Advances in Imaging & Electron Physics, Volume 122 (Advances in Imaging and Electron Physics)

ADVANCES IN IMAGING AND ELECTRON PHYSICS

VOLUME 122 Electron Microscopy and Holography II

ADVANCES IN IMAGING AND ELECTRON PHYSICS

VOLUME 122 Electron Microscopy and Holography II

EDITOR-IN-CHIEF

PETER W. HAWKES CEMES-CNRS Toulouse, France

ASSOCIATE EDITORS

BENJAMIN K A Z A N Xerox Corporation Palo Alto Research Center Palo Alto, California

TOM M U L V E Y Department of Electronic Engineering and Applied Physics Aston University Birmingham, United Kingdom

Advances in

Imaging and Electron Physics Electron Microscopy and Holography II

EDITED BY

PETER W. HAWKES CEMES-CNRS Toulouse, France

V O L U M E 122

ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo

This b o o k is printed on acid-flee paper. ( ~

Copyright 9 2002, Elsevier Science (USA) All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the Publisher. The appearance of the code at the bottom of the first page of a chapter in this book indicates the Publisher's consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for pre-2002 chapters are as shown on the title pages: If no fee code appears on the title page, the copy fee is the same as for current chapters. 1076-5670/02 $35.00 Explicit permission from Academic Press is not required to reproduce a maximum of two figures or tables from an Academic Press chapter in another scientific or research publication provided that the material has not been credited to another source and that full credit to the Academic Press chapter is given. Academic Press

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CONTENTS

CONTRIBUTORS

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vii

PREFACE .

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xi

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FUTURE CONTRIBUTIONS

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The Structure of Quasicrystals Studied by Atomic-Scale Observations of Transmission Electron Microscopy KENJI HIRAGA I. II. III. IV. V. VI. VII.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Quasiperiodic Lattices . . . . . . . . . . . . . . . . . . . . Experimental Procedures . . . . . . . . . . . . . . . . . . . Electron Diffraction of Quasicrystals . . . . . . . . . . . . . . H i g h - R e s o l u t i o n Electron M i c r o s c o p y Images of Quasicrystals . . . Structure of Icosahedral Quasicrystals . . . . . . . . . . . . . . Structure of D e c a g o n a l Quasicrystals and Their Related Crystalline Phases . . . . . . . . . . . . . . . . . . . . . . VIII. C o n c l u d i n g R e m a r k s . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

2 3 20 22 31 36 51 80 81

Add-On Lens Attachments for the Scanning Electron Microscope ANJAM KHURSHEED I. II. III. IV. V. VI.

Introduction . . . . . . . . . . . . . . In-Lens Attachments . . . . . . . . . . Single-Pole Lens Attachments . . . . . . Secondary Electron E n e r g y Spectrometers Multibore Objective Lenses . . . . . . . Summary . . . . . . . . . . . . . . . References . . . . . . . . . . . . . .

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87 102 125 135 163 170 170

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174 177 196 212 221

Electron Holography of Long-Range Electrostatic Fields G. MATTEUCCI, G. F. MISSIROLI, AND G. P o z z I I. II. III. IV.

Introduction . . . . . . . . . . . . . . . . . E l e c t r o n - S p e c i m e n Interaction . . . . . . . . . R e c o r d i n g and Processing o f Electron H o l o g r a m s Charged Dielectric Spheres . . . . . . . . . . V. p - n Junctions . . . . . . . . . . . . . . . .

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CONTENTS

VI. Investigation of Charged VII. Conclusions . . . . . . VIII. Update . . . . . . . . References . . . . . .

Microtips . . . . . . . . . . . . . . .

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235 242 243 245

Digital Image-Processing Technology Useful for Scanning Electron Microscopy and Its Practical Applications EISAKUOHO I. II. III. IV. V. VI. VII. VIII. IX.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . Proper Acquisition and Handling of S E M Images . . . . . . . . . Quality Improvement of S E M Images . . . . . . . . . . . . . . Image M e a s u r e m e n t and Analysis . . . . . . . . . . . . . . . . S E M Parameters M e a s u r e m e n t . . . . . . . . . . . . . . . . . Color S E M Images . . . . . . . . . . . . . . . . . . . . . . Automatic Focusing and Astigmatism Correction . . . . . . . . . R e m o t e Control of the S E M . . . . . . . . . . . . . . . . . . Ultralow Magnification and Wide-Area Observation Using the M o d e m Montage Technique . . . . . . . . . . . . . . . . X. Active Image Processing and Multimodal Microscopy . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

INDEX .

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252 253 264 287 289 303 312 314 317 321 324

329

CONTRIBUTORS

Numbers in parentheses indicate the pages on which the authors' contributions begin.

KENJI HIRAGA(1), Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan ANJAM KHURSHEED(87), Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260 G. MATTEUCCI (173), Department of Physics and National Institute for the Physics of Matter, University of Bologna, 40127 Bologna, Italy G. E MISSIROLI( 1 7 3 ) , Department of Physics and National Institute for the Physics of Matter, University of Bologna, 40127 Bologna, Italy EISAKU OHO (251), Department of Electrical Engineering, Kogakuin University, Tokyo 192-0015, Japan G. PozzI (173), Department of Physics and National Institute for the Physics of Matter, University of Bologna, 40127 Bologna, Italy

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PREFACE

The present volume is a sequel to the thematic volume 121, in which some earlier contributions scattered through different volumes of these Advances were brought together. The theme here is the same, electron microscopy and holography, and the opening chapter is concerned with quasicrystals, a fascinating application of the transmission electron microscope, by K. Hiraga, one of the most prolific contributors to our knowledge of these structures. He leads us authoritatively through the theory of the subject and illustrates his subject with numerous micrographs and diffraction patterns. This is followed by the first of two chapters on the scanning electron microscope; this chapter, in which A. Khursheed describes add-on lens attachments for the SEM, is a new contribution, not an updated version of an earlier chapter. In it, he examines in-lens attachments, some single-pole lens elements, and above all, spectrometers; there is also a section on the very new area of multibore lens arrays. The other chapter on the scanning electron microscope is by E. Oho, and deals with digital image processing of the SEM image. Although this is not strictly a new contribution, the author has revised his earlier chapter extensively and the present account contains many recent developments. Finally, we reproduce the chapter by G. Matteucci, G. F. Missiroli, and G. Pozzi, with some revisions, on electron holography of long-range electrostatic fields. This application of hologaphy is less well known than the study of magnetic field distributions, which is one of the reasons why we chose to reproduce it in this collection. I am most grateful to the authors of the revised chapters in this volume for consenting to reappear here and for the work of revision. Their chapters first appeared in vol. 99 (G. Matteucci, G. F. Missiroli, and G. Pozzi), vol. 101 (K. Hiraga), and vol. 105 (E. Oho). The chapter by A. Khursheed complements these very suitably.

Peter Hawkes

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FUTURE CONTRIBUTIONS

T. Aach Lapped transforms G. Abbate New developments in liquid-crystal-based photonic devices S. Ando Gradient operators and edge and comer detection A. Arn6odo, N. Decoster, P. Kestener and S. Roux A wavelet-based method for multifractal image analysis M. Barnabei and L. Montefusco Algebraic aspects of signal and image processing C. Beeli Structure and microscopy of quasicrystals I. Bloch Fuzzy distance measures in image processing

G. Borgefors Distance transforms B. L. Breton, D. McMullan and K. C. A. Smith (Eds) Sir Charles Oatley and the scanning electron microscope G. Calestani, P.G. Merli, M. Vittori Antisari (Eds; vol. 123) Microscopy, Holography and Spectroscopy with Electrons A. Carini, G. L. Sicuranza and E. Mumolo V-vector algebra and Volterra filters

Y. Cho Scanning nonlinear dielectric microscopy E. R. Davies Mean, median and mode filters H. Delingette Surface reconstruction based on simplex meshes A. Diaspro (vol. 126) Two-photon excitation in microscopy

xi

xii

FUTURE CONTRIBUTIONS

R. G. Forbes Liquid metal ion sources E. Fiirster and E N. Chukhovsky

X-ray optics A. Fox The critical-voltage effect L. Frank and I. Miillerovfi Scanning low-energy electron microscopy M. Freeman and G. M. Steeves

Ultrafast scanning tunneling microscopy A. Garcia Sampling theory L. Godo & V. Torra Aggregation operators E W. Hawkes Electron optics and electron microscopy: conference proceedings and abstracts as source material M. I. Herrera

The development of electron microscopy in Spain J. S. Hesthaven

Higher-order accuracy computational methods for time-domain electromagnetics K. Ishizuka

Contrast transfer and crystal images I. P. Jones

ALCHEMI W. S. Kerwin and J. Prince

The kriging update model B. Kessler

Orthogonal multiwavelets G. Kiigel Positron microscopy W. Krakow

Sideband imaging

FUTURE CONTRIBUTIONS

xiii

N. Krueger The application of statistical and deterministic regularities in biological and artificial vision systems B. Lahme Karhunen-Loeve decomposition B. Lencov~i Modem developments in electron optical calculations C. L. Matson

Back-propagation through turbid media S. Mikoshiba and F. L. Curzon Plasma displays M. A. O'Keefe Electron image simulation N. Papamarkos and A. Kesidis

The inverse Hough transform M. G. A. Paris and G. d'Ariano

Quantum tomography E. Petajan

HDTV E A. Ponce

Nitride semiconductors for high-brightness blue and green light emission T.-c. Poon Scanning optical holography H. de Raedt, K. E L. Michielsen and J. Th. M. Hosson

Aspects of mathematical morphology E. Rau

Energy analysers for electron microscopes H. Rauch

The wave-particle dualism R. de Ridder

Neural networks in nonlinear image processing D. Saad, R. Vicente and A. Kabashima

Error-correcting codes O. Scherzer Regularization techniques

xiv

FUTURE CONTRIBUTIONS

G. Schmahl X-ray microscopy S. Shirai CRT gun design methods 17. Soma Focus-deflection systems and their applications

I. Talmon Study of complex fluids by transmission electron microscopy M. Tonouchi Terahertz radiation imaging N. M. Towghi Ip norm optimal filters T. Tsutsui and Z. Dechun Organic electroluminescence, materials and devices

Y. Uchikawa Electron gun optics D. van Dyck Very high resolution electron microscopy J. S. Walker Tree-adapted wavelet shrinkage C. D. Wright and E. W. Hill Magnetic force microscopy E Yang and M. Paindavoine Pre-filtering for pattern recognition using wavelet transforms and neural networks

M. Yeadon (vol. 126) Instrumentation for surface studies S. Zaefferer Computer-aided crystallographic analysis in TEM

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 122

The Structure of Quasicrystals Studied by Atomic-Scale Observations of Transmission Electron Microscopy KENJI HIRAGA Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Quasiperiodic Lattices . . . . . . . . . . . . . . . . . . . . . . . . . A. O n e - D i m e n s i o n a l Quasiperiodic Lattices . . . . . . . . . . . . . . . . B. T w o - D i m e n s i o n a l Quasiperiodic Lattices . . . . . . . . . . . . . . . . C. T w o - D i m e n s i o n a l Quasiperiodic Superlattices . . . . . . . . . . . . . . 1. NaC1-Type Quasiperiodic Superlattice . . . . . . . . . . . . . . . . 2. CsC1-Type Quasiperiodic Superlattice . . . . . . . . . . . . . . . . D. Phason Strain and Crystalline A p p r o x i m a n t s . . . . . . . . . . . . . . . III. Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . A. Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. H i g h - R e s o l u t i o n Transmission Electron M i c r o s c o p y ( H R T E M ) . . . . . . . C. H i g h - A n g l e Annular Detector D a r k - F i e l d Scanning Transmission Electron Microscopy (HAADF-STEM) . . . . . . . . . . . . . . . . . . . . . IV. Electron Diffraction of Quasicrystals . . . . . . . . . . . . . . . . . . . A. Good- and Poor-Quality Quasicrystals . . . . . . . . . . . . . . . . . B. Icosahedral Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . C. D e c a g o n a l Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . 1. Characteristics of Diffraction Patterns of D e c a g o n a l Quasicrystals . . . . 2. M o d u l a t i o n s of D e c a g o n a l Quasicrystals . . . . . . . . . . . . . . . 3. D e c a g o n a l Quasicrystals with Different Periods . . . . . . . . . . . . V. H i g h - R e s o l u t i o n Electron M i c r o s c o p y Images o f Quasicrystals . . . . . . . . A. Icosahedral Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . B. D e c a g o n a l Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . VI. Structure o f Icosahedral Quasicrystals . . . . . . . . . . . . . . . . . . . A. Topological Features of Icosahedral Quasicrystalline Lattices . . . . . . . . B. A t o m i c A r r a n g e m e n t s of Icosahedral Quasicrystals . . . . . . . . . . . . C. Defects in Icosahedral Quasicrystals . . . . . . . . . . . . . . . . . . 1. L i n e a r Phason Strain . . . . . . . . . . . . . . . . . . . . . . . 2. Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Structure o f D e c a g o n a l Quasicrystals and Their R e l a t e d Crystalline Phases . . . A. F r a m e w o r k of C o l u m n a r A t o m Clusters . . . . . . . . . . . . . . . . . B. D e c a g o n a l Quasicrystals and Crystalline Phases with 0.4-nm Periodicity . . . 1. A t o m Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Structural M o d e l s of A t o m Clusters . . . . . . . . . . . . . . . . . 3. A r r a n g e m e n t s of A t o m Clusters . . . . . . . . . . . . . . . . . . . C. D e c a g o n a l Quasicrystals and Crystalline Phases with 1.2-nm Periodicity . . . 1. F u n d a m e n t a l Structural Units . . . . . . . . . . . . . . . . . . . .

2 3 3 5 10 11 13 15 20 20 20 22 22 23 24 27 27 29 29 31 33 35 36 36 39 44 44 49 51 51 52 54 58 64 68 68

1 ADVANCES IN IMAGING AND ELECTRON PHYSICS Copyright 2002, Elsevier Science (USA). All rights reserved. Volume 122 ISSN 1076-5670/02 $35.00 ISBN 0-12-014764-5

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2. Structure of A1-Pd-MnDecagonal Quasicrystal . . . . . . . . . . . . 3. CrystallineApproximantPhases . . . . . . . . . . . . . . . . . . D. Decagonal Quasicrystals and Crystalline Phases with 1.6-nm Periodicity . . . 1. Structure of A1-PdDecagonal Phase . . . . . . . . . . . . . . . . . 2. CrystallineApproximant Phases . . . . . . . . . . . . . . . . . . VIII. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 74 76 76 79 81 82

I. INTRODUCTION

The discovery of an icosahedral phase having noncrystallographic symmetry, by Shechtman et al. (1984), and the following theoretical explanation as a quasicrystal, by Levine and Steinhardt (1984), have had a strong impact on solid-state physicists. We had thought for a long time that solids were divided into two structural classes: crystalline with periodic atomic arrangements and amorphous with random atomic arrangements. Also, we had recognized that only crystals with periodic structures produce sharp diffraction peaks. The discovery by Shechtman et al. brought about a drastic change in attitudes concerning the structure of solids. The quasicrystals show diffraction patterns with noncrystallographic symmetries but, nonetheless, consisting of sharp peaks. That is, the quasicrystals have aperiodic structures producing sharp diffraction peaks. High-resolution transmission electron microscopy (HRTEM) has been developed to study aperiodic structures, such as the structures of defects, in solids, and so it is the most powerful tool for investigating the "real" structure of quasicrystals. Consequently, many HRTEM studies of the quasicrystals have been carried out, and the results have given us valuable information about the structure of the quasicrystals. Recently, atomic-scale observations with highangle annular detector dark-field scanning transmission electron microscopy (HAADF-STEM) have received much attention in addition to HRTEM for the study of atomic-scale structures, with the popularization of the transmission electron microscope with a field-emission gun (FE-TEM), which produces a sufficient small probe size of less than 0.2 nm. HAADF-STEM images, which are formed only from transmitted high-angle scattering reflections, produce contrast proportional to the square of the atomic number of constitutional elements (Jesson and Pennycook, 1995), so the positions of heavy atoms are reproduced as bright contrast. Consequently, from HAADF-STEM images of Al-transition-metal quasicrystalline alloys, the arrangements of minority transition-metal atoms can be directly determined without disturbance of majority A1 atoms. Conversely, the arrangement of the A1 atoms may be deduced from ordinary HRTEM observations. Therefore, more accurate structural models may be deduced by combining HRTEM and HAADF-STEM observations.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

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Our group has studied the structures of quasicrystals by HRTEM from the early stage, and recently by combining HAADF-STEM observations. In this review I discuss the real structures of the quasicrystalline alloys, primarily on the basis of the results of our group.

II. QUASIPERIODICLATTICES

A. One-Dimensional Quasiperiodic Lattices To make it easy to understand this article, I will briefly mention the projection method, which is one of the theoretical ideas that help to explain aperiodic structures showing sharp diffraction peaks. One-dimensional quasiperiodic lattices can be formed by the projection of a two-dimensional square lattice on a straight line with an irrational slope (Fig. 1), as can be seen in many articles (e.g., Elser, 1986; Katz and Duneau, 1986). An orthogonal coordinate system with axes labeled Xll and X• is superimposed on the coordinate system of a two-dimensional square lattice, which is rotated by an angle 0 = t a n - l ( 1 / r ) (r is the golden ratio) with respect to the former coordinate system. Xll and X• are called a physical subspace and an internal subspace, respectively. Basis vectors of the two-dimensional square lattice, el and e2, transform to ell l - - c o s 0 and eli2 - - s i n 0 on the physical space, and to e• = - s i n 0 and e• = cos 0 on the internal space. The square lattice points, which are described as the set of n 1el -k- n2e2 with integers n 1 and n2, are projected at the points of nlelll + n2el12 on the axis Xll and at the points of nle• + n2e• on the axis X• A one-dimensional quasiperiodic lattice can be obtained by projecting square lattice points, which are inside a strip parallel to the Xll axis, on the line Xll , as shown in Figure 1. The region obtained by projecting the strip on the axis X• called a window, is labeled W in Figure 1. That is, one can obtain lattice points on the physical subspace as follows: A square lattice point is projected on the internal space (i.e., on the axis X• If the projected point is inside the window, the square lattice point is projected on the physical subspace (i.e., on the axis Xll ). If the window is now taken as the size of projection of the square lattice unit on the line axis X• a quasiperiodic lattice, called the Fibonacci sequence, with two intervals L and S(L = r S), is obtained, as shown in Figure 1. The quasiperiodic lattice of the two intervals L and S has no periodic lattice, but it produces sharp diffraction peaks. A function showing lattice points inside the strip in Figure 1 is described by the product of two functions, namely, a delta function showing square lattice points (g(x, y)) and a function showing the strip (f(x, y)). The Fourier transform of lattice points inside the strip can be obtained as the convolution of the Fourier transforms of g(x, y) and

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KENJI HIRAGA

X_L

o 9

9 o

o

W

X//

4" FIGURE 1. Construction of a one-dimensional quasiperiodic (Fibonacci) lattice by the projection of a two-dimensional square lattice. By projecting lattice points inside a strip (broken lines) on the axis Xll, one obtains the Fibonacci lattice of intervals L and S.

f(x, y). The Fourier transform of g(x, y) is also a delta function, and that of f(x, y) is a function sharpened along the direction parallel to the strip, but elongated along the direction perpendicular to the strip. Therefore, the elongated function is convoluted at all reciprocal lattice points, as shown in Figure 2a. If the strip is a rectangular function with unity inside the strip and zero outside the strip, the elongated function is reduced with oscillating. However, in actual quasicrystals, the strip function is considered to be a gentle function, and so the elongation function is smoothly reduced, as shown in Figure 2a. The diffraction pattern of the quasiperiodic lattice projected on the XII axis is obtained by the intensity distribution on the line X~' indicated in Figure 2a. Thus, diffraction peaks appear at positions associated with the golden ratio and become very sharp (Fig. 2b).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

it

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y* _L

",.,.

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~176

Sharp in X//

b

1

x//

FIGURE 2. (a) Reciprocal space expression to understand a diffraction pattern of the onedimensional quasiperiodic lattice. (b) Diffraction pattern.

B. Two-Dimensional Quasiperiodic Lattices Two-dimensional quasiperiodic lattices are described by the projection of a five-dimensional hypercubic lattice. In this case, the physical subspace is two-dimensional space and the internal subspace is three-dimensional space. Lattice points X in the five-dimensional hypercubic lattice can be described 4 with the basis vectors of ej(j = 0, 1, 2, 3, 4) as follows: X - ~ j = 0 n j e j . Projected points of X on the physical subspace, Xll, are described as XII = ~_~=0 n jell j, where ellj -- (cos(2zrj/5), sin(2zrj/5)) (j -- 0, 1, 2, 3, 4). The window, which is obtained from the projection of the five-dimensional hypercubic unit, in three-dimensional space of the internal subspace, is shown in Figure 3a. The window is divided into components of the two-dimensional space, X• and a one-dimensional component perpendicular to the former two-dimensional z 4 z 4 z 9 space, Xz: thus X• = ~-~j=onje• and X• = ~-~j=onje• where e • 1s

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KENJI H I R A G A

A

b

D

FIGURE 3. (a) Windows in three-dimensional internal subspace that enable (b) the Penrose lattice to be constructed.

(cos(4yrj/5), sin(4yrj/5)) (j -- 0, 1, 2, 3, 4) and e~_j is (1/s/~)j (j = 0, 1, 2, 3, 4). The lattice points projected in the internal subspace are placed at five surfaces of ~-~=0 nj = 0, 1, 2, 3, 4, so only two-dimensional windows at 4 ~~j=0 n j - - 0, 1, 2, 3, 4 are necessary. Here, only lattice points inside the four pentagonal windows shown in Figure 3a are projected on the physical subspace, so the rhombic Penrose lattice (Fig. 3b) can then be obtained. As can be seen in Figure 4, lattice points in the rhombic Penrose lattice are all placed on straight lines parallel to 5-fold directions, and the lines of the lattice points are arrayed with a one-dimensional quasiperiodic arrangement of L and S. Thus, a diffraction pattern of the Penrose lattice has 10-fold rotational symmetry but, nonetheless, consists of sharp diffraction spots. One can use the same decagonal windows on five e~_j = (1/s/~)j ( j 0, 1, 2, 3, 4) planes and then obtain pentagonal Penrose lattices, as shown in Figure 5a. By reducing the size of the windows (Fig. 5d), some different types of pentagonal lattices are obtained, as shown in Figures 5b and 5c. The rhombic and pentagonal Penrose lattices produce different diffraction patterns, as shown in Figure 6. In particular, the rhombic Penrose lattice, which is obtained from different areas and shapes of the windows (Fig. 3a) at different positions of z X• produces extra reflections in addition to the diffraction pattem of the pentagonal Penrose lattice (Fig. 6b), as can be seen in Figure 6a. Various types of Penrose lattices can be obtained by using different windows. Figure 7 shows two types of Penrose lattices, which are obtained with two windows at the positions X~_ -- 2 and 3. That is, special lattice points located on small pentagons at X~_ - 1 and 4 (Fig. 3a) are lacking in Figure 7a, compared

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

LSLLS

7

LSL LSL L SLSL

FIGURE 4. Penrose lattice and Fibonacci sequence of lattice planes.

b

C

FIGURE 5. (a, b, and c) Three types of pentagonal Penrose lattices constructed by windows in (d). The lattices shown in (a), (b), and (c) are made by the windows A, B, and C in (d), respectively.

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KENJI HIRAGA

Z

FIGURE 7. (a and b) Penrose lattices formed by two windows at X• = 2 and 3. Note that the lattice of (b) has pentagonal symmetry.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

9

with Figure 3b. Also, it should be noted that the lattice of Figure 7a has 10-fold rotational symmetry, but that of Figure 7b has 5-fold symmetry, which can be seen from the same orientation of all star-shaped pentagons. As a first approximation, the structure of a quasicrystal can be described by the convolution of two functions, namely, a function of a quasiperiodic lattice and a function showing an atom cluster located at the quasilattice points. Therefore, if either the quasiperiodic lattice or the atom cluster has 5-fold rotational symmetry, the quasicrystal has 5-fold symmetry. Actually, pentagonal quasicrystals have been found as modulations of decagonal quasicrystals (Section VII.B) One can determine experimental lattice points, occupied by some atom 4 clusters, on the physical subspace (i.e., XII - ~ j = 0 n jell J) by HRTEM observations. For example, the positions of atom clusters on the physical subspace can be determined from ring contrasts in an HRTEM image of an A1-Co-Ni decagonal quasicrystals (Fig. 8). From these experimental lattice points on the physical subspace (Fig~ 9a), one can determine lattice points in the fivedimensional space, X - Y~j=0 njej, and then also lattice points on the internal

FIGURE8. HRTEMlattice image, showing an arrangement of atom clusters (ring contrasts), of the high-temperature phase of the A1-Ni-Co icosahedral quasicrystal (Hiraga, 1991c).

10

KENJI HIRAGA

FIGURE9. (a) Positions of the atom clusters, obtainedfrom Figure 8. (b) Distributionof the cluster positions on the intemal subspace. The decagon shows a window used to construct the pentagonal Penrose lattice.

subspace, X_L = ~ j =4 0 nje_Lj (Fig. 9b). The degree of scattering of the lattice points on the internal subspace shows the ordering degree of quasiperiodic arrangements and is related to the function of the window, that is, the function of the strip, f(x, y). If the degree of scattering of the lattice points increases, the elongated function of the Fourier transform of f(x, y) is quickly reduced. That is, low ordering degree of quasiperiodic arrangements results in the disappearance of weak spots in diffraction patterns. Figure 9b shows a highly ordered quasiperiodic arrangement. A three-dimensional quasiperiodic lattice can be constructed from the projection of a six-dimensional hypercubic lattice. In this case the physical subspace and internal subspace are a three-dimensional space. The threedimensional quasiperiodic lattice is called a three-dimensional Penrose lattice, and it is formed with a three-dimensional aperiodic arrangement of two types of rhombohedra with planes of a golden diamond, in which a ratio of long and short diagonals is the golden ratio. The construction manner and topological characteristics of the three-dimensional Penrose lattice were first discussed by Ogawa (1985).

C. Two-Dimensional Quasiperiodic Superlattices The preceding section describes a variety of two-dimensional Penrose lattices obtained from the projection method by using different window shapes. These quasiperiodic lattices obtained by the projection method produce diffraction

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

11

patterns consisting of sharp spots. In this section, two-dimensional quasiperiodic superlattices obtained from the projection of hypercubic superlattices in higher-dimensional space are mentioned.

1. NaCl-Type Quasiperiodic Superlattice Lattice points in a five-dimensional hypercubic lattice can be divided into two 4 groups of ~ j = 0 nj = even and odd. These groups are called even and oddparities. Different types of atoms or atom clusters are placed at the lattice points of even and odd parities, so a NaCl-type hypercubic superlattice can be obtained. A NaCl-type two-dimensional quasiperiodic superlattice can be obtained by projecting the NaCl-type hypercubic superlattice on two-dimensional space using the window of Figure 3a. Figure 10 is an obtained rhombic quasiperiodic superlattice, in which the lattice points of odd and even parities are distinguished as open and closed circles. From Figure 10, one can easily notice a specific ordering manner: two lattice points connected with a bond are always of different parity. This type of superlattice is actually found in an A1-Co-Ni decagonal quasicrystal (Hiraga, Ohsuna, Nishimura et al., 2001; Hiraga, Ohsuna, and Sun, 2001), as shown in Figure 11. Figure 1 l a is an HAADFSTEM image of an A1-Co-Ni decagonal quasicrystal, referred to as a type I superlattice, in an A171COla.sNi14.5 alloy annealed at 1000~ for 65 h. In the

b

q

t C~ FIGURE10. Rhombic Penrose lattice obtained from the projection of the NaCl-type hypercubic supeflattice. Open and closed circles correspond to odd and even parities, respectively.

12

KENJI HIRAGA

FIGURE 11. (a) HAADF-STEM image of the type I A1-Co-Ni decagonal quasicrystal in an

A171Co14.5Ni14.5alloy. (b)Tiling constructed by connecting the pentagonal contrasts in (a). Open and closed circles correspond to the pentagonal contrasts with different orientations (Hiraga, Ohsuna, Nishimura et al., 2001).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

13

image, one can see small pentagonal arrangements of bright dots, which are located at centers of atom clusters (indicated with a circle), although the pentagonal contrasts are deformed by sample drift during scanning of the sample with a focused beam. The pentagonal contrasts, namely, the centers of the atom clusters, are arranged with an aperiodic lattice with a bond length of 2.0 nm, as indicated by lines. Also, one can see the pentagonal contrasts with two orientations in Figure 1 l a; that is, there are two types of atom clusters with two orientations of pentagonal symmetry. Figure 1 lb shows a quasiperiodic lattice obtained from Figure 11 a by taking account of two types of atom clusters. In Figure 1 l b, the atom clusters are arranged in a rhombic lattice in a definite ordered manner so that two atom clusters connected by a bond are always different types of atom clusters, although this order is broken at pentagonal files existing as defects in this lattice. This superlattice can be said to correspond to that obtained from the projection of the NaCl-type hypercubic superlattice, shown in Figure 10. That is, the type I A1-Co-Ni decagonal quasicrystal can be concluded to be an example of the NaCl-type decagonal quasicrystal. An electron diffraction pattern of the NaCl-type decagonal quasicrystal includes superlattice reflections, as can be seen in Figure 25c.

2. CsCl-Type Quasiperiodic Superlattice Next, a body-centered hypercubic lattice with vertical points of no, n l, n2, n3, n4 and body-centered positions of no + 1/2, rtl + 1/2, n2 + 1/2, rt3-l- 1/2, n4 -t- 1/2 is dealt with. From the projection of the vertices and body-centered positions using the window of Figure 3a, two rhombic lattices can be obtained, as shown in Figures 12a and 12b. Figure 12a is an ordinary rhombic

b

c

|

FmURE 12. (a and b) Rhombic filings formed by the projections of (a) vertical points of no, n l , n2, n3, n4 and (b) body-centered positions of no + 1/2, nl + 1/2, n2 + 1/2, n3 + 1/2, n4 -]- 1/2. (C) Pentagonal filing formed by the projection of both the vertical points and the body-centered positions. Open circles surrounding a closed circle in (c) correspond to overlapping positions of vertical points and body-centered positions. (Reprinted from Ohsuna, T., Sun, W., and Hiraga, K., 2000. Decagonal quasicrystal with ordered body-centered (CsCl-type) hypercubic lattice. Philos. Mag. Lett. 80, pp. 577-583, with permission from Taylor & Francis Ltd., http://www'tandf'c~ ~

14

KENJI HIRAGA

a

b

2

FIGURE13. (a) Windowused to obtained tilings of Figure 12. (b) Windowused to remove overlapping positions in Figure 12.

Penrose lattice (Fig. 3b), and Figure 12b is one of generalized Penrose lattices (Ishihara and Yamamoto, 1988). The projection of the body-centered hypercubic lattice produces a pentagonal Penrose lattice, shown in Figure 12c, although it lacks some lattice points from the standard pentagonal Penrose lattice of Figure 5a. The bond length of the lattice of Figure 12c is 1 / r times as small as those of Figures 12a and 12b. It should be noted that the lattice of Figure 12c includes overlapping positions of the vertices and body-centered positions. However, in actual structures of two-dimensional quasicrystals, two atoms or two atom clusters cannot occupy one lattice point in the quasiperiodic lattice. Therefore, each of the overlapping positions in Figure 12c is occupied randomly by one atom or one atom cluster. The overlapping positions can be considered to come from an overlapping area in two windows separated with an interval of 1/2 + 1/2 + 1/2 + 1/2 + 1/2, as shown in Figure 13a. So that the overlapping positions can be taken off, a small window (Fig. 13b), in which the overlapping area is cut off, is used. However, lattice points on cutting surfaces of the small window still produce overlapping lattice points. These overlapping positions are scattered at the vertical and body-centered positions randomly. The quasiperiodic lattice, formed in this way, is shown in Figure 14. Although Figures 14a and 14b lack many lattice points, they can be said to be rhombic Penrose lattices. In Figure 14c, most of the vertical and body-centered positions are arranged in an ordered manner so that two lattice points connected by a bond always have different positions, although this order is broken at pentagonal tiles. The main feature of the CsCl-type quasiperiodic superlattice is that the fundamental pentagonal lattice with a bond length a is divided into two rhombic sublattices with a bond length a t .

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

a

b

15

c

O

O

FIGURE 14. (a and b) Rhombic tilings formed by the projections of (a) vertical points of no, nl,n2, n3, n4 and (b) body-centered positions of no + 1/2, nl h- 1/2, n2-b 1/2, n3 + 1/2, n4 -b 1/2. (C) Pentagonal tiling formed by the projection of both the vertical points and the body-centered positions, after removal of overlapping positions.

This CsCl-type quasiperiodic superlattice has been found in A1-Co-Ni (Hiraga, Ohsuna, and Nishimura, 2000; Hiraga, Ohsuna, and Sun, 2001) and A1-Ni-Ru (Ohsuna et al., 2000; Sun, Ohsuna, and Hiraga, 2000) decagonal quasicrystals. Figure 15 shows HRTEM images of an A1-Ni-Ru decagonal quasicrystal, which is found in a conventionally solidified A170Ni20RUl0 alloy, as well as the fundamental lattice and two superlattices. Ring contrasts in Figure 15a show atom clusters with a 2.0-nm diameter, and an enlarged image, Figure 15b, shows the existence of two types of atom clusters with different orientations of pentagonal symmetry. Figure 15c shows a fundamental lattice obtained by connecting the centers of all the ring contrasts in Figure 15a, and Figure 15d shows two supeflattices by distinguishing the two types of clusters with different orientations of pentagonal symmetry in Figure 15a. That is, the fundamental lattice with a bond length of 2.0 nm can be divided into two sublattices with a bond length of 2.0r = 3.2 nm. Figures 15c and 15d resemble Figures 14a and 14b, which are formed by the projection of a CsCl-type hypercubic superlattice, so that the A1-Ni-Ru decagonal quasicrystal can be concluded to be the CsCl-type decagonal quasicrystal. The same CsCl-type decagonal quasicrystal has been found in an A1-Co-Ni decagonal quasicrystal referred as to the Sl-type superlattice. An electron diffraction pattern of this decagonal quasicrystal includes many superlattice reflections, as shown in Figure 25b.

D. Phason Strain and Crystalline Approximants

The quasiperiodic lattices obtained from the projection of high-dimensional periodic lattices produce peculiar defects, called random phason strain and

16

KENJI HIRAGA

FIGURE 15. (a and b) HRTEM images of an A1-Ni-Ru decagonal quasicrystal. (c) The fundamental lattice formed by connecting all ring contrasts in (a). (d) Sublattices formed by connecting the ring contrasts with the same orientations of pentagonal symmetryas in (a). (Reprinted from Ohsuna, T., Sun, W., and Hiraga, K., 2000. Decagonal quasicrystal with ordered bodycentered (CsCl-type) hypercubic lattice. Philos. Mag. Lett. 80, pp. 577-583, with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/journals) linear phason strain, associated with a window function on the internal subspace. Figure 16 shows the random phason strain, which is formed with the strip function randomly varied with the coordinate of Xll. The random phason strain produces local disordering in the quasiperiodic arrangement of L and S in the one-dimensional quasilattice, and flipping of lattice points in the twodimensional quasilattice (Fig. 17). The random phason strain leads to a gentle function of the window from a rectangle function, and consequently results in the quick reduction of the elongation function of the Fourier transform of the window function. Consequently, the random phason strain causes the disappearance of weak spots in diffraction patterns and the appearance of diffuse scattering on the background.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

17

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18

KENJI

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QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

19

FIGURE20. Diffraction patterns of A1-Ru-Cu icosahedral quasicrystals (a) with and (b) without linear phason strain in (a) an as-casted A165Ru15Cu20alloy and (b) an annealed alloy at 850~ (Hiraga, Lee et al., 1989). Note large displacements of weak spots along the horizontal direction in (a).

with displacements of strong spots. The displacements of diffraction spots in Figure 20a occur along the horizontal direction, and so, compared with Figure 20b, Figure 20a clearly shows deformed pentagons formed by weak spots. If the slope of the strip in Figure 1 is changed from the irrational value to rational values, periodic arrangements of L and S appear, as shown in Table 1. It should be noted that the periods of the arrangements become large with a scaling of the golden ratio, as the rational value approaches from 1/ 1 to near 1/r. Crystalline phases with periodic arrangements formed by rational values approximating r are called crystalline approximants and have been found in many

20

KENJI HIRAGA TABLE 1 RATIONALVALUESAND PERIODICARRANGEMENTS Slope

Arrangement in a period

1/1 1/2 2/3 3/5 5/8

LS LSL LSLLS LSLLSLSL LSLLSLSLLSLLS

alloys around quasicrystalline alloys. For example, cubic phases, which can be understood with 1/ 1 and 2/1 approximations, have been found in A1-Pd-MnSi alloys, and they have lattice constants of about 1.2 nm and 2.0 (= 1.2r) nm, respectively (Hiraga, Sugiyama, and Ohsuna, 1998b; Sugiyama, Kaji, Hiraga, et al., 1998).

III. EXPERIMENTAL PROCEDURES

A. Samples As an aid to those who would like information about sample preparations and compositions, and details of the experimental procedures, in this section I briefly summarize the principal samples mentioned in this article and sample preparations for transmission electron microscopy (TEM). Metastable quasicrystals were formed in rapidly solidified (R. S.) alloys, which were prepared using a melt-spinning apparatus with a single copper roller 20 cm in diameter at 2000-4000 rev/min. Stable quasicrystals were formed in conventionally solidified (C. S.) alloys in an arc furnace under an argon atmosphere, annealed at proper temperatures, and then quenched mainly in water. Compositions and sample preparations for the quasicrystals mentioned in this article are as listed in Table 2.

B. High-Resolution Transmission Electron Microscopy (HRTEM) HRTEM images and electron diffraction patterns presented in this article were taken with a 200-kV (JEM-200CX) electron microscope having a resolution of 0.23 nm and a 400-kV electron microscope (JEM-4000EX) with a resolution of 0.17 nm. All images and diffraction patterns, except those of A1-Mn, A1Mn-Si, and A1-Fe-Cu icosahedral phases and an A1-Mn-Si decagonal phase,

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

21

TABLE 2 QUASICRYSTALCOMPOSITIONSAND SAMPLEPREPARATIONSa Icosahedral phases (IQ) and their crystalline approximants (CA) A1-Mn IQ R. S. A186Mn14alloy A1-Mn-Si IQ R. S. A174Mn20Si6 alloy A1-Fe-Cu IQ C. S. A165Fe15Cu20alloy A1-Ru-Cu IQ C. S. A165Ru15Cu20alloy A1-Pd-Mn IQ C. S. A170Pd20Mnlo alloy A1-Pd-Mn-Si CA C. S. alloy A1-Li-Cu IQ Zone-melted A1-Li-Cu alloy A1-Li-Cu CA C. S. alloy Decagonal phases (DQ) and their crystalline approximants (CA) DQ with 0.4- and 0.8-nm periods: A1-Cu-Co DQ C.S. A165CulsC020 alloy A1-Co-Ni DQs, CAs C.S. many A1-Co-Ni alloys Alloys A172Co8Ni20 A170Co12Ni18 A172.sCo11Ni16.5 A171Co14.5Ni14.5 A171.sCo16Ni12.5 A171.5Co16Ni12.5 A172.sCo17.sNi10 A171Co19Nilo A172.sCo20Ni7.5 A171.sCo25.sNi3 A1-Cu-Rh DQ A1-Ni-Fe DQ A1-Ni-Ru DQ DQ with 1.2-nm period: A1-Mn DQ A1-Mn CA A1-Pd-Mn DQ DQ with 1.6-nm period: A1-Pd DQ A1-Pd CA A1-Ni-Ru DQ

Heat treatments

Structures

900~ 14 h 900~ 48 h 900~ 40 h 1000 oC, 65 h 900~ 72 h 900 ~ 120 h 900~ 40 h llO0~ 11 h 900~ 280 h 1160~ 3 h

Ni-basic structure S 1-type superstructure S 1-type superstructure Type-I superstructure Type-II superstructure Crystalline approximant Co-rich basic structure One-dimensional quasicrystal W-(A1CoNi) crystalline phase Pentagonal superstructure

C. S. A163CUl8.5Rhl8.5 alloy C. S. A172Ni24Fe4alloy C. S. A170Ni20RUloalloy R. S. A186Mn14alloy C. S. A13Mn alloy C. S. A170PdloMn20, A170Pdl3Mnl7 alloys R. S. A13Pd alloy C. S. A13Pd alloy C. S. A175NilsRUlo alloy

aR. S., rapidly solidified; C. S., conventionally solidified.

were taken with the 400-kV electron microscope. Samples for electron microscopy were prepared by electrolytic polishing using an ice-cold solution of perchloric acid and methanol, in a 1:9 volume ratio, for A1-Mn and A1-Mn-Si quasicrystals. For the other quasicrystals and crystalline phases, crushed materials were dispersed on holey carbon films.

22

KENJI HIRAGA

Image contrast of HRTEM is very sensitive to experimental conditions such as sample thickness and defocus value. Particularly, the HRTEM structure images, having information about atomic arrangements, should be taken under strict experimental conditions. Defocus values in observed images can be estimated from Fresnel fringes at the edges of samples or amorphous films stuck on samples. Most of all HRTEM images presented in this article were confirmed as taken close to Scherzer defocus. Recently, it has been noticed that some quasicrystals easily undergo structural change under electron irradiation damage. Therefore, for those quasicrystals, structural changes by electron irradiation damage were checked using a low-light television camera, and HRTEM images were observed with an irradiation dose about one tenth of that normally used in HRTEM studies for A1-Cu-Rh, A1-Ni-Fe, and A1-Co-Ni decagonal quasicrystals.

C. High-Angle Annular Detector Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM) HAADF-STEM observations were made on a 200-kV transmission electron microscope (JEM-201 OF) operated in a scanning transmission mode. A beam probe with a half-width of about 0.2 nm was scanned on the sample, and a transmitted high-angle scattering beam was recorded using an annular detector of 60-160 mrad. The HAADF-STEM image is formed from high-angle scattering reflections during scanning with the incident beam, and so sample drift during scanning produces local deformation of the image contrast. Therefore, one should take account of this deformation when analyzing observed HAADF-STEM images. Most HAADF-STEM images presented in this article are filtered images reconstructed using Fourier diffractograms of original images and an aperture surrounding diffraction spots in the diffractograms, in order to reduce noise in the original images. Bright contrast in HAADF-STEM is proportional to the square of the atomic number of constitutional elements, so the positions of heavy atoms are represented. Consequently, from HAADFSTEM images of Al-transition-metal quasicrystalline alloys, the arrangements of minority transition-metal atoms can be directly determined without disturbance of majority A1 atoms. As a rough approximation, it can be said that images of HAADF-STEM have reversed contrasts of HRTEM images.

IV. ELECTRON DIFFRACTION OF QUASICRYSTALS The electron diffraction technique has been used widely to study quasicrystals because of its convenience, high sensitivity for weak reflections, and ability to take diffraction patterns from selected small areas, compared with X-ray and

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

23

neutron diffraction. In this section, we look at structural i n f o r m a t i o n obtained f r o m observation of electron diffraction patterns.

A. Good- and Poor-Quality Quasicrystals Figure 21 shows diffraction patterns for s o m e icosahedral and d e c a g o n a l quasicrystals, taken with the incident b e a m parallel to the 5- and 10-fold s y m m e t r y axes, respectively. Figure 2 l a is a pattern taken f r o m an A 1 - M n icosahedral

FIGURE 21. Electron diffraction pattems showing the structural quality of quasicrystalline structures, taken with the incident beam parallel to (a and b) the 5-fold symmetry and (c and d) the 10-fold symmetry axes. Pattems (a) and (b) are of A1-Mn metastable and A1-Fe-Cu stable icosahedral phases, respectively. Pattems (c) and (d) are of A1-Mn metastable and A1-Cu-Co stable decagonal phases, respectively.

24

KENJI HIRAGA

phase, first found by Shechtman et al. (1984) as a metastable phase, whereas Figure 2 l b is that from a stable A1-Fe-Cu icosahedral phase, found later by Tsai, Inoue, and Masumoto (1987, 1988), in an A165Fe15Cu20 alloy conventionally solidified and then annealed at 850~ for 48 h. From the comparison between the two patterns, one can clearly see the difference in the structural quality of the quasicrystals. That is, in the pattern of the A1-Fe-Cu icosahedral phase in Figure 21b, one can see a number of weak spots, which shows the existence of a highly ordered correlation in the atomic arrangement, and can see that their positions are located at perfect icosahedral symmetry positions. Conversely, the pattern of the A1-Mn icosahedral phase (Fig. 21a) shows the disappearance of weak spots due to poor correlation, and systematical shifts of diffraction spots, which can be clearly seen as the deformation of small pentagons formed with weak diffraction spots. The disappearance of weak spots in Figure 2 l a results from random phason strain, and the shifts of diffraction spots is caused by the existence of linear phason strain, as mentioned before. The difference in structural quality of decagonal quasicrystals can be seen from the comparison between Figures 21 c and 21 d, which were obtained from an A1-Mn metastable phase and a stable A1-Cu-Co phase in a conventionally solidified alloy. The A1-Mn decagonal phase was found by Bendersky (1985) and by Chattopadhyay et al. (1985), whereas the A1-Cu-Co decagonal phase was found in a later study by Tsai, Inoue, and Masumoto (1989b, 1989c). The appearance of many sharp weak spots at exact decagonal symmetry positions in Figure 21d shows that, compared with the A1-Mn decagonal phase, the A1-Cu-Co decagonal phase is a good-quality or highly ordered quasicrystal without any linear phason strain (Hiraga, Sun, and Lincoln, 1991). As mentioned previously, quasicrystals exist in wide structural regions from poor quality to good quality, so one should use good-quality quasicrystals to investigate the real structural characteristics of the quasicrystalline structures. As in the A1-Fe-Cu phase, good-quality icosahedral quasicrystals have been found in A1-Ru(or Os)-Cu (Tsai, Inoue, and Masumoto, 1988) and in A1-Pd-Mn (Tsai, Inoue, Yokayama et al., 1990), and good-quality decagonal quasicrystals in A1-Ni-Co (Tsai, Inoue, and Masumoto, 1989a), A1-Cu-Co (Tsai, Inoue, and Masumoto, 1989b, 1989c), A1-Pd-Mn (Beeli et al., 1991), A1-Ni-Fe (Lemmerz et al., 1994), A1-Cu-Rh (Tsai, Inoue, and Masumoto, 1989c), and A1-Ni-Ru (Sun and Hiraga, 2000; Sun, Ohsuna, and Hiraga, 2000). B. Icosahedral Quasicrystals

Figure 22 shows electron diffraction patterns of the stable A1-Cu-Fe icosahedral phase, taken with the incident beams parallel to the 2-, 3-, and 5-fold symmetry axes. They were taken with two different camera lengths to observe

Q U A S I C R Y S T A L S STUDIED BY A T O M I C - S C A L E O B S E R V A T I O N S OF TEM

25

FIGURE 22. Electron diffraction patterns of an icosahedral quasicrystal in an A170Fe15Cu15 alloy conventionally solidified and then annealed for 48 h at 1118 K, taken with the incident beams parallel to the (a and d) twofold, (b and e) threefold, and (c and f) fivefold symmetry axes. Pattems of (d), (e), and (f) were taken with a shorter camera length than that in (a), (b), and (c), to obtain diffraction spots in higher Lane zones and Kikuchi patterns. In the central parts of (e) and (f), pictures taken with different exposure times are inserted (Hiraga, Zhang et al., 1988).

26

KENJI HIRAGA

not only diffraction spots on the zeroth Laue zone and those on the higher zones, but also Kikuchi patterns. In Figures 22e and 22f, the patterns taken with different exposure times are inserted to yield a simultaneous view of diffraction spots in higher Laue zones and the Kikuchi pattern. In the patterns one can see a number of diffraction spots, which are very sharp and located at strict icosahedral symmetry positions without showing any systematic shifts due to linear phason strain. In Figure 22, diffraction patterns in a zeroth Laue zone and Kikuchi bands indicate 2-, 6-, and 10-fold rotational symmetries corresponding to the projection symmetry of the icosahedral phase, whereas diffraction spots in the higher Laue zones and Kikuchi lines show 2-, 3-, and 5-fold symmetries, which correspond to three-dimensional symmetry. For example, in Figure 22e one can clearly see the 3-fold rotational symmetry in the intensity distribution of diffraction spots on higher Laue zones and in the Kikuchi pattern formed with bright and dark lines. Pentagons drawn with bright and dark Kikuchi lines are observed in Figure 22f. The A1-Cu-Fe icosahedral phase is known to be an F-type icosahedral quasicrystal, which is interpreted in terms of face-centered six-dimensional hypercubic lattices (Ebalard and Spaepen, 1989; Ishimasa et al., 1988), in contrast to P-type quasicrystals derived from a primitive hypercubic lattice, which were observed primarily in the early stage of quasicrystal studies. The difference between the F- and P-type icosahedral quasicrystals can be seen in diffraction patterns taken with the incident beam parallel to the twofold axis, as shown in Figure 23. Figures 23a and 23b are electron diffraction patterns

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FIGURE23. Electron diffraction patterns of (a) P-type A1-Li-Cu and (b) F-type A1-Fe-Cu icosahedral phases, taken with the incident beam parallel to the twofold symmetry axis. Some examples of the extra reflections appearing in the F-type icosahedral quasicrystal are indicated by small arrowheads in (b).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 27 of the P-type A1-Li-Cu and F-type A1-Fe-Cu icosahedral quasicrystals, respectively. In the pattern of A1-Fe-Cu (Fig. 23b), there are a number of sharp diffraction spots in addition to the spots appearing in the pattern of A1-Li-Cu (Fig. 23a). Some examples of the extra spots appearing in only the F-type structure are indicated by small arrowheads in Figure 23b. It should be noted that most of the extra reflections appear on the five- and threefold axes, so no extra reflections appear in diffraction patterns taken with the incident beam parallel to the five- and threefold axes. Structural characteristics of the F- and P-type icosahedral quasicrystals were studied by HRTEM images taken with the incident beam parallel to the twofold axis (Hiraga and Shindo, 1989). The transformation from the P-type to the F-type icosahedral phase was observed by annealing a rapidly solidified A1-Ru-Cu icosahedral quasicrystal (Hiraga, Hirabayashi, Tsai et al., 1989).

C. Decagonal Quasicrystals 1. Characteristics of Diffraction Patterns of Decagonal Quasicrystals Decagonal quasicrystals are two-dimensional quasicrystals with two-dimensional quasiperiodic planes and a one-dimensional periodic axis along the 10-fold axis, so their diffraction patterns reveal reflection planes showing quasicrystalline structures and a periodic array of the reflection planes, as shown in Figure 24. Figure 24 shows electron diffraction patterns of a stable decagonal quasicrystal with 0.4-nm periodicity in an A172Ni24Fe4 alloy conventionally solidified and then annealed at 850~ for 50 h. The diffraction pattern of Figure 24b, taken with the incident beam perpendicular to the 10-fold axis, along the p axis indicated in Figure 24a, shows the existence of a period of about 0.4 nm along the vertical direction. In Figure 24c, the pattern was taken with the incident beam parallel to the q axis, and one can see an extinction rule that causes diffraction spots showing the period of 0.4 nm to disappear. The extinction rule suggests the existence of the c-glide (c is the periodic axis) plane or a 105 screw axis along the c axis and the space group P105/mmc (Yamamoto and Ishihara, 1988). This extinction rule has been widely found in the decagonal quasicrystals with other periods. It should be noted that diffuse scattering is apparently visible on the background around strong Bragg spots in diffraction patterns of the decagonal quasicrystals, taken with the incident beam parallel to the periodic axis, as can be seen clearly in Figures 2 ld and 24d. Such scattering results from local disordering from the ideal Penrose filing in an atomic arrangement. We know that the Penrose lattice, obtained mathematically from the projection of hypercubic lattices in the higher-dimensional space to three- or two-dimensional space, produces diffraction patterns consisting of sharp spots, described as a

28

KENJI HIRAGA

FIGURE24. Electron diffraction patterns of a decagonal phase in an A172Ni24Fe4 alloy conventionally solidified and then annealed at 850~ for 50 h, taken with the incident beam parallel to (a) the 10-fold axis and parallel to the (b) p axis and (c) q axis in (a). (d) Enlarged pattern of a part of (a). (Reprinted from Hiraga, K., Yubuta, K., and Park, K.-T., 1996. High-resolution electron microscopy of A1-Ni-Fe decagonal quasicrystal. J. Mater. Res. 11, pp. 1702-1705, with permission from The Materials Research Society.) delta function, and any local modification from the Penrose lattices (i.e., random phason strain) results in the rather high g• decay of diffraction intensities (Section II.D). Consequently, the local modification in the real structure of the quasicrystals produces diffuse scattering. The diffuse scattering in decagonal quasicrystals spreads out on two-dimensional reciprocal planes perpendicular to the periodic axis, whereas that in the icosahedral quasicrystals spreads out over three-dimensional reciprocal space. Therefore, one can clearly see the diffuse scattering in diffraction patterns of decagonal quasicrystals (Fig. 21d), compared with the patterns of icosahedral quasicrystals (Fig. 21b).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 29

2. Modulations of Decagonal Quasicrystals Some modulations of decagonal quasicrystals have been found by electron diffraction analysis. For example, Figure 25 shows six modulations of A1Co-Ni decagonal quasicrystals, referred to as the (a) Ni-rich basic structure; (b) S 1-type, (c) type I, and (d) type II superstructures; (e) Co-rich basic structure; and (f) pentagonal superstructure (Ritsch, Beeli et al., 1998). Figures 25a and 25e are similar to Figure 24a, so they are called Ni-rich and Co-rich basic structures. In the patterns of Figures 25b, 25c, 25d, and 25f, a number of extra spots in addition to the spots appearing in Figures 25a and 25e are observed with different intensity distributions. Most of the extra spots are superlattice reflections and can be interpreted by quasiperiodic superlattices, which have been mentioned before (Section II.C). It should be noted that intensity distributions of the superlattice reflections have r 2 scaling, as can be seen in the superlattice reflections around the spots, indicated by small white arrows in Figures 25b and 25c, with r scaling. Conversely, an intensity distribution of fundamental reflections appearing in Figure 25a has r scaling. Also, one can see pentagonal symmetry in the intensity distribution of Figure 25f, as indicated by small white arrows. The pentagonal symmetry results from the breakdown of Friedel's law by dynamical scattering in electron diffraction and shows that this quasicrystal has noncentral symmetry. This quasicrystal is called a fivefold, or pentagonal superstructure, because its diffraction pattern (Fig. 25f) includes superlattice reflections. A one-dimensional quasicrystal has been found as one of the modulations of the A1-Co-Ni decagonal quasicrystal (Ritsch, Radulescu et al., 2000). In Figure 26, one can see periodic arrangements of diffraction spots along the horizontal direction, whereas arrangements along the other directions have no periodicity. Consequently, this pattern shows a one-dimensional quasicrystal.

3. Decagonal Quasicrystals with Different Periods The decagonal quasicrystals also have some polytypes with different periods, such as 0.4 nm, 0.8 nm, 1.2 nm, 1.6 nm, and so on, along the 10-fold symmetry axis. Figure 27 shows diffraction patterns of the decagonal quasicrystals with about 0.8-, 1.2-, and 1.6-nm periods. The patterns were taken with the incident beam parallel to the two directions perpendicular to the periodic axis (the p and q directions in Fig. 24a). The diffraction patterns of Figures 27a, 27c, and 27e show 0.8-, 1.2-, and 1.6-nm periods along the vertical direction (viz., along the 10-fold symmetry axis). However, in Figures 27b, 27d, and 27f, one can see only diffraction spots showing 0.4-, 0.6-, and 0.8-nm periods, if weak diffuse

FIGURE 25. Electron diffraction pattems of six modulations, referred to as the (a) Ni-rich basic structure; (b) S 1-type, (c) type I, and (d) type II superlattices; (e) Co-rich basic structure; and, (f) pentagonal superlattice of A1-Co-Ni decagonal quasicrystals. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.)

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 31

FIGURE 26. Electron diffraction pattern of a one-dimensional A1-Co-Ni decagonal quasicrystal.

spots indicated by small white arrows are ignored. The extinction rule shows that the space group is P 105/mmc. The diffuse spots, which are often observed in decagonal quasicrystals between Bragg reflection planes, tend to weaken and disappear in good-quality decagonal quasicrystals with sharp stoichiometric compositions (Hiraga, Lincoln et al., 1991).

V. HIGH-RESOLUTION ELECTRON MICROSCOPYIMAGES OF QUASICRYSTALS Quasicrystals have aperiodic structures despite the presence of sharp spots in diffraction patterns, so HRTEM is the most powerful tool for investigating their real structures. Consequently, many HRTEM studies of the quasicrystals have been carried out and have given us valuable information about the structures and defects of quasicrystalline alloys, although there are limitations due to the limited resolution of an electron microscope, compared with diffraction techniques, and due to the use of projected images along the beam axis. In this section, I describe characteristic features of HRTEM images of the icosahedral and decagonal quasicrystals.

FIGURE 27. Electron diffraction patterns of decagonal quasicrystals with three different periods, taken with the incident beam perpendicular to the periodic axis. Pattems (a) and (b) are of a metastable decagonal phase with 0.8-nm periodicity in a rapidly solidified Al13Co4 alloy, pattems (c) and (d) are of a stable phase with 1.2-nm periodicity in a conventionally solidified A170Pdl0Mn20 alloy annealed at 800~ for 16 h and then quenched in water, and pattems (e) and (f) are of a metastable phase with 1.6-nm periodicity in a rapidly solidified AlaPd alloy.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

33

In the early stages of HRTEM of quasicrystals, almost all the observed images of quasicrystals were taken with 200-kV electron microscopes having resolutions of about 0.23 nm, so they gave us information about the topological features of lattices of the quasicrystals but little information about atomic arrangements, because of poor resolution and thick samples. Since then, HRTEM images, which directly reflect the projected potential of the quasicrystals, have been observed with a 400-kV electron microscope having a resolution of 0.17 nm. These images give us much valuable information that enables us to understand atomic arrangements of the quasicrystals. To distinguish between the two types of images, we have called them lattice images and structure images (Hiraga, Lincoln et al., 1991; Hiraga, Sun, and Lincoln, 1991). In this section, I describe characteristic features of the HRTEM lattice images and structure images.

A. Icosahedral Quasicrystals Figure 28 shows a lattice image and a structure image of icosahedral phases, taken with the incident beam parallel to the fivefold axis. These images were taken with 200- and 400-kV electron microscopes having resolutions of

FIGURE28. HRTEM (a) lattice image of a metastable A1-Mn-Si icosahedral phase and (b) structure image of a stable A1-Pd-Mn icosahedral phase. Images (a) and (b) were taken with the incident beam parallel to the fivefold symmetryaxis.

34

KENJI HIRAGA

0.23 nm and 0.17 nm, respectively. Figure 28a is a typical lattice image of an A1-Mn-Si icosahedral phase, and Figure 28b is a structure image of an A1-Pd-Mn icosahedral phase. The lattice image (Fig. 28a) was obtained from a relatively thick region of a few tens of nanometers, whereas the structure image (Fig. 28b) was taken from a thin region, less than about 5 nm. By comparing the two images, one can see image contrast with a higher resolution in Figure 28b than that in Figure 28a. Figure 29 shows Fourier diffractograms taken from the images, together with an electron diffraction pattern. Compared with the other spots, the diffraction spots indicated by the arrowheads in the electron diffraction pattern (Fig. 29a) have strong intensity in a kinematical approximation, just as in X-ray diffraction. These strong spots have lattice spacings of about 0.2 nm and result from the nearest-neighbor atom pairs. The Fourier diffractogram of Figure 29b, which was obtained from the image of Figure 28a, is formed by reflections inside the strong reflections with lattice spacings of about 0.2 nm, which are enhanced by multiple scattering in the relatively thick sample. This is the reason why the lattice image of Figure 28a has information about quasilattices but little information about atomic arrangements. The diffractogram of Figure 29c, however, obtained from the image of Figure 28b, reproduces well an intensity distribution of the electron diffraction pattern, so the structure image of Figure 28b can be considered to have information about the atomic arrangement. It can be said that the structure images taken under strict conditions and from thin samples reflect faithfully atomic arrangements projected along the fivefold symmetry axis, and the dark and bright regions in the observed images correspond to the high- and low-potential regions, respectively. The detailed interpretation of the lattice and structure images is mentioned again in the section VI.

FIGURE29. (a) Electron diffraction pattem of the A1-Mn-Si icosahedral phase, (b) Fourier diffractogram of the lattice image of Figure 28a, and (c) Fourier diffractogram of the structure image of Figure 28b.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

35

FIGURE30. HRTEMimage of an A1-Pd-Mn decagonal phase, taken with the incident beam parallel to the 10-fold symmetry axis. A structure image in a thin region of the left side and a lattice image in a thick region of the right side are observed.

B. Decagonal Quasicrystals Figure 30 shows an HRTEM image of an A 1 - P d - M n stable decagonal phase, taken with the incident beam parallel to the periodic axis. It is well known that image contrast of HRTEM images is extremely sensitive to instrumental conditions such as defocus value and sample thickness. From the Fresnel fringes at the edge of an amorphous film, indicated by a black arrowhead in Figure 30, one can see that the image was taken with an optimum defocus near the Scherzer defocus of 45 nm. In Figure 30, one can also see a contrast change with increasing sample thickness from the left side of the micrograph to the fight side. In the thin region on the left side in Figure 30, a structure image reflecting projected potential is observed, whereas a lattice image showing a distribution of some atom clusters, which are represented as ring contrasts, is observed in a thick region of the fight region. The structure image can give us valuable information about the atomic arrangement in a local region, and from the lattice image one can obtain the arrangement of some atom clusters in a wide region.

36

KENJI HIRAGA VI. STRUCTURE OF ICOSAHEDRAL QUASICRYSTALS

A. Topological Features of lcosahedral Quasicrystalline Lattices In the initial studies of quasicrystals, nearly all the HRTEM images reported were lattice images taken with a 200-kV microscope having a resolution of about 0.23 nm. Figure 3 l a is a typical lattice image, taken from an A1-Mn icosahedral quasicrystal. Figure 3 lb is an electron diffraction pattern and Figure 3 lc is a Fourier diffractogram of the lattice image. The micrograph was taken in the very early days, just after the report by Shechtman et al. (1984), with a 200-kV electron microscope with a resolution of 0.23 nm (Hiraga, Hirabayashi, Inoue, and Masumoto, 1985). In the image of Figure 31 a, one can clearly see a homogeneous distribution of sharp bright dots and their straight array on lines parallel to the fivefold directions. The existence of sharp bright dots in the image also shows that the topological features forming the bright dots are arrayed along lines parallel to the incident beam. The homogeneous distribution of bright dots ruled out the models that explain the diffraction patterns with icosahedral symmetry in terms of large unit cells and/or multiply twinned crystals (Field and Fraser, 1984-1985; Pauling, 1985) and showed clearly the existence of longrange quasiperiodicity producing a diffraction pattern with fivefold rotational symmetry. Characteristics of the bright-dot distribution in the lattice image can be seen clearly on the enlarged image in Figure 32a. In this image one can see the characters of the distribution of the bright dots: they form pentagons of various sizes as well as being arrayed on the straight lines parallel to the fivefold directions. These characteristics can also be seen in the projection of the three-dimensional Penrose lattice along the fivefold symmetry axis, as shown in Figure 33a. Open circles correspond to vertices of fundamental rhombohedral units forming the three-dimensional Penrose lattices. In Figure 33a, one can see that the open circles are arrayed on straight lines along the fivefold directions, indicated with long arrows, and form pentagons of various sizes associated with a r scaling, indicated by lines. In the observed image, a pentagonal tiling can also be constructed by connecting the bright dots with lines, as indicated in Figure 32b (Hiraga, Hirabayashi, Inoue, and Masumoto, 1987). Assuming that a lattice spacing of the icosahedral quasicrystal (corresponding to the edge length of the fundamental rhombohedra) is 0.46 nm, the pentagonal tiling in the observed image corresponds to a tiling of the pentagon, indicated by a short arrow, in Figure 33a. One-dimensional sequences of lattice planes (bright-dot rows) in Figure 32a can be described as an arrangement of two intervals, indicated by dl and ds (dl = rds). If the distances dl and ds are replaced with the unit vectors in the x and y

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

37

FIGURE 31. (a) HRTEM lattice image and (b) electron diffraction pattern of the A1-Mn icosahedral phase, taken with the incident beam parallel to the fivefold symmetry axis. (c) Optical diffractogram of the observed image in (a) (Hiraga, Hirabayashi, Inoue, and Masumoto, 1985).

38

KENJI HIRAGA

FIGURE32. (a) HRTEM lattice image of an A1-Mn-Si icosahedral phase. (b) A pentagonal tiling constructed by the connection of bright dots in (a).

directions, respectively, one obtains the diagram of Figure 33b, the slope of which is 1/z (Hiraga, 1991 a). This means that the one-dimensional sequence of lattice planes corresponds to a quasiperiodic lattice which can be obtained by the projection of square lattices onto a line with a slope of 1/z as shown in Figure 1. In quasicrystals with linear phason strain, a change of the average slope from 1/z was observed (Hiraga, Lee et al., 1989). It should be noted that lattice images such as Figure 32a show features of lattices averaged over a thickness of a few tens of nanometers. Topological

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FIGURE 33. (a) Projection of the three-dimensional Penrose tiling along the fivefold symmetry axis. Open circles are vertices of the fundamental rhombohedra. Note that the open circles lie along the fivefold directions and form pentagons of various sizes. Compare the arrangement of circles with that of the bright dots in Figure 32. (b) The one-dimensional sequence of lattice planes (arrays of bright dots) in Figure 32 is described by replacing ds and dl with the unit vectors in the y and x directions, respectively. Note that the slope of lines in (b) is 1/r (Hiraga, Lincoln et al., 1991).

features of the averaged quasilattices in the icosahedral quasicrystals are in good agreement with those of the three-dimensional Penrose lattices. The lattice images also give us information about linear phason strains and dislocations, but they provide little information about random phason strain corresponding to local modification, because the images observed are projections along the incident beam.

B. Atomic Arrangements of lcosahedral Quasicrystals Figure 34 shows HRTEM structure images of A1-Pd-Mn and A1-Li-Cu icosahedral phases, taken with the incident beam parallel to the fivefold axis. In the images we notice characteristic image contrast distributions consisting of 10 bright dots surrounding a bright ring and a central dark dot, as enclosed by circles. This image contrast distribution is called decagonal contrast in this section. The decagonal contrast can be interpreted as an atom cluster with icosahedral symmetry. It is well known that atom clusters with icosahedral symmetry are formed with nearly close-packed atomic arrangements. Figure 35d is a triacontahedral atom cluster, considered to be a structure unit of the Frank-Kasper-type icosahedral phase, exemplified by an AI-Li-Cu icosahedral phase (Audier

40

KENJI HIRAGA

FIGURE 34. HRTEM structure images of (a) A1-Pd-Mn and (b) A1-Li-Cu icosahedral phases, taken with the incident beam parallel to the fivefold axis. Note decagonal contrasts consisting of 10 bright dots surrounding a bright ring, indicated by black circles.

et al., 1986; Henley and Elser, 1986). Figure 35e is called a Mackay icosahedral atom cluster, which is suggested to be an important structure unit in the structure of A1-Mn (Elser and Henley, 1985; Guyot and Audier, 1985). These atom clusters can be formed from the basic icosahedral atom cluster of Figure 35a. There are two ways that atoms can be put on the icosahedral

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

41

FIGURE35. (a) Fundamental icosahedral cluster. (b) Tetrahedral arrangement on the icosahedral cluster. (c) Octahedral arrangement on the icosahedral atom cluster. (d) Triacontahedral atom cluster constructed by tetrahedral arrangement (b). (e) Mackay icosahedral atom cluster formed by octahedral arrangement (c).

cluster. One is a tetrahedral arrangement in which one atom is put on three atoms (Fig. 35b), and the other is an octahedral arrangement in which three atoms are rotated and put on three atoms of the icosahedral cluster (Fig. 35c). Putting atoms with the tetrahedral arrangement yields the triacontahedral atom cluster of Figure 35d, and the octahedral arrangement leads to the icosahedral atom cluster of Figure 35e. Atomic arrangements of the triacontahedral and icosahedral atom clusters, projected along the fivefold axis, are shown in Figures 36a and 36b, respectively. In these atomic arrangements, one can see a characteristic atomic arrangement, similar for both clusters, in the central part: that is, double decagonal atom tings surrounding a central atom and the large decagonal ring. From these atom arrangements, one can expect a structure image contrast, as shown in Figure 36c (Hiraga, 1990, 1991a, 1991b; Hiraga and Shindo, 1990). As mentioned before, in the structure images taken from thin regions, high-potential

42

KENJI HIRAGA

FIGURE36. Atomic arrangements of (a) the triacontahedral atom cluster and (b) the Mackay icosahedral cluster, projected along the fivefold symmetry axis. (c) HRTEM structure image calculated from an arrangement of the Mackay atom cluster (b).

regions (i.e., atom positions) are seen as dark regions, and low-potential regions without atoms are seen as bright regions. Thus, the central atom becomes a central dark dot, the double decagonal atom ring becomes a dark ring, the ring channel between the central atom and the double decagonal tings becomes a bright ring, and the 10 channels outside become 10 bright dots. The calculated image contrast (Fig. 36c) is in good correspondence with the decagonal contrast in Figure 34. It is suggested that the triacontahedral and icosahedral atom clusters occupy special positions in the three-dimensional Penrose lattice (i.e., the 12-fold positions proposed by Henley, 1986) (Yamamoto and Hiraga, 1988). The 12-fold positions can be considered to be the special sites on which the atom clusters are located to give dense packing in space by the three types of linkages of Figure 37. Figure 38a shows a projection of the 12-fold positions on the

FIGURE 37. Three types of linkages of triacontahedral atom clusters, located at 12-fold positions in the three-dimensional Penrose lattice.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

43

FIGURE 38. (a) Twelve-fold positions in the three-dimensional Penrose lattice, projected along the fivefold symmetry axis. Large and small dots correspond to the 12-fold positions and vertices of the fundamental rhombohedra forming the Penrose lattice, respectively. (b) Atomic arrangementformed by placingthe triacontahedral atom clusters (Fig. 36a) at the 12-foldpositions indicated by small black arrowheads in (a). (c) Expected image contrast. In (c), dark regions correspond to bright regions in the observed structure image of Figure 34b (Hiraga, 1990).

three-dimensional Penrose lattice along the fivefold axis. An atomic arrangement, which is formed by placing the triacontahedral atom clusters at the 12-fold positions indicated with black arrowheads in Figure 38a, is shown in Figure 38b, and the expected contrast distribution of bright regions is shown in Figure 38c. The image contrast distributions are observed in the observed structure image of Figure 34b. Hence, it can be concluded that the observed structure images of Figure 34 can be well interpreted by the model in which the icosahedral atom or triacontahedral atom clusters are situated at 12-fold positions. However, to our regret, from the image contrast we cannot distinguish between the triacontahedral and icosahedral atom clusters and cannot determine real three-dimensional arrangements of the atom clusters. Finally, it should be mentioned that an important atom cluster with icosahedral symmetry has recently been found in a crystalline approximant referred to as the fl-(A1PdMnSi) phase. The/3-(A1PdMnSi) phase, referred to as a 2/1 crystalline approximant, has a composition of approximate A170Pd23Mn6Si1, which is close to the composition A172Pd20Mn8 of the icosahedral phase, and a cubic structure with a lattice constant of 2.0211 nm and the space group of Pm3 (Sugiyama, Kaji, Hiraga et al., 1998). In this structure, a large dodecahedral atom cluster with icosahedral symmetry is located at the 1/2, 1/2, 1/2 position.

44

KENJI HIRAGA

The dodecahedral atom cluster can be divided into 19 atom shells, which are formed by atoms with similar distances from the 1/2, 1/2, 1/2 position, of polyhedra with icosahedral symmetry, as shown in Figure 39 (Hiraga, 1999; Hiraga, Sugiyama, and Ohsuna, 1998a). In the successive atom shells in Figure 39, one can see some interesting points associated with the golden ratio r. The atom shells in the actual atom cluster of the/3-(A1PdMnSi) structure have no exact icosahedral symmetry, owing to cubic symmetry, but "ideal" polyhedra of the atom shells can be considered to have icosahedral symmetry. That is, ideal polyhedra of the 1st, 3rd, 6th, 9th, and 15th shells are regular icosahedra, and the 2nd, 5th, 12th, and 19th shells are regular dodecahedra. The icosahedra of the 1st, 3rd, 6th, and 15th shells enlarge with a scaling of about r. The dodecahedra of the 2nd, 5th, and 12th shells are growing with a scaling of about r, and the size of the 19th shell is nearly (1 + 1/ r) times as large as that of the 12th shell. Also, it can be said that ideal polyhedra of the 4th and 10th shells are constructed with regular pentagons and deformed hexagons with two edge lengths having a ratio 1:r, and sizes of the 4th and 10th shells are associated with r. The polyhedron of the 7th shell is formed with regular pentagons, regular triangles, and golden rectangles with edge lengths having a ratio 1:r. The polyhedra of the 8th, 13th, and 17th shells with the same shape have sizes with a ratio of about 1: ( 2 - (1/r)):r. As mentioned previously, all the atoms are located at vertices of the polyhedra closely related to the golden ratio. The dodecahedron of the 12th shell internally touches the surface of the cubic unit cell and is joined to the same shells in adjoining unit cells by sharing an edge, as shown in Figure 40. At each vertex of the dodecahedron, an icosahedral atom cluster consisting of a central Pd atom and 12 A1 atoms is located. Therefore, the dodecahedral atom clusters are connected to each other by sharing two icosahedral atom clusters with so-called twofold linkages. The structure of an A1-Pd-Mn icosahedral quasicrystal can be considered to be formed by the same cluster and the same linkage of sharing two icosahedral clusters. From this dodecahedral atom cluster, a structure model of the A1Pd-Mn icosahedral quasicrystal has been proposed by the projection method (Yamamoto and Hiraga, 2000).

C. Defects in Icosahedral Quasicrystals 1. Linear Phason Strain By close examination of the image of Figure 31 with oblique viewing along the vertical direction, one can see frequent displacements of the bright-dot arrays. The displacements are often observed in the rapidly solidified quasicrystals and are interpreted in terms of quenched linear phason strain (Socolar et al., 1986).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

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FIGURE 39. Successive atom shells at the 1/2, 1/2, 1/2 position in a/3-(A1PdMnSi) crystalline phase. (Reprinted from Hiraga, K., 1998. Atom clusters in a 2/1 cubic approximant phase for understanding the structures of icosahedral phases. Mater. Res. Soc. Symp. Proc. 553, pp. 107-116, with permission from The Materials Research Society.)

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FIGURE 40. Edge-sharing linkage of the dodecahedral atom shell (12) of Figure 39 and icosahedral cluster located at vertices. (Reprinted from Hiraga, K., 1998. Atom clusters in a 2/1 cubic approximant phase for understanding the structures of icosahedral phases. Mater. Res. Soc. Syrup. Proc. 553, pp. 107-116, with permission from The Materials Research Society.)

The linear phason strain is considered to be related to the growth process of quasicrystalline domains (Hiraga and Hirabayashi, 1987a). Figure 41a is an ordinary bright-field electron micrograph showing dendritic growth of the A1-Mn-Si icosahedral phase. From the morphology of the dendrite, the quasicrystalline grain is supposed to grow from the left side to the fight side, as indicated by black arrows. Figure 41 b shows an HRTEM lattice image of the rectangular area indicated in Figure 41 a. In the lattice image, bright dots aligned along the fivefold directions, p, q, r, s, and t, are distributed homogeneously over the whole region. With close examination, by viewing Figure 4 l b obliquely along the fivefold directions, however, one notices that the bright-dot rows are frequently displaced. The density of the displacements of bright-dot rows depends on the directions, as illustrated schematically in Figure 42. That is, no shift appears along the t direction, which is nearly parallel to the growth direction of the quasicrystalline grain and a few shifts appear along the s and p directions, whereas a fairly high density of the shifts exists along the q and r directions. We also notice that the shifts along the q and r directions are concentrated at the upper region C of Figure 41 b, but almost disappear at the lower area D near the edge of the observed quasicrystalline grain. In Figures 41 c and 41 d, two optical diffractograms taken from the high-density

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

47

FIGURE 41. (a) Conventional transmission electron micrograph showing the growth morphology of an icosahedral quasicrystal in the melt-quenched A174Mn20Si6 alloy. Black arrows show growth directions of the quasicrystalline domains. (b) HRTEM lattice image of the rectangular region in (a). A large black arrow shows the growth direction. (c and d) Optical diffractograms taken from the C and D regions in (b) (Hiraga and Hirabayashi, 1987a).

48

KENJI HIRAGA

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rd

s

FIGURE42. Schematic illustration of displacements of lattice planes (lines of bright dots) in region C of Figure 41b (Hiraga and Hirabayashi, 1987a). area C and the low-density area D are inserted. Diffraction spots in the pattern of Figure 41 d are located at nearly the exact positions with fivefold symmetry, but those of Figure 4 l c are clearly shifted from the positions of fivefold symmetry along the vertical directions, as indicated by white arrows. The shifts of spots in reciprocal space as well as displacements of bright-dot rows in real space can be interpreted in terms of anisotropic phason strain (i.e., linear phason strain) (Socolar et al., 1986). If the linear phason strain persists along one of the fivefold directions, the diffraction spots shift along the corresponding direction in the reciprocal space. In the image of Figure 4 lb, the linear phason strain lies almost perpendicular to the t direction; that is, approximately to the quasicrystal growth direction. It is natural that the frozen linear phason strain is relaxed in the vicinity of the edges of grown quasicrystals. This is clear in the optical diffractogram of Figure 41 d taken from the D area near the edge of the quasicrystalline domain. In the pattern, all the spots are located very close to exact fivefold symmetry positions, showing no linear phason strain. The frozen linear phason strain can also be relaxed and virtually disappears by annealing at high temperatures for stable quasicrystal phases (Guryan et al., 1989; Hiraga, 1989). Figure 20 shows electron diffraction patterns of as-casted A1-Ru-Cu and annealed A1-Ru-Cu icosahedral quasicrystals at about 850~ In Figure 20a, the diffraction spots are systematically displaced from icosahedral symmetry positions. That is, one can apparently see zigzag arrays of spots, particularly weak spots, by viewing along the J and K directions, also along the I direction with smaller amounts of displacements. In contrast, the diffraction spots located on the lines parallel to the H direction show a straight-line array. The displacements can also be seen as the deformation of pentagons formed by the diffraction spots, particularly for small pentagons. The displacements of diffraction spots in Figure 20a disappear completely in the diffraction pattern of Figure 20b. That is, the frozen linear phason strain in the as-casted alloy is perfectly relaxed and disappears by

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 49 annealing at a high temperature of about 850~ The diffraction spots displaced from the icosahedral symmetry positions in Figure 20a are extremely sharp. The result shows that the linear phason strain exists as homogeneous strain with long-range correlation. 2. Dislocations

The existence of dislocations in icosahedral quasicrystals was first found by observations of HRTEM lattice images of the A1-Mn-Si icosahedral phase (Hiraga and Hirabayashi, 1987b). Figures 43a and 43b are lattice images showing dislocations. We may determine the Burgers vector on the plane perpendicular to the fivefold symmetry axis by counting the number of lattice fringes around the dislocations with two types of fringe distances, dl and ds in Figure 43. In Figure 43a, lattice fringes along the A and B directions are shown by black and white lines, respectively. These fringes make closed circuits STUS and P Q R P surrounding a dislocation core, where T U and QR coincide with the directions A and B, respectively. The difference in the number of lattice fringes along the A direction between the paths from S to T and from S to U is measured as 10 ds - 6dl, whereas that along the B direction between the paths from P to Q and from P to R is 2dl - 3ds. The number of lattice fringes in the upper side is always larger than that in the lower side. Taking account of the relation dl = r ds, the differences in fringe numbers, A, along the A, B, C, D, and E directions may be determined respectively as A A =

(10

--

6r)ds

AB = Ae = (2r - 3)ds = r-3ds

(1)

Ac = Ao = (5r - 8)ds In Figure 43b there are two dislocations, X and Y, whose Burgers vectors have the same magnitude with opposite signs. This is evident from the fact that the difference in fringe numbers between H - I and J - I around the dislocation X is ( 3 r - 5)d~, whereas that between I - K and I - L around the dislocation Y is (5 - 3r)ds. The differences in fringe numbers along the five directions around Y may be measured as follows: A a --- A B ~-- ( 5 -

3r)ds = r-4ds

Ac = Ae = (5r -- 8)d~ =

.~-1 aa

(2)

AD = 0 This type of dislocation is similar to that predicted by Levine et al. (1985) in the context of their density-wave description of icosahedral quasicrystals.

50

KENJI HIRAGA

FIGURE 43. HRTEM images of the A1-Mn-Si icosahedral quasicrystal, showing the existence of dislocations. Lattice fringes with distances dl and ds are marked by dark and white lines so that the number of fringes along the Burgers circuits around dislocation cores can be counted (Hiraga and Hirabayashi, 1987b).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

51

Equations (1) and (2) describe the Burgers vectors on the plane perpendicular to the fivefold symmetry axis. m E = m A ~-- (5 -

3r)ds

A 8 = A D = ( 5 r --

8)ds

(3)

Ac=O are derived from Eq. (2) by rotating the axis by an angle of re/5. The sum of Eqs. (2) and (3) corresponds to the relations of Eq. (1). This fact implies that the dislocation in Figure 43a is composed of two elemental dislocations with the equivalent Burgers vectors; the cores of the two dislocations are barely distinguishable, with bright and dark diffraction contrast.

V I I . STRUCTURE OF DECAGONAL QUASICRYSTALS AND THEIR RELATED CRYSTALLINE PHASES

Since the discovery of decagonal quasicrystals, by Bendersky (1985) and Chattopadhyay et al. (1985), in rapidly solidified Al-rich manganese alloys, many decagonal phases have been found as metastable or stable phases in A1based binary and ternary alloys. HRTEM images of decagonal quasicrystals, taken with the incident beam parallel to the periodic axis, are easily interpreted, compared with those of icosahedral quasicrystals, because of periodic structures along the incident beam, and they make it possible to determine two-dimensional quasiperiodic structures directly. Current HRTEM studies of the decagonal quasicrystals have shown that their structures are interpreted as two-dimensional quasiperiodic arrangements formed with definite linkages of columnar atom clusters having a large decagonal section. Also, it has been found that there are not only various sizes of the atom clusters, but also various tilings of the atom clusters. In this section, I present detailed results for some decagonal quasicrystals to facilitate understanding of the structural characteristics of all the decagonal quasicrystals, and also of icosahedral quasicrystals.

A. Framework of Columnar Atom Clusters

Columnar atom clusters with decagonal sections of various sizes have been found so far and their sections can be described in the rhombic Penrose lattice with a bond length of 0.25 nm, as shown in Figure 44. The sizes of the decagonal clusters, A, B, C, and D, increase with a scaling of r and are about 0.76-, 1.2-, 2.0-, and 3.2-nm, respectively, in diameter. The smallest decagon, A,

52

K_ENJIHIRAGA 0.25 nm

".2."

FIGURE44. Fourdecagonal sectionsof columnaratom clusters in the rhombicPenrose lattice.

was found in an A1-Pd decagonal quasicrystal with 1.6-nm periodicity (Hiraga, Abe et al., 1994). Conversely, the decagon C was found in many decagonal quasicrystals of A1-Pd-Mn with 1.2-nm periodicity (Hiraga and Sun, 1993b), and A1-Co-Ni (Hiraga, Sun, and Yamamoto, 1994) and A1-Ni-Ru (Sun, Ohsuna, and Hiraga, 2001) with 0.4-nm periodicity. This decagon can be characterized by a pentagonal and decagonal frame, shown by thin solid lines in Figure 44, and is formed by connecting the centers of pentagons. The largest decagon, D, was found in decagonal quasicrystals of A1-Co-Ni (Hiraga and Ohsuna, 2001 a), A1-Cu-Rh (Hiraga, Ohsuna, and Park, 2001), and A1-Ni-Fe (Hiraga and Ohsuna, 200 lb). The decagonal clusters are joined by the edgesharing linkage and interpenetrating linkage, as shown in Figures 45a and 45b. The bond distance in the interpenetrating linkage is 1/r times as short as that of the edge-sharing linkage and corresponds to a short diagonal of a thin rhombus, which is one tile in the rhombic Penrose tiling. The columnar atom clusters with decagonal sections are important structural units in the decagonal quasicrystals, and the edge-sharing and interpenetrating linkages of the decagonal clusters form bonds along the fivefold rotational directions and produce a bond-orientational order. This order is one of the important features of quasicrystal structures, as shown in Figure 45c.

B. Decagonal Quasicrystals and Crystalline Phases with 0.4-nm Periodicity The decagonal quasicrystals with 0.4-nm periodicity have been found in A1Co-Ni (Tsai, Inoue, and Masumoto, 1989a), A1-Co-Cu (Tsai, Inoue, and Masumoto, 1988), A1-Ni-Fe (Lemmerz et al., 1994), A1-Cu-Rh (Tsai, Inoue,

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 53

a

b

C

(

t

)

FIGURE45. (a) Edge-sharing and (b) interpenetrating linkages of the decagonal cluster D in Figure 44. (c) Pentagonal and rhombic quasiperiodic lattices formedby the two types of linkages. and Masumoto, 1989c), and A1-Ni-Ru (Sun, Ohsuna, and Hiraga, 2000) alloys, and all of them are stable and highly ordered decagonal quasicrystals. In particular, the A1-Co-Ni decagonal phase has received much attention, because of the appearance of several modulations of decagonal quasicrystals, showing highly ordered diffraction patterns or several different types of diffraction patterns with superlattice reflections, and some crystalline approximants (Edagawa et al., 1992; Grusko et al., 1998; Hiraga, Lincoln etal., 1991; Ritsch, Beeli et al., 1998; Tsai, Fujiwara et al., 1996; Tsai, Inoue, and Masumoto, 1989a). On the one hand, highly ordered diffraction patterns, which can be interpreted from a pentagonal Penrose filing (Hiraga, Sun, and Yamamoto, 1994), with a period of 0.4 nm along the periodic axis have been observed in the Ni-rich side. Therefore, this decagonal quasicrystal is called a Ni-rich basic structure (Ritsch, Beeli et al., 1998). On the other hand, decagonal

54

KENJI HIRAGA

quasicrystals with various types of diffraction patterns, most of which include so-called superlattice reflections, have been observed in the Co-rich side. In the diffraction patterns of these decagonal quasicrystals in the Co-rich side, diffuse reflections showing periodicity of 0.8 nm have been observed, and the intensity of the diffuse reflection enhances with increasing Co content. That is to say, in the A1-Co-Ni decagonal phase, there exist a variety of polymorphisms of decagonal quasicrystals, which have different structures on quasiperiodic planes perpendicular to the periodic axis and different periods along the periodic axis. So that the structures of these decagonal quasicrystals can be revealed, many studies have been made by electron diffraction analysis, HRTEM, and HAADF-STEM. Recently, precise structural analysis of a crystalline approximant, which is found in alloys around A172.sCo20.sNi7, annealed at 950~ for a long time (Hiraga, Ohsuna, and Nishimura, 2001 a), has been performed by X-ray diffraction analysis using a single crystal (Sugiyama, Nishimura et al., submitted). The structure of the crystalline approximant, which is called a W - ( A I C o N i ) crystal, enables us to discuss the structures of the A1-Co-Ni decagonal quasicrystals in detail. In this section, I mention the structural characteristics of A1-Co-Ni decagonal quasicrystals on the basis of results on the modulations of A1-Co-Ni decagonal quasicrystals--referred to as S 1-type (Hiraga, Ohsuna, and Nishimura, 2000), type I (Hiraga, Ohsuna, Nishimura et al., 2001), type II (Hiraga, Ohsuna, and Nishimura, 2001 b), and pentagonal superstructures (Hiraga, Ohsuna, and Nishimura, 2001 c); Ni-rich (Hiraga and Ohsuna, 2001 a) and Co-rich (Hiraga, Sun, and Ohsuna, 2001) basic structures; and one-dimensional quasicrystals (Hiraga, Ohsuna, and Nishimura, 2 0 0 1 ) all of whose diffraction patterns are shown in Figures 25 and 26, and two crystalline approximants (Hiraga, Ohsuna, and Nishimura, 2001a; Hiraga, Ohsuna, Yubuta et al., 2001). 1. A t o m Cluster

Figure 46 shows HRTEM images revealing contrast distributions of the clusters with decagonal sections of 2.0 and 3.2 nm in diameter, in the modulations of the Ni-rich basic structure (Fig. 46a), S 1-type (Fig. 46b) and type I (Fig. 46c) superstructures, and W-(A1CoNi) crystalline approximant (Fig. 46d), all of which are found in and around the A1-Co-Ni decagonal phase. The atom clusters with decagonal sections of 2.0 and 3.2 nm in diameter are called 2.0and 3.2-nm atom clusters hereafter. In Figure 46, one can see special image contrasts consisting of ring contrasts surrounding a wheel-like contrast. These contrast features can be characterized by a frame of pentagons surrounding a decagon, as shown by dotted lines in Figure 46. The ring contrasts and wheellike contrasts are located in the pentagonal and decagonal frames, respectively. The pentagonal and decagonal frame with a bond length of 0.47 nm and decagons of 2.0 and 3.2 nm in diameter correspond to those in Figure 44. The structure of the Ni-rich basic decagonal quasicrystal is formed by edge-sharing

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

55

FIGURE46. HRTEMimages of the atom clusters in the modulations of A1-Co-Ni decagonal quasicrystals: (a) Ni-rich basic structure, (b) S 1-type and (c) type I superlattices, and (d) W(A1CoNi) crystalline phase. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.) and interpenetrating linkages of the 3.2-nm clusters, as shown in Figure 45. The distance of two clusters in the interpenetrating linkage of Figure 45b is a short diagonal of a thin rhombus and 3 . 2 / r = 2.0 nm. The other modulations of the A 1 - C o - N i decagonal quasicrystals have structures formed by aperiodic arrangements of the 2.0-nm clusters, which are connected to each other by three linkages of Figure 47. The edge-sharing linkage (Fig. 47a) of the 2.0-nm clusters produces a bond with a length of 2.0 nm, and the interpenetrating linkage (Fig. 47b) with a distance of 2 . 0 / r = 1.2 nm corresponds to a short diagonal of the thin rhombus. A short diagonal of a fat rhombus is about 2.35 nm, and in this linkage the deformation of pentagonal frames occurs, as shown

56

KENJI HIRAGA a

C

I

i

1

w1 \

FIGURE47. Three types of linkages of the 2.0-nm clusters. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.) in Figure 47c. The linkages of the 2.0-nm clusters and the deformation of the pentagonal frames can be seen in Figures 46b and 46c. As for the W-(A1CoNi) crystalline structure (Fig. 46d), the 2.0-nm clusters are connected with each other by the linkages of Figures 47a and 47b and form a periodic arrangement with the pentagonal and rhombic frames of Figure 48. Figure 49 shows HAADF-STEM images of the same samples as those of Figure 46. Bright contrasts in the HAADF-STEM images correspond to transition-metal atoms, which have large atomic numbers. As a rough approximation, images of Figure 49 have reversed contrasts of those in Figure 46. In Figure 49, the 3.2- and 2.0-nm clusters are indicated by decagons. One can notice that Figures 49b, 49c, and 49d show the same contrast distribution of the 2.0-nm clusters, which consists of two decagonal circles of bright dots surrounding a pentagonal arrangement of bright dots, and that the clusters are connected with each other by sharing a bright dot in the outer decagonal circle with an interval of 2.0 nm and by sharing two bright dots in the inner decagonal

a/2

FIGURE48. Pentagonal and decagonal frame in the W-(A1CoNi) crystalline structure, obtained from Figure 46d.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

57

FIGURE49. HAADF-STEM images of the same samples as those of Figure 46. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 23542367, with permission from The Japan Institute of Metals.)

circle along a short diagonal of the thin rhombus. This feature can also be seen in the HAADF-STEM image of the W-(A1CoNi) phase (Fig. 49d). The contrast distribution of the 3.2-nm cluster in Figure 49a consists of fourfold decagonal circles of bright dots surrounding a central contrast. The decagonal circles of 20 and 10 bright dots surround the inner double decagonal circles, which are similar to those of the 2.0-nm cluster. From close examination of Figure 49, one can notice that, compared with bright dots in the other decagonal arrangements, bright dots (indicated by a pair of small white arrows in Fig. 49a) of the second decagonal circle surrounding central contrasts are slightly elongated along the circumference, and that the 20 bright dots of third circles in the 3.2-nm cluster (Fig. 49a) are arranged with long and short

58

KENJI HIRAGA

distances indicated by L and S. These features will be better understood from arrangements of transition-metal atoms, which are mentioned later. The pentagonal contrasts at the centers of the 2.0-nm clusters can be clearly seen with two orientations in Figure 49b and with one orientation in Figures 49c and 49d. These contrasts can barely be seen from the HRTEM observations of Figure 46. Thus, the combination of HAADF-STEM and HRTEM observations can give us more detailed information about the structures of decagonal quasicrystals. 2. Structural Models of Atom Clusters As can be seen from Figures 46 and 49, the structure of the W-(A1CoNi) phase is closely related to the structures of the A1-Co-Ni decagonal quasicrystals. Particularly, it has been found that electron diffraction patterns of the W-(A1CoNi) phase closely resemble those of the pentagonal A1-Co-Ni quasicrystal with 0.8-nm periodicity (Hiraga, Ohsuna, and Nishimura, 2001 a). Therefore, it is worthwhile to derive structural models of the atom clusters from the W-(A1CoNi) structure. The W-(A1CoNi) phase, which is found in an A172.sNiT.sCo20 alloy annealed at 950~ is slightly different from the W (A1CoPd) phase (Yubuta et al., 1997) and has a monoclinic structure with lattice parameters a = 3.99 nm, b = 0.82 nm, c = 2.36 nm, and fl = 90 ~ and the space group of Cm (No. 8). Therefore, the W-(A1CoNi) phase can be said to be a crystalline approximant of the A1-Co-Ni decagonal quasicrystals with 0.8-nm periodicity. However, in the A1-Co-Ni phase, decagonal quasicrystals with 0.8- and 0.4-nm periodicity exist in the Co-rich and Ni-rich sides, respectively, and both the quasicrystals are continuously changed, although in the intermediate state diffraction spots showing 0.8-nm periodicity become diffuse. In this section, I discuss models of two clusters with 0.8- and 0.4-nm periodicity from the W-(A1CoNi) structure. Figure 50 shows an atomic arrangement of the W-(A1CoNi) phase, which was determined by single-crystal X-ray diffraction, in the pentagonal and decagonal frame and rhombic Penrose lattice. The structure of the W-(A1CoNi) phase can be described by the four layers along the b axis. The layer of y = 1/2 is a mirror plane, so atomic arrangements in the y = 1/4 and 3/4 layers have mirror symmetry. However, the atomic arrangement of y = 1/2 corresponds to that of y = 0 shifted with x = 1/2 along the a axis. Therefore, the structure of the W-(A1CoNi) phase has a stacking of A B A ' B along the b axis. All atoms on the A and A' layers are located on y - - 0 and 1/2 planes, whereas atoms on the B layer are distributed in the range of y = 1/4 4- 0.06, as can be seen in Figure 50d, in which the projection of the structure along the c axis is shown. However, it should be noted that atoms distributed in the wide range are A1 atom and mixed atom positions, and transition-metal atom positions are localized in the narrow range of y = 1/4 • 0.002.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

;

.o.: o..o

.o

0

.-o-- 0-, .... ,,

" ' : d " d : : i - ....:'.: "O":i'

--:-,:ii%~P.~~-

..qii..~.i;;.r~

,::9.~...::::..>.:.ir ~ : .

qpt.

,...- :--~i-,: ii.o--~o:.

-.., P.:

59

A

.o--

;~:i t ~'" o: .... :o ".'4 ......o.'..."

"0

.....r ..--e,-,,. ~:-r

,..o::,:..,.::o.,,/o.:L;o~:.4,:i. A/~

"'o./.'.o-.'i~""o'~ " - - o " ~

"..

-(~:

-0.

6

:o

~

6"

"

6

i-"db-

d

v

b q P-o-~-o o.-,-.o.--o O-.o.O.--o o...o.--o.-o, o o-:---oi !"o-:.:-c~: , ,.--- .d'.--:' .: @':--,:;o ,,,---.,. , ,.'.- d'".--: ..: II --~:" : . . . . . " ""

~r

s...:,..,:;"a.a-:,

.::-~b:-q..~--.b--~o:"".oZ!.--o:--4:0--b.:,: 9 :o:"">/..,.-~: o~ 0 . . :i o--.."--o i..-c ~ p.. 1'o _ql"~::~174176 "~%ql".~ B -":

7"" '::":0 :" :O

" ' 4 i I .... "';:o it:

' -~" "~.--

"

0:1.>...o.:~ q"":c>~:..o.:-o:;..>--.c,-:!~q" ~/,.:-q:-q.l.b

~ ~ "...! 'o"~-o T..d:"% o--"'v;7170 --@-!...- --@ - '].-

~ "(

.... ~...~. b .....: e..~..o :.o./.: .o..... o. o. :

~.:.~o:.:o~i.--~:, .,..6..~,,.,s::.j~:. ~.o--?--O~ ....r ~ ~ ~ ' : - 6 r : s

o.:.1.:..o::; .J.-~

'. : i ~ ,..9

-::'q

'"Ji":::"8;i"~Y'::O:"i"~ii"r"~176

:.,.:.u.~:o ..o.X:i.~

:.u:~ ~176 :~

A'

~:-?o-:.~b-:"/--d~~:--;::-dZo-:?:-df:.~S

-..o~,::~...~:.::.?::~::o..:.:~.~7..o:..~.~ >:;i;- c

i~ ~176176

a~

d

l B A'

a~

A

FIGURE 50. Structure of the W-(A1CoNi) crystalline phase, which shows (a-c) atomic arrangements on three layers along the b axis and (d) the projection of the structure along the c axis. White and black circles correspond to A1 and transition-metal atom positions, respectively, and dark circles to mixed positions of A1 and transition-metal atoms. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. M a t e r Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.)

60

KENJI HIRAGA

FIGURE51. Simulated HRTEM image calculated from the structural model of Figure 50 along the b axis by using the multislice method with a sample thickness of 4 nm and a defocus of 45 nm.

In Figures 50a through 50c, one can see that transition-metal atoms are completely placed at lattice points of the rhombic Penrose lattice and form pentagonal lattices of bond lengths of 0.49 nm in the B layer and 0.77 nm in the A layer. Aluminum atoms are located at lattice points in the B layer, but some of the A1 atoms in the A layer are remarkably shifted from the lattice points. This shift and the distribution of atoms in wide regions around y = 1/4 and 3/4 planes in the B layer are caused by triangular arrangements of transition-metal atoms with slightly short atomic radii in the pentagonal frames of the A and A' layers. An HRTEM image of the W-(A1CoNi) phase, calculated from the model of Figure 50 along the b axis, is shown in Figure 51. One can see that the calculated image replicates well the contrast of Figure 46d, particularly ring contrasts and wheel-like contrasts. From the W-(A1CoNi) structure, it is worthwhile to derive structural models of the atom clusters. Figure 52 shows an ideal model of the 2.0-nm cluster with 0.8-nm periodicity, without taking account of the atomic shifts from lattice points. The structure of this cluster has a stacking of A B A'B along the columnar axis. It should be noted that atoms in the A and A' layers are placed on the planes of z = 0 and 1/2 (z is a coordinate along the columnar axis of the cluster), but most of the A1 atom and mixed atom positions in the B layer are distributed in some regions around z -- 1/4 and 3/4. In the model, one can see that the 0.8-nm periodicity of the cluster results from orientations of the rectangular arrangements of transition-metal atoms in the pentagonal frames. Therefore, the 2.0-nm cluster with 0.4-nm periodicity, which is found in the modulations in the Ni-rich side, can be presumed to have the structure shown in Figure 53. In this model, each of the triangular arrangements of transitionmetal atoms in the pentagonal frames of Figure 52 is replaced by a pair of transition-metal atoms. Consequently, this cluster has a stacking of A B along the columnar axis.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

61

FIGURE 52. Ideal structural model of the 2.0-nm cluster with 0.8-nm periodicity, which is shown by (a-c) atomic arrangements on three layers along the b axis. The structure of the cluster has a sequence of A B A ' B along the columnar axis. White and black circles correspond to A1 and transition-metal atom positions, respectively, and dark circles to mixed positions of A1 and transition-metal atoms. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.) The structures of m o s t of the A 1 - C o - N i d e c a g o n a l quasicrystals and their crystalline a p p r o x i m a n t s can be constructed by placing the structural m o d e l of the 2 . 0 - n m cluster of Figure 52 or Figure 53 in the p e n t a g o n a l and d e c a g o n a l flames of observed H R T E M images, such as in Figures 45b and 45c. Figure 54 shows a structural m o d e l of a crystalline a p p r o x i m a n t f o u n d in an A171.sCo16Ni12.5 alloy annealed at 9 0 0 ~ for 120 h (Hiraga, Ohsuna, and Nishimura, 2001 a). The crystalline phase, w h i c h is closely related to the type I

FIGURE 53. Ideal structural model of the 2.0-nm cluster with 0.4-nm periodicity, which is shown by (a and b) atomic arrangements on two layers along the b axis. The structure of the cluster has a sequence of A B along the columnar axis. White and black circles correspond to A1 and transition-metal atom positions, respectively, and dark circles to mixed positions of A1 and transition-metal atoms. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.)

62

KENJI HIRAGA

FIGURE 54. Atomic arrangement (on one layer) of a crystalline approximant found in an A171.5Co16Ni12.5alloy,obtained by placing the structural model of Figure 53 in the pentagonal and decagonal frame of an HRTEM image observed from this crystalline approximant. The atomic arrangement is shown in a half part of a unit cell. Dotted lines show thin and fat rhombuses. One can see three linkages of 2.0-nm clusters, shown in Figure 47, in this structure. White and black circles correspond to A1 and transition-metal atom positions, respectively, and dark circles to mixed positions of A1 and transition-metal atoms. A and B show the clusters with two different orientations of pentagonal symmetry. A 1 - C o - N i decagonal quasicrystal, has an orthorhombic structure with lattice parameters a = 5.2 nm, b = 0.4 nm, and c = 3.7 nm. From HAADF-STEM and HRTEM observations of the crystalline phase, its structure can be characterized by a periodic arrangement of the 2.0-nm clusters of two orientations with thin and fat rhombuses indicated by dotted lines in Figure 54, and described by a pentagonal and decagonal frame shown in Figure 54 (Hiraga, Ohsuna, and Nishimura, 2001 a). By assuming that these two types of clusters, A and B, are rotated at 180 ~ and shifted at c/2 (c is a period along the columnar axis in Figure 53), an arrangement of one layer in the crystalline phase can be derived easily from the structural model of Figure 53, as shown in Figure 54. Consequently, this atomic arrangement can be obtained directly by placing the structural model of Figure 53 in the pentagonal and decagonal frame obtained from an HRTEM image of this crystalline approximant, although there is the ambiguity of some transition-metal and mixed positions. In most of the modulations of A 1 - C o - N i decagonal quasicrystals, the diffuse scattering showing 0.8-nm periodicity is observed in their diffraction patterns and its intensity is gradually enhanced with increasing Co content. The diffuse scattering with peaks at definite positions associated with the golden ratio can be considered to be caused by the appearance of the clusters with 0.8-nm periodicity (Fig. 52) in an arrangement of the clusters of 0.4-nm periodicity (Fig. 53), or by the appearance of atomic arrangements such as that of Figure 52 in the structure of Figure 53.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

63

FIGURE55. Ideal structural model of the 3.2-nm decagonal columnar cluster with a 0.4-nm period along the columnar axis. The structure of the clusters has a sequence of A B along the columnar axis. White and black circles correspond to A1 and transition-metal atom positions, respectively. (Reprintedfrom Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama,K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants.Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.)

From the structural model of the 2.0-nm cluster with 0.4-nm periodicity, an ideal model of the 3.2-nm cluster in the Ni-rich basic structure can be derived, as shown in Figure 55. The diffraction patterns of the Ni-rich basic structure show that the 3.2-nm cluster has the c-glide (c is the periodic axis) plane or a 105 screw axis along the c axis. Also, an arrangement of transition-metal atoms can be estimated from the HAADF-STEM image of Figure 49a. The structure of Figure 55 is proposed as a positive model, which is derived by the HRTEM and HAADF-STEM images of the Ni-rich basic structure, and by speculation from the structures of the 2.0-nm clusters. The structural models of the 2.0- and 3.2-nm clusters (Figs. 52, 53, and 55) can easily be inferred to give contrast distributions of the atom clusters in observed HRTEM images (Fig. 46), from the structure and simulated image of the W-(A1CoNi) phase (Figs. 50 and 51). Also, it is easily understood that bright dots in HAADF-STEM images of the 2.0- and 3.2-nm clusters (Fig. 49) correspond to transition-metal atoms in the projections of the 2.0- and 3.2-nm clusters (Figs. 52, 53, and 55) along the columnar axes. The bright dot elongated along the circumference in the second decagonal circle surrounding the central contrast corresponds to two transition-metal atoms separated with an interval of 0.15 nm, and the bright dots arranged with two intervals of S and L (Fig. 49a) in the third decagonal circle in the 3.2-nm cluster corresponds to transition-metal atoms arranged with 0.47- and 0.40-nm intervals.

64

KENJI HIRAGA

3. Arrangements of Atom Clusters Columnar clusters of atoms with two different sizes of decagonal sections of 3.2 and 2.0 nm in diameter have been found in the modulations of A 1 - C o - N i decagonal quasicrystals. The structures of six m o d u l a t i o n s n t h e S 1-type, type I, and type II superstructures; the Co-rich basic structure; the pentagonal superstructure; and the one-dimensional q u a s i c r y s t a l n a r e described as aperiodic arrangements of the 2.0-nm clusters, whereas the Ni-rich basic structure is formed by the 3.2-nm clusters. In Figure 56, H A A D F - S T E M images of four modulationsmthe S 1-type (Fig. 56a) and type I (Fig. 56b) superstructures,

FIGURE 56. HAADF-STEM images of (a) the S 1-type superstructure, (b) the type I superstructure, (c) the Co-rich basic structure, and (d) the pentagonal superstructure of A1-Co-Ni decagonal quasicrystals, taken with the incident beam parallel to the periodic axis. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 23542367, with permission from The Japan Institute of Metals.)

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 65 the Co-rich basic structure (Fig. 56c), and the pentagonal superstructure (Fig. 56d)~are shown as examples. The HAADF-STEM images were formed during scanning of the incident beam, so the sample drift during scanning produced the local deformations of image contrasts. Although there are local deformations in Figure 56, one can easily see peculiar contrasts consisting of small pentagonal arrangements of bright dots in all the images, and that the pentagonal contrasts are arranged by aperiodic lattices with a bond length of 2.0 nm, as indicated by lines. The pentagonal contrast is surrounded by twofold decagonal arrangements of bright dots in the 2.0-nm cluster, as indicated by a circle in Figure 56a. Also, in Figure 56 one can see the existence of two types of pentagonal contrasts with two different orientations in Figures 56a and 56b, whereas all the pentagonal contrasts in Figures 56c and 56d have the same orientation. The aperiodic lattices, formed by connecting the pentagonal contrasts, namely, the centers of the 2.0-nm clusters, in observed HAADF-STEM images, are shown in Figure 57 for six modulations, namely, the S 1, type I, and type II superstructures; the Co-rich basic structure; the fivefold superstructure; and the one-dimensional quasicrystal. In Figure 57, two types of the clusters with different orientations of pentagonal symmetry are drawn by open and closed circles, respectively. It can be seen from Figures 57d and 57e that the structures of the Co-rich basic structure and the pentagonal superstructure are characterized as pentagonal and rhombic quasiperiodic arrangements of the 2.0-nm clusters with the same orientations, respectively. Thus, both the structures have pentagonal symmetry, which results from the symmetry of the 2.0-nm clusters. That is to say, it can be concluded that the Co-rich basic structure and the pentagonal superstructure can be characterized as pentagonal quasicrystals with pentagonal and rhombic quasiperiodic lattices, respectively. The structures of the S 1-type, type I, type II, and one-dimensional quasicrystals are formed by two types of the 2.0-nm clusters with different orientations of pentagonal symmetry. The lattices in Figures 57a and 57b can be characterized as pentagonal and rhombic quasiperiodic arrangements, respectively, because a deformed octagon existing mainly in Figure 57a can be divided into two pentagons and one thin rhombus, and a hexagon in Figure 57b into fat and thin rhombuses. In the arrangement of the two types of clusters in Figures 57a and 57b, one can see the definite order that two clusters connected with a bond are always different types of clusters, although this order is broken at pentagonal tiles in Figure 57b, as indicated by dotted lines. The pentagonal and rhombic lattices with this ordered arrangement can be interpreted from the projections of CsCl-type and NaCl-type hypercubic lattices, respectively (Section II.C). As for the type II superstructure (Fig. 57c), its structure is characterized as a mixed state of the Sl-type and type I superstructures, namely, pentagonal and rhombic quasiperiodic lattices. However, one can see locally ordered

66

KENJI HIRAGA

d

f

.- ~-QQQ Q

FIGURE 57. Quasiperiodic lattices of the (a) S 1-type, (b) type I, and (c) type II superstructures; (d) the Co-rich basic structure; (e) the pentagonal superstructure; and (f) the onedimensional quasicrystal of A1-Co-Ni decagonal quasicrystals, obtained from HAADF-STEM observations. Open and closed circles indicate two types of clusters with different orientations of pentagonal symmetry. Solid and dotted lines show bonds binding different types and the same types of clusters, respectively. (Reprinted from Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.) arrangements of the clusters, as indicated by solid lines in Figure 57c. This ordering produces superlattice reflections in Figure 25d. In Figure 57f, however, one can see a heterogeneous distribution of open and closed circles and a mixed state of pentagonal and rhombic lattices. In Figure 57f, lattice planes with a high density of clusters along the one direction are periodically arranged, as indicated by arrows. That is to say, the structure of the one-dimensional quasicrystal has no perfect periodic structure along the one direction, but it is formed by the periodic array of lattice planes with a high density of clusters along the one direction. A defectively ordered arrangement of the two types

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

67

of clusters in Figure 57f can be considered to produce weak diffuse reflection around strong spots in Figure 26. From the lattices in Figure 57, one can see the tendency that the density of clusters decreases with increasing Ni content, and finally the S 1-type superstructure with the highest Ni content in the modulations of Figure 57 has no thin rhombic lattices (Fig. 57a). In the Ni-rich basic structure with higher Ni content than that of the S 1-type superstructure, the 3.2-nm cluster becomes a structural unit, and the clusters are arranged with intervals of 3.2 and 2.0 nm, as can be seen in Figure 58. By viewing Figure 58 obliquely and paying attention to the dark lines indicated by arrowheads, one can notice a pentagonal quasiperiodic lattice of the 3.2-nm clusters indicated by a circle, as shown by lines. It should

FIGURE58. HAADF-STEMimage of the Ni-rich basic structure of the A1-Co-Ni decagonal quasicrystal,taken with the incidentbeam parallel to the periodic axis. (Reprintedfrom Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K., 2001. Structural characteristics of A1-Co-Ni decagonal quasicrystals and crystalline approximants. Mater. Trans. 42, pp. 2354-2367, with permission from The Japan Institute of Metals.)

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KENJI HIRAGA

be noted that no definite contrasts are observed at the centers of the 3.2-nm clusters and that a variety of contrast distributions with pentagonal, ring, and triangular shapes, which are indicated with small white arrows in Figure 58, are observed at the centers of the clusters. This feature of the central contrasts in the 3.2-nm clusters has also been found in HAADF-STEM images of highly ordered A1-Cu-Rh (Hiraga, Ohsuna, and Park, 2001) and A1-Fe-Ni (Hiraga and Ohsuna, 200 lb) decagonal quasicrystals with 0.4-nm periodicity. Also, the various arrangements of the atoms around the centers of atom clusters have been found in some crystalline approximants (Sugiyama, Kaji, and Hiraga, 1998; Sugiyama, Kaji, Hiraga et al., 1998; Sugiyama, Kato et al., 2000). The contrast distributions at the centers of the 3.2-nm clusters in Figure 58 can be assumed to have a decagonal distribution of bright contrasts, on average, because the diffraction patterns of the Ni-rich basic structure show the existence of the cglide (c is the periodic axis) plane or a 105 screw axis along the c axis. From this consideration, the model of Figure 55 for the 3.2-nm cluster was proposed. Conversely, the pentagonal symmetry of the 2.0-nm clusters observed in HAADFSTEM images clearly shows pentagonal symmetry with no c-glide plane. The decagonal structures formed with the 3.2-nm clusters have also been found in A1-Cu-Rh (Hiraga, Ohsuna, and Park, 2001) and A1-Ni-Fe (Hiraga and Ohsuna, 200 l b) decagonal quasicrystals with 0.4-nm periodicity, and the structure with the 2.0-nm cluster with pentagonal symmetry has been found in the A1-Ni-Ru (Sun and Hiraga, 2001) decagonal quasicrystal. The structure of the A1-Ni-Ru decagonal quasicrystal has been interpreted by the CsCl-type decagonal superlattice. C. Decagonal Quasicrystals and Crystalline Phases with 1.2-nm Periodicity 1. Fundamental Structural Units The structures of the A1-Pd-Mn decagonal quasicrystal and its related crystalline phases with 1.2-nm periodicity can be interpreted in terms of twodimensional arrangements formed with a definite linkage of two types of fundamental atom columns, which have a twofold screw relationship, as shown in Figures 59a and 59b (Hiraga and Sun, 1993b). The atom columns are composed of the pentagonal atom column of Figure 59c, which is formed with stacking of pentagonal arrangements of atoms and central atoms along the columnar axis, and decagonal atom tings surrounding the pentagonal atom column. The atomic arrangements in the atom columns were determined from structural analysis of the A13Mn phase by single-crystal X-ray diffraction (Hiraga, Kaneko et al., 1993; Li and Kuo, 1992). The atom columns are connected by edge sharing of pentagons with an edge length of 0.47 nm, as shown in the projected atomic arrangement at the bottom of Figures 59a and 59b, and make up two-dimensional arrangements. It should be noted that the

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

69

b

llm

.47 nm

FIGURE59. (a and b) Fundamental atom columns in decagonal quasicrystals and crystalline phases with 1.2-nm periodicity and (bottom) projected atomic arrangements along the columnar axis. (c) Pentagonal atom column inside the (a) column. Open and closed circles are A1 and transition metals, respectively (Hiraga, 1995).

pentagon with a 0.47-nm edge length has the same size as that of the pentagonal frame in Figure 44. Figure 60 shows some structural units, which are important units for understanding the structures of the decagonal and crystalline phases, formed by the edge sharing of the pentagons of the atom columns. The hexagonal (H-), star-shaped pentagonal (P-), decagonal (D-), and ship-shaped octagonal (O-) units with an edge length of 0.65 nm are the units that form aperiodic or periodic tilings in the decagonal and crystalline phases (Hiraga, 1995). Exact atomic arrangements in the H-, P-, and D-units can be seen in Figure 63 (Hiraga and Sun, 1993b).

2. Structure of A1-Pd-Mn Decagonal Quasicrystal Figure 61 is an HRTEM structural image taken with the incident beam parallel to the periodic axis. In the image, one can see small ring contrasts consisting

005nm, H-unit

i P-unit

D-unit

O-unit

FIGURE60. Four units formed with edge sharing of pentagons. Edge lengths of the pentagons and the units are 0.47 and 0.65 nm, respectively. H, hexagonal; P, star-shaped pentagonal; D, decagonal; Q, ship-shaped octagonal.

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KENJI HIRAGA

FIGURE61. HRTEM structural image of the A1-Pd-Mn decagonal phase, taken with the incident beam parallel to the periodic axis. An image calculated from an atomic arrangementin the atom cluster (Fig. 63) is inserted. of a dark ring surrounding a bright ring and a central dark dot. The ring contrasts correspond to the projection of the atom columns of Figure 59 along the columnar axis. An arrangement of the ring contrasts in the image is drawn schematically in Figure 62. The ring contrasts form decagons, star-shaped pentagons, and squashed hexagons, which correspond to the D-, P-, and H-units, respectively, in Figure 60. All the decagonal atom clusters are joined with a definite linkage, namely, by sharing two ring contrasts, and gaps in an arrangement of the decagonal clusters are perfectly filled up with the P- and H-units, without any overlaps and without gaps, as can be seen in Figure 62. Thus, the determination of atomic arrangements in the three polygons leads to a solution for the structure of the A1-Pd-Mn decagonal quasicrystal. Figure 63 is a structural model in the D-, P-, and H-units, which was proposed from the HRTEM structural image of Figure 61 with the aid of computer simulation, as well as from the structure of the A13Mn crystalline phase (Hiraga and Sun, 1993b). The atomic arrangements in the P- and H units are unequivocally determined by placing the atom columns of Figure 59 in the pentagonal framework, and the atomic arrangement near the center of the D-unit, which remained ambiguous, was proposed from the observed HRTEM structural image. In Figure 63, atomic arrangements only on the layers from

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

71

,I IIIII

FIGURE 62. Schematic illustration showing an arrangement of the ring contrasts (small circles) and decagonal atom clusters (large circles), obtained from Figure 61.

(

t 9

...

00:Z=3/4

o: Z = 0 . 6 2

,o : Z = 0 . 5 6

FIGURE 63. Atomic arrangement in decagonal, pentagonal, and hexagonal units in Figure 60. Open and closed circles are A1 and transition metals, respectively. (Reprinted from Hiraga, K., and Sun, W., 1993. The atomic arrangement of an A1-Pd-Mn decagonal quasicrystal studied by high-resolution electron microscopy. Philos. Mag. Lett. 67, pp. 117-223, with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/journals)

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Z = 1/4 to Z = 3/4 perpendicular to the periodic axis are drawn, because layers of both z = 1/4 and z = 3/4 are mirror planes. An image contrast of the decagonal atom cluster, calculated from the model, was inserted in the observed image of Figure 61. One can see a good correspondence between the calculated and observed contrasts. The A1-Pd-Mn decagonal quasicrystal formed by annealing alloys around the A17oPdl0Mn20 composition has strong linear phason strain, because it grew up from crystalline phases (Hiraga, 1993; Hiraga, Sun, Lincoln et al., 1991). Thus, as a way to examine characteristics of a tiling of the decagonal atom clusters in a wide region for the A1-Pd-Mn decagonal quasicrystal with little

FIGURE64. HRTEMlattice image of the A1-Pd-Mn decagonal quasicrystal, grown from an icosahedral phase, in an A170Pd20Mnl0alloy annealed at 800~ for 56 h, taken with the incident beam parallel to the periodic axis (Hiraga and Sun, 1993a).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

73

linear phason strain, an HRTEM lattice image of the A1-Pd-Mn decagonal phase, which was partially grown from the icosahedral phase, was observed. Figure 64 is the lattice image of the A1-Pd-Mn decagonal phase grown from the icosahedral phase by annealing an A170Pd20Mnl0 alloy (Hiraga and Sun, 1993a). The image was taken with the incident beam parallel to the periodic axis. Ring contrasts in Figure 64, which are slightly different in a thin region on the bottom side and in a thick region on the upper side, show the positions of the decagonal atom clusters. From the arrangement of the ring contrasts in Figure 64, we can directly determine the arrangement of the atom clusters in a wide region, and then form a tiling of the atom clusters, as shown in Figure 65. A tiling constructed by connecting the linkages of a bond length of 2 nm with lines is formed of many kinds of polygons in addition to pentagons, as shown in Figure 65a. In this case, a few thin rhombuses are observed, but they may be considered as defects in this tiling. It should be noted that the tiling in Figure 65a may also be represented as a space-filling tiling using three types of files, decagons (D), star-shaped pentagons (P), and squashed hexagons (H) (Hiraga and Sun, 1993a). From Figure 65b, which shows the distribution of the atom cluster positions projected on the internal subspace, the A1-Pd-Mn decagonal phase is said to be a comparatively high-ordered decagonal quasicrystal with little phason strain. However, the A1-Pd-Mn decagonal quasicrystal grown up from crystalline phases was found to have strong linear phason strain because of the influence of directional structure in the crystalline phases.

b 9

"9 9

9

9

";

," L:'.'..:" L : ' : .

" .~' . . ~ a . ; , ' , . . . 9

".~.oe

"

ooe, eo e~o

9

o

.

9

- ~ .9 . "~

9

.

:::"

9; , ' i ' . ~ ' e " ,a 9

.s

"

2rim FIGURE 65. (a) Tiling constructed by connecting ring contrasts (decagonal atom clusters) in Figure 64. (b) Distribution of the atom cluster positions on the internal subspace and a decagonal window used to construct the pentagonal Penrose tiling.

74

KENJI HIRAGA a

b

c

d

e

0.65 nm FIGURE66. Periodic tilings of H-, P-, D-, and O-units in structures of some crystalline phases (Hiraga, 1995; Li and Hiraga, 1996).

3. Crystalline Approximant Phases Many periodic tilings can be formed with the structural units of Figure 60. Figure 66 shows seven examples of periodic tilings, observed in crystalline approximants with 1.2-nm periodicity (Hiraga, 1995; Li and Hiraga, 1996). Unit cells indicated with dotted lines in Figure 66 can be estimated from the edge length of the D-, P-, and H-units: 0.65 nm as (a) 0.76 and 2.35 nm, (b) 1.48 and 1.25 nm, (c) 2.38 and 2.00 nm, (d and e) 2.38 and 3.28 nm, (f) 2.0 and 6.1 nm, and (g) 3.8 and 5.23 nm. The tiling of Figure 66a, called a zr phase, is observed to coexist with the A13Mn phase (Hiraga, 1995; Li and Kuo, 1994), and the tiling of Figure 66b is in the A13Mn phase. The filings of Figures 66c through 66e, formed with the H- and P-units, are in the crystalline phase of A1CuFeCr (Li, Dong et al., 1995), A1CuFeCr (Li, Dong et al., 1995), and A1CrPd called an O phase (Sun, Yubuta et al., 1995), respectively. Also, the tilings of Figures 66f and 66g including the D-units are observed in A1-Pd-Mn alloys, as coexisting phases with the A1-Pd-Mn decagonal phases (Hiraga, 1995). Figure 67 shows HRTEM structural images of the A13Mn phase and O phase. In the images, one can clearly see tilings with the (a) H-unit, and (b) H- and

FIGURE 67. HRTEM structural images of the A13Mn phase and 0 phase. Tilings of the H- and P-units are indicated by white lines. Calculated images from structural models are inserted in each image. (Reprinted from Sun, W., Yubuta, K., and Hiraga, K., 1995. The crystal structure of a new crystalline phase in the A1-Pd-Cr alloy system, studied by high-resolution electron microscopy. Philos. Mag. B 71, pp. 71-80, with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/joumals)

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P-units, formed with ring contrasts corresponding to the projections of the pentagonal atom columns (Fig. 59). The image contrasts in Figure 67 correspond well to those of the calculated images inserted. From these types of images, one can directly determine two-dimensional arrangements of atom columns.

D. Decagonal Quasicrystals and Crystalline Phases with 1.6-nm Periodicity 1. Structure of AI-Pd Decagonal Phase A fundamental atom column in the A1-Pd decagonal quasicrystal and its related crystalline phases with 1.6-nm periodicity was derived from the structure of the A13Pd crystalline phase (Matsuo and Hiraga, 1994), as shown in Figure 68a. Atom columns are connected to each other with edge sharing of the decagons with an edge length of 0.24 nm, as shown in Figure 68c, and make up two-dimensional tilings of decagons. Thus, the tilings are formed with the edge-sharing linkage of the A-sized atom clusters shown in Figure 44. Figure 69 shows an HRTEM structural image of the A1-Pd decagonal quasicrystal in a melt-quenched A13Pd alloy, taken with the incident beam parallel to the periodic axis. Bright ring contrasts in the image correspond to the projection of the decagonal atom columns (Fig. 68a) along the columnar axis.

b

c

G @

(3 G 9

@

t t

0.76nm

FIGURE68. (a) Decagonal atom column forming structures of decagonal quasicrystals and crystalline phases with 1.6-nm periodicity. (b) Atomic arrangements on successive layers along the columnar axis. Open and closed circles correspond to A1and transition-metal atoms. (c) Some polygons constructed by sharing an edge of the decagonal atom columns. Only atoms on the top layer are shown (Hiraga, Abe et al., 1994).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

77

FIGURE69. HRTEM structural image of the A1-Pd decagonal phase. Bright ring contrasts correspond to the projection of the decagonal atom column of Figure 68a along the columnar axis. (Reprinted from Hiraga, K., Abe, E., and Matsuo, Y., 1994. The structure of an A1-Pd decagonal quasicrystal studied by high-resolution electron microscopy. Philos. Mag. Lett. 70, pp. 163-168, with permission from Taylor & Francis Ltd., http//www'tandf'c~176 In the image, the ring contrasts are arranged with an interval of 0.76 nm. Figure 70a shows a schematic illustration of an arrangement of the decagonal atom columns, obtained from Figure 69, and Figure 70b is a tiling drawn by connecting the ring contrasts in Figure 69 by bonds with a 0.76-nm length and ignoring the differences in contrast of the bright tings. In the illustrations, one can see clearly an arrangement of the decagonal atom clusters and the manner of tiling. In Figure 70, there are some areas with no distinguishable ring contrasts. The absence of ring contrasts or weak ring contrasts may be caused by the lack of correlation of atomic arrangements along the incident beam. The sample thickness in the image of Figure 69 is possibly about 10 nm, and so disordering of atomic arrangements in the thickness results in the weak

78

KENJI HIRAGA

C

9

9

9

3rim

9176

9

,,.

9 9

9. . . .

FIGURE 70. (a) Schematic illustration of an arrangement of the decagonal atom clusters, obtained from Figure 69. (b) Tiling of the decagonal atom columns constructed by connecting the bright rings in Figure 69 with lines. (c) Distribution of the atom cluster positions on the internal subspace and a decagonal window used to construct the pentagonal Penrose tiling. (Reprinted from Hiraga, K., Abe, E., and Matsuo, Y., 1994. The structure of an A1-Pd decagonal quasicrystal studied by high-resolution electron microscopy. Philos. Mag. Lett. 70, pp. 163-168, with permission from Taylor & Francis Ltd., http://www.tandf.co.uk/journals)

contrasts or the absence of ring contrasts, because the quasicrystal was formed in a rapidly solidified alloy. However, most of the ring contrasts show apparent contrast, which reveals long-range correlation of atomic arrangements along the 10-fold axis. Although there are some gaps due to the lack of ring contrasts in Figure 70, one can see features of the arrangement of the decagonal atom clusters. Most of the atom clusters are on straight lines parallel to the 10-fold directions, as can clearly be seen by obliquely viewing Figure 70a along the 5-fold directions. Almost all the atom clusters except for central ones of decagons are connected with a bond length of 0.76 nm. In the tiling of the atom clusters, there are many types of polygons (i.e., pentagon, squashed hexagon, decagon, and so on). Atomic arrangements in the polygons can be interpreted by edge-sharing linkage of the decagonal atom columns, as in Figure 68c.

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 79 The A1-Pd decagonal quasicrystal is a metastable phase formed in a rapidly solidified alloy. Thus, a distribution of decagonal atom cluster positions on the internal subspace (Fig. 70c) is scattered compared with that of the A1-Ni-Co (Fig. 9), but it shows that the A1-Pd decagonal phase is a highly ordered quasicrystal with little linear phason strain. Although the tiling of Figure 70b has some gaps with no atom clusters, it shows features of the pentagonal tiling of Figure 5c.

2. Crystalline Approximant Phases Crystalline phases with simple structures formed with the decagonal atom column of Figure 68a were found in conventionally solidified alloys around an A13Pd composition. Figure 71 shows HRTEM structural images of crystalline phases observed in A13Pd and A175Pd20Mn5 alloys (Hiraga, 1995). Figure 7 l a is the A13Pd phase and Figure 7 lb is another crystalline phase. In the images, the decagonal atom columns are represented as bright tings arranged with a nearest-neighbor distance of 0.76 nm. From the images, one can obtain two simple filings of decagons, as shown in Figure 72. The atomic arrangement in Figure 72a was determined by single-crystal X-ray diffraction (Matsuo and Hiraga, 1994).

FIGURE71. HRTEM structural images of two crystalline phases with 1.6-nm periodicity. The bright circles in the images correspond to the projection of the decagonal atom columns of Figure 68a alongthe columnaraxis. (a) A13Pdphase; (b) anothercrystallinephase (Hiraga, 1995).

80

KENJI HIRAGA

a

b

0.76 nm FIGURE 72. Periodic arrangements of decagonal atom clusters obtained from Figure 71 (Hiraga, 1995).

Besides the two simple structures, various types of arrangements with the edge sharing of pentagons can be formed. Actually, many types of structures were observed as modulated structures of the A13Pd phase in the A1-Pdtransition-metal alloy system. Figure 73 shows four tilings of the modulated structures (Hiraga, 1995). These tilings show the possibility of the appearance of various tilings with more complex links. It should be noted that a stable and high-quality decagonal quasicrystal with 1.6-nm periodicity has been found in an A175NilsRu10 alloy (Sun and Hiraga, 2000) and that its structure is clearly different from the structure of the A1-Pd decagonal quasicrystal (Sun, Ohsuna, and Hiraga, 2001). That is, the structure of decagonal quasicrystals varies depending on the quasicrystalline alloys.

a

b

d

FIGURE73. Four periodic arrangements of decagonal atom clusters with edge sharing of decagons, obtained in some crystalline phases (Hiraga, 1995).

QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM

81

VIII. CONCLUDING REMARKS

In this article, I summarized the current results of our group's atomic-scale HRTEM and HAADF-STEM studies of quasicrystals. From the studies, it can be concluded that the structures of quasicrystals can be described as aperiodic arrangements of some atom clusters, which have special shapes depending on the symmetry of the quasicrystals; that is, a decagonal prism in decagonal quasicrystals and polyhedrons with icosahedral symmetry in icosahedral quasicrystals. These polyhedrons are connected to each other by definite linkages, which lead to the bond-orientation order. The aperiodic arrangements of the atom clusters and atomic arrangements in the atom clusters vary depending on the quasicrystalline alloys. It can be said that HRTEM and HAADF-STEM are the most powerful tools for studying the varied structures. However, it should be noted that transmission electron microscopy has many limitations for carrying out precise structural analysis of atomic arrangements, because of its limited resolution, compared with that of the diffraction method, and because of the use of projected images along the incident beam. So that more precise structural analysis of the quasicrystals can be achieved, combination of various techniques of transmission electron microscopy and the diffraction method becomes more important. In particular, the structural determinations of crystalline approximants, which are considered to have structural units similar to those in quasicrystals, are important. It should be mentioned that the atomic arrangements of the A1-Co-Ni, A1-Pd-Mn, and A1-Pd decagonal quasicrystals, presented in this article, were proposed by the aid of the structures of the crystalline approximants determined by X-ray diffraction. Finally it should be noted that a new structural model has been proposed by Steinhardt et al. (1998) from HAADF-STEM and HRTEM observations of the Ni-rich basic A1-Co-Ni decagonal quasicrystal by Saito, Tsuda, et al. (1997) and Abe et al. (2000). This model is quite different from the cluster models, which can clearly explain all the structures of quasicrystals presented in this article. These researchers' observations have not revealed the 3.2-nm cluster, which is clearly observed in our HAADF-STEM and HRTEM studies of the Ni-rich basic A1-Co-Ni decagonal quasicrystal. In our recent study, we found that the structure of the A1-Cu-Rh quasicrystal formed by the same 3.2-nm cluster easily undergoes structural change under electron irradiation (Hiraga, Ohsuna, and Park, 2001), which leads to the disappearance of the 3.2-nm cluster contrasts. This structural change led to the proposition of a wrong model with no large atom cluster in previous articles (Li and Hiraga, 1997; Li, Hiraga et al., 1997). After that, we noticed that most quasicrystals undergo extensive structural change by irradiation damage. Therefore, we have conducted careful HAADF-STEM and HRTEM observations with low

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irradiation doses for recent electron microscopic studies. This experience taught us the important lesson that HRTEM and HAADF-STEM images observed without careful technique should be doubted before the interpretation of the images. ACKNOWLEDGMENTS

I sincerely thank Profs. M. Hirabayashi, D. Shindo, M. Matsuo, and E J. Lincoln; Drs. K. Sugiyama, T. Ohsuna, W. Sun, A. Yamamoto, E. Abe, K. Yubuta, and K.-T. Park; and Mr. S. Nishimura for their cooperation in carrying out this work. This work has been supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan. REFERENCES Abe, E., Saito, K., Tanaka, M., Tsai, A. E, Steinhardt, E J., and Jeong, H.-C. (2000). Quasi-unitCell model for an A1-Ni-Co ideal quasicrystal based on clusters with broken tenfold symmetry. Phys. Rev. Lett. 84, 4609-4612. Audier, M., Sainfort, E, and Dubost, B. (1986). A simple construction of the A1CuLi quasicrystalline structure related to the (A1, Zn)49Mg32 cubic structure type. Philos. Mag. B 54, L105-L111. Beeli, C., Nissen, H.-U., and Robadey, J. (1991). Stable A1-Mn-Pd quasicrystals. Philos. Mag. Lett. 63, 87-95. Bendersky, L. (1985). Quasicrystal with one-dimensional translational symmetry and a tenfold rotaion axis. Phys. Rev. Lett. 55, 1461-1463. Chattopadhyay, K., Raganathan, S., Subbanna, G. N., and Thangaraj, N. (1985). Electron microscopy of quasi-crystal in rapidly solidified Al-14%Mn alloys. Scr. Metall. 19, 767-771. Ebalard, S., and Spaepen, E (1989). The body-centered-cubic-type icosahedral reciprocal lattice of the A1-Cu-Fe quasi-periodic crystal. J. Mater. Res. 4, 39-43. Edagawa, K., Ichihara, M., Suzuki, K., and Takeuchi, S. (1992). New type of decagonal quasicrystal with superlattice order in A1-Ni-Co alloy. Philos. Mag. Lett. 66, 19-25. Elser, V. (1986). The diffraction pattern of projected structures. Acta Crystallogr. A 42, 36-43. Elser, V., and Henley, C. L. (1985). Crystal and quasicrystal structures in A1-Mn-Si Alloys. Phys. Rev. Lett. 55, 2883-2886. Field, R. D., and Fraser, H. L. (1984-1985). Precipitates possessing icosahedral symmetry in a rapidly solidified A1-Mn-alloy. Mater Sci. Eng. 68, L 17-L21. Grusko, B., Holland-Moritz, D., Wittmann, R., and Wilde, G. (1998). Transition between periodic and quasiperiodic structures in A1-Ni-Co. J. Alloys Comp. 280, 215-230. Guryan, C. A., Goldman, A. I., Stephens, E W., Hiraga, K., Tsai, A. E, Inoue, A., and Masumoto, T. (1989). A1-Cu-Ru: An icosahedral alloy without phason disorder. Phys. Rev. Lett. 62, 24092412. Guyot, P., and Audier, M. (1985). A quasicrystal structure model for AI-Mn. Philos. Mag. B 52, L15-L19. Henley, C. L. (1986). Sphere packings and local environments in Penrose tilings. Phys. Rev. B 34, 797-816.

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Henley, C. L., and Elser, V. (1986). Quasicrystal structure of (A1, Zn)49Mg32.Philos. Mag. Lett. B 53, L59-L66. Hiraga, K. (1989). High-resolution electron microscopy of quasicrystals. Mater. Res. Soc. Symp. Proc. 139, 125-134. Hiraga, K. (1990). High-resolution electron microscopy and atomic arrangement of an A1-Li-Cu quasicrystal. In Quasicrystals, Vol. 93 (Springer Series in Solid-State Sciences), edited by T. Fujiwara and T. Ogawa. Berlin: Springer-Verlag, pp. 68-77. (Proceedings of the Twelfth Taniguchi Symposium, Shima, Mie Prefecture, Japan, 1989.) Hiraga, K. (1991 a). High-resolution electron microscopy of quasicrystals. J. Electron Microsc. 40, 81-91. Hiraga, K. (1991b). High-resolution electron microscopy of quasicrystals. In Quasicrystals: The State of the Art, Vol. 11 (Directions in Condensed Matter Physics), edited by D. P. DiVincenzo and P. J. Steinhardt. Singapore: World Scientific, pp. 95-110. Hiraga, K. (199 l c). High-resolution electron microscopy of decagonal quasicrystals. Sci. Rep. Res. Inst. Tohoku Univ. A 36, 115-127. Hiraga, K. (1993). Structure of A1-Pd-Mn decagonal quasicrystal studied by high-resolution electron microscopy. J. Non-Cryst. Solids 153/154, 28-32. Hiraga, K. (1995). The structures of decagonal and quasicrystalline phases with 1.2 nm and 1.6 nm periods, studied by high-resolution electron microscopy. In Proceedings of the International Conference on Aperiodic Crystallagraphy (Aperiodic '94), Les Diablerets, Switzerland, 1994, edited by G. Chapuis and W. Paciorek. Singapore: World Scientific, pp. 341-350. Hiraga, K. (1999). Atom clusters in a 2/1 cubic approximant phase for understanding the structures of icosahedral phases. Mater Res. Soc. Symp. Proc. 553, 107-116. Hiraga, K., Abe, E., and Matsuo, Y. (1994). The structure of an A1-Pd decagonal quasicrystal studied by high-resolution electron microscopy. Philos. Mag. Lett. 70, 163-168. Hiraga, K., and Hirabayashi, M. (1987a). Quenched phason strains in A1-Mn-Si icosahedral quasicrystal studied by high-resolution electron microscopy. J. Electron Microsc. 36, 353360. Hiraga, K., and Hirabayashi, M. (1987b). Dislocations in an A1-Mn-Si icosahedral quasicrystal observed by high-resolution electron microscopy. Jpn. J. Appl. Phys. 26, L155L158. Hiraga, K., Hirabayashi, M., Inoue, A., and Masumoto, T. (1985). Icosahedral quasicrystals of a melt-quenched A1-Mn alloy observed by high resolution electron microscopy. Sci. Rep. Res. Inst. Tohoku Univ. A 32, 309-314. Hiraga, K., Hirabayashi, M., Inoue, A., and Masumoto, T. (1987). High-resolution electron microscopy of A1-Mn-Si icosahedral and A1-Mn decagonal quasicrystals. J. Microsc. 146, 245-260. Hiraga, K., Hirabayashi, M., Tsai, A. P., Inoue, A., and Masumoto, T. (1989). Atomic disordering in an A1-Ru-Cu icosahedral quasicrystal. Philos. Mag. Lett. 60, 201-205. Hiraga, K., Kaneko, M., Matsuo, Y., and Hashimoto, S. (1993). The structure of A13Mn: Close relationship to Ddcagonal quasicrystals. Philos. Mag. B 67, 193-205. Hiraga, K., Lee, K. H., Hirabayashi, M., Tsai, A. P., Inoue, A., and Masumoto, T. (1989). Phason strains and periodicity in A1-Ru-Cu icosahedral quasicrystals. Jpn. J. Appl. Phys. 28, L1624L1627. Hiraga, K., Lincoln, E J., and Sun, W. (1991). Structure and structural change of A1-Ni-Co decagonal quasicrystal by high-resolution electron microscopy. Mater Trans. JIM 32, 308314. Hiraga, K., and Ohsuna, T. (2001a). The structure of an A1-Ni-Co decagonal quasicrystal studied by atomic-scale electron microscopic observations. Mater Trans. 42, 509-513.

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Hiraga, K., and Ohsuna, T. (2001b). The structure of an A1-Ni-Fe decagonal quasicrystal studied by high-angle annular detector dark-field scanning transmission electron microscopy. Mater. Trans. 42, 894-896. Hiraga, K., Ohsuna, T., and Nishimura, S. (2000). An ordered arrangement of atom columnar clusters in a pentagonal quasiperiodic lattice of an A1-Ni-Co decagonal quasicrystal. Philos. Mag. Lett. 80, 653-659. Hiraga, K., Ohsuna, T., and Nishimura, S. (2001 a). A new crystalline phase related to an A1-Ni-Co decagonal phase. J. Alloy Comp. 325, 145-150. Hiraga, K., Ohsuna, T., and Nishimura, S. (2001b). The structure of type-II A1-Ni-Co decagonal quasicrystal studied by atomic-scale electron microscopic observations. Mater. Trans. 42, 1081-1084. Hiraga, K., Ohsuna, T., and Nishimura, S. (2001c). The structure of an A1-Ni-Co pentagonal quasicrystal studied by high-angle annular detector dark-field electron microscopy. Philos. Mag. Lett. 81, 123-127. Hiraga, K., Ohsuna, T., and Nishimura, S. (2001). Mater. Trans. 42, 1830-1833. Hiraga, K., Ohsuna, T., Nishimura, S., and Kawasaki, M. (2001). An ordered arrangement of columnar clusters of atoms in a rhombic quasiperiodic lattice in an A1-Ni-Co decagonal phase. Philos. Mag. Lett. 81, 109-115. Hiraga, K., Ohsuna, T., and Park, K.-T. (2001). A large columnar cluster of atoms in an A1Cu-Rh decagonal quasicrystal studied by atomic-scale electron microscopy observations. Philos. Mag. Lett. 81, 117-122. Hiraga, K., Ohsuna, T., and Sun, W. (2001). Ordered structures in decagonal quasicrystals with simple and body-centered hypercubic lattices. Mater. Sci. Eng. A 312, 1-8. Hiraga, K., Ohsuna, T., Sun, W., and Sugiyama, K. (2002). Mater. Trans. 42, 2354-2367. Hiraga, K., Ohsuna, T., Yubuta, K., and Nishimura, S. (2001). The structure of an A1-Co-Ni crystalline approximant with an ordered arrangement of atomic clusters with pentagonal symmetry. Mater. Trans. 42, 897-900. Hiraga, K., and Shindo, D. (1989). Structural difference between A1-Fe-Cu and A1-Li-Cu quasicrystals studied by high-resolution electron microscopy. Jpn. J. Appl. Phys. 28, 2556-2560. Hiraga, K., and Shindo, D. (1990). High-resolution electron microscopy and atomic arrangements of A1-Mn-Si and A1-Li-Cu icosahedral quasicrystals. Mater. Trans. JIM 31, 567-572. Hiraga, K., Sugiyama, K., and Ohsuna, T. (1998a). A large dodecahedral cluster containing about 480 atoms in a 2/1 cubic crystalline approximant. J. Phys. Soc. Jpn. 67, 1501-1504. Hiraga, K., Sugiyama, K., and Ohsuna, T. (1998b). Atom cluster arrangements in cubic approximant phases of icosahedral quasicrystals. Philos. Mag. A 78, 1051-1064. Hiraga, K., and Sun, W. (1993a). Tiling in A1-Pd-Mn decagonal quasicrystal, studied by highresolution electron microscopy. J. Phys. Soc. Jpn. 62, 1833-1836. Hiraga, K., and Sun, W. (1993b). The atomic arrangement of an A1-Pd-Mn decagonal quasicrystal studied by high-resolution electron microscopy. Philos. Mag. Lett. 67, 117-123. Hiraga, K., Sun, W., and Lincoln, F. J. (1991). Structural change of A1-Cu-Co decagonal quasicrystal studied by high-resolution electron microscopy. Jpn. J. Appl. Phys. 30, L302-L305. Hiraga, K., Sun, W., Lincoln, E J., Kaneko, M., and Matsuo, Y. (1991). Formation of decagonal quasicrystal in the A1-Pd-Mn system and its structure. Jpn. J. Appl. Phys. 30, 2028-2034. Hiraga, K., Sun, W., and Ohsuna, T. (2001). Structure of pentagonal quasicrystal in A172.sCo17.sNi10 Studied by high-angle annular detector dark-field scanning transmission electron microscopy. Mater. Trans. 42, 1146-1148. Hiraga, K., Sun, W., and Yamamoto, A. (1994). Structures of two types of A1-Ni-Co decagonal quasicrystals studied by high-resolution electron microscopy. Mater. Trans. JIM 35, 657-662. Hiraga, K., Yubuta, K., and Park, K.-T. (1996). High-resolution electron microscopy of A1-Ni-Fe decagonal quasicrystal. J. Mater. Res. 11, 1702-1705.

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Hiraga, K., Zhang, B.-E, Hirabayashi, M., Inoue, A., and Masumoto, T. (1988). Highly ordered icosahedral quasicrystal in A1-Fe-Cu alloy studied by electron diffraction and high-resolution electron microscopy. Jpn. J. Appl. Phys. 27, L951-L953. Ishihara, K. N., and Yamamoto, A. (1988). Penrose patterns and related structures. I. Superstructure and generalized Penrose patterns. Acta Crystallogr. A 44, 508-516. Ishimasa, T., Fukano, Y., and Tsuchimori, M. (1988). Quasicrystal structure in A1-Cu-Fe annealed alloy. Philos. Mag. Lett. 58, 157-167. Jesson, D. E., and Pennycook, S. J. (1995). Incoherent imaging of crystals using thermally scattered electrons. Proc. R. Soc. London A 449, 653-659. Katz, A., and Duneau, M. (1986). Quasiperiodic patterns and icosahedral symmetry. J. Phys. 47, 181-196. Lemmerz, U., Grushko, B., Freiburg, C., and Jansen, M. (1994). Study of decagonal quasicrystalline phase formation in the A1-Ni-Fe alloy system. Philos. Mag. Lett. 69, 141-146. Levine, D., Lubensky, T. C., Ostlund, S., Ramaswamy, S., Steinhardt, P. J., and Toner, J. (1985). Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520-1523. Levine, D., and Steinhardt, P. J. (1984). Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53, 2477. Li, H. L., and Kuo, K. H. (1992). The structural model of A1-Mn decagonal quasicrystal based on a new A1-Mn decagonal quasicrystal based on a new A1-Mn approximant. Philos. Mag. A 65, 525-533. Li, H. L., and Kuo, K. H. (1994). Some new crystalline approximants of A1-Pd-Mn quasicrystals. Philos. Mag. Lett. 70, 55-62. Li, X. Z., Dong, C., and Dubois, J. M. (1995). Structural study of crystalline approximant of the A1- Cu- Fe -Cr decagonal quasicrystal. J. Appl. Crystallogr. 28, 96-104. Li, X. Z., and Hiraga, K. (1996). On the crystalline approximants of the A1-Mn, A1-Pd and A1-Mn-Pd type decagonal quasicrystals. Sci. Rep. Res. Inst. Tohoku Univ. A 42, 213-218. Li, X. Z., and Hiraga, K. (1997). Structure of the A1-Rh-Cu decagonal quasicrystal: II. A higherdimensional description. Physica B 240, 338-342. Li, X. Z., Hiraga, K., and Yubuta, K. (1997). Structure of the A1-Rh-Cu Decagonal Quasicrystal: I. A unit-cell approach. Physica B 240, 330-347. Matsuo, Y., and Hiraga, K. (1994). The structure of A13Pd: Close relationship to decagonal quasicrystals. Philos. Mag. Lett. 70, 155-161. Ogawa, T. (1985). On the structure of a quasicrystal-Three-dimensional Penrose transformationJ. Phys. Soc. Jpn. 54, 3205-3208. Ohsuna, T., Sun, W., and Hiraga, K. (2000). Decagonal quasicrystal with ordered body-centered (CsCl-type) hypercubic lattice. Philos. Mag. Lett. 80, 577-583. Pauling, L. (1985). Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals. Nature 317, 512. Ritsch, S., Beeli, C., Nissen, H.-U., G6decke, T., Scheffer, M., and Ltick, R. (1998). The existence regions of structural modifications in decagonal A1-Co-Ni. Philos. Mag. Lett. 78, 67-75. Ritsch, S., Radulescu, O., Beeli, C., Warfington, D. H., LUck, R., and Hiraga, K. (2000). A stable one-dimensional quasicrystal related to decagonal A1-Co-Ni. Philos. Mag. Lett. 80, 107-118. Saito, M., Tsuda, K., Tanaka, M., Kaneko, K., and Tsai, A. P. (1997). Structural study of an A172Ni20Co8 decagonal quasicrystal using the high-angle annular dark-field method. Jpn. J. Appl. Phys. 36, L 1400-L1402. Shechtman, D., Blech, I., Gratias, D., and Cahn, J. W. (1984). Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951-1953. Socolar, J. E. S., Lubensky, T. C., and Steinhardt, P. J. (1986). Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345-3360.

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Steinhardt, E J., Jeong, H.-C., Saito, K., Tanaka, M., Abe, E., and Tsai, A. E (1998, Nov.). Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature 396, 55-57. Sugiyama, K., Kaji, N., and Hiraga, K. (1998). Crystal structure of a cubic A167PdllMn14Si7; a new 1/1 rational approximant for the A1-Pd-Mn icosahedral Phase. Z. Kristallogr. 213, 168173. Sugiyama, K., Kaji, N., Hiraga, K., and Ishimasa, T. (1998). Crystal structure of a cubic A170Pdz3Mn6 Si; a 2/1 rational approximant of an icosahedral phase. Z. Kristallogr. 213, 90-95. Sugiyama, K., Kato, T., Ogawa, T., Hiraga, K., and Saito, K. (2000). Crystal structure of a new 1/1-rational approximant for the A1-Cu-Ru icosahedral phase. J. Alloy Comp. 299, 169174. Sugiyama, K., Nishimura, S., and Hiraga, K. (in press). J. Alloy Comp. Sun, W., and Hiraga, K. (2001). A new highly ordered A1-Ni-Ru decagonal quasicrystals with 1.6 nm periodicity. Philos. Mag. Lett. 80, 157-164. Sun, W., and Hiraga, K. (2001). Structural study of a superlattice A1-Ni-Ru decagonal quasicrystal using high-resolution electron microscopy and a high-angle annular dark-field technique. Philos. Mag. Lett. 81, 187-195. Sun, W., Ohsuna, T., and Hiraga, K. (2000). Quasiperiodic superstructure with an ordered arrangement of atom columnar clusters in an A1-Ni-Ru decagonal quasicrystal with 0.4 nm periodicity. J. Phys. Soc. Jpn. 69, 2383-2386. Sun, W., Ohsuna, T., and Hiraga, K. (2001). Structural characteristics of a high quality A1-Ni-Ru decagonal quasicrystal with 1.6 nm periodicity, studied by atomic-scale electron microscopy observations. Philos. Mag. Lett. 81, 425-431. Sun, W., Yubuta, K., and Hiraga, K. (1995). The crystal structure of a new crystalline phase in the A1-Pd-Cr alloy system, studied by high-resolution electron microscopy. Philos. Mag. B 71, 71-80. Tsai, A. E, Fujiwara, A., Inoue, A., and Masumoto, T. (1996). Structural variation and phase transformations of decagonal quasicrystals in the AI-Ni-Co system. Philos. Mag. Lett. 74, 233-240. Tsai, A. E, Inoue, A., and Masumoto, T. (1987). A stable quasicrystal in A1-Cu-Fe system. Jpn. J. Appl. Phys. 26, L 1505-L 1507. Tsai, A. E, Inoue, A., and Masumoto, T. (1988). New stable icosahedral A1-Cu-Ru and A1-Cu-Os alloys. Jpn. J. Appl. Phys. 27, L 1587-L 1590. Tsai, A. E, Inoue, A., and Masumoto, T. (1989a). New decagonal A1-Ni-Fe and A1-Ni-Co alloys prepared by Liquid quenching. Mater. Trans. JIM 30, 150-154. Tsai, A. E, Inoue, A., and Masumoto, T. (1989b). A stable decagonal quasicrystal in the A1-Cu-Co system. Mater Trans. JIM 30, 300-304. Tsai, A. E, Inoue, A., and Masumoto, T. (1989c). Stable decagonal A1-Co-Ni and A1-Co-Cu quasicrystals. Mater Trans. JIM 30, 463-473. Tsai, A. E, Inoue, A., Yokayama, Y., and Masumoto, T. (1990). New icosahedral alloys with superlattice order in the A1-Pd-Mn system prepared by rapid solidification. Philos. Mag. Lett. 61, 9-14. Yamamoto, A., and Hiraga, K. (1988). Structure of an icosahedral A1-Mn quasicrystal. Phys. Rev. B 37, 6207-6214. Yamamoto, A., and Hiraga, K. (2000). Six-dimentional model of an i-A1-Pd-Mn quasicrystal compatible with its 2/1 approximant. Mater Sci. Eng. 294-296, 228-231. Yamamoto, A., and Ishihara, K. N. (1988). Penrose patterns and related structures II. Decagonal quasicrystals. Acta Crystallogr. A 44, 707-714. Yubuta, K., Sun, W., and Hiraga, K. (1997). A new crystalline phase related to decagonal quasicrystals with non-central symmetry in A1-Co-Pd alloys. Philos. Mag. A. 75, 273-284.

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 122

Add-On Lens Attachments for the Scanning Electron Microscope ANJAM KHURSHEED Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. C o m p a r i s o n of Conventional and I m m e r s i o n Objective L e n s e s . . . . . . . B. Resolution Limits for I m m e r s i o n L e n s e s . . . . . . . . . . . . . . . . II. In-Lens Attachments . . . . . . . . . . . . . . . . . . . . . . . . . . A. Magnetic In-Lenses . . . . . . . . . . . . . . . . . . . . . . . . . B. M i x e d - F i e l d Lenses . . . . . . . . . . . . . . . . . . . . . . . . . III. Single-Pole Lens Attachments . . . . . . . . . . . . . . . . . . . . . . IV. Secondary Electron E n e r g y Spectrometers . . . . . . . . . . . . . . . . . A. T i m e - o f - F l i g h t Voltage Contrast Spectrometers . . . . . . . . . . . . . B. Deflection Voltage Contrast Spectrometers . . . . . . . . . . . . . . . C. Material Contrast Spectrometer . . . . . . . . . . . . . . . . . . . . D. M i x e d - F i e l d I m m e r s i o n Lens Spectrometers . . . . . . . . . . . . . . V. Multibore Objective Lenses . . . . . . . . . . . . . . . . . . . . . . . A. Single-Pole Lens Array . . . . . . . . . . . . . . . . . . . . . . . B. Multibore I m m e r s i o n Lens A r r a y . . . . . . . . . . . . . . . . . . . VI. S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87 90 97 102 103 121 125 135 138 144 151 157 163 163 169 170 170

I. INTRODUCTION

In most scanning electron microscopes (SEMs), the specimen is placed in a field-free region some 5-20 mm below the objective lens, as shown in Figure l a. This distance, known as the working distance, limits the SEM's spatial resolution. For optimum performance, the specimen should be placed in the lens gap, at the axial field peak. However, this is impractical because the electron detectors that form the output signalmthe scintillator and backscattered electron detectorsmare usually situated below the objective lens, and there is usually no access to the space inside the lens or above it. The type of lenses in which the specimen is placed in the magnetic gap are known as in-lens or immersion objective lenses, and they typically improve the spatial resolution of SEMs by a factor of 3 (Khursheed, 2001; Nakagawa et al., 1991). Figure lb depicts the schematic diagram of a magnetic in-lens objective lens. Because a specimen in-lens arrangement significantly improves the SEM's 87 ADVANCES IN IMAGING AND ELECTRON PHYSICS Copyright 2002, Elsevier Science (USA). All rights reserved. Volume 122 ISSN 1076-5670/02 $35.00 ISBN 0-12-014764-5

FIGURE 1. Scanning electron microscope (SEM) objective lenses: (a) conventional lens, (b) magnetic in-lens, and (c) retarding field lens. PE, primary electron; SE, secondary electron.

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performance, several SEMs have been specially designed to function in this way (JEOL JSM-6000F: JEOL Ltd., 1-2 Musashino 3-chome, Akishima, Tokyo, Japan; Hitachi S-5000: Nissei Sangyo America, Ltd., Chicago, IL). These systems are more expensive than conventional SEMs. They usually have the disadvantage of restricting the specimen thickness to less than 3 mm and are more complicated to operate (Joy and Pawley, 1992; Pawley, 1990). Another important class of high-resolution SEMs is based on immersing the specimen in an electric field (Mtillerov~i and Lenc, 1992). These SEMs use an electric retarding field lens, which slows the primary electron beam from an energy of around 10 keV to 1 keV within a few millimeters above the specimen, as shown in Figure l c. A magnetic field is superimposed onto the electric retarding field so that the primary beam can be focused. These retarding field systems are particularly advantageous at low primary beam landing energies, typically 1 keV and less (Khursheed, 2001). The LEO Gemini 1500 series (LEO Electron Microscopy Ltd., Clifton Road, Cambridge CB 1 3QH, UK) of SEMs currently operates in this way. The concept of an add-on SEM lens attachment is that a small high-resolution lens unit is placed below the objective lens of a conventional SEM column, as shown in Figure 2. The specimen is placed within the add-on unit, where

9

j

Existing SEM

I

Add-on lens

FIGURE2. Add-onlens principle.

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ANJAM KHURSHEED

it is immersed in a strong field region. The main advantage of using add-on lenses is that they can improve the resolution of conventional SEMs, without the need to redesign the whole column. In fact, the SEM can operate as normal. There are three other advantages: First, the add-on lens can extend the operating range of a conventional SEM to very low primary beam voltages (down to 100 V or less). Second, the add-on lens can be designed to function as a secondary electron energy spectrometer, which transforms a conventional SEM into a flexible analytical tool that can provide quantitative material and voltage contrast information. Third, add-on lenses are a convenient way of testing novel objective lens ideas. Some early work on add-on lenses was carried out by Hordon, Huang, Browning, et al. (1993) and Hordon, Huang, Maluf, et al. (1993). They used an add-on lens to investigate low-energy limits to electron optics and proposed it as a way of obtaining low landing energies (100-800 eV) in conventional SEMs. They used a conventional field-emission SEM (Hitachi S-800). Their initial results for a purely magnetic add-on lens were not a significant improvement over the SEM's normal mode of operation (Hordon, Huang, Browning, et al., 1993): they obtained an image resolution of around 200 nm at a landing energy of 1 keV. However, better results were obtained with an add-on mixed-field electric-magnetic lens (Hordon, Huang, Maluf, et al., 1993), which was able to provide a resolution of 40 nm at a landing energy of 300 eV. The advantages of using a combination of mixed electric-magnetic fields had been reported earlier by Yau et al. (1981). Later, Hordon and Monahan (1996) developed an electron-optical column based on using a mixed-field objective lens approach for low landing energies, and they obtained an image resolution of better than 5 nm at a landing energy of 600 eV. Although little information is given on the precise objective lens used, they did not refer to it as an add-on lens. Another recent proposal based on using a mixed electric-magnetic field combination was made by Knell and Plies (2000). Recent progress in designing add-on lenses has come from research work carried out on portable permanent magnet SEMs (Khursheed, 2000). This work has been carried out by the author and his colleagues at the National University of Singapore and has led to several successful add-on lens designs (Khursheed and Karuppiah, 2001; Khursheed, Karuppiah, et al., 2001; Khursheed, Yan, et al., 2001). This article discusses add-on lens designs for a wide class of problems, demonstrating how they can be used in practice.

A. Comparison o f Conventional and Immersion Objective Lenses

Before specific add-on lens designs are examined, it is important to classify immersion lenses in general terms and to compare their performance with that of

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conventional lenses. There are three possible immersion lens categories: lenses that immerse the specimen in a magnetic field, those that immerse the specimen in an electric field, and those that immerse the specimen in a mixed electricmagnetic field combination. These different configurations are depicted in Figures 3a through d, in terms of pole-piece layout and axial field distribution. Figure 3a shows the conventional objective lens layout, in which the specimen is placed outside the lens field. Magnetic immersion objective lenses typically involve inserting the specimen between the pole pieces of a magnetic lens, as shown in Figure 3b. The limiting magnetic field strength at the specimen is around 1 T (tesla), set by saturation in the iron circuit.

FIGURE 3. Objective lens axial field distributions: (a) conventional lens, (b) magnetic immersion lens, (c) retarding field lens, and (d) mixed-fieldimmersionlens.

(c) FIGURE 3.

(Continued)

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93

FIGURE 3. (Continued)

Figure 3c shows an electric field immersion lens of the retarding field type. An electric field along the axis of the beam is created either through biasing the specimen to a large negative voltage or by using a high-voltage liner tube. In both cases, the landing energy of the primary beam is substantially lower than its energy at the lens entrance. The advantages of doing this are that the gun brightness is relatively high (compared with operating the electron gun at low primary beam voltages) and there are fewer adverse effects from stray electromagnetic fields. The strength of the electric field at the specimen is limited by the 10-kV/mm electric field breakdown value for vacuum. The auxiliary magnetic focusing lens is placed so that it leaves the specimen free of a magnetic field. The axial field distribution of the focusing lens can be approximated by the following Glaser field distribution: B(z) =

B0

[1 + (z/a)2] 2

(1)

where B0 is the peak of the distribution, and the parameter a controls how sharply the distribution falls on either side of the peak value.

94

ANJAM KHURSHEED

A mixed-field immersion lens type is depicted in Figure 3d. The magnetic field strength increases as the beam energy is lowered. In the following analysis, an aperture lens model is used which assumes that all electrodes in the immersion lens are infinitely thin, as shown in Figure 4a, and that the field reaches a constant value on either side of the aperture. If the field on the fight-hand side of the lens is E = -(V2 - V1)/W, and if a field-free region is assumed on the left-hand side, then the potential along the z axis, V(z),is given by (Hawkes and Kasper, 1989)

V(z)-

V 1 - - z2E -z

E R ( 1 +- z

Jr

R

tan- l (z/R) )

(2)

Note that as the aperture radius R tends to zero, the potential distribution is linear in z, as expected. Figure 4b shows how the aperture axial potential distribution compares with that of a finite element potential solution that takes into account the aperture electrode thickness. The immersion lens in this case has a 3-mm-thick aperture plate, an aperture hole radius of 1 mm, and a working distance of 1 mm. The finite element program used to calculate this field distribution is part of the KEOS package written by the author (Khursheed, 1995). The aperture electrode is located at z = 0. The two axial potential distributions are similar, except the aperture electrode distribution is shifted to the left by around 0.3 mm and rises a little less steeply than the finite element solution. The simple aperture lens model is a convenient way of generating a wide range of immersion lens axial field distributions so that the conditions for which the axial aberrations are a minimum can be investigated. The focal length, f ; the axial chromatic aberration coefficient, Cc; and the axial spherical aberration coefficient, Cs, were calculated through the use of the KEOS software (Khursheed, 1995). Some way of combining spherical, chromatic, and diffraction aberrations is required if the much more complicated full wave solution technique for calculating the aberration-limited probe size is to be avoided. Various formulas have been presented. At one extreme, the standard quadrature formula provides the largest estimate of the probe size (Reimer, 1998). At the other extreme, a root-sum formula by Bath and Kruit (1996) based on the probe's containing 50% of the electron current gives the lowest estimate. For the purposes of this article, the following formula presented by Zach (2000) is used: ,

- + ~ Cs ,~p + Clp2 _ [ C 2+(0.6)~)2] %2

cg- 4Ip

Cc---y-

2 Ogp

(3)

95

A D D - O N LENS A T T A C H M E N T S FOR THE SEM W

..............

A

x

i

,

s

............................................................

>

EorB

V2

Vs

V1

Immersion lens

V2

Aperture lens approximation

(a) 1.20

-

-

/

Axial potential distribution of immersion lens R=lmm / _

0

>

-- --

FEM solution, 3 mm thick aperture

'//

/

0.80 - -

0 "F_

1 V conductor boundary

1

._m e-

0.40 ta

_

0.00

"

-1.00

I -0.50

'

I ' 0.00 Distance along axis (ram)

I 0.50

' 1.00

(b) FIGURE 4. Aperture lens model: (a) lens layout and (b) simulated axial field distributions. FEM, finite element method.

96

ANJAM KHURSHEED

where dp is the probe diameter, Ip is the probe current, fl is the gun brightness, Up is the semiangle at the image plane, AVis the primary beam voltage spread, Vis the primary beam voltage at the specimen, and X is the de Broglie wavelength for electrons, related to the primary beam voltage by )~ = 1.226(V) -1/2. In this case, V is in volts and )~ is in nanometers. Zach claims that this formula is equivalent to assuming that the electron spot contains 59% of the electron current. In practice, this formula provides an estimate approximately midway between the standard quadrature formula and the root-sum formula reported by Bath and Kruit (1996). After the magnetic field strength is set at 1 T and the electric field strength at 10 kV/mm, the aperture lens electrode diameter is varied systematically so that the calculated probe diameter at a landing energy of 1 keV is a minimum. The results are shown in Table 1. The spot sizes in this table neglect the effect of the source and are therefore aberration-limited spot sizes, representing the ultimate limit on the lens image resolution performance. A schematic diagram for the conventional lens used in these calculations is shown in Figure 5. This objective lens was used in the Cambridge S 100 SEM. The energy spread in the primary beam was taken to 0.15 eV, a value typical for field-emission sources. The optimum semiangle at the specimen was found for each probe diameter calculation. In the case of the magnetic immersion lens, the working distance of 0.3 mm was measured from the focal point to the aperture lens electrode. In the case of the electric retarding field lens and the mixed-field immersion lens, the strength of the magnetic field was adjusted to provide a focal point 1 mm below the aperture lens electrode. Table 1 shows that the magnetic immersion lens is predicted to be more than seven times better in resolution than the conventional lens, and its aberration

TABLE 1 SIMULATIONOF CONVENTIONALAND IMMERSIONLENS ON-Axis ABERRATIONSUSING THE APERTURE LENS MODELa

Lens type Conventional lens Magnetic immersion lens (1 T) Electric retarding field lens (10 kV/mm) Mixed-field immersion lens

Working distance (mm)

f (/xm)

Cs (#m)

Cr (#m)

dp (nm)

5 0.3

15,700 257

30,810 168

13,300 187

9.71 1.31

1

860

713

144

1.68

1

163

50.45

58.2

0.891

aprimary beam landing energy = 1 keV.

bf, focal length; Cs, axial spherical aberration coefficient; Cc, axial chromatic aberration coefficient; dp, probe diameter.

ADD-ON LENS ATTACHMENTS FOR THE SEM

97

FIGURE5. CambridgeS100 SEM conventionalobjective lens. coefficients are around two orders of magnitude smaller. In practice, the factor of improvement may be somewhat lower because of the effect of inaccuracies in the aperture lens model, the finite size of the source, and a nonoptimum final semiangle. It is also interesting to note that the mixed-field immersion lens is predicted to be significantly better than its pure-field counterparts and that the magnetic immersion lens is predicted to provide smaller probe diameters than those provided by the electric retarding field lens.

B. Resolution Limits for Immersion Lenses For a more comprehensive comparison among electric, magnetic, and mixedfield immersion lenses, the landing energy needs to be varied. Figures 6a through 6d show simulation predictions for how Cs and Cc vary with landing energy at electric field strengths of 2, 5, and 10 kV/mm and a peak magnetic field of 1 T. The electric field strengths of 2 and 5 kV/mm are of particular interest because 10 kV/mm is rarely used in practice. Designing a lens to operate close to the vacuum electrical breakdown value is not easy. The magnitude of the electric field may be less than the breakdown limit in some parts of the lens, while in other parts, typically around comers, it may exceed the limit. Unlike magnetic saturation, electrical breakdown is not a self-limiting process.

4000

--

Electric(2 kV/mrn) 3000

,o .u_ E

--

2000 - -

ul u

Electric(5 kV/rnm)

1000

-

-

Electric(10 kV/rnm) Magnetic(1 T) '

I

'

I

500

'

1000

Landing

I

'

I

1500

Energy

'

I

2000

(eV)

2500

(a)

300

--

Magnetic(1 T)

200

--

~ 100

Mixed(2 kV/mm) Mixed (5 kV/mm)

--

Mixed (10 kV/mm)

0

' 0

I 500

'

I 1000

Landing

' Energy

(b)

I 1500

(eV)

'

I 2000

'

I 2500

FIGURE 6. Simulated immersion lens aberration coefficients as a function of primary beam landing energy: (a) spherical aberration for magnetic immersion and electric retarding field lenses, (b) spherical aberration for magnetic immersion and mixed-field immersion lenses, (c) chromatic aberration for magnetic immersion and electric retarding field lenses, and (d) chromatic aberration for magnetic immersion and mixed-field immersion lenses.

ADD-ON LENS ATTACHMENTS

1000

-

99

FOR THE SEM

-

Electric(2 kV/mm) 800

-

-

600

u~ ctJ

E

v

400

agnetic(1 T)

200

0

'

I

'

500

0

I

'

I

'

I

1000 1500 Landing Energy (eV)

'

I

2000

2500

(c) 300

~

200

Magnetic(1 T)

/

--

Mixed (2 kV/mm)

u-} r-

E Mixed (5 kV/mm)

{j 100

Mixed (10 k V / m m )

0

'

0

I

500

'

I

'

I

1000

1500

Landing

Energy (eV)

(d) FIC~U~ 6. (Continued)

'

I

2000

'

I

2500

100

ANJAM KHURSHEED

The simulation results shown in Figures 6a through 6d indicate that mixedfield immersion lenses are predicted to have significantly lower aberration coefficients than those of pure-field immersion lenses (for all the energies examined). The electric retarding field lens has comparable or better aberration coefficients than those of the magnetic immersion lens at low landing energies: at an electric field strength of 10 kV/mm, the spherical aberration coefficient is better for landing energies less than 200 eV, whereas for the chromatic aberration coefficient, it is better for landing energies less than 1500 eV. However, this advantage is dramatically reduced as the electric field strength is decreased. Figures 7a through 7c show the simulation results for the aberration-limited probe diameter as the landing energy is varied. The energy spread in the primary beam is taken to be 0.15 eV. For an electric field strength of 10 kV/mm and landing energies less than 500 eV, electric retarding field lenses are predicted to provide smaller aberration-limited probe diameters than those for magnetic immersion lenses, whereas for landing energies greater than 500 eV, magnetic immersion lenses are expected to perform better. Mixed-field immersion lenses

3.00

Crossing point

2.50

E ("

v

2.00

(1) (D

E

.m

.c~ o (~.

1.50

Electric (10 kV/rnm) --

Magnetic (1 T)

l

1.00

-

-

Mixed 0.50

' 0

500

I

'

1000

I 1500

Landing Energy(eV)

'

I 2000

'

I 2500

(a)

FIGURE 7. Simulated probe diameters as a function of landing energy for immersion lenses: electric field strength of (a) 10 kV/mm, (b) 5 kV/mm, and (c) 2 kV/mm.

3.00 - -

Crossing Point

2.50 m

E r-

L I1) (1)

2.00

Electric (5 kV/mm)

E

o

"' o

1.50

- -

1.00

--

I

Magnetic (1 T) Mixed

0.50

I

500

'

I

'

I

1000 1500 Landing Energy (eV)

'

I

2000

I 2500

(b) 4.00

3.00

E r"

v

E

._~

Electric

2.00

ot._

(2 kV/mm)

-

1.00

Magnetic (1 T) Mixed

--

0,00

' 0

I 500

'

I

I

1000

I 1500

Landing Energy (eV)

(c)

FIGURE 7.

(Continued)

'

I

I

2000

2500

102

ANJAM KHURSHEED

are consistently predicted to provide smaller probe diameters, ranging from a factor of 1.5 to a factor of 2 of improvement in the probe diameter. It is also apparent that as the electric field strength decreases, the landing energy at which the magnetic immersion lens and the electric retarding field lens are predicted to give a comparable aberration-limited probe size also drops. At an electric field strength of 5 kV/mm, the crossing point drops to just under 250 eV, whereas for 2 kV/mm, the crossing point falls to around 110 eV (not shown for reasons of scale). The simulation results shown in Figures 6a through 6d and 7a through 7c indicate that for most practical situations, when an electric field strength of 5 kV/mm or less is used, the electric retarding field lens is advantageous for only very low landing energies (<200 eV). The best form of immersion lens in all cases is the mixed-field immersion lens. These considerations are important when one is designing an add-on immersion lens for the SEM. Low primary beam voltages (<2 kV) are often required to minimize the effect of charging on dielectric specimens (Joy, 1989). Very low voltages (<50 eV) are used for studying surface crystallinity, when diffraction in the beam becomes dominant. The low-energy electron microscopy (LEEM) technique, in general, has been reported to be a versatile surface analytical tool (Bauer, 1994; Frank and MtillerovL 1999).

II. IN-LENS ATTACHMENTS For an immersion lens to fit into the space below a conventional SEM, it must be relatively small; most SEMs allow for a maximum distance of only 4050 mm between the specimen stage and the objective lens pole piece, and this therefore restricts the height of the add-on lens unit to typically less than 40 mm. This consideration points toward the use of permanent magnets as a way of energizing the magnet circuit, as opposed to the conventional method of using current-carrying coils. Figure 8 shows one possible way of designing a small, compact immersion lens. This type of design has been proposed in the context of developing portable SEMs (Khursheed, 2000). In this case, a ring magnet is placed in a magnetic circuit that surrounds the specimen. The strength of the axial field in the lens gap is proportional to the permanent magnet coercive force, Hc, and varies inversely with the size of the gap. An estimate of the effective excitation strength of the magnet is obtained by multiplying the magnet height, L, by the coercive force, Hc. For a 1-cm-high magnet, for which Hc = 0.9 • 106 A/m (a typical value for many types of permanent magnet materials such as NbFeB), the effective excitation strength is 9000 AT. In general, the two pole pieces above and below the specimen are at the magnetic potentials, qJ = HcL/2 and qJ = -HcL/2. As a way to vary the landing energy and apply an electric field at the specimen surface, the

ADD-ON LENS ATTACHMENTS FOR THE SEM

103

FIGURE8. A compact permanent magnet immersionlens design. specimen potential can be biased negatively while all other electrodes are left at zero potential. Permanent magnet add-on lens designs need to account for adverse coupling effects of stray fields between the lens and the specimen chamber walls. Figure 9 shows a simulated (by using the KEOS programs) field distribution demonstrating how the specimen chamber walls can act as a path for stray fields if the permanent magnet is not properly screened. There is a return path for the flux that creates a large negative leakage field in the region above the electron lens. The primary beam will therefore be prematurely focused before entering the add-on electron lens unit and the probe resolution will be significantly degraded.

A. Magnetic In-Lenses Figure 10 shows a schematic drawing of an add-on lens design that screens the permanent magnet from the specimen chamber walls. The permanent magnet is located completely inside the magnetic circuit and there is no leakage field. The add-on lens is placed onto the specimen stage. The SEM is operated in the normal way, using its own secondary electron and backscattered electron detectors, lenses, and deflection system. A secondary electron image of the lens top plate can be formed, and the SEM optical axis can be aligned to the add-on lens axis by normal specimen-stage movement.

104

ANJAM KHURSHEED

t_____

I0 cm

i 0.29 T

0T

Specimen chamber

-0.07T

Axial magnetic field strength FIGURE9. Stray-field problem inside a specimen chamber created by an unscreened permanent magnet add-on lens.

Lower pole piece of SEM objective lens

Primary Beam [ '~ ....................i ~A~'-

"

Backscattered Electrons

~

............................................................. /~.....Deflector and filter ! ! ]1 .......................i Screws

................................................................. ~

~

!

..............

/ e c ~~'~_1~m e n SO ............ l [

~

,w

i

]

~ ~ ~ t~~~?e-~a' , , ~ ~ , . , ~ !

=i5 =

~],:~~:::i.

'~._''-:,_.~

Magnetic -Icircui t

i

Specimen

FIGURE 10. A magnetic immersion add-on lens design that suppresses stray fields.

ADD-ON LENS ATTACHMENTS FOR THE SEM

105

The magnetic circuit completely encloses the specimen and is of the in-lens type. The magnetic gap size typically ranges from 5 to 15 mm. The specimen is placed within a few millimeters of the lens top plate. A specimen thickness of up to 1 cm can be used. Before the specimen is mounted into the add-on lens assembly, the lens top plate must be removed. The secondary electrons that leave the specimen are collimated by the strongly decreasing field gradient at and above the specimen, and spiral up through the top plate bore. After emerging through the top plate bore, the secondary electrons are directed toward the scintillator by the use of a deflector arrangement that may be entirely electrostatic or that may employ mixed magnetic and electrostatic fields (such as a Wien filter (Tsuno, 1994)). The distance between the top plate and the specimen surface (working distance), the top plate bore diameter, and the coercive force, Hc, of the permanent magnet determine the spatial resolution of the lens. Permanent magnets can be used in the add-on lens in several ways. Figures 1 l a and 1 l b show the simulated flux lines for a tube magnet and a ring magnet. The ring magnet provides greater space directly below the specimen, which may be useful for specimen movement. For both lenses shown in Figures 1 l a and 1 l b, the magnetic flux is confined to lie within the lens

FIGURE11. Simulatedflux lines for a magnetic immersionadd-on lens: (a) tube permanent magnet and (b) ring permanent magnet.

106

ANJAM KHURSHEED

assembly. For the ring magnet shown in Figure 1 lb, for which the size of the gap is 7.5 mm and a 16-mm-high NbFeB permanent magnet is used, the peak axial field strength lies around 0.3 T. For the tube magnet shown in Figure 11 a, for which a gap of 1 cm and a 5-mm-high magnet is used, the peak field was simulated to be approximately 0.4 T. A tube magnet placed under the specimen is therefore a more efficient way of energizing the magnetic circuit. Hall probe measurements were carried out for the ring magnet arrangement and are shown in Figure 12. These experimental results correlate well with the simulated results produced by KEOS (shown on the same graph). There are two basic ways by which the normal SEM objective lens can prefocus the primary beam for the add-on lens. In both cases, the objective lens is used for fine focusing. However, depending on the primary beam energy and the specimen working distance inside the add-on lens, the beam may be weakly prefocused before it enters the add-on lens, as shown in Figure 13a, or a precrossover point above the lens may be formed, as shown in Figure 13b. A precrossover focusing action is generally undesirable because it has greater aberrations associated with it. Ideally, the primary beam should enter the add-on

FIGURE12. Experimentallymeasuredand simulatedaxial fielddistributions for the magnetic immersion add-on lens with a ring permanent magnet.

ADD-ON LENS ATTACHMENTS FOR THE SEM

107

Objective lens

Add-on lens

(a)

(b)

FIGURE13. Demagnification action of the SEM objective lens" (a) weak prelens focusing and (b) prelens crossover.

lens as parallel as possible, which means that the objective lens of the existing SEM should be set to its weakest position. For many conventional SEMs, the working distance is usually provided on the monitor display screen. This working distance is not measured physically but is estimated electronically by calibrating the coil current in the final lens. When one is operating the addon lens, comparing the SEM electronic working distance with the physical working distance (distance from the final lens pole piece to the specimen surface) provides useful information. Doing so can, for instance, help reveal whether the final lens is weakly prefocusing the primary beam or whether it is creating a precrossover point. When the electronic working distance is smaller than the physical working distance, a precrossover point exists, and the height of the specimen needs to be readjusted. The total image demagnification (1/M) of the SEM and the add-on lens is obviously given by 1

M

=

1

1

MfMa

(4)

where Myis the image magnification of the SEM and Ma is the image magnification of the add-on lens. Note that the add-on lens demagnification can be

108

ANJAM KHURSHEED

inferred from images taken on test calibration specimens. The image demagnification information of the SEM is usually provided on its monitor display screen. With the presence of the add-on lens, this demagnification scale is no longer correct, but it can easily be recalibrated. A test pattern on the specimen holder may in principle provide a convenient way to achieve this. The on-axis lens aberrations can be calculated from the axial field distributions shown in Figure 12. The KEOS programs predict that a 1-keV beam focuses 1.24 mm below the lens top plate and that the spherical and chromatic aberration coefficients are 0.537 and 0.788 mm, respectively. A parallel incoming beam is assumed. These aberrations are around an order of magnitude better than those for conventional SEMs, which means that if the projected source size at the specimen is sufficiently small, as in the case of field-emission SEMs, there will be significant improvement in the minimum features that can be resolved. The focal length for the add-on lens at a beam energy of 1 keV is predicted to be 1.14 mm, also an order of magnitude smaller than its corresponding value for conventional SEMs. The demagnification of the primary beam spot is inversely proportional to the focal length. This means that when the final SEM probe size is dominated by the projected size of the source, as is usually the case in tungsten gun SEMs, the add-on lens should also provide significant improvements in the spatial resolution attainable for a given beam current. The predicted aberration coefficients for primary beam energies of 1, 5, and 10 keV are given in Table 2. They are all around an order of magnitude smaller than those of conventional SEM objective lenses. The predicted probe diameter-probe current dependence of the add-on lens compared with that of a conventional SEM objective lens is shown in Figure 14a. These results were calculated for a tungsten gun operating at a primary beam energy of 5 keV. The brightness of the gun was assumed to be 8 • 104 Acm -2 sr -1. The aberration coefficients for the conventional lens, f = 15.7 mm, Cs = 30.81 mm, and Cc = 13.3 mm, were calculated for the lens shown in Figure 5 operating at a working distance of 5 mm. The optimum beam semiangle was found for each point on the graph. The simulated probe size of the add-on in-lens lens is typically around a factor of 3 times better than that predicted for the conventional lens. At 1 pA, the predicted probe diameter is TABLE 2 SIMULATION OF ON-AXIS ABERRATIONS FOR THE PROTOTYPE MAGNETIC IMMERSION ADD-ON LENS

Beam energy Workingdistance (keV) (mm) f(mm) Cs(mm) Cc(mm) 1 5 10

1.24 2.93 4.9

1.14 1.9 2.49

0.537 1.23 1.89

0.788 1.38 1.85

100

--

Primary Beam energy of 5 key Tungsten gun

Conventional lens W D = 5 mm

80--

E t-

6 0 - -

1_

40

m

-on in-lens 2 . 93 mm

c}_

=

20--

'

'

'''"I

'

'

I0

'

'''"I

'

Probe current (pA)

'

I

I

I

I

I II

I

i000

I00

(a)

4.50

Primary Beam energy of 1 keY Field emission SEM

4.00 --

E r-

/

--

/

3.50 --

E

-

.~_ -~

o

3.00

--

2.50 --

2.00

' 1.00

'

'

'

'"'I

'

'

i0.00

'

'

''"I

'

i00.00

Probe current (pA)

I

I

I I Ill

I

1000.00

(b)

FIGURE 14. Comparison of the predicted probe diameter-probe current dependence of the magnetic immersion add-on lens with that of a conventional objective lens: (a) a tungsten gun source at a primary beam voltage of 5 keV and (b) a field-emission gun at a primary beam voltage of i keV. WD, working distance.

110

ANJAM KHURSHEED

Widened iron top plate Iron top plate

(b)

(a) 0.20

0,16

e-

E

0.12 ~

i

L_

._u (-. "~

0.08

-

-

t~

E

widened bore normal bore

...

0.04

0.00

1

1-8.00

1 12.00

T

] 16.00

Distance through top plate hole (mm) (c)

r-----

1 20,00

FIGURE 15. Simulated field distribution around the magnetic immersion lens bore: (a) flux lines below 10 # W b in a normal bore, (b) flux lines below l0 # W b in a widened bore, and (c) axial field distributions.

ADD-ON LENS ATTACHMENTS FOR THE SEM

111

4.54 nm for the add-on lens and 14.08 nm for the conventional lens. In practice, a tungsten gun SEM is usually operated at probe currents higher than 1 pA because of signal-to-noise limitations of the detection-and-display system. The predicted probe diameter-probe current dependence for a field-emission SEM operating at a beam voltage of 1 keV and using the add-on lens is shown in Figure 14b. In this case, the brightness of the gun was assumed to be 107 Acm -2 sr -1. At 1 pA, the predicted probe size is around 2.3 nm, a factor of 3 to 4 better than that for a conventional field-emission SEM operating at 1 keV. The design of the add-on lens must take into account saturation effects. It may be tempting to widen the top plate bore so that the collection of secondary electrons is improved. However, as shown in the simulation results depicted in Figures 15a and 15b, widening the top plate bore introduces extra saturation effects. In these figures, flux lines are plotted below 10/zWb for the normal bore and a widened bore. In the case of the widened bore, flux lines appear above the top plate and, in effect, widen the axial field distribution, which increases lens aberrations. Figure 15c shows the simulated axial magnetic field distribution, with and without widening of the lens top plate bore. Figure 16 shows secondary electron trajectory paths, for initial energies of 3 eV, leaving the specimen at various angles (predicted by the KEOS programs). They are collimated initially by the strongly decreasing magnetic

FIGURE16. Simulatedsecondaryelectrontrajectorypaths at an initial energyof 3 eV leaving the specimen for the magnetic immersionadd-on lens.

112

ANJAM KHURSHEED

field gradient below the top plate, and then they spread out when the field value is small. These electrons are then attracted to the scintillator detector, as in conventional SEMs. Simulation results predict that most secondary electrons with energies less than a few electron volts will go through the top plate hole, and so the transport efficiency of secondary electron collection with the add-on lens is expected to be comparable to its normal value without the add-on lens. A prototype add-on lens was constructed and placed on the specimen stage of a JEOL 5600 tungsten gun SEM. Figure 17 shows images of a tin-on-carbon specimen, without and with the add-on lens. Primary beam voltages of 5, 2, and 1 kV were used. A working distance varying between 3 and 5 mm and a demagnification of 70,000 was used for the image obtained by the conventional objective lens (without the add-on lens). A 50-/zm-diameter final aperture was used in the JEOL 5600 SEM for all add-on lens experiments. All other operating conditions were identical. These images demonstrate that the add-on lens improves the spatial resolution performance of the JEOL 5600 SEM by around a factor of 3 for a 5-kV primary beam: the minimum feature separation is approximately 20 nm without the lens and around 7 nm with the lens. The resolution was measured by estimating the minimum distance separating two objects in the image. As the primary beam voltage was lowered, the relative performance of the add-on lens improved. For a 1-kV primary beam voltage, the add-on lens improvement with respect to the conventional SEM is estimated to be around a factor of 4. Figures 18a and 18b show 5-kV backscattered electron add-on lens images of a polished stainless-steel specimen from the tungsten gun JEOL 5600 SEM. Both composition and topographic modes are shown and the best estimated resolution is around 30 nm. The backscattered electron detector used was the conventional one mounted below the objective lens pole piece. These results demonstrate that the add-on lens is compatible with the conventional backscattered electron detection mode of operation. Figure 19 shows a low-magnification image of a grid specimen, in which the 4-mm-diameter lens borehole around the edges of the image can be seen. The grid structure consists of 50 x 50-/zm squares. The field of view is clearly limited to a central region of around 500 x 500/zm. Beyond this central region, there are serious distortions of the grid lines. This field of view is several times smaller than it is for the conventional SEM mode of operation, but this is not unusual for high-resolution objective lenses. Figure 20 shows images from a field-emission SEM (Philips XL30 FEG) operating without and with the add-on lens for a primary beam voltage of 1.1 kV. A tin-on-carbon specimen was imaged at a demagnification factor of greater than 100,000. The specimen height was varied to optimize the lens performance. These images show that, as before with the tungsten gun SEM, there is an improvement of greater than 3 in the image resolution when the

ADD-ON LENS ATTACHMENTS FOR THE SEM

113

FIGURE 17. Secondary electron images, obtained from a tungsten gun SEM without (lefthand images; demagnification, 70,000) and with (right-hand images) the magnetic immersion add-on lens, of a tin-on-carbon specimen for primary beam voltages of (a) 5 kV, (b) 2 kV, and (c) 1 kV.

114

ANJAM KHURSHEED

FIGURE 18. Images, obtained from a conventional backscattered electron detector in a tungsten gun SEM using the magnetic immersion add-on lens, of a polished stainless-steel specimen: (a) composition image and (b) topographic image. Beam voltage, 5 kV; resolution, ~30 nm (smallest diameter of holes).

FIGURE 19. Low-magnification secondary electron image, obtained from a tungsten gun SEM using the magnetic immersion add-on lens, of a 50-/zm grid pattern specimen at a primary beam voltage of 5 kV.

FIGURE 20. Secondary electron images of a tin-on-carbon specimen, obtained from a fieldemission SEM (Philips XL30 FEG) operating (a) without and (b) with the magnetic immersion add-on lens for a primary beam voltage of 1.1 kV. Demagnification, 100,000.

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ANJAM KHURSHEED

FIGURE 21. Add-on lens schematic drawing illustrating specimen movement through the use of step motor drives.

add-on lens is used. The image resolution using the add-on lens was estimated to be less than 2 nm (found from line scans across the image). This result is slightly better than the simulation predictions shown in Figure 14b. A 50-/zmdiameter final aperture was used in the field-emission SEM for all add-on lens experiments. The specimen can be moved within the add-on lens assembly by the use of small motors. The motors are located outside the lens but have spindles that penetrate the lens walls and connect onto a movable specimen holder. Figure 21 shows an isoparametric view of a possible add-on lens design (the top plate lid is open) that incorporates specimen movement. It has three motors: two for specimen x - y movement and one for specimen z movement. Specimen height movement is crucial in optimizing the add-on lens performance. The resolution of the final image was found to increase with the add-on lens demagnification. For a given primary beam energy, the working distance must be adjusted so that add-on lens demagnification is high, typically greater than 10. How the add-on lens demagnification strength varies with working

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distance for different primary beam energies is shown in Figure 22. These resuits were obtained experimentally by imaging grid specimens with known grid spacing. Higher demagnification strengths can potentially be obtained at lower primary beam energies, but the working distance must be suitably readjusted. This observation highlights the importance of incorporating specimen height movement into the add-on lens design. Figure 23 shows the photograph of an add-on lens prototype in which the vertical motion of the specimen is controlled by two motors located at the top of the lens, and a sliding lid section in the lens top plate provides access to the specimen holder. This photograph demonstrates the compact size of the add-on lens unit. The use of two motors to control the height of the specimen was found to provide better control for keeping the specimen horizontal, which is essential when one is doing high-resolution work. Figure 24 shows experimental results for the JEOL 5600 SEM for a goldon-carbon test specimen. As for the tin-on-carbon specimen, the add-on lens

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ANJAM KHURSHEED

FIGURE23. Photographof a magnetic immersion add-on lens prototype.

improved the resolution by more than a factor of 4. Also shown in Figure 24 is the comparison of a 20-kV conventional SEM image (without the add-on lens) with an image obtained from using the add-on lens at a primary beam voltage of 3 kV. The images are comparable in resolution, which illustrates the ability of the add-on lens to provide low-voltage images at a similar resolution to what a conventional SEM obtains, only at high primary beam voltages. The interaction volume in this case does not limit the image resolution because the surface layer of gold on the specimen is thin (several nanometers thick). Deflection of the secondary electrons toward the scintillator can significantly improve the transport efficiency of secondary electron detection. This strategy of improving the secondary electron collection is not usually compatible with the SEM's normal mode of operation because it introduces astigmatism on the primary beam and significantly increases the working distance. In this case, as with other through-the-lens (TTL) collection schemes (Khursheed, 2001), deflection of the secondary electrons off-axis does not affect the working distance. One possibility is to use a negatively biased circular metal strip that is partially open on one side, as shown in Figure 25. The secondary electrons will experience a transverse field attracting them to the open side. An electrostatic deflector arrangement of the type depicted in Figure 25 was constructed and mounted on top of the add-on lens unit. The deflector plate had a diameter of 51 mm and was 10 mm high. The output signal obtained by varying the deflector plate from 0 to - 3 0 V is shown in Figure 26. The peak position lies approximately between - 7 . 5 and - 1 3 V. This variation shows that to maximize the image signal-to-noise ratio, there is an optimum value for VD.

FIOtrRE 24. Tungsten gun SEM images of a gold-on-carbon specimen, taken without (lefthand images) and with (fight-hand images) the magnetic immersion add-on lens: primary beam voltages of (a) 1 kV, (b) 3 kV, and (c) 20 kV (left) and 3 kV (fight).

120

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ADD-ON LENS ATTACHMENTS FOR THE SEM

121

B. M i x e d - F i e l d L e n s e s

One obvious improvement to the add-on lens design described so far is to allow for the flexibility of biasing the specimen to large negative voltages. This, in effect, creates a mixed electric-magnetic field immersion lens. Just as in the electric retarding field lens case, the primary beam is allowed to traverse most of the column with a moderate- to high-energy beam (typically 5 kV and greater) and is deaccelerated just before it strikes the specimen surface. Specimen voltage variation also helps in the fine focusing of the primary beam. The lens top plate and its casing remain at ground potential so that a large electric field is created between the specimen and its surroundings. This add-on lens design is similar to that presented by Hordon, Huang, Maluf, et al. (1993). Simulations for a 5-mm cylindrical block magnet design using a lens bore size of 4 mm and a gap of 10 mm, based on the design shown in Figure 11 a, predict that a 6-kV primary beam focuses onto a - 5 - k V specimen at 2 mm below the lens top plate. The landing energy for these conditions is 1 keV and the simulation results also predict that f - 0.719mm, C s - 0.235 mm, and Cc = 0.251 mm. These aberration coefficients are typically more than a factor of 2 smaller than those predicted for the corresponding pure magnetic immersion lens, for which a 1-keV primary beam focuses 1 mm below the lens top plate, with f -- 1.08 mm, Cs -- 0.482 mm, and Cc -- 0.733 mm. Figure 27a depicts the simulation of 3-eV secondary electrons leaving a - 5 0 0 - V specimen over a wide range of emission angles. Most of these electrons travel straight back up the SEM column and therefore the output signal level is expected to be much smaller than in the case in which the purely magnetic add-on immersion lens is used. Figure 27b shows the simulation of 500-eV backscattered electrons under the same field conditions. Their trajectory paths, as compared with the 3-eV secondary electron trajectory paths, are much more spread out in the radial direction. This means that when the specimen is biased to large negative voltages, the influence of backscattered electrons on the final secondary electron detector image is expected to be much greater than is usually the case. However, as the landing energy decreases (<2 keV), the beam interaction volume of the backscattered electrons also strongly decreases and secondary and backscattered electron images become more and more comparable in resolution. One particularly attractive feature of the mixed-field immersion add-on lens is that it can combine conventional semiconductor backscattered electron detection with low landing primary beam energies at the specimen. Signal-tonoise constraints usually mean that the conventional backscattered electron detector can image only electrons that have energies of at least 5 keV or greater incident upon it. If the specimen is biased to - 5 kV, and a 6-kV primary beam

122

ANJAM KHURSHEED

FIGURE 27. Simulated electron trajectories leaving a specimen o f - 5 0 0 V in the mixed-field add-on lens: (a) 3 eV and (b) 500 eV.

ADD-ON LENS ATTACHMENTS FOR THE SEM

123

is used, then a landing energy of 1 keV at the specimen is achieved. The secondary electrons will strike the backscattered electron detector at an energy of 5 keV, and the backscattered electrons will strike it at 6 keV. These kind of voltage conditions allow for the acquisition of low landing energy backscattered electron images with a conventional SEM. Obviously, the landing energy can be lowered to very low voltages (<100 eV). The advantages of using the backscattered electron detector to image low landing energies is that backscattered electrons are less affected by specimen charging. They are also much more sensitive to material contrast and can in principle be used to provide material composition information. As with the purely magnetic immersion add-on lens, the mixed-field immersion add-on lens also needs to adjust the working distance within the lens to achieve high resolution. It should be noted that if images are to be obtained by means of a conventional (semiconductor) backscattered electron detector, as the working distance is made small (<1 mm), care should be taken to avoid electric field breakdown. Figure 28 shows secondary electron images taken at landing energies of 1, 0.8, and 0.6 keV with a prototype mixed-field immersion add-on lens. The JEOL 5600 tungsten gun SEM was used. In this case, a 5-mm-high cylindrical block permanent magnet excited the magnet circuit, of the type shown in Figure 11 a. The primary beam voltage was increased to 7 kV. The specimen used was a fin-on-carbon specimen in which the tin spheres ranged from 10 to 100 nm in diameter. A conventional SEM image (taken without the add-on lens) for a primary beam energy of 1 keV was taken for comparison under the same specimen conditions. The spatial resolution was estimated by measuring the 25-75 % rise time of the signal over a sphere edge in the line scan acquisition mode. At 1 keV, the resolution for the mixed-field immersion lens was found to be less than 4 nm, while the resolution of the corresponding conventional SEM image for the same specimen was so much poorer that it could not be estimated. The resolution for the 600-eV image also was less than 4 nm. These results show that the mixed-field immersion add-on lens can extend the energy range of normal SEMs and thus enable them to provide high-resolution images at low landing energies. It should be noted that high resolution of this kind at relatively low landing energies (< 1 keV) is not usually possible with tungsten gun SEMs. Figures 29a and 29b show secondary and backscattered electron images at a landing energy of 1 keV for the same conditions. These images are comparable, which demonstrates that the add-on lens can provide high-resolution images at low landing energies by means of the use of a conventional backscattered electron detector. The resolution of these images is estimated to be better than 4 nm.

124

ANJAM KHURSHEED

FIGURE 28. (a) Conventional SEM image for a primary beam energy of 1 keV (demagnification, 100,000; working distance, 3 mm). (b)-(d) Low-voltage secondary electron images of a tin-on-carbon specimen, obtained from a tungsten gun SEM using the mixed-field immersion add-on lens: (b) landing energy, 1 keV; primary beam voltage, 7 kV; -6-kV specimen; (c) landing energy, 0.8 keV; primary beam voltage, 7 kV; -6.2-kV specimen; (d) landing energy, 0.6 keV; primary beam voltage, 4 kV; -3.4-kV specimen.

ADD-ON LENS ATTACHMENTS FOR THE SEM

125

FIGURE29. Comparisonof low-voltage (a) secondary electron and (b) backscattered electron images, obtained from a tungsten gun SEM using the mixed-field immersion add-on lens, of a tin-on-carbon specimen. Demagnification, 100,000; primary beam energy, 7 kV; -6-kV specimen; landing energy, 1 keV. The biasing of the specimen voltage in the add-on immersion lens gives it much more flexibility. When a strong electric field cannot be used at the specimen surface, or when high primary beam voltages are required, the addon lens can operate mainly as a magnetic immersion lens. In contrast, when moderate electric field strengths can be used (1-5 kV/mm), mixed immersion fields within the add-on lens can provide high-resolution images at low primary beam landing energies.

III. SINGLE-POLE LENS ATTACHMENTS The size of the add-on immersion lens limits the size of the specimen that can be fitted into it. Given the space available in a conventional SEM among the specimen stage, scintillator cage, and the final lens lower pole piece, the addon lens must typically be less than 100 mm in diameter and less than 40 mm high. Relatively thick specimens, up to 10 mm high, can be used. Taking into account the need to have x - y specimen stage movement, the diameter of these specimens is restricted to less than 50 mm. One inconvenience of this lens is that part of the top lid must be removed every time the specimen is changed. In the case of thin specimens, typically those 2 mm high or less, a singlepole add-on lens can be used. This lens avoids the need to have a magnetic top plate and allows for an easier change of specimen. Also, it is not restricted by the size of the magnetic circuit, so that it can accommodate larger specimens, typically those having diameters up to 100 mm or more (in conventional SEM specimen chambers).

126

ANJAM KHURSHEED

FIGURE 30. Simulated flux lines for a single-pole add-on lens.

A single-pole add-on lens design is shown in Figure 30. A conical highsaturation iron pole piece is placed on top of a cylindrical block permanent magnet, which is in turn located at the center of a rotationally symmetric iron circuit. The single-pole tip protrudes above the surrounding iron casing. A thin specimen is positioned to lie as close as possible to the central pole tip. The magnetic axial field strength falls sharply from the surface of the central single-pole tip, and its peak value is limited by saturation effects. For a 2-mm-diameter tip and a 10-mm-high permanent magnet, simulation resuits predict that the peak field strength lies just beyond 0.7 T, as shown in Figure 31. If a 5-mm-high magnet is used, the predicted peak axial field strength is only marginally lower, which indicates that saturation effects at the pole tip limit the strength of the peak axial field. The working distance in this case is defined to be the distance from the central single-pole tip to the specimen surface. A prototype single-pole lens was constructed, having a 2-mm-diameter pole tip and a 5-mm-high cylindrical NbFeB block permanent magnet. Mild steel was used in the iron circuit of a lens design comparable to that depicted in Figure 30. A grid specimen having 12.7/zm between the center of its lines and having rectangular holes measuring approximately 5 x 6 # m was used. The specimen was approximately 300 nm thick and was placed directly onto the central pole tip of the lens, so that the working distance lay below 0.5 mm. Images of the specimen without and with the single-pole add-on lens at a primary beam voltage of 2 kV are shown in Figures 32a and 32b, respectively.

ADD-ON LENS ATTACHMENTS FOR THE SEM

127

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These experimental results show that the add-on lens provides more surface detail at the grid surface, which indicates that it improves the resolution of the SEM. The probe demagnification strength of the single-pole add-on lens for these conditions was greater than 10. The normal SEM objective lens was used to achieve fine focusing in combination with the add-on lens. Because in this case the specimen was placed directly on the single-pole tip, the primary beam voltage was adjusted until high-demagnification strength was obtained (>10). In principle, z movement of the specimen can be incorporated into the lens design and the working distance can then be varied to always arrive at high-demagnification operating conditions for a given primary beam voltage. An obvious extension of the single-pole add-on lens is to bias the specimen so that the primary beam is focused onto the specimen by mixed electric-magnetic fields. The specimen can be biased negatively, as shown in

FIGURE 32. Secondary electron images obtained from a tungsten gun SEM of a copper grid specimen: (a) conventional image and (b) with the single-pole add-on lens.

ADD-ON LENS ATTACHMENTS FOR THE SEM

129

FIGURE33. Retarding field single-pole add-on lens: (a) biasing the specimen and lens and (b) biasing the specimen, lens, and shielding plate. Figure 33a, or it can be placed behind a shielding plate, which is biased to the same voltage as that of the specimen, as shown in Figure 33b. This latter layout substantially reduces the electric field strength at the specimen surface, which for some specimens helps in minimizing local charging effects. A 0-V nonmagnetic top plate is positioned approximately 3 - 6 mm above the central singlepole tip, which localizes the region in which the primary beam is retarded. Figure 34a shows simulated equipotential lines for the mixed-field singlepole lens when the specimen and lens casing is biased to - 5 kV. The electric retarding field is confined to the region between the specimen and the 0-V nonmagnetic top plate. There is noshielding plate in front of the specimen in this case. Simulation results for an incoming parallel beam predict that a 6-kV primary beam will focus at a working distance of 1 mm (distance

130

ANJAM KHURSHEED

FIGURE34. Simulation of the retarding field single-pole add-on lens: (a) equipotential distribution and (b) secondary electron trajectories. from single-pole tip to the specimen surface) in this lens design. The effective landing energy is 1 keV and an electric field strength of 1.25 kV/mm is created at the surface of the specimen. Under these conditions, simulation results predict that f = 1.06 mm, Cs = 0.214 mm, and Cc = 0.318 mm. For a landing energy of 500 eV at the same working distance, simulation results predict that f = 0.7 mm, Cs = 0.147 mm, and Cc = 0.2 mm. When the shielding plate

ADD-ON LENS ATTACHMENTS FOR THE SEM

131

is added, the field strength is decreased to 288 V/mm, and the predicted aberrations become f = 0.946 mm, Cs = 0.359 mm, and Cc = 0.484 mm. The mixed-field single-pole add-on lens, like its full immersion lens counterpart, is thus also expected to provide high resolution at low primary beam landing energies. Simulation of secondary electron trajectories in the mixed-field single-pole lens shows that they are strongly collimated and travel up close to the electronoptical axis. Figure 34b shows the simulated trajectory paths of 3-eV secondary electrons that leave the specimen over a wide range of emission angles. The specimen voltage is biased to - 5 kV. On the basis of these results, the collection efficiency of secondary electrons is expected to be low because most of them will travel up the objective lens bore. The experimental results shown in Figure 35 confirm that the drop in secondary electron collection efficiency is significant in practice. These images were generated from the JEOL 5600 tungsten gun SEM. The prototype magnetic single-pole add-on lens used in the previous experiment was slightly modified to incorporate the possibility of specimen biasing, and a removable nonmagnetic top plate was placed on top of the lens once the specimen had been fitted into position. In this figure, secondary and backscattered electron images are compared for the situation in which the specimen voltage changes from - 3 to - 5 kV, with a primary beam voltage of 7 kV. Normally, the secondary electron image has better signal-to-noise characteristics than those of the backscattered electron image, as shown in Figure 35a, in which a specimen voltage of - 3 kV was used (giving a landing energy of 4 keV). However, in the case of a -5-kV specimen voltage (landing energy of 2 keV), the secondary image is noisy and is poorer than the backscattered electron image. This reduction in collection efficiency of the secondary electrons was found to depend on the specimen bias voltage. Generally, the secondary electron image became noisier as the specimen voltage was biased to greater negative voltages. The secondary electron image quality became excessively noisy when the specimen was biased to voltages greater than 5 kV in magnitude (in the JEOL 5600 SEM used for these experiments). For these types of strong retarding field conditions, ways to improve the secondary collection need to be found. One approach is to use a Wien filter, consisting of transverse electric and magnetic fields that are orthogonal to each other and perpendicular to the primary beam axis (Tsuno, 1994). Figure 36 shows simulation results for the trajectory paths of 3-eV secondary electrons as they leave the specimen over a wide range of emission angles in the presence of a Wien filter. The Wien filter has an excitation strength of 20 AT on the magnetic pole faces. The simulation results predict that the path of the secondary electrons will be significantly deflected from the optical axis, so considerable improvement in the collection of the secondary electrons can be expected. However, the Wien

132

ANJAM KHURSHEED

FIGURE 35. Comparison of secondary (left-hand images) and backscattered (right-hand images) electron images obtained from a tungsten gun SEM using the retarding field single-pole add-on lens: (a) 4-keV landing energy and (b) 2-keV landing energy. Primary beam voltage, 7 kV; specimen voltage, - 3 kV for (a) and - 5 kV for (b).

ADD-ON LENS ATTACHMENTS FOR THE SEM

133

FIGURE36. Simulated3-eV secondaryelectrontrajectories in the retardingfield single-pole add-on lens using a Wien filter. filter will influence the primary beam, and adverse aberration effects need to be minimized by carefully matching its transverse electric and magnetic field distributions (Lencova, 2000). Figures 37a through 37f show backscattered electron images for specimen voltages of 0, - 1, - 2 , - 3 , - 4 , and - 5 kV and a primary beam voltage of 7 kV, which give landing energies of 7, 6, 5, 4, 3, and 2 keV, respectively. The image becomes brighter and has better resolution as the magnitude of the specimen voltage is increased. These results show that better images are obtained for lower landing energies, the reverse of what is normally expected. In this case, the working distance is fixed, so as the landing energy is decreased (specimen becomes more negative), the demagnification strength of the add-on lens is increased. Also, the beam-specimen interaction volume is smaller for lower landing energies. For these reasons, the conventional backscattered electron detector is able to provide better-quality images at low landing energies. For more practical single-pole add-on lenses, provision for varying the specimen

134

ANJAM KHURSHEED

FIGURE 37. Backscattered electron images taken by using the retarding field single-pole add-on lens in a tungsten gun SEM with a 7-kV primary beam voltage: specimen voltages of (a) 0 kV, (b) -1 kV, (c) - 2 kV, (d) -3 kV, (e) - 4 kV, and (f) -5 kV.

height is required, so that the highest point of demagnification can always be found for a given primary beam landing energy. The experimental results presented for the single-pole add-on lens demonstrate that this lens is in principle feasible and that when specimens are thin (<2 mm), it can be used as an alternative to the full immersion add-on lens to improve the optics of an existing SEM.

ADD-ON LENS ATTACHMENTS FOR THE SEM

135

IV. SECONDARYELECTRON ENERGY SPECTROMETERS

The add-on lens unit can be modified to function as a voltage contrast spectrometer. Quantitative information on a specimen's surface potential can at present be obtained by systems known as electron beam testers (EBTs) (Plies, 1990; Thong, 1993). Although normal SEMs do exhibit some measure of voltage contrastmthat is, the brightness of a point on the image changes when its corresponding point on the specimen changes voltagemit is not easy to quantify. An EBT is a dedicated SEM system that quantifies this effect and is most popularly used to probe waveforms on integrated circuit specimens. It functions by detecting changes in the initial secondary electron energy distribution. The output signal of these systems shifts linearly as the specimen voltage changes. The central component of EBT systems is a voltage contrast spectrometer, which acts like an energy filter on the secondary electrons. The type of energy filter used so far in commercial EBT systems is known as a retarding field spectrometer, which is in effect a high-pass filter allowing for the collection of secondary electrons that can surmount a potential barrier. Figure 38a depicts how a retarding field spectrometer functions. A potential barrier is created within the spectrometer by biasing a retarding electrode or grid to a voltage VR. The strength of the potential barrier is given by VR -Vs, where Vs is the specimen voltage. Only electrons having initial energies greater than e(VR -- Vs) will surmount the potential barrier and contribute toward the output signal (represented by the shaded area in Fig. 38a). When VR is varied, an integrated form of the secondary electron energy spectrum is obtained, as illustrated in Figure 38b. This output signal is sometimes referred to as an S curve. Shifts in the output signal are therefore obtained when the specimen voltage changes (indicated byVs2, and Vsl in Fig. 38b). For quantitative voltage measurements, retarding field spectrometers are normally operated in the closed feedback loop mode, in which the strength of the potential barrier is adjusted to keep the output current constant, as illustrated in Figure 38a. The output current is continually compared with an offset current level. Adjustments in the retarding electrode voltage to keep the output current constant are therefore equal to specimen voltage changes, A VR -- V S 2 - - gs1.

Figure 39 shows a schematic diagram of the EBT reported by Richardson and Muray (1988). In this case, the integrated circuit specimen is placed in the magnetic field of a semi-in-lens objective lens. The secondary electrons are allowed to spiral up through the lens bore. After traversing the lens, they are energy filtered by a retarding grid electrode. An electrostatic deflection arrangement is then used to steer them onto a scintillator detector located off-axis. Richardson and Muray predicted through simulation that many secondary electrons will collide into the objective lens bore walls, and they used a weak solenoid coil to counteract this effect.

136

ANJAM KHURSHEED ~el ~

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The permanent magnet add-on lens can be designed to operate as a voltage contrast detector and overcome many well-known disadvantages of conventional EBT systems. In particular, it can function as an open-loop multichannel voltage contrast spectrometer, from which a quantitative voltage measurement is directly obtained from an output signal, without the need to use feedback. Open-loop voltage contrast spectrometers require only that an output signal be stored before proceeding to acquire another signal. Time may be needed to acquire the output signal, but this can be done relatively fast (in fractions of a microsecond). This feature allows for the possibility of time multisampling

ADD-ON LENS ATTACHMENTS FOR THE SEM

137

FIGURE39. The retarding field voltage spectrometer designed by Richardson and Muray (1988). of periodic signals on the specimen; that is, in one period, many voltage measurements can be made, each at a different phase point of the specimen signal being probed. This advantage is important for waveforms that have relatively long time periods, typically several hundred microseconds or longer. In comparison, the feedback system of retarding field spectrometers is usually limited to a single voltage measurement every waveform cycle. An open-loop mode of operation also allows for voltage measurements of dc levels. Retarding field spectrometers cannot operate in this way because they require a feedback loop detecting voltage specimen changes. A multichannel voltage contrast spectrometer provides output signals that change form and shift when the specimen voltage changes. Once the system is calibrated, a voltage measurement can be directly obtained from a single output signal.

138

ANJAM KHURSHEED

A multichannel voltage contrast spectrometer uses secondary electrons collected over the whole energy spectrum to make the voltage measurement. Conventional retarding field spectrometers collect electrons at a single point on the S curve (integrated form of the secondary electron energy spectrum). This difference is important when one is considering the signal-to-noise ratio characteristics of a voltage measurement. Retarding field spectrometers, by integrating electrons over a wide energy range, are much less sensitive to specimen voltage variations than are multichannel voltage contrast spectrometers. Khursheed (1992) has demonstrated that multichannel voltage contrast spectrometers have signal-to-noise ratios that are a factor of more than 30 times better than those of retarding field spectrometers.

A. Time-of-Flight Voltage Contrast Spectrometers An open-loop multichannel voltage contrast detector was designed and tested by Khursheed and Dinnis (1990). Their proposal was based on using the time of flight of the secondary electrons. The primary beam is pulsed, as is normally required for time-resolved voltage contrast measurements. The specimen is placed in a magnetic immersion lens, and the secondary electrons are collimated as they travel up the objective lens bore. A high-bandwidth detector system collects the secondary electrons at the top of the objective lens. The lens bore acts as a drift-tube region for the secondary electrons. The sharply decreasing axial field strength through which the secondary electrons initially travel will not only collimate the secondary trajectory paths, but make their time of flight relatively independent of their initial emission angle. Under these conditions, the output signal will be directly related to the form of the initial secondary electron energy spectrum (Kruit and Read, 1983). Neglecting the effect of the initial emission angle, a secondary electron having an initial energy, E (in eV), has a time of flight, T, given approximately by d

T = - =

v

c

~/E+(Vd-

Vs)

(5)

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P(T)-

dN dN dE C2 = = 2~--zQ(E) 1~ dE dT dT

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The limited bandwidth of the detection system will tend to distort the output signal, and its influence may be approximated by a low-pass filter response

ADD-ON LENS ATTACHMENTS FOR THE SEM

139

with a single time constant, r, in which case, the output signal, S(T), is given by

S(T) -- ( 1 / v ) e x p ( - T / v ) fo T P(x) exp(x/v) dx

(7)

The Chung-Everhart energy distribution can be used for the secondary electron energy distribution at the specimen (Chung and Everhart, 1974):

Q(E) --

6W2E

(8)

(E + W) 4

where W is the specimen work function. Using the four preceding equations allows the output signal of the time-of-flight spectrometer to be predicted. Khursheed and Dinnis (1990) used a modified Cambridge S 100 SEM to test the time-of-flight spectrometer concept. A schematic drawing of the experimental layout they used is shown in Figure 40. They pushed a small copper Primary beam

...................................... Output . . . . . . . .Signal MCP secondary_electron detector[. . . . . . . . . . .

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S 100 Objective lens Copper stub specimen placed in lens gap FIGURE40. Time-of-flightvoltage contrast experimentperformedby Khursheed and Dinnis (1990). MCP, multichannel plate.

140

ANJAM KHURSHEED

stub specimen into the middle of the S 100 objective lens gap and used a multichannel plate detector with a high-bandwidth transimpedance head amplifier to obtain the output signal. The final signal was displayed on a 400-Msa/s digitizing oscilloscope that was also linked to a personal computer for data capture. Originally, it was thought that the detection system bandwidth was around 140 MHz, but subsequent analysis of the output signals revealed that it was in fact around 10.6 MHz (r = 15 ns). Experimental results, for the specimen voltage changing in 1-V steps from - 1 to - 5 V and a drift-tube voltage of 0 V, are shown in Figure 41 (Khursheed, 1992). Five hundred time channels were used and the effective drift distance was 11.9 cm. Figure 42 shows that the theoretical predictions based on using the preceding equations match quite well with the experimental results.

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0.00

'

40.00

80.00

I

'

120.00 Time of Flight (ns)

I

160.00

'

..... I

200.00

FIGURE 41. Experimental time-of-flight voltage contrast output signals obtained by Khursheed (1992).

ADD-ON LENS ATTACHMENTS FOR THE SEM

14 1

1.00 - ' -S V

0.80

--

Head amplifier time constant of 15 ns experimental

tn e-

.>

.4,,-I Ct~

.......

0.60

simulated

--

V 4-a r(D k_ kL)

0.40 - -

Ca. .Ca

o

,

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-1 V

, i

,,,'~ =. .

0.00

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f .

.

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.

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I

.

I00.00

'

i

'

150.00

Time of flight (ns)

=_

I

200.00

I 250.00

FIGURE42. Comparison of experimental time-of-flight voltage contrast signals with those predicted by simulation.

Convenient ways to quantify the specimen voltage for multichannel spectrometers can make use of the signal mean,/z, and variance, 0., lz --

0 .2

-

-

/o"

T f (T) dT

f0 Tc(T --/z)2f(T) d T

(9)

(10)

where f(T) is the output signal probability density function. This function is obtained by normalizing each output signal, S(T), to its total area. Figures 43a and 43b show how the signal mean,/z, and variance, 0., are predicted to vary as functions of specimen voltage. These graphs were plotted by using Eqs. (5)-(8).

With suitable postprocessing, these graphs can be linearized, and for a given output signal, an estimate of the specimen potential can be readily obtained.

ii0,00

-

-

100.00 - -

u% c~ e-

90.00

E rc -

J

C~

80.00 - -

J

70.00

'

I

-4.00

-5,00

....i............. I

"

-3.00 Specimen voltage (volts)

I

' ............. 1

-2.00

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(a)

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36.00

o'/ r--

--,

--

32.00

"r"

~ ._~

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24.00

20'00

II

-s.oo

'

I

-4.00

I

I

'

-3.00

Specimen voltage (volts)

I -2.00

'

I

-1.00

(b)

FIGURE 43. S i m u l a t e d variation o f time-of-flight output signal parameters with s p e c i m e n voltage: (a) signal m e a n and (b) signal standard deviation.

ADD-ON LENS ATTACHMENTS FOR THE SEM

143

FIGURE44. Possible time-of-flightvoltage contrast spectrometermode of operation for the magnetic immersionadd-on lens. The add-on lens can in principle be operated in the time-of-flight voltage contrast mode. Figure 44 shows one possible layout that can be used to achieve this. The microchannel plate/transimpedance head amplifier detection system needs to be placed below the SEM objective lens, typically by using a specimen chamber side port as is employed for mounting the conventional backscattered electron detector. The SEM must be fitted with blanking plates. One important aspect about the time-of-flight spectrometer is that it is capable of capturing the whole energy distribution of scattered electrons in the SEM, from secondary electrons close to 0 eV to near perfectly elastic backscattered electrons (Khursheed and Dinnis, 1992). This means that it can also in principle be used to acquire Auger and backscattered electrons, which thus means that the SEM time-of-flight spectrometer is potentially a very powerful analytical tool.

144

ANJAM KHURSHEED

To make use of Auger electrons, one must have an ultrahigh-vacuum environment. In the case of backscattered electron detection, the time-of-flight spectrometer provides a convenient way of achieving energy filtering. Separating the more elastic backscattered electrons from inelastic ones by means of energy filtering can provide significant improvements in topographic contrast (Wells, 1971). Rau and Robinson (1996) have bandpass filtered backscattered electrons in order to provide topographic images at different depths in multilayered structures. Incorporating a time-of-flight spectrometer into an SEM transforms it into a powerful analytical multicontrast tool, and there is no reason why SEMs cannot be designed to function in this way in the future.

B. Deflection Voltage Contrast Spectrometers Another method of producing multichannel open-loop voltage contrast with the add-on lens, more compatible with an SEM's normal mode of operation, is to deflect the secondary electrons off-axis. The secondary electrons can be deflected off-axis relatively early in their trajectories, that is, while they are still close to the optic axis. This allows for the possibility of obtaining their energy spectrum spread in the vertical direction, where the detector plane is situated to one side, far off-axis. For a given deflection field strength, the lower-energy secondary electrons will experience more deflection than those with higher energy, and their relative positions at the detector plane will be directly related to their initial energies. Because the secondary electrons are strongly collimated by the add-on lens magnetic field, their trajectory paths will be relatively independent of their initial emission angles. Simulation results demonstrating this effect are shown in Figure 45. In this case, a Wien filter with radius of 1 cm uses 1 AT on its magnetic coils and is designed to operate with a primary beam voltage of 1 kV. The trajectory paths

FIGURE45. Simulatedenergy dependence on the deflection of secondary electron trajectory paths in the magnetic immersion add-on lens.

ADD-ON LENS ATTACHMENTS FOR THE SEM

145

of secondary electrons having initial energies of 1, 3, and 5 eV emitted over a wide range of angles are well separated after deflection. The energy spectrum can be detected either by a multichannel detector (such as a microchannel plate detector) or by a single detector. In the latter case, the strength of the deflector field is varied with time, which produces a time-varying output signal. This method has the merit of not requiting an additional detector because it makes use of the SEM's existing Everhart-Thornley detection system. One way to increase the energy resolution is to include a slit aperture in front of the detector. A plate with a slit can be mounted onto the add-on lens, as shown in Figure 46a. E1 and E2 (E2 > El) represent secondary electrons that leave the specimen with different energies. Changes in the specimen voltage, indicated by the transition of Vsl to Vs2 in Figure 46a, will cause linear shifts

FIGURE46. Slit aperture collectionfor quantitative voltage contrastusing the magnetic immersion add-on lens: (a) mounted onto the lens top plate and (b) enclosing the scintillator cage.

146

ANJAM KHURSHEED

in the output signal, and in this way the add-on lens can operate as a voltage contrast spectrometer. An alternative way of creating a slit aperture is to wrap the scintillator cage with metal foil, as shown in Figure 46b. A voltage measurement can be made by monitoring the output signal's mean value in terms of the deflection strength, VD. If the deflection voltage takes n values in constant steps of A VD, the mean value,/z, is given by n

Y~j-I VDjG Y~j=I lj

(11)

n

/L - -

where/j is the jth output current sample obtained at the jth deflection voltage VDj. The mean value is then a function of specimen voltage Vs, Iz(Vs). By a simple procedure of calibration, the specimen voltage associated with any output signal can then be inferred. As a way to test if this deflection voltage contrast effect is feasible, an experiment was performed with the add-on lens unit in a JEOL 5600 tungsten gun SEM. The scintillator cage was wrapped in metal foil which had a 5mm-wide slit cut into its underside, and a horseshoe deflection plate arrangement was used, as shown in Figure 47. The horseshoe deflector plate had a diameter of 51 mm and was 10 mm high. The output current signals obtained by varying the deflector plate voltage from 0 to - 6 0 V for specimen

Add-on lens

Detector

FIGURE 47. Plan view of a horseshoe electrostatic deflector placed above the add-on lens top plate.

ADD-ON LENS ATTACHMENTS FOR THE SEM

147

300.00

r r ::3 (D

200.00

--

.> 4..a fO 0) i.. 4..a r (1.) l_

t.) :3 C)_ 4..a ::3

Specimen voltages

100.00

O

0.00

I 0.00

20.00

40.00

60.00

Deflection voltage magnitude (volts) FIGURE 48. Experimental voltage contrast signals obtained by using slit aperture collection and the horseshoe electrostatic deflector with the magnetic immersion add-on lens.

voltages o f - 5 , 0, and 5 V are shown in Figure 48. A polished copper stub specimen was used. There was clearly significant voltage contrast. As expected, the signal level for the 5-V specimen had a lower height than that of the other signals. This was because there was a potential barrier between the specimen and the 0-V lens upper plate and only electrons that had initial energies greater than 5 eV were collected. The negative specimen voltage was of particular interest because it was shifted to the fight and broadened with respect to the 0-V case. Approximately 1000 channels (time steps) were used in this experiment. The mean values of VD calculated from the output signals for the specimen voltages of 0 and - 5 V were - 1 5 . 2 4 and - 2 2 . 6 9 V, respectively. These results provided initial confirmation that the add-on in-lens unit could be operated as a quantitative multichannel voltage contrast spectrometer. Of particular interest was the substantial broadening of the - 5 - V specimen

148

ANJAM KHURSHEED

output signal. The higher-energy secondary electrons appeared to produce a greater voltage contrast effect (falling edge of the signal) than did the lowerenergy one (rising edge). This is not possible with conventional retarding field spectrometers. The voltage contrast spectrometer presented in Figures 46 and 47 is expected to be less sensitive to the adverse effects of local transverse fields at the specimen surface. These fields can cause large errors in the voltage measurements of conventional retarding field spectrometers (Khursheed and Goh, 1997). In the case of the output signal for the - 5 - V specimen, if there are local fields at the specimen that create a potential barriermin effect filtering out all secondary electrons that have initial energies less than 5 eV and distorting the output signal shapemthe correct specimen voltage can nevertheless be measured by using the higher-energy secondary electrons (falling edge of the output signal). Moreover, these electrons give rise to a considerable amount of voltage contrast, which enables one to arrive at an accurate estimate of the specimen voltage. An alternative to using a slit in front of the scintillator cage is to restrict the deflector opening area through which secondary electrons pass by placing an extra plate at the top of the deflector electrode. In this case, the deflector has a narrower energy pass range, as illustrated in Figure 49. The extra plate

I

i i I

Scintillator cage

i

....................................................... _

/

pole pieceFinal(01enSv) lower

,,g

.i ~

E3 Secondary electrons At energies E/< E2 < E3

El

~ -VD(t)Deflector voltage II I Add-on lens top plate (0 V) Primary beam

FIGURE49. The bandpass electrostatic deflector principle.

ADD-ON LENS ATTACHMENTS FOR THE SEM

149

Compensation on primary beam

-VD

FIGURE50. Horseshoe bandpass electrostatic deflector which compensates for adverse shifts on the primary beam.

also compensates for adverse shifts on the primary beam. Without any form of compensation scheme, the image at high resolution inevitably shifts as VD changes. Figure 50 shows a deflector design that has a horseshoe shape, as previously used, but in addition has a top plate that has an opening in the direction opposite that of the scintillator. This scheme was found to be effective in deflecting the secondary electrons off-axis toward the scintillator while leaving the primary beam unaffected. Unlike the Wien filter deflector that can also be used for the same purpose, this electrostatic deflector does not require readjustment as the beam energy is changed. Figure 51 shows voltage contrast results from the add-on lens when a deflector structure of the type shown in Figure 50 is used. Compared with the previous deflector (used to generate the results shown in Fig. 48), this deflector has a smaller diameter and a larger height, so that the range of the deflection voltage is reduced. The output signals were recorded for specimen voltages o f - 5 , 0, and 5 V. As previously, there is considerable voltage contrast. The output signals have the same type of variation as those obtained by using a slit at the scintillator. Together with the peak height of each signal, these kind of results enable the add-on lens unit to function as a multichannel voltage contrast spectrometer. So that an estimate of the minimum detectable specimen voltage difference associated with the output signals shown in Figure 51 could be obtained, 16 signals were recorded for a specimen voltage of - 5 V. The mean and the variance of each signal were calculated, and a root-mean-square noise value

150

ANJAM KHURSHEED 250.00

--

200.00

--

150.00

--

100.00

--

~ r

.>_ v ok.. k.. t)

ov

Cl

-5v

Specimen voltages

0

50.00 - -

ooo

1 I

-4.00

'

0.00

4.00 - Deflection

8.00

12.00

16.00

voltage (volts)

FIGURE 51. Experimental voltage contrast signals obtained by using the horseshoe bandpass electrostatic deflector and normal scintillator collection with the magnetic immersion add-on lens.

for the mean was found. These data are given in Table 3. The root-mean-square noise value for the signal mean, 0.0145 V, was then compared with the change in mean value for the specimen voltage switching from - 5 to - 4 V. The output signals corresponding to the specimen voltages o f - 5 and - 4 V are shown in Figure 52. The change in the mean value was found to be 0.2751 V. This provides a signal-to-noise ratio of 18.52, which gives a minimum detectable specimen voltage difference of 53.98 mV. This parameter depends on data acquisition time, which in this case was 0.16 s for each signal. Because the spectrometer's signal-to-noise ratio depends on many operating factors such as the primary beam current and detector efficiency, it is difficult to compare it with other voltage contrast systems. However, the results demonstrate that the magnetic immersion add-on lens unit can be operated as a multichannel voltage contrast spectrometer. As a way to investigate the deflector's influence on the primary beam, images of a grid specimen having 500 • 500-nm spacing between the grid lines were

ADD-ON LENS ATTACHMENTS FOR THE SEM

151

TABLE 3 SIGNAL MEAN AND STANDARD DEVIATION FOR EXPERIMENTALLY MEASURED OUTPUT SIGNALS TAKEN FROM THE MAGNETIC IMMERSION ADD-ON VOLTAGE CONTRAST SPECTROMETER a

Signal sample number

Signal mean (V)

Signal standard deviation(V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2.73110 2.73359 2.76117 2.75907 2.75820 2.72010 2.72234 2.73994 2.75382 2.74940 2.72504 2.74027 2.74110 2.72793 2.71920 2.71995

1.40634 1.40950 1.40606 1.40665 1.40621 1.39277 1.39538 1.40547 1.41037 1.40415 1.39462 1.40377 1.40881 1.40194 1.40738 1.39641

a VS ._ --5 V; root-mean-square noise on mean signal value = 0.0145 V.

recorded. The deflector voltage was changed from 0 to - 1 0 V, and its corresponding effect on the image was noted. These results are shown in Figure 53. Points A, B, and C represent identical points on the specimen and indicate that the shift on the image when the deflector voltage is - 1 0 V is less than 50 nm. The shift, as expected, occurs only in the direction in which the electrons are deflected. Because a m i n i m u m of --6 V on the deflector plates is required to generate the results shown in Figure 51, the m a x i m u m shift in the primary beam is estimated to be less than 30 nm, assuming that the image shift varies linearly with deflection voltage strength. With greater precision in the mechanical manufacture of the deflector and its better alignment to the primary beam axis, this shift can be further reduced.

C. Material Contrast Spectrometer

The add-on spectrometer can also be used to quantify material contrast. Figure 54a shows a secondary electron image taken along the interface of

152

ANJAM KHURSHEED 160.00

120.00 .1 r

> .1

Kv .4...a e-

80.00

L. :::3 U

-4V

UU

'1 -5 V

:::3 :3

O 40.00

0.00

I

I

0.00

2.00

'

I 4.00

' ....

F 6.00

'

Deflection voltage magnitude (volts)

I 8.00

'

1 10.00

FIGURE 52. Experimental voltage contrast created by the specimen voltage's changing by 1 V in the magnetic immersion lens voltage contrast spectrometer.

two different materials. A region of copper lies on the left-hand side of the image, while a region of brass lies to the fight. The two material regions are separated by glue. The specimen was coated with a 25-nm layer of carbon. The specimen used was the S 1922 Universal Standards Set produced by Agar Scientific Ltd. (66A Cambridge Road, Stansted, Essex CM24 8DA, England), which has different materials embedded in a 25-mm block of brass. Figure 54a, taken with the add-on lens, shows that it is difficult to distinguish between the copper and brass regions in the normal secondary electron image. However, when the deflection voltage was scanned from + 2 to - 1 8 V in the vertical scan direction, differences in the brightness between the copper and brass regions became visible, as shown in Figures 54b and 54c. These images were recorded for a specimen voltage o f - 5 V. Figure 54c represents the same region on the specimen, but rotated through 180 ~ so that the positions of the brass and copper

ADD-ON LENS ATTACHMENTS FOR THE SEM

153

FIGURE53. Experimentallymeasured shift on the primarybeam for the magnetic immersion add-on lens voltage contrast spectrometer: grid specimen, 500 x 500 nm; beam voltage, 5V; demagnification, 40,000. A, B, and C are identical points on the specimen. (Top left) Vo = O. (Top fight) Vo = -10 V (deflection direction). (Bottom) Vo = -10 V (perpendicular to deflection). regions are inverted. This was done to verify that the observed contrast effect was not an artifact of the spectrometer. The results show that the copper region consistently gives a brighter image than does the brass region. Vertical line scans were taken from the images shown in Figures 54a through 54c and are presented in Figures 55a through 55c. Figure 55a shows that it is difficult to distinguish between the line scan taken from the copper region and that taken from the brass region using the normal secondary electron image. However, in Figures 55b and 55c, in which the line scans are directly related to the secondary energy spectrum, the copper signals are clearly broader and higher than the brass signals. There is also a difference in shape between the signals shown in Figure 55b and those in Figure 55c. However, this does not represent a genuine difference in the secondary electron spectrum and can easily be accounted for. The relative positions of the copper and brass regions were swapped by rotating the specimen stage (rather than the specimen), and this required that the deflector plates be repositioned. This procedure was

154

ANJAM KHURSHEED

FIGURE 54. Secondary electron images of a copper-glue-brass junction specimen, obtained from the magnetic immersion add-on lens spectrometer: (a) normal image (primary beam voltage, 5 kV; demagnification, 1600), (b) deflection voltage changing from 2 to - 18 V along the vertical scan, and (c) deflection voltage changing from 2 to - 1 8 V along the vertical scan with the specimen rotated through 180~

ADD-ON LENS ATTACHMENTS FOR THE SEM

155

FIGURE54. (Continued)

carried out manually and was inevitably inaccurate, so that the deflector plates were in a slightly different position relative to the center of the lens than they had been initially. This accounts for the difference in spectrum shape and highlights the importance of properly aligning the deflector plates to the optical axis of the lens. However, the relative difference between the copper and brass signals is identical in each case, which confirms a genuine material contrast effect. So that these material contrast results could be quantified, 16 line scans on copper were taken from the image shown in Figure 55b. Table 4 shows the sample mean and standard deviation values calculated from these signals. In this case, the standard deviation was found to provide greater contrast than that provided by the signal's mean value. The root-mean-square noise on the signal's standard deviation was 0.0256 V, while the difference in standard deviation obtained between the copper and brass signals was 0.3 V, which gave a signal-to-noise ratio of 11.72. Considering that the copper and brass regions were at first indistinguishable in the normal secondary electron image, this signal-to-noise ratio performance is significant and demonstrates the add-on spectrometer's high sensitivity to the material contrast effect. More work is required to test this technique on a wider range of materials.

156

ANJAM KHURSHEED

200,00I

I

Carbon coated specimen

VerUcal line scan Zero deflector and specimen voltages

9

-......

Brass

GlueIi~~i

Copper

Copper

160.00 !

~.~

120.00

@~i',1%

~ 9

,

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) 8

80.00

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40,00

0.00

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I

200.00

'

I

'

1

'

400.00 600.00 Vertical Line (pixel number)

I

800.00

'

I

1000.00

(a)

FIGURE 55. Vertical line scans of a copper-glue-brass junction specimen, obtained from the magnetic immersion add-on lens spectrometer: (a) normal image, (b) deflection voltage changing from 2 to - 1 8 V along the vertical scan, and (c) deflection voltage changing from 2 to - 1 8 V along the vertical scan with the specimen rotated through 180 ~

One way of improving quantitative material contrast measurements in practice is to embed a variety of material types in the specimen holder, so that with fast specimen movements, line scans on a wide range of materials are available for comparison. It is also in principle possible to store images for different values of the deflector voltage, so that quantitative material contrast can be performed pixel by pixel. The result can then be displayed in terms of a material contrast color-coded map. The technique of quantifying material contrast through collection of the secondary electron energy spectrum can be extended to analyze nonmetallic specimens. The method may provide a useful way to monitor surface charging.

ADD-ON LENS ATTACHMENTS FOR THE SEM

157

300.00

Copper

Carbon coated specimen Copper

Glue

Brass

tD

i-

200.00

(D

4-1

~J L_ tJ

100.00 0

-5 V Specimen voltage

0.00

I

0.00

I

5.00

'

I

10.00

- Deflector voltage (volts)

15.00

(b) FIGURE 55. (Continued)

D. Mixed-Field Immersion Lens Spectrometers The secondary electron energy spectrum can in principle be obtained with the mixed-field immersion add-on lens design. One approach is to use the conventional backscattered electron detector, shown in Figure 56. The secondary electrons are deflected off-axis by a Wien filter, and the voltage of a filter grid placed in front of the backscattered electron detector is varied, which acts like a high-pass filter for the collected electrons. There is an extra 0-V grid which shields the filter grid from the rest of the chamber. Equipotential lines from a simulated electric field distribution for this arrangement are shown in Figure 57. The specimen and a shielding plate are biased to - 5 kV. The shielding plate is there only for added flexibility, providing the possibility of

158

ANJAM KHURSHEED

300.00I Copper Carbon coated specimen 1,r t'-

Brass

200.00

GlueI Copper

r v r

lJ

ca. 0

100.00

-5Vspecimen voltage 0.00

I o.oo

'

I

'

I

5.oo io.oo - Deflector voltage (volts)

'

! 15.oo

(c)

FIGURE 55.

(Continued)

lowering the electric field strength at the specimen surface if needed. Simulation of trajectory paths for 3-eV secondary electrons leaving the specimen surface over a wide range of emission angles are shown in Figures 58a and 58b. In both cases, the Wien filter excitation strength is 20 AT. Figures 58a and 58b depict simulated trajectory paths for the filter grid changing from - 4 to - 4 . 5 kV, respectively, and predict that energy filtering of the secondary electrons should in principle be possible. Secondary electrons can be collected by a conventional backscattered electron detector, because their energies at the detector will be greater than 5 keV. Another way of incorporating voltage contrast into the mixed-field immersion add-on lens is to use the conventional secondary electron detector. This arrangement is similar to the previous one, but in this case there is no 0-V shielding grid in front of the filter grid and the Wien filter is adjusted to

ADD-ON LENS ATTACHMENTS FOR THE SEM

159

TABLE 4 SIGNAL MEAN AND STANDARD DEVIATION FOR EXPERIMENTALLY MEASURED MATERIAL CONTRAST OUTPUT SIGNALS TAKEN FROM A COPPER SPECIMEN BY USING THE MAGNETIC IMMERSION ADD-ON SPECTROMETER a

Signal sample number

Signal mean (V)

Signal standard deviation (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

6.69698 6.67778 6.65987 6.61703 6.56469 6.50925 6.52669 6.54373 6.57224 6.56879 6.60583 6.62112 6.62424 6.64481 6.60623 6.65250

3.74650 3.73002 3.73483 3.72376 3.68985 3.66659 3.65645 3.66657 3.67601 3.68708 3.68593 3.69378 3.70472 3.71138 3.71475 3.71052

a Copper specimen at -5 V; root-mean-square noise on the standard deviation = 0.0256 V.

provide wider off-axis deflection. The filter grid operates by reflecting back the secondary electrons onto the conventional Everhart-Thornley detector. The voltage on the filter grid can alter the pass energy of the collected electrons. Figures 59a and 59b show 3-eV simulation results depicting trajectory paths of secondary electrons leaving the specimen over a wide range of emission angles for this arrangement, when the filter grid voltage is changed from - 4 8 0 to - 4 3 0 V, respectively. These simulation results show that in principle it should be possible to energy filter secondary electrons by using the conventional Everhart-Thornley detector. In this case no shielding plate is used above the specimen, so that there will be moderately large electric field strengths (1-5 kV/mm) at the specimen surface. In general, for voltage contrast applications, these kinds of high electric field strengths at the specimen surface are desirable (Clauberg 1987a, 1987b; Khursheed and Goh, 1997). As yet, the preceding proposals to achieve secondary electron energy filtering in the mixed-field add-on lens have not been experimentally investigated by the author. Further work is required to determine whether they are feasible in practice.

160

A N J A M KHURSHEED

FIGURE 57. Simulated equipotential lines for the mixed-field immersion add-on lens spectrometer using backscattered electron detector collection.

ADD-ON LENS ATTACHMENTS FOR THE SEM

161

FIGURE 58. Simulated 3-eV secondary electron trajectory paths in the mixed-field immersion add-on lens spectrometer using backscattered electron detector collection: filter grid of (a) - 4 . 0 kV and (b) -4.5 kV.

162

ANJAM KHURSHEED

FIGURE 59. Simulated 3-eV secondary electron trajectory paths in the mixed-field immersion add-on lens spectrometer using the conventional Everhart-Thornley detector: filter grid of (a) - 4 8 0 V and (b) - 4 3 0 V.

ADD-ON LENS ATTACHMENTS FOR THE SEM

163

W. MULTIBORE OBJECTIVE LENSES Add-on lenses provide a simple and convenient platform for testing novel objective lens designs. Objective lens arrays are central to multicolumn electron beam designs. The motivation for designing objective lenses that can simultaneously focus many primary electron beams comes from a variety of applications. It comes first from the miniaturization of SEM columns. As SEMs become smaller, their field of view naturally decreases, and designing multicolumn electron beam systems is one possible way of compensating for the reduction of the field of view. Second, in electron beam lithography, because multicolumn instruments can in principle write in parallel, they promise to significantly shorten throughput times. A similar advantage exists for the automated SEM inspection of large devices, such as integrated circuit wafers. Multibeam columns may also find applications in dynamic fault imaging, in which images from different specimens or different parts of the same specimen are rapidly compared with one another. Multicolumn SEMs give rise to the possibility of each column's operating differently, each providing a different resolution, probe demagnification strength, and field of view. In a multicolumn SEM instrument, the gun, condenser lens, objective lens, deflector, and detection system all need to be designed to allow for multiple beam operation. In this section, only multibeam objective lenses are considered. Two such objective lens designs are considered: a single-pole lens array and a multibore immersion lens. Both lens designs incorporate the use of permanent magnets and are a natural extension of add-on lens concepts already presented. Prototype versions of these lenses were made as add-on lenses and were tested by using a conventional SEM. The multibeam objective lenses considered in this section can be operated as mixed electric-magnetic lenses that incorporate the retarding field concept.

A. Single-Pole Lens Array Figure 60 shows the layout of a 2 • 2 multi-tip lens array. High-saturation iron tips are mounted on an iron plate, which is placed on top of a single cylindrical block permanent magnet. The pole tips and magnet are located at the center of a magnetic casing, whose top plate has holes through which the tips protrude. A photograph of prototype tips is shown in Figure 61. The pole tips are placed 16 mm apart, and each tip has a tip diameter of 2 mm. Different-size tips can be used at each pole, which gives rise to the possibility of creating a different axial field distribution. Three-dimensional simulation of the field distribution of the multipole permanent magnet lens depicted in Figure 60 was carried out by the use of the

164

ANJAM KHURSHEED

FIGURE 61. Photograph of a 2 x 2-mm-tip prototype 2 x 2 multi-tip permanent magnet lens array.

ADD-ON LENS ATTACHMENTS FOR THE SEM

165

FIGURE62. Simulatedflux lines for a 2 x 2 multi-tip permanent magnet objective lens array.

program TOSCA (Vector Fields Ltd., 24 Bankside, Kidlington, Oxford OX5 1JE, UK), and a cross-sectional map of the simulated flux lines for the lens is given in Figure 62. The magnet height in this design layout was 10 mm and the lens height was 35 mm. A prototype lens was made by using mild steel for the iron circuit and a NbFeB (grade 35) cylindrical block permanent magnet. Figure 63 compares the simulation prediction for the axial field distribution of this lens layout with the field distribution measured by a Hall probe. The match between these two field distributions is good; less than 5% difference is obtained for field values up to 4 mm from the pole tip. There was no measurable difference between the axial field distributions of each pole tip. Another prototype lens was constructed. In this instance, a 1-mm-diameter pole tip was made (pole 1), while the other three tips measured 2 mm in diameter (poles 2-4). The magnet height was reduced to 5 mm (which decreased the lens height to 30 mm). Figure 64 shows the measured axial field distributions for each tip. A significant difference between the 1-mm-tip field distribution and the distributions from the 2-mm-diameter pole tips was obtained. As expected, the field distribution from the 1-mm pole tip was lower in strength than the

166

ANJAM KHURSHEED

FIGURE63. Comparisonof the measured and simulated axial field distribution above a pole tip for the 2 x 2 multi-tip permanent magnet lens array.

others but rose more sharply closer to the tip surface. There were also small variations among the field distributions for the 2-mm pole tips. This is because variations of up to 1 mm in pole-tip height were deliberately introduced so that their effect on the final image could be investigated. A thin copper grid specimen was placed on each pole tip, and the resulting SEM images are shown in Figure 65. These images were obtained from a tungsten gun 5600 JEOL SEM operating at a primary beam voltage of 2 kV. The multipole lens was placed on the SEM specimen stage and used as an SEM add-on lens. In this case, no biasing of the specimen was used. Each pole tip was aligned to the primary beam optic axis by normal specimen-stage movement (by monitoring a secondary electron image of the lens). The distance between the grid center lines for this specimen was around 12.7/zm, and the image

ADD-ON LENS ATTACHMENTS FOR THE SEM

167

FIGURE64. Measured axial field distributions above each tip in the 2 • 2 single-pole permanent magnet lens array prototype.

demagnification strengths varied from 3000 to 7000. The distance separating each pole tip was 16 mm. These results demonstrate that the multibeam singlepole tip lens array is in principle feasible and that the design of each tip may be varied in order to alter the image demagnification strength. A difference of around 1 mm in tip height can typically cause two- to three-times difference in the final image demagnification strength. For a wafer measuring more than 250 mm in diameter, a 10 x 10 array is feasible. The lens can be redesigned to incorporate a closer distance between pole tips and to therefore increase the number of pole tips for a given specimen area. Just how close these tips can be positioned together without degrading their optical properties needs to be investigated.

168

ANJAM KHURSHEED

16 rnm

iw,,-~

Pole 1

Pole 2 ~

~

16 btm - - - - - ~ 1 6 m m

Pole 4

Pole 3

FIGURE 65. Secondary electron images of a copper grid specimen, obtained from the 2 x 2 single-pole permanent magnet lens array prototype used as an add-on lens in a tungsten gun SEM.

Upper plate

Lower plate

!

NdFeB Magnet

,.,.,.,,.,___ FIGURE 66. Multibore magnetic immersion lens design.

ADD-ON LENS ATTACHMENTS FOR THE SEM

169

B. Multibore Immersion Lens Array Figure 66 shows a layout diagram depicting a multibeam immersion lens design. The design is similar to that of the add-on immersion lens already presented, only in this case there are four holes in the lens top plate. Different demagnification characteristics for each beam can be obtained by varying the size of the top plate hole. A prototype multibeam immersion lens was made, in which each of the top plate holes measured 4 m m in diameter and their centers were 8 m m apart. The lens height was less than 30 m m and the permanent magnet was 10 m m high. No discernible difference was found in the field distribution through each hole, and they all behaved in a way similar to that of the single-bore immersion add-on lens already presented. The multibore add-on lens was placed on the specimen stage of a tungsten gun 5600 JEOL SEM, and images of a 10 x 10-mm integrated circuit from each top plate hole were obtained; they are shown in Figure 67. A 1.5-kV primary beam voltage was used. Each top plate hole was successively aligned to the primary beam

I

..........

8

mm

,-1

Hole 1

Hole 2 8 mm

-"~,

60 btm

,,-".

.

.

.

.

.

~

~

......

Hole 3

Hole 4

FIGURE 67. Secondary electron images of a microbolometer infrared detector specimen, obtained from a 2 x 2 multibore magnetic immersion lens prototype used as an add-on lens in a tungsten gun SEM.

170

ANJAM KHURSHEED

axis through specimen-stage movement. The integrated circuit specimen used for this experiment was a microbolometer infrared detector. Each lens bore produced an image demagnification of around 1000. These images represent four 60 • 60-/zm regions on the specimen that are 8 m m apart. These results show that a multibore immersion objective lens design is in principle feasible and demonstrate how add-on lenses can be used to test novel objective lens designs.

VI. SUMMARY This article summarized recent work carried out on add-on lens attachments for the SEM. It described how add-on lenses can be used to improve the resolution of conventional SEMs by a factor of 3 or more. Add-on lenses do not require any fundamental change to the SEM's normal mode of operation and are mounted conveniently onto the specimen stage. Theoretical and experimental work was presented to illustrate how add-on lenses can be used to lower the landing energy of the primary beam at the specimen in a conventional SEM. Research work demonstrating how add-on lenses can transform a conventional SEM into a flexible analytical tool capable of acquiring the secondary electron energy spectrum was reported. By obtaining this kind of information, a conventional SEM can operate in a quantitative voltage contrast or material contrast mode, providing voltage or compositional information on the nanoscale range. Last, it was shown how the add-on lens concept provides a simple and convenient platform for testing novel objective lens ideas.

REFERENCES Bath, J. E., and Kruit, E (1996). Addition of different contributions to the charged particle probe size. Optik 101(3), 101-109. Bauer, E. (1994). Low energy electron microscopy. Rep. Progr. Phys. 54, 895-938. Chung, M. S., and Everhart, T. E. (1974). Simple calculation of low-energy secondary electrons emitted from metals under bombardment. J. Appl. Phys. 45, 707-709. Clauberg, R. (1987a). Microfields in stroboscopic voltage measurements via electron emission. I. Response function of the potential energy. J. Appl. Phys. 62(5), 1553-1559. Clauberg, R. (1987 b). Microfields in stroboscopic voltage measurements via electron emission. II. Effects on electron dynamics. J. Appl. Phys. 62(10), 4017-4022. Frank, L., and MtillerovL I. (1999). Strategies for low- and very-low-energy SEM. J. Electron Microsc. 48(3), 205-219. Hawkes, P. W., and Kasper, E. (1989). Principles of Electron Optics, Vol. 2. San Diego: Academic Press, p. 632. Hordon, L. S., Huang, Z., Browning, R., Maluf, N., and Pease, R. E W. (1993). Optimization of low-voltage electron optics, in Proceedings of the International Society for Optical Engineering (SPIE), Vol. 1924. Bellingham, WA: Int. Soc. Opt. Eng., pp. 248-256.

ADD-ON LENS ATTACHMENTS FOR THE SEM

171

Hordon, L. S., Huang, Z., Maluf, N., Browning, R., and Pease, R. E W. (1993). Limits of lowenergy electron optics. J. Vac. Technol. Bll(6, Nov/Dec), 2299-2303. Hordon, L. S., and Monahan, K. M. (1996). Ultralow voltage imaging. J. Vac. Sci. Technol. B14(6), 3770-3773. Joy, D. C. (1989). Control of charging in low-voltage SEM. Scanning 11, 1-4. Joy, D. C., and Pawley, J. B. (1992). High-resolution scanning electron microscopy. Ultramicroscopy 47, 80-100. Khursheed, A. (1992). Multi-channel vs. conventional retarding field spectrometers, Proceedings of the Third European Conference on Electron and Optical Beam Testing of lntegrated Circuits. Microelectron. Eng. 16(1-4), 43-50. Khursheed, A. (1995). "KEOS," The Khursheed Electron Optics Software [Computer software]. Electrical Engineering Department, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. Khursheed, A. (2000). Magnetic axial field measurements on a high resolution miniature scanning electron microscope. Rev. Sci. Instrum. 71(4), 1712-1715. Khursheed, A. (2001). Recent developments in scanning electron microscope design, in Advances in Imaging and Electron Physics, Vol. 115, edited by P. W. Hawkes. San Diego: Academic Press, pp. 197-285. Khursheed, A., and Dinnis, A. R. (1990). A multi-channel time dispersion voltage contrast detector. J. Vac. Sci. Technol. B7, 1908-1912. Khursheed, A., and Dinnis, A. R. (1992). Experimental results from a time-of-flight spectrometer for electron beam testing. Microelectron. Eng. 17, 451-454. Khursheed, A., and Goh, S. P. (1997). Experimental investigation into the use of microextraction fields for electron beam testing. Microelectron. Eng. 34, 171-185. Khursheed, A., and Karuppiah, N. (2001). An add-on secondar-y electron energy spectrometer for scanning electron microscopes. Rev. Sci. Instrum. 72(3), 1708-1714. Khursheed, A., Karuppiah, N., and Koh, S. H. (2001). A high-resolution add-on lens attachment for scanning electron microscopes. Scanning 23, 204-210. Khursheed, A., Yan, Z., and Karuppiah, N. (2001). Permanent magnet objective lenses for multicolumn electron beam systems. Rev. Sci. Instrum. 72(4), 2106-2109. Knell, G., and Plies, E. (2000). Initial resolution measurements of an improved magneticelectrostatic detector objective lens for LVSEM. Ultramicroscopy 81, 123-127. Kruit, P., and Read, F. H. (1983). Magnetic field paralleliser for 2zr electron-spectrometer and image magnifier. J. Phys. E: Sci. lnstrum. 16, 313-324. Lencova, B. (2000). Computations of Wien filter properties and aberrations, in Proceedings of the Twelfth European Congress on Electron Microscopy (EUREM 12), Brno Czech Republic. III. Instrumentation and Methodology. Edited by P. Torfianek and R. Kolafik, Brno, Czech Republic, pp. 87-88. Miillerov~, I., and Lenc, M. (1992). Some approaches to low voltage SEM. Ultramicroscopy 41, 399. Nakagawa, H., Nomura, N., Koizumi, T., Anazawa, N., and Harafuji, K. (1991). A novel highresolution scanning electron microscope for the surface analysis of high-aspect-ratio threedimensional structures. Jpn. J. Appl. Phys. 30(9A), 2112-2117. Pawley, J. B. (1990). Practical aspects of high-resolution LVSEM. Scanning 12, 247-252. Plies, E. (1990). Secondar-y electron analyzers for electron-beam testing. Nucl. Instrum. Methods Phys. Res. A298, 142-155. Rau, E. I., and Robinson, V. N. E. (1996). An annular toroidal backscattered electron energy analyser for use in scanning electron microscopy. Scanning 18, 556-561. Reimer, L. (1998). Scanning Electron Microscopy, 2nd ed. Berlin/New York: Springer-Verlag, p. 32.

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Richardson, N., and Muray, A. (1988). An improved magnetic-collimating secondary electron energy filter for very large scale integrated diagnostics. J. Vac. Sci. Technol. B6, 417-421. Thong, J. T. L. (1993). Electron Beam Testing Technology. New York: Plenum. Tsuno, K. (1994). Simulation of a Wien filter as beam separator in a low energy electron microscope. Ultramicroscopy 55, 127-140. Wells, O. C. (1971). Low-loss image for the scanning electron microscope. Appl. Phys. Lett. 19, 232-235. Yau, Y. W., Pease, R. E, Iranmanesh, A. A., and Polasko, K. J. (1981). Generation and applications of finely focused beams of low-energy electrons. J. Vac. Sci. Technol. 19(4), 1048-1052. Zach, J. (2000). Aspects of aberration correction in LVSEM, in Proceedings of the Twelfth European Congress on Electron Microscopy (EUREM 12), Brno Czech Republic. III. Instrumentation and Methodology. Edited by P. Torfianek and R. Kolafik, Brno, Czech Republic, pp. 169-172.

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 122

Electron Holography of Long-Range Electrostatic Fields G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI Department of Physics and National Institute for the Physics of Matter, University of Bologna, 40127 Bologna, Italy

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. E l e c t r o n - S p e c i m e n Interaction . . . . . . . . . . . . . . . . . . . . . A. The P h a s e - O b j e c t A p p r o x i m a t i o n . . . . . . . . . . . . . . . . . . B. Wave-Optical Analysis of the Electron Biprism . . . . . . . . . . . . C. Effect of the Biprism on the I m a g e Wavefunction . . . . . . . . . . . . D. On the Validity of the P h a s e - O b j e c t A p p r o x i m a t i o n . . . . . . . . . . . E. The Electrostatic A h a r o n o v - B o h m Effect . . . . . . . . . . . . . . . 1. E x p e r i m e n t a l M e t h o d s and Results . . . . . . . . . . . . . . . . III. Recording and Processing of Electron H o l o g r a m s . . . . . . . . . . . . . A. H o l o g r a m R e c o r d i n g . . . . . . . . . . . . . . . . . . . . . . . 1. A m p l i t u d e Division Interferometry . . . . . . . . . . . . . . . . 2. W a v e - F r o n t Division Interferometry . . . . . . . . . . . . . . . . B. H o l o g r a m R e c o n s t r u c t i o n and Processing . . . . . . . . . . . . . . . 1. Theoretical Considerations . . . . . . . . . . . . . . . . . . . . 2. Optical Reconstruction and Phase Detection . . . . . . . . . . . . . C. D o u b l e - E x p o s u r e Electron H o l o g r a p h y . . . . . . . . . . . . . . . . IV. Charged Dielectric Spheres . . . . . . . . . . . . . . . . . . . . . . A. Recording and Processing o f Electron H o l o g r a m s . . . . . . . . . . . B. Interpretation of the E x p e r i m e n t a l Results . . . . . . . . . . . . . . . C. Numerical Simulations of C o n t o u r M a p s . . . . . . . . . . . . . . . V. p-n Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. E x p e r i m e n t a l Results . . . . . . . . . . . . . . . . . . . . . . . 1. S p e c i m e n Preparation and Electron M i c r o s c o p y Observations . . . . . 2. Optical R e c o n s t r u c t i o n and Processing of Electron H o l o g r a m s . . . . . B. Theoretical Interpretation . . . . . . . . . . . . . . . . . . . . . . 1. The Electrostatic Field M o d e l . . . . . . . . . . . . . . . . . . . 2. N u m e r i c a l Simulations of H o l o g r a p h i c Contour M a p s . . . . . . . . VI. Investigation of Charged Microtips . . . . . . . . . . . . . . . . . . . A. The Field M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . B. E x p e r i m e n t a l Results . . . . . . . . . . . . . . . . . . . . . . . VII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Volume 122 ISBN 0-12-014764-5

174 177 177 179 182 188 191 193 196 196 197 199 205 205 207 210 212 212 216 219 221 221 221 224 227 227 233 235 236 239 242 243 245

173 ADVANCES IN IMAGING AND ELECTRON PHYSICS Copyright 2002, Elsevier Science (USA). All rights reserved. ISSN 1076-5670/02 $35.00

174

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI I. INTRODUCTION

About 15 years ago it was foreseen that, thanks to the introduction of high brightness and coherence sources such as field emission guns (FEGs), electron holography would play an increasing role in electron microscopy (Missiroli et al., 1981). Reality has shown itself to be greater than expectations as witnessed by the dedicated sessions at international meetings and by the success of the first international workshop on the subject (Tonomura, Allard, et al., 1995). In general, we may divide the field of electron holography into two main streams: One, pursued mainly by H. Lichte and his co-workers (Lichte, 1991, 1995), aims at the realization of the original Gabor dream, that is, to correct the spherical and other residual aberrations in order to improve the resolution limit in electron microscopy down to the physical limit set by the chromatic coherence of the electron beam. Unfortunately, the main obstacle is represented by the extremely high accuracy, a fraction of a percent, by which the aberration coefficients need to be known in order to carry out effectively the reconstruction process; in fact, other experimental troubles linked to the instrumentation are about to be solved (Lichte, 1995). The other main stream is related to the application to problems in the medium-low resolution range. In this range, with respect to the standard phase contrast methods in electron microscopy (Chapman, 1984; Wade, 1973), holography allows the extraction of quantitative information with increased sensitivity limits owing to the use of image-processing and phase-amplification methods which have no counterpart in electron microscopy (Hanszen, 1982, 1986; Tonomura, 1986, 1987a, 1987b, 1992, 1993). Among these problems, a prominent place is held by the application of electron holography to a basic issue in quantum physics, that is, the significance of electromagnetic potentials, also known as the A h a r o n o v - B o h m effect (Aharonov and Bohm, 1959). The lively theoretical and experimental debate concerning this effect (Olariu and Popescu, 1985; Peshkin and Tonomura, 1989) culminated in the outstanding experiments by Tonomura and his group (Tonomura, Osakabe, et al., 1986), who reached an almost ideal shield of the magnetic field by surrounding a micro toroidal magnet by means of superconducting niobium. The offspring of this research eventually led to the first successful observation of quantized flux lines in superconductors by means of Lorentz (Harada et al., 1992) and holographic (Bonevich, Harada, et al., 1993) methods. The interest of our group in electron holography was motivated by its many applications for the investigation of materials science problems. The developments in magnetic information storage technology and microelectronics require the characterization of the magnetic recording media, junction devices,

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 175 and interfaces in terms of magnetic and electric field distributions. The study of magnetic fields (Matteucci, Missiroli, and Pozzi, 1984) developed from the first experiments aimed at demonstrating the possibility of displaying magnetic lines of force in a thin film (Lau and Pozzi, 1978) to more recent experiments regarding the magnetic probes used in magnetic force microscopy (Frost, van Hulst, et al., 1996; Matteucci and Muccini, 1994; Matteucci, Muccini, and Hartmann, 1994). As far as electric fields are concerned, following the pioneering work of Titchmarsh and Booker (1972) and in collaboration with the Lamel-CNR laboratory, we started in the mid-1970s to investigate reversebiased p - n junctions, first by standard Lorentz methods (Merli et al., 1973, 1975), then by means of interference electron microscopy (Merli et al., 1974), and finally by mapping the electric field across a reverse-biased p - n junction by means of off-axis image electron holography (Frabboni, Matteucci, and Pozzi, 1987; Frabboni, Matteucci, Pozzi, et al., 1985). The problems encountered in the reconstruction of holograms of reversebiasedp-n junctions (Frabboni, Matteucci, and Pozzi, 1987) demonstrated unambiguously that the long-range field perturbed the so-called reference wave. A basic assumption of holography was thus manifestly violated and in order to assess the consequences of this fact we started to investigate other specimens with long-range electric fields, namely, charged dielectric particles (Chen et al., 1989; Matteucci, Missiroli, Nichelatti, et al., 1991) or biased tips (Matteucci, Missiroli, Muccini, et al., 1992), having, with respect to p - n junctions, the advantages of an easier specimen preparation and of a simpler theoretical description. In 1996, we reviewed the work done by our group, with the main emphasis on the experimental results (Matteucci, Missiroli, and Pozzi, 1996). However, for the particular class of problems investigated, the theoretical interpretation is equally important, since on one hand it helps to clarify the obtained results with their sometimes puzzling aspects, and on the other hand it allows the extraction of maximum useful information from the recorded patterns. The aim of this article is, therefore, to give a balanced review of the work done so far with emphasis on the fact that the interest of some issues is not limited to the particular field of investigation, but could be potentially useful to everyone engaged or wishing to engage in the exciting field of electron holography. Section II deals with the fundamental theoretical considerations underlying the observation of electric fields. The basic tool, that is, the phase-object approximation, is applied to the case of the electron biprism, in order to obtain its transmission function and to analyze its effect on the image wavefunction within an interferometric or holographic setup. The validity range of the phase-object approximation is then considered, and we show that it can be safely applied to the electric fields investigated in this work. Last but not least,

176

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

the fact that the potentials and not the fields enter the basic equations has the consequence that quantum nonlocal effects can be detected also with electrostatic fields, in close analogy with the more striking and fundamental effects linked to magnetic fluxes. A short account of the basic ideas and experiments is therefore given, as a reminder that sometimes, starting from an applicative problem, we may touch a fundamental issue. Section III recalls the basic principles of holographic recording and processing, with the modifications introduced by the long-range behavior of a particular class of electric fields, namely, the perturbation of the reference wave. Although the main emphasis is on image electron holography by means of an electron biprism, Fresnel holography using a single-crystal film as an amplitude beam splitter is also briefly described, since this method can be carfled out even if the microscope is not equipped with an FEG. Moreover, in the analysis of the reconstruction process, we have limited considerations to our experience in the optical realm. Today, with the introduction of digital imagerecording devices like the charge-coupled-device (CCD) cameras (de Ruijter and Weiss, 1992), the way is paved for carrying out in-line the whole process of image recording and processing by digital methods. The interested reader is referred to the recent papers of the pioneers in this field (Ade, 1994, 1995; Lehmann and Lichte, 1995; Lichte, 1995; Vrlkl, Allard, and Frost, 1995). However, owing to the complete analogy between Fourier optics and Fourier analysis, the optical considerations reported in this article can be profitably transferred to the digital realm, although the reverse may not always be true, as demonstrated by the brilliant alternative method to extend the spatial resolution of an electron hologram, realized by Ade and Lauer (1994). The last three sections deal with applications of the formerly developed ideas and methods. First, the case of charged dielectric spheres is treated in Section IV. This specimen can be considered as an ideal test object, since it is easy to prepare and is described by a simple theoretical model, which gives an analytical expression for the associated phase shift. Theoretical modeling is considerably more complicated for the case of reverse-biased p - n junctions (Section V). Also the specimen preparation is challenging, especially if the p - n junction needs to be biased: according to our experience, this is a mandatory requirement for an unambiguous interpretation of the experimental data. Last but not least, charged microtips are analyzed in Section VI. Fortunately, in this case too an analytical model for the phase shift is available, which allows the interpretation of the puzzling features of the experimental data. In fact, contrary to the naive expectations, according to which the equiphase lines are a good representation of the equipotential surfaces of the field, in this case there is a striking difference which stresses how cautious the interpretation should be. The conclusions and an update complete the article.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 177 II. ELECTRON--SPECIMENINTERACTION The aim of this section is to introduce the phase-object approximation (POA), which gives the basic theoretical tool for the interpretation of the effects associated with the interaction of the electron beam with electrostatic fields at the mesoscopic level. This approximation will then be applied to the case of the electron biprism which, being the most diffused type of electron interferometer, has been extensively investigated from both a theoretical and an experimental point of view. It turns out that the biprism can be described by a very simple and useful transmission function. This function is at the basis of the theoretical analysis regarding the effects of the biprism on the image wavefunction. The validity limits of the POA are then considered with particular reference to the case in which some authors claimed that the POA would no longer be valid with regard to reverse-biased p - n junctions. However, we will recall and discuss how this conclusion is superseded by new calculations based on the multislice approach. Finally, the electrostatic Aharonov-Bohm effect is briefly reviewed, and it is shown how nonlocal quantum effects can arise with a particular configuration of electrostatic fields.

A. The Phase-Object Approximation Let us recall some fundamental theoretical aspects concerning the interaction of electrons with static electric (Glauber, 1959; Landau and Lifshitz, 1965) and magnetic (Wohlleben, 1971) fields. If we consider only elastic scattering events, the solution of the time-independent, nonrelativistic Schrrdinger equation in the high-energy approximation gives the transmission function (i.e., the ratio between the complex amplitudes of the ingoing and outgoing wavefunctions) as T (r) = e ir

(1)

where r = (x, y) is a bidimensional vector perpendicular to the optic axis z, which is parallel and in the same direction as the electron beam, and ~b(r) is the phase term, given by ~b(r) -- ~

ef

V(r, z) dz - -~

Az(r, z) dz

(2)

The integrals in Eq. (2) are taken along a trajectory s parallel to the optic axis z; V(x, y, z) and Az(x, y, z) are the electrostatic potential and the z component of the magnetic vector potential A(x, y, z);e, &,E, and h are the absolute value of the electron charge, the de Broglie electron wavelength,

178

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

the accelerating voltage of the electron microscope in the nonrelativistic approximation, and the Planck constant divided by 2zr, respectively. Moreover, the fact that electrons can be either stopped by a thick specimen or scattered by the specimen atoms at large angles until they are cut off by the aperture of the objective lens can be accounted for by introducing a real amplitude term C(r) in the object wavefunction, so that Eq. (1) becomes (3)

T(r) = C(r)e gear)

In order to understand better the validity range of the preceding approximation, we should reconsider how it is derived. The starting point is the time-independent Schr6dinger equation:

V21~r- 2eA'hi V~p +

2me --~(V

+ E)~-

e2 -A2~h

--0

(4)

where the additional constraint div A - - 0 has been imposed on the vector potential. In the purely electrostatic case, (A = 0), the crystal potential energy eV(x, y, z) is considered as a small perturbation with respect to the kinetic energy eE of the incident electron beam (Glauber, 1959; Landau and Lifshitz, 1965). Therefore, if the plane wave solution of the unperturbed Schr6dinger equation propagating parallel to the optic axis z is given by ~o - exp

(5)

then the solution of the perturbed Schr6dinger equation is looked for in the form - ~PoX

(6)

The resulting equation for X is given by V2X-~

47ri 0X 4rr2 )~ Oz ~ - ~ v x - 0

(7)

The POA is obtained when the V2X term is neglected; in this case, the equation for X results as 8X

7ri = ~ V(x, y, z)X Oz ~E

(8)

which can be immediately integrated along the trajectory ~ to give the first phase term in Eq. (2).

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 179 Let us introduce, for the sake of completeness, in the same approximation, also the effect of a magnetic field. The equation for X, once the V2X term is neglected, is dx yr i = ~Vx dz ZE

-

ie

~-

Az

X

ie 2 )~ - ~mA2

4re h 2

~.e

X - 2 - ~ A" VX

(9)

As can be seen, with respect to Eq. (8) we have three additional terms. The first, ie - - - A z ( x , y, z ) x

(1 O)

can be simply added to the electrostatic term in Eq. (8) and the integration can be carried out in the same manner as before. It ensues that the resulting phase shift is the magnetic contribution reported in Eq. (2). Therefore, the standard POA for magnetic fields amounts to neglecting the other two terms of Eq. (9), as shown by Wohlleben (1971). This approximation is no longer valid for the magnetic lens case, in which the main shift, Eq. (10), vanishes identically and, as shown by Pozzi (1995), the other two terms are responsible for the focusing and image rotation effects.

B. W a v e - O p t i c a l A n a l y s i s o f the E l e c t r o n B i p r i s m

The preceding considerations can be applied to the study of the particular configuration of the electrostatic field such as that produced by the electrostatic bipfism invented by M611enstedt and Dfiker (1956). It consists of a thin charged wire W whose axis is coincident with the y direction. The wire is placed between two earthed plates as shown in Figure l a. When the observations are carried out near the central region of the wire, far from the edge of the supporting apertures, a bidimensional approach for the electrostatic field can be usefully employed. Two equivalent models have been proposed for the electric field associated to an electron biprism, differing only in their boundary conditions. The first starts from the field of a line charge lying along the y axis and placed between two earthed plates as shown in Figure lb (Septier, 1959); the second considers the field as that arising from a cylindrical condenser as sketched in Figure 1c (Komrska, 1971). Let us extend the Septier approach to the case of an asymmetric line charge placed between two earthed plates as shown in Figure 2 (Matteucci, Medina,

180

G. M A T T E U C C I , G. E MISSIROLI, A N D G. POZZI

(a)

i

X

/

//

X

v

l

f

'

(b)

(c)

FIGURE 1. Elements of an electron-optical biprism. (a) M611enstedt-Dtiker arrangement. (b) Septier's model. (c) Komrska's model. In (b) and (c) the central wire is along the y axis.

et al., 1992). If a is the distance between the plates and b that of the line charge from the left one, by considering a coordinate system as in Figure 2a we find that the potential is given by (Durand, 1966)

V(x,z)--

o" ~EO

In

cosh ~ - cos ~ c~ yrz]-a - cos

a

yr(x+b)a

(11)

where o is the line charge density and e0 is the vacuum dielectric constant. The trend of the equipotential surfaces (solid lines) and of the lines of force (dashed lines) are reported in Figure 2a. It can be easily ascertained that near the charged line, the field is negligibly influenced by the boundaries (as shown in Fig. 2b, which reports an enlarged view of the region around the line charge) and is identical to the logarithmic

ELECTRON HOLOGRAPHYOF LONG-RANGEELECTROSTATIC FIELDS 181

/ --

/

I

/

"7

\

:

/

%

/

Z (a)

(b)

FIGURE 2. Potential (solid) and field (dashed) distributions of the electrostatic field due to a charged line between two earthed plates. (a) Large scale: a, distance between the two plates; b, distance between the left plate and the line charge. (b) Small scale near the charged line: R radius of the charged cylinder (dashed region).

field of a single charged line without boundaries. The potential is given by rrr 2

In

V(r)---2Jre---~176

2a sin ( - ~ )

(12)

r being the radial distance from the charged wire. Therefore, this model describes also the field of a macroscopic charged cylinder of radius R (dashed central region in Fig. 2b) brought to the potential Vw with respect to the earthed plates. The relation among the wire potential, line charge density, and radius R is given by 7rR 2

Vw=

o- In 2Jre0

2a sin ( ~ )

(13)

The phase shift suffered by the electron wave impinging on the biased biprism can be calculated by introducing in Eq. (2) the potential of Eq. (11)

182

G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

and by considering that for the electrostatic field of the wire the vector potential is zero. It tums out that the resulting integral can be reduced to a tabulated definite integral (Gradshteyn and Ryzhik, 1980) by means of the substitution cosh (fez~a) -- 1/t. After some calculations, the following result is obtained for the phase shift: 7f

O"

7t"

O"

ok(x) -- ~ - - x ( a s e0

b)/a

~(x)-- ~--(a-x)b/a ~.E e0

for 0 < x < b -

(14a)

forb<x -

(14b)


By taking into account that the electrons impinging on the wire are stopped, and by considering the symmetric case in which b = a / 2 (i.e., the wire is centered between the two earthed plates), we find that the following transmission function adequately describes the effect of the biprism on the electron beam: TB(rB) -- exp

-

-~--IrBil

TB(rB) -- 0

for

for

IxBI <

IxsI >

R

R

(15a) (15b)

where r8 -- (xB, YB) is the coordinate vector in the biprism plane (z - zB) centered on the wire axis. ct - tr/4Eeo is the classical angular deflection due to the biprism which, according to Eq. (13), is directly proportional to the wire potential.

C. Effect of the Biprism on the Image Wavefunction The basic features of an electron microscope modified for interferometry or holography experiments are schematically shown in Figure 3. The electron beam emitted by the microscope filament crosses the specimen S under investigation and then, after being focused near the back focal plane of the objective lens Ob, enters in the biprism region. The biprism is usually inserted at the selected area aperture plane and its central wire W splits the incoming wave into two parts, which travel on the left- and fight-hand sides of the wire itself. The specimen wavefunction in the presence of the biprism can be calculated, according to Glaser's paraxial theory (Glaser, 1952, 1956), by following its propagation through the microscope in two steps. The first one is that from the object to the biprism plane, the second from the biprism, described by the transmission function of Eq. (15), to the observation plane OP. The remaining lenses PS of the microscope (which includes the intermediate lens and the

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 183

FIGURE3. Schematicray diagramof an interference microscope. S, specimen; Ob,objective lens; W, biprism wire; OP,observation plane; PS,projector system; IP, image plane. projector system) provide a further magnification of the intermediate image in the final imaging plane IP. The resulting wavefunction is complicated. However, the main features of the image, including diffraction effects, can be derived by using the asymptotic approximation (Pozzi, 1975, 1980a) assuming that the electron wavelength is the small parameter. In this section, the main results of this analysis are briefly summarized. If

ft(xi, Yi)-- A(xI' YI)exp [ 2zriqg(xl' I XyI)

(16)

represents the wavefunction which is formed at the first intermediate image plane (z = z i) in the absence of the biprism, the image wavefunction taking

184

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

into account the effect of the biprism is given by the following expression: ~I(Xl,

Yl)

--

exp[i y]

) ~ 2 ( Z l __ Z B ) 2

9exp

9exp

f f dx dy ~(x, y)

[irc(x2+y2)]ffdxsdy8

7ts(xB, ys)

)~(z8 - zi)

[

-2:rri [ x s ( x l - x ) + y B ( y l - y ) ] ] zi)

(17)

X(z8 -

where x i, Yl are the coordinates in the intermediate image plane, x and y are dummy integration variables, and y is an unessential phase factor. It should be stressed that this expression holds also for zi < ZB and can also be obtained by applying the Kirchhoff integral twice between the planes Zl and zs. By inserting Eqs. (15) and (16) in Eq. (17) we find after some calculations that

aPl(Xi, Yl) = exp[iy] [l[fA(Xl, Yl) + ~B(Xl, Yt)]

(18)

where I[rA(Xl,

YI)

--

~I~r(OgA, y / ) e x p

X(z~ ---zs)

irrx 2

+

1 Zlz~ -zBI

2rciro (X -- O9A)] )~ Zl -- Z8

9exp - ~.(zt - zs)

.

f

dx ~(x, YI)

~(Zl

2rri(x

-- ZB) - - OgA)

(18a) with OgA ~-- X l - - ( Z l - - Z B ) Ol

(18b)

and 1_ OB(xl, yI) -- ~O(ogB, y l ) e x p

I.(--~i - zB)

irrx 2 9exp

- ~.(zl - zs)

+

X

1 - X]zl - zBI

zi - z8

2zri(x - o98) (18c)

with con -- x / + ( z / - zB)ct

(18d)

lpa and 7t8 represent the wavefunctions to the left and right respectively of the biprism wire. Owing to the oscillatory behavior of the phase, it can

ELECTRON HOLOGRAPHY OF LONG-RANGEELECTROSTATIC FIELDS 185 be assumed that the main contributions to the values of the integrals arise from small intervals surrounding the singular points x = COA and x -- cob and the points of stationary phase SA and SB, which are solutions to the implicit equations

YI) - ro -

SA --- 0

(19a)

( Z l -- ZB)q91x(SS, Y l ) + ro -- s n = 0

(19b)

(ZI -- ZB)qgtx(SA,

and X I --- S B as functions of the parameter yi define curves in the plane, which do not depend on the angle or8 and represent the shadow images of the wire edges when the biprism is held at zero-volt applied potential. For points far from the unfolded edge, the intervals are disjointed and the asymptotic approximation to ~ a c a n be written as X I ~--- S A

(X I, Y I )

~rA(XI,

YI) -- exp X ~ ---zs) +

" ~(COA, YI)

-- ~sign(wA

--

SA)

~-~S~ YI)~~j'U~exp Ei~t'sign(zI4 m ZB)I iJr(COA -Z

.exp

SA) 2

(

,Ox'SAY'')I]

1 (z~ - z s )

(20)

whereas across the edge, the asymptotic wavefunction is given by

I[s

YI) -- exp ~(ZI -- ZB) 9

sign(zi - -

ZB)"

"

~(O)A, YI) -- l~rso(coA, YI)

SA)} ~~A exp I--iYrEA].F(U, 4

(21)

where @so((DA,

with ~

YI) -- exp - ~

qg(SA, YI)

+ q3~(SA,

YI)6

+ qgtxt(SA,

Yl)-~

(21a)

= COA - - S A,

E A --

[1

sign (zi - zs)

-

q3txt(SA'

- - qgtxt(SA,

(z~ - z s )

YI)

Yl)

]

(COA - - S A )

(21b)

(21c)

186

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

and

F(u, eA) --

/onE] exp

iTreAt2 2

dt

(21d)

In the case of no object present, Eqs. (18), (20), and (21) are reduced to the exact wavefunction of a defocused opaque half plane and to its asymptotic approximations, respectively. Then the two expressions join together because, as long as Itzl > 1.8, no relevant error is made in taking either of the two wavefunctions. If this criterion is extended to the general case (object present), we should assume that the object phase can be approximated by its second-order Taylor expansion over an interval having the same width as that of the first Fresnel fringe. When this condition is not fulfilled, the asymptotic image presents features such as unexpected maxima and discontinuities at the joining points, which indicate the failure of the approximation. Some calculations carried out for the case of ferromagnetic domain walls (Pozzi, 1980b) or reverse-biased p - n junctions (Pozzi and Vanzi, 1982) suggest that a reasonable upper limit for the phase error is about 0.1 Jr. The preceding equations allow the interpretation of the main features of the observed interferograms. When the potential of the wire Vw = 0, on the imaging plane IP an in-focus image of the specimen can be observed although part of it is hidden by the shadow of the wire as shown in Figure 3. The portions of the image on the left and on the fight of the shadow are of the same extension, provided that the wire is centered on the optical axis. The shadow of the wire may be distorted if the first partial derivative of the object phase in the direction normal to the wire axis is different from zero; similarly, the second derivative affects the spacing of the diffraction fringes at the edge of the shadow of the wire, as impressively shown in Figure 4a in the case of a magnetic specimen. These effects are independent of the voltage applied to the wire and may be useful to detect local electric and magnetic fields and thickness variations in the specimen. Upon application of a bias voltage to the biprism, the shadow will widen or shrink depending on the overall electron-optical conditions. In the case of shrinkage, by increasing Vw the left-hand side and fight-hand side partial images, corresponding to two different regions of the specimen, move toward each other in a direction perpendicular to the wire by an amount proportional to Vw, until the shadow disappears. When the voltage is further increased, the two images overlap which produces an interference pattern in which both amplitude and phase differences between the two waves are encoded in the appearance of modulated interference fringes.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS

187

FIGURE4. Effect of the magnetic field of a thin permalloy film on the biprism wire shadow. (a) Biprism wire at 0 V. The wire shadow is affected by the magnetic field of a thin permalloy film. Convergent C and divergent D domain walls can be seen since the specimen image is recovered slightly out of focus. (b) Interference pattern obtained with the biprism wire at 4.2 V. The specimen is the same as in (a). (c) As in (b) but with the specimen recorded at a larger opposite defocus. It should be noted that the boundaries of the interference field, together with diffraction effects (Fig. 4b), have the same profile as that of the distorted shadow (Fig. 4a), although with left-right inversion. These effects can be better appreciated by examining Figure 4c, where the specimen features at the right and left of the biprism distorted shadow are evidenced by the larger opposite defocus, so that the divergent wall D in the upper part of the figure becomes a convergent one, whose bright contrast line can be easily seen also within the interference field. When the interference field is much larger than the first Fresnel fringe width, the diffraction effects due to the wire edge do not affect appreciably the trend of the interference fringes in the central part of the overall interference field. In this case the interferogram can be considered as a hologram, although the borderline between interferograms and holograms is not well defined. As a rule of thumb, the fringe number should be larger than 100, but the larger the better, although the upper limit is set by the finite lateral coherence of the illuminating beam.

188

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

D. On the Validity of the Phase-Object Approximation A question arises as to whether or not the use of the POA is always justified to describe the interaction between the electron beam and electric fields. The answer is based on the knowledge accumulated in the interpretation of a few case studies. As described in Sections II.B and II.C, from the POA the following simple model of the biprism effect on the electron wavefunction can be justified. The wavefunction is the sum of two waves, each wave describing the diffraction of the electrons, originating from a virtual point source, by an opaque half plane. A careful analysis made by Komrska et al. (1967) shows a fairly good agreement between the theoretical predictions and the experimental data. Therefore, several efforts have been made in order to justify this simple model and the POA on conceptually more satisfactory grounds. The scattering of electrons by the electrostatic field of the biprism has been investigated within the framework of the scalar diffraction theory developed by Komrska (1971) for the case of weak electrostatic fields. The wavefunction in the observation plane can be expressed in this case in terms of a diffraction integral. Numerical calculations are, however, necessary in order to derive the intensity distribution of the out-of-focus pattern. It turns out that the intensifies calculated according to the POA and to the diffraction integral agree at least to four decimal places. This fact prompted Komrska and Vlachova (1973) to investigate and successfully demonstrate, by means of the method of stationary phase, the equivalence of the two descriptions. For the case o f p - n junctions calculations based on the Komrska diffraction integral were carried out by Lo Vecchio and Morandi (1979), who, on the contrary, found a striking disagreement with the results calculated according to the POA. Their results led them to state that the POA is hardly tenable for the interpretation of experimental data. The experience recently gained in the analysis of electromagnetic lenses by means of the multislice method (Pozzi, 1995), as well as the continuing interest toward the observation of p-n junctions by transmission electron microscopy (TEM) methods (Capiluppi, Migliori, et al., 1995), for which the POA is an invaluable tool, stimulated a reconsideration of the whole issue (Pozzi, 1996a). The main results of this reconsideration are reported next. Let us recall that the basic idea of the multislice method is to divide the electric field under investigation into thin slices perpendicular to the direction of the incident beam and to project each slice into the entrance plane, which acts as a two-dimensional phase object. The propagation of the electron wavefunction between two neighboring slices is then calculated according to the HuygensFresnel principle in the paraxial (Fresnel) approximation (Goodman, 1968).

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 189 In the computer-oriented versions of this method, Fourier transforms are used to reduce the convolution between the object wavefunction after the slice and the Fresnel propagator between the two slices to a multiplication in the Fourier space, taking advantage of the existence of appropriate numerical algorithms like that of the fast Fourier transform (FFT). The availability of a high-level language like Mathematica (Wolfram, 1994) allows the writing of transparent codes and the analysis and display of the results with outstanding graphic capabilities. Let us consider the case of a one-dimensional reverse-biased p - n junction parallel to the y axis, present in a specimen of thickness t, whose internal field is described by the Spivak model (Spivak et al., 1968), given by V(xo)-

VR arctan

(Xo)

(22)

where VR and d are the junction reverse bias and half-width respectively. This topography has the advantages that both the external potential and the phase shift associated to each slice can be calculated in an analytical form (Capiluppi, Merli, et al., 1976; Lo Vecchio and Morandi, 1979). Therefore, numerical calculations have been carried out with the multislice method for the same data as those used by Lo Vecchio and Morandi (1979), that is, assuming an illuminating spherical wave originating from a point source at 10 cm from the specimen, of thickness t = 0.3 #m, in which a junction is present with reverse bias VR = - 4 V and d = 0.4/zm. The observation plane has been placed to an out-of-focus distance up to 20 mm. Larger distances were not allowed because, owing to the periodic continuation inherent in the numerical FFT methods, leakage from neighboring intervals introduces severe artifacts in the out-of-focus images. In order to minimize these effects calculations were made over an interval of width 16 /xm across the junction with N = 1024 sampling points, introducing also a modified cosine window. Fortunately, the practical upper limit to the defocus values is not a limiting factor, since, according to Lo Vecchio and Morandi (1979), the larger discrepancies between the two approximations should be more evident for comparatively small values of the defocus distance. Thus, the difference between the rectilinear paths used in the Komrska approximation and the z parallel path used in the POA is more marked. Another important parameter, the cutoff distance, should be taken as low as possible, in order to improve the accuracy of the multislice calculations. By means of the POA this value has been chosen equal to 25d, for which it has been checked that the intensity approximates that obtained for larger values of the cutoff with an error lower than 0.001. The upper and lower external fields

190

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

from the specimen surfaces up to the cutoff have been divided into Ns slices and the specimen internal field has been taken as a single slice, for a total of 2Ns + 1 slices. Figure 5a reports the results of the numerical calculations, over an interval of 4 / z m in width across the junction, for )~ and E corresponding to 100-kV electrons and the following values of the defocus: 5 mm, curve 1; 10 mm, curve 2; and 20 mm, curve 3. All the images calculated for the POA and multislice case, with Ns -- 10 and Ns = 20, are indistinguishable. Therefore, Figures 5b through 5d report on an expanded scale the differences A I between the POA case and the multislice calculation with Ns = 1O, curves (1), whereas curves (2) report the differences between two multislice calculations with Ns = 10 and Ns -- 20. It can be seen that, as expected, these differences increase with larger defocus distance: (b) 5 mm, (c) 10 mm, and (d) 20 mm. It is also worthwhile to note that curves (1) are offset by a roughly constant amount with respect to curves (2), which indicates that the main effect of the transition between the POA and the multislice approximation is the taking into account of a quadratic term in the phase, corresponding to a weak lens effect. From the data it can be ascertained that the m a x i m u m difference

0.0005

i ~

1.5

1

....AI

2

ta) S

~

21

0.5

(b) -0.0005

1 2

2

(c)

(d)

1~tm

FIGURE5. (a) Intensity distributions I across the out-of-focus image of the p-n junction for the following values of the defocus: curve (1), 5 mm; curve (2), 10 mm; curve (3), 20 mm. (b-d) Differences A I between the POA case and the multislice calculation with Ns = 10, curves (1), and differences between two multislice calculations with Ns = l0 and Ns = 20, curves (2), for the above values of the defocus: (b) 5 mm; (c) 10 mm; (d) 20 mm.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 191 between the POA and each of the multislice calculations never exceeds 5 . 1 0 -4; that is, all the calculations agree to three decimal places, as found by Komrska and Vlachova (1973) for the case of an electron biprism. As the multislice approach is an improvement with respect to the Komrska diffraction integral, since in the limit of very large Ns the action is calculated along a piecewise rectilinear path approaching more and more the classical electron trajectory, we may conclude that the POA is validated by this approach.

E. The Electrostatic Aharonov-Bohm Effect In 1959, in a famous paper, Aharonov and Bohm, hereafter referred to as AB, called attention to the significance of the electromagnetic potentials in quantum theory. They proposed two different electron interference experiments in order to test their conclusions. The first, concerning the effect of the vector potential associated to a static magnetic field, has stimulated a wealth of experimental work (for reviews see Olariu and Popescu, 1985; Peshkin and Tonomura, 1989), which shows the attempts of the experimentalists to satisfy the everincreasingly stringent conditions required by the theoreticians, especially by those who do not believe in the effect. Much less attention has been paid to the second experiment regarding the electric scalar potential: In this case a coherent electron beam is split into two parts and chopped. Subsequently, each part is allowed to enter a long cylindrical metal tube, the electric potential of which is varied only when the electron wave packets are well inside. The beams are then recombined to give an interference pattern. This experiment (which so far has never been carried out) should show a phase difference due to the time-dependent scalar potential even though no force is ever exerted on the electron wave packets. In 1973 Boyer, in his considerations on the AB effect, noticed that if the experiment involving time-dependent electric fields is carried out by static potentials, its result will be very similar to that produced in the magnetic AB effect. When electrons enter and leave the tubes, they experience classical electrostatic forces, which produce no net change of momentum or energy but only a classical time lag. This can be related to the phase difference A4~ calculated in the Wentzel-Kramers-Brillouin (WKB) approximation (Boyer, 1973) through the de Broglie wavelength )~:

~AV1 (23) )~E where A V is the potential difference between the two tubes of length l, and E, in the nonrelativistic case, is the accelerating potential. Ar =

192

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

A different point of view in considering these experiments has been expressed by Aharonov (1984) who, in addition to the "true" AB effects (which are defined as type 1 nonlocal phenomena), introduced a new kind of quantum nonlocal phenomenon (referred to as type 2). In the type 2 phenomena the particles experience local interactions with fields (or other forces), which result in a change in their semiclassical action independent of the trajectory, and hence a change of phase for the quantum state of the particle. The electrostatic AB experiment proposed by Boyer (1973) can therefore be regarded as a nonlocal type 2 phenomenon. The use of the two tubes proposed by Boyer (1973) requires a highly sophisticated experimental setup. A modified version of Boyer's experiment was realized with a single tube by Schmid (1984). To overcome the difficulties inherent in the realization of two microtubes, we conceived a different and simpler method (Matteucci, Missiroli, and Pozzi, 1982c). The central wire of the electrostatic biprism was evaporated on one side with a thin layer of a different metal (Fig. 6a). In this way, the contact potential difference AV between the two metals produces an electrostatic potential distribution around the wire given by g ( x , z) --

7g

arctan

X 2 -~-Z 2 -

R2

(24)

The following facts should be noted: If the radius R of the wire tends to zero, while R A V = const, the potential distribution becomes that of a line of dipoles and it can be easily verified in this case that the electrons do not suffer any lateral deflection and leave the bimetallic wire with the same energy as

FIGURE 6: (a) Modified biprism version as a bimetallic wire. (b) Schematic representation of the cross section and charge distribution of the bimetallic wire. (c) Electric field due to two lines, having opposite charges.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 193 when they enter its field (Boyer, 1987; Matteucci and Pozzi, 1987). Moreover, a constant phase difference given by A4~ =

4zra AV I.E

(25)

is introduced between the two split parts of the electron beam, which travel on both sides of the wire. These same conclusions hold also for the wire with finite diameter (Matteucci, Missiroli, and Pozzi, 1982c). Comparing Eq. (25) with Eq. (23) reveals that the device is equivalent to two tubes of length 4a. For electrons accelerated at 100 kV, with a wire radius of 0.3/zm and a contact potential difference of 0.5 V, the phase difference amounts to 1.6zr. This effect can be explained also on the basis of the following heuristic considerations: In general, the contact potential difference between the two metals causes a charge redistribution (Fig. 6b) in such a way that the resulting field is equivalent to that produced by two parallel linear charge densities of opposite sign (no net charge on the bimetallic wire), which are laterally displaced, one with respect to the other (Fig. 6c). Therefore, the bimetallic wire can be modeled by a system of two biprisms of opposite power. In the region between the two lines of charge the phase shift varies linearly; this effect cannot be observed for the case of the bimetallic wire because the wire itself acts as an impenetrable barrier for electrons, but can be revealed in the case of two wires carrying opposite charges, which thus allows the measurement of the total phase difference. This consideration has led us to develop a further shifting device (Matteucci and Pozzi, 1987). It consists of two parallel conducting wires held at opposite potentials by an external voltage supply. They act as a macroscopic line of dipoles with the additional advantage, with respect to the bimetallic wire, of controlling its strength. 1. Experimental Methods and Results a. Bimetallic Wire A schematic drawing of the whole setup of our first experiment (Matteucci, Missiroli, and Pozzi, 1982c) is shown in Figure 7a. The coherent electron beam coming from a field-emission source S propagates to the biprism plane, located at the level of the selected area aperture of a Philips EM 400T electron microscope. The wire W was coated laterally for half its length with a thin layer of gold (black region), thus becoming a bimetallic biprism. The biprism wire splits the wave front of the incoming beam, and its electrostatic field produces a deflection and a subsequent overlapping in the plane OP below the wire, where a system of interference fringes will be observed. The interference fringe systems of the wire recorded in correspondence to uncoated (Fig. 7b) and coated (Fig. 7c) regions are shown in the fight part of Figure 7. The displacement

194

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 7. (a) Schematic drawing for the electron interference experiment, S, electron source; W and P, wire and earthed plates of the biprism; OP, observation plane. (b and c) Interference patterns corresponding to the (b) uncoated and (c) coated part of the biprism wire. of the interference fringe system due to the constant phase difference with respect to the unperturbed diffraction envelope is clearly visible through a change of symmetry of the pattern: the central maximum corresponding to the uncoated part becomes nearly a minimum in the coated part, which thus indicates a phase difference of about Jr. In this experiment, the phase difference cannot be varied since the rotation of the wire around its axis is not allowed. The dependence of the effect on the angle 0 cannot be revealed by this setup. Different experiments were made to display this dependence by using interference electron microscopy (Matteucci, Missiroli, Porrini, et al., 1984) and diffraction methods (Matteucci and Pozzi, 1985).

b. Macroscopic Dipole This experiment was realized by inserting in a special specimen holder, provided with electrical contacts, a macroscopic electric dipole D (Fig. 8a). Two platinum wires soldered on platinum apertures were superimposed and electrically insulated (Matteucci and Pozzi, 1987). The wires were oriented in parallel and the whole assembly was inserted in the microscope. The lower wire was earthed, whereas the upper one could be biased by means of an external voltage supply. Observations were carried out by means of interference electron microscopy, the instrument being equipped also with a conventional electron biprism (Fig. 8a). Surprisingly, application of 24 V to the upper wire allowed the condition to be achieved when the two wires carried opposite charges. This fact was easily detectable by observing the relative alignment of the outer system of interference fringes.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 195

FIGURE8. (a) Schematic setup for the interference fringe formation in the case of a macroscopic dipole D acting as a shifting device. The essential elements are the same as in Figure 7a. (b) Interferencepattern according to (a). D, projected dipole shadows; N, region of the interference pattern where the phase shift is revealed; M, unaffected interference region. In this arrangement the interference region in the OP plane due to the biprism is divided into three parts by the projected shadows D of the macroscopic dipole. In the outer regions M, provided the wires are carrying opposite charges, two wave fronts with the same phase shift overlap and, therefore, a symmetric fringe system is expected, equal to that observable with the biprism alone. In the region N between the shadows, the waves coming from the opposite sides of the dipole overlap. Thus, electrons experience different phase shifts and a resulting phase difference arises. The net effect is a lateral displacement of the interference fringes with respect to the unperturbed system or to the diffraction envelope. Owing to the different geometry and to the value of the electrostatic potential of the dipole, the effect is much larger than in the case of the bimetallic wire. In our arrangement, by tilting the assembly by an angle of 1~ we can observe directly on the screen the changes in the interference fringe system between the two shadows, whereas the outer fringes are stationary. The static recording on a photographic plate does not adequately render the observed phenomena, as shown in Figure 8b. However, tilting the macroscopic dipole in order to obtain a configuration of the two lines of charge equivalent to that in Figure 6c allows electrons to travel also in the region between the two wires. The expectation is to observe not a single shadow D as in Figure 8b, but the projected shadows of both wires of the dipole.

196

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE9. (a) Interference pattern with the dipole rotated so that the two wire shadows D1 and D2 are no longer overlapping. (b) Magnified view of the region between Dl and D2.

In the interference pattern shown in Figure 9a the shadows Dl and D2 of the two wires are clearly distinguishable together with the region between them, shown enlarged in Figure 9b. The linear increase of the phase is evident and it can be estimated that the phase difference is larger than 407r. These results show that a quantum phase shift can be introduced by a macroscopic dipole and detected in an interference experiment. This phase shift arises through a local interaction of electrons with the electrostatic field of the dipole and can be interpreted either as a classical lag effect or as a local effect of the electric scalar potential. A deeper analysis has also demonstrated that this effect is due to the dipole field and cannot be interpreted as arising from the asymmetric section of the bimetallic wire (Matteucci, Medina, et al., 1992).

III. RECORDING AND PROCESSING OF ELECTRON HOLOGRAMS

A. Hologram Recording The close similarity between light optics and electron optics is used to classify interferometry devices into two categories: (1) division of amplitude

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 197 (e.g., Michelson's interferometer in light optics) and (2) division of wave front (e.g., Fresnel biprism). (For a review see Missiroli et al., 1981.) The electrostatic biprism (Section II.B), which belongs to the second category, is by far the most used device in electron optics and its performance is discussed further in Section III.A.2. Moreover, for the sake of completeness, in Section III.A. 1 we present the operating principle of amplitude division interferometry, originally realized for holography purposes by Matteucci, Missiroli, and Pozzi (1981, 1982a) and Pozzi (1983). 1. Amplitude Division Interferometry The electron-optical setup of the amplitude division interferometer is shown in Figure 10. A thin single crystal C, used as an amplitude division beam splitter and inserted in the standard specimen holder, is oriented in such a way that one first-order Bragg reflection is strongly excited. The objective lens Ob forms the Fraunhofer diffraction pattern in its back focal plane, where the two spots 1 and 2 (the zeroth order and one of the first order, respectively) are selected by the objective aperture A. The illumination is tilted so that the microscope optic axis bisects the angle formed by the direct and the Bragg-reflected beams. The

FIGURE10. Ray diagram for an amplitude division interferometer. C, single crystal; Ob, objective lens; A, aperture; 1 and 2, direct and diffracted beams; S, specimen; OP, observation plane.

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

specimen S under investigation, assumed to be a thin film of constant thickness, is inserted below the objective lens, in our case at the level of the selected aperture plane. A lattice fringe system is formed in the observation plane OP, which is conjugate to the final imaging plane through the remaining lenses of the microscope. As depicted in Figure 10, the plane OP does not coincide with the specimen plane so that an out-of-focus image of S is observed in the plane OP, superimposed on the lattice fringes of the single crystal C. These fringes will no longer be straight and parallel as they are in the absence of the object but are modulated by the phase shift introduced by the specimen. This interferogram is called the Fresnel hologram. The performance regarding intensity, coherence, and versatility of an electron microscope equipped with an amplitude division interferometer compared with that of one which uses an electrostatic biprism is briefly summarized next. However, some basic differences in the two setups render this comparison difficult. In both cases it is necessary to insert at the level of the diffraction aperture plane either the object or the electrostatic biprism. In the case of the electrostatic biprism the main difficulty is the production of the thin conducting wire; however, once mounted, the interferometry device can operate with specimens which can be easily changed through the standard specimen air lock. Moreover, it is possible to observe the specimen both out of focus and in focus. The fringe spacing can be varied simply by changing the biprism voltage. However, if interferograms with a large number of fringes are required, it is necessary to use an FEG. In any case diffraction effects modulate the intensity of the interference fringe system near the edges of the interference pattern. In the case of the amplitude division interferometer, unless an additional air lock is built, the specimen change requires a break of the vacuum in the column. However, as the diffraction aperture holder can carry up to three apertures, three specimens can be observed on each run. The limitation, due to the fact that the fringe spacing can be varied only by changing the crystal orientation or the crystal itself, is compensated by the much less experimental effort required in setting up the beam-splitting device. Moreover, with respect to the electrostatic biprism, a much wider interference field, limited only by the lateral dimension of the crystal, is available; edge diffraction effects are negligible since the crystal is observed nearly focused. Other points to consider are the brightness and the coherence. In the amplitude division interferometer the weakening of the beam, due to the crystal thickness, is compensated by the greater intensity available and by the less stringent coherence condition for illumination. Ru et al. (1994) have adopted the amplitude division interferometer in a modified form to record electron holograms of latex spheres and charged microtips (Ru, 1995a, 1995b). In addition, problems related to the formation and

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 199 reconstruction of electron holograms in a non-FEG, nonbiprism TEM using an amplitude division interferometer have been analyzed by Wang (1995).

2. Wave-Front Division Interferometry a. Theoretical Considerations As we demonstrated in Section II, the interferometric technique is a very powerful method to reveal the phase difference introduced by electrostatic fields. Such a phase difference is measured directly in the interferogram, for example, as a deviation from the rectilinear trend of the central brightest fringe. However, the achievement of a complete map of the phase variations related to electromagnetic fields through a thin foil or of the stray fields outside it can be obtained in a much more appealing fashion by using electron holography. As already discussed in Section II.C, by applying a suitable voltage to the wire, an overlapping region can be obtained, as the two object wavefunctions, each passing on either side of the biprism filament, are shifted respectively by + D / 2 and - D / 2 in the direction normal to the wire, D being the vector that connects the points brought to interfere. Henceforth, the modulus of D will be called the interference distance. In this overlapping region the total wavefunction, referred back to the object plane, is described by the following equation, which neglects diffraction effects due to the biprism edges and unessential multiplying phase factors (see Section II.C): 1

7t(r)--T

(o) r-~-

+T

(o) r+~-

e -i~fr

(26)

where f, parallel to D and perpendicular to the biprism axis, is the spatial frequency wave vector corresponding to the interference fringes, referred to the object plane. In absence of the object, it is found that the image displays an interference pattern in which the fringes are parallel to the biprism axis and spaced s -- 1/If]. The trend of these fringes is modified by the object wavefunction in such a way that information on it can be obtained either by the direct analysis of the fringes, when these are few and refer to one-dimensional objects (interference electron microscopy), or by analog or digital processing of the interferogram when the fringe number is increased and the interferogram can be considered a hologram. Let us analyze first the ideal situation, reported in Figure 1 l a in which a plane wave P W illuminates a specimen S. Only that part of the wave O which has passed through S suffers a phase modulation. The reference wave R travels outside the specimen rim through a field-free region and is not affected by any field (Matteucci, Missiroli, Nichelatti, et al., 1991). The biased biprism

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G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

J

Pw

J

J

Pw J

s ~

R/

(a)

(b)

FIGURE 1 1. Sketch of electron hologram formation with (a) a reference plane wave and (b) a perturbed reference wave. PW, incident plane wave; S, specimen; 0 and R, object and reference waves; W, biprism wire.

provides the superposition of the object and reference wave. In this condition the reference wave can be written as

( ~

~rref(r) - - T r + ~-

(27)

From Eq. (3) it follows that C(r + D/2) = 1 and q~(r + 1)/2) = constant = q~0 so that the interferogram results as the superposition of the object wave ~obj(r) = T ( r -- D/2) with a reference w a v e 1/tre e ( r ) = T(r + D/2) = e i4'~ The intensity distribution is therefore given by 2

xcos

C(~ 4~ r - ~

D

-4~0+2~rf'r

]

(28)

It should be noted that, apart from the unessential constant phase factor 4~0, the object phase 4~ is stored in the hologram.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 201 The situation is completely different when the specimen gives rise to longrange electric and/or magnetic fields as sketched in Figure 1 l b where two electrostatic charges (black dots) generate a field, which extends all around the object and will perturb electron motion (Matteucci, Missiroli, Nichelatti, 1991). The resulting phase-modulated reference wave can be written as 7tref(r)- T ( r + D )

(29)

- - e i4~(r+D/2)

The intensity distribution in the hologram becomes

_1+

o ~

(r (r 0

r]

In this case the hologram stores the information due to a fictitious specimen, whose amplitude and phase are given by

(~

C'(r) = C r - ~-

(31 a)

A4~(r)- 4~(r -D) -- 4~(r + D)

(31b)

b. Experimental Setup Since the specimens are rather coarse phase objects, to record electron holograms of long-range electric or magnetic fields, it is necessary either to use low-magnification objective pole pieces or to switch off the objective lens in order to obtain useful holograms with a large enough interference field. The operating mode has been chosen involving a minimum modification of the instrument. A Philips EM 400T equipped with an FEG was used in the experiments presented in this review. The essential electron-optical arrangement for hologram formation of electric and magnetic fields is sketched in Figure 12. A coherent beam illuminates the specimen S placed off-axis so that the reference beam travels outside the object rim. The objective lens is switched off and the microscope operates in the diffraction mode. The electron interferometer operates at the selected area plane. The intermediate lens, included in the projector lens system PS, is used to focus the specimen plane in the imaging plane IP. The final magnification is in the range of (1000-2500)• In this case the biprism should be negatively biased, which gives a virtual hologram on the specimen plane that becomes a real one in the image plane. Condenser lenses (not shown in Fig. 12) are usually strongly excited, so that

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FIGURE 12. Schematic ray diagram for hologram formation. S, specimen; W, biprism wire; PS, projector lens system; IP, imaging plane.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 203 the highest possible lateral coherence on the specimen plane can be obtained: this means that often it can be safely assumed that the specimen is illuminated by a plane wave. However, especially for electron microscopes equipped with field-emission sources, the demanding lateral coherence requirements can be met also with the effective electron source located at a smaller distance from the biprism and object planes. In this case illumination can be better modeled by means of a spherical (instead of a plane) wave. The divergence of the illumination introduces the following modifications of the main features of the interferogram, which can be accounted for by simple geometric optical considerations (Missiroli et al., 1981). Let us denote by a the distance between the effective source plane and the biprism plane, a being positive if, along the optical axis, the source plane precedes the biprism plane, and negative in the opposite case. Similarly, b is the distance between the biprism and specimen planes, b being negative when the specimen plane precedes that of the biprism. The interference distance D is then given by D = 2lb~l

(32)

where ot is the biprism deflection angle. D is unaffected by the beam divergence, which modifies both the fringe spacing s and the interference field width WF, given respectively by a+b

s--;~ WF -- 2

2aot

a

a+b

--s0 ~

a+b

a

(33) R

)

(34)

where So and 2R are, respectively, the fringe spacing and the biprism wire shadow for parallel illumination. It should be noted that the same projection factor (a + b ) / a enters the fringe spacing and the projected shadow of the biprism plane, both referred to the specimen plane. The same consideration holds if diffraction effects are taken into account by means of the asymptotic approximation (Section II.C; Pozzi, 1975, 1980a). It ensues that both the shadow effect (i.e., the deformation of the biprism edges caused by the presence of the specimen) and the defocus distance entering in the Fresnel diffraction fringe spacing around the edges follow the same similarity relation with respect to the plane wave illumination. Therefore, the possibility of varying the divergence of the beam offers an additional degree of freedom to the experimenter: in fact, keeping ot fixed, and hence D, because b is dictated by the experimental setup, the experimenter can vary the fringe spacing and the interference field width according to Eqs. (33) and (34). These considerations are illustrated by our experimental observations on an array of parallel reverse-biased

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 13. Electron holograms taken with (a) the objective lens switched off and (b) a weakly excited objective lens. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reversebiased p-n junctions, pp. 29-38, Copyright 1987, with permission from Elsevier Science.)

p - n junctions with a spacing of 8 # m and an expected depletion layer width

of 1.4 # m (Frabboni, Matteucci, and Pozzi, 1987). Figure 13a shows a hologram taken with a reverse bias of 2 V and a voltage applied to the electron biprism of 18 V. The first condenser of the FEG was at its maximum excitation, and the second condenser formed the image of the source above the specimen, inserted in the normal eucentric position. The interferogram contains about 200 fringes, of spacing 45 # m , and the interfering distance D is 5/zm. The electron-optical magnification was 1800x. As a way to increase the interfering distance, the objective lens was weakly excited (0.6 A); this allowed the formation of the effective source image below the specimen and hence to suitably vary a and the associated projection factor. The hologram obtained under these new operating conditions is shown in

E L E C T R O N H O L O G R A P H Y OF L O N G - R A N G E E L E C T R O S T A T I C FIELDS

205

Figure 13b. The biprism potential has been raised to 40 V, corresponding to a doubled interference distance with respect to Figure 13a. The electron-optical magnification was 1200x and the fringe spacing 70/~m. It can be ascertained that the projection factor has been increased by a factor of 4, which corresponds to the doubling of the Fresnel fringe spacing at the biprism edges. Moreover, in Figure 13b, we also have a stronger deformation of the edges (shadow effect) due to the same amplification effect of the projection factor, and possibly to the rotation between specimen and biprism axis introduced by the objective lens. Finally, the interference field is not doubled because part of the increased interference distance is lost in the enlarged projected shadow of the biprism wire. The exposure times were, in both cases, about 10 s. Although our instrument was equipped with an FEG, with an expected brightness of about 108 Acm -2 sr -1, the measured brightness was, in our case, an order of magnitude lower, in agreement with other measurements (Hanszen et al., 1985).

B. Hologram Reconstruction and Processing 1. Theoretical Considerations As is well known, Gabor's idea (Gabor, 1948, 1949, 1951) was to recover the information contained in a hologram by optical means. This is the second step of the holographic method consisting in the reconstruction and processing of the object wave stored in the hologram. In other words, the electron hologram, registered on a photographic emulsion, is first developed so that its amplitude transmittance becomes a linear function of the recorded intensity given by Eqs. (28) and (30). The plate is then inserted in an optical bench and illuminated by a coherent plane laser wave 7tz given by l~rL = e i2rrk~

(35)

where ko is the spatial frequency vector of the optical wave. The wavefunction after the hologram is given by ~(r) = e i 2 ~ k ~

~r(O) + 1/f(+l) -31-1/r(_1)

q/C0> -- [1 + C'(r)]e i2Jrk~ 7f<+1> -- C'(r)eia*(r)e i2~(k~ ~f (-1) -- C' (r) e-i A4'(r)eizJr(k~

The three terms in Eq. (36) correspond respectively to

(36)

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

1. The intermodulation wave ~<0>, which propagates in the same direction as the laser beam and is therefore spread around the spatial frequency k0 2. The primary wave ~/+1/ and its twin wave ~k<-l/, separated by the term ~/0/ These two waves spread around the spatial frequencies (k0 + f) and (k0 - f). The object phase information we want to decode is contained in the wave term ~/+l/, which can be isolated from the others, since the beams travel in different directions and achieve their maximum spatial separation in the back focal plane of the reconstructing lens, where an aperture can be inserted (see Section III.B.2). In order to display the phase information stored in the optically reconstructed beam, it is possible to overlap it to a plane optical interferometric wave

~g(r): 7tg(r)

=

CR ei(27rkR'r+ckR)

(37)

where CR is the amplitude, kR the spatial frequency wave vector, and 4~R the longitudinal phase, so that the observed intensity in the image plane is given by

I ( r ) - [r

~R(r)] 2

= [C'(r)]: + [CR] 2 + 2C'(r)CR • cos[Aq~(r) + 2zrk/ 9r - CR]

(38)

where kl - - ( k 0 - kR + f) is the resulting spatial frequency wave vector. In the wave vector ki unknown contributions are also included, being due to the misalignment of the optical bench or of the hologram plate, not always under the experimenter's control. In this optical interferogram the trend of the interference fringes indicates the local phase distribution of the fictitious object. Contrary to electron interferometry experiments, azimuth and spacing of the fringes can now be adjusted to meet the actual needs. In principle, by putting ki = 0, a particular interferogram called a contour map is obtained. This is very useful because a direct physical meaning can be attached to these fringes. (Tonomura, 1986, 1987a, 1987b, 1992; Wahl and Lau, 1979). In fact, when no leakage fields are present, according to Eq. (2), in the case of ferromagnetic specimens the optical contour fringes represent the lines of force of the magnetic field (averaged along the electron trajectory), whereas in the electrostatic case they represent the equipotential lines of the projected potential.

ELECTRON H O L O G R A P H Y OF L O N G - R A N G E ELECTROSTATIC FIELDS

207

FIGURE 14. Reconstruction of an electron hologram using an in-line optical bench. L, laser;

BE, beam expander; H, hologram; RL, reconstruction lens; F, filter, S, observation screen.

2. Optical Reconstruction and Phase Detection a. In-Line Optical Bench The conventional reconstruction of the electron hologram can be carried out with an in-line optical bench (Fig. 14) equipped with an He-Ne laser source L and a beam expander BE so that a plane wave illuminates the hologram H. In the back focal plane the reconstruction lens RL performs the Fourier transform of the intensity distribution of the hologram H. A spatial filter F intercepts all the other beams except the (+ 1), which allows a free propagation of the (+ 1) beam. In this way the inverse Fourier transform is performed and in the observation screen S the intensity distribution replica of the object wavefunction is displayed. If the screen location can be freely varied along the optical axis, its position can be chosen to correct the defocus aberration present in the electron hologram (Hanszen, 1982, 1986; Matteucci, Missiroli, and Pozzi, 1984; Tonomura, 1986, 1987a, 1987b, 1992). So that the phase information from the hologram can be obtained in the form of a contour map, a parallel coherent optical interferometric wave is superimposed on the reconstructed image wave. This can be achieved by inserting in the in-line bench of Figure 15 the hologram H2 of the object to be investigated

FIGURE 15. Image reconstruction and phase detection with an in-line optical bench. HI, electron interference pattern without the object;/-/2, object hologram; the other elements are the same as in Figure 14.

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G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

in contact with the hologram H1 recorded without the object (Wahl and Lau, 1979). The interference pattern//1 gives an additional plane wave, which superimposes on the reconstructed wave front. The two waves are then filtered and imaged as discussed before with reference to Figure 14. In the observation screen the parallelism condition is realized when the interferometric wave is made parallel to the background wave (i.e., a plane wave) of the reconstructed image (Hanszen, 1982) in such a way that this region presents a contrast as uniform as possible. This contrast may be bright or dark according to the longitudinal phase difference 4~R between the waves (Hanszen, 1982, 1986). It is clear that for objects whose fringing field affects the electron reference wave (Matteucci, Missiroli, Nichelatti, et al., 1991; Matteucci, Muccini, and Hartmann, 1994), the contour maps cannot be pursued because 1. There is no unequivocal criterion for the parallel superposition of the "presumed" reconstructed object wave with the optical reference wave. 2. The object phase is "buffed" in the phase difference registered in the hologram and there is no way to "unearth" it with optical processing. In any case even if point (1) is overcome, at the end of the process only the fictitious and not the original wavefunction is reconstructed.

b. Mach-Zehnder Interferometer and Phase Amplification A more versatile optical setup used for the reconstruction of the hologram is the Mach-Zehnder interferometer, as it allows many different processing schemes to be performed in addition to the standard ones used with the inline bench (for reviews, see Hanszen, 1982, 1986). In particular, we used the Mach-Zehnder interferometer reported in Figure 16 to carry out experiments of phase-difference holography. Processing two holograms /-/1 and H2 of the same object in two different states (in our case a p - n junction at two different reverse applied potentials) allows the change of the phase corresponding to the change of the state to be displayed. In this case phase changes correspond to different projected equipotential configurations. A coherent light wave, coming from a laser L and a beam expander BE, is divided into two beams by the beam splitter A. The two beams are deflected by mirrors M to illuminate the two holograms H~ and H2. A second splitter B allows the parallel recombination of the two beams and the formation of images and contour maps on the final screen S as described before for the in-line bench. The versatility of this bench is demonstrated by its use for obtaining phasedifference amplification maps, which give more detailed information concerning the trend of equiphase lines (see Tonomura, 1986, 1987a, 1987b, 1992).

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS

209

FIGURE 16. Mach-Zehnder interferometer for hologram reconstruction and processing. A and B, beam splitters; M, mirrors; the other elements are the same as in Figure 14.

In Figure 17 the basic phase-difference amplification setup using a MachZehnder interferometer is sketched. The electron hologram H is illuminated by the two coherent beams coming from the two interferometer arms and each of them forms a set of (+ 1), (0), and ( - 1 ) diffracted beams. The mirrors are adjusted to superimpose on the focal plane of the lens R L the (+ 1) order of the beam, which comes from one arm to the ( - 1 ) generated by the other arm. The spatial filter F prevents the propagation of all the other beams. In this way the optically reconstructed object wave ((+ 1) beam) and its conjugate wave ( ( - 1 ) beam) interfere, which gives the desired two-times amplification.

FIGURE 17. Optical setup of a Mach-Zehnder interferometer used to perform two-times amplification maps.

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

More generally, a 2n-times amplification factor can be performed by developing the electron hologram nonlinearly and using higher-order diffracted beams (+n) and ( - n ) (Matsumoto and Yakahashi, 1970), or by using the iterative method suggested by Bryngdahl (1969). C. Double-Exposure Electron Holography

In the foregoing section we briefly outlined the problems related to achieving the contour map condition. In fact, it is impossible to determine unequivocally the parallelism between the optically reconstructed object wave and the reference wave (see Section Ill.B) used to extract phase information. This ambiguity can be removed by the electron double-exposure method (Matteucci, Missiroli, Chen, et al., 1988; Wahl, 1975). An off-axis image hologram is first recorded as described in Section III.A.2 and, after removal of the specimen from the beam, the interference pattern between two unperturbed waves is recorded on the same plate (this last recording provides the most reliable reference wave front). This recording process guarantees the parallelism between the object and reference wave vectors, since these waves are registered with the same tilt angle (which is related to the biprism potential). The whole procedure is analytically described by considering that the intensity function of the first hologram is given by I1 (r) = 1 + cos[Aq~(r) - 2:rf. r]

(39)

The second hologram is simply a linear grating, whose intensity is /2(r) = 1 + cos(2:rrf, r)

(40)

so that the total intensity stored in the double-exposure hologram is, apart from an unessential multiplying factor, ]tot(r) = 2 + cos(2rrf, r) + cos[A~(r) - 2zrf. r]

(41)

These phase-dependent intensity variations will appear directly on the plate once it has undergone a linear photographic development. Figure 18 shows a double-exposure electron hologram of charged latex spheres. The most interesting feature of this micrograph is the contrast variation of the interference fringe system, which presents regions of a strongly reduced contrast in the form of bands. These regions map the in-plane projected potential distribution of the electric field directly (Chen et al., 1989; Matteucci, Missiroli, Chen, et al., 1988; Matteucci, Missiroli, Nichelatti, et al., 1991). If the double-exposure hologram is inserted in the optical bench of Figure 14 and is illuminated by a plane laser wave, the carrier fringe system is removed in the reconstructed image, which leaves an optical interferogram alone that

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 211

FIGURE18. Double-exposureelectron hologram of electrostatic charged spherical particles assembled on the rim of a carbon film. The regions where the interference fringes are blurred map the projected potential distribution.

displays the map of the phase difference A~b. Moreover, contrary to the optical interferometry techniques, it should be emphasized that double-exposure electron holography also eliminates any possible additional longitudinal phase term. As experimentally demonstrated in the following section, the importance of recording double-exposure holograms is due to the fact that in the reconstruction and processing of a standard hologram taken with a perturbed reference wave, no objective criterion exists for determining the correct phase-difference map condition (i.e., for recovering the object phase unambiguously). These problems become more serious when phase-difference amplification techniques are employed (Hasegawa etal., 1989; Tonomura, 1986, 1987a, 1987b, 1992; Tonomura, Matsuda, et al., 1985). With the lack of a double-exposure hologram which could be used as a reference to compare the phase-difference maps, the physical interpretation of the final amplified map suffers the same shortcomings as for those obtained with the optical arrangements shown in Figures 14 and 15. These considerations suggest a standard procedure for mapping and amplifying the stored phase difference. When possible, it is worth taking a set of three electron micrographs of the same specimen: 1. A single-exposure hologram. 2. An image of the interference field without the object. This fringe system is used to generate the interferometric wave to extract the phase-difference map. 3. A double-exposure hologram. This furnishes directly the map of the phase difference between the object and the perturbed reference wave and can be used also as a "guide" hologram when the phase amplification methods are applied.

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However, it should be borne in mind that even if one uses the double-exposure method, it will not be possible to avoid the distortion of the contour map, which is caused by the perturbation of the reference wave in the presence of long-range fields, and whose effect can be investigated only by computer simulation. Moreover, an additional merit of the double-exposure method is that the mapping of electric or magnetic fields on a larger area than that recorded on a single micrograph can be obtained by a suitable montage of holograms. A number of double-exposure holograms are taken of successive adjacent areas of the field under investigation and then pasted together. Careful attention must be paid when the object is shifted with respect to the biprism. Reliable results can be obtained particularly when a theoretical model is available to take into account the phase differences recorded on each hologram.

IV. CHARGED DIELECTRIC SPHERES

A. Recording and Processing of Electron Holograms The specimens were prepared by depositing on a conducting carbon film, of about 30 nm in thickness, a little drop of an aqueous suspension of spherical polystyrene latex particles of diameter 2a = 0.31 /zm. Under the action of the electron beam the randomly distributed latex spheres acquire a stationary positive charge Q as a result of a dynamical equilibrium of charging up by secondary emission, and neutralizing by field emission (Drahos et al., 1969). The magnitude and the distribution of the stationary charge depend on the material, on the geometry of the scattering object, and on the energy and current density of the electron beam. As regards the field outside the sphere, it can be fairly well approximated by the field of a point charge Q located in the sphere center at a distance a from the conducting grounded plane (Drahos et al., 1969). The off-axis electron holograms were recorded by the setup schematically shown in Figure 12. The holograms have an interference field of about 120 fringes of 85-/zm spacing, which allows for a resolution referred to the specimen of about 0.1 /zm. Exposure times were of the order of a few seconds. The conventional reconstruction of electron holograms has been carried out in an in-line optical bench. In Figure 19 the reconstructed specimen image is shown. Only the amplitude information is present in this image, showing a set of opaque dielectric spheres deposited on the thin carbon film F and the edge of the hole H. Note the presence of two single spheres: A near and B far from the edge of the carbon film F. Phase-difference maps were performed by two different experimental methods: The first made use of the optical arrangement represented in Figure 15.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS

213

FIGURE 19. Optical reconstruction of an electron hologram showing latex particles. F, carbon film; H, hole in the carbon film; A and B, charged spheres near (A) and far (B) from the edge of the carbon film. (Reprinted with permission from Chen, J. W., Matteucci, G., Migliori, A., Missiroli, G. E, Nichelatti, E., Pozzi, G., and Vanzi, M., Phys. Rev. A 40, 1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

The second made use of the double-exposure technique which allows the recording of the correct trend of the contour fringes (Wahl, 1975). In Figure 20 the phase-difference map of the same region of Figure 19 is shown, obtained by the optical reconstruction of the double-exposure electron hologram. Note that the contour fringes suffer an abrupt discontinuity when

FIGURE 20. Optical reconstruction of a double-exposure hologram showing a map of the phase difference of the same region as in Figure 19. (Reprinted with permission from Chen, J. W., Matteucci, G., Migliori, A., Missiroli, G. E, Nichelatti, E., Pozzi, G., and Vanzi, M., Phys. Rev. A 40, 1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 21. (a-d) Optical interferograms of the same region as in Figure 19 showing four different possible configurations of the phase difference. (Reprinted with permission from Matteucci, G., Missiroli, G. E, Nichelatti, E., Migliori, A., Vanzi, A., and Pozzi, G., Electron holography of long range electric and magnetic fields, Journal of Applied Physics, 69(4), pp. 1835-1842. Copyright 1991, American Institute of Physics.)

they cross the edge of the film. The importance of this map is better shown by considering that if the optical experimental procedure is repeated, the wave vector kt [see Eq. (38)] slightly changes and the interferogram displayed shows different trends of the field under investigation. These considerations are demonstrated by the experimental results reported in Figures 21 a through 21 d as compared with the optical reconstruction of the double-exposure electron hologram of Figure 20. Each of the parts of Figure 21 reports an optical interferogram obtained with small angular variations of ki (of the order of 10 -3 rad) with respect to the interferometric plane wave. The different trends of the various maps is immediately perceived. For this reason we regard the double-exposure hologram as a "guide hologram" with which the trend of the phase-difference fringes obtained by the reconstruction of a single-exposure hologram should be tested and the phase-difference map selected. In conclusion, the experimental results reported in Figure 21 show that the optical processing of an electron hologram can produce a large number of different interferograms, which do not represent the most reliable phase-difference

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 215

FIGURE22. (a) Two-times and (b) four-times phase-difference-amplified contour maps obtained from the same hologram of Figure 20. (Reprinted with permission from Chen, J. W., Matteucci, G., Migliori, A., Missiroli, G. E, Nichelatti, E., Pozzi, G., and Vanzi, M., Phys. Rev. A 40, 1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

map. The latter can be obtained only by comparing the optical interferograms with the double-exposure hologram. More detailed information about the trend of equipotential lines can be obtained with the technique of the phase-difference amplification as discussed in Figure 17, Section III.B.2. Figure 22a shows a two-times amplification contour map of the same region reported in Figure 20, whereas Figure 22b shows a four-times amplification contour map. In these figures two neighboring equipotential fringes differ in phase of Jr and of zr/2, respectively. Figures 23a and 23b show a magnified image of the phase distribution around the two single dielectric spheres A and B of Figure 19, amplified by a factor of 4. It can be seen that whereas the trend of the fringes has a circular symmetry

216

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 23. Four-times phase-difference-amplified maps of the single charged spheres labeled A and B in Figure 19. (Reprinted with permission from Chen, J. W., Matteucci,G., Migliori, A., Missiroli, G. F., Nichelatti, E., Pozzi, G., and Vanzi,M., Phys. Rev.A 40,1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

in the vicinity of the particle B, which is far from the edge of the carbon film, this symmetry is no longer present for the sphere A located near the edge. That is, the presence of the edge has a detectable effect on the phase distribution.

B. Interpretation of the Experimental Results In order to interpret the results of the foregoing paragraph, the electric field around the spherical particles has been modeled by that of a point charge Q localized at the center of the sphere of radius a and placed in front of a conducting plane. For a particle far from the edge, whose center is positioned at

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 217 the point (x0, y0, a), the potential in the half-space z > 0 can be calculated by means of the image charge method (Feynman, 1967) and is given by the expression V ( x , y, z) =

Q[ Q[

4ZrEo [(x

-

X o ) 2 --~

1 1

]

(y - yo) 2 + (z - a ) 2 ] 1/2

]

4zr ~o [(X - - Xo) 2 + (y - yo)2 + (z + a)2] 1/2

(42)

while in the half-space z < 0, V ( x , y, z) = 0. The phase shift 4~ can be calculated analytically from Eq. (42). It follows that ~b(x, y) --

[Q ]arcsin.[ 2E0)~E

a

[(x -- x0) 2 + (y --y0)2] 1/2

]

(43)

Simulations of the contour map images produced by the phase distribution [Eq. (43)], in which the edge effects of the carbon film and of the perturbed reference wave have been momentarily neglected, have been carried out by using an IBM PC/AT personal computer equipped with a video board able to display 512 x 512 pixels at 256 gray levels. Figure 24 shows the results for our point charge distribution of Figure 20 assuming Q - 400e - 6.4- 10 -17 C and a - 0.155/zm. This value of the charge is in agreement with the findings of Komrska (1971), who measured a charge of 1100e on spheres of radius 0.28/zm by studying their diffraction patterns.

FIGURE24. Simulatedcontour map of the same distribution of charged spheres as shown in Figure 20. (Reprinted with permission from Chen, J. W., Matteucci, G., Migliori, A., Missiroli, G. E, Nichelatti, E., Pozzi, G., and Vanzi, M., Phys. Rev. A 40, 1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

218

G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

FICURE25. Coordinate system for the potential and phase calculations in the conducting half-plane problem. (x0, Y0, a), position ofthe point charge; (x, y, z), observationpoint; (0, Y0,a), projection of the position of the point charge on plane yz; (0, y, z), projection of the observation point on plane y z. The overall similarity between calculated and experimental images is satisfying far from the edge, which confirms the main hypotheses made and allows, within this framework, the determination of the charge Q with an accuracy of 20%. Of course, near the edge, differences are detectable because of the fact that the simple model does not take into account the discontinuity of the conducting film. If the actual shape of the edge is replaced by a straight line, the electrostatic problem still has an analytical solution (Durand, 1966). Referring to Figure 25 for the definition of/3 and 9, we find that the solution reads as follows: V ( x , y, z) -

where h+ --

[

1

Q ](h_-h+) 2rr2E0

(44)

]

[r 2 -}- (z --1-a)2]l/2 arctan [ [(p + ro) 2 + (x - Xo)2] 1/2 + •

/

[7;-$- ~z + a~2] '/2

+ yyo T za)] '/2 ]

/

(45)

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 219 and r0 -- (a 2 + yg) l/2

(46)

r = [(x - x0) 2 + (y - y0)2] 1/2

(47)

/9 = (y2

_+_Z2)1/2

1,

0 ~ [0, 7r - 15]

Y+--

-1,

0 6 [Jr-/5,2Jr]

Y---

1, -1,

O~[0, zr+/5] 06[Jr+/5,2zr]

(48) (49a)

(49b)

Since no analytical expression for the phase shift was found, it has been calculated by numerical integration of Eq. (2). Figure 26 shows the results of the contour map simulation for the charged sphere on the whole plane WP and on the half-plane HP. Here again it can be ascertained that the effect of the edge E is to break the circular symmetry of the contour lines around the particle and that their distortion increases as the particle is located at diminishing distances from the edge. However, it is not responsible for the step observed experimentally, which is entirely due to, and can be properly accounted for, the introduction of a constant phase shift in the half plane due to the mean inner potential of the carbon film.

C. Numerical Simulations of Contour Maps In order to evaluate the influence of the perturbing phase term r D/2) which appears in Eq. (30), we next present and discuss computer-simulated contour maps, relative to the two experimental cases considered in this work. The function I (r) which describes intensity variations through the contour map is given, after a translation of D/2, by I(r) = 1 + cos[$(r) - ~b(r - D)]

(50)

in which the term of the phase perturbation due to the reference wave is evident [See also Eq. (30).] The intensity variation of Eq. (50) was displayed by means of an IBM PC/AT personal computer equipped with a Matrox PIP 1024-B video board. The set of images in Figure 27 shows four simulations of the interference maps of the field associated with a system of charges like that in Figure 22 for increasing values of the interfering distance D. The sphere diameter and charge are 0.31/zm and Q = 400e. The values of D for each micrograph of Figure 27 are:

220

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE26. Comparison of simulated contour maps of a single charged sphere located on the whole conducting plane WP (upper part of each picture) and near the edge (lower part) of a half conducting plane HP. The vertical line E marks the edge position. Distance between the sphere and the edge: (a) 5/zm; (b) 2/zm: (c) 0.155/xm. (Reprinted with permission from Chen, J. W., Matteucci, G., Migliori, A., Missiroli, G. E, Nichelatti, E., Pozzi, G., and Vanzi, M., Phys. Rev. A 40, 1989, pp. 3136-3146. Copyright 1989 by the American Physical Society.)

(a) D = 3 # m ; (b) D = 5/zm; (c) D = 8/zm; and (d) D = oo; this latter value corresponds to the case of an unperturbed reference wave. It can be ascertained that differences arise between the patterns, which are more detectable in the regions far from the particle centers. According to theoretical expectations, such differences become smaller as the distance D between interfering points is increased. In practice, further simulations show that the actual contour map is indistinguishable from the unperturbed one (Fig. 27d) only when D is greater than 15 # m . However, near the particles, where the phase shift is larger, the effect of the perturbation is less and, for values of D wider than 5 # m , the overall trend of the fringes is not substantially affected. Taking into account that the upper value of the interference distance of our experimental setup is of about 10/zm, we can see that the ideal condition can

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 221

FIGURE27. Simulated contour maps of the potential distribution generated by the charges located as in Figure 20 for different values of the interfering distance D: (a) D = 3 /~m; (b) D = 5 /zm; (c) D - - 8 /xm; and (d) D = c~. (Reprinted with permission from Matteucci, G., Missiroli, G. E, Nichelatti, E., Migliori, A., Vanzi, A., and Pozzi, G., Electron holography of long range electric and magnetic fields, Journal of Applied Physics, 69(4), pp. 1835-1842. Copyright 1991, American Institute of Physics.) almost be reached. For lower values the effect of the perturbed reference wave becomes important. Since latex-sphere samples can be easily prepared and can be used to check the holographic method, our experiments have been repeated by Frost, Allard, et al. (1995). Their results show the possibility of revealing a small amount of charge of the order of magnitude of 10 electrons.

V. p - n JUNCTIONS A. Experimental Results In this section we present and discuss the experimental results obtained by applying electron holography techniques to the observation of reverse-biased p - n junctions.

1. Specimen Preparation and Electron Microscopy Observations The procedure that was used to obtain a specimen suitable for TEM from an n-type silicon wafer follows. The surface layer of the sample was preamorphized by implanting Si + ions in order to minimize channeling phenomena.

222

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

!

In

i

ip

""

ITiAg

H

FIGURE28. Schematic drawing of the ion-implantedp-n junctions.

Boron ions with a dose of 1015 cm -2 were successively implanted at 10 keV. The wafer was then annealed at 900~ for 30 min in a nitrogen atmosphere. The implantation was carried out through a SiO2 mask consisting of parallel slits 8 / z m wide and of 8-/zm spacing in order to produce a set of parallel diodes. The resulting p - n junctions have a depletion-layer width W = 1.4/zm, and a built-in potential of V = 0.76 V. As a way to bias the junctions, one end of the structure made up with parallel slits was electrically shorted by vacuum deposition of a TiAg layer; this continuous layer connects the p regions and is isolated from the n regions by the SiO2 layer used for ion implantation. Far from the TiAg layer, the SiO2 mask was removed by photolithography (Fig. 28). A flat rectangular region was obtained, which consists of a set o f p - n junctions. The junctions can be biased with an external voltage source applied between the TiAg layer and the back of the wafer. The implanted wafer was subsequently chemically thinned, from the side of the backing material, in correspondence to the region where the SiO2 mask was removed. By protracting the thinning up to the formation of a hole Hit was possible to obtain around it a thin area containing several parallel junctions side by side. Since the lower portion of the junctions has been removed by the thinning process, the remaining part of them is perpendicular to the wafer surface. In order to carry out the observations in the electron microscope, the thinned specimen was mounted on a special specimen holder equipped with electrical contacts for biasing the junctions. When a reverse bias is applied to the array, an enhancement of the electrostatic field of the junctions is produced both inside and outside the specimen. The inner field lines of the

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 223

H FIGURE 29. Sketch of the intersections of the equipotential surfaces associated with the external field of p-n junctions with planes parallel and perpendicular to the optic axis z. (Reprinted with permission from Frabboni, S., Matteucci, G., Pozzi, G., and Vanzi, M. Phys. Rev. Lett. 55, 1985, pp. 2196-2199. Copyright 1998 by the American Physical Society.) junctions are parallel to the upper specimen surface and perpendicular to the beam. Figure 29 is intended to show schematically the trend of the equipotential surfaces around the specimen by means of their intersection with (1) the plane inside the specimen parallel to the direction z of the electron beam, and perpendicular to the junction boundary, and (2) the x y plane at the edge of the hole H. The equipotential surfaces spread out from the upper and lower surfaces of the specimen where the junctions are localized and extend as far as the edge of the hole where they rotate. Figure 30 shows an out-of-focus electron image of the specimen area where two p - n junctions are present. The reverse bias was 4 V, the defocus distance - 1 . 2 5 mm, and the electron-optical magnification 1700x. The micrograph shows sharp contrast lines (see arrows), with a fine waveoptical structure, which arise in correspondence with the depletion layer, or more precisely, in correspondence with the regions having the highest phase gradient (i.e., the highest electric field). Unfortunately, it is difficult to extract quantitative information from these patterns, since the relation between image intensity and the phase shift of the object wavefunction is highly nonlinear and depends on other parameters such as defocus, spherical aberration, and intensity distribution of the electron source, which limit the accuracy of the obtained results. Similar criticism can be applied to the other methods of Lorentz microscopy (Chapman, 1984). Electron holography, with its unique capability of reconstructing the twodimensional object wavefunction, both in amplitude and phase, could be the answer to the problems posed by the standard methods of observation. As shown

224

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FICURE 30. Out-of-focus image of a region where two p-n junctions are present. Arrows mark contrast lines associated with depletion layers. Reverse bias, 4 V. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reverse-biased p-n junctions, pp. 29-38, Copyright 1987, with permission from Elsevier Science.)

in Section III.A.2b holograms containing about 200 fringes at two interfering distances, 5 and 10/zm, were taken with exposure times of about 10 s (Fig. 13).

2. Optical Reconstruction and Processing of Electron Holograms In this section we report the results concerning the optical processing of the image holograms recorded under the experimental conditions of Figure 13 (Section III.A.2), with the largest interference distance, for which the effect of the fringing field spreading outside the specimen should be minimized. The p - n junctions were reverse biased at 0, 2, and 4 V; in addition, the hologram of the interference field without the object was recorded. The optical setup used for the reconstruction of the holograms was a M a c h Zehnder interferometer, whose versatility allowed us a choice of different processing schemes. Figure 31 shows the contour map obtained with the hologram of the specimen at 0 V reverse bias and a plane wave obtained from a hologram recorded without the specimen. Two regions S and H can be observed: the lower part of the figure, S, refers to the in-focus image of the specimen, whereas the upper part, H, refers to the hole. The reconstructed specimen area, which extends laterally over a distance of about 20 #m, contains the same two junctions as reported in the out-of-focus image of Figure 30. The interference fringes superimposed on the specimen do not reveal any distortion attributable to the electric field generated by the contact potential (0.76 V) between the areas n and p, although, as demonstrated in the following, the sensitivity of the method is high enough to detect such potential difference. The fringe behavior in region S, however, is related to the variations in the

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS

225

FIGURE 31. Contour map of the specimen at 0 V reverse bias. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reverse-biasedp - n junctions, pp. 29-38, Copyright 1987, with permission from Elsevier Science.) specimen thickness and reflects the wedge shape around the edge due to the chemical thinning. In area H a bright field can be observed, with some shadows whose origin can be sought in the weak perturbing electrostatic fields originated by impurities on the biprism wire or in the photographic plates used for the holograms whose thickness varies within the reconstruction field. Figure 32 shows an interferogram obtained by the simultaneous reconstruction of one hologram at 2 V reverse bias and another without the specimen. First, we verified the parallelism between the two transmitted beams by checking the absence of optical interference fringes within the field of view when the filter was removed. On examination of the interferogram obtained by reinserting the filter, it was impossible to decide the correct condition of the contour map, since we could choose among a large number of possible superpositions

FIGURE 32. Optical interferogram of the specimen at 2 V reverse bias. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reverse-biased p - n junctions, pp. 29-38, Copyright

1987, with permission from Elsevier Science.)

226

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

between the diffracted spot generated by the hologram with the specimen and the one generated by the reference hologram as demonstrated in Figure 21. The former spot, in fact, is broadened because of the electric field while the latter is a dotlike spot. Superimposition of the interference fringes of the two holograms in unperturbed regions is not applicable in this case, since the carrier fringes of the holograms recorded at 2 V are strongly distorted all over by the electric field. All these drawbacks could be eliminated if the double exposure of the holograms gave reliable results when it was recorded directly in the electron microscope. Despite the uncertain optical conditions, the interferogram shows that the optical fringes propagate in the whole interference field and fan out through the hole connecting the neighboring junctions, whereas within the specimen they are influenced also by its thickness variations and topographical features. Considerable improvement of information about the trend of the electric field distribution within the specimen can be obtained if two holograms of the specimen, recorded at different reverse biases, are simultaneously reconstructed. With respect to the foregoing case, once the parallelism is achieved as before, the coincidence of the two Gaussian images of the specimen eliminates the degree of freedom due to the relative rotation of the holograms, so that reproducible and reliable results can be obtained. Figure 33 shows the differential contour map obtained by superimposing the reconstructed images relative to the holograms of the specimen at 0 and 4 V reverse bias. As the fringes represent the positions of the points where the difference between the phases of the reconstructed waves is constant, since it is the same for both waves, the thickness contribution to the phase is eliminated. The improvement of Figure 33 with respect to Figure 32 is evident, and in this case the contour fringes directly display the trend of the in-plane projected

FIGURE33. Differential contour map between two holograms recorded with the junctions at, respectively, 0 and 4 V reverse bias. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reverse-biasedp-n junctions, pp. 29-38, Copyright 1987, with permission from Elsevier Science.)

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 227

FICURE34. Differential contour map between two holograms recorded with the junctions at, respectively, 2 and 4 V reverse bias. (Reprinted from Ultramicroscopy, 23(1), Frabboni, S., Matteucci, G., and Pozzi, G., Observation of electrostatic fields by electron holography: The case of reverse-biasedp-n junctions, pp. 29-38, Copyright 1987, with permission from Elsevier Science.) equipotential surfaces resulting from the total electric field associated with the junctions. In the depletion-layer areas, the contour lines are parallel to each other and to the junction and show a different spacing on both sides of the p - n junctions, which reflects the local asymmetry of the electric field, usually described by one-sided step models. Outside the edge of the specimen, the contour lines fan out again to join the nearest junction, as before. Finally, Figure 34 shows the differential contour map obtained with two holograms of the specimen held at reverse biases of 2 and 4 V, respectively. The density of the contour fringes is diminished roughly by a factor of 2 when compared with the density of Figure 33; that is, it is linear with the reverse bias, which confirms that the sensitivity of the technique is adequate enough to clearly detect a potential difference of 0.76 V (i.e., the built-in potential). B. Theoretical Interpretation

In this section we show how the analytical solution can be obtained for the electrostatic field associated to a periodic array of alternating p and n regions lying in a semi-infinite plane. From this solution the phase shift can be calculated and used for the interpretation of the main features of the holographic contour maps. 1. The Electrostatic Field Model

Let us consider the following boundary value problem (Wendt, 1958), that is, finding the electrostatic potential produced by a parallel array of stripes having pitch b, which lie in the half-plane z - 0 , x > 0 and are biased at alternate

228

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 35. Schematic drawing of the specimen and coordinate system.

potential, namely, + V0 for 2nb < y < (2n + 1)b and -V0 for (2n + 1)b < y < (2n + 2)b, n being an arbitrary positive or negative integer (see Fig. 35). On the half plane, the potential is given by

V(x, y, O) --

4Vo ~ sin Z 7/" k=0

-----~Try 2k + 1

(51)

so that, considering each Fourier component separately, we have to find a solution of Laplace's equation in the form G~(x, y, z) -- ~ ( x ,

z)sin0~y)

(52)

where )~ = ((2k + 1)/b)rc. It follows that ~z (x, z) should satisfy the following differential equation: O2 (I),k OX 2

O2 (I),k ~"

OZ 2

~.2 (I)~ = 0

(53)

with the boundary condition Ox(x > O, O ) = 1

(54)

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS

~=3 ~ ~=2~.

~ Z

~

~ 1 /

229

n=3

_I ~n=2

~=1

rl=l

~--0

~--

n--0

X

~'--- 1

11=1

~=-2

11=2 ~=-3 f

I

~ 11=3

FIGURE 36. Cartesian and parabolic cylinder coordinates. (Reprinted from Capiluppi, C., Migliori, A., and Pozzi, G., 1995. Microsc. Microanal. Microstruct. 6, pp. 647-657, with permission.)

As the half-plane z = 0, x > 0 can be considered as the limiting case of an infinite parabolic cylinder, it is convenient to solve Eq. (53) by the method of separation of variables in parabolic coordinates ~, r/related to the Cartesian coordinates x, z by the relations (~.2__ /.}2)

x z-

(55)

2 ~r/

(56)

w h e r e - o o < ~ < oo, and 0 < r / < oo. The orthogonal system of surfaces consists of parabolic cylinders with foci at the origin (Fig. 36) and the specimen half plane corresponds to the value r / - 0. In this coordinate system, Eq. (53) for the Fourier component of the electrostatic potential V takes the form

~2~_~2

a~2 +

at/2

-

=0

(57)

for which a solution is sought by the method of separation of the variables

230

G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

(Lebedev, 1965). Writing

~x = A(~)B(~?) we find that the following equations result:

d2A d~ 2

dZB dr/2

(/Z + ~,2~2)A --- 0

(58)

(--//~ -~-~.2r/2)B -- 0

(59)

where/z is a constant. If we introduce the new variables u = ~ / ~ parameter v related to/z by the formula

and v = ~/2-Xr;, and a new

/z = -,k(2p + 1)

(60)

Eqs. (58) and (59) can be reduced to the form

dZA ( 1 _ du 2 t- v-t 2

~

and

[

u2) 4 0

1 u2]

d v 2 }- ( v - 1)-~ 2

4

(61)

0

(62)

respectively. The solutions Dv(u)ofEq. (61), called Weber's equation, [or of the otherwise identical Eq. (62) with index - v - 1] are called parabolic cylinder functions or Weber-Hermite functions and their properties are summarized in the book edited by Erd61yi (1953), whose notation will hereafter be strictly followed. In addition to D~(u) also D~(-u), D~_l(iu), and Dv_l(-iu) satisfy Weber's equation. As there are only two linearly independent solutions, the preceding solutions are connected. In particular, if v - n is a nonnegative integer, then D n ( u ) -- 2 -(1/2)n exp

(u2) --~

Hn(2-1/2u)

(63)

where Hn(u) is the Hermite polynomial of degree n, being Ho(u) = 1, whereas if v is a negative integer, then Dr(u) can be expressed in terms of the complementary error function Erfc defined by Erfc(x) --

e x p ( - t 2) dt fx ~176

(64)

ELECTRON HOLOGRAPHY OF LONG-RANGEELECTROSTATICFIELDS 231 that is, D-m-l(U)

--

21/2~(--l)m exp (-- --~) s m!

[ exp ( - ~ - ) Erfc (2-1/2u)]

(65)

so that

D_I (u)--21/2 exp ( - ~ ) grfc (2-1/2u)

(66)

Unfortunately, the solution of Eq. (53) with the boundary condition of Eq. (54) cannot be found by using Hermite polynomials, as outlined by Lebedev (1965), since the value of the function at the boundary does not satisfy the conditions for its expansion in series of Hermite polynomials. Therefore, we should use the more general Hermite functions. When v is not an integer, D~(u) and D~(-u) are linearly independent, so that a particular solution of Eqs. (61) and (62) can be written as

A(u) -- PD,:(u) + QDv(-u)

(67)

B(v) -- RD_,,_I(V) + SD_~_I(-v)

(68)

and

respectively. The required solution of Eq. (53) should be symmetric with respect to the plane (x, y), so A(u) should be unchanged by the substitution of u --+ - u , which implies that P = Q. It follows that the most general solution for the Fourier component of the potential can be put in the fo~xn

f [D~(u) + Dv(-u)][RD_,:_l(V) + SD_v_I(-V)] dv

(69)

where the coefficients R and S are functions of v, and should be determined in such a way that ~x satisfies the boundary condition, which in parabolic coordinates becomes 9 z(u, 0) = 1

(70)

Putting S -- 0 for simplicity, we must determine only the function R, and this can be done by comparing our expression with the one which can be deduced from Erd61yi's Eq. (11) in Section 8.5.2 of Erd61yi (1953), specifying there c -- - 1 / 2 , t = 1, and y -- 0: (17.() 1/2

2Jr i

-1/2+ioo d - - 1 / 2 - - i oo

dv

[Dv(x)D-v_l (O) + Dv(-x)D_v_l (O)] sin(_vrg ) = 2-1/2 (71)

232

G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

It results that R =

i

(72)

2~/-~- sin vzr

so that our solution for the field in the whole plane can be written as

f -1/2 +ioo r

--

i --

d--1/2--ic~

[Dv(u)D-v-l(V)

+ Dv(-u)D-v-l(V)]

2~/-~- sin vrr

dv (73)

Our final solution can be changed into a more manageable form, if it is compared with Cherry's Eq. (8) in the same Section 8.5.2 of Erdrlyi (1953), which, rewritten by putting ~b = zr/2, h( = u, and hrl = v, becomes

- x / 2 i Do

~

D_ 1

~/~

- a-1/2-i~ D~(u)D_v_l(V) sin vrr

D_I

~

(74)

so that it finally ensues that

9~ = , / ~l

/ Doi

~

+Do

,/5

D_I

~ (75)

It should be noted that Cherry's formula has been derived with complex arguments in relation to the solution of the Helmholtz equation to find Sommerfeld's secondary wave, while in our case we are dealing with real arguments and the solution of Laplace's equation. Nonetheless, it can be easily ascertained that our final solution is the fight one, being the correct combination of parabolic cylinder functions and satisfying the boundary condition, but with the peculiarity that its orientation has been rotated by Jr/2 with respect to the original one (Fig. 36). If we use the inverse transform between parabolic and Cartesian coordinates -- sign(z)v/v/x 2 + -

V/v/x 2 + z 2 -

Z 2 -+-

(76)

X

(77)

x

Eq. (75) can be transformed, in the half-space z > 0, into ~x(x, z) -- --

exp(~z)Effc

~

2 + Z 2 _~_ Z

7/"

+ exp - z

+

(78)

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 233 for x > 0, whereas for x ~ 0 it results that q~x(x, z) -- -- exp(kz)Effc ~/k

2 + z2 + z

+exp(-)~z)Erfc(~/~/v/x2 + z2 - z)]

(79)

The symmetric form holds for the half-space z < 0. Finally, the expression for the electrostatic potential in the whole space satisfying the required boundary conditions is given by

V(x, y, z ) -

4Vo ~ sin rt k=0

2k+ 1 ---~rry

)

2k --~ 1

t~)((2k+l)/b)zr(X,Z)

(80)

2. Numerical Simulations of Holographic Contour Maps As shown in Section II.A, once the phase shift 4~(r) is calculated inserting into Eq. (2) the electrostatic potential given by Eq. (80) the ideal contour map is given by I(r) = 1 + cos[q~(r)]

(81)

whereas the real contour map, taking into account the perturbed reference wave, Eq. (3 l b), is given by I(r) - 1 + cos[A4~(r)]

(82)

Figure 37 shows the ideal contour map due to the external field alone of our

p - n junctions array, calculated for a pitch b = 8/zm and a potential V0 -- 0.5 V (Fig. 37a) and V0 = 1 V (Fig. 37b), the potential difference being the double of this value (A V = 2 V0). It should be remembered that the ideal contour map is the optical interferogram which would be obtained when the reference wave in the recording step is an unperturbed plane wave, and the optical wave in the recording step is plane and parallel to the object wave. It can be seen that the trend of the contour fringes, giving the configuration of the projected potential distribution, is in good agreement with what is expected on the basis of naive assumptions regarding the potential distribution in Figure 29 (Frabboni, Matteucci, Pozzi, et al., 1985). The fringes are running in parallel to the junctions far from the specimen edge, and at the edge they fan out and connect neighboring regions.

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 37. Calculated ideal contour map of the phase distribution. (a) AV = 1 V. (b) A V = 2 V. (Reprinted from Capiluppi, C., Migliori, A., and Pozzi, G. (1995). Microsc. Microanal. Microstruct. 6, pp. 647-657, with permission.)

However, it should be remarked that experimental results show unexpected features, like closed loops of the equiphase lines between the junctions in Figures 32, 33, and 34 (Frabboni, Matteucci, and Pozzi, 1987). This effect can be accounted for by considering the real contour map, Eq. (82), where the phase difference is inserted instead of the phase itself. Figure 38 shows the real contour maps obtained for different values of the interference distance D whose direction has been taken parallel to the junctions. Figure 38a refers to D = 4/zm; Figure 38b to D = 6/zm; Figure 38c to D = 8 #m; and Figure 38d to D = 10 /zm. V0 has been taken equal to 1 V and, hence, the potential difference is 2 V. It can be seen that, as expected, the closed contour lines become increasingly elongated along the junctions as the interference distance D increases, which corresponds to a lessening of the effect of the fringing field on the reference wave. It is also interesting to note that the radius of curvature of the loops is larger near the edge toward the vacuum region and smaller far from the edge within the specimen, as observed also experimentally. Finally, the figures refer to a very large area, side 2b = 16 #m, whereas the actual reconstructed differential contour maps display only a strip, parallel to the biprism wire, a few microns wide. However, an image like those reported could be obtained by reconstructing several double-exposure holograms and pasting them together, as recently demonstrated for the mapping of the electrostatic field around charged microtips (Matteucci, Missiroli, Muccini, et al., 1992).

E L E C T R O N H O L O G R A P H Y OF L O N G - R A N G E E L E C T R O S T A T I C FIELDS

235

FIGURE 38. Calculated phase-difference contour maps for the case of A V = 2 V, for different values of the interference distance D. (a) D = 4 / z m ; (b) D = 6 / z m ; (c) D = 8 /~m; (d) D = 10/zm. (Reprinted from Capiluppi, C., Migliori, A., and Pozzi, G. (1995). Microsc. Microanal. Microstruct. 6, pp. 647-657, with permission.)

In view of the importance for semiconductor devices, further attempts to observe the field distribution of such junctions with electron holography have been undertaken by McCartney et al. (1994) and Frost, Joy, et al. (1995). V I . INVESTIGATION OF CHARGED MICROTIPS

As a further example of the capability of electron holography, we present the study of the electrostatic field around a charged microtip (Matteucci, Missiroli, Muccini, et al., 1992), which has so far been studied only by means of interference electron microscopy (Kulyupin et al., 1978-1979) with the final aim of investigating the monoatomic point sources (Fink, 1988). This kind of source is meeting an ever-increasing interest in low-voltage electron holography (Fink et al., 1995; Spence, Zhang, et al., 1995).

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G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

With the aid of a theoretical model for the field around the tip, which gives an analytical result for the projected potential, it has been possible to predict the general trend of the experimental contour map. Moreover, the comparison between theoretical and experimental results is made more accurate by making a montage of reconstructed contour maps of adjacent regions, by using the double-exposure technique. In this way, it has been possible to partly overcome the experimental limitations due to the reduced width of the interference field of a single hologram.

A. The Field Model The theoretical analysis of the electrostatic field in the outer space of a charged tip first involves consideration of the simple model made by two linear segments (see Fig. 39) each of length 2c and whose centers are 2h distant, placed along the y axis in a symmetric position with respect to the xz plane of an xyz coordinate system. Each segment has a constant and opposite charge density o-. The analytical expression of the potential distribution V(x, y, z) can be obtained (Durand, 1966) by integrating the formula

V(x y, z) = '

1 f+c 4:reo

c

cr v/X 2 -+- (y - h - t) 2 -+- Z 2

1 [+c + 4zr Eo J_c

dt

-a

dt

v/X2 _~_ (y + h - t)2 _+_ z 2

(83)

The integration leads to

V(x, y,z) = ~ [ eo sinh-l (c ~/x - (y - sinh-l ( - c %IX- 2(y._~-Z 2h) 2 +- Zh)) 2 + sinh -I

( - c - (y + h)) _ sinh-~ (c Z (y +_h)]] ~/X2 + Z 2

~/X 2 + Z2 ,]

(84)

and it can be seen that the potential distribution has a rotational symmetry and is zero when y -- 0. Near and around the extremities of the two charged lines, the equipotential surfaces behave approximately as a family of hyperboloids of rotation. Therefore, it is reasonable to assume that the field described by Eqs. (83) and (84) may be used to represent, at least in a first approximation, the field produced by a charged tip in front of a conducting plane (y = 0). The distance between the tip vertex and the conducting plane (y = 0) was 15 /zm. The charge density cr was chosen in order to obtain the equipotential surface that represents the tip shape at about 10 V.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 237

FIGURE39. Theoretical model used to calculate the field near a charged microtip. The free parameters h and c are shown together with the equipotential surfaces near each charged segment of length 2c. In Fig. 40 are shown the simulated equipotential lines around the tip in the specimen plane (z = 0). In order to display such a distribution a set of equipotential surfaces was chosen with a constant potential difference. The region T inside the equipotenfial surface (which more closely resembles the tip) was darkened. From the analytical expression of the potential, the phase q~(x, y) can be calculated by performing the integral of Eq. (2).

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G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

FICtrRE 40. Computer simulation of equipotential lines, in the xy plane, of a charged microtip. (Reprinted from Ultramicroscopy, 45(1), Matteucci, G., Missiroli, G. E, Muccini, M., and Pozzi, G., Electron holography in the study of electrostatic fields, pp. 77-83, Copyright 1992, with permission from Elsevier Science.)

The integration leads again to an analytical expression: 2~ ty { [ - c + ( y - h ) ] l n v / x 2 + [ c - ( y - h ) ] 2 q~(x, y) = ~.E 4n'Eo + [ - c - (y - h)] In v/X 2 + [c + (y - h)] 2 + [c + (y + h)] In v/x 2 + [c + (y + h)] 2 + [c - (y + h)] In v/X 2 + [c - (y + h)] 2

-c+(y-h)) c+(y-h,) ( c+(y+h) )

+ 2ix. sin_l (

v/X 2 + [c - (y - h)] 2

_ 2lxl sin_l (

v/x 2 + [c + (y - h)] 2

+ 21xl sin -1

- 2[xl sin -1

v/X 2 + [c + (y + h)] 2

v/x 2 + [c - (y + h)] 2

The holographic method reveals the loci of points with constant phase shift as a set of curves with a phase difference of 2rr between two successive dark and white ones.

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 239

FIGURE41. Computersimulationof the equiphase lines around the tip T. (Reprinted from Ultramicroscopy, 45(1), Matteucci, G., Missiroli, G. E, Muccini, M., and Pozzi, G., Electron holography in the study of electrostatic fields, pp. 77-83, Copyright 1992, with permissionfrom Elsevier Science.)

Figure 41 shows the computer simulation of the equiphase lines obtained by the coherent superposition of the object wave, Eq. (85), and a plane reference wave. While the trend of the potential in the (x, y, z -- 0) plane is easy to guess (Fig. 40), the interpretation of Figure 41, where the equiphase lines seem to enter the tip shadow T, is less intuitive because the phase shift, suffered by electrons along their trajectories, is related to the potential distribution around the tip integrated along the z axis. However, when experimental observations are made of the field close to the tip apex, we must consider that also the reference beam is modulated by the field of the tip which extends microns away from the tip itself. Therefore, the final contour map will show the loci of constant phase difference between the perturbed reference wave and the object wave and does not exactly represent the object phase variations. In our case by using Eq. (85) and by taking into account the distance between the interfering points (in the electron microscope), we can calculate the perturbed reference wave and display the resulting interferogram directly in the computer. In the following section this theoretical result is compared with the experimental results.

B. Experimental Results A standard electrolytic thinning process was used to obtain the tips from a polycrystalline tungsten wire (0.25 mm diameter), in a cell with 2% NaOH solution through which 2-V, 50-Hz alternating voltage was applied (Dyke and Dolan, 1956). One tip was mounted in the center of a 2-mm aperture, which

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

FIGURE 42. Double-exposurehologramdisplaying equiphase difference lines near the apex of a charged microtip T. (Reprintedfrom Ultramicroscopy, 45(1), Matteucci, G., Missiroli,G. E, Muccini, M., and Pozzi, G., Electron holography in the study of electrostatic fields, pp. 77-83, Copyright 1992, with permissionfrom Elsevier Science.)

was inserted on a special specimen holder equipped with electrical contacts connected to an external voltage supply. The aperture and the tip, electrically insulated from the microscope, could then be biased and, by rotating the aperture, it was possible to arrange the tip and the biprism axis in a mutually perpendicular position. A voltage of the order of 10 volts was applied to the tip. Holograms were recorded according to the electron optical arrangement of Figure 12. Double-exposure holograms were recorded with an interference distance of about 5 lzm. Figure 42 shows a double-exposure electron hologram in which the reference wave is perturbed by the near-apex electric field. The dark regions represent the equiphase lines in the area near the tip T when it was held at 7.5 V. In the previous example dealing with charged latex spheres, we showed that the equiphase lines were strictly related to and displayed the trend of the projected equipotential surfaces. On the contrary, in the present case, the equiphase lines observed in the final interferogram cannot be related simply to the equipotential surface shape. Since the investigated area around the tip is fairly limited to about 5/zm, the overall trend of these lines cannot be displayed in a large enough region. So that their trend around the tip could be followed in a wider area, three double-exposure holograms were taken from parallel and adjacent regions and then mounted together. It is important to note that the success of this procedure is linked to the fact that double-exposure holograms are recorded, so that the interferometric wave for the contour mapping is provided by the hologram without object. Figure 43a shows a montage of these three regions (labeled 1, 2, and 3) in which the useful interference field extending along the tip axis is about 15/zm. The three strips are of different width since the overlapping regions

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 241

FIGURE 43. (a) Collage of three (1, 2, 3) double-exposure holograms taken from adjacent regions showing the trend of the equiphase difference lines in a wider area. (b) Computer simulation of the equiphase lines obtained with a perturbed reference wave. (Reprinted from Ultramicroscopy, 45(1), Matteucci, G., Missiroli, G. E, Muccini, M., and Pozzi, G., Electron holography in the study of electrostatic fields, pp. 77-83, Copyright 1992, with permission from Elsevier Science.) were removed. It can be noted that in this overall map the equiphase difference lines circle around the vertex of the tip T and then join the tip itself, behavior that could not be inferred previously. Figure 43b reports the computer simulation obtained by the coherent superposition of the object wave and the perturbed reference wave and adjustment of the parameters h, c, and the charge density cr to fit with the experimental data. The number of equiphase difference lines is the same as what would be obtained by a double-exposure electron hologram performed with a perturbed reference wave passing 5 / z m distant from the object wave and with the same relative orientation of the biprism and the tip as that shown by the electron holograms of Figure 43a. The satisfactory agreement between experimental and theoretical results is evident. The comparison between Figures 41 and 43b clearly shows the difference between the trend of the phase distribution displayed by a hologram recorded with an unaffected reference wave instead of a modulated one. Our results regarding the mapping of electric field distribution around charged tips have been confirmed by Ru et al. (1994) and Ru (1995a, 1995b)

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G. MATTEUCCI, G. F. MISSIROLI, AND G. POZZI

who used an amplitude division interferometer (Section III.A.1; Matteucci, Missiroli, and Pozzi, 1982b; Pozzi, 1983) instead of a biprism.

VII. CONCLUSIONS The main experimental and theoretical results obtained by our group in the investigation of long-range electrostatic fields (i.e., not strictly localized in the sample from which they arise) by holographic techniques were reviewed in this work. We demonstrated how the POA can be reliably adopted for the calculation of the phase shift associated with these electric fields (obtaining in most cases an analytical expression for it) and how this phase shift (proportional to the projected electrostatic potential) can be strikingly different from the shape of the equipotential surfaces. Moreover, the external fringing field, usually treated as a perturbation with respect to the internal one, may also be the main responsible cause of the observed effects, as shown especially by the case of reverse-biased p - n junctions. As a consequence, when researchers are dealing with electrostatic fields, extreme care should always be paid to the interpretation of the experimental data. In fact, another disturbing feature of the fringing field is that it can affect the reference wave, which can no longer be considered an unperturbed plane wave, as is customary in electron holography. It turns out that the artifacts introduced in the reconstructed images were thoroughly investigated in this work. Our conclusion is that it is highly recommended to have a good model for the field under investigation. Preliminary attempts have been carried out to cope with this central issue in a general way (Kou and Chen, 1995) from the theoretical point of view, but we are still far from a satisfying solution. From the experimental point of view, the solution is to increase the interference distance far above the currently obtainable values, in the range of about 10/zm. This could be done, in principle, by using a multiple biprism setup, as developed in Ttibingen for the experiments on the magnetic Aharonov-Bohm effect (Schaal et al., 1966/67) or by using mixed-type arrangements combining amplitude and wavefront division beam splitters (Matteucci and Pozzi, 1980). However, for this, radical changes in the basic instrument may be necessary. In conclusion, since electron holography is a very powerful technique, able to solve problems at the frontier of modem technology, we hope that our work, in addition to clarifying the basic elements involved in this technique and giving warning of some of the pitfalls that occur when one is searching for a reliable interpretation of the data, will pave the way to further developments. Some examples are represented by the study of ferroelectric domain walls (Spence, Cowley, et al., 1993; Zhang et al., 1992) and by the observations of charged grain boundaries in Mn-doped strontium titanate (Lin et al., 1995; Ravikumar

ELECTRON HOLOGRAPHY OF LONG-RANGE ELECTROSTATIC FIELDS 243 et al., 1995), a case in which some of the knowledge accumulated in the investigation of reverse-biased p - n junctions can be profitably applied (Pozzi,

1996b). There are also prospects that the potential distribution of charged dislocations could be detected by holographic methods (Cavalcoli et al., 1995; Matteucci, Muccini, and Cavalcoli, 1995). The commercial availability of holographic electron microscopes up to 300 kV and their increasing diffusion in university and research laboratories will open a wide range of new applications. We hope that some of our ideas described in this work will be useful for a better understanding of the problems at hand and will help researchers to develop a critical attitude so that they can extract the maximum useful information from holograms.

VIII. UPDATE Since the first publication of this review article the activity in electron holography has steadily proceeded. A recent book (Vrlkl, Allard, and Joy, 1999) gives an overview of the state of the art of the whole field and presents a rather complete bibliography. With reference to the specific issue of electron holography investigations of electrostatic fields, in addition to the survey papers (Bonevich, Pozzi, et al., 1999; Frost and Matteucci, 1999) published in the aforementioned book, a number of new research papers have appeared, testifying to the vitality of this field. Charged dielectric spheres have become a favorite test specimen owing to the simplicity of both the specimen preparation and the analytical models describing the field and the phase shift. Frost and Vrlkl (1998) used charged spheres (in addition to the electric field at p - n junctions and the magnetic leakage field of a memory cell) to test the reliability of quantitative phase measurements by low-magnification electron holography. A careful analysis of the electron-optical conditions is presented in Frost, Vrlkl, et al. (1996) and Frost (1999a). In particular Frost (1999b), by using a special procedure to process holograms acquired under different conditions of charge equilibrium, was able to disentangle the phase shift due to the sample from other contributions connected to electric fields arising from different elements of the experimental setup. In this way an excellent agreement has been found with the model of the uniformly charged sphere, which is to be preferred to the sphere having the charge on its surface. Latex spheres have also been used by Tanji et al. (1999) for testing an electron trapezoidal prism made by two parallel electron biprisms. In this new device the reference wave is perpendicular to the object plane and parallel to the optic axis. The object wave alone is tilted, which makes it easier to record and interpret differential holograms obtained by a double-exposure method. The same group (Yamamoto, Kawajiri, et al., 2000) also managed to increase

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G. MATTEUCCI, G. E MISSIROLI, AND G. POZZI

the precision of phase measurements, achieving a lower limit of 2zr/300 in the reconstructed image of a latex particle. This improvement is due to the correction of the phase distortion due to the Fresnel diffraction at the biprism edges, as demonstrated by Yamamoto, Tanji, et al. (2000). Also, the study of p - n junctions has proceeded. From the theoretical viewpoint, the importance of the fringing field on the phase contrast has also been emphasized by Dunin-Borkowski and Saxton (1996), who used a different approach based on the solution of the Poisson equation in the presence of a given charge distribution. The effect of neglecting and including the fringing field is thoroughly analyzed in Dunin-Borkowski and Saxton (1996, 1997), respectively. Recently our group extended the theoretical analysis to the case of a junction tilted with respect to the specimen edge (Beleggia et al., 2000). It is interesting to note that this result was obtained by a less formal and more intuitive approach than that reported in preceding sections of this article. From the experimental viewpoint, the two-dimensional mapping of electrostatic potential in transistors by electron holography (Rau et al., 1999) has raised a lot of interest owing to the importance of this method for transferring into reality the road map toward submicron devices. However, recent results have shown that further work is needed before the influence of artifacts in the images can be fully understood (Dunin-Borkowski, Newcombe, et al., 2000; Twitchett et al., 2000). Electron holography has been applied to the investigation of space-charge distribution across internal interfaces in electroceramics (Ravikumar et al., 1997a, 1997b), and the results have been interpreted on the basis of a simple capacitor model (Frost, Rodrigues, et al., 1999). When a current is applied to the specimen, in situ electron holography has allowed direct observation of the breakdown of an internal grain boundary barrier (Johnson and Dravid 1999a, 1999b, 2000). Finally electron holography has been used to profile the piezoelectric field across strained InGaN/GaN single quantum well structures (Cherns et al., 1999).

ACKNOWLEDGMENTS

We are deeply indebted to our collaborators in the field, C. Capiluppi, J. W. Chen, S. Frabboni, E E Medina, P. G. Merli, A. Migliori, M. Muccini, E. Nichelatti, and M. Vanzi. The critical reading of the manuscript by and the helpful comments of M. Beleggia and R. Patti are gratefully acknowledged. Finally, the skillful technical assistance of Stefano Patuelli in preparing the drawings is highly appreciated.

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245

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ADVANCES IN IMAGINGAND ELECTRON PHYSICS,VOL. 122

Digital Image-Processing Technology Useful for Scanning Electron Microscopy and Its Practical Applications EISAKU OHO Department of Electrical Engineering, Kogakuin University, Tokyo 192-0015, Japan

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Proper Acquisition and Handling of S E M Images . . . . . . . . . . . . . A. Digital Recording and Processing System . . . . . . . . . . . . . . . B. Superiority and Problems in the Quality of S E M Images Taken by On-Line Digital Recording . . . . . . . . . . . . . . . . . . . . . 1. Superiority in Image Quality . . . . . . . . . . . . . . . . . . . 2. Problems in Image Quality . . . . . . . . . . . . . . . . . . . . 3. Examples of the Adverse Effects of Undersampling and Their Solutions in S E M Images . . . . . . . . . . . . . . . . . . . . . . . . . 4. Proper Expansion of an S E M Image . . . . . . . . . . . . . . . . III. Quality Improvement of S E M Images . . . . . . . . . . . . . . . . . . A. Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . B. Noise Removal . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Complex Hysteresis Smoothing (CHS) . . . . . . . . . . . . . . . 2. Other Nonlinear Methods . . . . . . . . . . . . . . . . . . . . 3. Noise Reduction in Fast-Scan S E M Images . . . . . . . . . . . . . C. Fine Details Enhancement . . . . . . . . . . . . . . . . . . . . . 1. Highlight Filter . . . . . . . . . . . . . . . . . . . . . . . . 2. Enhancement of Backscattered Electron (BSE) Images . . . . . . . . 3. Reduction of Unfavorable Effects . . . . . . . . . . . . . . . . . IV. Image M e a s u r e m e n t and Analysis . . . . . . . . . . . . . . . . . . . A. Precautions for the Effective Use of Conventional Statistical M e a s u r e m e n t . B. Critical Dimension M e a s u r e m e n t and Foreign Material Observation on the Wafer for Semiconductor Process Evaluation . . . . . . . . . . . C. Surface Topography Measurement . . . . . . . . . . . . . . . . . . V. S E M Parameters M e a s u r e m e n t . . . . . . . . . . . . . . . . . . . . . A. Electron B e a m Diameter . . . . . . . . . . . . . . . . . . . . . . B. Resolution (Highest Spatial Frequency) . . . . . . . . . . . . . . . . 1. Advanced Superposition Diffractogram . . . . . . . . . . . . . . . 2. Caution in the Utilization of the Superposition Diffractogram . . . . . C. Signal-to-Noise Ratio (S/N) . . . . . . . . . . . . . . . . . . . . VI. Color S E M Images . . . . . . . . . . . . . . . . . . . . . . . . . . A. B a c k g r o u n d of the Generation of Natural Color S E M ( N C - S E M ) Images . . B. Method for Obtaining an N C - S E M Image . . . . . . . . . . . . . . . C. Principle of N C - S E M Based on the Frequency Characteristic of the H u m a n Visual System . . . . . . . . . . . . . . . . . . . . . . . . . . D. Experiment for Confirming the Usefulness of the Frequency Characteristic of the H u m a n Visual System in N C - S E M . . . . . . . . . . . . . . .

Volume 122 ISBN 0-12-014764-5

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VII. AutomaticFocusing and AstigmatismCorrection . . . . . . . . . . . . . VIII. RemoteControl of the SEM . . . . . . . . . . . . . . . . . . . . . . IX. UltralowMagnification and Wide-Area ObservationUsing the Modem Montage Technique . . . . . . . . . . . . . . . . . . . . . . . . . A. Procedure and Precautions of the Montage for SEM Images . . . . . . . B. Examinationof Large Specimens . . . . . . . . . . . . . . . . . . X. ActiveImage Processing and MultimodalMicroscopy . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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I. INTRODUCTION

For a number of years, scanning electron microscopy (SEM) has provided outstanding high-resolution images with very great depths of field in biophysics, material science, and so forth. In the early years, several digital image-processing techniques as well as many analog techniques were introduced to the SEM field (McMillan et al., 1969; White et al., 1968). Since the SEM image is essentially the electric signal, it is very suitable for utilizing these image-processing techniques. Analog image-processing techniques were mostly employed for SEM signal enhancement in the early stages (Baggett and Glassman, 1974) because digital techniques were in the developmental stage and the cost of using them was extremely high in our field. Analog techniques are still used as required. However, compared with the transmission electron microscopy (TEM) image, SEM image information (digital data) could easily be provided by digitizing it through an analog-to-digital (AD) converter and storing the result in memory. Hence, the performance of the on-line SEM image-recording system has been improved rapidly (e.g., Oron and Gilbert, 1976). At first, many digital techniques were simply introduced from the field of image processing (see Jones and Smith, 1978). These introductions were novel and significant in those days. For several purposes unique to SEM, the Cambridge group and other groups devoted their energy to the study of these techniques from the 1970s into the 1980s (e.g., Erasmus and Smith, 1982; Holburn and Smith, 1979; Unitt and Smith, 1976). Unfortunately, for the last decade, the number of high-level studies in SEM image processing has decreased somewhat because some simple studies have already been achieved and the number of researchers has seen little increase. However, with the recent advances in computer technology, a high-performance and inexpensive personal computer applicable to digital image processing has fully taken root in the field of SEM, and the general-purpose SEM user can examine many digital image-processing techniques (Oho, Ichise, and Ogashiwa, 1996; Postek and Vladar, 1996). In addition, the electron microscopy field as well as other fields is interested in the related technology of networking (e.g., the Internet; Chand et al., 1997; Chumbley et al., 1995; Voelkl et al., 1997). From the viewpoint of

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microscopists, this situation is one of the best opportunities for moving forward toward the new generation of SEM technology that uses on-line digital image recording and processing as well as networking technology. The results of several studies from among many have survived and been utilized in commercialized and/or prototype SEMs (e.g., Edwards et al., 1986; Erasmus, 1982; Oho, Ichise, and Ogashiwa, 1995; Oho and Ogashiwa, 1996). Contrary to general belief, there are few practical studies. Microscopists may not have realized yet how to make the best use of digital image-processing technology as related to the SEM field. So that many techniques of image processing can be used effectively, the successful combination of a highly advanced SEM equipped with various functions for acquiring necessary data and concomitant techniques is the most important issue to be resolved. As one solution, a new concept has been proposed based on the "active image processing" (Oho, Hoshino, and Ogashiwa, 1997). This method gives priority to the development of various functions for acquiring SEM signals including sufficient information as well as to the image-processing techniques. Several important subjects closely related to the SEM field are discussed in this article. Many techniques are suitably utilized and compared in the following sections. We have not tried to explain systematically all imageprocessing techniques, since doing so may not be helpful for microscopists. For further reference, for instance, see Rosenfeld and Kak (1982) and Gonzalez and Woods (1992). II. PROPER ACQUISITION AND HANDLING OF SEM IMAGES

A. Digital Recording and Processing System Various systems of image recording and processing have been used for SEM since the SEM instrument was first developed. In the 1970s, expensive minicomputer systems equipped with special hardware of their own making were generally used. In the early 1980s, microscopists began to use a combination of the personal computer (PC) and off-the-shelf hardware to acquire and/or process SEM images. The performance of this sort of system was typically 256 x 256 pixels x 8 (,~12)-bit acquisition, 256 x 256 pixels x 4 bits on the display, and RAM of ,~0.256 MB (Desai and Reimer, 1985; Joy, 1982). Of course, these systems could not perform the digital image processing at a high speed. The same kind of system, which especially reinforced processing speed and the amount of memory then appeared (Oho and Kanaya, 1990). In this ar-ticle, old-fashioned systems are not referred to any further because systems of this kind will not be useful in the future. Currently, we can easily find many commercial systems for image processing of SEM images based on a standard PC without any additional special hardware and equipped with an AD

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converter, which may often have a performance of 2048 x 2048 (~4096 x 4096) pixels x 8 (~12)-bit acquisition, 1280 x 1024 (~2048 x 1536) pixels x 8 bits on the display, RAM of 1 GB or more, and so forth. In addition, many modem SEMs with a built-in computer (PC-SEM, personal computercontrolled SEM) are quickly replacing old-type SEMs. More improvements will follow in the near future.

B. Superiority and Problems in the Quality of SEM Images Taken by On-Line Digital Recording 1. Superiority in Image Quality Many SEM users still utilize a conventional recording system consisting of a video monitor with a resolution of about 2000 lines and a high-performance camera. It is generally believed that the conventional system is satisfactory in image quality for the average SEM user. However, serious deterioration in information obtained by this method has been confirmed by comparing it with an on-line digital-recording system which is closer to the ideal for SEM images (Oho and Kanaya, 1990; Oho, Sasaki, and Kanaya, 1986). It should be noted that SEM images are essentially the electric signal. Let us compare the difference in quality of on-line digital recording versus that of conventional recording of the SEM image. The micrographs (2048 scanning lines) in Figures 1a and lb are digitized and conventional SEM images, respectively. The micrographs shown in Figures 1a' and 1b' are extremely enlarged images of Figures 1a and 1b, respectively, obtained by the cubic convolution (interpolation) method based on the sampling theorem and a darkroom enlarger, respectively. Although surface structures are visible in Figure l a, those in Figure 1b are disturbed by the film-grain noise and blur, which may originate from a nonideal point-spread function in the conventional recording system. It should be noted that the image degradation caused by conventional systems is more severe than expected. The validity of structures in digitized images can be confirmed by observing an image (same view as in Fig. l a) recorded at a much higher magnification than that of Figure 1a (Oho, Sasaki, and Kanaya, 1986). In addition, since some SEMs constructed by state-of-theart technologies have 4096 or more scanning lines, the difference in both may appear more remarkably. An ultra-high-quality SEM image of a rat kidney, with 2745 x 3767 pixels (a part of 4096 x 4096 pixels), is shown in Figure 2a (Oho, Ichise, and Ogashiwa, 1995). A 26-fold enlargement from the original SEM magnification (identified by a square in Fig. 2a) is exhibited in Figure 2b. This is equivalent to a 43-fold enlargement from 6 x 7-cm negative film. Although the original recording magnification indicated in the SEM instrument is only 500, we can clearly observe a glomerular podocyte (well-known

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FIGURE 1. Superiority of a high-definition on-line digital-recording system. (a) Digital SEM image of a large-scale integration (LSI) chip recorded with the on-line system and, (b) conventional SEM image recorded on film, together with the extremely enlarged versions of each (at) and (bt). It should be noted that the image degradation caused by the conventional recording system is very severe.

structure) in Figure 2b (when conventional 2048 or 1024 scanning lines are used, the structure is severely deformed).

2. Problems in Image Quality The scan coils of the S E M are generally used to perform a fast scan in the x direction and a slow scan in the y direction. The former produces a continuous signal, while the latter gives what is called a sampled signal. In this section, we will first discuss the characteristics of the sampled signal (y direction). Then, the sampling of a continuous signal (x direction) is also considered.

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FIGURE 2. Ultra-high-quality digital SEM images recorded with the on-line system. (a) SEM image, 2745 • 3767 pixels, of a biological sample. (b) Its expanded image.

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The SEM is operated under various conditions of electron beam size, incident current, number of scanning lines per frame, and magnification. In addition, the resolution, which is strongly related to the sharpness, signal-tonoise ratio (S/N), contrast, and so on, of the SEM image is much influenced by the characteristics of the sample. Hence, in SEM image recording, it may be difficult to achieve the optimal scanning condition proposed by Crewe (1980) and by Crewe and Ohtsuki (1981). The concept of this optimal scanning is equivalent to the use of a fixed magnification (line spacing d) chosen to sample at the Nyquist sampling rate 2fc (d -- 51 f C, fc: cutoff frequency, which is mainly determined by the property of a specimen as well as by the resolving power of the microscope) in the direction perpendicular to the scanning line (i.e., in the y direction). Generally, most SEM images are taken in an over- or underscanning (sampling) condition (Oho, Ichise, and Ogashiwa, 1996).

a. Underscanning (d > i f c) SEM images taken with underscanning are contaminated by the aliasing error (artifact) to a greater or lesser extent. In other words, the fine structures of the specimen are not accurately converted into an analog SEM image. However, except for some particular specimens and conditions (Remier, 1985), this may not fatally disturb observation of the specimen experimentally. (If an expansion technique is used after digital acquisition of the SEM image, some problems occur in an expanded image; these will be discussed later.) b. Optimal Scanning (d -- 89 fc) It is very difficult in routine work to find the optimal scanning condition for each SEM image, as mentioned previously, although information included in an analog SEM image may have validity and the largest areas can be recorded without the aliasing error. However, from the viewpoint of the S/N in the SEM image, this scanning might produce a noisier result than that of the overscanning condition (using a higher magnification). c. Overscanning (d < i f c) In the overscanning condition, an analog SEM image can generally be obtained without the aliasing error. However, excessive overscanning may aggravate the effects of radiation damage, contamination, vibration, stray magnetic fields, and/or charging problems from the specimen. It should be noted that these influences are likely to increase rapidly beyond our expectations as an SEM image is magnified. Conversely, in SEM signal (x-direction) digitization through an AD converter, the sampling aperture (a sort of averaging filter) should generally have a width r roughly equal to the sample spacing (sampling interval) At. This has

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the effect of reducing noise and aliasing error (Castleman, 1979). This setup can be accomplished by using an analog integrating amplifier or a low-pass filter (anti-aliasing filter) at the input of the AD converter. However, it is very difficult to develop an ideal anti-aliasing filter (analog low-pass filter with a very steep cutoff frequency). Unfortunately, if that sort of filter is employed as the anti-aliasing filter, there will be a certain amount of distortion of the original waveform owing to the phase distortion in the filter. In our AD converter for SEM, first a 6.25-MHz ultrahigh sampling rate considering the slow-scan instrument is used so as not to produce aliasing error and next a great many sampled data obtained from this sampling rate are reduced by proper averaging into new data (pixel data) consisting of, for example, 4096 pixels/line with 8-bit resolution, as depicted in Figure 3 (Oho, Ichise, and Ogashiwa, 1995). The effect of this operation is similar to that of r -~ At. Moreover, the present AD converter has ease of use (clearly selecting the optimal parameters for a variety of scanning speeds) as well as very high effectiveness for reducing noise and aliasing error. An obtained digital image may be almost equal to the analog image in S/N (seemingly, it may be better depending on the digitization condition). This process is very important for SEM images which usually do not have a high S/N. Of course, it is necessary to use the device which can obtain a high-quality digital SEM image as much as possible (the performance of each commercial AD converter is not the same), because the image-processing technology is utilized more effectively in a high-quality SEM image.

3. Examples of the Adverse Effects of Undersampling and Their Solutions in SEM Images SEM images acquired with the underscanning (-sampling) condition in the x and/or y direction are influenced by the aliasing more or less as described in the preceding section. The effects of the aliasing error are brought to light

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FIGURE 4.

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Example of the adverse effects of undersampling in SEM images. See text for

details. in this section (Oho, Ichise, and Ogashiwa, 1996). Figures 4a through 4d are SEM images of a mesh recorded in SEM instrument magnifications of 100, 400, 1600, and 6400, respectively (a series of increasing magnification). In this sample with a periodic structure, we may be able to pinpoint easily the effects of the aliasing error. Since the number of scanning lines was 512 and the measured beam diameter was approximately 2 nm (Oho, Kobayasi, et al., 1986), all the SEM images in Figure 4 are underscanned images. The condition of r < At and low-density scanning of 512 lines was deliberately selected to show the severe effects of the aliasing error. Although the effects of aliasing cannot be seen at the original magnifications, they can be observed clearly when these images are enlarged. Figures 4al, 4a2, and 4a3 show 4-, 16-, and 64-fold expanded images by the cubic convolution method for Figure 4a, respectively. Also, Figures 4bl and 4b2 are 4- and 16-fold for Figure 4b, and Figure 4Cl is 4-fold for Figure 4c, respectively. In short, digital expansions (four times) were performed as explained by the direction of arrows in Figure 4. When we compare Figure 4al with Figure 4b (same view), periodic artifacts in Figure 4a produced by the aliasing error can be specified. In a comparison

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among Figures 4d, 4Cl, 4b2, and 4a3, the effects of aliasing in a common structure (not periodic) are recognized as a blur, but this complicated blur is essentially different from the effects of a low-pass filter. Thus, the effects of aliasing error are serious in digital expanded SEM images which may be utilized increasingly in routine work. To prevent a flood of artifacts by aliasing, we must utilize the high-performance AD converter. That is to say, when using both the scan generator attainable to an ultrahigh scanning density [in our case, 4096 (max. 8192) scanning lines/image] and the AD converter with an ultrahigh sampling rate (6.25-MHz sampling rate), we can obtain SEM images without aliasing error in all operating conditions. Subsequently, a great many data are reduced by the proper averaging into new data consisting of, for example, 2048 x 2048 pixels. In contrast, SEM noise with all frequency components is always undersampied. Therefore, a digital SEM image with some considerable noise frequently has a serious problem (Oho, Ichise, and Ogashiwa, 1995). To show a typical example of the effects, we obtained noisy SEM images of gold particles on carbon, with 1024 scanning lines/frame (Fig. 5a) and with 4096 lines/frame (Fig. 5b) at the same recording time (80 s) and area of scanning, and we adjusted the conditions of the AD converter optimally in each case. In Figure 5a, none of the gold particles retained their real structures owing to the severe influence of undersampled noise. On the contrary, since the ultrahigh scanning density was applied in Figure 5b for reducing the aliasing error of noise, gold particles can be seen even though the total electron dose was the same. However, decreasing the number of incident electrons per pixel (increase of the number of pixels per frame) affects our SEM images in S/N. If necessary, after image acquisition, the resolution of the 4096 lines can be reduced to 2048 or 1024 lines for improvement of the S/N; moreover, we can use several methods to reduce noise in Figure 5b. Images processed by a common averaging filter for Figures 5a and 5b are shown in Figures 5c and 5d, respectively. This conventional filter is effective for removing noise in Figure 5b. However, not all smoothing filters are effective for reducing the severe aliasing error, as shown in Figure 5c. In this case, we used enlarged images to show the difference clearly (eight times for Figures 5a and 5c, twice for Figures 5b and 5d).

4. Proper Expansion of an SEM Image The cubic convolution method used in various sections is a highly precise expansion technique based on the sampling theorem. In other words, digital data which satisfy the sampling theorem can be interpolated (expanded) very accurately by this method. On the basis of the characteristics of the digital SEM image, we should now discuss some useful expansion methods, because

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FIGURE5. The difference between (a) a digitized low-electron-dose SEM image with 1024 scanning lines and (b) an image with 4096 lines. (c and d) Low-pass filtered images for (a) and (b), respectively.

most SEM images will be treated as digital data in the very near future and these methods will be utilized increasingly in routine work. The cubic convolution method used in the space domain is easily explained in the Fourier domain as illustrated in Figure 6 (an example of three-times expansion). Bold arrows in Figure 6 indicate the flowchart for obtaining expanded images. First, the digitized original waveform (a) is expanded three times by the insertion of zero samples in the computer as shown in (b). A power spectrum of (a) is calculated in (a') (sampling the analog signal makes its spectrum

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FIGURE6. Explanation in the Fourier domain of the cubic convolution (expansion) method. See text for details. periodic by replicating the original spectrum at intervals 1/At). The (b') diagram depicts a power spectrum of (b). Next, a net signal is extracted by the ideal low-pass filter [rectangular solid line in (b')] as indicated in (c'), and it is inverse-transformed to obtain the accurately expanded waveform shown in (c). This procedure is almost equivalent to the cubic convolution method using the sampling function as the interpolating function (the Fourier transform of the sampling function is a rectangular pulse; that is, the shape of the ideal low-pass filter). Figure 7 is an example of the use of the procedure shown in Figure 6.

FIGURE7. Example of an expanded SEM image obtained through the procedure shown in Figure 6. (a) Original SEM image of gold-coated magnetic tape. (a') Power spectrum of (a). (b) Expanded image by the insertion of zero samples. (b') Power spectrum of (b). (c) Final result processed through the inverse Fourier transform from a net signal [inside a small square in (b')]. Horizontal field width of (a)= 178 nm.

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An original SEM image of gold-coated magnetic tape and its power spectrum are shown in Figures 7a and 7a', respectively. Figure 7a is a roughly optimalscanned image with a high S/N. A processed image corresponding to (b) in Figure 6 is shown in Figure 7b, together with its power spectrum (Fig. 7b'). An inverse-Fourier-transformed image (Fig. 7c) is obtained from inside a small square (ideal low-pass filter) in Figure 7b'. This is a nearly perfectly expanded image of Figure 7a. In the case in which the data depicted in Figure 6a are oversampled data and include appreciable noise (SEM images of this kind are seen frequently), we should utilize a common low-pass filter [dotted line in (b') of Fig. 6] for the ideal low-pass filter, because the noise has a spatial frequency component with infinite spread and is always undersampled. That is to say, the common lowpass filter is roughly equivalent to the well-known "bilinear interpolation" in the space domain and has little effect in emphasizing the noise while keeping the high fidelity for expansion of the oversampled signal. On the contrary, the ideal low-pass filter relatively enhances the undersampled noise. As an example, a high-magnification (oversampling condition) image of latex balls coated with gold is shown in Figure 8a. Images expanded by a factor of 5• by the cubic convolution method and bilinear interpolation are indicated in Figures 8b and 8c, respectively. Noise ("worms") is conspicuous in Figure 8b, as expected. In contrast with this result, the bilinear interpolation (Fig. 8c) can accurately enlarge Figure 8a without the noise enhancement. However, for some images

FIGURE 8. Optimal expansion method for an oversampled (-scanned) SEM image with a small amount of noise. (a) Original SEM image of gold-coated latex balls. Five-times expanded images (b) by the cubic convolution method and (c) by bilinear interpolation (the optimal method). Horizontal field width of (a) = 400 nm.

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with a high S/N taken with roughly optimal scanning, for example, Figure 7a, the bilinear interpolation may produce blurred results compared with those of the cubic convolution method. Nevertheless, since bilinear interpolation has the advantage of insensitivity to noise, its ease of use is helpful for fairly noisy images in all scanning conditions. Incidentally, nearest-neighbor interpolation (simple expansion of each pixel) is not so useful for SEM images because of low precision. We can easily find these techniques in some well-known retouching software (e.g., Adobe Photoshop).

III. QUALITY IMPROVEMENT OF SEM IMAGES

A. Generalization

SEM images are disturbed by noise, blur, an excessively wide dynamic range, and so forth. Since these are general problems in many fields which relate to digital image processing, we may be able to find many solutions (Gonzalez and Woods, 1992; Rosenfeld and Kak, 1982). In the early stages, many techniques for image enhancement were introduced in our field. For example, a low-pass (conventional averaging) filter was applied to SEM images for noise removal (Yew and Pease, 1974). Several histogram-processing techniques were used for contrast improvement. (Artz, 1983; Oron and Gilbert, 1976). The gradient, Laplacian, or other derivative operators were utilized for image sharpening (Oron and Gilbert, 1976; Unitt and Smith, 1976). However, these techniques may not be so practical for the improvement of SEM image quality because SEM images are taken under various operating conditions and these images have various characteristics which are not found in other fields; that is, effects of charging, radiation (thermal) damage, contamination, stray magnetic field, vibration, and so forth. Nevertheless, an SEM image has an ultrahigh scanning density (e.g., 4096 lines/frame) and this scientific instrument is frequently utilized for observing an object with unknown structures. Hence, the following basic processing requirements must be met for the enhancement of SEM images: 1. Smallest image details must be preserved. Many conventional processing methods allow enhancement of certain image details but often degrade the overall image, for example, producing a blurred or noisy image. Since the SEM has many scanning lines, to use them effectively one must avoid these degradations. 2. Processing artifacts must be minimized. In general, most imageenhancement methods produce artifacts to varying degrees. Since in a processed image

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artifacts and intrinsic image details are generally not distinguishable, useful processing methods must minimize spatial processing artifacts. 3. Processing parameters f o r enhancements must be eliminated as much as possible. Most conventional image-enhancement methods require complex parameters which differ from image to image and depend on the varying visual perception of operators. Specifically, processing in the space domain requires the determination of optimal masks (size, mask shape, and number of iterations), and processing in the Fourier domain requires the definition of optimal filters (frequency characteristic). Unfortunately, it is very difficult to predict optimal processing parameters since SEM images, even when obtained from the same sample, vary considerably in image content (gray-level number and distribution, size of detail structures, extent of noise, etc.) if magnification, electron dose, accelerating voltage, or signal source is changed. Since routine microscopy requires a constant change of these imaging parameters, digital image enhancement is challenged in providing useful tools for image evaluation during a microscopic session. Although the rationale just discussed seems ordinary, it becomes essential in SEM imaging. In the following sections, several methods which satisfy the foregoing requirements are discussed, related to the SEM image characteristics.

B. Noise Removal

Since the SEM was first developed, noise in SEM images has been one of the most difficult problems. The use of a field emission gun dramatically improved the S/N of SEM images. However, even in low-magnification conditions, as well as in high-magnification conditions, we cannot settle this problem as yet, because the image quality depends strongly on the characteristics of the specimen. In each field of SEM (Auger electron spectroscopy, electron probe microanalysis, etc., as well as conventional observations of surface structures), users require noise-free images for their work, if possible. A few techniques for noise removal were introduced to the SEM field in the 1970s (Herzog et al., 1974; Lewis and Sakrison, 1975; Oron and Gilbert, 1976; Yew and Pease, 1974). There are now several additional types of techniques for noise removal in the field of digital image processing (for a general review, see Wang et al., 1983; Rosenfeld and Kak, 1982; and Gonzalez and Woods, 1992), but an ideal method for SEM noise removal does not yet exist because a nearly perfect separation of structures and noise is usually impossible. As a result, we have to submit to the side effects of processing; that is, the degradation

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of information. In addition, since most techniques have some processing parameters (e.g., mask size, shape, and weight, and the number of iterations), the users have to determine them optimally for every original image according to their experience and knowledge. Otherwise, we may often see unfavorable results with many artifacts as well as a low degree of noise removal. This is a very difficult task for the SEM user (some operators may often utilize techniques for noise removal without adequate care). Under these circumstances, conventional methods do not find wide application in conventional microscopy.

1. Complex Hysteresis Smoothing (CHS) As a solution to the aforementioned problem, a very different idea for noise removal, complex hysteresis smoothing (CHS), has been proposed (Oho, Ichise, Martin, et al., 1996). This technique has essentially only one processing parameter, which can be readily determined. In addition, it intrinsically does not worsen the resolution of the original image. These characteristics are favorable for SEM images which contain various sizes of structures. This method also satisfies the basic processing requirements mentioned previously. In order to explain the principle of CHS, we must illustrate standard hysteresis smoothing (Ehrich, 1978), which is a one-dimensional processing method, with an original waveform and its processed result (a thicker line) shown in Figure 9. A hysteresis cursor (vertical line) is established whose width is at least equal to the size of the largest waveform peak or valley to be removed. The sole processing parameter is this cursor width (CW). The cursor is first placed over the left end of the waveform and is then pushed toward the fight end. When the cursor moves to the right, it follows the waveform upward if the waveform reaches the top of the cursor (see 9 in Fig. 9), and in the same manner it follows the waveform downward if the waveform has reached the bottom of the cursor (see v). The processed result is produced by recording the movement of a reference point at the center of the cursor as the cursor moves across the waveform.

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FIGURE 10. Principle of complex hysteresis smoothing (CHS). (a) Noisy SEM image of latex balls coated with Pt-Pd. (bl-b3) Images processed by standard hysteresis smoothing (arrows indicate the direction of processing). (c2) Image processed by CHS [cursor width (CW)= 50] through (bl)-(b3) and many processed images obtained from other directions. Images (Cl) and (Ca) are results processed by CHS with a different value of CW. See text for details. Unfortunately standard hysteresis smoothing produces a severe artifact. Figure 10a (original image) is a noisy SEM image of latex balls of 0 . 5 / x m diameter coated with Pt-Pd. Its image smoothed by the standard hysteresis technique in question is shown in Figure 10bl (see remarkable artifact). It is not surprising that we can choose to process in any arbitrary direction, since this is a one-dimensional technique. Figures 10b2 and 10b3 shows processed results obtained from other directions, and the arrows in Figures 10bl through 10b3 indicate the direction of processing. The CW used in processing Figures 10bl through 10b3 was 50 (gray levels, 256). In some experiments, we found that when the direction of processing was changed, that of the artifact was also changed according to the processing direction as shown in Figures 10bl through 10b3. However, except for this, no obvious relation of the processing artifacts was seen among the three images. The artifacts are very similar to those of

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random noise in each SEM image which is obtained from multiple scanning (such as a series of SEM images recorded at TV rates). We have applied this principle to 16 images (including Figs. 10bl through 10b3) with the particular artifacts obtained from 16 different directions of processing. As a result, the severe artifacts were nearly perfectly removed. Figure 10c is a final processed result of Figure 10a obtained by CHS (through 16 images). The noise as well as the artifacts are seen to be dramatically reduced. Finding the optimal CW (processing parameter) and the controlling property of a processed image, however, is usually not difficult. In the original image (Fig. 10a), it was assumed that the structures indicated by arrows in Figure 10a were a part of the "important information." Therefore, on the basis of the principle of hysteresis smoothing, we can easily find the optimal CW (CW = 50) by choosing values close to the information in the processed result. In this case, we cannot see the difference in the processed results at all, even if the numerical value of the CW is changed to some degree. This is an advantage from the viewpoint of ease of use. In the case in which the magnitude of the CW is much changed, as shown in Figure 10Cl (CW = 25) and 10c3 (CW = 100), we can easily recognize the effect of different CWs. A value of CW = 25 produced an insufficient effect of noise removal because the CW is smaller than the typical amplitude of the noise. A value of CW = 100 destroyed important signal detail (increased secondary electron signal at edges caused by diffusion contrast, see arrows in Figs. 10a and 10c3). Thus, it is easy to control the properties of a processed result. A simple simulation was performed to confirm the high ability of CHS to preserve structural details composed of a few pixels. The result of CHS was compared with the results of a 3 • 3 weighted averaging filter (weight = 3, iteration = 1) and a 3 x 3 median filter (iteration = 1). We utilized these values for processing parameters because the two filters are not in a disadvantageous position (these combinations may produce one of the highest powers for preserving structural details in the practical use of each filter). The former is a conventional smoothing filter with unfavorable blurring effects; the latter is also a common nonlinear-type filter and highly rated from the viewpoint of its ability for edge preservation and noise smoothing in the field of digital image processing (Chin and Yeh, 1983). Figure 1 la is a simulated original image with an SEM noise and minimum size structures (written with single-pixel width). So that the difference could be shown clearly, all images were 16-times expanded by nearest-neighbor interpolation. Figure 11 b shows the processed result of CHS (CW = 40). The noise was nearly perfectly removed while structural details were preserved. Conversely, the median filter (Fig. 11 c) produced a terrible artifact; that is, two lines were perfectly removed and a new line appeared in a strange location. Also, when the averaging filter was used, two lines became a single, wider line from blurring effects. In addition, neither filter

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FIGUV.E11. Comparison of the resolution of images processed by two conventional smoothing filters with that of images processed by CHS. (a) Simulated original image with a random noise and minimum size structures. (b) Image of (a) removed of noise by CHS (CW = 40). (c) Three-by-three median-filtered image. (d) Three-by-three averaging-filtered image. could remove the lower spatial frequency components of noise (a weak fluctuation of contrast in Figs. 1 lc and 1 ld), which are not conspicuous in the original image. If we would use a larger mask size, the components would be somewhat reduced, but we would have to accept a processed image with a lower resolution as well as more severe artifacts, compared with that of a 3 • 3 mask size. Next, another advantage of CHS is presented. In principle, an SEM image is characterized by resolution, contrast, edge sharpness, S/N, and structure sizes, all of which depend on the operating magnification and the properties of

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the sample. These characteristics may be different in each SEM image, even though the same SEM instrument condition and specimen preparation techniques are utilized. In addition, the use of digital image processing allows us to obtain various different magnifications after the acquisition of an SEM image. However, this produces additional changes of the image characteristics. When using conventional techniques for noise removal in the space domain or the Fourier domain, the user has to choose optimally a few or several processing parameters for every SEM image with different characteristics. Microscopists may be unhappy about this situation. Fortunately, CHS is mostly free from these difficulties. In fact, the processed results of CHS are rarely influenced by the change of characteristics (SEM magnification, size of various surface structures, magnifying power of the digitized image) of the object image to be processed. In order to show the practical advantages of CHS for SEM, we performed the following experiment including two procedures. Figure 12a is an original SEM image of latex balls including fine details and heavy noise (this is the same image that we used in Fig. 10a). Procedure 1 in Figure 12 consists of an expansion technique as a first step and CHS processing as a second step. Procedure 2 is the same as Procedure 1 except the two steps are performed in reverse order. The expansion technique (similar to alteration of SEM magnification or observation of another structure with different size) is

FIGURE 12. Special advantage of CHS for SEM. (a) Noisy SEM image of latex balls. (bl) Expanded image of (a). (cl) Image of (bl) processed by CHS. (dl) Median-filtered image for comparison with (el). (b2) Image of (a) processed by CHS. (c2) Expanded image of (bE). (dE) Another median-filtered image for comparison with (c2). See text for details.

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employed for changing image characteristics. When we use CHS as a noiseremoval technique, the same result is expected from each procedure despite the change of characteristics of an object image to be processed. In procedure 1, the expanded noise and structures are shown in Figure 12bl (a part of Fig. 12a). Figure 12Cl is a successful noise-reduced image of Figure 12bl by CHS (CW = 50). In procedure 2, a processed result of Figure 12a by CHS and its expanded image are obtained in Figures 12b2 and 12c2, respectively. Comparing Figures 12Cl and 12c2, we observe no difference, as expected. This example demonstrates that everyone can easily utilize CHS without failure for images with various characteristics. This advantage originates in the properties of CHS which fairly satisfy the aforementioned requirements (no degradation of resolution, only one easily chosen processing parameter, and no processing artifacts). Conversely the results of a 9 • 9 median filter (Figs. 12dl and 12d2) obtained through procedures 1 and 2 are very different from each other. Procedure 1 produced an insufficient amount of noise removal because of a mask size smaller than the noise structure size. Procedure 2 destroyed important signal detail because of an excessively large mask size for structural details. This experiment confirmed that common smoothing filters, represented by median filters, had difficulties when they were used for SEM images (e.g., the necessity of finding optimal parameters based on information from SEM magnification, size of structural details, amount of noise, contrast, and magnifying power of digitized image). As another example, a very noisy SEM image of a large-scale integration (LSI) chip and its noise-reduced image by CHS are shown in Figures 13a and 13b, respectively. The surface structures which have been buried in the noise up to now can be observed clearly. Although the noise with large amplitude remains as many isolated points composed of just a few pixels, observation of the surface structures is not disturbed. CHS for noise removal satisfies the basic processing requirements mentioned previously. However, occasionally it cannot distinguish between signal and noise. Thus, it is necessary to develop a method with a more powerful criterion for noise removal that also satisfies the basic processing requirements. 2. Other N o n l i n e a r M e t h o d s

A few nonlinear methods for noise removal from SEM images have been proposed. Compared with a conventional low-pass filter in the Fourier domain, a filtering technique using the two-dimensional autocorrelation function (Baba et al., 1985) can successfully assort signal and noise. Smoothing by averaging along edges (Oho, M. Baba, et al., 1987; Oho, N. Baba, et al., 1984) was also introduced and improved in high accuracy for processing a noisy SEM image of an uncoated biological specimen (Fig. 14a). When an edge is present, this

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FIGURE 14. Effect of smoothing by averaging along edges. (a) Noisy SEM image of an uncoated biological specimen (glomerular podocyte in rat kidney). (b) Image following noise removal.

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method can take the directional average, involving only those neighbors that lie in a direction along the edge. As a result, the noise involved in an SEM image can be removed without blurring effects (Fig. 14b). Unfortunately, since these methods do not satisfy the aforementioned requirements, it is not easy to use them in routine work (very small image details may be removed in Fig. 14b). 3. Noise Reduction in Fast-Scan SEM Images

Fast-scan (e.g., TV scan) images have some useful advantages in SEM. When one is adjusting the instrument and finding important objects, it is very convenient. In addition, this mode may be helpful in observing insulator and/or low-melting-point samples (Welter and McKee, 1972). Unfortunately, fastscan images have a very low S/N as a result of the small number of electrons making up each pixel. As a way to reduce noise in SEM images taken at TV scan rates, averaging over multiple digitized SEM images is effective (Erasmus, 1982). The averaging is equivalent, to acquiring a slow-scan image. When n images are averaged, the S/N improves x/-d times. One disadvantage of the averaging is that it produces an improved image with a high S/N only once every n frames. The use of a recursive filter can solve this disadvantage, since it produces results continuously. The output of this filter is a weighted sum of all previous input frames, with the most recent input frame having the largest weight and the weights decaying exponentially for earlier inputs. This technique has been employed by many SEM manufacturers. However, the ability of the common (first-order) recursive filter to improve the S/N is generally lower than that of the averaging filter. The recursive filter using Kalman filter theory can produce only the same noise reduction as that produced by averaging. Nevertheless, since specimen motion and/or deformation blurs the output, we may not be able to use long averaging times. In Figures 15a through c, averaging of 2, 64, and 1024 frames, respectively, was performed at a TV scan rate. Blurting effects are clearly seen in Figure 15c, although the S/N is improved remarkably.

C. Fine Details Enhancement

It has generally been assumed that the limit of resolution of SEM is determined by such factors as finite electron beam size and surface penetration effects. Only beam size especially influences a secondary electron (SE) image of a sample coated with a heavy metal. Therefore, first, we should use an electron beam size much smaller than the size of the object, if possible. We should not rely on the effects of digital image-processing techniques without much

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FIGURE 15. Example of a frame-averaging technique performed at a TV scan rate. Result of averaging (a) 2 frames, (b) 64 frames, and (c) 1024 frames. Blurring effects are clearly seen in (c), althoughthe S/N is improvedremarkably. thought. Even if these techniques are utilized for deblurring some SE images, practical results will rarely be obtained owing to the noise problem in the original image. However, in the case in which observation of an SEM sample which is appropriately prepared is disturbed by undesirable effects peculiar to SEM, despite the use of an electron beam of small enough size, it is necessary to use digital techniques. Many techniques were developed for detail enhancement (e.g., edge enhancement, sharpening). However, these techniques did not find wide acceptance in the field of SEM because they required first a determination of specific and image content-dependent processing parameters. Correctly determining such parameters is extremely difficult. In addition, such techniques may enhance the noise component, rather than the structural information exclusively, and have processing artifact problems. From experiential and experimental results, it was understood that conventional methods did not satisfy the aforementioned basic processing requirements. It seems clear that practical methods for digital image enhancement must provide specific new advantages for microscopy before they are accepted and widely used in SEM.

1. Highlight Filter A method for the fine detail enhancement of SEM images is described as follows (Oho, 1992). The method works best on detail-rich images as found in well-focused SEM images of various magnifications. In other words, this method is useful for an SEM (SE) image including potentially sufficient highfrequency components (but it is obscured by some degradations). The method

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presents a "highlight" filter and satisfies most of the basic processing requirements discussed previously, since it adjusts automatically and without need of processing parameters the overall contrast of the image under normal operating conditions, it enhances the contrast of small details, and it produces only few image artifacts. Compared with a few widely used image-enhancement techniques, the highlights filter for SEM images has some advantages, as mentioned later. Images contain two different image-related contrast types. The major and obvious contrast variations come from macrostructures and are summarized in the brightness image. In the SEM, brightness information comes from large features and is enhanced by backscattered electron signals as well as by charging phenomena. The other contrast information comes from small subdued signal variations generated at small surface features and at steep surface edges (microstructures). They are summarized in the highlight image, which contains contrast contributed mainly by the SE signal. In principle, the new filter separates from the image the brightness and the highlight information, enhances the contrast of the highlight image, and mixes it with the unchanged brightness image at a preset ratio. The highlight filter method involves five processing steps (Fig. 16):

original Image

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Step 1. The image is digitally acquired through an AD converter, with 4096 x 4096 • 8 bits. An obtained image will not be influenced by the adverse effects of aliasing error. Then, the original image is reduced in size to a 1024 x 1024 x 8-bit image for improvement of the S/N. The resulting image is the reduced image. Step 2. First, the brightness image is extracted from the reduced image. This task can be established by use of a median filter with an unusually large mask size (e.g., 19 x 19 pixels, although this depends on the system employed), because edge sharpness of the macrostructures is nearly perfectly preserved. Altering the mask size in the vicinity and applying the filter more than a few times did not significantly influence the final processing result. Therefore, a special step for determination of processing parameters (mask size and number of iterations) becomes obsolete. Step 3. Then, subtracting the brightness image from the reduced image generates the highlight image. The highlight image usually has very little contrast except for some cases. Step 4. Next, the contrast of the highlight image is enhanced by histogram equalization, which produces the enhanced (highlight) image. This technique does not need any parameter and the resulting enhancement is generally favorable. Enhancement limitation often occurs in contrast enhancement by histogram equalization of the reduced image including the brightness information (see Fig. 17d). Owing to the possible wide-range intensity distribution, the processing result will vary and be limited by the image content. The enhanced image provides valuable information on the highlight contrasts and the maximum detail enhancement obtainable by this filter. At present, from the viewpoint of automatization, conventional contrast stretching is not applied because of the possible large variation of the maximal intensity range. However, it can also be utilized as an enhancer by modifying the problem. Step 5. Finally, to regain the brightness information, the enhanced (highlight) image and the brightness image are mixed at a preset ratio (1 : 1), which produces thefinal image. (If necessary, the ratio can easily be changed.) Thus, the whole procedure can be performed automatically without any input of processing parameters. The highlight filter has proven very valuable in routine microscopy on difficult samples. A typical problem specimen is found in noncoated semiconductor samples. Microscopy of an LSI chip was frequently hindered by lack of contrast at high accelerating voltages, or by excessive charging and contamination deposition at low accelerating voltages. Conventional image processing could not produce a satisfactory image despite an extensive search for and combination of different processing techniques. The automatic highlight filter produced immediately the pertinent image without any user interactions under

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FIGURE 17. Comparison of SEM image enhancement using the highlight filter, histogram equalization, and SEM imaging techniques. (a) Partial image of a noncoated LSI sample acquired at 25 kV. (b) Image enhancement of (a) through the automatic highlight filter. (c) Partial image acquired at 3 kV with no image processing applied. (d) Image enhancement of (a) through histogram equalization. routine microscopic imaging conditions and provided valuable information on the detail contrast content. As an example, a noncoated LSI sample was investigated. Routine highvoltage (25-kV) imaging conditions for it allowed easy generation of micrographs since charging phenomena were mostly suppressed (Fig. 17a). However, only the macrofeatures of the sample were revealed owing to lack of detail features. According to expectations, the automatic highlight filter produced an image of balanced contrast and rich in detail contrast (Fig. 17b). It should be noted that effective contrast of structural details can be dramatically improved while the macrocontrast obtained by high-voltage conditions is accurately retained. The enhancement revealed detail structures present in the data but visually inaccessible due to low contrast. To prove the existence of such structures on the sample, we imaged the same sample area with low-voltage microscopy (Fig. 17c). On this sample, microscopy was optimized at 3 kV but was cumbersome and severely limited by surface charging and high rates of

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contamination deposition. However, reasonable surface detail contrasts were obtained. The low-voltage application provided a larger excitation volume for local detail contrast generation and thus increased the local signal and improved the local S/N (box in Fig. 17c). Although the macrostructures are obscured by the charging effects, low-voltage microscopy revealed a microstructure very similar to that revealed in high-voltage images after enhancement with the highlight filter (box in Fig. 17b). The image enhancement made possible a direct comparison of both low-voltage and high-voltage images and provided a new exciting tool for the analysis of detail contrast mechanisms. Conversely, the use of conventional contrast enhancement methods [e.g., histogram equalization (Fig. 17d), contrast stretching] could not unveil the detail structures. Such methods are effective only for images lacking a brightness component (SEM images often have a large brightness component). The highlight filter was also compared with unsharp masking, which is widely used for sharpening (deblurring) of blurred images. The unsharp masking does not fulfill the basic processing requirements. The filter is seemingly easy to use, but it needs some processing parameters and combination with other processing methods to achieve a "suitable" enhancement, since it has a noise problem. The enhancement product is strongly dependent on the image content and is not predictable; thus it requires a trial-and-error approach (there is no criterion for the optimal processing image). Figures 18a and 18b are an SEM image of gold-coated magnetic tape and its highlight-filtered image, respectively. Many gold particles can clearly be seen in Figure 18b. In addition, the processing result obtained by the highlight filter is not influenced by the set value of processing parameter for enhancement (because the highlight filter does not originally have the processing parameter). On the contrary, unsharp masking (Fig. 18c) cannot demonstrate its maximum performance owing to failure of parameter setting (too small size of mask and excessive enhancement ratio). Unfortunately, when we improve these values, another problem occurs. Several limitations of conventional image enhancement have been demonstrated clearly (Oho and Peters, 1994), and several applications of the highlight filter were shown elsewhere (Oho, 1992). As another example, an SEM image of an uncoated biological specimen influenced by weak charging phenomena (Fig. 19a) was processed by the highlight filter. Enhancement of fine structures as well as reduction of the effects of charging phenomena is successfully indicated in Figure 19b. In a different case, in order to settle a problem sensitive to noise in unsharp masking, Oho, Ogihara, et al. (1990) proposed a nonlinear pseudo-Laplacian filter for enhancement of high-resolution SE images. However, this method is not easy to use in routine work owing to several processing parameters, although it did improve performance.

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FIGURE18. Comparisonof SEM image enhancement using the highlight filter and unsharp masking. (a) SEM image of gold-coatedmagnetic tape. (b) Imageprocessedby the highlightfilter; gold particles can be observed clearly. (c) Image processed by conventional unsharp masking.

2. Enhancement of Backscattered Electron (BSE) Images In principle, the resolution of backscattered electron (BSE) images can be little improved except for particular samples, even though an infinitely small beam size is achieved by various improvements in the intrinsic instrument. In other words, surface penetration effects of the incident beam greatly influence the

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FIGURE 19. Suppression of the effects of weak charging phenomena by the highlight filter. (a) Unprocessed SEM image. (b) Image processed by the highlight filter. Enhancement of fine structures as well as reduction of the effects of charging phenomena was successfully performed. resolution of a BSE image. If the resolution of BSE images could be improved beyond previously accepted classic limits, they would be a more attractive tool for many SEM users, since BSE images have superior advantages to those of SE images. We contend that the best way to improve the resolution of the BSE image is to utilize digital image-processing techniques based on the characteristics of BSE images. However, the aforementioned highlight filter will not be suitable for enhancement of a BSE image because it may not be able to successfully separate the brightness and the highlight information from a BSE image disturbed by various blurs. High-emphasis filters, which can improve the image resolution in principle, have not been used often in practical applications, owing to the existence of noise in the SEM image. However, if an image without noise did exist, very useful processing results could be obtained by using refined imageenhancement techniques. Fortunately, BSE images may not be degraded by contamination or charging phenomena, unlike the situation for an SE image, and degradation caused by the radiation damage is not conspicuous at the level of resolution of normal BSE images for most specimens. Hence, a combination of an ultra-high-performance BSE detector, a long recording time, and appropriate image-processing techniques may be able to produce a BSE image with an extremely high S/N. As a result, a high-emphasis filter may be able

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to significantly improve the resolution of BSE images with an extremely high S/N. The procedure to obtain a high-resolution BSE image follows these steps (Oho, Ogihara, and Kanaya, 1991):

Step 1. The BSE image (e.g., 4096 x 4096 pixels) is stored through the AD converter in the image memory. Here, the BSE image must be recorded at a high magnification to attain the oversampling condition and for as long a time as possible to obtain a very high S/N image without SEM shot noise and aliasing noise. Consequently, a noise-reduced and blurred BSE image may be acquired. Step 2. The BSE image consisting of quite a lot of pixels is reduced into a new image consisting of, for example, 512 x 512 pixels. Since each new pixel was obtained as a properly averaged value of many pixels, the S/N has increased. The information contained in the BSE image is little degraded by this reduction because the original, blurred image is taken under the oversampling condition. In other words, the blurred image can be represented accurately by a comparatively coarse sampling. Step 3. The reduced image now has an extremely high S/N, which allows enhancement of its high-frequency component. The image is subsequently processed by a high-emphasis filter in the Fourier domain or the space domain (e.g., unsharp masking). It should be noted that unsharp masking without appreciation in enhancement of SE images is useful for BSE and video microscope (mentioned later) images which contain remarkable blur. Filters of this kind have been successfully applied to a blurred telescopic image (O'Handley and Green, 1972). As an example, a BSE image, obtained through steps 1-3, of a piece of paper from a word processor, coated with 20 nm of A1, is shown in Figure 20a. The image was recorded under the following conditions: accelerating voltage of 30 kV, incident current of 5.5 x 10 -1~ A, and recording time of 320 s (with the use of a semiconductor BSE detector). The filtered image is shown in Figure 20b. The images in Figures 20a and 20b were enlarged to show the difference more clearly (Figs. 20a' and 20b', respectively, same views). The processed image illustrates an impressive improvement in resolution due to the ultrahigh S/N of the original image. It is easy to produce a successful design of a high-emphasis filter, because the forms of the filter for the various BSE images under consideration closely resemble one another. An SE image of the same region as in Figure 20a is shown in Figure 20c. As compared with Figure 20c, the processed images (Fig. 20b) has a similar resolution but very different contrast information (of course, the sample coated with heavy metal may produce a higher resolution in an SE image). Hence, both SE and BSE images can be

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FIGURE 20. High-resolution enhancement for the BSE image. (a) BSE image, with an extremely high S/N, of a piece of ~aper (obtained with the use of a semiconductor BSE detector, an incident current of 5.5 x 10- 0 A, and a recording time of 320 s). (b) Image processed with a high-emphasis filter in the Fourier domain, together with expanded images (a') and (b'). (c) SE image, same view as in (a).

effective tools for high-resolution studies. In the case of a BSE image with a low S/N (Fig. 21 a), we cannot obtain successful results, as shown in Figure 2lb. As a way to reduce an electron dose, a YAG (yttrium aluminum garnet) single crystal is used as the scintillator with a very high efficiency. A BSE image of aluminum foil (Fig. 22a) was acquired with the YAG detector (accelerating voltage of 30 kV, incident current of 1 • 10 -1~ A, and recording time of 160 s). The electron dose was reduced to 1/9. The enhanced image is shown in Figure 22b. Fine structures can be seen dramatically because Figure 22a has a sufficient S/N. Incidentally, an SE image of the same sample did not produce important additional information. In contrast, the Wiener filter has been used for restoration of blurred SE images (Lewis and Sakrison, 1975). However, since the properties of the signal and noise in an image must be known for the development of the optimal image

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FIGURE 21. Example of an unsuccessfully processed result. (a) BSE image with a low S/N. (b) Image processed with a high-emphasis filter excessively disturbed by the effects of noise.

filter, it is not easy to utilize the Wiener filter. Moreover, it may not be possible to obtain more information than that in Figures 20b and 22b because the present BSE images originally have a sufficient S/N.

3. Reduction of Unfavorable Effects Noise, contrast, and blur problems in SEM images have been fairly improved, as mentioned in the preceding sections. However, these images have various

FIGURE22. Improvement ofrecording conditions (with the use ofa YAG scintillator detector, an incident current of 1 x 10 -1~ A, and a recording time of 160 s). (a) BSE image of aluminum foil. (b) Enhanced image of (a).

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characteristics which are not found in other fields, such as the effects of vibration, contamination, and field-emission noise. In this section, after these latter adverse effects are reviewed, we will describe how much they can be improved. As the recording magnification is increased, the visual effect of vibration on an observed image may increase. Hence, in the case in which vibration is a serious problem, the image should be recorded at the lowest magnification that satisfies the sampling theorem, and, if necessary, the image subsequently should be expanded by the interpolation technique. However, in this process, since the expanded image differs from an image recorded originally at higher magnification, in terms of the number of incident electrons per unit area in the specimen, the S/N of the expanded image may be degraded. Therefore, it may be necessary to average a few SEM images with the identical view for increasing the S/N (decreasing random noise). This averaging as well as recording at the low magnification can also reduce the effects of vibration, because, as in the case of SEM noise, no obvious relation of the effects of vibration can be seen among several images (Oho, Sasaki, and Kanaya, 1986). As an example, through the aforementioned techniques, a processed (four-times expanded) image without the adverse effects of vibration is shown in Figure 23a (gold-coated latex balls). For comparing the quality of this image, an originally high-magnification image (Fig. 23b) was taken under the same conditions except for the recording

FIGURE 23. Reduction of the effect of vibration in an SEM image. (a) Vibration-reduced image obtained by using the optimal scanning and digital expansion technique. (b) Highmagnification image with the effect of vibration, taken under the same conditions. See text for details.

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FIGURE24. Removalof the effects of contamination. (a) ContaminatedSEM image of gold particles deposited on a carbon. (b) Processed image by homomorphicfiltering.

magnification. It can be seen that the image is severely disturbed by the effects of vibration. Contamination is another serious problem in SEM. A method using homomorphic filtering, which is a combination of logarithmic transformation of the gray scale and use of a high-emphasis filter in the Fourier domain, was applied for reducing the effects of contamination in the case in which an SEM image is once more observed at a lower magnification after a high-magnification observation (Oho, Sasaki, and Kanaya, 1985; Oho, Sasaki, Ogihara, et al., 1987). Figure 24a is an SEM image of gold particles. We can see the contaminated region easily. The homomorphic filtered images is shown in Figure 24b. The effects of contamination are successfully reduced and there is high-resolution enhancement. Noise in the field-emission (FE) source is sometimes remarkable in SEM images taken by the FE-SEM (Fig. 25a). This noise may have a frequency characteristic as shown by the arrows in a power spectrum (Fig. 25b; the scanning is in the horizontal direction). When successfully removing this component in the Fourier domain, we can obtain a noise-removed image (Fig. 25c) without the degradation of fine structures. Unfortunately, all these methods are not optimal strategies. In other words, these methods were developed to patch over each problem temporarily as it arose. A fundamental improvement is necessary in each case. Nonetheless, mastering these techniques and knowledge (i.e., sampling theorem, averaging, filtering in the Fourier domain) may be useful for many microscopists.

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FIGURE 25. Removal of the effects of noise in the field-emission (FE) source. (a) Noisy FE-SEM image together with (b) its power spectrum. (c) Noise-removed image.

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IV. IMAGEMEASUREMENTAND ANALYSIS A. Precautions for the Effective Use of Conventional Statistical Measurement After SEM images are acquired using the on-line computer system, they are frequently analyzed by using a statistical measurement method. There are many commercial systems for image statistical analysis of SEM images based on a standard PC. However, this kind of measurement may not be very useful because it was introduced from the field of pure digital image processing without consideration of the characteristics of SEM images. To utilize this method effectively, we must solve some problems. When SEM images to be analyzed by statistical measurement are disturbed by noise, blur, an excessively wide dynamic range, and so forth, some preprocessing techniques (symptomatic therapy) have to be employed to reduce these unfavorable effects. For example, it may be helpful when one is determining the threshold in binary processing to remove the brightness image (described in Section III) from an SEM image with a wide dynamic range. This technique is similar to shading correction. More important, however, is suitably choosing the SEM operating conditions for the statistical measurement. Naturally, it is necessary to decrease the noise and blur in the SEM image as much as possible. For example, utilizing a comparatively long recording time effectively reduces the noise. And for many samples with large unevenness, employing a condition that produces great depth of focus may be helpful. Otherwise, a fine structure size in out-of-focus areas will be different from a true size.

B. Critical Dimension Measurement and Foreign Material Observation on the Wafer for Semiconductor Process Evaluation The semiconductor industry use the design rule approaching the 0.1-/zm in ULSI (ultra-large-scale integration). Many specialized high-performance SEMs are currently employed for semiconductor process evaluation. These are designed considering fully the characteristics of the sample (wafer) (Otaka et al., 1995). In these instruments, some statistical measurement techniques are utilized for precisely measuring the size of line and hole patterns. Foreign material (particles) and/or wafer defects, which are found through other systems based on a certain light microscope with a high sample throughput but low resolving power, are inspected and analyzed by the SEM used for detailed observation (statistical measurement) of them as required. In this procedure, the measurement coordinates in light microscopy are sent, by using

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digital-processing techniques, to the SEM. The automatic foreign material and defect classification system using a variety of image-processing techniques has become a very important field (Chou et al., 1997). In the future, the state-of-the-art will be built into the total system to facilitate better semiconductor process evaluation. The feature size will undoubtedly be reduced for higher device integration and density. Not surprisingly, since improvement of the SEM instrument which follows it may gradually become difficult, especially with regard to resolving power, digital image-processing technology will become more and more important in this field. However, as there are not many references concerning this field, it is necessary to confirm the current state of the system by observing and experiencing a commercial state-of-the-art SEM.

C. Surface Topography Measurement In the field of SEM, we can find several techniques for obtaining height information. Surface topography measurement using digital image processing generally falls into one of three categoriesmthe multiple-detector, focusing, or stereometric method. These methods have some advantages, respectively. By using multiple detectors, one may relate detected intensities (either a BSE or an SE signal) to the surface slope of the area being scanned by the incident beam. The profile is obtained by numerical integration of the slopes in the direction of the scan line (Lebiedzik, 1979). In the reconstruction process of surface topographies, the noise in the digitized detector signals accumulates in an unpredictable way during the course of the integration, which thereby leads to artifacts that heavily distort the resulting surface. In order to solve this problem, Carlsen (1985) used least-square techniques which are a type of image-smoothing techniques. This kind of system is suitable for specimens with protrusions, or with depressions with less steep slopes such as on compact discs (Suganuma, 1985). The stereometric technique is used to acquire stereo-pair images and determine the height by measuring deviations of corresponding points in the two images (Boyde, 1975). Hence, it is necessary to find the points in two digitized images. For example, Koenig et al. (1987) employed a combination of the normalized cross-correlation and the least-squares solution to very accurately determine homologue pairs of points. Unfortunately, the drawbacks of this method are enormous processing time and detection failure. In the focusing method, the fact that the focus of the objective lens is a monotonic function of the lens excitation is used. This characteristic can be applied as an absolute measure of the height at any point by focusing the electron beam there. Holburn and Smith (1982) used a digital method for focusing based on the two-dimensional gradient of acquired data. However, as

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the SEM has great depth of focus, the measurement accuracy of this method may be inadequate. As already mentioned, there are some disadvantages specific to each method. In order to improve the accuracy of surface topography measurement, a combination of multiple detectors and stereoscopy was performed through some digital image-processing techniques (Beil and Carlsen, 1990). As a result, stereo mismatch and wrong detector calibration were reduced. Likewise, the focusing method was successfully combined with the stereometric method to improve the precision (Thong and Breton, 1992). This method uses measurement of the parallax between a stereo pair for more accurate focusing on the specimen surface. Cross-correlation was used to determine the parallax in a small area including the point of interest. With the development of recent computer graphics technology, the data obtained through each of the aforementioned methods can easily be expressed in three dimensions as in the case of the CT (computed tomography) scanner.

V. SEM PARAMETERS MEASUREMENT The performance of an SEM and a scanning transmission electron microscope (STEM) is roughly determined by the incident electron beam size involving a sufficient electron current (to obtain an image with a sufficient S/N). The resolution of an STEM image is limited by the scanning beam diameter, and that of an SEM image is influenced by both the beam diameter and the interactions of electrons with a specimen. Although these parameters are theoretically calculated easily, the result of calculation is frequently not suitable for an actual situation because of many indefinite factors. Hence, these parameters should be measured from a recorded image. When the measured values can be effectively used, it is useful for various work and study in SEM.

A. Electron Beam Diameter

The electron beam diameter is conventionally measured from the rise time in a transmitted electron signal, or an SE signal, when the beam is scanned across a suitable target with a sharp edge (e.g., Joy, 1974). However, as the beam diameter decreases, it is difficult to measure it, because of insufficient edge sharpness, a low S/N, the buildup of contamination layers, and several other problems. Unfortunately, at the limit of resolution, this method tends to produce inaccurately measured values. In order to solve part of these problems (insufficient edge sharpness, the buildup of contamination layers), we must examine a crystalline specimen with an SEM or an STEM to obtain a sharp edge and two-dimensional information,

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instead of measuring the rise time (Reimer et al., 1979). In this step, we must pay attention that no "clipping" of the width of an edge takes place by the signal saturation in the AD converter. As the next step, the data on the blurring of an edge obtained from the SEM image is transformed into reliable data by suitable digital-processing techniques for reducing the effect of a low S/N (Oho, Sasaki, and Kanaya, 1985). A series of procedures described next gives an accurate value of the beam diameter. To confirm the accuracy of this method, we can perform a simple simulation. This simulation is based on the assumption that scanning images are approximately formed by convoluting an image function s(x, y) of the specimen scanned by an infinitely small beam with a practical electron beam distribution defined as a Gaussian function. Figure 26a is an image of the simulated specimen with a sharp edge scanned by an infinitely small beam, together with its three-dimensional representation (Fig. 26a'). Figure 26b is a simulated image scanned by the Gaussian spot of 2rs diameter. Figure 26c is a simulated image which represents Figure 26b plus SEM noise. This image is considered to be approximately equal to an image which is taken under a highresolution condition in SEM or STEM. We must then attempt to measure the scanning beam diameter (= 2rs) from information contained in Figure 26c. For the measurement of the beam diameter, the noise involved in Figure 26c must be appropriately removed as a preprocessing step. In this processing, it should be noted that a change of ramp steepness (edge sharpness) after noise reduction is closely related to a measured value of the beam diameter. From the viewpoint of the extent of unchanged ramp steepness after the processing, median filtering is used in the present method. It is a nonlinear type of smoothing technique. A mask size, which is roughly equal to the statistical size of the noise, was utilized in the present study (Oho, N. Baba, et al., 1984). Since median filtering does not blur edges, it can be repeated. And, as a result of several median filterings, there will be "stationary states"; the processing no longer improves or degrades the image. In contrast, other smoothing techniques generally change the state of blurring of the edge whenever they are repeated. Hence, judging from the ease of use, median filtering may be the best technique for the present study. The processed image shown in Figure 26d is obtained by removing the noise contained in Figure 26c by using median filtering. This result of noise removal allows us to observe the edge. Nevertheless, as may be obvious from the threedimensional image shown in Figure 26d', the ramp steepness at each position is different from the true one shown in Figure 26b'. Hence, inaccurate measured values will be obtained from each line profile in Figure 26e (it shows the square of the differential image for Fig. 26d). However, since these measured values are distributed around the true value (= 2rs), a synthetic image (Fig. 26f), which is averaged in all lines with matching peak positions of all line profiles in Figure 26e, can indicate the real beam diameter (=2rs). As a result of

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FIGURE26. Simulationfor confirming the validity of the measured electron probe diameter. See text for details. simulation, we are able to measure the diameter of a fine electron probe beam under a high-resolution condition by the present method. An automatic measurement has been developed on the basis of the aforementioned study (Oho, Kobayasi, et al., 1986). The procedure of automatic measurement is shown in Figure 27. The main steps are summarized as follows. The STEM image of a crystalline hole in a gold thin film [with the use of field emission gun, a focal length of 7.5 m m (working distance, 0 mm), an accelerating voltage of 30 kV, an objective aperture semiangle of 5 • 10 -3 rad, and a detector

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start !

Stop1

Input A p p o i n t m e n t of e d g e s Magnification Sampling interval P a r a m e t e r s of t h e m e d i a n

filter

! Selection of the appointed regions ! Stop3 t Rotation of the selected regions Step2

9R e d u c t i o n

Step4 Step5

9n o r m a l

9e x p a n s i o n

! Averaging coupled with matching ! Differentiation mask _-size_l

9siz e2_

9~i,z~ 3_

laJbrclar Size1 ........ Size2 ........ ___S_i_z_~_3_. . . . . . . .

Step6

l a-bl l a-cl [I~_+_b_1:(z_+__d)_[ v

Measurement of beam diameter ! Judgment of validity of measured value ! End FIGURE 27. Procedure of automatic measurement of the scanning beam diameter.

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FIGURE28. STEM image of crystalline holes in (a) a gold thin film and (a') its enlarged image for detecting blurring of the edge. aperture of 7 x 10 -3 rad (Oho, M. Baba, et al., 1987)] has already been stored in the image-processing system.

Step 1. Some parameters necessary for the present measurement (e.g., the SEM instrument magnification) are input. Next, the users must appoint several edges in the image, which should be measured. An ideal sharp edge may be included in these edges. The STEM image of crystalline holes and its photographically enlarged image of a part of an edge are shown in Figures 28a and 28a', respectively. Step 2. Several square regions including each appointed edge are selected from the stored image as processing regions. Step 3. A rotating program, which does not change the edge sharpness, is performed to align the edges in the same direction. Under the condition of relatively low magnification and high resolution, the aliasing error will increase. The computer can detect this by searching the number of pixels which

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Relation between the beamdiameter d

and the distance Xc

S

d = 2 9r(l/e) =

XO

c: d i s t a n c e between c e r t a i n I n t e n s i t y 0 i n t s C(0,5 _< C <.. 0,8)

~ = 2 rW.)

1

\

1.~=37 % "

~

,

i

~

i

0 FIGURE 29. The profile of statistical data obtained by steps 1-6. The part between 50 and 80% of the maximum value, shown as oblique lines, contains the information on the scanning beam diameter.

compose the edge. If these conditions exist, the number of pixels is increased by an interpolation technique for decreasing the adverse effects of error. Step 4. As preprocessing, the noise involved in the STEM image is removed by median filtering. The noise-removal image consists of many line profiles. The statistical edge profile is obtained by averaging all lines coupled with matching. Step 5. Its differentiated value is calculated, which represents the beam size. In this step, a proper mask size for differentiation is automatically chosen. This statistical processing result includes the information on the scanning beam diameter. Step 6. The scanning beam diameter is measured from the statistical data. Compared with the real profile of the scanning beam, the profile of the obtained data may be deformed by the interaction of incident electrons with the specimen. For the ideal sharp edge, and if we ignore the noise, interactions, and so forth, the distance d = 2r(1/e) between 37% intensity points may correspond to the scanning beam diameter (Fig. 29). Under high-resolution conditions, only a particular part of the profile may be equal to the scanning beam profile having the Gaussian distribution. According to our study, the part between 50 and 80% of the maximum value, shown in Figure 29 as oblique lines, is equivalent to that part. From an equation in Figure 29, the relationship between the beam diameter d and the distance Xc between certain intensity points C (50-80%) is obtained. Consequently, the measured values can be calculated from Xc at each intensity point, and the average of the measured values, except obviously erroneous values involved in these measured values, is adopted as the candidate of the scanning beam diameter. Ultimately, the minimum value

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of candidates obtained from several processing regions which are appointed in step 1 is adopted as the final measured value of the scanning beam diameter. The present method accurately measures the beam diameter of 1.5 nm from the STEM image shown in Figure 28 (Oho, 1987).

B. Resolution (Highest Spatial Frequency) As a well-known method in electron microscopy, the diffractogram (equivalent to the two-dimensional Fourier transform) can be used for measuring the highest spatial frequency included in an image, which is closely related to image resolution. Concerning objectivity and repeatability of the measured value, this statistical method must be superior to conventional edge-to-edge or point-to-point resolution in the space domain. However, since it is very difficult for the diffractogram to detect accurately the highest spatial frequency in a noisy image, it is inadequate for a common SEM image including noise more or less. As a way to ameliorate this disadvantage, the superposition diffractogram method was experimented with. This method was proposed by Frank (1972) and applied to SEM images (Erasmus et al., 1980; Reimer et al., 1978). However, as far as it is possible to tell, it could not fully show its real ability (why this is so will be explained later). In this section, the latent ability of the superposition diffractogram method is successfully demonstrated by an essential improvement. In order to successfully obtain a superposition diffractogram used in resolution measurement, one must first acquire, two images from the same area. Second, one of the two images is shifted by some pixels in the x- (horizontal) and/or y- (vertical) direction and next the shifted image and another image are superposed. Finally, the result (superposed image) is Fourier-transformed to obtain the superposition diffractogram. The superposition diffractogram (see Fig. 30) can distinguish between structural detail and noise in an SEM image, because structural detail is present in both SEM images, but noise, although it is present in the two images, is not correlated between them. Consequently, the part of the superposition diffractogram corresponding to structures included in the SEM image is modulated by a periodic interference fringe pattern (like Young's interference fringes), while that of noise is not changed. The superposition diffractogram shown in Figure 30 was obtained from a high-resolution SEM image of Au particles on carbon taken with our somewhat old field-emission SEM (Hitachi S-800, accelerating voltage of 30 kV, working distance of 4 mm). The number of shifted pixels is equal to the number of periodic patterns, if these fill the whole image. It is not seemingly difficult to identify visually the highest spatial frequency in the superposition diffractogram. However, the conventional superposition diffractogram is helpful only for the SEM image recorded under certain ideal

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FIGURE 30. Highly precise resolution measurement of SEM images using the superposition diffractogram and autocorrelation function (ACF) processing. (a) Data of the region surrounded by the dotted lines in the superposition diffractogram, which is divided into small areas with 32 x 8 pixels. (b) Results processed by the ACF of (a). (c) Contrivance for increasing the detectability of the outermost fringe (the highest spatial frequency) lost in noise. conditions. The following discussions are important to establish an advanced m e t h o d with practical use based on the superposition diffractogram.

1. Advanced Superposition Diffractogram We need a special scanning m o d e and digital image-processing technology to construct an a d v a n c e d superposition diffractogram for high-precision measurement of S E M resolution (Oho, Hoshino, et al., 1997; O h o and Toyomura, 2001).

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a. Acquisition of Two SEM Images with the Perfectly Identical View Theoretically, the superposition diffractogram has a very high ability for measuring resolution in an SEM image. However, two images with the nearly perfectly identical view are necessary for producing the valid superposition diffractogram with the desired ability. In the case of a conventional SEM without a special function for obtaining the identical-view images, two unsuitable images obtained by the iteration of usual scanning, which may have the adverse effects of specimen deformation (damage), drift, stray magnetic field, and so forth, are utilized involuntarily. As a result, we have to endure a serious error in the measured value (the degree of the error differs greatly according to SEM operating conditions, etc.). So that the two images with the identical view can be obtained, an oddlooking SEM image with an incorrect aspect ratio is recorded by scanning each line twice, and two images with the correct aspect ratio are reconstructed by thinning out lines properly from the SEM image. These images obtained through this special scanning provide nearly perfectly identical views (Oho, Hoshino, et al., 1997). However, images of this kind are also composed of the data acquired continuously twice from the same coordinates. (It is necessary to rearrange suitably the data for obtaining two SEM images with the identical view.) The decision as to which special mode of scanning will be most suitable for the present method depends on the property of disturbance (e.g., frequency of vibration) as mentioned later. b. Detection of the Highest Spatial Frequency In conventional superposition diffractograms, we usually identify the highest spatial frequency (located on the outermost fringe) visually. However, it is difficult to detect accurately the highest spatial frequency in a high-frequency domain in which the adverse effect of noise is dominant. A high-precision and highly sensitive technique for finding the highest spatial frequency in the superposition diffractogram has to be developed so that we can use it more practically. In order to detect a fringe lost in the noise, we can apply the autocorrelation function (ACF), which is obtained by performing an inverse Fourier transform of the power spectrum, in the region including the highest spatial frequency. The ACF is frequently utilized to detect periodic structures lost in the noise. A little different usage is performed in the present study. First, we have to suitably determine the number of pixels, which is a distance between two images, for employing the superposition diffractogram. When an SEM image with 512 • 512 pixels was used, the amount of shift was experimentally decided to 64 pixels from the viewpoint of a compromise between the precision of measurement and the sensitivity of fringe detection. This is equivalent to a fringe consisting of 8 pixels per cycle in the superposition

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diffractogram. These conditions were used to obtain the superposition diffractogram in Figure 30 (although the viewability may not be so good in this line width, we can obtain higher precision of measurement). Next, a long and narrow rectangular region in the superposition diffractogram is selected. Figure 30a shows the data of the portion surrounded by the dotted lines in the rectangular region, which should include the highest spatial frequency. The data have already been divided into small areas. Finally, each small area with 32 x 8 pixels, which includes one cycle of the fringe, is processed by the ACF to find the highest spatial frequency (outermost fringe). These processing results are indicated in Figure 30b (from the data of the higher spatial frequency which is not indicated in Figures 30a and 30b, we cannot obtain the significant result). Data below the dotted line in Figures 30a and 30b show a fringe (original datum) near the center of the superposition diffractogram, which is not so disturbed by the noise, and its ACF result, respectively. Supposing the effective signal is included in an original datum with 32 x 8 pixels, the original datum includes a black line (as a center line), and its processed result (ACF) includes the white line. From the comparison of Figures 30a and 30b, we can see the difference in the detected highest spatial frequency between visual identification and the present method using the ACE At least, a 5.4-nm resolution (the reciprocal of the spatial frequency) is clearly measured, as shown by the arrow in Figure 30b. In addition, there is quite a possibility that signal information is included in slightly higher spatial frequency q (1/q > 5.1 nm), although an ACF result corresponding to 5.1-nm resolution does not show the horizontal stripe. Hence, it may be said that the resolution [reciprocal of the highest spatial frequency (the minimum specimen periodicity)] is 5.3 + 0.1 nm. On the contrary, we cannot obtain an accurate measured value by visual identification. The conventional superposition diffractogram with visual identification tends to underestimate the highest spatial frequency. In this final step, the result of the ACF for a small area with 32 x 8 pixels near the outermost fringe may often be disturbed by noise components including low frequencies. We solve this problem by shifting the rectangular region in the superposition diffractogram a little horizontally (more than one selection should be tried to obtain a successful result). The effective shift may be less than ~-4-10 pixels in the case of the utilized data size (SEM image with 512 x 512 pixels, small area with 32 x 8 pixels processed by the ACF), because a small area ceases to include important information (outermost fringe) gradually. By this contrivance to increase detectability, several fringe images (Fig. 30c) are obtained from the area with the identical spatial frequency, and since the conditions of the low-frequency components of noise in these images are probably altered favorably for the processing of the ACF at least once, we

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can detect the outermost fringe lost in noise. In fact, the result (5.4 nm) shown by the arrow in Figure 30b was obtained through many processing results in Figure 30c. In this example, we can obtain successful results from the shift of - 4 and - 8 pixels. In addition, a very effective method for detecting the fringe (horizontal stripe) lost in noise is to repeat the ACF processing as shown in Figure 30c, although this method may be rare as directions for use of the ACE Incidentally, as a result of several ACF processing iterations, there will be stationary states (the processing no longer changes the image).

2. Caution in the Utilization of the Superposition Diffractogram The performance of the superposition diffractogram has been improved as mentioned previously. However, if the following caution is not observed, the (advanced) superposition diffractogram cannot demonstrate its real ability (this caution was observed in Fig. 30).

a. Proper Acquisition of SEM Images First, the superposition diffractogram erroneously regards the partially saturated areas as true signal with high-frequency components, because these areas without the least difference are included in the two images used for producing the superposition diffractogram. Hence, we have to carefully acquire the SEM images without saturated areas for the accurate measurement of resolution. Next, we must use SEM images which satisfy the sampling theorem to measure the resolution (Crewe, 1980; Erasmus et al., 1980). A low-magnification condition may not satisfy this theorem. Strictly speaking, whether the sampiing theorem is satisfied is decided in relation to the electron beam diameter, the number of scanning lines, the recording magnification, and the property of the specimen (Oho, Ichise, and Ogashiwa, 1995, 1996a). b. Properties of the Specimen We need to adhere to the following precautions to optimize the properties of the specimen for resolution measurement: 9 Removal of the charging effects which strangely emphasize the dynamic range or partially saturate the SEM signal should especially be performed successfully. 9 An SEM image with large features (e.g., deep hollows) may be unsuitable for measuring the resolution, because SEM signals are likely to be trapped or enhanced. Such images should not be used. 9 According to the properties of individual samples and the accelerating voltage, the secondary electron halo signal at the edges caused by diffusion

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contrast increases too much, and it may sometimes be considered by mistake as a useful signal for resolution measurement. Such a mistake should be avoided. 9 In the case of common SEM samples without isotropy, the direction of fine structures should be adjusted so that many fringes appear in a predetermined region (see Fig. 30). 9 In the measurement under high-resolution conditions, we employ a specimen consisting of very fine heavy-metal particles. This specimen should have high contrast, a high S/N, a low contamination rate, and isotropy.

c. Direction of Image Shift to the Scanning Direction So that we can obtain the superposition diffractogram, one of two images is shifted by some pixels as mentioned previously. The image should be horizontally shifted to the scanning direction, because the stray magnetic field and/or the vibration disturbs the two SEM images more or less, and this may produce many artificial structural details (jaggies of the edge) vertically to the scanning direction. By employing this direction (horizontal to the scanning direction), we can considerably prevent the measured value from being misestimated by the adverse effects of disturbance. d. Application of the Hanning Window When we use the fast Fourier transform (FFT) ideally, it is desirable, for reducing some adverse effects of edges, to match fight and left edges or top and bottom edges in an original image. Especially, it is a serious problem in the present study that a large step function at the edge is produced, because a central cross (this may disturb the resolution measurement) appears relatively frequently in the power spectrum according to circumstances. In order to settle this problem, we employ the Hanning window in the spatial domain, which is commonly used for reducing adverse effects of edges in the Fourier spectrum. (Other similar windows also may be able to be used for this work.) These precautions were utilized for the results of Figure 30. By using the advanced superposition diffractogram, we can accurately recognize differences of several percentage points in the resolution as indicated in Figure 30. However, as another problem, the measured value in question depends on the accuracy of the magnification of the SEM instrument. Hence, the SEM magnification has to be checked with a calibration specimen whenever precise measurements are required. Similarly, this measured value is closely related to the electron beam size when we utilize the ideal sample for high-resolution observation. However, the electron beam size is not numerically in agreement with the current measured

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value, as they each have different definitions (Erasmus et al., 1980). The reciprocal of the highest spatial frequency (the minimum specimen periodicity) may be of the order of twice the electron beam diameter or the conventional edge-to-edge resolution (Reimer, 1985).

C. Signal-to-Noise Ratio (S/N) SEM images are usually recorded in a slow-scan mode to obtain a suitable S/N (TV-rate SEM images have a poor S/N as a result of the small number of electrons consisting of each frame). These images are complicated by noise problems to a greater or lesser extent because of unfavorable effects peculiar to SEM. Therefore it is important to know the S/N of an SEM image in microscopy. In order to measure the S/N of an SEM image, Erasmus (1982) used two images (i1 and i2) of the same specimen area and the following equation: cov(il, i2) S / N --

,,/var(im) v - ~ 2 i - cov(im, i2)

The definition of this S/N is equivalent to (the signal standard deviation)/(the noise standard deviation) in an SEM image. It is assumed that the SEM noise is additive, has a zero mean, and is independent of the signal. Of course two images must share the identical signal (view) with each other except for noise components. Otherwise, we may obtain an inaccurate measured value. The aforementioned digital scan generator can acquire the ideal images for this work. As an example, a measurement of the S/N in an SEM image taken in air or helium gas was performed (the use of helium gas is for reducing the amount of scatter of the primary electron beam). At a few different pressures,, the S/N was precisely measured from a pair of BSE images (identical view) of a nonconductive sample (insect). The experiment was performed in a Hitachi S-3000N variable pressure (VP)-SEM with the standard hairpin cathode under the condition of an accelerating voltage of 1.5 kV, an incident current of 1.8 nA (measured value with a Faraday cup at a full vacuum), and a working distance of 9.7 mm. BSE images were obtained with a conventional semiconductor BSE detector. A series of BSE images was acquired in air and in helium gas at 20, 40, and 50 Pa, respectively (low-voltage, low-vacuum condition). Each image shown in Figure 31 has an image size of 640 x 480 pixels and an acquisition time of 10 s. The short acquisition time and the small image size were chosen to acquire the series of BSE images under an identical SEM condition except for the pressure. Measured values of the S/N obtained from data in Figure 31

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FIGURE 31. A series of low-voltage (1.5-kV) BSE images acquired in air and in helium gas at 20, 40, and 50 Pa.

were made into a graph, shown in Figure 32. A dramatic difference in S/N (S/N in helium/S/N in air = 5.4) can be seen in the vicinity of 50 Pa, which is a pressure frequently employed in routine VP-SEM work (Oho, Asai, et al., 2000). When we can accurately measure both the highest spatial frequency and the S/N in an SEM image, "quantitative evaluation of SEM image quality," which was impossible until now, may be attempted. Studies of this kind are very

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important in the field of SEM. Fortunately, as the aforementioned special SEM image has the information needed for producing both of them, it is possible not only to take time but also to accurately measure them. This study is in the developmental stages.

VI. COLOR SEM IMAGES The SEM is very superior to the conventional light microscope (LM) in the resolution, depth of focus, ease of altering magnification, and so on. However, unfortunately we have obtained these excellent advantages in exchange for the complete lack of color information which may be effective for the observation, interpretation, and analysis of various samples. As a way to support the SEM image (monochrome), the pseudocolor (color coding) has been discussed and often utilized in many papers and works. This function may be effective for enhancement of a weak contrast, for example, voltage contrast, electron-beam-induced current (EBIC), and superimposing of SE and BSE images. Many new commercial SEMs are equipped with this function. On the other hand, the cathodoluminescence mode produces a "real" color image in SEM. However, this color is different from a natural color perceivable by the function of the human eye. The principles and applications

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of cathodoluminescence and color coding have been reviewed by Saparin and Obyden (1988). In addition, a cathodoluminescence mode, which can show two-dimensional and three-dimensional information, has been developed by Saparin et al. (1997).

A. Background of the Generation of Natural Color SEM (NC-SEM) Images SEM images with the natural colors determined by the nature of the light reflected from the object [natural color (NC)-SEM images] have been obtained by a successful combination of the low-vacuum or low-voltage SEMs, a very small-sized video microscope (VM), and a high-performance PC for digital image processing (Oho and Ogashiwa, 1996). Since the human eye is essentially the organ for observing color and can discern thousands of color shades and intensities compared with roughly only two dozen shades of gray and because the human brain judges various things according to color information from eyes, NC-SEM images are helpful for many samples. On the other hand, most ordinary microscopes can appropriately represent information on fine structures included in a certain physical phenomenon as an informative image. In other words, each microscope was invented or designed to exploit a particular physical phenomenon. Contrarily, the NC-SEM is a microscope developed by actively employing the frequency characteristic of the human visual system to improve its performance (Oho and Watanabe, 2001). TV sets, video printers, video cameras, video compression-decompression boards, and so forth are typical examples of this kind of instrument.

B. Method for Obtaining an NC-SEM Image To obtain an NC-SEM image, we employ the superimposition of the SEM image which contains structural details and the VM image which contains the color component. The VM image is obtained from the very small-sized device which combines a special LM with a color charge-coupled device (CCD) camera. Compared with the conventional LM, the VM has a much better depth of focus (DOF) in exchange for a slight degradation of resolution. The procedure for obtaining an NC-SEM image is shown in Figure 33. Since the SEM image and the VM image are different in DOF, it is necessary to improve the DOF in the VM image beforehand (if the unevenness of the sample is not too extreme, this is not necessary). So that a VM image with sufficient DOF can be obtained, a series of VM images are acquired by moving the specimen (axial scanning) and subsequently these images are superimposed. However, since the superimposed image is blurred throughout, a high-emphasis filter in the Fourier or the space domain is utilized suitably.

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FIGURE33. Procedure for obtaining an NC-SEM image from SEM and video microscope (VM) images (See color insert). Next, the RGB (red, green, blue) data in the VM image is converted to the HSI (hue, saturation, intensity) representation, which is frequently utilized for color image manipulation (we can use another color space, such as the L*a*b* model, for this purpose). Subsequently, so that an NC-SEM image with both the fine-scale structures included in the SEM image and the color information

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included in the VM image can be produced, VM brightness and VM highlight are separated from the VM-intensity component and SEM brightness and SEM highlight are also separated from the monochrome SEM image (intensity) by using a median filter with an unusually large mask size and the subtraction process. The "brightness" comes mainly from macrostructures while the "highlight" comes from microstructures (see Section III.C.). An image constructed by H (hue), S (saturation), VM-brightness, and SEMhighlight components is the NC-SEM image in question. As the characteristics of the human visual system, since the color of a very small area is not accurately recognized by the human eye, the color information on microstructures is not indicated in the NC-SEM image. If necessary, we have to increase the magnification of the NC-SEM to obtain additional information. To be more specific, H and S of the NC-SEM image are the data obtained from the VM image and its I (intensity) is constructed with VM brightness and SEM highlight. (An image constructed with H, S, and VM brightness shows only the color information.) In addition, it should be noted that fine structures are rendered conspicuous by emphasizing the SEM-highlight component in the NC-SEM image. An example of comparison between the NC-SEM image and the SEM image (uncoated color toner powder spread on a paper for a copying machine) is shown in Figure 33 (compared with all the smaller correlated images, it is rotated 90~ The effectiveness of the NC-SEM image is obvious upon observation of this sample. To be concrete, the difference in the kind of toner powder can be recognized in only the NC-SEM image, even though the SEM image is obtained from a BSE mode with material contrast. This advantage is also helpful for finding important objects in X-ray microanalysis. In the following sections, the validity of the construction method of the NC-SEM image is discussed.

C. Principle of NC-SEM Based on the Frequency Characteristic of the Human Visual System The principle of NC-SEM, which utilizes the Mach and masking effects in the frequency characteristic of the human visual system, is explained as follows (Fig. 34). The signal from a specimen viewed by human eyes has the information on surface structure and color. When the human visual system is considered, the signal is separated to the luminance channel (which relates to surface fine structures with various sizes) and the color channel [which mainly shows the information on chromaticity (it relates only to hue and saturation)] in the retina. A significant difference in characteristics of these channels appears clearly in the spatial frequency domain. That is to say, the former has characteristics of a bandpass filter with a wide bandwidth (a sort of

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FIGURE34. Principle of NC-SEM based on the frequency characteristic of the human visual system.

high-emphasis filter) and the latter has those of a low-pass filter with a narrow bandwidth. In other words, the luminance channel includes the information necessary for a high-resolution signal, and the color channel (there are strictly two channels of red-green and yellow-blue) has only the information for a low-resolution signal. The effect of the aforementioned bandpass filter

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(luminance channel) is equivalent to that of Mach bands in the space domain, which has the ability to enhance or deblur the edges (see Fig. 34). In addition, from the viewpoint of SEM, Mach bands may be visually similar to the well-known edge effect in the SE image although there is no relation at all from a physical standpoint. Under such a background, the luminance channel is replaced with the image of SEM-highlight + VM-brightness components and the color channel is formed from the image of VM-chromaticity components obtained from H and S as shown in Figure 33 [SEM and VM (intensity) images contain two different image-related contrast types, i.e., highlight and brightness components as mentioned previously]. Subsequently when the two channels are combined, an obtained color SEM image (NCSEM image) hardly receives the adverse effect visually, despite the use of low-resolution components from the relatively blurred VM image, because this procedure is based on the frequency characteristic of the human visual system. The aforementioned masking effect apparently produces this desirable situation as depicted in Figure 34. This shows an effect of concealing blur in contour parts of the chromaticity pattern by the superimposition of the luminance signal with the high-frequency component. As a result, an NCSEM image with a resolution roughly equivalent to that of the SEM image utilized in NC-SEM can be obtained up to several thousand magnifications. This limitation may be caused by a resolution of SEM as well as that of the LM, because deblurring of the color component by the masking effect is produced by a sharp SEM image. Not infrequently, a blurred SEM image of a specimen uncoated with a heavy metal is obtained in a magnification which is not too high. Also, VP-SEM used in the present study may have a comparatively low resolution in exchange for an excellent charge neutralization effect.

D. Experiment for Confirming the Usefulness of the Frequency Characteristic of the Human Visual System in NC-SEM We performed the following experiment to confirm the validity of the aforementioned discussion. A close-textured cloth (uncoated sample) was selected for this experiment, because the structures included in the SEM and VM images could be compared easily. A VP-SEM (Hitachi S-3000N, BSE mode operated with a pressure of 40 Pa and an accelerating voltage of 20 kV) and a VM (Hirox KH-2400, equipped with a variable numerical aperture) were utilized. According to the aforementioned principle and procedure, an image of SEM highlight + VM brightness (Fig. 35a) and a VM-chromaticity image (Fig. 35b) were obtained from an unprocessed SEM image (Fig. 35d) and VM image (Fig. 35e), respectively. Figure 35a corresponds to I (intensity) in the

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FIGURE35. Experimentfor confirming the usefulness of the frequency characteristic of the human visual system in NC-SEM. See text for details (See color insert).

NC-SEM image. Here, the ratio in resolution between the VM image and the SEM image (VM/SEM) is approximately 5. This value was roughly estimated from each power spectrum in Figures 35d and 35e. (A series of accurate values of the variable numerical aperture is unpublished.) As a final result, and NCSEM image (Fig. 35c) was produced from Figures 35a and 35b according to the contents of Figures 33 and 34. Despite the decided difference in resolution

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FIGURE36. Comparison between a common SEM image and an NC-SEM image. (a) SEM image of gold ore recorded under the low voltage of 2 kV. (b) NC-SEM image. Horizontal field width = 245/xm (See color insert). between both microscopy images, we cannot see the blur in Figure 35c. As a matter of fact, when we employed two examples of smaller (worse) numerical apertures, the blur also could not be seen in the NC-SEM images [Figs. 35c' (VM/SEM -~ 10) and 35c" (VM/SEM -~ 20)]. Figures 35b' and 35b' (VM chromaticity) are the components of Figures 35c' and 35c", respectively. Incidentally, the intensity components (not illustrated) of Figures 35' and 35c" are not visually distinguished from Figure 35a. As an example, a common SEM image of gold ore (low voltage of 2 kV) and an NC-SEM image are compared in Figures 36a and 36b, respectively. The NC-SEM image with both very fine structures and color information is shown in Figure 36b. It should be noted that each piece of important information is completely indicated in the NC-SEM image without the

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FIGURE37. Comparison between a VM image and an NC-SEM image. (a) VM image of a tubular flower of composite. (b) NC-SEM image (See color insert).

obstruction (i.e., adverse effects of blur in color image and change in the color). As another example, VM and NC-SEM images of a tubular flower of composite are indicated in Figures 37a and 37b, respectively. (An SEM image utilized for Fig. 37b was recorded by using the VP-SEM + a specimen stage with the cooler.) It is understood that the NC-SEM is much more useful even in a low-magnification observation which must be suitable for the VM.

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It is often difficult to perform a precise alignment of the SEM image and the VM image visually, because these images are different in magnification, and shift and rotation, respectively, even in the case of the high correlation between two images. We deal with this problem by the combination of Adobe Photoshop utilized for rotation, shift, and change of magnification, and Gatan's DigitalMicrograph utilized for the cross-correlation function in the Fourier domain. In the near future, when an acquisition system for obtaining the SEM and VM images with the identical view is successfully constructed with ease of use, the NC-SEM will be widely accepted and utilized in the field of SEM, because many NC-SEM images may be able to simplify the observation, interpretation, and analysis of various samples.

VII. AUTOMATIC FOCUSING AND ASTIGMATISM CORRECTION

Accurately focusing and correcting the astigmatism of an SEM is timeconsuming and difficult. Of course we cannot obtain the highest resolving power of the SEM without doing so. In addition, because the demand for automation of various measurements has increased (e.g., in SEM for semiconductor process evaluation), this kind of study will become more and more important. Hence, automatic focusing and astigmatism correction using digital image-processing technology is one of the most interesting areas in SEM. As far as we know, SEM manufacturers have supplied the SEMs equipped with these functions because they have adequate room for the various improvements expected over the next decade or so. Automatic focusing and astigmatism correction systems generally fall into one of two categories. One is a method of applying the derivative or gradient of the SEM signal or image, and another is a method of analyzing the power spectrum of the SEM image. When a certain solution is not considered, both methods may be influenced by the adverse effects of the noise component in the SEM signal (SEM images are frequently very noisy under various conditions as well as at high magnifications and at TV scan rates). SEM manufacturers have generally employed a method based on differentiating the video signal or a similar technique so as to reduce processing time and production costs, although this may yield unsatisfactory performance in high-resolution microscopy. In a certain SEM instrument, the optimal values of the exciting current of each lens are automatically searched out from among one million combinations. In order to more precisely perform automatic focusing and astigmatism correction, Erasmus and Smith (1982) developed an automatic method based on computing the covariance of two SEM images with the identical view. This method can operate under the condition of very noisy images, because the covariance is not essentially influenced by the noise. According to these researchers, the accuracy and speed of the method were at least as good as

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FIGURE 38. Comparison between the image covariance and the differentiation in the noise immunity. (a) Result obtained from the whole image (520 x 480 = 249, 600 pixels). A solid line and a dotted line indicate covariance and differentiation, respectively. (b-d) Results obtained from only 7200 pixels (see narrow boxes); only the image covariance with a simple curved line could detect the best focus position because of powerful noise immunity. See text for details.

those which could be achieved manually by an experienced operator, these findings came mostly from a previous study. On the other hand, a focusing and astigmatism correction method based on the power spectra of SEM specimens including highly directional features as well as for ordinary samples (Ong et al., 1997, 1998).

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Recently, in our laboratory, the aforementioned covariance method became more technologically advanced by using a special scanning (see Section V) and digitally controlling SEM instrument. If identical-view images cannot be obtained (even in one pixel drift), serious computing error beyond our expectations is introduced by the neglect of statistics (in our case, these were composed of the data acquired continuously twice from the same coordinates). The noise immunity was confirmed by the comparison of the covariance method and the conventional method which consists of a differentiation process. Figure 38 shows very noisy SEM images of an LSI chip (two images in a series of SEM images for focusing), and the behavior of the image covariance and derivative (using a 2 x 2 kernel) as a function of defocus was measured (the derivative was obtained from the averaged value of the two images with the identical view). In this case, the amount of data necessary for accurate focusing was greatly different in the derivative and covariance of the SEM image. Figure 38a was obtained from the whole image (520 x 480 = 249, 600 pixels). Both methods can detect a best focus position. On the contrary, in Figures 38b through 38d, which were obtained from only 7200 pixels (see boxes), only the image covariance with a simple curved line could detect the best position because of powerful noise immunity. It should be noted that the image covariance can find an effective signal even in a defocused image (we hardly can see the effective signal). The metrics for focusing can be operated under the condition of very noisy SEM images and be effective for many specimens which have very weak contrast.

VIII. REMOTE CONTROL OF THE S E M

In the microscopy domain, several applications of networking technology have been attempted in order to determine the potential of remote control of the SEM. Until now, whether such remote control would be useful was unknown. However, attractive data and possibilities for microscopists have already been shown in some studies. According to recent research, remote-controlled SEM using the networking technology may be helpful in remote control, remote diagnosis, virtual microscopy for education, real-time collaboration, and so forth. In fact, in the field of medicine, the prototype system, which has been used to diagnose illness from a distant location, has already approached practical use.

In order to construct a system for remote controlling an SEM, some combinations from among the modem SEM (PC-SEM) which is fully controlled by sophisticated software packages which work on the PC, local area network (LAN), Internet, Intranet, integrated services digital network (ISDN), and so forth, and the physical layer of networking (e.g., modem, Ethernet) must be

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considered according to the purpose of the system. Moreover, we may need the de facto standard software packages, such as DigitalMicrograph to include some commands for microscope control, TimbuktuPro to provide remote control capabilities, and CUSeeMe for videoconferencing as well as necessary hardware. Examples of actual applications include the following. Chumbley et al. (1995) have developed the multiuser SEM environment for supporting SEM teaching within a university. Chand et al. (1997) have constructed a World Wide Web (WWW)-controlled SEM system. It can fully remote control SEM operation through the Internet, and request SEM diagnostic parameters (e.g., beam current, magnification, etc.) and receive the response. Of course, the remote user can see and acquire small-sized live SEM images. When transferring a large-sized image (e.g., 1024 x 768 x 8 bit), however, we may need a few minutes at least. Voelkl et al. (1997) have also tried remote operation of SEM and TEM to gain a perspective on the current state of SEM and TEM instruments, networking technology, and other areas. For the aforementioned merits of remote-controlled SEM to be truly advantageous, it is necessary to improve both the microscope and the network as follows: (a) A much higher speed is required for smooth communications, and sufficient performance requires a huge investment. (b) It is necessary to redesign the electronics and the interface of present microscopes for controlling the main parameters of electron optics. These improvements are likely to follow very quickly as society demands them. Then, as many general SEM users become interested in the utility value of technology related to the Internet and it can actually be used, the true value of this kind of study and work will quickly be understood. In the immediate future, an excellent SEM operator with the ultra-high-performance SEM, optimal sample making, and scholars far away will be able to have virtual meetings for high-level real-time collaboration. Of course, this system may be useful for electron microscope-related education (e.g., an expensive SEM would be bought by an academic institution and then successfully connected to many inexpensive computers located in various places). The number of teachers would be reduced. On the other hand, if the remote diagnosis of the SEM instrument becomes routine, service may improve, for example, quick repair, reduction in repair cost, and warning of the state of the SEM instrument beforehand. (Actually, many SEM users may be able to test remote control of the SEM instrument by using ordinary software and hardware, because high technology on the PC-SEM and networking can be easily used now.) As the limited bandwidth of networks, especially the Internet, is improved, these possibilities move into a practical realm. Also, the performance improvement of the image-compression technology [e.g., JPEG (Joint Photographic Experts Group), Fractal, Wavelets, and so on] will promote the advancement

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FIGURE39. Imagecompression of an SEM image. (a) Originalimage. (b) Imagecompressed into 1/14 by JPEG. (c) Image compressed into 1/14 by fractal technology.

of this field. For instance, fractal compression might produce better results. Figure 39a is an original SEM image. This data file is compressed into 1/14 by conventional JPEG (Fig. 39b) and fractal technology (Fig. 39c), respectively. Although many unfavorable artifacts can be observed in Figure 39b, an image compressed by fractal technology with seemingly only few artifacts is produced in Figure 39c (however, SEM noise in Fig. 39a cannot be shown in Fig. 39c). These images have been expanded to show the difference clearly. The advancement of this important field is very rapid, although it is still in the developmental stages. The latest trend is that JPEG2000 based on wavelet

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transform, which is examined as a succeeding version of JPEG, may be used very widely as a standard image-compression technology because of its highperformance.

IX. ULTRALOW MAGNIFICATION AND WIDE-AREA OBSERVATION USING THE MODERN MONTAGE TECHNIQUE

A disadvantage of the SEM is the difficulty in observing very low magnification (e.g., x 15) because we may find some problems such as distortion and shading in the periphery of an SEM image acquired by low magnification. However, if possible, we would frequently like to use the very low or lower (ultralow) magnification observation during an SEM session. In the present section, a method using the PC-SEM for obtaining ultralow magnification is described. This method uses a "montage" technique: this is occasionally employed in various fields as well as in the SEM field for obtaining a combined image from a set of subimages (individual images recorded with an operating magnification). Although previously this was prepared by hand labor only, very recently works of this kind--that is, precise adjustment of SEM operating conditions, acquisition of many subimages, precise alignment of the subimages, and image processing for gray-level correction--have been considerably helped with computer technology. A successful combination is the modem SEM equipped with a motor drive stage fully controlled with a PC and digital image-processing techniques for automatic montage (Oho, Okugawa, and Kawamata, 2000).

A. Procedure and Precautions of the Montage for SEM Images We can easily find several (semi)automatic methods for the montage work. However, several problems peculiar to SEM images must be solved for the practical use of the montage. This method is roughly divided into three categories: subimage acquisition, alignment of subimages coupled with matching, and gray-level correction. The procedure for a montage through steps 1-4 is shown in Figure 40.

Step 1. First, SEM operating magnification (adoption of a nearly parallel projection condition), the number of subimages, image size, pixel overlap (enough for the matching), and so forth, which are closely related to the magnification and size of the combined image, are properly determined, and subsequently the subimages are automatically recorded. Also, compensation of the rotation angle (adjustment between the x and y directions of a specimen stage and those

318

EISAKU OHO Step 1

Sub-image acquisition 9Compensation of raster rotation 9Determination of SEM

Step 2

operating conditions

I Alignment of sub-images 9Matching 9SEM highlight component

Step 3

Gray level

Step 4

U l t r a - l o w mal~nification

correction 9Normalization by mean value and standard deviation 9Smoothing of gray level

9Combined image

observation

9Variable magnification

FIGURE40. Procedure for obtaining an ultra-low-magnification SEM image.

of electronic scanning) is semiautomatically performed with 0.1 ~ precision beforehand. In addition, we should pay attention to the charging phenomenon. Serious error may result in a combined image as shown in Figure 41 (insect), if these precautions are ignored. Step 2. A precise alignment of subimages is performed on the computer coupled with the matching technique. This step is usually not so difficult, because the raster rotation and the peripheral distortion have already been reduced sufficiently in step 1. On the other hand, despite various efforts in the SEM session, adverse effects (abnormal image contrast) originated in the charging phenomenon may disturb the automatic image alignment and accentuate the seams by both the failure of alignment and the difference of gray level in overlapping areas for the matching. In order to solve this problem, we must employ the highlight component (see Section III.C) in an SEM image. The following equation is employed as a match measure: (fh -- gh)2 ~ Minimum

(1)

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FIGURE41. Montage (insect) including serious error caused by the charging phenomenon and excessive low magnification of the subimage. wherefh and gh are highlight components of adjacent overlapping areas (identical view) in subimages ( f a n d g). Step 3. As a way to avoid visible seams where adjacent images meet, two effective techniques for gray-level correction are employed. One is the normalization of the gray level by using the mean value ( f and ~,) and the standard deviation (try and ag) of the overlapping areas according to the following equation:

g _ o g ( f _ f ) --1-g crI

(2)

That is to say, the mean value and the standard deviation are compulsorily adjusted to the same values, respectively. This technique can reduce the

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difference of gray levels in overlapping parts. Nonetheless, the combined image may have some visible seams due to the adverse effect of charging phenomena and so forth. In this situation, discontinuity in the boundary region is smoothed according to the following equation (one-dimensional processing) for obtaining smoothed gray level h(i): h(i) -- (1

i-1) J

p(i) +

(i-1)

q(i)

1 < i < j + 1

J

-

(3)

_

where j is the number of overlap pixels, and p(i) and q(i) are different gray levels of the identical point in overlapping parts. As a final result, we can observe a combined image without visible seams. Step 4. An ultra-low-magnification SEM image has not yet been obtained. The combined (large-area) image has the SEM operating magnification used in step 1, because only proper alignment and gray-level correction of many subimages have been performed. However, under these circumstances, we can quickly obtain the combined image under variable magnification by using a function (e.g., zoom tool) in various software packages for image processing. Generally, it may be a huge-sized image, as long as the number of scanning lines of a subimage has not been decreased considerably.

B. Examination o f Large Specimens

If an SEM conventionally has an ultra-low-magnification capability, this function is used frequently, because finding relationships and interactions between large objects and observation of a dynamic process over a large area are so important. In addition, it should be noted that SEM and optical images are obviously different in image characteristics (e.g., image contrast) even though their magnification is roughly equal. From another viewpoint related to recent progress in computer technology, first, many SEM images are recorded beforehand by using the present automatic system, and subsequently finding important objects is performed by semi- or full automation. Such use can be anticipated in a state-of-the-art PC-SEM. An example of ultra-low-magnification observation is shown in Figure 42a (an old wristwatch). The whole image of the internal structure of the reverse side is successfully viewed with a BSE signal which may not be disturbed by the adverse effects of the charging phenomenon. It should be noted that problems of raster rotation, peripheral distortion (working distance, 40 mm; diameter of diaphragm, 50/zm; magnification, x60), and alignment coupled with matching (number of subimages, 260) have almost been solved. As one

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FIGURE42. Whole image of an old wristwatch. (a) Ultra-low-magnification SEM image. (b) Image recorded by a digital camera. A fingerprint left as a result of grease on the hand (large dark area) can be seen only in (a). of the characteristics included in Figure 42a, surface contamination is clearly observed, because it was recorded at a low accelerating voltage of 5 kV. Especially, a fingerprint left as a result of grease on the hand is not seen by visual observation (see Fig. 42b recorded by a digital camera). As another example, an SEM image of a car key is shown in Figure 43. This is the maximum area which can be observed in our system. The limitation is mainly produced from the performance of the motor drive specimen stage.

X. ACTIVE IMAGE PROCESSING AND MULTIMODAL MICROSCOPY As discussed in the previous sections, after acquiring a digital SEM image through the AD converter, we use digital image-processing techniques for a designed purpose. In other words, a digital SEM image is first conventionally recorded, and then we determine a purpose of the image processing as the need arises; finally, a suitable image-processing technique is chosen for the recorded image. Image-processing techniques of this kind are called passive image processing. To be concrete, contrast stretching, histogram equalization, low-pass filtering, median filtering, and unsharp masking, among others, were utilized in the present article as passive image-processing techniques. We can easily find these techniques in some image analysis or retouching software. Most passive image-processing techniques often require fairly complex parameters, which differ from image to image and depend on the varying

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FIGURE43. Whole image of a car key. This is the maximum area which can be observed in our system. visual perception of operators. According to circumstances, these may adversely affect the measured value (recorded image) obtained through a scientific instrument. Some low-quality SEM images are especially disturbed by these techniques; that is, change of the measured value, unsatisfactory degree of image-quality improvement, and/or processing artifacts. Therefore, the

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adaptation of passive techniques to SEM image processing was not successful. However, if we can use SEM images that always have a constant characteristic, for example, concerning resolution, sharpness, S/N, or contrast, the foregoing problems may be reduced because some processing parameters can be determined easily. In addition, because increasing the information included in the recorded image is impossible through the image processing, it is necessary beforehand to secure an information content sufficient for utilizing a certain digital image-processing technique. These may be the roots of the concept of

active image processing. In contrast with passive image processing, when using the foregoing active image processing, we must first decide on the "purpose of the image processing in electron microscopy" before acquiring a digital SEM image. Then, in order to obtain "sufficient information for accomplishing the purpose," various operating conditions and the performance of every device related to the SEM instrument are examined and, if necessary, altered and improved. Although we recently introduced the digital scan generator, an ultra-high-efficiency YAG detector, and a video microscope in order to obtain additional information [as part of multimodal microscopy (Glasbey and Martin, 1996)], this setup is still insufficient for the successful development of various methods based on active image processing. In parallel with this consideration, some "digital image-processing techniques utilized in active processing" are also determined. Of course we purposely design these techniques so that the properties of obtained data will fit the properties required by the techniques. Although this technology may seem ordinary, it becomes essential in SEM digital imaging (Oho, Hoshino, and Ogashiwa, 1997). In the previous sections, several methods based on the concept of active image processing were already discussed. To be concrete, suppression of the aliasing error, enhancement of the BSE image, measurements of resolution and the S/N, the proposal of an NC-SEM image, metrics based on the image covariance for focusing, and ultra-low-magnification observation using the montage technique are categories of active image processing. For example, in measurements of resolution and the S/N (see Section V), "purposes of image processing" are measurement of these parameters. In order to obtain "sufficient data for attaining the purpose," we have newly developed the aforementioned digital scan system equipped with the special functions. When one is utilizing this system, "image-processing methods" for the measurements are adequate. As a result, we can obtain very high-performance methods for measuring the resolution and S/N of an SEM image. On the contrary, if we employ the concept of passive image processing--for example, use of the SEM without remodeling and the conventional power spectrum for the measurements of resolution and the S / N ~ w e obtain an unfavorable result.

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The successful combination of a highly advanced SEM equipped with various functions for obtaining necessary data and digital image-processing techniques useful for the data is an essential part of the present study. With appropriate employment of this technology, we can probably benefit from various designs because specially acquired data may always have sufficient information for attaining whatever purpose is determined. With the use of a user-friendly PC system for SEM, digital control and adjustment of SEM parameters and functions (scanning, accelerating voltage, electron dose, motor drive specimen stage, and so on) are developing more and more in order to acquire sufficient information for active image processing. On the other hand, in multimodal microscopy [e.g., a useful combination among the SEM, SPM (scanning probe microscope), and VM], this technology will be actively applied in the near future in order to improve the performance and usability of the hybrid SEM system. The author believes that as advanced new methods based on the concept of active image processing are developed, a new generation of SEM technology will follow.

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Oho, E. (1992). Automatic contrast adjustment for detail recognition in SEM images using online digital image processing. Scanning 14, 335-344. Oho, E., Asai, N., and Itoh, S. (2000). Image-quality improvement using helium gas in lowvoltage variable pressure scanning electron microscopy. J. Electron Microsc. 49, 810-812. Oho, E., Baba, M., Baba, N., Muranaka, Y., Sasaki, T., Adachi, K., Osumi, M., and Kanaya, K. (1987). The conversion of a field-emission scanning electron microscope to a high-resolution, high-performance scanning transmission electron microscope, while maintaining original functions. J. Electron Microsc. Tech. 6, 15-30. Oho, E., Baba, N., Katoh, M., Nagatani, T., Osumi, M., Amako, K., and Kanaya, K. (1984). Application of the Laplacian filter to high-resolution enhancement of SEM images. J. Electron Microsc. Tech. 1, 331-340. Oho, E., Hoshino, Y., and Ogashiwa, T. (1997). New generation scanning electron microscopy technology based on the concept of active image processing. Scanning 19, 483-488. Oho, E., Ichise, N., Martin, W. H., and Peters, K.-R. (1996). Practical method for noise removal in scanning electron microscopy. Scanning 18, 50-54. Oho, E., Ichise, N., and Ogashiwa, T. (1995). The necessity and utility of a scanning electron microscope with 4096 lines. J. Electron Microsc. 44, 390-398. Oho, E., Ichise, N., and Ogashiwa, T. (1996). Proper acquisition and handling of SEM images using a high-performance personal computer. Scanning 18, 72-80. Oho, E., and Kanaya, K. (1990). The utility of an on-line digital image recording system for SEM. Scanning 12, 141-146. Oho, E., Kobayasi, M., Sasaki, T., Adachi, K., and Kanaya, K. (1986). Automatic measurement of scanning beam diameter using an on-line digital computer. J. Electron Microsc. Tech. 3, 159-167. Oho, E., and Ogashiwa, T. (1996). A natural color scanning electron microscopy image. Scanning 18, 331-336. Oho, E., Ogihara, A., and Kanaya, K. (1990). A new non-linear pseudo-Laplacian filter for enhancement of secondary electron images. J. Microsc. 159, 33-41. Oho, E., Ogihara, A., and Kanaya, K. (1991). A method using on-line digital computer for improvement of resolution of backscattered electron images. J. Microsc. 164, 143-152. Oho, E., Okugawa, K., and Kawamata, S. (2000). Practical SEM system based on the montage technique applicable to ultralow magnification observation. J. Electron Microsc. 49, 135-141. Oho, E., and Peters, K.-R. (1994). Practical methods for digital image enhancement in SEM. J. Electron Microsc. 43, 299-306. Oho, E., Sasaki, T., and Kanaya, K. (1985). Removal of the effects of contamination in SEM image by homomorphic filtering. J. Electron Microsc. 34, 427-429. Oho, E., Sasaki, T., and Kanaya, K. (1986). A comparison of on-line digital recording with conventional photographic recording for scanning electron microscopy. J. Electron Microsc. Tech. 4, 157-162. Oho, E., Sasaki, T., Ogihara, A., and Kanaya, K. (1987). An improvement in digital homomorphic filtering and its practical applications to SEM images. Scanning 9, 173-176. Oho, E., and Toyomura, K. (2001). Strategies for optimum use of superposition diffractogram in scanning electron microscopy. Scanning 23, 351-356. Oho, E., and Watanabe, M. (2001). Natural color SEM based on the frequency characteristic of human visual system. Scanning 23, 24-31. Ong, K. H., Phang, J. C. H., and Thong, J. T. L. (1997). A robust focusing and astigmatism correction method for the scanning electron microscope. Scanning 19, 553-563. Ong, K. H., Phang, J. C. H., and Thong, J. T. L. (1998). A robust focusing and astigmatism correction method for the scanning electron microscope. Part III: An improved technique. Scanning 20, 357-375.

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Oron, M., and Gilbert, D. (1976). Combined SEM-minicomputer system for digital image processing. Proceedings of the Ninth Annual Conference on Scanning Electron Microscopy Symposium, Part I, edited by O. Johari. Chicago: liT Research Institute, pp. 120-127. Otaka, T., Moil, H., Yamada, O., and Todokoro, H. (1995). Critical dimension measurement scanning electron microscope for ULSI. Hitachi Rev. 44, 113-118. Postek, M. T., and Vladar, A. E. (1996). Digital imaging for scanning electron microscopy. Scanning 18, 1-7. Reimer, L. (1985). Scanning Electron Microscopy (Springer Series in Optical Sciences, Vol. 45). Berlin/New York: Springer-Verlag, pp. 13-56. Reimer, L., Volbert, B., and Bracker, P. (1978). Quality control of SEM micrographs by laser diffractometry. Scanning 1, 233-242. Reimer, L., Volbert, B., and Bracker, P. (1979). STEM semiconductor detector for testing SEM quality parameters. Scanning 2, 96-103. Rosenfeld, A., and Kak, A. C. (1982). In Digital Picture Processing, 2nd ed. NY, in Computer Science and Applied Mathematics, Vol. 1. Ed: W. Rheinboldt. Academic Press, pp. 209-352. Saparin, G. V., and Obyden, S. K. (1988). Colour display of video information in scanning electron microscopy: principle and applications to physics, geology, soil science, biology, and medicine. Scanning 10, 87-106. Saparin, G. V., Obyden, S. K., Ivannikov, P. V., Shishkin, E. B., Mokhov, E. N., Roenkoy, A. D., and Hofmann, D. H. (1997). Three-dimensional studies of SiC polytype transformations. Scanning 19, 269-274. Suganuma, T. (1985). Measurement of surface topography using SEM with two secondary electron detectors. J. Electron Microsc. 34, 328-337. Thong, J. T. L., and Breton, B. C. (1992). In situ topography measurement in the SEM. Scanning 14, 65-72. Unitt, B. M., and Smith, K. C. A. (1976). The application of the minicomputer in scanning electron microscopy, in Proceedings of the Sixth European Congress on Electron Microscopy, Vol. 1. Jerusalem: TAL International, pp. 162-167. Voelkl, E., Allard, L. F., Nolan, T. A., Hill, D., and Lehmann, M. (1997). Remote operation of electron microscopes. Scanning 19, 286-291. Wang, D. C. C., Vangnucci, A. H., and Li, C. C. (1983). Digital image enhancement: a survey. Comput. Vis. Graphics Image Proc. 24, 363-381. Welter, L. M., and McKee, A. N. (1972). Observations on uncoated, nonconducting or thermally sensitive specimens using a fast scanning field emission source SEM, in Proceedings of the Fifth Annual Conference on Scanning Electron Microscopy Symposium, Part I, edited by O. Johari. Chicago: IIT Research Institute, pp. 161-168. White, E. W., McKinstry, H. A., and Johnson, G. G., Jr. (1968). Computer processing of SEM images, in Proceedings of the Symposium on the Scanning Electron Microscope Symposium, edited by O. Johari. Chicago: IIT Research Institute, pp. 95-103. Yew, N. C., and Pease, D. E. (1974). Signal storage and enhancement techniques for the SEM, In Proceedings of the Seventh Annual Conference on Scanning Electron Microscopy Symposium, Part I, edited by O. Johari. Chicago: IIT Research Institute, pp. 191-198.

Index

A

C

Active image processing, 323-324 Add-on lens attachments. See Scanning electron microscopes (SEMs), add-on lens attachments Aharonov-Bohm effect, 174, 191-196 A1-Pd, structure of, 76-79 A1-Pd-Mn, structure of, 69-73 Amplitude division interferometry, 197-199 Analog image-processing techniques, 252 Astigmatism corrections, 312-314 Atom clusters arrangements of, 64-68 columnar, 51-52 structural models of, 58-63 2.0- and 3.2-nm, 54-58 Autocorrelation function (ACF), 297-299

Charged dielectric spheres interpretation of results, 216-219 numerical simulations of contour maps, 219-221 recording and processing of electron holograms, 212-216 research in, 243 Chung-Everhart energy distribution, 139 Color images. See Images, SEM natural color Columnar atom clusters, 51-52 Complex hysteresis smoothing (CHS), 266-271 Contamination problems, 285 Contour maps, 206, 208, 226-227 numerical simulations of, 219-221,233-235 Crystalline approximants, 19-20, 43, 74-76, 79-80 CsC1 quasiperiodic superlattice, 13-15 Cubic convolution method, 260, 261-263 Cursor width (CW), 266-268, 271 Cutoff distance, 189-190

B Backscattered electron (BSE) images, 279-283 B ilinear interpolation method, 263-264, 284 Biprism effect of, on image wavefunction, 182-187 wave-optical analysis of electron, 179-182 Brightness image, 275, 276

D de Broglie wavelength, 191 Decagonal contrast, 39 Decagonal quasicrystals electron diffraction of, 27-31 HRTEM of, 35 329

330

INDEX

Decagonal quasicrystals, structure of A1-Pd, 76-79 of A1-Pd-Mn, 69-73 columnar atom clusters, 51-52 crystalline approximants, 74-76, 79-80 with 0.4-nm periodicity, 52-68 with 1.2-nm periodicity, 68-76 with 1.6-nm periodicity, 76-80 Deflection voltage contrast spectrometers, 144-151 Delta function, 3, 4 Diffractogram for measuring highest spatial frequency, 295-301 Digital image processing. See Scanning electron microscopes (SEMs), digital image processing and Dislocations, in icosahedral quasicrystals, 49-51 Double-exposure electron holography, 210-212

E Electric scalar potential, 191 Electromagnetic potentials, 174 Electron beam diameter, 289-295 Electron beam testers (EBTs), 135, 136 Electron diffraction of quasicrystals for decagonal, 27-31 fivefold/pentagonal superstructure, 29 for good- and poor-quality, 23-24 for icosahedral, 24-27 use of, 22-23 Electron holography See also p-n junctions, electron holography and reverse-biased

amplitude division interferometry, 197-199 charged microtips, 235-241 contour maps, 206, 208, 219-221, 226-227, 233-235 double-exposure, 210-212 influence of, 174 in-line optical bench, 207-208 Mach-Zehnder interferometer and phase-difference amplification, 208-210, 224 reconstruction and processing, 205-210, 212-216 recording, 196-205 research on, 174-175,243-244 wave-front division interferometry, 199-205 Electron interference experiment, 193-196 Electron-specimen interaction Aharonov-Bohm effect, 174, 191-196 biprism effects on image wavefunction, 182-187 phase-object approximation, description of, 177-179 phase-object approximation, validity of, 188-191 wave-optical analysis of electron biprism, 179-182 Electrostatic field model, 227-233 See also Electron holography charged microtips and, 235-241 Enhanced image, 276 Even parities, 11 Everhart-Thornley detection system, 145, 159

F Fast Fourier transform (FFT), 300 Fast-scan images, SEM and, 273

INDEX Fibonacci sequence, 3 Field emission guns (FEGs), 174 Focusing method, 288-289 Fourier transforms, 3-4, 189 Frank-Kasper-type icosahedral phase, 39 Fresnel approximation, 188 Fresnel fringe, 186, 187 Fresnel hologram, 198

G Glaser field distribution, 93 Glaser paraxial theory, 182

I-I Hanning window, 300-301 Helmholtz equation, 232 High-angle annular detector dark-field scanning transmission electron microscopy (HAADF-STEM) of quasicrystals, 2 sample preparations, 20-22 Highest spatial frequency, measuring, 295-301 Highlight filter, 274-279 Highlight image, 275, 276 High-resolution transmission electron microscopy (HRTEM), images of quasicrystals, 2 decagonal, 35 icosahedral, 33-34 sample preparations, 20-22 Histogram-processing techniques, 264 Holography. See Electron holography Homomorphic filtering, 285

331

Horseshoe electrostatic deflector, 146-147, 149, 150

Icosahedral quasicrystals electron diffraction of, 24-27 HRTEM of, 33-34 Icosahedral quasicrystals, structure of atomic arrangements, 39-44 defects, 44-51 dislocations, 49-51 linear phason strain, 44-49 topological features, 36-39 Image enhancement methods, SEM and, 264-265 backscattered electron (BSE) images, 279-283 contamination problems, 285 factors affecting, 273-274 highlight filter, 274-279 vibration problems, 284-285 Images active image processing, 323-324 brightness, 275,276 enhanced, 276 final, 276 highlight, 275, 276 lattice versus structure, 33 measurement and analysis, 287-289 passive image processing, 321-323 quality problems for SEM, 255, 257-258 quality superiority for SEM, 254-255 reduced, 276 resolution, 295-301 Images, SEM natural color, 303 generation of, 304

332

INDEX

Images, SEM natural color (Cont.) method for obtaining, 304-306 principle of, and frequency characteristic of human visual system, 306-308 validity of frequency characteristic of human visual system, 308-312 Immersion (in-lens) lenses compared to conventional lenses, 90-97 defined, 87 magnetic, 103-120 mixed-field, 121-125, 157-162 multibore, 169-170 resolution limits, 97-102 In-line optical bench, 207-208 Interference distance, 199, 203 Interferometry amplitude division, 197-199 Mach-Zehnder, and phase-difference amplification, 208-210, 224 wave-front division, 199-205 Internal subspace, 3, 5 Interpolation method, bilinear, 263-264, 284

K KEOS software, 94, 106, 108, 111 Kirchhoff integral, 184

L Laplace's equation, 228, 232 Laplacian filter, nonlinear pseudo, 278 Latex spheres, 243 Lattice images, 33 Least-square techniques, 288

Linear phason strain, 15-20 in icosahedral quasicrystals, 44-49 Low-pass filter, SEM images and, 264 LSI chip example, 276-278

M Mach-Zehnder interferometer and phase-difference amplification, 208-210, 224 Mackay icosahedral atom cluster, 40 Magnetic immersion lens, 91-92, 96-97 backscattered electron, 112, 114 description of, 103-120 examples, 112-116 image demagnification, 107-108 predicted probe diameter-probe current dependence, 108-109, 111 prefocusing, 106-107 saturation effects, 110, 111 secondary electron trajectories, 111-112, 118 specimen movement, 116-117 tube and ring magnets, 105-106 working distance, 107 Material contrast, 151-156 Mathematica, 189 Microtips, electrostatic field model and, 235-241 Mixed-field immersion lens, 94, 96 backscattered electron and low energy landing, 121,123-125 description of, 121-125 obtaining secondary electron energy spectrum with, 157-162 secondary electron trajectories, 121,122 working distance, 123

INDEX Montage technique for observing ultra-low magnification, 317-321 Multibore objective lenses, 163-170 Multichannel voltage contrast spectrometers, 137-138 Multiple detectors, 288 Multislice method, phase-object approximation and, 188-191

N NaC1 quasiperiodic superlattice, 11-13 Ni-rich basic structure, 55 Noise ratio, signal-to-, 301-303 Noise removal methods, SEM and complex hysteresis smoothing (CHS), 266-271 in fast-scan images, 273 field-emission sources, 285-286 low-pass filters, 264 problem with, 265-266

O Objective lenses, multibore, 163-170 Odd parities, 11 One-dimensional quasiperiodic lattices, 3-10 Open-loop voltage contrast spectrometers, 136-137

description of, 177-179 validity of, 188-191 Phason strain, random and linear, 15-20 Physical subspace, 3, 5 Piezoelectric field, 244 p-n junctions, electron holography and reverse-biased, 175 electrostatic field model, 227-233 numerical simulations of contour maps, 233-235 optical reconstruction and interference fringes, 224-227 solutions, 227-235 specimen preparation and observations, 221-224 Precrossover point, 106-107 Projection method, 3--4

Q Quasicrystals See also under type of

electron diffraction of, 22-31 fivefold/pentagonal superstructure, 29 HRTEM of, 31-35 sample preparations, 20-22 Quasiperiodic lattices crystalline approximants, 19-20 one-dimensional, 3-10 random and linear phason strain and, 15-20 two-dimensional, 10-15

P Parabolic cylinder functions, 230 Passive image processing, 321-323 Penrose lattices, 6-10 Phase-difference amplification, 208-210, 211 Phase-object approximation (POA)

333

R Random phason strain, 15-20 Reference wave, 175 Remote control, SEM, 314-317 Resolution limits, for immersion lenses, 97-102

334 Retarding field lens, 89, 93 Retarding field voltage contrast spectrometers, 135, 136

S Sampled signal, 255,257-258 Scalar diffraction theory, 188 Scanning electron microscopes (SEMs) comparison of conventional and immerison objective lenses, 90-97 resolution limits for immersion lenses, 97-102 retarding field lens, 89 types of lenses, 87-89 Scanning electron microscopes (SEMs), add-on lens attachments See also Spectrometers advantages of, 89-90 magnetic lenses, 103-120 mixed-field lenses, 121-125 multibore objective lenses, 163-170 single-pole lens attachments, 125-134 size issues, 102-103 Scanning electron microscopes (SEMs), digital image processing and active image processing, 323-324 automatic focusing and astigmatism corrections, 312-314 color images, 303-312 contamination problems, 285 contrast improvement methods, 264

INDEX conventional statistical measurement, 287 electron beam diameter, 289-295 expansion models, 260-264 fast-scan images, 273 foreign material and defect classification, 287-288 highest spatial frequency, measuring, 295-301 image enhancement methods, 264-265, 273-286 image quality problems, 255, 257-258 image quality superiority, 254-255 image recording and processing, 253-254 montage technique for observing ultra-low magnification, 317-321 noise removal methods, 264, 265-273 on-line versus conventional recording, 254 optimal scanning for, 257 overscanning, 257-258 passive image processing, 321-323 remote control, 314-317 research on, 252-253 signal-to-noise ratio, 301-303 surface topography measurement, 288-289 underscanning, 257, 258-260 vibration problems, 284-285 Scanning transmission electron microscope (STEM), 289-295 Schrtidinger equation, 177, 178 Signal-to-noise ratio (S/N), 301-303 Single-pole lens attachments, 125-134

INDEX backscattered electron and low energy landing, 133-134 noise, 131, 133 objective, 163-168 secondary electron trajectories, 130, 131,132 Wien filter, 131,133 Sommerfeld's secondary wave, 232 Space-charge distribution, 244 Spectrometers deflection voltage contrast, 144-151 material contrast, 151-156 mixed-field immersion lens, 157-162 multichannel voltage contrast, 137-138 open-loop voltage contrast, 136-137 retarding field voltage contrast, 135, 136 time-of-flight voltage contrast, 138-144 Split aperture, 145-146, 147 Stereometric technique, 288 Structure images, 33 Surface topography measurement, 288-289 Symptomatic therapy, 287

T Taylor expansion, second-order, 186 Three-dimensional Penrose lattice, 10 Time-of-flight voltage contrast spectrometers, 138-144 Time-probability density function, 138 Transmission electron microscopy (TEM)

335 See also High-angle annular

detector dark-field scanning transmission electron microscopy (HAADF-STEM); High-resolution transmission electron microscopy (HRTEM) phase-object approximation and, 188 Transmission function, 177 Two-dimensional quasiperiodic superlattices, 10-15 Type I superlattice, 11

U Ultra-low magnification, montage technique for observing, 317-321 Unsharp masking, 278

V Vector potential, 191 Vibration problems, 284-285 Voltage contrast deflection, 144-151 material contrast, 151-156 mixed-field immersion lens and, 157-162 multichannel, 137-138 open-loop, 136-137 retarding field, 135, 136 time-of-flight, 138-144

W Wave-front division interferometry, 199-205

336 Wavefunction, biprism effects on image, 182-187 Wave-optical analysis of electron biprism, 179-182 Weber-Hermite functions, 230 Weber's equation, 230

INDEX Wentzel-Kramers-B rillouin (WKB) approximation, 191 Wien filter, 131,133, 144, 149 Window, 3, 5 Working distance, 87, 107, 123

FIG. 4.33. images.

Procedure for obtaining an NC-SEM image from SEM and video microscope (VM)

FIG. 4.35. Experiment for confirming the usefulness of the frequency characteristic of the human visual system in NC-SEM. See text for details.

FIG. 4.36. Comparison between a common SEM image and an NC-SEM image. (a) SEM image of gold ore recorded under the low voltage of 2 kV. (b) NC-SEM image. Horizontal field width = 245 /.zm.

FIG. 4.37. Comparison between a VM image and an NC-SEM image. (a) VM image of a tubular flower of composite. (b) NC-SEM image.

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90090

ISBN

0-12-014764-5