhold and Weschenfelder [8] have studied the speed of erosion or deposition of thin carbon layers (100–200 nm), that simulated the surface of internal elements in a tokamak fusion device. To do this, they measured the real time color recording of these layers, with the observed color being related to the thickness. Finally, Hartl et al. [9] have determined the lubricant film thickness within a mechanical contact using a method similar to the one that will be described in Section 12.4.
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Although most of these applications call for the principles of trichromatic colorimetry, other methods can be used. For example, Spitzer et al. [10] have identified the color of painted surfaces by using an algorithm linked to the measurement of the reflectivity as a function of the incident angle of the light.
12.3.2 Colorimetric encoding From a physical point of view, the color of monochromatic light is related in a bi-univocal way to the wavelength of the considered radiation. The traditional spectrum extending from the purple to the red regions corresponds to the wavelength interval from 400 to 760 nm. The color characterization of polychromatic radiation requires a very different approach. In 1802, Young highlighted the possibility of expressing all the visible colors as being based on only three principal colors, red, green, and blue, even though radiations of different spectral compositions could give an identical visual feeling. The additive trichromatic representation of colors is based on the fact that it is possible to reconstitute, within experimental uncertainties,
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the majority of colors by the superposition of three basic colors taken by using a linear combination of their respective intensities. Thus, colorimetric space is provided with a linear algebra, and any triplet can constitute a base of it. Using this property, many systems of colorimetric representation have been developed, whose objectives have been the analysis of color and, more especially, its faithful reproduction. Their application is widespread and is in daily use such as photography and videos, to quote two of these applications. The change from one encoding system to another is realizable by means of a linear transformation and the matrix transforms between several common primary systems are given in reference 11. In 1931, the International Commission on Lighting, the CIE (Commission Internationale de l’Eclairage), formulated the first standards in this area, followed by multiple evolutions and updates, such as those of the National Television Systems Committee (NTSC). The simplest system, the RGB (red green blue) encoding, takes its basis from the intensities of the three primary colors: red (610 nm), green (540 nm), and blue (470 nm). The triplet of normalized trichromatic co-ordinates (r, g, b) is obtained from the dimensionless relation, r þ g þ b ¼ 1. In addition to the numerous linear representations of colorimetric space, the use of non-linear systems should also be mentioned. In general, the aim here is to simulate the non-linear response of the human eye with respect to colors and to light intensities. The HSL (hue saturation lightness) system, a common everyday encoding system, introduces a new concept, the hue value. It is associated with saturation and luminance (or lightness) parameters. An illustration encompassing both RGB and HSL encodings is familiar to any user of a personal computer that functions under the WindowsTM operating system. A utility that defines customized colors utilizes a technique close to these two systems by explicitly carrying out an encoding transformation, and associating it with the visualization of the reconstituted color. The (L*a*b*) system is also frequently used. It is based on the differences between non-linear combinations of the colorimetric triplet terms, and it highlights small differences between colors. The choice of a suitable representation depends both on the hardware used for analyzing or reconstituting a color, and on the significant sensitivities required to represent the expected signal changes. For example, Hay and Hollingsworth [12] compared three close, but slightly different, definitions of the hue parameter during the calibration of liquid crystal responses to temperature variations.
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12.3.3 Detectors The most frequently used detector in current use is the CCD array, which is the main component of many optical cameras and video cameras. These devices ensure the complete capture of an image, and reproduce it in a digitized form. Two types of detectors exist. The more current detector consists of a single CCD matrix. A red, green, or blue colored filter is associated with each pixel of the detector. By accepting some loss of spatial definition of the image, it is therefore possible to generate trichromatic information encoded according to the RGB system using only one device. Another more sophisticated device uses three CCD sensors. The incident light is divided once into three beams using three different colored filters, and three associated images are formed separately on each CCD matrix. The whole system still provides a trichromatic signal, but preserves the initial spatial resolution of the CCD. The use of moderately selective colored filters does not allow the attainment of three rigorously monochromatic images, as one could expect by strictly applying the principles of trichromatic colorimetry. Nevertheless, experience shows that this approximation leads to sufficiently precise and reproducible information, and that this can be exploited in most applications, so long as the spectral characteristics of the CCD filters are well adapted to this use. At the present time, these characteristics are well defined, and are driven by the needs of the development of video applications. Further details regarding this can be found in Ref. [13]. Although the CCD array is currently the most employed detector, many applications use the most elaborate tool available for colorimetric analysis: the spectrometer. Utilizing this device requires techniques derived from spectral analysis, and requires extracting from the spectrum one or more significant sets of data, usually the peak wavelength or the peak maximum intensity. However, using a spectrometer to analyze the spectrum is sometimes difficult, or it can be insufficient, when the objective of the exercise concerns the fine characterization of colors. A major limitation when using a spectrometer results from the fact that it is not easy to associate spectral analysis with image analysis, because the spectrum results from light emitted from all the surface of the sample
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under study, and not from a single point source. The method that has been developed for surface analysis proceeds by performing a spatial scan along a line or directly across the whole surface, by employing a translatory movement either across the sample, or across the optical input of the spectrometer. Another solution is to use a multichannel spectrometer connected to a matrix of microlenses. Each input channel of the spectrometer is associated with a single pixel of the image to be analyzed, and thus, the light resulting from each pixel is characterized by its spectrum. Such devices are rare and very expensive, as the method was recently developed for astrophysics to perform spectral analysis of images from stellar objects. However, current trends toward device miniaturization, and the development of integrated optics enable us to foresee its implementation in other types of research laboratories.
12.4 Colorimetric Interferometry 12.4.1 Methods using colorimetric interferometry in lubrication One domain that is rich in the application of interferometric methods is the study of lubrication. The thickness of films of interest in lubrication lies in the range 1–1000 mm, and the thickness of the lubricant film is a capital parameter in the evaluation of working machine elements involving lubrication systems. This thickness range is similar to that concerning surface contamination. In lubrication studies, experiments are often carried out using contact simulators instead of using real mechanisms, since these are often too complicated for the purpose of evaluation. In these test devices, it is possible to realize an optical access to the contact zone. Thus, many experimental studies concentrated on lubrication issues have used film thickness measurements that have contributed to the development of colorimetric interferometry methods. Table 12.1 presents the principal characteristics of these interferometry methods.
12.4.2 New developed method Owing to the pseudo-periodicity of the relation between the light intensity and film thickness, knowledge of only one value of the colorimetric triplet is not enough for us to deduce a unique film thickness. In this new method, the three triplet intensities are used to avoid making an assumption regarding
Colorimetry: image analysis in the L*a*b* system
Fringes of equal chromatic order (FECO) þ spectrometer in SFA Ultra thin interferometry (UTI) with spacer layer; spectrometer for wavelength identification Colorimetry: image analysis based on the hue value; visual recognition of interference orders
Use of a spacer layer (constant then variable thickness)
White lighting Basic interferometry: visual color recognition
Techniques and/or Methods
Kirk [14] Gohar and Cameron [15] Westlake and Cameron [3] Spikes and Guangteng [16] Israelachvili [17] Johnston et al. [18] Gustafsson et al. [19] Cann et al. [20] Hartl et al. [21]
Authors
0.1 1 1
1
1991 1994 1996 1997
10
40
1973
1988
1967
1962 1963
Year
Resolution (in nm)
1–800
10–700
1–1,000
0.1–50
10–1000
100–1000
Range (in nm)
Table 12.1 List of the Main Interferometric Methods that have been Developed for Lubrication Studies
ET AL.
(Continued)
1
3
Spatial Resolution (in mm)
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Multichannel interferometry, any calibration
Lacey and Talke [28] Wahl et al. [29] Baugh et al. [30] Lord et al. [31]
2000
1995 1998
1992
1996 1997
1988
1969
1999 1999
1997
Year
<5
1
2
100
3
3
20–100
20–200
1–120 >40
>25
40–5000
1–800 40–1000
>50
1.5
18
1
Spatial Resolution (in mm)
OF
Trichromatic lighting Image analysis on head/magnetic media contacts
Foord et al. [24] Ohkubo and Kishigami [25] Luo et al. [26] Bassani and Ciulli [27]
Akei and Mizuhara [22] Molimard [2] Mazuyer et al. [23]
Authors
Range (in nm)
CHARACTERIZATION
Fringes count by image analysis Pattern recognition of fringes by image analysis
Photodetector and laser
Colorimetry: image analysis in the RGB system Hue based image analysis; visual recognition of interference orders Monochromatic lighting Basic interferometry
Light intensity evaluated by photodetector
Techniques and/or Methods
Resolution (in nm)
Table 12.1 List of the Main Interferometric Methods that have been Developed for Lubrication Studies (Cont’d)
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687
c
R G B
150
Intensity
ET AL.
100
50
0
b
0
200 400 600 Film thickness(nm)
800
d
Figure 12.2 Colorimetric analysis applied to interferograms: (a) static ball/plate contact interferogram; (b) calibration curves; (c) contact interferogram under pure rolling condition; (d) the resulting film thickness map.
the interference order. This leads us to define a calibration connecting in a bi-univocal way the film thickness to the colorimetric triplet intensities. This calibration can be graphically represented as a set of three curves. Figure 12.2(b) shows such a whole set of curves in the RGB colorimetric system. The data in Figure 12.2(b) was obtained using a static contact held between a sphere made of steel and a glass disc that were initially separated by a lubricating oil film. The interferogram resulting from the contact led to the formation of Newton’s rings [see Figure 12.2(a)] with a center that could be accurately located. Hertzian theory (of the static
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contact between elastic solids) permits us to determine the shape of the deformed surface, and thus in the gap outside the contact area, the variation of lubricant thickness versus the radial distance. Colorimetric analysis applied to the digitized images allows us to establish the calibration curves from each pixel by linking the lubricant thickness to its RGB intensity triplet. The choice to use the RGB colorimetric system here was dictated by several factors resulting from a comparative study of the RGB, L*a*b*, and HSL systems, conducted in a systematic way, and using data from the same interferograms. The shape of the calibration curves resulting from the same image was more regular and homogeneous for the RGB system. In form, they were like damped quasi-sinusoidal. This was not the case for the L*a*b* or the HSL systems. The concept of sensitivity can be defined by the derivative of each colorimetric component with respect to the film thickness. The comparative study of the sensitivities of the three systems showed the following tendencies. 1. The L*a*b* system showed a complete loss of sensitivity appearing quasi-periodically that led to the formation of ‘‘blind zones’’ occurring approximately every 100 nm. 2. The HSL encoding system showed significant fluctuations in sensitivity owing to the complexity of the calibration curves, and to the presence of large transitions that behaved like discontinuities. 3. The RGB representation showed a loss of sensitivity corresponding to the extremes of the calibration curves that was distributed over the whole domain without being superimposed. We found that at least two elements of the colorimetric triplet were always usable, whatever the film thickness, except for those in a zone situated around 80 nm. The use of this calibration procedure to analyze the interferograms resulting from an unspecified thin film requires a specific methodology. The measured colorimetric triplet associated with a given pixel provides three sets of possible thickness values. The real thickness at the considered point is given by the intersection of these three sets. Measurement uncertainties force us to define a tolerance value for the colorimetric triplet to guarantee the authenticity of the solution. This methodology has led Molimard [2] to
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develop image-processing software to exploit interferograms. Various algorithms have been implemented based on line analysis to obtain film thickness profiles, or to exploit a whole image to carry out film thickness mapping. As an example, Figure 12.2(c) shows the interferogram resulting from the same mechanical contact as that in Figure 12.2(a), but with a sphere rolling without slipping on the plane. Compared with the earlier static case, strong deformation of the geometry of the contact zone occurs. This arises from the coupling between the hydrodynamic pressure generated within the lubricating fluid and the resulting elastic strain of the solid bodies. Figure 12.2(d) shows the resulting complex film thickness distribution. Within the framework of the above-mentioned studies on lubrication, this experiment demonstrates the validity of the analytical method until a maximum thickness of about 800 nm is reached. Beyond this limit, higher interference orders complicate any colorimetric analysis. The spacer layer technique described in Section 12.2.2 allows us to reduce the lower limit of the thickness range down to values as low as a few nanometers. The precision of this measurement is very sensitive to the quality of the calibration process. Under well-controlled conditions, the absolute uncertainty lies within a few nanometers. Thus, the lower limit for the preservation of the accuracy in the measurements seems to be located at around 10 nm. The spatial resolution obtained obviously depends on the optical assembly. The photographs in Figure 12.2 were obtained using a normal metallographic microscope and a powerful tri-CCD camera. These photographs have a resolution in the order of 1 mm. Finally, the temporal resolution is limited only by the sensitivity of the CCD detector, and by the available lighting. The technique described imposes a necessary condition: the nature and the properties of the film under test must be rigorously the same during the calibration and under measurement in order to maintain a constant refractive index of the medium. In the same way, the experimental conditions must lead to the observation of the same phase change (owing to the presence of reflections in particular).
12.5 Conclusions In the field of surface contamination and its removal, colorimetric interferometry seems to constitute a powerful tool to characterize the thickness of the contaminant layers. A broad spectrum of potential applications
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appears open to exploitation. With a lower limit of a few nanometers, it can approach molecular dimensions, even if its principles do not seem to enable it to reach much lower in thickness scales using the rather simple conditions described. The interaction between the incident radiation and contaminated interfaces implies very weak energies, and this means that it is a nondestructive and non-evasive method. This is valuable because it does not modify the physiochemistry of the surface under study. The possibility of generating interference phenomena by transmission, as well as by reflection, is another additional favorable factor. The spatial and time resolution can be adapted to suit particular conditions, as can the environment of the surface at the time of its characterization. The optical instrumentation that can be employed offers a broad spectrum of possibilities from this point of view. Last, the optical character of this technique confers the advantage of it being able to be coupled with other apparatus, in particular with those using the broad range of visible light, and so is likely to provide complementary information on the chemical or physical nature of the layers under investigation. Presently, the main constraint seems to be the need for a precise calibration that needs to be carried out under conditions as close as possible to those used during measurements. The practical difficulty is to constitute a starting point for this calibration, that is, to form defined layers of a known thickness. For this purpose, we have to fabricate thin layers using a controlled process, even if the film formation process is different from that responsible for the surface contamination. In all cases, we will not avoid the need to know the properties of the medium under evaluation. Finally, constant attention needs to be given to the instrumentation, both from the optical aspects (i.e., choice of system lighting and imaging, adjustments, alignments, and drift with time), and from those concerning picture digitalization and extraction of colorimetric information.
References 1. J. -M. Georges, Frottement Usure et Lubrification, CNRS and Eyrolles Editions, Paris (2000). (in French). 2. J. Molimard, Etude Experimentale du Regime de Lubrification Limite en Film Mince—Application aux Fluides de Laminage, These de Doctorat, Institut National des Sciences Appliquees de Lyon, n 99 ISAL 0121 (1999). (in French). 3. F. J. Westlake and A. Cameron, ‘‘A Study of Ultra-Thin Lubricant Films Using an Optical Technique,’’ Proc. Inst. Mech. Eng. Pt 3G 182, 75 (1967–1968). 4. K. M. K. K. Prasad, S. Raheem, P. Vijayalekshmi and C. Kamala Sastri, ‘‘Basic Aspects and Applications of Tristimulus Colorimetry,’’ Talanta 43, 1187 (1996).
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5. T. Tl aczal a and A. Bartecki, ‘‘Electronic Spectroscopy and Trichromaticity Colorimetry of Some Inorganic Pigments and Their Mixtures,’’ Dyes Pigments 28, 47 (1995). 6. J. Zhang, S. Sokhansanj, S. Wu, R. Fang, W. Yang and P. Winter, ‘‘A Transformation Technique from RGB Signals to the Munsell System for Color Analysis of Tobacco Leaves,’’ Comput. Electron. Agric. 19, 155 (1998). 7. P. Wienhold, F. Weschenfelder and J. Winter, ‘‘Colorimetric Measurements of Carbon Erosion and Deposition Rates on Extended Areas of Plasma Facing Components in TEXTOR,’’ J. Nucl. Mater. 220–222, 452 (1995). 8. P. Wienhold and F. Weschenfelder, ‘‘Two-Dimensional Measurements of Thin Film Erosion and Deposition by Colorimetry of Interference Colors and its Application in Fusion Devices,’’ Vacuum 47, 919 (1996). 9. M. Hartl, I. Krupka, R. Poliscuk and M. Liska, ‘‘Computer-Aided Chromatic Interferometry,’’ Comput. Graph. 22, 203 (1998). 10. D. Spitzer R. Gottenbos, P. van Hensbergen and M. Lucassen, ‘‘A Novel Approach to Color Matching of Automotive Coatings,’’ Prog. Org. Coatings 29, 235 (1996). 11. W. K. Pratt, Digital Image Processing, 2nd Edition, Wiley, NY (1991). 12. J. L. Hay and D. K. Hollingsworth, ‘‘A Comparison of Trichromic Systems for use in the Calibration of Polymer-Dispersed Thermochromic Liquid Crystals,’’ Exptl. Therm. Fluid Sci. 12, 1 (1996). 13. J. D. Foley, A. van Dam, S. K. Feiner and J. F. Hugues, Computers Graphics: Principles and Practice in C, 2nd Edition, Addison-Wesley, Reading, MA (1996). 14. M. T. Kirk, ‘‘Hydrodynamic Lubrication of Perspex,’’ Nature 194, 965 (1962). 15. R. Gohar and A. Cameron, ‘‘Optical Measurement of Oil Film Thickness under Elastohydrodynamic Lubrication,’’ Nature 200, 458 (1963). 16. H. A. Spikes and G. Guangteng, ‘‘Properties of Ultra-thin Films Using Wedged Spacer Layer Optical Interferometry,’’ Proc. 14th Leeds-Lyon Symp. on Tribology, D. Dowson, C. M. Taylor and M. Godet (Eds.), pp. 275–279, Elsevier, London (1988). 17. J. N. Israelachvili, ‘‘Thin Film Studies Using Multiple Beam Interferometry,’’ J. Colloid Interface Sci. 44, 259 (1973). 18. G. J. Johnston, R. Wayte and H. A. Spikes, ‘‘The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts,’’ STLE Tribol. Trans. 34, 187 (1991). 19. L. Gustafsson, E. Hoglund and O. Marklund, ‘‘Measuring Lubricant Film Thickness with Image Analysis,’’ Proc. Inst. Mech. Eng. 208, 205 (1994). 20. P. M. Cann, H. A. Spikes and J. Hutchinson, ‘‘The Development of a Spacer Layer Imaging Method (SLIM) for Mapping Elastohydrodynamic Contacts,’’ STLE Tribol. Trans. 39, 915 (1996). 21. M. Hartl, I. Krupka and M. Liska, ‘‘Differential Colorimetry: A Tool for Evaluation of the Chromatic Interference Patterns,’’ Opt. Eng. 36, 9, 2391 (1997). 22. M. Akei and K. Mizuhara, ‘‘The Elastohydrodynamic Properties of Lubricants in Refrigerant Environments,’’ STLE Tribol. Trans. 40, 1 (1997). 23. D. Mazuyer, E. Varenne, A. A. Lubrecht, J. -M. Georges and B. Constans, ‘‘Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding,’’ Proc. 25th Leeds-Lyon Symp. on Tribology, D. Dowson, C. M. Taylor, T. H.C. Childs, G. Dalmaz, Y. Berthier, L. Flamand, J. -M. Georges and A. A. Lubrecht (Eds.), pp. 493–504, Elsevier, London (1997).
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24. C. A. Foord, L. D. Wedeven, F. J. Westlake and A. Cameron, ‘‘Optical Elastohydrodynamics,’’ Proc. Inst. Mech. Eng. 184, 487 (1969–1970). 25. T. Ohkubo and J. Kishigami, ‘‘Accurate Measurement of Gas-lubricated Slider Bearing Separation using Visible Laser Interferometry,’’ ASME J. Tribol. 110, 148 (1988). 26. J. Luo, S. Wen and P. Huang, ‘‘Thin Film Lubrication Part I: Study on the Transition between EHL and Thin Film Lubrication using a Relative Optical Interference Intensity Technique,’’ Wear 194, 107 (1996). 27. R. Bassani and E. Ciulli, ‘‘Lubricant Film Thickness and Shape using Interferometry and Image Processing,’’ Proc. 23rd Leeds-Lyon Symp. on Tribology, D. Dowson, C. M. Taylor, T. H.C. Childs, G. Dalmaz, Y. Berthier, L. Flamand, J. -M. Georges and A. A. Lubrecht (Eds.), pp. 81–90, Elsevier, London (1997). 28. C. Lacey and F. E. Talke, ‘‘Measurement and Simulation of Partial Contact at the Head/Tape Interface,’’ ASME J. Tribol. 114, 646 (1992). 29. M. H. Wahl, S. Casmer and F. E. Talke, ‘‘Multi-Wavelength Intensity-based Interferometry for Flexible Head/Medium Interfaces,’’ STLE Tribol. Trans. 38, 533 (1995). 30. E. Baugh, J. Swenson and F. E. Talke, ‘‘Simultaneous Three-wavelength Interferometry for Head/Tape Spacing Measurement,’’ ASME J. Tribol. 120, 549 (1998). 31. J. Lord, O. Marklund and R. Larsson, ‘‘Multi Channel Interferometry for Measurements of the Thickness of Very Thin EHL Lubricant Films,’’ Proc. 26th LeedsLyon Symp. on Tribology, D. Dowson, C. M. Taylor, T. H. C. Childs, G. Dalmaz, Y. Berthier, L. Flamand, J. -M. Georges and A. A. Lubrecht (Eds.), pp. 711–717, Elsevier, London (2000).
13
Wettability Techniques to Monitor the Cleanliness of Surfaces William Birch1, Alain Carre 2, and Kashmiri L. Mittal 3
1
Institute of Materials Research and Engineering (IMRE), Singapore
2
Corning S.A., Corning European Technology Center, Avon, France 3
Hopewell Junction, NY, USA
13.1 Background and Introduction In the broad spectrum of contamination control, a major concern is the presence of organic contamination on various inorganic surfaces. This is especially the case in the aerospace and semiconductor industries, where an extremely low level of contamination has a disproportionate impact on yield, reliability and performance. In order to control surface contamination of materials, a rapid detection method is required that does not adversely affect the surface. Wettability measurements provide a convenient and rapid method for probing the outermost surface of a material. The technique is highly surface specific, generally exceeding the sensitivity of electron spectroscopies and is sensitive to a fraction of a monolayer. The term contamination has diverse meanings when applied to surfaces. As more sophisticated techniques are developed for examining surfaces, there is more concern with cleanliness on atomic scale, such that adsorbed gases or trace amounts of oxides on metals, for example, may be considered as contaminants. Organic materials commonly found in the laboratory environment are generally hydrophobic in nature (vacuum-pump oil vapor, for example). This consideration led to the development of the atomizer test where the surface to be tested was sprayed with a fine mist of water. If the deposited drops spread on the surface, it was considered clean. If they remained as
R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 693–723 ª 2008 William Andrew, Inc.
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droplets, the surface was considered to be contaminated by an organic material [1]. For many years the atomizer test was used in the electronics industry to evaluate and monitor various cleaning procedures. It was used primarily in vacuum-tube manufacturing, where there appeared to be no particular problems with this technique, which was really just a means of estimating the wettability of the surface by water. The advent of semiconductor technology, which used very pure silicon as a starting material, changed this point of view. One of the steps in the preparation and cleaning of polished silicon wafers is the treatment with hydrofluoric acid to remove the oxide from the surface. After removal of the oxide on silicon, the resulting silicon hydride surface was hydrophobic, giving a water contact angle of about 50 . The surface could be made hydrophilic by heating it in air or treating it with an aqueous oxidizing solution, known to remove organic contaminants. It was assumed that these oxidizing treatments removed trace amounts of organic contaminants from the silicon surface. However, the increase in wettability (i.e., decrease in water contact angle) after oxidation appeared larger than would be expected from the removal of small amounts of organic materials. In fact, the heating of the silicon surface in air or its exposure to an oxidizing solution regenerated the hydrophilic silicon oxide on the silicon substrate, by removing the hydrophobic silicon hydride surface. Except for a few exceptions, discussed below (noble metals, oxide-free inorganic surfaces), it appears that the wettability of oxide surfaces may be directly related to the amount of organic contaminant present on the surface. Contamination may be considered as an adsorption phenomenon. Surfaces become contaminated at different rates and to different extents. The primary driving force for surface contamination is a reduction of the surface free energy. Perfectly clean oxidized metals, ceramics or glass surfaces will be rapidly contaminated on exposure to ambient air, because of their high surface free energies.
13.2 Fundamentals All surfaces are energetically unfavorable, since they have a positive free energy of formation. A simple explanation may be given by considering the formation of two new surfaces by cleaving a solid. Bonds have to be broken between atoms or molecules on both sides of the cleavage plane, splitting the solid and creating two new surfaces. Breaking the bonds requires work, resulting in a positive contribution to the total free energy
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of the system. The majority of this added energy generates the surface free energy of the two new surfaces. The surface free energy may be minimized in several ways. For example, the optimum shape is a sphere having the lowest surface area/volume ratio. This is why liquid droplets in free space are spherical when external forces, such as gravity, are negligible. The reorganization of molecules or atoms at surfaces can also cause a reduction in the surface free energy. The adsorption of molecules on high surface energy solids can strongly reduce the surface free energy. The mechanism that generates organic contamination on clean inorganic surfaces is similar to the phenomenon of molecular adsorption. Another example of the spontaneous reduction of the surface free energy is the reduction of the surface tension of water by the adsorption of a surfactant, an abbreviation for ‘‘surface active agent.’’ For liquids, the surface tension is equivalent to the surface free energy. Surfactant molecules are amphiphilic, rendering them surface active at interfaces between water and air, or water and non-polar materials. They are generally poorly soluble in water. Below the critical micellar concentration, the excess concentration of molecules at the water surface, G, and the concentration in water, c, are related by the Gibbs adsorption equation, giving the reduction of the surface tension of water, g, as dg = GRT d ln c, where R is the universal gas constant and T is the temperature. Physical adsorption (physisorption) and chemical adsorption (chemisorption) are the two principal modes of adsorption of molecules on surfaces. The basis of this distinction is the nature of the bonding between the molecules and the surface. In physisorption, the bonding mechanism involves van der Waals (non-polar forces) or polar forces. In chemisorption, a chemical bond, involving substantial rearrangement of electron densities in the adsorbate molecules and the substrate molecules, is formed. The nature of this bond may be ionic, covalent, or metallic. Polar molecules have a weak, partial negative charge at one end of the molecule and a partial positive charge elsewhere. For example, for water molecules, there is a weak partial negative charge on the oxygen atom and a weak partial positive charge on the hydrogen atoms. Thus when water molecules are close together, their positive and negative regions are attracted to the oppositely charged regions of nearby molecules. This force of attraction is called a hydrogen bond. Hydrogen bonding is generally listed as a type of dipole–dipole force. However, the details of this interaction are subtle and the bonds formed have some covalent bond character. Hydrogen bonds form only between limited numbers of elements, typically when the partially positively charged hydrogen atom lies between strongly electronegative atoms, namely oxygen, nitrogen, or fluorine.
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Acid–base interactions are another specific class of intermolecular forces. Lewis acids, which are electron pair acceptors, and Lewis bases, which are electron pair donors, react to form adducts in which a coordinate covalent bond is formed. Acid–base interactions are becoming the subject of growing interest in the field of wetting and adhesion phenomena [2–4]. The knowledge of the nature of molecular interactions between contaminants and surfaces is particularly relevant as it can help in the identification of efficient strategies adapted to remove contaminants from a particular surface.
13.3 Theoretical and Experimental Investigations In condensed phases, e.g. a liquid or a solid, molecules or atoms experience different interaction forces, giving the condensed phase its cohesion. Depending on the nature of the liquid or solid, the inter-atomic or intermolecular forces may be different in nature. Whatever the chemical nature of a liquid or a solid, the forces responsible for the cohesion of the material are also responsible for the surface properties of the material. This is specifically the case for surface tension, which results from unbalanced interaction forces at the free surface of a liquid. A molecule in a liquid is surrounded by other molecules. On average, it is equally attracted in all directions. A molecule on the surface experiences a resultant attraction toward the bulk liquid, due to a greater number of molecules per unit volume in the liquid phase than in the vapor phase. The consequence of this inward pull is that the liquid surface always tends to contract to the smallest possible area. In order to extend the area of a liquid surface, it is necessary to do work, bringing molecules from the bulk of the liquid to its surface. This work is done against the inward attractive force from the neighboring molecules in the bulk liquid. The work required to increase the area by one unit is called the surface free energy, or surface tension of the liquid. To increase the surface area of the liquid by dA, the work, dW, to be done is dW ¼ g dA
Eq. (13-1)
where g is the surface free energy. As a result of its tendency to contract, the liquid surface behaves as if it were in a state of tension. The force acting along a length of the liquid surface is proportional to this length, and its value per unit length is called
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the surface tension. The surface tension of liquids is equal, both numerically and dimensionally, to the surface free energy. The most widely used quantitative measure of wettability is the contact angle. When a drop of a liquid with a sufficiently small size is placed on a smooth, flat, homogeneous solid substrate, the drop takes the shape of a spherical cap (Figure 13.1). The shape of the drop approximates that of a spherical cap when the forces other than the surface tension become negligible. In the case of gravity, the ratio of surface forces to gravitation for a drop is expressed by the capillary length, k1 = (g/rg)1/2, where r is the liquid density and g is the acceleration due to gravity. A drop placed on a smooth, flat, homogeneous solid surface whose diameter is substantially smaller than the capillary length will adopt the shape of a quasispherical cap. Each solid and liquid (and vapor phase) combination gives rise to a specific degree of wettability. The parameter defining the wettability is the observed contact angle, y; the lower the contact angle, the higher the wettability. This angle is measured between a tangent to the liquid surface where it meets the solid substrate and the plane of the solid substrate, as shown in Figure 13.1. The angle is always measured inside the liquid phase, not in the vapor phase. The contact angle may be influenced by the spreading history of the liquid drop, as described below. For a smooth, planar surface, the contact angle value depends on the liquid surface tension, the surface free energy of the solid, and the interactions between the two materials. The equilibrium value of the contact angle, also known as the wetting angle, satisfies Young’s equation [5], which may be written as: gSV ¼ gSL þ g LV cos y
γ LV
q
L
γ SL
γ SV S
Figure 13.1 Profile of a liquid drop on a solid surface.
Eq. (13-2)
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where g SV is the surface free energy of the solid, gSL is the interfacial free energy between the liquid and the solid, and g LV is the liquid surface tension, as shown in Figure 13.1. Depending on the value of y, different wetting regimes can be considered as follows:
y y y y
„ „ = =
0 (from 0 to 90 ): partial wetting 0 (from 90 to 180 ): partial dewetting 0: complete or full wetting 180 : complete or full dewetting
The case of partial wetting is most frequently encountered. The case of complete wetting is generally found for a low surface tension liquid on a solid surface, or for the majority of liquids on clean inorganic surfaces. The case of partial dewetting is encountered with specific, and frequently engineered, systems, while the case of complete dewetting is only a theoretical situation that may not happen in practice. In order to predict the behavior of a liquid in contact with a solid surface, the free energy of the dry solid must be compared with the free energy of the wetted surface. The difference between these two energies is called the spreading parameter, S [6]. Its value can be expressed in terms of the parameters defined in Young’s equation: S ¼ g SV ðgSL þ g LV Þ
Eq. (13-3)
If S ‡ 0, the liquid fully wets the solid and the observed static contact angle is zero. When S < 0, the liquid does not fully wet the solid and the observed static contact angle achieves a finite value. The above definitions apply to the solid/liquid/vapor contact angle. A similar set of definitions can be applied to describe a solid/liquid/liquid contact angle, where two immiscible liquids wet a solid substrate. In this case the liquid surface tension is replaced by the interfacial tension between the two liquids and the surface free energy of the solid is replaced by its interfacial free energy when wetted by one of the liquids. Care must be taken to specify the extent of mutual saturation of the two liquids. This is the equivalent to considering the vapor phase saturation for a solid/ liquid/vapor system. According to Eq. (13-2), the contact angle of a liquid on a surface is exactly defined by the interfacial free energies of the solid/vapor, liquid/ vapor, and solid/liquid interfaces. This ideal case has not been observed: wetting angles for a specific system are observed to adopt a continuum of values between two extreme limits. These limits are referred to as the
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advancing contact angle, ya, observed when the stationary liquid has just started to advance across the solid surface, and the receding contact angle, yr, observed when the stationary liquid has just started to recede across the solid surface. These limiting values are considered to be reproducible for a given solid/liquid (and vapor) combination, or for a solid/liquid/liquid combination. Several hypotheses have been formulated to explain the wetting hysteresis (ya – yr), whose sources are considered to be: surface roughness on the solid surface [7], chemical heterogeneities on the solid surface (can be generated by adsorption of contaminants [8]), re-arrangement of the solid surface when in contact with a liquid (for example, a polar polymer in contact with a polar liquid) [9, 10], local deformation of the solid surface [11–13]. No wetting situation with a finite observed contact angle is completely free of wetting hysteresis. The case of the complete wetting is, by definition (y = ya = yr = 0), free of hysteresis. Low wetting hysteresis (y ya yr) has been observed for some highly uniform solid surfaces with ultra-low surface energy, such as a silicon wafer coated with Self-Assembled Monolayers (SAMs) of a hydrophobic silane [14]. Surfaces are classified into two types: high-energy surfaces and lowenergy surfaces. High-energy surfaces include metals, metal oxides, glasses, and ceramics. Low surface energy solids are primarily organic and polymeric materials. Liquids generally spread on high-energy solid surfaces, since the liquid surface tension is considerably less than the surface free energy of the solid substrate [15, 16]. Some exceptions to this rule exist. Gold and other metal surfaces absolutely free of oxides, as well as HF-etched silicon are not completely wetted by water. The issue of the wettability of gold by water has been a controversial one, with both wettability and non-wettability of gold being reported in the literature [17]. For a gold surface, standard cleaning procedures to remove the residual organic contamination, such as oxidation, did not alter the hydrophobic nature of the gold surface. Heating the gold surface to 1000 C in air also left it hydrophobic. At the time, the explanation was made that organic materials were strongly adsorbed onto gold and were, therefore, more difficult to remove. However, this was not consistent with the generally low adsorptive character of a gold surface. During an investigation of gold wetting, it was found
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that the gold could be made wettable by anodically growing an oxide layer on its surface [18]. When heated, the unstable oxide decomposed to gold and oxygen and the surface reverted to its hydrophobic behavior. Thus, an oxide-free gold surface was non-wetting to water. The formation of an oxide rendered the surface hydrophilic. A similar behavior is found for a silicon surface, which is hydrophobic after the oxide has been removed and becomes hydrophilic when the surface is re-oxidized. The wettability behavior of metals with water was confirmed by Erb [19]. Continual condensation of water onto metal surfaces for many thousands of hours showed that only noble metals continued to have dropwise condensation of water, indicating hydrophobic behavior. Indeed, aluminum, chromium, and other metals known to form oxides had hydrophilic surfaces after prolonged exposure to the water vapors. Fowkes developed a theoretical confirmation of the inherent hydrophobic nature of oxide-free metal surfaces by considering the dispersion forces involved in wetting of solid surfaces [20, 21]. However, the controversy is not fully resolved, since Schrader [22] has reported that a pure gold surface prepared in ultra-high vacuum is wettable by water. Any test of surface cleanliness involving wettability by water cannot be used on metal surfaces that have an indeterminate oxide layer. It is tempting to assume that any clean metal oxide surface would be hydrophilic, but even this rule may have some exceptions. Extensive contact angle data are available in the literature. Most measurements are of advancing contact angles. Generally, small advancing contact angles on metal surfaces are obtained only on extremely clean surfaces.
13.4 Instrumentation The most common method of contact angle measurement is the direct observation of a sessile drop. The contact angle is determined from the profile of the drop where it meets the solid surface. This may be done directly with a contact angle goniometer equipped with an eyepiece. The drop is viewed from the side and a tangent is aligned with the liquid surface at the point where it meets the solid substrate. Alternatively, a drop of known volume is placed on the solid substrate and the drop is viewed from above. The diameter of the drop gives its contact angle. A non-circular drop profile indicates a non-uniform wettability on the solid substrate. The advancing and receding contact angles can be measured by adding or withdrawing liquid from the drop. Neither of these techniques
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requires a prior knowledge of the surface tension or the density of the liquid. The accuracy of both methods is typically –1 , which is also the typical error bar in contact angle measurements on a variety of uniform surfaces. Contact angle measurements provide a simple, rapid, and non-destructive technique for probing the surface chemistry of a solid surface. The wettability is very sensitive to the exposed surface chemistry. Wetting properties have a high degree of correlation to surface reactivity and adhesion properties of the surface of the solid substrate. The heart of a contact angle goniometer is an optical bench. Some examples of contact angle goniometers are shown in Figure 13.2. At one end of the bench is the light source and at the other end we find the
Figure 13.2 Examples of contact angle goniometers.
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measurement optics, consisting of a binocular with a cross hair and a goniometer in the eyepiece. In between these two is placed the solid substrate and a syringe to dispense the probe liquid. The solid substrate is maintained horizontal for sessile drop measurements and may be inclined perpendicular to the optical axis for advancing and receding contact angle measurements. The basic version of the instrument is equipped with a micrometer driven syringe and a mechanical stage, allowing an accurate dosing and reliable positioning of the liquid drop on the solid substrate. The eyepiece contains a protractor scale with 1 division for easy measurements. This flexible design allows many different accessories to be adapted. Manual measurements can be made with the goniometer eyepiece, which a trained operator can use to determine contact angles rapidly and easily. Manual contact angle measurement is rapid and reliable. It avoids errors that can be induced by automation and allows a direct observation of the liquid drop behavior on the sample. To achieve automation, the eyepiece in the goniometer bench may be replaced by an image acquisition system connected to a computer, allowing rapid sample analysis and routine documentation of results. Eliminating the influence of the operator can improve the reliability of the results. However, the automated system rarely achieves higher accuracy than a trained operator and an automated image analysis system that is incorrectly calibrated or aligned will generate erroneous data. Image processing software is used to analyze the acquired images and reliably define the drop boundary. The software can analyze not only images of sessile drops, but also images of enclosed bubbles and pendant drops. It can calculate several parameters of interest from these drop shapes, such as static or equilibrium contact angles, advancing and receding contact angles, liquid surface tension, interfacial tension between two liquids, surface energy from contact angles, and Zisman critical wetting tension [16] from the contact angles of a homologous series of liquids, such as alkanes. The wetting or contact angle can also be determined indirectly from capillary rise measurements, such as the Wilhelmy plate technique, where a plate is immersed vertically into the liquid until it partially covers the plate. The liquid forms a meniscus, whose shape is determined by Laplace’s equation, as shown in Figure 13.3. From this equation, a relationship can be derived for the contact angle as a function of the capillary rise height, h, of the liquid on the plate: sin y ¼ 1
rg 2 h 2g
Eq. (13-4)
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F e
F = mg +P.γ.cosq - b P = 2(L + e)
h
q L
Figure 13.3 Principle of contact angle measurement with the Wilhelmy plate.
where r is liquid density and g the acceleration of gravity. This principle has been used to develop Dynamic Contact Angle Analyzers (DCAs), which measure both advancing and receding contact angles on solids. Instead of measuring the capillary rise, a DCA uses a microbalance to measure the wetting force exerted by the liquid meniscus on the solid surface. This force corresponds to the weight of the liquid meniscus, w, which satisfies the following equation: w ¼ Pg cos y
Eq. (13-5)
where P is the solid perimeter. The solid plate hangs from the microbalance which measures the vertical force, F, acting on the plate. The substrate is generally small and light, allowing optimal functioning of the microbalance. The contact angle is derived by measuring the vertical force on the sample during immersion and emersion of the sample from the liquid medium. The measured force, F, is composed of the sample weight, mg, where m is the sample mass, the buoyancy force, b, from the displaced liquid, and the meniscus force, Pg cos y, as shown in Figure 13.3. Thus, the force, F, measured by the microbalance is F ¼ mg þ Pgcos yb
Eq. (13-6)
The programming of a DCA apparatus allows either determining the liquid surface tension when the wetting angle is zero, or determining the advancing and receding wetting angles with a liquid probe of known surface tension. The advancing and receding contact angles correspond to the immersion or emersion of the solid from the liquid, respectively.
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The calculation performed by a DCA takes into account the buoyancy correction, b, generated by the solid substrate displacing the bulk liquid. An advantage of a DCA is that wetting measurements can be performed on flat as well as on cylindrical solids. Further, since the heart of the equipment is a microbalance with a precision of 108–109 N, the wetting properties of extremely thin fibers, such as glass fibers or hair, can easily be measured. The observed contact angle on a solid substrate depends not only on the intrinsic surface characteristics of the substrate, but also on any material adsorbed onto the substrate surface. Both the advancing and receding water contact angles on freshly cleaned glass or platinum surfaces are 0 . The recommended cleaning procedure for these materials is exposure to the hot portion of a gas flame. Following cleaning, exposure of the clean plate to ambient atmosphere generally results in a rapid increase in advancing contact angle. This increase is caused by a lowering of the surface energy as organic contaminants contained in the atmosphere are adsorbed onto the clean surfaces. The observed contact angle then depends on the type and amount of adsorbed contamination. The advancing or receding of a meniscus across the substrate measures the average wettability along its length. The measured wettability is sensitive only to the outermost surface. It can be used to detect minor levels of organic molecules adsorption that generate variations in the surface energy of the substrate. The DCA analysis is well suited to making contact angle measurements on solid surfaces: the contact angle is averaged over the line formed by the meniscus and the measurement is recorded during immersion of the entire substrate. This allows a rapid examination of the wettability of the entire surface. Surface inhomogeneities are easily detected from distortions of the contact line, which generate corresponding fluctuations in the force measured by the microbalance. Moving the solid downward and upward measures advancing and receding contact angles, respectively, at a given displacement speed of the contact line. A zero receding contact angle on the solid substrate is easily determined. When this occurs, the force generated by the meniscus is equal to the product of the solid perimeter and the liquid surface tension. The DCA (Figure 13.4) uses the microbalance technique coupled with software to provide a simple and flexible analytical tool. Its measurements are based on a highly precise and accurate microbalance that provides a high sensitivity and reproducibility. The force resolution is 109 N (corresponding to 107 g), allowing studying wetting on single fibers. For thin and lightweight solid substrates, the apparatus can measure advancing and receding contact angles, liquid surface tension, interfacial tension
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B
Figure 13.4 Example of a DCA used for surface tension and dynamic contact angle measurements. This system can be applied to many types and geometries of solid surfaces, including single fibers. Picture A shows the basic equipment (a microbalance) and Picture B shows the force diagram in advancing and receding modes leading to the contact angle hysteresis.
between two immiscible liquids, surface energy from contact angles, and Zisman critical wetting tension. It can also be used to measure wicking rate and contact angles on granulated materials.
13.5 Examples of Applications Contact angle measurements can be used to investigate the result of a cleaning process, contributing to the optimization of cleaning procedures. Measuring both advancing and receding contact angles allows a range of adsorption and contamination processes to be monitored. This can avoid the use of more laborious and occasionally less informative methods of analysis, such as ultra-high vacuum analysis techniques, which can eventually be used as a final method of confirmation. High surface energy materials, such as metals, glass, and ceramics, when exposed to ambient air, are generally coated with a partial layer of organic molecules. These coatings reduce the surface free energy of these materials from its intrinsic value and render the final surface hydrophobic. Such contamination may generate large advancing contact angles, up to about 80 . Degreasing the surfaces generally reduces the advancing contact angle to about 30 , which corresponds to residual adsorbed hydrocarbons, most of which generally come from the degreasing agent. To obtain a higher wettability, all residual adsorbed organic
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molecules must be removed. Only highly clean oxidized metal surfaces are fully wetted by water, with both the advancing and receding contact angles being 0 . Small levels of hydrophobic contamination on a hydrophilic surface lead to a rapid increase in the observed advancing contact angle [23]. For example, a full coverage of a planar surface by small organic molecules can be achieved with only 1 g per 1000 m2 of surface. Even less than a full-layer coverage is sufficient to cause a finite advancing contact angle on the contaminated surface. In industrial environments, metal surfaces are generally contaminated, making their advancing contact angles difficult to predict. In most cases, these fall in the range from 40 to 80 . The receding contact angle is generally smaller than 20 , thus generating a large contact angle hysteresis. Hence, both advancing and receding contact angles are needed to completely describe the wettability of these surfaces. High-energy solid surfaces such as metallic oxides or metals are highly prone to contamination from organic vapors in the atmosphere. The large change in the surface wettability toward water makes the presence of contamination easy to detect. O’Kane and Mittal [24] have used surface wettability to study hydrophobic organic contamination and the rate of contaminant adsorption by rhodium and iron-cobalt (Fe–Co) alloy surfaces. Auger electron spectroscopy provided identification of the impurity elements and an estimate of their concentrations on the metal surfaces. Figure 13.5 shows the rate of adsorption of hydrophobic contaminants on the surface of Fe–Co as measured by the water contact angle. A freshly evaporated surface of Fe–Co shows a slow rate of adsorption which is indicated by the increase of the contact angle from less than 5 to 51 over a period of 15 days. A badly contaminated surface of Fe–Co (initial water contact angle of 83 ) was plasma cleaned to produce a contact angle of less than 5 . After exposure to laboratory air, the contact angle increased to 50 in 9 days (Figure 13.5). This apparent higher rate of adsorption of impurities for the plasma cleaned surfaces may be caused by active surface sites generated. The change in surface wettability for various surface cleaning conditions is reported in Table 13.1. The results of Table 13.1 show that cleaning with organic solvents was not as effective as plasma cleaning in the removal of surface contaminants. The results concerning the rhodium substrate showed that the surface wettability was dependent on the length of time in the plasma. Plasma cleaned Fe–Co surfaces were equivalent to freshly evaporated surfaces in terms of water wettability (contact angle lower than 5 , Figure 13.5). No significant difference was observed in the cleaning efficiency of the plasma
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Figure 13.5 Rate of adsorption of hydrophobic contaminants on Fe–Co alloy surfaces. Closed circles: plasma cleaned surface. Open circles: freshly evaporated surface [24].
Table 13.1 Change in Water Wettability as a Function of Surface Cleaning Conditions [24]
Type of Surface Fe–Co
Rhodium
Method of Cleaning No cleaning of contaminated surface Organic solvents Organic solvents and helium–oxygen plasma (10 W for 1 min) Freshly evaporated Fe–Co surface Vapor degreasing Vapor degreasing + argon plasma (40 W for 1 min) Vapor degreasing + argon plasma (40 W for 3 min) Vapor degreasing + argon plasma (40 W for 6 min)
Water Contact Angle ( º ) 96 80 <5 <5 38 19 13 8
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when argon was substituted for the helium–oxygen mixture. Argon was preferred to avoid the possibility of metal oxidation in the plasma. The contamination rates for six metallic oxides were probed by Matsunaga and coworkers [25, 26]. The solids examined were: crystalline quartz glass (SiO2), titanium oxide (also known as rutile, TiO2), chromium oxide (also known as chromia, or Cr2O3), alumina Al2O3, nickel oxide NiO, and strontium titanate SrTiO3. The samples were polished with an emery paper, followed by polishing with diamond powder. They were then cleaned with ultrasonic agitation in a detergent solution, followed by thorough rinsing in double-distilled water. Following cleaning, the metal oxide surfaces were fully wettable by water. These samples were then dried for 1 hour in an enclosure containing P2O5. To generate surface contamination by adsorption of organic molecules, the clean samples were exposed to liquid-paraffin vapor. This was done in a Petri dish with two small containers. One container was filled with paraffin and the second container was filled with water to generate a humid atmosphere. Figure 13.6 shows the water contact angles plotted against time for clean samples exposed to paraffin vapor in a dry atmosphere and Figure 13.7 shows data from clean samples exposed to paraffin vapor in an atmosphere saturated with water vapor. In a dry atmosphere, the most rapidly contaminated sample was rutile. The contact angles on silica and alumina surfaces increased much slowly. In the wet atmosphere, the extent of contamination was significantly reduced for all the surfaces, with the largest attenuation recorded for the silica and alumina surfaces, with only minor increase in their contact angles after 40 hours of exposure to paraffin vapor. However, the trends in the contamination rate versus material were the same for dry and humid atmospheres. We may deduce from this study that a surface having a larger affinity to water will be contaminated more slowly by adsorption of organic molecules. A similar conclusion was found following a study of the wettability of glasses with different compositions. This study is described in Section 13.6. It is tempting to deduce that all clean oxide surfaces are hydrophilic. However some caution is necessary. White [27] cleaned a polished fused silica surface by degreasing and boiling in 30% hydrogen peroxide. He then heated the cleaned surface in oxygen at various temperatures. By measuring the contact angle of water immediately after cooling to room temperature, he showed that wettability of the surface decreased with increasing heating temperature, as shown in Figure 13.8. Cleaning the silica surface by etching with NH4F–HF solution generates even lower surface wettability following heating in oxygen. This increase in the
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Figure 13.6 Contamination rates (in terms of increase in water contact angle with time) on metallic oxide surfaces under dry atmosphere [26].
water contact angle with heating is probably caused by dehydration of the silica surface, forming siloxane bridges (Si–O–Si) from the neighboring silanol (Si–OH) sites. The siloxane groups have a more hydrophobic behavior than the original silanol groups (Si–OH). The higher contact angle values measured following fluoride etching are believed to be caused by the formation of silicon fluoride (Si–F) bonds. Sonders et al. [28] give an interesting example of the effect on the wetting properties of ion exchange at the surface of soda-lime glass, which has been cleaned in sulfuric acid containing potassium dichromate. Adding a trace of sodium fluoride to the sulphuric acid causes the OH groups to be replaced by F ions at the glass surface. After a few seconds fluorine ions have replaced the hydroxyl groups and the acid forms little droplets on glass similar to water on a greasy surface. As for the fluoride–etched silicon wafer, the Si–F groups are hydrophobic, leading to higher water contact angles on the silica surface. As seen above, not all clean metal oxide surfaces are wettable by water. Some caution must be used when interpreting contact angles on these
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Figure 13.7 Contamination rates (in terms of increase in water contact angle with time) on metallic oxide surfaces under wet atmosphere [26].
Figure 13.8 Effect of heating in dry oxygen on water contact angles on fused silica plate [27].
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surfaces. However, it has been found that all clean metal oxide surfaces are fully wettable by water, provided they are not heated to high temperatures. The wettability of oxide surfaces may be directly related to the amount of organic contaminant present on the surface. If we expose clean oxide surfaces to ambient air containing organic contaminants, we expect the contact angles to increase with time. A study was made of the contamination rate on a number of different surfaces [27]. Metal surfaces were prepared by polishing high-purity metal samples to a mirror finish with alumina powder, followed by degreasing in trichloroethylene and acetone. The samples were then heated in air at 400–500 C for 30 minutes, completely removing any residual organic contaminants and growing an oxide layer on the metal surface. Glass substrates were cleaned with dichromatesulfuric acid cleaning solution and then fired in air in the same manner as the metals. A clean mica surface was obtained by cleaving a piece of mica immediately before using. The contact angle of deionized water, as measured by the reflection goniometry technique was between 3 and 8 on all surfaces immediately after cleaning. These surfaces were then exposed to laboratory air for various periods of time and the contact angle of water measured after each exposure. Figure 13.9 shows the water contact angles as a function of exposure time to laboratory air [27]. The contact angles on metal surfaces, particularly nichrome (a nickel and chromium alloy) and aluminum, attain higher final values than those on mica. They also show
Figure 13.9 Contamination rates (in terms of increase of water contact angle with time) of surfaces exposed to laboratory air [27].
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a higher initial rate of increase, suggesting that the surfaces are not being contaminated at the same rate. A consistent contaminating atmosphere was used for an experiment designed to avoid the contaminant variations in ambient air. A number of metals surfaces were cleaned by White [27], using the processes described above. The samples were then exposed to Nujol (a mineral oil) vapor for 2 hours in a closed container. The measured values of water contact angles are shown in Figure 13.10. Contact angles on glass and mica show only a small increase, while aluminum and magnesium show higher values. Transition metals show the largest increase in measured contact angles. If we assume the measured water contact angles to be directly correlated to the amount of organic material on the surface, the various surfaces are reacting differently to the available organic contamination in the atmosphere. This confirms the adsorption phenomenon of organic contamination, where each metal oxide has its specific rate and final coverage of adsorbed contamination. From the lower increase in observed water contact angles, mica and glass show lower levels of adsorbed contamination when compared to the transition metal oxides. From this study, we may infer that the transition metal oxides are the most sensitive for detecting organic contamination, since they show the greatest change in wettability when exposed to organic vapors. This means that a clean oxidized nichrome surface will give a better indication of ambient organic contamination than a less adsorptive surface, such as glass or mica [27].
Figure 13.10 Water contact angles on oxidized metal surfaces exposed to Nujol [27].
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The concept of organic contamination as an adsorption phenomenon has led to an interesting technique for storing clean surfaces [27]. Since oxidized metal surfaces have a higher affinity for organic vapors than glass or mica, they will preferentially adsorb ambient organic contaminants. A container with a relatively large surface area of a clean metal oxide is expected to maintain an organic-free atmosphere by reason of its high affinity for organic molecules. This was tested by heating degreased aluminum shots to 500 C in an aluminum desiccator. During this process, organic material would be desorbed from the surface of the aluminum and an aluminum oxide layer would be grown. A piece of mica that had been contaminated by exposure to ambient air was placed into this container and the contact angle measured periodically, probing its level of adsorbed organic contamination. Results showed that the water contact angle on contaminated mica decreased from 15 to 7.5 after 100 hours of storage, indicating that organic contaminants were desorbing from the mica surface and adsorbing onto oxidized aluminum surface. While this cannot be a practical routine technique for reducing contamination on mica or glass surfaces, it is a demonstration of surface adsorption and desorbtion on different materials. To examine the effectiveness of various containers for maintaining clean surfaces, samples of nichrome were placed into various containers for 16 hours [27]. Nichrome was chosen as a test surface, due to its high affinity for adsorbing organic contaminants. Prior to storage, the samples were made fully wettable by water by cleaning and oxidation, as described above. Water contact angles were measured as a function of storage time, probing the contamination level on the surface. Figure 13.11 shows results obtained for a variety of storage conditions. Exposure to laboratory air for 16 hours results in a contact angle of 35 . For the same storage time, the contact angle following storage in a groundglass stoppered weighing bottle is only slightly lower, indicating only marginal improvement. Storage in an empty aluminum desiccator shows a significantly lower surface contamination, as evidenced by the contact angle of only 18 . The storage conditions are further improved by placing activated charcoal or activated alumina inside the desiccator. The best storage condition is obtained when cleaned and oxidized aluminum shots are placed in the aluminum desiccator, where no increase in the contact angle obtained immediately after cleaning is observed. Figure 13.12 shows the effectiveness of storing nichrome and aluminum samples in this environment for 120 hours. Water contact angles were measured on the samples at regular intervals and the samples were returned to the storage container after each measurement. It is interesting to note that
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Figure 13.11 Evaluation of storage condition on water wettability of nichrome [27].
Figure 13.12 Water contact angles on surfaces stored in an aluminum container with aluminum as a getter [27].
the contact angle on cleaned nichrome surfaces slowly increases over a period of several days, while the oxidized aluminum surface maintains its original low wetting angle, indicating a lower level of contamination. This result confirms the change in the level of contamination on different
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surfaces exposed to the same atmosphere. In a manner similar to water on dehydrating agents, an oxidized aluminum surface eventually becomes saturated with contaminants. The surface must then be regenerated by removing the adsorbed organic contaminants. This can be achieved by degreasing the aluminum container and aluminum shots and heating them in air to 500 C. For the majority of practical applications, aluminum provides an adequate material for adsorbing ambient organic contaminants and maintaining surface cleanliness. Pohlack and Wendler demonstrated how the initial condition of a glass surface (Schott BK7) influenced its wettability toward water after each step of the cleaning operation [29]. Glass that had been freshly polished using a pitch polisher, followed by drying on a linen cloth, gave contact angles ranging from 20 to 70 . The two sides of the same sample did not give the same contact angles. When an organic solvent was used to clean the glass, the contact angle decreased but continued to show a relation with the initial value. Glow discharge cleaning always gave low contact angles, as shown in Figure 13.13. Small differences in contact angles, with values near zero, were difficult to detect. Thus, it is not certain whether glow discharge cleaning erases any influence of the initial surface condition. Figure 13.14 shows the increase of the water contact angle, measured at different times after glow discharge cleaning. The cleaning was performed using two different high-voltage power inputs [29]. The results
Figure 13.13 Change in water contact angle on glass after cleaning as follows: 1, polished and dried; 2, organic solvent; 3, chromic acid; 4, glow discharge [30, 31]. The three symbols correspond to different initial wettability conditions.
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Figure 13.14 Change in water contact angle on glass with time after glow discharge cleaning for (a) 2 kV, 0.2 A, 3.5 minutes, and (b) 3.8 kV, 0.2 A, 3.5 minutes [30, 31].
suggest that more effective cleaning of the glass causes it to be contaminated more rapidly on exposure to a contaminating atmosphere. A saturation level of contamination may be indicated by the asymptotic values of the two curves, suggesting that an improved cleaning leads to a higher level of contamination of the glass surface. The recontamination of clean glass surfaces exposed to a contaminating atmosphere is a fast process. It begins immediately after cleaning and the surface is saturated with contaminant after only a couple of hours.
13.6 Recent Developments The surface contamination of different glass surfaces as a function of glass composition and cleaning process was recently studied [30]. The susceptibility of glass surfaces to strongly adsorbed organic contaminants was found to depend both on the glass composition and the cleaning procedure. Silica surfaces show a large difference in their contamination behavior following pyrolysis cleaning or cleaning in a saturated potassium dichromate solution in concentrated sulfuric acid (this solution, known as Chromerge, is prepared by completely dissolving 20 g of potassium dichromate in 90 g of water. To this is slowly added 900 g of concentrated sulfuric acid. The mixing reaction is highly exothermic, exposing the operator to a high risk from spattering. This solution could be re-used as long as it remained brown, rather than green, indicating the oxidation state of the dichromate).
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In this study, pyrolysis cleaning consisted of heating the glass substrates to 500 C for 5 hours. The pyrolyzed samples were held in a glass rack and placed in a glass container which was closed with folded aluminum foil. Following removal from the oven, the glass samples remained clean for as long as 1 week or longer, provided the lid was not opened. Following opening of the container, the clean glass samples were used within 5 minutes. The glass samples were cleaned by immersing them for 20 minutes in the Chromerge solution at room temperature. They were then rinsed in pure water and dipped for 20 minutes in a 1:1 concentrated hydrochloric acid/ water solution. This was designed to remove chromium ions, which may strongly adsorb organic contaminants from the glass surface. The samples were then rinsed in pure water and dried under a stream of clean nitrogen. Before cleaning, the glass samples showed no macroscopic organic contamination on their surface. Hence, the samples had only a limited amount of organic contamination, consisting of a monolayer or submonolayer coverage of molecules. This layer, removed by the pyrolysis or Chromerge cleaning, generally has a thickness of the order of 1 nm or less, corresponding to less than 1 g per 1000 m2 of planar surface. Following cleaning, glass samples were verified to be fully wettable by water, as a deposited 1 ml drop of pure water was observed to spread on the sample. On tilting the sample, the water drop migrated easily, leaving a liquid streak behind, which indicated a zero degree receding contact angle. While aluminoborosilicate Corning code 1737 glass shows some change in its surface properties after pyrolysis or Chromerge cleaning, sodalime glass shows immunity to contamination after pyrolysis cleaning. However, for the sodalime glass surface, its contamination behavior is similar to an acid-cleaned silica surface following Chromerge cleaning. Despite the notion of a glass surface being a high energy substrate that is found to attract ambient organic contamination, these results suggest that the sensitivity to organic contamination depends on the composition of the glass surface. This composition is determined by the bulk glass composition and also by the cleaning procedure. It appears that increasing hydrophilicity of the glass surface may reduce its affinity for adsorbing organic contaminants. This result corroborates the conclusion of the study by Matsunaga and coworkers on the contamination rate of several oxides [25, 26]. DCA measurements allow measurement of wettability on small cylindrical solids, such as optical fibers with a diameter of 125 mm. A typical force diagram corresponding to the wetting and dewetting processes is given in Figure 13.15. The wettability of an optical fiber was measured following each step in its cleaning, consisting of mechanical and chemical
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Figure 13.15 Measurement of the wetting force with a DCA analyzer during the wetting and dewetting cycles.
stripping of its cladding. The UV-curable acrylic polymer cladding was first stripped mechanically. The fiber was then cleaned with ethanol and, finally, residual cladding was removed by etching the glass fiber in hydrofluoric acid. The results are presented in Figures 13.16–13.18. The wetting cycle allows determination of the advancing contact angle, while the dewetting cycle gives the receding contact angle. The results indicate an increase of the glass wettability by water and a decrease of the wetting hysteresis, as expressed by the difference between cosines of the advancing and receding contact angles.
13.7 Future Directions The optimization and validation of cleaning procedures to remove contamination from surfaces remain difficult. The required level of cleanliness depends on the application for which the product is manufactured. This level will determine which analytical method is suitable to monitor surface cleanliness. Analytical techniques such as X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (TOF-SIMS) are extremely powerful. However, they are expensive
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Figure 13.16 Wetting and dewetting cycle of water on an optical fiber of 125 mm diameter after mechanical stripping (ya = 78.8 , yr = 60.4 ).
Figure 13.17 Wetting and dewetting cycle of water on an optical fiber of 125 mm diameter after mechanical stripping and ethanol washing (ya = 74.9 , yr = 55.2 ).
techniques that operate under vacuum and require a high level of skill in their operation. They are poorly suited to routine quality control procedures. While these techniques may determine surface cleanliness, the ability to measure the kinetics of cleaning or contamination presents an even greater challenge. Few studies have been published in the literature [31–34]. TOF-SIMS is a relatively new technique for identifying
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Figure 13.18 Wetting and dewetting cycle of water on an optical fiber of 125 mm diameter after mechanical stripping, ethanol washing and HF etching (ya = 37.6 , yr = 22.3 ).
organic contaminants on solid surfaces in a ‘‘routine’’ contamination laboratory environment. However, it is a versatile method that offers a wide field of application, especially in the semiconductor industry [34]. Contact angle measurements provide a powerful analysis tool. They are able to monitor small levels of contaminants on solid surfaces in a rapid and non-destructive manner. They allow the removal rate of organic contaminants and recontamination of the surface to be determined with ease. They provide an easy tool for the routine control of surface contamination on metals, glasses, ceramics, and other inorganic oxide surfaces. Although they give no direct information on the chemical composition of the contaminant, however, correlating these measurements with TOF-SIMS data can provide an accurate characterization of the contaminants. Using dynamic contact angle measurements, probed by a liquid advancing or receding at a finite speed across a solid substrate, Davies et al. [35] examined the removal kinetics of proteins immobilized on a range of solid surfaces, including glass, stainless steel, and polymeric substrates. The substrates coated with proteins were immersed in a cleaning solution of sodium hydroxide and Triton X-100 detergent. Protein removal kinetics was deduced from analysis of the DCA adsorption profile. The results were used to determine optimum soak times in the cleaning solution. Glass and silicon substrates were cleaned in a few minutes, while stainless steel required cleaning times of the order of 1 hour.
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Testing surface cleanliness by measuring wettability toward water may be misleading if the surface is contaminated with hydrophilic impurities. For example, if the surface is covered with a layer of surfactant or an inorganic salt, water will spread on the contaminants and this may be incorrectly interpreted as a clean surface. For testing the cleanliness of low energy surfaces, such as polymers, wettability measurements can be used but in this case one needs a table of values of contact angles on clean plastics (as a reference) which is usually available in the literature (e.g., see Ref. [15]). Contact angle measurements offer a quick and simple test for hydrophobic organic contaminants. The ASTM standard recommends this method to detect hydrophobic organic contamination on glass [36]. This technique can be complemented with highly sensitive surface analytical techniques such as TOF-SIMS to identify the chemical nature of contaminants.
References 1. D. O. Feder and D. E. Koontz, ‘‘Detection, Removal and Control of Organic Contaminants in the Production of Electron Devices,’’ in Proc. Symp. Cleaning of Electronic Device Components and Materials, ASTM Spec. Tech. Publ. No. 246, pp. 40–65, American Society for Testing and Materials, Conshohocken, PA (1959). 2. W. R. Jensen, ‘‘The Lewis Acid-Base Concepts: Recent Results and Prospects for the Future,’’ in Acid–Base Interactions. Relevance to Adhesion Science and Technology, K. L. Mittal and H. R. Anderson, Jr. (Eds.), p. 3, VSP, Utrecht, The Netherlands (1991). 3. K. L. Mittal (Ed.), Acid–Base Interactions: Relevance to Adhesion Science and Technology, Volume 2, VSP, Utrecht, The Netherlands (2000). 4. K. L. Mittal (Ed.), Contact Angle, Wettability and Adhesion, Volume 4, VSP/ Brill, Leiden, The Netherlands (2006). 5. T. Young, ‘‘An Essay on the Cohesion of Fluids,’’ Phil. Trans. Roy. Soc. London 95, 65 (1805). 6. W. D. Harkins and A. Feldman, ‘‘Films. The Spreading of Liquids and the Spreading Coefficient,’’ J. Amer. Chem. Soc. 44, 2665 (1922). 7. R. E. Johnson, Jr. and R. H. Dettre, ‘‘Contact Angle Hysteresis,’’ in Contact Angle, Wettability and Adhesion, Adv. Chem. Ser. 43, p. 112, American Chemical Society, Washington DC (1964). 8. A. W. Adamson, Physical Chemistry of Surfaces, p. 347, John Wiley, New York (1967). 9. H. Yasuda, A. K. Sharma and T. Yasuda, ‘‘Effect of Orientation and Mobility of Polymer Molecules at Surfaces on Contact Angle and its Hysteresis,’’ J. Polym. Sci.: Polym. Phys. 19, 1285 (1981).
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10. A. Carre, S. Moll, J. Schultz and M. E. R. Shanahan, ‘‘A Novel Interpretation of Contact Angle Hysteresis on Polymer Surfaces,’’ in Adhesion 11, K. W. Allen (Ed.), p. 82, Elsevier Applied Science, London (1987). 11. G. R. Lester, ‘‘Contact Angles of Liquids at Deformable Solid Surfaces,’’ J. Colloid Sci. 16, 315 (1961). 12. M. E. R. Shanahan and P. G. de Gennes, Equilibrium of the Triple Line Solid/ Liquid/Fluid of a Sessile Drop,’’ in Adhesion 11, K. W. Allen (Ed.), p. 71, Elsevier Applied Science, London (1987). 13. A. Carre and M. E. R. Shanahan, ‘‘Viscoelastic Braking of a Running Drop,’’ Langmuir 17, 2982 (2001). 14. J. B. Brzoska, N. Shahidzadeh and F. Rondelez, ‘‘Evidence of a Transition Temperature for the Optimum Deposition of Grafted Monolayer Coatings,’’ Nature 360, 719 (1992). 15. S. Wu, Polymer Interface and Adhesion, Marcel Dekker, New York (1982). 16. H. W. Fox and W. A. Zisman, ‘‘The Spreading of Liquids on Low Energy Surfaces. I. Polytetrafluoroethylene,’’ J. Colloid Sci. 5, 514 (1950). 17. K. L. Mittal, ‘‘Surface Contamination: An Overview,’’ in Surface Contamination: Genesis, Detection, and Control, Volume 1, K. L. Mittal (Ed.), p. 3, Plenum Press, New York (1979). 18. M. L. White, ‘‘The Wetting of Gold Surfaces by Water,’’ J. Phys. Chem. 68, 3083 (1964). 19. R. A. Erb, ‘‘Wettability of Metals under Continuous Condensing Conditions,’’ J. Phys. Chem. 69, 1306 (1965). 20. F. M. Fowkes, ‘‘Attractive Forces at Interfaces,’’ Ind. Eng. Chem. 56, 40 (1964). 21. F. M. Fowkes, ‘‘Additivity of Intermolecular Forces at Interfaces,’’ I. Determination of the Contribution to Surface and Interfacial Tensions of Dispersion Forces in Various Liquids,’’ J. Phys. Chem. 67, 2538 (1963). 22. M. E. Schrader, ‘‘Surface Contamination Detection through Wettability Measurements,’’ in Surface Contamination: Genesis, Detection, and Control, Volume 2, K. L. Mittal (Ed.), p. 541, Plenum Press, New York (1979). 23. A. Horsthemke and J. J. Schro¨der, ‘‘The Wettability of Industrial Surfaces: Contact Angle Measurements and Thermodynamic Analysis,’’ Chem. Eng. Process 19, 277 (1985). 24. D. F. O’Kane and K. L. Mittal, ‘‘Plasma Cleaning of Metal Surfaces,’’ J. Vac. Sci. Technol. 11, 567 (1974). 25. T. Matsunaga, ‘‘Relationship Between Surface Energy and Surface Contamination,’’ in Surface Contamination: Genesis, Detection, and Control, Volume 1, K. L. Mittal (Ed.), p. 47, Plenum Press, New York (1979). 26. Y. Tamai, T. Matsunaga and K. Suzuki, ‘‘The Effect of Water Vapor on Contamination of Metallic Oxide Surfaces,’’ Bull. Chem. Soc. Jpn. 50, 1881 (1977). 27. M. L. White, ‘‘The Detection and Control of Organic Contaminants on Surfaces,’’ in Clean Surfaces: Their Preparation and Characterization for Interfacial Studies, G. Goldfinger (Ed.), p. 361, Marcel Dekker, New York (1970). 28. L. R. Sonders, D. P. Enright and W. A. Weyl, ‘‘Wettability, a Function of the Polarizability of the Surface Ions,’’ J. Appl. Phys. 21, 338 (1950). 29. H. Pohlack and S. Wendler, Jenaer Jahrbuch, VEB Carl Zeiss, Jena, Germany p. 41 (1958).
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30. W. Birch, S. Mechken and A. Carre, ‘‘Influence of Cleaning on the Surface of Model Glasses,’’ in Surface Contamination and Cleaning, Volume 1, K. L. Mittal (Ed.), p. 85, VSP, Utrecht, The Netherlands (2003). 31. Y. Li, D. Ryding, C. Liu, T. M. Kuzay, M. W. McDowell and R. A. Rosenberg, ‘‘X-Ray Photoelectron Spectroscopy Analysis of Cleaning Procedures for Synchrotron Beamline Materials at the Advanced Photon Source,’’ J. Vac. Sci. Technol. A 13, 576 (1995). 32. N. Kaufherr, A. Krauss, D. M. Gruen and R. Nielsen, ‘‘Chemical Cleaning of Aluminum Alloy Surfaces for Use as Vacuum Material in Synchrotron Light Source,’’ J. Vac. Sci. Technol. A8, 2849 (1990). 33. S. Alberici, A. Dellafiore, G. Manzo, G. Santospirito, C. M. Villa and L. Zanotti, ‘‘Organic Contamination Study for Adhesion Enhancement Between Final Passivation Surface and Packaging Molding Compound,’’ Microelectronic Engineering 76, 227 (2004). 34. P. Rostam-Khani, J. Philipsen, E. Jansen, H. Eberhard and P. Vullings, ‘‘Quantitative Analysis of Surface Contaminants on Silicon Wafers by Means of TOFSIMS,’’ Appl. Surf. Sci. 252, 7255 (2006). 35. J. Davies, C. S. Nunnerley, A. C. Brisley, J. C. Edwards and S. D. Finlayson, ‘‘Use of Dynamic Contact Angle Profile Analysis in Studying the Kinetics of Protein Removal from Steel, Glass, Polytetrafluoroethylene, Polypropylene, Ethylenepropylene Rubber, and Silicone Surfaces,’’ J. Colloid Interface Sci. 182, 437 (1996). 36. ASTM C813-90(2004), ‘‘Standard Test Method for Hydrophobic Contamination on Glass by Contact Angle Measurement,’’ American Society for Testing and Materials, Conshohocken, PA (2004).
PART III METHODS FOR REMOVAL OF SURFACE CONTAMINATION
14 The Use of Surfactants to Enhance Particle Removal from Surfaces Michael L. Free Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT, USA
14.1 Introduction 14.1.1 Industrial perspective Many of the items we use daily must be manufactured in environments that require particulate materials, yet the particles that are essential to production must be removed to extremely low levels following the relevant manufacturing processes. A single particle remaining at a critical place on a semiconductor circuit during the manufacturing process can cause circuit failure in a finished integrated circuit. Consequently, particle removal technologies are vital to electronic circuit manufacturing [1–18]. Other industries such as optical component manufacturing also rely upon particle removal technologies to create quality components with appropriate finishes. In many industries, particles are handled in aqueous media, and particle removal from surfaces is also performed in aqueous media. Removal techniques vary from simple brush scrubbing techniques [19–22] and megasonic vibration [23–26] for wet surfaces to laser treatment [27–30] and snow [31–32] or air [33] cleaning for dry surfaces. Particles adhere to surfaces due to natural attractive forces between particles and surfaces. Surfactants can effectively reduce natural attractive forces between particles and surfaces, thereby enhancing particle removal. This chapter discusses the use of surfactants in enhancing particle removal from surfaces in aqueous environments, although the discussion presented here can also be applied to other environments.
R. Kohli and K. L. Mittal (eds.), Developments in Surface Contamination and Cleaning, 725–758 ª 2008 William Andrew, Inc.
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14.1.2 Historical perspective Powders have been used for grinding and polishing of jewelry and ornaments for millennia, yet an understanding of how particles interact with surfaces was relatively obscure until the 1940s [34]. Most of the present knowledge about particle–surface interactions can be related to research that developed in the 1940s. However, direct, accurate measurement of such interaction forces between fine particles and surfaces has only been possible with the inventions of the surface force apparatus and the atomic force microscope that were developed in the 1970s and 1980s, respectively.
14.2 Surfactant Behavior in Solution Surfactants are chemical compounds that are surface active or more prevalent at surfaces or interfaces than in bulk media due to their dual property nature. Molecules that are surface active in aqueous media consist of both hydrophobic and hydrophilic entities. The hydrophilic entity is polar in nature and gives the molecule its ability to dissolve in water. Most often the hydrophilic portion consists of an ionic functional group such as sulfate, sulfonate, carboxylate, or amine, or it contains hydrophilic segments such as ethylene oxide. The hydrophobic portion of the molecule consists typically of CH2 groups that are usually connected in continuous alkyl chains consisting of 4–18 CH2 groups. The hydrophobic portion of the molecule is non-polar in nature and is more favorably associated with other non-polar entities such as air or other hydrocarbon entities, rather than water. Consequently, the dual nature of surfactant molecules is more readily accommodated at water–air or water–oil interfaces than in bulk water. Moreover, surfactant molecules are found in higher concentrations at interfaces than in bulk aqueous media because the hydrophilic portion of the molecule can associate with water molecules at the same time as the hydrophobic portion associates with non-polar media or hydrocarbon segments from other surfactant molecules. The tendency for surfactant molecules to associate with interfaces and other surfactant molecules leads to a high tendency for adsorption and aggregation, which increases as the hydrocarbon chain length increases and/or when the polarity of the solvent increases. As surfactant concentration increases, the surfactant’s tendency to adsorb and/or form aggregate structures increases. At low concentrations, surfactant molecules do not have sufficient energy to form aggregates or
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adsorb at high concentrations at interfaces as illustrated in Figure 14.1, although they adsorb at higher concentrations at interfaces than in bulk media. At moderate concentration levels, surfactant molecules also adsorb at interfaces at higher levels than in the bulk solution. The accumulation of surfactant molecules at interfaces such as the air– water interface results in a lowering of the surface tension. In other words, the accumulation of surfactant molecules at interfaces lowers the interfacial energy due to the fact that the surfactant molecules have both hydrophilic and hydrophobic sections that are attracted to the water (polar) and air (non-polar) phases, respectively. Surface tension is often measured using a balance and a suspended hydrophilic object such as a plate or a ring. As shown in Figure 14.2, the presence of surfactant molecules at the air–water interface lowers the tendency of the water to climb up a hydrophilic substrate such as the plate shown in the figure, resulting in a reduced downward force on the object as indicated by the arrows in Figure 14.2. A typical plot of surface tension versus the natural logarithm of the concentration is shown in Figure 14.3. Note that the surface tension decreases rapidly with increasing surfactant concentration above a minimum concentration level. At higher concentrations it reaches a minimum value at a specific concentration level that surfactant molecule
air
hydrophobic portion hydrophilic portion
air
Monolayer level adsorption
air
micelle
solution
solution Sub-monolayer level adsorption
substrate far below cmc and sac
Bi-layer, multilayer, or surface micelle surfactant adsorption
solution
substrate
substrate
slightly below cmc and sac
above cmc and sac
Figure 14.1 Schematic diagrams illustrating surfactant aggregation and adsorption as a function of relative surfactant concentration.
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Figure 14.2 Schematic comparison of surface tension force exerted by water on a plate with (right side) and without surfactant (left side) present.
S U R F A C E T E N S I O N
cmc
LN(SURFACTANT CONCENTRATION)
Figure 14.3 Sketch of typical surface tension versus ln(surfactant concentration) plot showing the critical micelle concentration (cmc).
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is known as the critical micelle concentration (cmc) that will be discussed in more detail later. The excess concentration of surfactant at an interface can be quantified using surface tension data and the Gibbs equation. The surface excess or concentration at the interface that is in excess of the bulk concentration can be expressed as [35] 1 dg G¼ RT dlnðcÞ
Eq. (14-1)
below the cmc for constant temperature tests in which no phase transformations occur, where R is the gas constant, T is the absolute temperature, g is the surface tension, and c is the concentration of surfactant. Note that the slope of the surface tension plot shown in Figure 14.3 is used in the calculation of the surface excess, which is also nearly equivalent to the adsorption density. The adsorption of surfactant molecules at interfaces is often evaluated using the Langmuir model, which begins with the equilibrium adsorption reaction: A þ S ¼ AS
Eq. (14-2)
in which A is the adsorbate, S is the surface site available for adsorption, and AS represents a surface site on which the adsorbate, A, is adsorbed. Using a simple equilibrium expression, the equilibrium constant K 0A can be expressed as K 0A ¼
CAS CA CS
Eq. (14-3)
in which CAS is the surface concentration of adsorbed adsorbate, CS is the surface concentration of unoccupied surface adsorption sites, and CA is the bulk solution concentration of adsorbate. Using Eq. (14-3) with a surface site balance and substitution for the concentration of available sites (CS = Ctot – CAS) leads to a common expression for the fraction of surface covered by the adsorbate: u¼
CAS CTotalSites
¼
K 0A CA 1 þ K 0A CA
Eq. (14-4)
However, it should be noted that this expression is only valid at concentration levels below those needed for surfactant aggregation. It is also
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important to realize that surfactant aggregation at solid surfaces, which is referred to as the surface aggregation concentration (sac), often occurs at concentrations that are below the critical micelle concentration. Thus, the cmc applies to surfactant micelle aggregate formation in solution and the sac applies to surfactant aggregate formation on solid surfaces. As the surfactant concentration reaches levels that exceed the sac, the surfactant molecules have already exhausted interfacial adsorption sites at the monolayer level, and the free energy of the system warrants additional association and aggregation in the form of bilayers and/or multilayers at interfaces. Similarly above the cmc, micelles form in solution. Micelles are spherical aggregates of surfactant molecules in which the hydrocarbon portions of the molecules associate with the hydrocarbon portions of other surfactant molecules in the interior of a spherical structure. The outer wall of the micelle structure is formed with the hydrophilic functional groups of the surfactant molecules as depicted in Figure 14.1. The tendency for surfactant molecules to aggregate and associate at interfaces is influenced strongly by the length of the hydrocarbon portion of the surfactant molecules. As the hydrocarbon chain portion of the surfactant molecule increases, the tendency of the surfactant to aggregate or adsorb increases to relieve energetically unfavorable interactions between polar solvent molecules and non-polar hydrocarbon groups. Consequently, the critical concentration for aggregation (cmc or sac) decreases as the chain length increases because the aggregation event occurs at decreasing concentration levels as the hydrocarbon chain length increases. The effect of increasing hydrocarbon chain length on the aggregation concentration (cmc for solutions) can be observed readily from the data in Table 14.1. The data in Table 14.1 indicate that the
Table 14.1 Comparison of Hydrocarbon Chain Length and cmc for Alkyl Trimethyl Ammonium Chlorides in Water [34]
Number of Alkyl CH2 Segments 10 12 14 16 18
cmc (M) 6.3 1.9 4.5 1.3 3.4
· · · · ·
102 102 103 103 104
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Table 14.2 Comparison of Surfactant cmc Values as a Function of Ionic Strength and Surfactant Type. Data were taken from Refs. [34, 36]
Surfactant Sodium octyl sulfate Sodium octyl sulfate Sodium decyl sulfate Sodium decyl sulfate Sodium dodecyl sulfate Sodium dodecyl sulfate Cetyl pyridinium chloride Cetyl pyridinium chloride
Ionic Strength
Chain Length (No. CH2s)
cmc (M)
0.3 0.07 0.3 0.007 0.3 0.0007 1.0 0.0003
8 8 10 10 12 12 16 16
6.7 · 102 1.3 · 101 6.9 · 103 3.3 · 102 7 · 104 8.1 · 103 3 · 106 3 · 104
cmc of alkyl trimethyl ammonium bromide surfactants decreases by approximately a factor of three for every two CH2 units added to the surfactant molecule. The tendency for surfactant molecules to adsorb and/or aggregate in solution is also influenced by the solution environment. As the solution becomes more polar, the tendency for surfactant molecules to aggregate in solution and/or adsorb at interfaces increases. One factor that quantifies the polar nature of the solvent is the ionic strength. Consequently, the effect of ionic strength on surfactant aggregation is very significant as evidenced by the cmc values given in Table 14.2. Note that the cmc values in Table 14.2 are considerably lower in high ionic strength media. The data in Table 14.2 also indicate that the effect of ionic strength is more pronounced as the hydrocarbon chain length increases, indicating that the surfactant molecules with longer alkyl hydrocarbon chains have an increased tendency to leave the solution to form surface and solution aggregates as the solvent polarity increases. The combined effects of environment and hydrocarbon chain length on the cmc of a surfactant can be predicted based upon a combination of theory and empirical information. The following equation is very useful in predicting the cmc (or sac if slightly different values for x, DGc.l. and k are used) of surfactant molecules under a variety of chain length and ionic strength scenarios [36] cmc ffi exp
1 ½ðL xÞDGc:l: þ kðL xÞRT lnðg m Þ RT
Eq. (14-5)
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in which R is the gas constant, T is the absolute temperature, L is the total number of consecutive CH2 units in the surfactant molecule, DGc.l. is the free energy increment for each CH2 unit (1500 J/mol is a good estimate for some surfactants [36]), x is the number of CH2 units in the surfactant molecule necessary to initiate surface activity (usually around 5), k is a solvent polarity factor (usually 1.0–1.5 for surfactants for which L is 12–18 [36]), and gm is the activity coefficient determined using an ionic activity coefficient equation, such as the Davies equation, which can be expressed as [37]: 0:5083z2
gm ¼ 10
pffi I
ffi
p 0:2I 1þ I
Eq. (14-6)
at 25 C, where z is the charge of the surfactant ion (usually 1) and I is the ionic strength [37] I ¼ 0:5
n X
mj z2j
Eq. (14-7)
j¼1
where j = 1 to n represents all positively and negatively charged species in solution and m is the molality. More exact values of the various constants can be obtained using cmc data based on calibration plots as described by Free et al. [36]. Understanding how surfactants behave in solution in terms of their tendency to aggregate and adsorb at interfaces is a critical prerequisite to understanding how they can enhance particle removal as will be demonstrated in a subsequent section.
14.3 Interfacial Forces and Particle Removal 14.3.1 Introduction to interfacial forces Interaction forces between molecules and surfaces can be very powerful and influential. The forces between molecules determine the physical state of groups of molecules. Such groups of molecules make up surfaces and become the origin of the forces that exist between surfaces. The forces between molecules and surfaces in aqueous media are often separated into electrostatic, van der Waals, structural, and hydrophobic forces. In situations involving non-immersion scenarios, capillary forces must also be considered, although in the remainder of this chapter they will be neglected.
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van der Waals forces arise from the interaction of atomic and/or molecular dipole interactions [38]. van der Waals forces between molecules or atoms are attractive in nature, and such attractive forces exist even when the atom or molecule does not have a permanent dipole, since the dipole can be induced [38]. The van der Waals force between a sphere and a plate can be expressed as [39] FðhÞ ¼
Ar 6h2
Eq. (14-8)
where A is the Hamaker constant, r is the radius of curvature of the particle, and h is the separation distance between the particle and the plate. The electrostatic force between a sphere and a plate is given as [39] FðhÞ ¼
128pRr¥ kTg1 g 2 exp ðxhÞ x
Eq. (14-9)
where the surface charge for each surface (1 and 2 as denoted by subscript) is defined as [39] zeC0 ð1 or 2Þ Eq. (14-10) gð1 or 2Þ ¼ tanh 4kT and the Debye length, x, is given as [39] x¼
2000e2 INA e0 em kT
1=2 Eq. (14-11)
in which z is the ion valence, e is the electrical charge, r¥ is the bulk dissolved ion density, C0 (1 or 2) is the surface potential P for the surface of interest (surface 1 or 2). I is the ionic strength (0.5 z2r¥ for all positive and negative ions), 1 NA is Avogadro’s number, e0 is the dielectric permittivity of vacuum, and em is the dielectric constant of the medium between the two surfaces. In many aqueous environments involving hydrophilic surfaces, the forces between surfaces are dominated by the electrostatic and van der Waals forces, since structural forces tend to be oscillatory in nature and tend to average to a near-zero net effect. In other words, the structural forces show up as oscillations above and below the other net forces. The trend of the other forces remains dominant despite the local oscillations that arise as surfaces come close to contact and individual layers of water
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are removed or added in a stepwise manner, causing stepwise oscillations in the overall force. Such structural oscillations are often observed within a few nanometers of the surface [34]. The use of the combination of electrostatic and van der Waals forces to describe surface interactions was demonstrated extensively by Derjaguin, Landau, Verwey, and Overbeek. Their work and use of surface force theory has become widely known as the DLVO theory [38]. Furthermore, when only the electrostatic and van der Waals forces are considered in a surface force analysis, the resulting interaction force is sometimes referred to as the DLVO force. In situations involving hydrophilic substrates in low ionic strength media, the DLVO theory is often adequate to describe the forces between particles and surfaces before contact occurs. Although the DLVO theory accounts for surface forces in many situations, it does not describe the effect of forces between hydrophobic surfaces that can far exceed the attractive forces predicted by the DLVO theory. The strong, attractive forces between hydrophobic surfaces are often referred to as hydrophobic forces [38, 40, 41]. There is considerable debate regarding the origin of these forces [38]. However, the most commonly accepted hypotheses suggest that the forces are related to water structuring effects and/or gas entrainment/cavitation effects [38].
14.3.2 Measurement of surface forces Surface forces can be measured by different instruments. Most commonly, surface forces are measured using the atomic force microprobe (AFM) and the surface force apparatus (SFA), both of which are capable of measuring interaction forces between surfaces at varying separation distances. The AFM, which was developed in the mid 1980s by Binnig and coworkers [42], utilizes a thin cantilever beam that bends in response to surface forces experienced by the tip as the surface is moved closer to it by a piezocrystal (see Figure 14.4). The change in the angle of the cantilever causes a change in the angle of the light that is reflected off the tip of the cantilever (see Figure 14.4). Because the light that is reflected off the cantilever is measured by a set of detectors with respect to both quantity and position, a determination of the force can then be made based upon the cantilever properties and dimensions combined with the position and intensity of the deflected light. The distance is measured based upon the applied piezocrystal voltage change combined with the properties of the piezocrystal actuator and a calibration procedure.
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The SFA, which was developed by Tabor and coworkers approximately 30 years ago [34], has a significantly different design than the AFM (see Figure 14.5). The SFA consists of a cantilever to measure the force based upon deflection as is done in the AFM. However, the
Light detectors (position sensitive)
Incident light (usually from a laser source)
cantilever
particle substrate
Piezocrystal (capable of 3-D motion under applied voltage)
Figure 14.4 Schematic diagram of an atomic force microscope (AFM). Transmitted light – to spectrometer piezocrystals
thin, atomically smooth films with a very thin silver reflective underside (The films are attached to support material.)
Transparent support materials
cantilever
incident white light
Figure 14.5 Schematic diagram of a surface force apparatus (SFA).
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separation between surfaces is measured using white light diffraction techniques that utilize a spectrometer to analyze the various wavelengths of light. The surfaces that are used in the SFA must be atomically smooth, and they are generally mounted as thin films onto cylindrical, optically transparent support structures as shown in Figure 14.5. The films must be coated with a very thin layer of silver or other reflective metal on the back side to allow significant light transmission while also allowing significant reflected light. As light reflects between the silvered back sides of the layers that approach contact, interference fringe patterns are created. The interference fringe patterns can be analyzed spectroscopically to determine the separation distance between surfaces to within approximately 1 A˚ [34].
14.3.3 Adhesion Particles adhere to surfaces due to favorable interaction forces between them. The dominant force of attraction between particles and surfaces is the van der Waals force. This force is so strong that the particle and surface are deformed upon natural contact. The extent of the deformation is determined by the elastic moduli of the substances involved as well as the magnitude of the attractive force. The deformation is large for soft materials and small for hard materials. Several theories have been proposed to calculate the deformation and forces involved in the adhesion of particles to surfaces [43–48]. The attractive forces remain the same despite the material deformation, but the effect of material deformation leads to an increased requirement for particle removal [34]. Adhesion forces can be estimated from the sum of the known forces. The force calculation is usually made at a particle-to-surface separation distance that is between 0.1 and 0.5 nm in aqueous media. The separation distance is not zero because the continuum theories used to derive the force expressions do not accurately account for the discrete nature of the atoms at the interfaces at close separation distances. Also, in aqueous media, surface layers of water are bonded to the surfaces and may affect the effective separation distance. Another approach, the surface energy/ acid–base theory, also provides useful approximations of adhesion forces, although this technique will not be discussed further because it cannot be applied as easily to systems involving surfactant adsorption as the sum-offorces approach described previously. In addition, the surface energy/ acid–base theory does not account for electrostatic forces that can be important in particle–surface systems.
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14.3.4 Particle removal forces Particles can be removed from surfaces by pulling, rolling, or sliding them off, yet each of these techniques requires an external force. The most common external force that is used for these techniques is fluid drag that is created by fluid flow. The force of fluid drag on a particle under laminar flow conditions can be expressed as [49] F ¼ 3pd0 Vm
Eq. (14-12)
where F is the force, d0 is the particle diameter, V is the fluid velocity, and m is the viscosity. However, the fluid velocity at any given position relative to the particle is proportional to distance above the substrate surface [50]. Consequently, the fluid elements that are capable of moving the particle are located at a distance from the surface that is proportional to the particle diameter. Thus, as is intuitively apparent, the force of removal due to fluid drag is surface area dependent based upon fluid flow near a substrate surface and an attached particle at the surface. Consequently, the actual removal force on a particle at a surface due to fluid drag is directly proportional to the diameter squared. Thus, as particles become smaller, the force available for removal from fluid movement decreases rapidly. In contrast, the forces such as van der Waals and electrostatic forces that control adhesion are linearly related to particle diameter and do not diminish as rapidly as the traditional removal forces. Therefore, large particles are easily washed away from surfaces, and small particles are not easily washed away from surfaces unless the surface forces are reduced or the removal forces enhanced, although in this chapter only surface force modification using surfactants will be discussed as a means of enhancing particle removal.
14.3.5 Modification of surface forces using surfactants The adsorption of surfactant molecules at the surfaces of particles and substrates can alter the van der Waals attractive force between the particles and substrates as well as the electrostatic, structural, and hydrophobic forces. The effect of surfactant adsorption on the van der Waals force is most easily quantified using an approximate expression developed by Israelachvili [34] (for surfaces with adsorbed layers that are separated by a
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medium such as water) that has been modified from a plate–plate interaction force to a plate–sphere interaction force using the Derjaguin approximation [39] " pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # A545 A323 A121 A343 A121 A545 R A432 þ FðhÞ ¼ 2 2 6 h2 ðh þ tp Þ ðh þ ts Þ ðh þ tp þ ts Þ2 Eq. (14-13) where 1 is the surface of the substrate, 2 is the coating on the substrate surface, 3 is the medium separating the surfaces, 4 is the coating on the particle, 5 is the surface of the particle, ts is the thickness of the coating on the substrate surface, and tp is the thickness of the coating on the particle surface. However, in order to utilize this force expression, it is necessary to know the Hamaker constants between the various substances. A useful expression for determining the Hamaker constant based upon Lifshitz theory is given by Israelachvili [34] as 3 e1 e3 e2 e3 A132 kT 4 e1 þ e3 e2 þ e3 " # 3hne ðn21 n23 Þðn22 n23 Þ þ pffiffiffi 8 2 ðn21 þ n23 Þ1=2 ðn22 þ n23 Þ1=2 ½ðn21 þ n23 Þ1=2 þ ðn22 þ n23 Þ1=2 Eq. (14-14) where A132 is the non-retarded Hamaker constant between surfaces 1 and 2 across medium 3, k is the Boltzmann constant, T is the absolute temperature, e is the dielectric constant of specified medium, h is Planck’s constant, ne is the average absorption frequency, and n is the refractive index. The justification for using a multiple layer model to determine the effect of surfactant adsorption on the van der Waals force is made on the basis of experimental observation, which shows the effect of the adsorbed layer on the van der Waals force becomes increasingly important as the surfaces approach contact [34]. The adsorbed layer(s) of surfactant molecules also provides a steric barrier to direct contact between the particle and the substrate. The adsorption of surfactant molecules on the substrate and particle surfaces also tends to significantly alter the charges on the surfaces as is depicted with an adsorbed cationic surfactant molecule at a charged surface in Figure 14.6. The effect of surfactant adsorption depends upon the existing charge prior to surfactant adsorption, the charge of the surfactant
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+ +
-
+
-
Substrate
-
-
-
+
Figure 14.6 Schematic diagram of a cationic surfactant molecule adsorbed onto a charged substrate. Note that the charge on the substrate is generally due to adsorbed ions such as OH and H+ that are not shown. Also note that water molecules, which play an important role at interfaces in aqueous media, are not shown.
molecule, and the surface concentration of surfactant on each surface after adsorption. In some cases, the adsorption of ionic surfactant can have a very substantial effect upon the electrostatic force between the substrate and particles in solution. In some particle removal applications, the particles have a charge that is opposite to that of the substrate, making the natural electrostatic force between the surfaces an attractive one (negative force). If an ionic surfactant adsorbs on the surfaces of the particles and the substrate, which is generally observed, both types of surfaces will likely develop the same charge as the surfactant, making the electrostatic interaction force between the surfaces a positive or repulsive force, thereby reducing particle adhesion and enhancing particle removal. In cases involving substrates and particles with similar natural charge, the adsorption of properly selected ionic surfactant molecules can enhance the existing repulsive electrostatic force. Thus, in most cases the adsorption of ionic surfactant molecules facilitates particle removal by providing or enhancing electrostatic repulsive forces in addition to providing a steric barrier to direct contact between the particle and the substrate. Although it is clear that surfactant adsorption can reduce van der Waals attractive forces and create or enhance electrostatic repulsion between particles and surfaces, surfactant adsorption can lead to a hydrophobic attractive force, which tends to make particle removal more difficult. Because particle removal is the objective in this chapter, it is desired that the adsorbed surfactant molecules be arranged with hydrophilic ends projecting into aqueous media or hydrophobic ends projecting into a hydrophobic solvent. Using the illustrations shown in Figure 14.7, it is easily observed that for aqueous media and naturally hydrophilic surfaces
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Effects of surfactant availability on particle-surface interactions for naturally hydrophilic surfaces particle particle particle substrate
substrate
substrate
above sac level below sac level no surfactant strong steric repulsion, some steric repulsion, van der Waals attraction, electrostatic attraction or some electrostatic repulsion, strong electrostatic repulsion, repulsion due to inorganic some hydrophobic attraction, no hydrophobic attraction, reduced van der Waals reduced van der Waals ions attraction attraction (hydrophilic surfaces) (hydrophilic surfaces) (hydrophobic surfaces)
Figure 14.7 Schematic diagrams illustrating the effect of surfactant concentration and adsorption on the particle–substrate interaction for surfaces that are naturally hydrophilic. Note that water molecules and other ions such as counter ions have been omitted to simplify the drawings. Although the diagram shows bilayer formation above the sac, it is also common to observe surface micelles and multilayer level adsorption above the sac.
this desired outcome is achieved only above the sac where bilayers, multilayers, or surface micelles form to provide an exposed interface of hydrophilic functional groups. The effect of the orientation of the head group and hydrocarbon tail of the adsorbed surfactant molecules on the attractive hydrophobic force has been demonstrated by Freitas and Sharma [51], who showed a strong attractive force between hydrophilic silica particles and substrates below the sac, where hydrocarbon tails of adsorbed surfactant molecules extended into solution to produce a hydrophobic interface. However, above the sac, where only functional groups from a bilayer, multilayers, or surface micelles extended into aqueous media, the interaction force became very weak. It should be noted that no complete explanation for such hydrophobic interaction forces has been developed. The net force between a particle and a substrate can be calculated using the equations described previously for the van der Waals and electrostatic force components, which are the most important overall forces as long the surfaces are hydrophilic. Many surface force studies have been performed [52–65], and there is at least general agreement that experimental data can
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be modeled using the applicable theory [56, 65]. Thus, it is useful to examine the effects of surfactant adsorption on the net interaction force between a particle and a substrate. A sample comparison of DLVO forces that have been normalized by dividing by particle radius versus the separation distance between bare and film-covered surfaces is presented in Figure 14.8 for an ideal alumina sphere that is approaching a quartz surface in aqueous media at a near-neutral pH. Note that the net normalized force is highly negative as the particle approaches the surface when no surfactant is present. The attraction in the absence of surfactant is due to the van der Waals attractive force and an attractive electrostatic force. However, in the presence of cetyl pyridinum chloride (CPC) surfactant at a level of 0.0028 M, which is well above the cmc of 0.0003 M (also above the sac of around 0.0001 M) for this solution, it results in a positive or repulsive force at separation distances that are representative of contact. It should be noted that in applying the DLVO theory in aqueous media, contact is assumed to occur at a separation distance greater than zero 10.00 with surfactant 5.00
F/R (mN/m)
without surfactant 0.00 0 -5.00 -10.00 -15.00
5
10
15
20
25
DLVO force evaluation for coated and uncoated particles: 1 micrometer alumina particles, quartz surface , I = 0.003, Zeta potentials, respectively, of 36 and -30 mV without surfactant, and 88 and 100 mV with cetyl pyridinum chloride (CPC) (assuming a 2 nm film of CPC).
-20.00
Separation distance (nm)
Figure 14.8 Comparison of normalized DLVO force (normalized by dividing by particle radius) versus separation distance for alumina particles approaching a quartz surface. Note that the Hamaker constant was calculated using Eq. (14-14) with refractive index and dielectric constant data from Ref. [34]. The forces were calculated using Eqs. (14-9)–(14-11), (14-13), and (14-14). Note that the zeta potential values shown in the figure are values that were measured using ground quartz and alumina particles in a 0.003 M KCl solution at 22 C. The surface potential, c, was calculated based upon the zeta potentials using the relationship: c = zeta potential [exp(x/1nm)] (assumes that the zeta potential is 1 nm from surface).
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10.00 with surfactant
F/R (mN/m)
5.00 0.00 0 -5.00 -10.00 -15.00
without surfactant
5
10
15
20
25
DLVO force evaluation for coated and uncoated particles: 1 micrometer quartz particles, quartz surface, I = 0.003, Zeta potentials, respectively, of -30 mV without surfactant, and 88 mV with 0.0028 M cetyl pyridinum chloride (CPC) (assuming a 2 nm film of CPC).
-20.00 Separation distance (nm)
Figure 14.9 Comparison of normalized DLVO force (normalized by dividing by particle radius) versus separation distance for quartz particles approaching a quartz surface. Note that the Hamaker constant was calculated using Eq. (14-14) with refractive index and dielectric constant data from Ref. [34]. The forces were calculated using Eqs. (14-9)–(14-11), (14-13), and (14-14). Note that the zeta potential values shown in the figure are values that were measured using ground quartz and alumina particles in a 0.003 M KCl solution at 22 C. The surface potential was calculated based upon the zeta potentials using the relationship: c = zeta potential [exp(x/1nm)] (assumes that the zeta potential is 1 nm from surface).
(often around 0.4 nm) as explained previously. In this particular case, the result of adding surfactant is quite dramatic because the surfaces had opposite charges prior to surfactant adsorption. Thus, the addition of the surfactant made an enormous difference in the surface forces. In systems involving similar surfaces, surfactant molecules do not alter the forces as dramatically, yet the addition of surfactant molecules can enhance repulsive forces as shown in Figure 14.9 for a quartz sphere approaching a quartz surface, thereby enhancing the potential for removal. Other studies also show that surfactants have a significant impact on particle–surface interaction forces [65–68].
14.3.6 Measurement of particle removal Particle removal effectiveness is nearly always measured by optical methods. One simple approach is to capture digital images of appropriately magnified sections of a surface that has residual particles. The digital
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images can then be analyzed using image analysis software to determine the number of residual particles. A similar method that is often used in the electronics industry to inspect wafer contamination involves the use of laser scanning and associated detectors that measure light that is scattered by particles or defects on the surface.
14.3.7 Enhanced-particle removal results associated with surfactant use Surface force calculations show that surface forces can be reduced significantly by the presence of surfactant, and it is, therefore, anticipated that the addition of sufficient surfactant will enhance particle removal. Several studies show that surfactants can assist in reducing the number of residual particles on a surface [39, 51, 56, 69–73]. Several sets of particle removal data are presented in Figures 14.10–14.15. Each figure shows that the presence of surfactant has a significant influence on the removal of particles from the associated substrates. Figures 14.10–12 and 14.15 show that the effectiveness of particle removal generally increases with increasing surfactant concentration. The observed removal effect associated with increasing surfactant concentration in Figure 14.15 is generally consistent with the theoretical force considerations that were
Figure 14.10 Residual particle density following CMP processing on copper in 1% ferric nitrate medium versus cetyl pyridinium chloride concentration at 31 C. Data obtained and adapted from Ref. [71].
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Residual Particles Per Square Centimeter
10,000,000
1,000,000
100,000
10,000
1,000 1.0E-07
1.0E-05
1.0E-03
Surfactant Concentration (M)
Figure 14.11 Comparison of residual particle density and cetyl pyridinium chloride (CPC) concentration following polishing of a tungsten-coated surface using 0.7mm diameter alumina particles.
Figure 14.12 Comparison of residual particle density and surfactant concentration following polishing of a tungsten-coated surface using 0.7 mm diameter alumina particles. (DTAB = dodecyl trimethyl ammonium bromide, TTAB = tetradecyl trimethyl ammonium bromide, CTAB = cetyl trimethyl ammonium bromide).
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Fraction of Particles Removed
presented in Figures 14.8 and 14.9, which predicted an attractive force without surfactant and a repulsive force with sufficient surfactant. Figure 14.15 shows that the effectiveness of the surfactant is significantly greater above the cmc. Because the cmc is generally significantly greater than the sac due to higher interfacial energy at solid surfaces 1 0.8 0.6
without surfactant 0.0001 M CTAB 0.001 M CTAB
0.4 0.2 0 0
0.01 0.02 0.03 Hydrodynamic Force/R (mN/m)
Figure 14.13 Effect of cetyl trimethyl ammonium bromide concentration on the removal of 10 mm hydrophilic glass particles from a hydrophilic oxidized silicon wafer substrate. Data adapted from Ref. [51]. The x-axis shows the hydrodynamic removal force due to fluid flow that is normalized by dividing by the particle radius to give a quantitative assessment of the relative removal force. 1 0.8 0.6 0.4 without surfactant
0.2
with surfactant
0 0
0.2
0.4
0.6
0.8
1
Figure 14.14 Polystyrene latex particle removal efficiency versus particle size from silicon substrates using 0.5% HF with and without surfactant. Data adapted from Ref. [74].
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Figure 14.15 Comparison of residual particle density and cetyl pyridinium chloride (CPC) concentration following polishing of quartz glass using 0.7 mm diameter alumina particles. Note that the cmc of the supernatant solution, which is based upon the total CPC added to solution, is much higher than the normal cmc (3 · 104 M) due to surfactant adsorption on alumina particles. In other words, the supernatant cmc indicates that the free, non-adsorbed surfactant concentration is close to the normal cmc even though the initial CPC concentration was much higher.
relative to the air–water interface, it is likely that the removal is largely ineffective below the sac. However, Figure 14.13 shows that if the adsorption of surfactant onto a hydrophilic substrate leads to a hydrophobic surface as depicted in Figure 14.7 through the adsorption of less than a bilayer or multilayer, removal is inhibited (see the data for 1 · 104 M surfactant, which is below the sac). However, above the sac, the surface becomes hydrophilic as depicted in Figure 14.7 and removal is facilitated (see the 1 · 103 M data set in Figure 14.13). These findings suggest that for hydrophilic substrate/particle systems the equilibrium solution surfactant concentration should exceed the sac for maximum cleaning benefits. In contrast, however, the results shown in Figure 14.13 also lead to the inference that if the surfaces are naturally hydrophobic, enhanced removal will likely be encountered with surfactant at concentrations below the sac. This inference can be explained on the basis of surface hydrophilicity. Because the surface will become more hydrophilic and charged with increasing surfactant adsorption below the sac, the potential for hydrophobic attraction will be minimized and the opportunity for particle removal will be enhanced. It will also be enhanced above the sac, since additional adsorption above the monolayer level occurs in paired layers or micelles, which always have hydrophilic exposed interfaces.
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However, it should be understood that hydrophobicity/hydrophilicity cleaning predictions discount the effect of surface charging that is associated with surfactant adsorption as discussed in connection with electrostatic forces. Consequently, it is possible to observe enhanced particle removal when the surfaces have less than bilayer or multilayer coverage of surfactant molecules. However, due to the competing electrostatic repulsion and hydrophobic attraction associated with surfactant coverage below the multilayer level, particle removal is not likely to be as effective as it would be with coverage above the multilayer level, which occurs above the sac. Non-ionic surfactant molecules have been tested for their ability to assist in particle removal, but they tend not to perform as well as ionic surfactants [69]. This finding is not surprising when it is considered that the effect of enhanced favorable electrostatic forces can be generated by the adsorption of ionic surfactant but not non-ionic surfactant. The overall surfactant cleaning results show that the effect of surfactant adsorption on surface charge, surface hydrophobicity/hydrophilicity, and steric interactions is significant within the context of enhancing particle removal. The results also highlight the importance of understanding the natural surface charge and hydrophobicity/hydrophilicity as well the sac, which are strong functions of ionic strength and surfactant properties as discussed previously in Section 14.2. In comparing cleaning data sets it is also important to account for the difference between equilibrium and initial surfactant concentrations, which are often very different due to the high surface area associated with fine particles that can adsorb large quantities of surfactant and reduce the surfactant concentration in solution.
14.3.8 Post-cleaning surfactant removal After removing particles with the assistance of a surfactant, it is often necessary to remove the residual surfactant. Because most surfactant adsorption events are physical in nature, the surfactant can be removed, to some extent, by simply removing the surfactant from the surrounding solution in a rinsing operation. However, because adsorbed surfactant molecules bond with each other, they can resist removal during rinsing with pure water. Their resistance to removal is related to the number of carbons in the hydrocarbon chain. The longer the hydrocarbon segment, the more resistant they are to removal. The resistance to removal can be overcome to some extent through the addition of effective ions that compete for surface adsorption sites, form complexes, or react with the
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adsorbed surfactant. It has been shown that the exposure of CPC coated tungsten surfaces to a solution of 1 M ammonium hydroxide for five minutes results in removal of the CPC, whereas simple rinsing in deionized water is only partially successful in removing the surfactant molecules [74]. The rare exception to easy removal with appropriate ions is the removal of chemisorbed surfactant molecules, which may require more aggressive removal environments.
14.3.9 Selection of surfactants for cleaning purposes The selection of surfactant molecules for enhanced particle removal from surfaces should involve the assessment of several important factors. One important selection criterion is the behavior of the surfactant molecule at the temperature of the application. Some surfactants have low solubility at the temperature of the desired application and should not be considered. Most often solubility is controlled predominantly by the number of hydrocarbon units in the alkyl chain, so chain length is an important parameter to consider with respect to solubility issues. Although increasing the chain length reduces solubility, it increases surfactant adsorption and aggregation tendencies. Consequently, the effect of chain length must be balanced between adsorption and solubility considerations. Other factors that need to be considered are functional groups and the application environment. Anionic surfactants are not effective in highly acidic media because they form precipitates, and cationic surfactants are not effective in highly alkaline media due to precipitation. Zwitterionic surfactants are usually only effective in solutions with a near neutral pH and the absence of highly-charged ions. Some environments that contain highly charged ions may induce precipitation of surfactant ions with opposite charges. Non-ionic surfactant molecules are not subject to the same precipitation concerns although their solubility can change significantly with temperature.
14.3.10 Mathematical modeling of enhanced-particle removal using surfactants Recent modeling efforts have shown that enhanced particle removal using surfactants can be predicted using an adsorption site inhibition or
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an energy-based approach [75]. The adsorption site inhibition approach consists of traditional Langmuir adsorption modeling with the assumption that surfactant coverage is not limited to surface adsorption sites on the surface of a solid substrate. Instead, it is asserted that adsorption sites are limited by the interaction of surfactant with the substrate and/or a surfactant covered substrate. Consequently, the coverage used in the Langmuir adsorption model for the site inhibition approach is an effective coverage that is limited by a combination of factors such as interfacial charge, surface sites, and surfactant adsorption. Although this modeling approach tends to fit residual particle density data well for most typical data ranges, it does not predict a lower limit for enhanced particle removal. The energy-based approach, which utilizes an energy-based equation that has a functional form that is analogous to the Arrhenius equation, has been shown to be a more effective approach to the modeling of enhanced particle removal using surfactants than the adsorption site inhibition model [75]. The energy-based model leads to the equation [75] n KðC=sacÞ P ¼ P0 exp z 1 þ KðC=sacÞ
Eq. (14-15)
where P is the residual particle density with surfactant present, P0 is the residual particle density without surfactant present, z is an energy-based constant, K is a surfactant adsorption constant, C is the surfactant concentration, sac is the surface aggregation concentration, and n is a constant. The value of P0 can be obtained by direct measurement. A plot of ln|ln (P0/P)| versus the natural logarithm of (1 + KC/sac)/(KC/sac) can be used to calculate the other constants based on the rearranged form of the energy-based residual particle density modeling equation: P0 1 þ KðC=sacÞ ¼ n lnðzÞ þ n ln ln ln P KðC=sacÞ
Eq. (14-16)
Thus, the slope of the resulting plot will be equal to n and the value of n, combined with the intercept of the plot, can be used to determine z. The value of sac can be estimated using Eq. (14-5). The value of K can be estimated using surface tension plots, corrosion inhibition data, or Langmuir–Blodgett film compression tests [76]. The results of the fit of the energy-based model to residual particle density data, which are presented in Figures 14.16 and 14.17, show that this modeling approach is effective
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Figure 14.16 Comparison of residual particle density and cetyl pyridinium chloride (CPC) concentration following polishing of quartz glass using 0.7 mm diameter alumina particles in 1% ferric nitrate medium at 31 C. The energy-based model fit, which is shown as the solid line, used the following parameters: P0 = 1,500,000 particles per cm2, z = 14,500, K/sac = 15,000 l/mol, and n = 0.99 (data adapted from Ref. [75]).
Figure 14.17 Comparison of residual particle density and cetyl pyridinium chloride (CPC) concentration following polishing using 0.7 mm diameter alumina particles on copper in 1% ferric nitrate medium at 31 C. The energy-based model fit, which is shown as the solid line, used the following parameters: P0 = 600,000 particles per cm2, z = 12,000, K/sac = 11,500 l/mol, and n = 1.27 (data adapted from Ref. [75]).
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in predicting the effect of surfactant in enhancing alumina particle removal from both copper and quartz substrates.
14.4 Summary Surfactants can enhance particle removal from surfaces by modifying the particle–surface interaction forces. Adsorbed surfactant molecules can alter the van der Waals attractive force, electrostatic force, hydrophobic force, as well as provide a steric barrier to contact. The effect of surfactant on these forces can result in greatly enhanced particle removal efficiency. Surfactant adsorption density and structure are important factors in determining removal enhancement performance associated with surfactants. Cleaning is generally most effective above the surface aggregation concentration (sac), which for naturally hydrophilic surfaces allows for bilayer or multilayer level surfactant coverage that provides significant charge repulsion as well as a steric barrier. Adsorption below the monolayer level renders naturally hydrophilic substrates hydrophobic, which tends to reduce removal efficiency. In contrast, naturally hydrophobic surfaces are likely to benefit from both sub-monolayer and multilayer coverages of surfactant that occur, respectively, below and above the sac. Existing adsorption theory and available formulas can aid in the prediction of the sac, which is an important parameter in predicting the performance of surfactants in particle removal enhancement. Equations are also available to predict the effectiveness of surfactants in enhancing particle removal.
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5. T. L. Meyers, M. A. Fury and W. C. Krusell, ‘‘Post-Tungsten CMP Cleaning: Issues and Solutions,’’ Solid State Technol. 38, 59 (1995). 6. M. A. Martinez, ‘‘Chemical-Mechanical Polishing: Route to Global Polishing,’’ Solid State Technol. 37, 26 (1994). 7. W. J. Patrick, W. L. Guthrie, C. L. Standley and P. M. Schiable, ‘‘Application of Chemical Mechanical Polishing to the Fabrication of VLSI Circuit Interconnections,’’ J. Electrochem. Soc. 138, 1778 (1991). 8. A. Iqbal, S. R. Roy, G. B. Shinn, S. Raghavan, R. Shah and S. Peterman, ‘‘Investigating the Effect of Secondary Platen Pressure on Post-Chemical Mechanical Planarization Cleaning,’’ Microcontamination 12, 45 (1994). 9. Y. Hayashi, M. Sakurai, T. Nakajima, K. Hayashi, S. Sakaki, S. Chicaki and T. Kunio, ‘‘Ammonium Salt Added Silica Slurry for Chemical Mechanical Polishing of the Interlayer Dielectric Film Planarization in ULSI’s,’’ Jpn. J. App. Phys. 34, 1037 (1995). 10. F. B. Kaufman, D. B. Thompson, R. E. Broadie, M. A. Jaso, W. L. Guthrie, D. J. Pearson and M. B. Small, ‘‘Chemical Mechanical Polishing for Fabricating Patterned W Metal Features as Chip Interconnects,’’ J. Electrochem. Soc. 138, 3460 (1991). 11. M. Itano, F. W. Kern, Jr., M. Miyashita and T. Ohmi, ‘‘Particle Removal from Silicon Wafer Surface in Wet Cleaning Process,’’ IEEE Trans. Semiconductor Manuf. 6, 258 (1993). 12. S. Verhaverbeke, R. Messoussi, H. Morinaga and T. Ohmi, ‘‘Recent Advances in Wet Processing Technology and Science,’’ Mater. Res. Soc. Symp. Proc. 386, 3 (1995). 13. H. Fusstetter, A. Schnegg, D. Graf, H. Kirschner, M. Brohl and P. Wagner, ‘‘Impact of Chemomechanical Polishing on the Chemical Composition and Morphology of the Silicon Surface,’’ Mater. Res. Soc. Symp. Proc. 386, 97 (1995). 14. D. J. Riley and R. G. Carbonell, ‘‘Mechanisms of Particle Deposition from Ultrapure Chemicals onto Semiconductor Wafers: Deposition from Bulk Liquid during Wafer Submersion,’’ J. Colloid Interface Sci. 158, 259 (1993). 15. S. R. Roy, I. Ali, G. Shinn, N. Furusawa, R. Shah, S. Peterman, K. Witt, S. Eastman and P. Kumar, ‘‘Postchemical-Mechanical Planarization Cleanup Process for Interlayer Dielectric Films,’’ J. Electrochem. Soc. 142, 216 (1995). 16. M. Itano, T. Kezuka, M. Ishii, T. Unemoto and M. Kubo, ‘‘Minimization of Particle Contamination During Wet Processing of Si Wafers,’’ J. Electrochem. Soc. 142, 971 (1995). 17. Y. Ein-Eli, E. Abelev, E. Rabkin and D. Starovetsky, ‘‘The Compatibility of Copper CMP Slurries with CMP Requirements,’’ J. Electrochem. Soc. 150, C646 (2003). 18. T. C. Hu, S. Y. Chiu, B. T. Dai, M. S. Tsai, I. -C. Tung and M. S. Feng, ‘‘Nitric Acid-Based Slurry with Citric Acid as an Inhibitor for Copper Chemical Mechanical Polishing,’’ Mater. Chem. Phys. 61, 169 (1999). 19. M. K. Jain, ‘‘Mechanical Scrubbing for Particle Removal,’’ U. S. Pat. 5, 551, 986 (1996). 20. A. Sethuraman and W. C. Koutny, Jr., ‘‘System for Cleaning a Surface of a Dielectric Material,’’ U. S. Pat. 6, 302, 766 (2001).
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21. K. Ueki, ‘‘Semiconductor Wafer Cleaning Method using a Semiconductor Wafer Cleaning Device that Supports a Lower Surface of the Wafer,’’ U. S. Pat. 6, 254, 690 (2001). 22. W. C. Krusell, J. M. de Larious and J. Zhang, ‘‘Mechanical Brush Scrubbing for Post-
