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Author: Paula M. Vilarinho | Yossi Rosenwaks | Angus Kingon

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Scanning Probe Microscopy: Characterization, Nanofabrication and Device Application of Functional Materials

NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Division Sub-Series I. II. III. IV. V.

Life and Behavioural Sciences Mathematics, Physics and Chemistry Computer and Systems Science Earth and Environmental Sciences Science and Technology Policy

IOS Press Kluwer Academic Publishers IOS Press Kluwer Academic Publishers IOS Press

The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized bij scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organised and there are currently Five Sub-series as noted above. Please consult the following web sites for information on previous volumes published in the Series, as well as details of earlier Sub-series. http://www.nato.int/science http://www.wkap.nl http://www.iospress.nl http://www.wtv-books.de/nato-pco.htm

Series II: Mathematics, Physics and Chemistry – Vol. 186

Scanning Probe Microscopy: Characterization, Nanofabrication and Device Application of Functional Materials edited by

Paula Maria Vilarinho University of Aveiro, Portugal

Yossi Rosenwaks Tel Aviv University, Ramat - Aviv, Israel and

Angus Kingon NCSU, Raleigh, NC, U.S.A.

Kluwer Academic Publishers Dordrecht / Boston / London Published in cooperation with NATO Scientific Affairs Division

Proceedings of the NATO Advanced Study Institute on Scanning Probe Microscopy: Characterization, Nanofabrication and Device Application of Functional Materials Algarve, Portugal 1–13 October 2002 A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 1-4020-3018-5 (PB) ISBN 1-4020-3017-7 (HB) ISBN 1-4020-3019-3 (e-book)

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.

Printed on acid-free paper

All Rights Reserved © 2005 Kluwer Academic Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.

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TABLE OF CONTENTS

PREFACE ON THE NATO ASI ON THE BOOK ACKNOWLEDGEMENTS PHOTO OF THE GROUP ADDRESS LIST OF THE AUTHORS LIST OF PARTICIPANTS

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Part I – Fundamentals of Functional Materials FUNCTIONAL MATERIALS: PROPERTIES, PROCESSING AND APPLICATIONS P.M. Vilarinho 3 SCALING OF SILICON-BASED DEVICES TO SUBMICRON DIMENSIONS A.I. Kingon

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UNSOLVED PROBLEMS IN FERROELECTRICS FOR SCANNING PROBE MICROSCOPY J.F. Scott 51

Part II – Fundamentals of Scanning Probe Techniques PRINCIPLES OF BASIC AND ADVANCED SCANNING PROBE MICROSCOPY 77 D.A. Bonnell and R. Shao NANOSCALE PROBING OF PHYSICAL AND CHEMICAL FUNCTIONALITY WITH NEAR-FIELD OPTICAL MICROSCOPY L.M. Eng 103 NANOSCALE ELECTRONIC MEASUREMENTS OF SEMICONDUCTORS USING KELVIN PROBE FORCE MICROSCOPY Y. Rosenwaks and R. Shikler 119 EXPANDING THE CAPABILITIES OF THE SCANNING MICROSCOPE K.F. Kelly, Z.J. Donhauser, B.A. Mantooth and P.S. Weiss

TUNNELING 153

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FUNCTIONS OF NC – AFM ON ATOMIC SCALE S. Morita, N. Oyabu, T. Nishimoto, R. Nishi, O. Custance, I. Yi and Y. Sugawara 173

Part III – Application of Scanning Techniques to Functional Materials SCANNING PROBE MICROSCOPY OF PIEZOELECTRIC AND TRANSPORT PHENOMENA IN ELECTROCERAMIC MATERIALS S.V. Kalinin and D.A. Bonnell 199 SFM-BASED METHODS FOR FERROELECTRIC STUDIES A. Gruverman

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SCANNING TUNNELING SPECTROSCOPY: LOCAL DENSITY OF STATES AND SPIN DISTRIBUTION OF INTERACTING ELECTRON SYSTEMS M. Morgenstern 251 NANOINSPECTION OF DIELECTRIC AND POLARIZATION PROPERTIES AT INNER AND OUTER INTERFACES IN FUNCTIONAL FERROELECTRIC PZT THIN FILMS 275 L.M. Eng MICROSCALE CONTACT CHARGING ON A SILICON OXIDE S. Morita, T. Uchihashi, K. Okamoto, M. Abe and Y. Sugawara

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CONSTRUCTIVE NANOLITHOGRAPHY S.R. Cohen, R. Maoz and J. Sagiv

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NANOMETER-SCALE ELECTRONICS AND STORAGE K.F. Kelly, Z.J. Donhauser, P.A. Lewis, R.K. Smith and P.S. Weiss

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Part IV – Contributed papers STM TIPS FABRICATION FOR CRITICAL DIMENSION MEASUREMENTS A. Pasquini, G.B. Picotto and M. Pisani

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SCANNING PROBE MICROSCOPY CHARACTERIZATION OF FERROELECTRICS DOMAINS AND DOMAINS WALLS IN KTiOPO4 363 C. Canalias, R. Clemens, J. Hellström, F. Laurell, J. Wittborn and H. Karlsson IMAGING LOCAL DIELECTRIC AND MECHANICAL RESPONSES WITH DYNAMIC HETERODYNED ELECTROSTATIC FORCE MICROSCOPY D.R. Oliver, K.M. Cheng, A. Pu, D.J. Thomson and G.E. Bridges 371

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AFM PATTERNING OF SrTiO3-δ THIN FILMS AND DEVICE APPLICATIONS L. Pellegrino 387 NANOSCALE INVESTIGATION OF A RAYLEIGH WAVE ON LiNbO3 J. Yang and R. K Koch

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SCANNING CAPACITANCE FORCE MICROSCOPY AND KELVIN PROBE FORCE MICROSCOPY OF NANOSTRUCTURES EMBEDDED IN SiO2 G. Tallarida, S. Spiga and M. Fanciulli 405 ELECTRICAL CHARACTERISATION OF III-V BURIED HETEROSTRUCTURE LASERS BY SCANNING CAPACITANCE MICROSCOPY 413 O. Douhéret, K. Maknys and S. Anand PROBING THE DENSITY OF STATES OF HIGH TEMPERATURE SUPERCONDUCTORS WITH POINT CONTACT TUNNELING SPECTROSCOPY L. Ozyuzer, J.F. Zasadzinski, N. Miyakawa and K.E. Gray 425 ANNEALING INFLUENCE ON CO ULTRATHIN FILM MORPHOLOGY IN MBE GROWN Co/Au BILAYERS A. Wawro, L.T. Baczewski, P. Pankowski, P. Aleszkiewicz, M. Kisielewski, I. Sveklo and A. Maziewski 435 CORRELATION BETWEEN THE SURFACE RELIEF AND INTERFACES STRUCTURE OF Fe/Cr SUPERLATTICES AND ELECTROMAGNETIC WAVES PENETRATION A.Rinkevich, L.Romashev and V.Ustinov 443 MAGNETORESISTANCE AND MICROSTRUCTURE OF MAGNETIC THIN FILM MULTILAYERS J. Neamtu, M. Volmer 449 SPM INVESTIGATION OF THIOLATED GOLD NANOPARTICLE PATTERNS DEPOSITED ON DIFFERENT SELF-ASSEMBLED SUBSTRATES 457 F. Sbrana, M. T. Parodi, D. Ricci and E. Di Zitti AFM OF GUANINE ADSORBED ON HOPG UNDER ELECTROCHEMICAL CONTROL A. M. Chiorcea and A.M. Oliveira Brett 467 DYNAMICS IN MODEL MEMBRANES AND DNA-MEMBRANE COMPLEXES USING TEMPERATURE CONTROLLED ATOMIC FORCE MICROSCOPY Z.V. Leonenko and D.T. Cramb 475

INDEX

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PREFACE Today, a wide range of analytical techniques can be used for materials research. The most commonly used high-resolution surface analysis techniques are Scanning Electron Microscopy (SEM) and Scanning Probe Microscopy (SPM). Although both techniques resolve surface structure down to the nanometer scale, the different image formation mechanisms result in different types of information about the structure of the surface, making these techniques complementary. In SEM, an electron beam, guided by a complex array of lenses, interacts with the sample and electrons are emitted from the sample, either as back-scattered or secondary electrons. Secondary electron emission is commonly used for surface morphology analysis. The first SEM equipment was constructed between 1938 and 1942. Improvements in resolution and the development of several types of detectors for local compositional analysis (X-rays, Auger electrons, backscattered electrons, cathodoluminesce) took place since then. Compared to electron microscopy, SPM techniques are quite new. Scanning Tunneling Microscopy (STM), the earliest of the SPM techniques, was invented in 1981 at IBM Zurich Research Laboratory by G. Binnig and H. Roher. STM was the first instrument to generate three dimensional real-space images of surfaces with atomic resolution. This invention earned them the Nobel Prize in Physics in 1986. In STM a sharp conducting tip, with a bias voltage applied between the tip and the sample, scans the surface of the sample. The scanning motion is at the angstrom level and the tip does not contact the sample. The resulting tunnelling current, exponentially dependent on the tip – sample spacing, is the signal used to create the STM image. Since 1981, a large family of SPM related techniques, based on various types of interactions between the tip and the sample, has been developed. It has been demonstrated that the SPM approach allows manipulation of single atoms and molecules. Various SPM techniques such as atomic force microscopy (AFM), magnetic force microscopy (MFM), electrostatic force microscopy (EFM), scanning capacitance microscopy (SCM), near-field scanning optical microscopy (NSOM) and others were proved to be capable of measuring the local physical properties of materials with nanoscale resolution. As a consequence, presently there is an explosion in the application of SPM techniques in a wide spectrum of fields of science, ranging from condensed matter physics, chemistry and materials science, to medicine and biology. Currently, SPM is widely used for nanoscale characterisation of materials by using mechanical, electrical, magnetic, optical and chemical interactions between the probing tip and the surface. Compared to electron microscopy techniques (SEM, TEM, HRTEM, etc), SPM is a low cost analytical method in terms of equipment, maintenance, accessories and sample preparation. In addition, it can operate in ambient m environment forbidden to electron microscopy. Consequently, it is expected that a growing number of university research groups and R&D industry divisions will acquire such equipment for research, quality control and fabrication. At the same time, the role of SPM in the field of nanotechnology is also growing in importance. The continuous need for the miniaturisation of electronic devices, with improved speed and functionality, has been a ix

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constant driving force pushing towards the development and manipulation of nanoscale devices. However further scaling of digital electronic devices necessitates fabrication and application of materials with nanoscale features. In this sense, SPM is becoming an indispensable tool, playing a key role in nanoscience and nanotechnology. One of most rapidly evolving, yet relatively unknown, fields of material science and of functional materials is the field of ferroelectric thin films. These materials possess a unique set of physical properties, such as switchable polarization, piezo- and pyroelectricity and high nonlinear optical activity, which make them extremely attractive for a number of applications. Over the last 10 years there have been serious efforts to develop ferroelectric memories, which combine nonvolatility with high-speed access, almost unlimited endurance and extreme radiation hardness. Due to these significant advantages of ferroelectric memories, it is expected that they will continue to replace other types of nonvolatile memory systems in many applications. In addition, ferroelectric materials can be used in a variety of other devices that exploit their unique properties, such as piezoelectric transducers and actuators, t infrared sensors, optical switches and computer displays. Recent advances in the processing of high quality ferroelectric films resulted in development of 4 Mb nonvolatile ferroelectric random access memories (NVFRAMs) at Samsung and Matsushita. However, the tremendous potential of ferroelectric films is far from being realized, as further developments in this area are hindered not only by the integration issues related to the present state of the NVFRAM technology, but also by a lack of fundamental knowledge related to reliability, performance and scaling of ferroelectric devices. Integration of ferroelectric thin films into Gigabit memory devices requires substantial improvement in the understanding of the properties and device physics of these materials, and this in turn requires the implementation of new tools suitable for in situ testing of ferroelectric nanostructures. One of the most promising approaches is based on using scanning probe techniques. Recently, SFM has been successfully applied for nanoscale characterization of ferroelectric thin films. Several qualitative experiments demonstrating the capabilities of SFM in controlling domains as small as 20-50 nm in diameter have already been performed. SFM was also used for nanoscale studies of degradation effects, such as ferroelectric fatigue and retention loss. Another very important branch of applications is related to SPM-based electrical characterization. As the characteristic dimensions of electronic devices continue to shrink, the ability to characterize their electronic properties at the nanometer scale has come to be of outstanding importance. Scanning probe microscopy has opened new opportunities to measure semiconductor electronic properties with unprecedented spatial resolution. For example, scanning spreading resistance microscopy (SSRM), and scanning capacitance microscopy (SCM) have already demonstrated device measurements with ~2 and 10-20 nm spatial resolution respectively. Kelvin probe force microscopy (KPFM) has been used for measuring electrostatic forces and electric potential distribution and has found many diverse applications in recent years. In the area of functional molecular materials, SPM is also proving to be an invaluable tool. It is being used as a probe to contact molecular structures in order to characterize their electrical properties, as a manipulator to assemble nanoparticles and nanotubes into simple devices, and as a tool to pattern molecular nanostructures.

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To contribute to the development in these technological and scientific fields, there is a need to “collect” and disseminate this new and growing knowledge at the cross disciplinary level. The NATO Advanced Study Institute (ASI) on “Scanning Probe Micrsocopy: Characterization, nanofabrication and device application of functional materials,” held in Albufeira, Algarve, Portugal from the 1stt to the 13th October 2002, by bringing together highly expertise researchers from the nanoscale techniques and functional materials disciplines, by presenting the fundamentals, technological advances and the needs for further developments in their respective fields and by stimulating active discussions, contributed to foster new scientific contacts and to develop new ideas in the field.

Paula Maria Vilarinho Aveiro, Portugal, June 2004 Yossi Rosenwaks Ramat – Aviv, Israel, June 2004 Angus I. Kingon Raleigh, USA, June 2004

ON THE NATO ASI The main objective of this ASI was to disseminate knowledge concerning the new and emerging applications of SPM to the field of material science, especially in the areas of characterisation, device application and nanofabrication of functional materials. Timing of the proposed meeting was extremely appropriate, as the subject reflects the growing importance of SPM as a key tool for further development of nanoscale science and technology. Rapid progress in the field of SPM and functional materials demands energetic efforts on organising meetings to contribute to the scientific education of a new generation of engineers and scientists with new expertise and deeper understanding of nanoscale device physics. The ASI was attended by 83 researchers, postt doctoral and students from 24 countries, including: Austria, Belgium, Canada, Czech Republic, France, Germany, Greece, Israel, Italy, Japan, Korea, Latvia, Portugal, Poland, Romania, Russia, Spain, Slovenia, Sweden, Switzerland, Turkey, Ukraine, United Kingdom and United States of America. To achieve the proposed objectives the scientific programme of the ASI comprised three main parts: Part I - SPM Techniques and Functional Materials, Part II – SPM in Functional Materials: Characterization and Part III – SPM in Functional Materials: Nanofabrication and Device Application. Introduction, development and the expanding capabilities of SPM, as a powerful nanoscience technique, were addressed in Part I. To complete Part I, the scientific and technological importance of the fundamental knowledge of structure / properties / applications relationships of functional materials were presented and discussed. In Part II recent progress in nanoscale SPM characterization of advanced functional materials, namely semiconductors, magnetics, dielectrics, ferroelectrics, were covered. The newest advances on fabrication of nanostructures and the links between nanofabrication and nanoscale characterization were discussed in Part III. During 10 working days these topics were systematically presented and treated in depth by an interdisciplinary team of leading scientists in lecture format. This tutorial activity was complemented by rump sessions on related subjects, namely: (i) Comparision and direction of SPM methods and (ii) Fabrication: future of the bottom up approach. In addition, to stimulate scientific contacts and discussion, poster sessions and short presentations by the participants were held on their own scientific activities in the field. At these discussions the participants were motivated to expand themselves, to be innovative in the field of characterisation and fabrication with SPM, and to present their own innovative ideas on the topic. The theme for this ASI has its own scientific value. Its uniqueness is in the combination of the fundamental nanoscale research with the progress in fabrication of realistic nanodevices. In addition, it developed new educational advances. By bringing together leading researchers from the material science and SPM communities, relevant information and experience was conveyed that allowed scientists to learn more about the actual developments and future trends of each field. Contacts among the scientists xiii

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were fostered and in this way contributed to the development of this new and technological important interdisciplinary field of science. For PhD students and postdoc scientists, participation in this meeting ledd to significant improvement in their knowledge of the basic properties of functional materials, as well as in application of SPM techniques. With SPM becoming a ‘must-know’ technique in many scientific disciplines, this meeting helped to improve the qualification level of university graduates from different countries and provided manpower with new expertise in the field of nanotechnology and SPM.

ON THE BOOK This book is the output of the ASI NATO meeting on Scanning Probe Micrsocopy: Characterization, nanofabrication and device application of functional materials. The book content reflects the scientific content of the school by itself presenting the main lectures that were given, and some of the participants works that were also presented and discussed during the school. The book is organised in four parts. Part I, Fundamentals of Functional Materials, is an introductory chapter that addresses the general properties of functional materials, highlights some of the unsolved problems of functional materials and reports the progress in silicon technology from the perspective of scaling to submicron devices and the expected performance at the end of the silicon scaling era. Part II, Fundamentals of Scanning Probe Techniques, presents the principles and basics of various SPM techniques, such as near-field optical microscopy, kelvin probe force microscopy and non-contac – AFM, showing the capacity of the techniques to measure the local physical properties of materials with nanoscale resolution. The application of SPM techniques to the characterization of specified functional materials such as piezoelectric ceramics and ferroelectric materials is discussed in Part III, Application of Scanning Tecnhiques to Functional Materials, which also presents the utilization of such techniques to the fabrication of some nano electronic devices. Part IV, Contributed papers, includes some of the R&D work related to the utilization of SPM techniques to functional materials, as presented by the participants.

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ACKNOWLEDGMENTS

The Directors of the ASI (P. M. Vilarinho and Y. Rosenwaks) acknowledge the financial support of NATO, through the Scientific f and Environmental Affairs Division, of the Instituto de Cooperação Científica e Tecnológica (ICCTI) of the Portuguese Ministry of Science and Tecnology, of the Luso – American Foundation (FLAD), of the Fundação para a Ciência e Tecnologia (FCT), of the Portuguese Ministry of Science and Technology and of the University of Aveiro. The travel support of some of the participants by the Portuguese, Greek and Turkish NATO Agencies and National Science Foundation (NSF), USA is also acknowledged. The Directors are grateful to Isabel Salvado, Aiying Wu, Javier Perez de la Cruz and Gerardo Gonzalez for their help with all the organizational details before and during the school. The Directors wish to acknowledge the assistance of Alexander Tkach in the text preparation process. The Directors are particularly thankful to the authors for their contribution to this book. One of the directors (P. M. Vilarinho) expresses her gratitude to Angus Kingon. The idea of organising such an event came from m the discussions had with Angus Kingon during her stay at North Caroline State University (NCSU), USA, on a sabbatical leave. The recognition that Scanning Probe Microscopy was an emerging technique, namely in the field of Functional Materials and that was not addressed in a systematic way, combining expertises coming from different fields of materials science, such as physics, processing and device construction, was the embryo m of this ASI. Alexei Gruverman is also thanked for his valuable contribution and help in finding the lecturers and for the critical analysis of the proposal for such ASI.

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Participants in the Group 38. Markys CAIN 39. Jenica NEAMTU 40. Angus KINGON 41. Cristina ROTARU 42. Hiroshi TOKUMOTO 43. Karlis KUNDZINS 44. Nassima KHALFAOUI 45. Lutfi OZYUZER 46. Alexei GRUVERMAN 47. Luca PELLEGRINO 48. Viktor BOVTUN 49. Paulo MOREIRA 50. Derek OLIVER 51. Lukas ENG 52. Vladimir SHVARTSMAN 53. Claudia RITTER 54. Bert STEGEMANN 55. Maria SHVEBELMAN 56. Oren TAL 57. Isabel SALVADO 58. Waldemar NAWROCKI 59. Gabriella LEO 60. Valeria FERRANDO 61. Grazia TALLARIDA 62. Jianshu YANG 63. Márcia C. NEVES 64. Carlota CANALIAS 65. Dawn A. BONNELL 66. Ana-Maria CHIORCEA 67. Zoia LEONENKO 68. Anton MAIDYKOVSKI 69. Esra OZKAN 70. Ana VIANA 71. Metan TANOGLU 72. Kevin F. KELLY 73. Pascal MARCHET 74. Paula Maria VILARINHO

1. Andrey GAL 2. Olivier DOUHERET 3. Dionizy CZEKAJ 4. Agata Lisiska CZEKAJ 5. Krzysztof PIELICHOWSKI 6. Javier PÉREZ 7. Ioannis TSIAOUSSSIS 8. Marian LEHOCKY 9. Martin PUSTKA 10. Fabiano ASSI 11. Stefan KUYPERS 12. Marlies VAN BAEL 13. Vismants ZAULS 14. Sascha KREMMER 15. Domenique WEINER 16. Sangmin SHIN 17. James SCOTT 18. Gerardo GONZALEZ 19. ALBERTO PASQUINI 20. Stefano GARIGLIO 21. Francesca SBRANA 22. Adrian Mihail MOTOC 23. Cristiano ALBONETTI 24. Maria José MATOS 25. Yossi ROSENWAKS 26. Andrei KHOLKIN 27. Teresa SIERRA GARCIA 28. Harvey AMORIN 29. Jesús RICOTE 30. Elena SOLERA CARLAVILLA 31. Alexander TITKOV 32. Monika KRISTKOVA 33. Maciej WOJTAĝ 34. Silvia KARTHÄUSER 35. Markus MORGENSTERN 36. Lech Tomasz BACZEWSKI 37. Sidney COHEN

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ADDRESS LIST OF THE AUTHORS Germany Phone: 49 351 463 3427 Fax: 49 351 463 7065 Email: [email protected]

Paula Maria VILARINHO Department of Ceramics and Glass Engineering University of Aveiro 3810-193 Aveiro Portugal Phone: 351 234 370354/259 Fax: 351 234 425300 Email: [email protected]

Yossi ROSENWAKS Department of Physical Electronics Faculty of Engineering Tel-Aviv University Ramat-Aviv 69978 Israel Tel: 972-3-6406248/7974 Fax: 972-3-6423508 Email: [email protected]

Angus KINGON North Carolina State University Materials Research Center, NCSU 1001 Capability Drive, Centennial Campus Raleigh NC 27695-7919 USA Phone: (voice Email) 1 919 515 8636 Fax: 1 919 515 3419 Email: [email protected]

Kevin F. KELLY ECE Dept., MS-366 Rice University PO Box 1892, Houston, TX 770051892 USA Phone: 1 713 348-3565 Fax: 1 713 348-5686 Email: [email protected]

James SCOTT Department of Earth Science University of Cambridge Cambridge CB2 3EQ England Phone: 44 1223 333461 Fax: 44 1223 333450 Email [email protected]

Seizo MORITA Department of Electronic Engineering Graduate School of Engineering, Osaka University 2-1 Yamada-Oka, Suita, Osaka 5650871 Japan Phone: 81 6 6879 7761 Fax: +81 6 6879 7764 Email:[email protected]

Dawn A. BONNELL Materials Science and Engineering Director, Center for Science and Engineering of Nanoscale Systems The University of Pennsylvania 3231 Walnut Street Philadelphia, PA,19104 USA Phone: 215 898 6231 Fax: 215 573 2128 Email: [email protected]

Alexei GRUVERMAN North Carolina State University Department of Materials Science and Engineering 1010 Main Campus Drive, EGRC, Rm 339, Campus Box 7920 Raleigh, NC 27695 USA Phone: 1 919 513-3319 Fax: 1 919 515-3027

Lukas ENG Institut für Angewandte Photophysik Technical University of Dresden 01062 Dresden xxi

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Email: [email protected]

Email: [email protected]

Markus MORGENSTERN Institute of Applied Physics Hamburg University Jungiusstrasse 11 D-20355 Hamburg Germany Phone: 49 40 42838 3282 Fax: 49 40 42838 2944 Email: [email protected]

Luca PELLEGRINO Dipartimento di Fisica Università di Genova via Dodecaneso 33 16146 Genova Italy Phone: 39 010 353 6323 Fax: 39 010 311066 Email:[email protected]

Sidney COHEN Department of Materials and Interfaces The Weizmann Institute of Science Rehovot 76100, Israel Phone: 972 8-934 2703 or 3422 Fax: 972 8 934 4137 Email: [email protected] Alberto PASQUINI Strada Delle Cacce 73 10135 Turin Italy Phone: 39 011 3977471 Fax :39 011 3977459 Email :[email protected] Carlota CANALIAS Department of Physics Royal Institute of Technology Roslagsvägen 30b, S-11347 Stockholm Sweden Phone: 46 8 55378192 Fax: 46 8 55378216 Email: [email protected] Derek OLIVER Electrial & computer Eng. University of Manitoba Winnipeg MB R3T 5V6 Canada Phone: 1 204 4749563 Fax: 1 204 2614639

Grazia TALLARIDA Laboratorio MDM-INFM Via Olivetti 2 20041 Alrate Brianza, Milan Italy Phone: 39 039 6036540 Fax: 39 039 6881175 Email: [email protected] Olivier DOUHERET Department of Microelectronics & Information Technology KTH, Royal Institute of Technology Isafjordsgatan 22, P.O. Electrum 229 S-164 40 KISTA, Sweden Phone: 46 8 752 1166 Fax: 46 8 750 5173 Email: [email protected] Lutfi OZYUZER Department of Physics Izmir Institute of Technology Gulbahce Campus, Urla TR-35437 Izmir Turkey Phone: 90 232 4987518 Fax: 90 232 4987509 Email: [email protected] Lech Tomasz BACZEWSKI Institute of Physics Polish Academy of Sciences Al. Lotnikow 32/46, 02-668 Warszawa,

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Poland Phone: 48 22 8431331 Fax:48 22 8430926 Email:[email protected] Anatoly RINKEVICH Institute of Metal Physics Ural Division of Russian Academy of Sciences 18, S.Kovalevskaya St, GSP-170 Ekaterinburg 620219 Russia Phone: 007 3432 499395 Fax: 007 3432 745244 Email: [email protected] Jenica NEAMTU ICPE-CA, Advanced Research &Development Institute for Electrical Engineering, SplaiulUnirii 313, Bucharest 030138 Romania Fax. 40 21 346 82 99 Email:[email protected]; [email protected] Francesca SBRANA DIBE-Università di Genova via All’Opera Pia 11a-16145 GenovaItaly Phone: 39 010 3532167 Fax: 39 010 3532290 Email: [email protected] Ana-Maria CHIORCEA Instituto Pedro Nunes Quinta da Nora, Rua Pedro Nunes 3030-199 Coimbra Portugal Phone: 351 239 700 978 Fax: 351 239 700 965 Email: [email protected] Zoia LEONENKO Department of Chemistry

University of Calgary 2500 University Drive NW Calgary, AB, T2N 1 N4, Canada Phone: 1 403 220 6248 Fax: 1 403 289 9488 Email: [email protected]

List of participants Wagistrasse 2 CH-8952 Schlieren Phone: 41(1)6336168 Fax. 4181)6331048 Email: [email protected]

Cristiano ALBONETTI Institute for Study of Nanostructured Material (I.S.M.N.) C.N.R. Bologna Via Gobetti 101, 40129 Bologna ITALY Phone: +390516398523 Fax: +390516398539 Email: [email protected]

Lech Tomasz BACZEWSKI Institute of Physics Polish Academy of Sciences Al. Lotnikow 32/46, 02-668 Warszawa, POLAND Phone: 48-22-8431331 Fax: 48-22-8430926 Email:[email protected]

Marin ALEXE Max-Planck Institute Microstructural Physics Weinberg, 2, D – 06120, Halle Germany Phone: 49-351-463 33427 Fax: Email: [email protected]

Andreja BENCAN Institute Jozef Stefan Jamova 39, 1000 Ljubljana Slovenia Phone: 38614263126 Fax: 38614263126 e-mail: [email protected]

Harvey AMORIN Ceramics and Glass Engineering Department University of Aveiro 3810-193 Aveiro PORTUGAL Phone: 351 234 370354 Fax: 234 351 425300 Email: [email protected]

Dawn A. BONNELL Materials Science and Engineering Director, Center for Science and Engineering of Nanoscale Systems The University of Pennsylvania 3231 Walnut Street Philadelphia, PA, 19104 Phone: 215 898 6231 Fax: 215 573 2128

Fabiano ASSI ETH Zurich

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Email: [email protected] Viktor BOVTUN Microelectronics Department National Technical University Ukraine “Kiev Polytechnic Institute” Peremogy ave. 37, 252056 Kiev UKRAINE Phone: 38 (044) 236 96 76 Fax: 38 (044) 236 96 76 Email: [email protected] Markys CAIN National Physical Laboratory Queens Road, Teddington Middlesex, Tw11 0lw UK Phone: 44 (0) 208 943 6599 Fax: 44 (0) 208 943 2989 Email:[email protected] Carlota CANALIAS Department of Physics Royal Institute of Technology Roslagsvägen 30b, S-11347 Stockholm SWEDEN Phone: +46 8 55378192 Fax: +46 8 55378216 Email: [email protected] Elena SOLERA CARLAVILLA Electroceramic Department

INSTITUTO DE CERAMICA Y VIDRIO CSIC -CAMPUS DE CANTOBLANCO Camino de Valdelatas, s/n 28049 -MADRID SPAIN Phone: (34) 91 735 5840 fax (34) 91 735 5843/5 EMAIL: [email protected] Ana-Maria CHIORCEA Instituto Pedro Nunes Quinta da Nora, Rua Pedro Nunes 3030-199 Coimbra PORTUGAL Phone: 351 239 700 978 Fax: 351 239 700 965 Email: [email protected] Sidney COHEN Department of Materials and Interfaces The Weizmann Institute of Science Rehovot 76100, Israel, Phone: 972 -8-934 -2703 or 3422 Fax: 972-8-934-4137 Email: [email protected] Agata Lisiska CZEKAJ Department of Materials Science University of Silesia

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Part I – Fundamentals of Functional Materials

FUNCTIONAL MATERIALS: PROPERTIES, PROCESSING AND APPLICATIONS

P.M. VILARINHO Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, 3810 – 193, Aveiro, Portugal

Contents 1. 2. 3. 4. 5. 6.

Introduction Fundaments of Properties of Functional Materials: General Concepts Functional Materials Functional Materials Processing Technologies Applications of Functional Materials Future Trends in Functional Materials

“On September 7, 2001, doctors in the United States performed the first long distance operation, with surgeons in New York performing a laparoscopic cholecystectomy on a patient in Strasbourg, France. The surgery was successful, and the patient was discharged from the hospital with no complications 48 hours later. The ability to perform complex surgical manipulations from remote locations will eliminate geographical constraints and make surgical expertise available throughout the world, improving patient treatment and surgical training. Needless to say, the potential uses of such remote, robotic technology are boundless, not only in medical settings but in search and rescue missions, scientific discovery missions, and countless other arenas…” – in http://www.stanford.edu/telemedicine [1]. Keywords: Piezoelectrics, Pyroelectrics, Ferroelectrics, Incipient Ferroelectrics, Ferroelectric Relaxors, Applications, Fabrication

1. Introduction It is extremely difficult for anybody not to recognise the importance of the so called Information Technology. Even for those not aware of it, Information Technology dominates our life today. There are numerous examples m with the “first long distance medical operation” being just one among them. The introduction of robotic and computer technology into surgical operations allows surgical procedures to be carried out from a distance (telesurgery). Besides the expert surgeons, these telesurgeries 3 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 3-33. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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require a secure, reliable and fast network connecting the two points (surgeon to patient) and a robotic system capable of translating the surgeon's hand movements in place A (New York, in this case) to the instruments inside the patient in place B (Strasbourg, France) [1]. From a narrower perspective - materials science and technology - this is possible due to the sustained research and development of materials, namely functional materials. As the name suggests, the definition of functional materials reflects the ability of a material to perform a certain “function” under a determined stimulus. In this general definition a wide spectrum of materials can be included together with an ample range of material properties and applications. However, the classification off functional materials is usually related to materials whose “function” f is associated with their electric, magnetic, and or optical properties. This group of functional materials mainly includes dielectrics, pyroelectrics, piezoelectrics, ferroelectrics, ferroelectric relaxors, incipient ferroelectrics, semiconductors, ionic conductors, superconductors, electro-optics and magnetic materials. It is common to identify the class of functional materials with applications such as Materials for Information Technology, Materials for Electrical Energy Conversion, Materials for Biologic Applications, Materials for Space Technology, among others. The application of functional materials, typified by electroactive materials including piezoelectrics, pyroelectrics and ferroelectrics, for sensing and actuation spans most if not all industrial sectors. This includes medical diagnostics such as ultrasonic imaging, aerospace such as accelerometers and micropositioners, automotive such as solid state piezoelectric fuel injectors, and chemical and process control, which requires the use of thermal, strain and force sensors. Although the discovery of certain properties off functional materials goes back to the nineteenth century some of the materials that exhibit such properties became useful only during the Second World War and others very recently. (see references [2, 3] for more details on the history of such functional materials). The utility off functional materials in these applications reflects their unique properties, such as spontaneous polarization, piezoelectricity, superconductivity and magnetoresistance. All these properties are directly dependent on the chemical composition, singularities of the crystallographic structure and manufacture process. The knowledge of the relationships between composition, structure, processing and properties allows the production of improved materials for known applications as well as for new uses and in an economic way. Materials scientists, chemists and physicists have been searching for these relationships for years. The characterization of the bulk properties of functional materials and their description by theoretical models were their main activities in the recent past. Nowadays a considerable knowledge on the relationships between composition, microstructure, processing and macroscopic properties can be established for a wide variety of functional materials. But researchers developing and producing materials try to optimize materials to meet tomorrow’s needs and this “materials bulk approach” has recently changed. If the progressive miniaturisation of electronic components is to proceed with the speed of the past decades devices of nanometric dimensions will be needed soon (see part I of this book by A.I. Kingon). Figure 1 shows the scales involved in some of the actual microelectronic devices and those that will be involved in the future. Starting from m the semiconductor of microelectronics and

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following the Moore's law, which predicts the exponential decrease of the size of technological components [4], a progression into the field of nanoelectronics is happening, and because of the approaching of a limit to the size of current electronic systems molecular electronics is gaining importance. Molecular electronics looks for the fabrication with electronic devices of molecular dimensions and also from molecular components so as to perform functions in electronic circuitry now performed by semiconductor devices. Individual molecules are very small and electronic devices constructed from molecules will be very small (100 x smaller than semiconductor-based counterparts). Besides the dramatic reduction in the size, the ability to produce billions of identical molecules is important benefits of molecular electronics [5, 6]. For more details on molecular electronics t see part III of this book.

Figure 1. Dimensions of microelectronic devices: microsensors, microelectricalmechanical systems (MEMS), nanoelectricalmechanical systems (NEMS), micromachines, integrated circuits (IC) [7].

Consequently, the drive for smaller size, greater functionality and the replacement of products by services emphasise on the less mature study of nanostructural attributes of materials: electrical, optical, magnetic and biological. Many of these attributes are properties of films, surfaces or interfaces. The use of conventional techniques is inadequate to evaluate properties at a nanoscale level, to design nanofeatures and to

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hold a position of functional molecules. Nanoscale tools are required. Due to its nanometer lateral and subangstrom vertical resolution Scanning Probe Microscopy (SPM), with its various techniques, is now a fundamental tool for the nanoelectronics era. The following text is mainly dedicated to some functional materials, technologically important in the present day. The text is not intended to treat all the functional materials and their peculiarities. In view of this and in relation to the final applications emphasis is given to a few electrical properties, such as piezoelectricity, pyroelectricity and ferroelectricity, the family of materials, for example perovskite type and materials formulations and their fabrication. The limitations of the materials and processes will be highlighted from the point of view of the new materials requirements and industry demands, and related with the future “materials nanostructure t approach”. The aim of this text is to introduce the reader to the following texts in which the Scanning Probe Techniques devoted to the characterization (part II), fabrication and device application of functional materials (part III) are presented and discussed. Along the text, references to extended literature or text books on the reported topics will be given.

2. Fundaments of Properties of Functional Materials: General Concepts In this section, the most representative properties of some functional materials, such as dielectrics, pyroelectrics, piezoelectrics, ferroelectrics, ferroelectric relaxors and incipient ferroelectrics are briefly presented in order to justify their actual applications. Exhaustive descriptions on these properties can be found in several text books and reviews [8-15]. Dielectrics are a class of materials with high electrical resistivities. Dielectrics do not conduct electricity due to the very low density of free charge carriers and, because of this, they can perform insulating functions. However, dielectrics exhibit a number of unique assets when placed under the effect of an electrical field. The ability of the dielectric to store charge in a capacitor is related to the polarization of the dielectric under the electric field and is the simplest practical application of a dielectric. Nonetheless, the various polarization responses of the dielectric under an electric field are being increasingly used in micro and nanoelectronic devices and open a wide range of new devices. When an electric field E is applied to an ideal insulator, there is no long-range charge transport, as in a conductor, solely a short-range dislocation of the positive and negative charge centre which causes the appearance of electric dipole moments in the material. The material is called a dielectric. The dielectric is said to be polarised. Several polarization mechanisms were identified: atomic, ionic, dipolar and space charge; each is related to the nature of the charged entities which suffer charge displacement or to the nature of the displacement. The charge displacement process in dielectrics is systematically described in references [11, 15]. If there is a linear relationship between the applied field E and the induced polarization P and P disappears when E is removed the material is called a linear dielectric. If at zero field conditions a mechanical stress provokes the development of electric charges (polarization) these materials are called piezoelectric. Piezoelectricity is

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the ability of certain crystalline materials to develop an electrical charge proportional to a mechanical stress or vice versa. Of the 32 classes of symmetry, 11 possess a centre of symmetry and are non-polar. For these an applied stress t results in symmetrical ionic displacements so that there is no net change in the dipole moment. The remaining 21 point groups do not have a centre of symmetry (i.e. non-centrosymmetric) and possess one or more crystallographically unique directional axes; all non-centrosymmetric point groups, except the point group 432, exhibit piezoelectric effect along unique directional axes. In a piezoelectric the relationship between the applied deformation and the induced polarization is linear and reversible. This effect is different from the electrostriction effect. All the materials suffer a small change in dimensions when subject to an electric field. However, if the resultant strain is proportional to the square of the field, the effect is called electrostriction (equation 1). x = ξE 2 , (1) where ζ is the electrostrictive coefficient. In a piezoelectric the magnitude of P depends on the magnitude of the stress and the sign of the produced charge depends on the type of applied stress (tensile or compressive). The polarization generated from a mechanical stress is called the direct or generator effect, while the converse or motor effect is associated with the mechanical deformation derived from an applied electric field. The relationships between the strain x, stress σ, electric field strength E, electric polarisation P in a piezoelectric material are: P = dσ (direct effect), (2) x = dE (converse effect), (3) where d is the piezoelectric coefficient or strain constant (dij relates a field along the i axis to the strain in the j direction). The d33 coefficient is the most commonly cited of these coefficients and it is the corresponding coefficient for both strain and field along the polar axis. Another important parameter to evaluate the performance of a piezoelectric is the effective coupling coefficient (kefff) which is a measure of the amount of electrical energy that is converted into strain and defined as: electrical energy converted in mechanical energy (4) Keff 2 = (direct effect) input electrical energy mechanical energy converted in electrical energy 2 Keff = (converse effect) (5) input mechanical energy For the fundamentals of piezoelectricity references [8, 9, 14] are suggested. If, in zero field conditions, there are dipolar moments due to a non-symmetric structure, the materials will have spontaneous polarization and they are called pyroelectrics. Ten of the crystallographic groups contain a unique polar axis and are, therefore, spontaneously polarised. In a pyroelectric the change in temperature produces a change in spontaneous polarisation. The pyroelectric effect can be described in terms of the pyroelectric coefficient p that relates to the change in spontaneous polarisation dPs as a function of temperature (dT) as: p = dPs / dT (6) As for piezoelectrics, since polarisation is a vector, the value of the pyroelectric coefficient is different depending on the direction in which it is measured: pi = ¨Psi / ¨T (7)

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where i = 1,2,3. Two figures of merit are defined for the pyroeletric performance of a material FV and FD in the form of: FV = p / 'c İ , (8) where İ is the dielectric permittivity and 'c is the volume specific heat, which describes the effectiveness of a pyroelectric element in terms of materials properties and usually has units of m2/C. In an imaging array, where noise is of primary concern, the figure of merit FD, defined as: (9) FD = p / ('c İ1/2 tan1/2į) , where tanį is the loss and typically expressed in (µm3/J)1⁄2 is more useful. Some pyroelectric materials have an additional property; the direction of spontaneous polarisation can be switched by an applied electric field. These materials are called ferroelectrics. If the spontaneous polarization direction is changed by mechanical stresses the materials are called ferroelastic. Ferroelectricity and ferroelasticity, in opposition to the other two polar phenomena, cannot be predicted from the crystalline symmetry but need to be experimentally verified. All ferroelectrics are piezoelectric and pyroelectric but a piezoelectric or a pyroelectric is not inevitably a ferroelectric. For example, materials such as ZnO and tourmaline ((Na,Ca)(Li,Mg,Al)3(Al,Fe,Mn)6(BO3)3(Si6O18)(OH)4) have a non-reversible dipole but are still pyroelectric. For a material that contains electric dipoles, the local electric field will promote the dipole alignment in a certain region, contributing to the increase of the polarization, which, by itself, will promote the increase of the local field. These co-operation phenomena will align the dipoles along the same direction, resulting in the spontaneous polarization of the material. Consequently, the electric polarization in pyroelectrics and ferroelectrics does not vary linearly with the applied field and hence they are called non-linear dielectrics. In ferroelectrics the relationship between the applied field and the polarization is described by a hysteresis loop (figure 2) similar to the one exhibited by the ferromagnetic materials. The name ferroelectrics refers to the analogy with ferromagnetic behaviour although, for ferroelectrics, the phenomena is not related with the presence of iron. The application of a low electric t field to a non-polarized ferroelectric provokes a linear and reversible increase of the polarization as the field increases. The slope of this variation corresponds to the initial dielectric permittivity of the material. As the field increases, the further increase of the polarization is non-linear and, for high field values, the variation of P with E is small and approaches to a saturation value. The polarization value extrapolated for zero field (E=0) gives the saturation polarization Ps. When the external field is removed, the polarization does not fall to zero, keeping a remnant value designated as remnant polarization Pr. To cancel this value, a field in the opposite direction and of magnitude Ec should be applied. This field Ec required to reduce the polarization to zero is called the coercive field. Further increasing of the field in the negative direction will cause the switching of the polarization. Reversing the field direction once again will complete the hysteresis cycle.

9

Figure 2. Typical hysteresis loop of a ferroelectric (adapted from [11]).

The hysteretic behaviour of ferroelectrics is related to their domain structure. A ferroelectric possesses regions with uniform polarization called domains. Within a domain all the dipoles are aligned in the same direction, differing from the direction of the neighbour domain in such a way that for zero applied field the material macroscopic polarization is null. The several existing domains are separated by interfaces called domain walls which typically have the dimensions of 1 to 2 lattice spacing. For materials with a tetragonal symmetry the polarization direction between domains can form 180˚ or 90˚ angles. For a low applied electric field (region of linear relationship between P and E) the field is not large enough to switch any domain, therefore the ferroelectric will behave as a linear dielectric. As the applied electric field increases, a number of domains, which have a polarization opposite to the direction of the field, will be switched in the direction of the applied field and the polarization will increase rapidly until all domains are aligned in the field direction. Eventually, for a high applied field, the sample will only be a mono domain. As the field strength decreases, the polarization will generally decrease but not return to zero. When the field is reduced to zero the majority of the domains will remain aligned in the applied field direction and the ferroelectric will exhibit a remnant polarization Pr. Usually, the value of Pr is inferior to the value of the saturation polarization Ps since some of the domains will reassume their original orientation. The process of switching all the domains under a single orientation is called poling. The remnant polarization Pr in a ferroelectric cannot be removed until the applied field in the opposite (negative) direction reaches the value of the coercive field Ec. Further increasing of the field in the negative direction will cause a complete alignment of the dipoles in this direction. Reversing the field direction once again will complete the hysteresis cycle. A ferroelectric material can undergo a phase transition adopting a non-polar centrosymmetric structure at a temperature called TC (the temperature of the phase transition). Above TC, with the loss of the polar structure, t the material does not exhibit

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spontaneous polarization and it is said to be paraelectric. Below TC, due to the appearance of the spontaneous polarization and to the mutual interaction between the dipoles which causes a significant increase of the local field, the material exhibits ferroelectricity. The structural phase transition from the paraelectric to the ferroelectric phase is reversible. Near TC due to a distortion in the crystalline lattice as the phase structure changes, the thermodynamic properties, including dielectric, elastic, optical, and thermal constants show an anomalous behaviour; the permittivity raises, reaching a maximum at TC (figure 3). In the ferroelectric region the increase of the thermal agitation as the temperature approaches TC facilitates the growing of the domains oriented along the field. Above TC the permittivity of the material decreases and at the same time a sudden reduction of the resistivity and a marked increase in the losses is observed.

Figure 3. Dielectric permittivity as a function of temperature for BaTiO3 [17].

In most ferroelectrics, the temperature dependence of the dielectric constant above TC can be described by the Curie-Weiss law: İr = İ0 (1 + C/(T í Θ) (10) where İr is the dielectric permittivity of the materials, İ0 is the dielectric permittivity of vacuum, C is the Curie-Weiss constant, T is the temperature and Θ is the Curie-Weiss temperature, which is in general smaller than TC. For first order transitions Θ < TC, while for second order phase transitions Θ = TC. In ferroelectrics the non-linear variation of P as a function of E is also detected in the optical properties. Electro optical effects such as square birefringence (Kerr effect) and linear birefringence (Pockles effect) are some of the optical effects whose magnitude depends on the intensity and direction of the applied field. By analogy with magnetic dipoles, the relative orientation of electric dipoles may create different polarization patterns; electric dipoles can orient in a parallel or antiparallel way. If the electric dipoles are oriented in an antiparallel way, visualised as upward and downward directions, the total polar momentt is null and the material is said to be antiferroelectric. Antiferroelectrics (antipolar materials) can revert to a ferroelectric state when subjected to a sufficiently high electric field. The polarization

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dependence on the electric field of an antiferroelectric is displayed in figure 4. For low electric fields the induced electric polarization is quite low. Only after the application of a high enough electric field, able to break the antiferroelectric order, the polarization increases. For high fields a hysteric behaviour, similar to the one observed in ferroelectrics, is visible [16, 17].

Figure 4. Antiferroelectric hysteresis loops [18].

For additional information on pyroeletricity and ferroeletricity the references [9, 10, 13] should be consulted. Although the majority of the ferroelectrics, such as BaTiO3 (BT), exhibit a transition from a low symmetry and temperature ferroelectric phase to a high symmetry and temperature paraelectric phase, this is not a necessary condition to possess ferroelectricity. Some ferroelectrics, such as BaMgF4 (BMF), melt at temperatures lower than the transition temperature. On the other hand, incipient ferroelectrics (or quantum paraelectrics) such as SrTiO3 (ST), that exhibit structural phase transitions do not possess ferroelectric behaviour. ST falls into the unique category of ferroelectrics known as incipient ferroelectrics along with KTaO3, CaTiO3 and TiO2 [19]. As the temperature decreases, the cubic ST undergoes a transition to the tetragonal phase at 105 K [20] and at 65 K a transition from the tetragonal to the orthorhombic structure [21]. However, no ferroelectric long range order is established. The first transition is purely structural with almost no influence on the dielectric response. For T > 50 K the temperature dependence of dielectric permittivity of ST obeys Curie-Weiss law, although, at lower temperatures the permittivity versus temperature dependence deviates from Curie-Weiss law and saturates reaching high values (~24000 for single crystals [22]) as the temperature approaches 0 K. Quantum fluctuations of the atomic positions are thought to suppress the ferroelectric transition and lead to a stabilization of paraelectric state characteristic for a quantum paraelectric limit [22]. Consequently, the ferroelectric anomaly can be easily induced in incipient ferroelectrics by the application of high enough electric field [20], uniaxial stress [23], chemical substitutions in the lattice [24-26] or oxygen isotope exchange [27]. A certain class of ferroelectrics, designated as relaxors, differenciate themselves from conventional ferroelectrics by the following typical characteristics [28], depicted in figure 5:

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a) A broad phase transition, in which the sharp peak in the dielectric permittivity versus temperature curve related to the phase transition of a classical ferroelectric at Curie temperature at TC is substituted in a ferroeletric relaxorr by a broad peak that occurs over a range of temperatures. This particular feature can also be seen in other properties related to the phase transition. b) A strong frequency dependence of the dielectric properties. While the properties of classic ferroelectrics do not vary intensely with the frequency in the radio frequency range, the dielectric properties of relaxors are strongly dependent on the frequency in rf frequency range. The peak of the dielectric permittivity decreases in value and shifts to higher temperatures as the frequency increases. c) The absence of a macroscopic polarization below the temperature of the permittivity maximum. At temperatures well below the permittivity maximum, no evidence of optical anisotropy or of X-ray line splitting is found. This characterizes the absence of a macro-volume changing to a polar phase, usually observed in classic ferroelectrics. No macroscopic domain state can be observed except when strong electric fields are applied (during hysteresis or under bias). There is not a uniform atomic shift throughout the entire crystal, therefore the net polarization remains nil, but microscopic polar domains develop. In the absence of a field, relaxors contain very small nanodomains that differ from each other in some detail of structure or composition

Figure 5. Schematic representation of (a) dielectric permittivity and (b) spontaneous polarization versus temperature for classic ferroelectrics (curve 1) and ferroelectric relaxors [29].

A common feature of relaxors, in both perovskite and tungsten bronze structures, is that more than one type of ions occupies equivalent crystallographic lattice sites [28]. Although this is a necessary condition, it is not a sufficient one, for there are numerous solid solutions where sharp behaviour is preserved throughout the whole composition range. However, it is generally accepted that ferroelectric relaxors are highly heterogeneous materials and that the compositional fluctuations markedly affect the macroscopic response. There is strong evidence that the physics of relaxorr behaviour is intimately linked to nanoscale chemical heterogeneity. The ferroelectric relaxor behaviour has been the subject of research for many years; several models have been proposed to explain it and have been reviewed by Ye [30]. Smolenskii et al. [31] originally proposed that the dielectric “diffuse phase transition” of relaxors was due to the local compositional fluctuations. In A(B’B’’)O3 perovskites the random distribution

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of B cations creates a range of Curie temperatures that results in the broadened macroscopic variation of permittivity versus temperature. Though this model fails to explain why the “transition temperature” (temperature of the maximum) shifts to higher temperatures as the frequency increases. Later Cross [28] considering the regions of short-range chemical order as nanoscale polar clusters, proposed that the dipole moment of the clusters thermally switches between equivalent directions so macroscopic polar domains never form after the structural transition, as in classical ferroelectrics (superparaelectric model). By analogy with superparamagnetic behaviour it was proposed that there is no interaction between clusters. In this model the frequency dependence of the temperature of the dielectric maximum should obey a simple Debye relationship. However, physical unrealistic values for both activation energy and characteristic frequency were obtained. The dipolar glass-like behaviour, suggested by Viehland et al. [32], is an extension of the superparaelectric model, in which the interactions between polar clusters are considered. Accordingly, the interactions between the polar microregions control the kinetics of the polarization fluctuations and the development of a frustration state near the freezing temperature (Tf) leading to a broadening of the relaxation-time distribution and strong deviations from the Curie Weiss behaviour near Tf. Above Tf the ferroelectric clusters are superparaelectric with dipole moments fluctuating between identical orientations and, as the temperature decreases, the superparaelectric moments freeze into a glassy state due to correlations between dipole moments. The polar nanosized regions are claimed to appear at a temperature above the dielectric maximum, at the so-called Burns temperature [33, 34], and to grow during the cooling till the freezing temperature. Another theory invokes the contributions from a quenched random field which is again due to the compositional heterogeneity [35]. In this model the relaxor state is a ferroelectric state broken up into nanodomains under the constraint of quenched random fields. Charged compositional fluctuations are considered as sources of random fields. In a more recent theory, Spherical random-bond - random-field (SRBRF) model [36], the relaxor is considered as a new type of dipolar glasses, namely, the spherical vector glass, in which the polar clusters are formed when two or more cations, moving in a multisite potential, create a m fluctuations – single reorientable polar unit. Accordingly the regions of compositional “chemical clusters” are essentially static. The above mentioned models generally agree thatt the physical origin of the dielectric peak in relaxors is then different from the one in classical ferroelectrics; in relaxors it is related to the thermal slowing of dynamic polar nanoregions rather than a paraelectric-ferroelectric phase change as in classical ferroelectrics. However, the relationships between the local chemical heterogeneities, the local polar clusters and their dynamics are not yet clearly established. Some of the models consider the regions of short-range chemical order as nanoscale polar clusters [28, 32, 37] and others, the charged compositional fluctuations as sources of random fields. A universal model for ferroelectric relaxorr behaviour is still missing. The full understanding of the relaxor behaviour, due to its nanometric scale, requires the investigation of the polar cluster dynamics at a local level. Until now the majority a of the results on the polar nanocluster structure of relaxors have been acquired by indirect approaches. The classical visualization of ferroelectric domains by optical methods, which have a limited resolution, is not suitable for this purpose. Methods with higher resolution are required.

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The high spatial resolution, down to a few nanometers, and the high sensitivity to local polarization make Piezo Force Microscopy (PFM) a well suited technique for these studies. Indeed, Scanning Force Microscopy (SFM) has been recently successfully applied for nanoscale characterization of ferroelectric thin films [38]. Several qualitative experiments demonstrating the capabilities off SFM in controlling domains as small as 20-50 nm in diameter have already been performed (see A. Gruverman, part II of this book). However, few results have been reported on the observation of the polar structure of relaxors via PFM [39-41]. 3. Functional Materials Among the functional materials which exhibit piezoelectric, pyroelectric, ferroelectric and ferroelectric related properties, four mainn groups of materials have been considered: hydrogen bonded systems, ionic crystals, narrow gap semiconductors [17] and organic polymers. One of the most important is the group of the ionic crystals. Within this group a main type of structure should be considered the corner sharing oxygen octahedral, which includes the four following important families (structures) of materials: bronze tungsten (A2B2O6), perovskite (ABO3), pyrochlore (A2B2O7) and bismuth-layer (Bi4Ti3O12) structures (Figure 6). Among these, the perovksite group is particularly significant, from the point of view of applications. This is because such materials undergo a phase transition on cooling from a high symmetry temperature phase (cubic paraelectric phase) to a non-centrosymmetric ferroelectric phase. The materials with the highest piezoelectric coefficients belong to the lead based perovskite family. Materials with a high ferroelectric transition temperature show piezoelectricity at room temperature, whereas those with transition near or below the room temperature exhibit an important electrostrictive effect. For these, due to the large anharmonicity of the ionic potential, the electrostriction is extraordinarily large [14]. Besides the ability to design the physical properties required for certain applications, by formation of solid solutions, the possibility of fabrication as single crystals, ceramics, textured ceramics and thin and thick films adds value to this family of materials. The ideal structure of the perovskite is cubic with a spacial group Pm3m. The general crystal structure can be thought of as either (i) a body centred cubic (BCC) lattice with A ion (+2) at the centre surrounded by four B ions (+4), each at a corner, and twelve O ions (-2), each of which occupies the midpoint of the edge, or (ii) as a face centred cubic (FCC) lattice with a B ion at the centre surrounded by six O ions, each at a face centre, and four A ions, each at a corner. In the non-polar state the geometric centres of A, B and O coincide giving rise to a non-polar lattice. In the polar state the A and B ions are displaced from their geometrical centres with respect to O2- ions, giving a net polarity to the lattice. These ionic displacements are concomitant with the structural phase transitions that take place as the temperature of the crystal changes. The lattice constant of perovskites is close to 4 Å due to the rigidity of the oxygen octahedra network and the well defined oxygen ionic radius of 1.35 Å. A large number of cations can be accommodated in the cages formed by the oxygen anions, giving rise to wide variety of materials. Complete solid solutions are easily formed between many cations. Moreover, many different cations can be substituted in both A and B sites of the

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perovskite lattice without drastically changing the overall structure. The occupancy of A and B sites of the perovskite structure by more than one type of ions creates complex structures, (A’A”)BO3 or A(B’B”)O3, in which the A or B ions distribution varies, originating different degrees of cation order either as randomly, completely ordered or partially ordered structures. The dependence of the macroscopic properties on the degree of order is well known for different types y of materials such as lead based relaxors [42] and titanates for microwave applications [43]. Moreover, depending on the materials stoichiometry different ratios of order can be defined, such as: 1:1, 1:2 or 2:1. It is then possible to manipulate the material’s properties such as TC, piezoelectric constant or lattice constant with only a small substitution of a given cation, which is very valuable from the technological perspective. Barium Titanate (BaTiO3 - BT), Lead Titanate (PbTiO3 - PT), Lead Zirconate Titanate (PZT), Lead Lanthanum Zirconate Titanate (PLZT), Lead Magnesium Niobate (PMN), Strontium Titanate (SrTiO3), Potassium Niobate (KNbO3 - KN), Potassium Sodium Niobate (K KxNa1-xxNbO3 – KNN) and Potassium Tantalate Niobate (K(TaxNb1-x)O3 - KTN) are some of the technological important functional materials that crystallize with a perovskite type structure.

a

b

c

d

Figure 6. Corner sharing octahedral structures: (a) perovskite, (b) pyrochlore, (c) tungsten bronze and (d) bismuth layer (adapted from [44])

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According to Haertling [18] the discovery of non-linear dielectric properties in BT associated with very high values of the dielectric permittivity, was crucial for the development of the new generation of electronic t materials, which have occurred since the Second World War up to the current day. Hence, BT is among the most systematically studied and widely used ferroelectrics and considered as the prototype ferroelectric ceramic. The temperature dependence of the spontaneous polarization and dielectric constants of BT is shown in figure 3. Three anomalies can be observed: Firstly, above 130 °C BT possess a paraelectric cubic phase and the net polarization is null. The centre of positive charges (Ba2+ and Ti4+ ions) coincides with the centre of negative charge (O2-). At 130 °C, the Curie point, the discontinuity observed is related with the phase transition from a cubic (non-ferroelectric) phase to a tetragonal (ferroelectric) phase which develops on cooling through TC. The centre of Ba2+ and Ti4+ ions are displaced in relation to the O2- ions leading to the formation of electric dipoles. The vector of spontaneous polarization has the [001] direction. The other two discontinuities are associated with transitions from a ferroelectric phase to another one. Between 0 °C and -90 °C, the ferroelectric orthorhombic phase is stable with the polarization direction along the [011] direction. On decreasing the temperature below 90 °C the phase transition from the orthorhombic to ferroelectric rhombohedral phase leads to polarization in the [111] direction. The peaks observed in the dielectric permittivity curve accompany the polarization discontinuities. BT was firstly used as piezoelectric ceramic transducers. However, due to the discovery of better piezoelectric properties in other materials, namely the solid solution between lead titatante and lead zirconate (PZT), BT found use mainly as the high permittivity dielectric in ceramic multilayer capacitors. To optimize the properties for certain applications, BT has been combined with different additives. Various A and B site substitutions in different concentrations have been tried to tailor the dielectric and ferroelectric properties of BT. It was observed thatt solid solutions with isovalent substitutions do not significantly alter the dielectric permittivity versus temperature response. Their main effect is the alteration of the transition temperatures. Ba, Pb and Sr ions can be mixed in any proportions forming complete solid solutions while the solubility of Ca in BT lattice is limited. A site substitution with Srr2+ was found to reduce the Curie point linearly towards room temperature, m whereas differently the substitution of Pb2+ for Ba2+ raises the Curie point. The effect of various isovalent substitutions on the transition temperatures of BaTiO3 ceramic is described in detail in [11]. For multilayer capacitors the modifications of BT are done to maximize the dielectric permittivity value; accordingly the dielectric permittivity maximum should occur near the operation temperature of the device and the dependence of the dielectric permittivity on the temperature should be minimized. Following these modifications, X7R and Z5U ceramic capacitors are fabricated [12]. The formation of complete solid solution in the BaTiO3-SrTiO3 system allows the transition temperature of BT to be shifted from 120 ºC to room temperature. TC and the magnitude of the permittivity can be modulated by the ST content, which makes it very attractive for practical applications. The high dielectric constant, charge storage capacity, dielectric non-linearity, breakdown field, low leakage and microwave loss make the solid solution BST suitable for applications such as Gigabit Dynamic Random Access Memories (DRAMs) and high frequency devices. Moreover the volatilities of

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BST components are lower than the Pb-based ferroelectrics t materials thereby making it relatively easier to introduce into fabrication facilities. For DRAMs applications the material should be in the paraelectric phase in which the hysteretic effects are absent. The basic parameters for applying capacitor thin films on DRAMs are the dielectric constant, leakage current density and reliability. More information on BST for DRAMs is given in the reviews of Ezhilvalavan [45] and H. Schroeder and A. Kingon [46]. In recent times a strong interest appears to exploit the non-linear dielectric response of ferroelectrics and incipientt ferroelectrics above the TC to fabricate tunable microwave devices. Tunable capacitors and resonators devices are based on the tunability effect, i.e., on a dc-electric-field dependence of permittivity that is strengthened on approaching from above the paraelectric-ferroelectric phase transition, at which the dielectric permittivity is maximized, but the dielectric losses remain still sufficiently low. SrTiO3 reveal a high tunability at 80 K and is therefore suitable for planar tunable High Temperature Superconducting (HTS) devices. On the other hand BST solid solution with the maximum of tunability shifted to higher temperatures is ideal for room temperature applications. [47]. The solid solution between lead titanate (PbTiO3) and led zirconate (PbZrO3) is presently the most commonly used compositional system for piezoelectric applications. PT is a ferroelectric material with a transition temperature at 420 °C and PZ is antiferroelectric material with a transition to the paraelectric cubic state at 230 °C [9]. The solid solution between PT and PZ is complete forming the (Pb(ZrrxTi1-x)O3) system known as PZT. PZT has a perovskite type structure with Ti4+ and Zr4+ ions occupying randomly the B site. The PZT phase diagram is represented in figure 7.

Figure 7. PT – PZ phase diagram [8]

The richness of the PbZrO3-PbTiO3 system comes from the existence of several ferroelectric, antiferroelectric and paraelectric phases with various symmetries: tetragonal, rhombohedral, orthorhombic and cubic [8]. The transition temperature TC

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varies from 230 °C to 490 °C depending on the Zr/Ti ratio. Above TC the solid solutions exhibit a cubic structure and are paraelectric. There is no atomic displacement of Zr/Ti ions and no spontaneous polarization is established. Below TC the adopted structure depends on the Zr/Ti content. For high Ti content the ferroelectric phase is tetragonal and the polarisation vectors are along the <001> directions of the pseudocube; therefore, there are six possible orientations. The Zr/Ti ions are displaced along the tetragonal caxis. Because the centres of the positive and negative charge are no longer coincident, a dipole is created originating a spontaneous polarization. For higher Zr concentrations the ferroelectric phase is rhombohedral and the polarisation is along <111> or the body diagonals of the pseudocube, which are eight. In this case the lattice distortion is accompanied by the movement of Zr/Ti ions towards the face centre of the oxygen octahedral. Similarly, the centres of positive and negative charges are displaced and a spontaneous polarization builds up. Below the Zr/Ti ratio of 95/5 the solid solution is antiferroelectric with an orthorhombic phase. Another significant feature of the PZ-PT phase diagram is the existence of an abrupt structural change, with composition at constant temperature the so-called morphotropic phase boundary (MPB). It occurs close to the composition where PZ:PT is 1:1, namely Pb(Zr0.52Ti0.48)O3 - PZT 52/48. MPB compositions exhibit enhanced dielectric and piezoelectric properties [8]. It is believed that due to the 14 possible directions of polarisation (eight [111] directions for the rhombohedral phase and six [001] directions for the tetragonal phase) in MPB compositions the reorientation of the polar axis is facilitated and the electrical properties enhanced [8]. Figure 8 depicts the coupling coefficient kp and the dielectric permittivity İr across the PZ – PT solid solution showing the maximization of the properties in the MPB region. Hence, these compositions are technologically very important and PZT MPB compositions are the most exploited for piezoelectric applications.

Figure 8. Coupling coefficient kp and dielectric permittivity İr values across the PZT compositional range [11].

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The reasons behind the increase of the dielectric properties at the MPB are not yet completely explained. Several justifications have been proposed for the origin of the maximum of electric properties at MPB [48, 49]. As in other materials the PZT properties may be tailored by doping (additives added in concentrations ≤ 3 %) [18]. Doping PZT with acceptor ions such as K+, Na+ (for A site) and Fe3+, Al3+, Mn3+ (for B site) creates vacancies at the oxygen sublattice and usually have limited solubility in the lattice. Such materials are named hard PZT. The highly mobile oxygen vacancies can be re-oriented under an applied field. The aligned dipoles will provide a field, stabilising the domain structure, reducing most of the properties that are enhanced by domain wall motion. Therefore, hard PZT's are characterized by lower permittivities, smaller dielectric losses and lower piezoelectric coefficients and are more difficult to pole and depole (higher coercive fields, poorly developed hysteresis loops) [18]. Hard PZT are then suitable for applications in which it is required to transmit as much power as possible. In contrast, doping PZT with donor ions such as La3+ (for A site) and Nb5+, Sb5+ (for B site) originates A site vacancies in the lattice and the materials are termed soft PZT. In donor-doped PZT the content of oxygen vacancies is minimised reducing the number of domain-stabilising pairs and enhancing domain reorientation. Therefore, soft PZT's possess higher permittivities, higher losses, higher piezoelectric coefficient, maximum coupling factors and are easy to pole and depole (low coercive fields, square hysteresis loops, high remnant polarization). The donor dopants counteract the natural p-type conductivity of PZT and, thus, increase the electrical resistivity of the materials. They can be used for applications requiring very high piezoelectric properties such as sensors [18]. PZT containing 3 to 12 mol% of La forms a relevant class of functional materials, lead lanthanum zirconate titanate (PLZT), with important dielectric, piezoelectric and electro-optic properties. The solubility of La in the PZT lattice is a function of the composition, namely on the PT content. The PLZT phase diagram is well described in [18]. The incorporation of La considerably improves the properties of PZT, explicitly increases the squareness of the hysteresis loop, decreases the coercive field, increases the dielectric permittivity, maximum coupling coefficients and mechanical compliance and enhances the optical transparency. It is believed that the observed transparency is related on one hand to the lowering of the cell distortion caused by La introduction that reduces the optical anisotropy and on the other hand to the uniform grain growth and densification of as a pore free microstructure for La doped materials [18]. Thus, PLZT is very important as an electroptical functional material. Perovskite lead-based relaxor ferroelectrics (Pb(B´1-xB´´x)O3 exhibit excellent dielectric properties, a broad dielectric maximum and large piezoelectric and electrostrictive coefficients. Together with the possibility of designing the properties by solid solution formation with other ABO3 members, relaxor ferroelectric materials are very attractive for multilayer capacitors, piezoelectric transducers and electrostrictive actuator applications to operate under different frequency and temperature conditions [50]. It is well know that the fabrication of monophasic lead based relaxors is difficult. A pyrochlore type phase (A2B2O7-δ), with low dielectric permittivity, precedes the formation of the perovskite phase. Due to its high stability the pyrochlore is difficult to eliminate and, depending on the systems, it remains as a second phase, degrading the

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final properties. Hence, from the technological point of view, is crucial to obtain a single perovskite phase material in these systems [29]. Niobate relaxor compounds, Pb(B1-xNbx)O3, typified by PMN are the most studied. In opposition lead based tantalate (Pb(B1-xTax)O3) and tungstate (Pb(B1-xWx)O3), in which B is Zn2+, Mg2+, and Ni2+, with a low temperature of the dielectric maximum are considerably less studied. However, these are important candidates for utilization in cryogenic conditions such as low temperature capacitors and actuators for space applications [51]. One of them, Pb(Fe2/3W1/3)O3 (PFW) gained higher attention in recent years due to its high dielectric permittivity and low sintering temperature (~950 ºC). These characteristics make it a good material for multilayer capacitors with inexpensive low temperature melting electrodes (such as Ag-Pd alloys). The solid solution formation with PT modifies the relaxor properties of PFW and a dielectric response closer to a classical ferroelectric behaviour is observed [52]. A composition-induced transition from pseudocubic relaxor to a tetragonal ferroelectric state was found in (1-x)PbFe2/3W1/3O3 – xPbTiO3 (PFW–PT) with increasing x. A MPB was reported in the range x = 0.20-0.37 at T = 300 K and x = 0.25-0.35 below 280 K and the phase diagram of this system was proposed [53, 54]. Another interesting feature of PFW is related to the multiferroic magnetoelectric behaviour, i.e. the coexistence of electric and magnetic polarization observed in this material [55]. The coupling between the ferroelectric and magnetic activity provides the possibility to manipulate the magnetic properties through electric fields and vice versa, giving to these materials a wide potentiality for applications in spintronics, multiple state memory elements, or memory devices which use electric and/or magnetic fields for read/write operations [55]. However, the magnetodielectric multiferroism is very rare, being restricted to only a few materials like ferroelectric-ferromagnetic BiMnO3, YMnO3 and Pb2(CoW)O6 and ferroelectric-antiferromagnetic PbFe2/3W1/3O3, PbNi1/3Nb2/3O3 and Pb2(FeTa)O6 [55]. This phenomenon opens a wide range of new possible applications for PFW based materials, although not well studied yet. Moreover, recent studies showed the existence of a core shell structure in PFW-PT system and its effect on the dielectric response [56]. The dependence of the core-shell on the processing parameters was established allowing to tailor the dielectric response of PFW [57]. Bi-layered perovskites are at the present being considered as substitutes for lead based perovskites. The ferroelectric nature of Bi-containing layered perovskite was reported by Smoslenskii and co-workers in the sixties [58]. Nevertheless only recently they become technological important materials due to their almost fatigue free behaviour [59]. Bi-layered perovskites belong to the multilayered Aurivillius family of compounds with the general chemical formula of (Bi2O2)2+ (Am-1BmO3m+1)2- consisting of m perovskite units sandwiched between oxide layers. In SrBi2Ta2O9 (SBT) the perovskitetype groups (SrTa2O7)2- and (Bi2O2)2+ layers are stacked alternately along the pseudotetragonal c axis (Figure 6). The Bi2O2 layers and TaO6 octahedra are considerably distorted and atomic displacements along the a axis give rise to spontaneous polarization. The ferroelectric phase crystallizes with the orthorhombic structure and transforms to the paraelectric phase (with a tetragonal structure) near 600 K [60]. The bismuth layer structure can have perovskite blocks with different thickness depending on the stoichiometry and it was recently shown that there is a dependence of the polarization direction (a-b plane or c axis) on the number of octahedral thickness [17]. The few allowed directions for the spontaneous polarization seems to be the reason for the lower polarization values when compared with PZT. Consequently the

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maximization of the ferroelectric properties and the utilization of bismuth-layered materials in memory devices depend on the ability of producing highly oriented materials. Moreover the structural and physical properties of Bi-layered materials are not completely understood.

4. Functional Materials Processing Technologies The technology to fabricate functional materials depends mainly on their final applications. Current applications require functional materials either in a bulk (polycrystalline ceramics, texturized ceramics and single crystals) or in a film form (thin and thick films). Moreover among each technology the specific application will also define the details of the integration of the functional material into the device. The general processing of polycrystalline ceramic functional materials includes the following steps [11]: (1) synthesis of the powder; (2) milling, usually with additive mixing (lubricant, plasticizers, binders); (3) drying; (4) forming (with the simultaneous application of metallic electrodes for multilayer structures); (5) firing; (6) finishing (including slicing, lapping, polishing, electroding, encapsulation and poling) and (7) evaluation. The critical steps, those determine the microstructure and the final properties of the ceramics are the synthesis of the powders, in which the preparation of monophasic powders, with fine and homogeneous particle size distribution is required, and the sintering, at which the reduction of the porosity is crucial. Details on the preparation technologies of functional ceramics can be found in [11, 12]. There are now innumerable methods to produce synthetic oxide and non-oxide powders with the required high quality characteristics in terms of size, shape and purity. Powder precursors for the fabrication of functional materials can be synthesised by solid, liquid or vapour reactions [61]. Solid-solid reactions commonly involve the mixture of the precursors (carbonates, nitrates, oxalates, etc) followed by a thermal treatment (800-900 ºC) at atmospheric pressure to obtain the desired product. Due to its simplicity and low costs solid state reaction methods are often used and numerous functional materials compositions have been prepared, such as BT and lead based perovskite. For the case of lead perovskite it is well known that the preparation through this methodology usually originates a multiphasic material. The perovksite phase formation occurs via a sequential phase formation process in which intermediate phases, such as pyrochlore type ones, are formed and transformed into the perovskite phase for higher temperatures [29]. Due to the high temperatures required for the nucleation and growth of the new phase, the obtained powders are usually aggregated and require a milling step after. Several comminution techniques, which allow milling until fine particle sizes (tens of nanometers) in shortt periods of time and thus avoiding the undesirable contamination by the milling step, are now available. Fluid impact mills are one of such examples [62]. Recently, comminution techniques have also been used for synthesis of complex oxides. The high energy liberated by the impact of hard milling media can be used to promote the solid-solid reaction between precursors, nucleating new solid phases. The synthesis of complex perovskite oxides has been reported by high energy ball milling, also known as “mechanochemical synthesis” [63-66]. Another modern solid-state reaction technique is the microwave-assisted synthesis (MAS).

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Microwave dielectric heating is related to the ability of substances to absorb microwave energy and to convert it into heat so as to obtain the required energy for the reaction. The attractive features of this technology include the very short time required to complete the reaction (sometimes chemical reaction times can be reduced from hours to minutes with all the related benefits); the reduction of side reactions; the yield increase and the improvement of reproducibility. R&D activities on MAS synthesis of materials were reviewed by Mingos [67], Rao [68] and Adam [69]. If powders with high purity, homogeneity and reactivity are required then other methodologies, although more expensive, should be used. Solution synthesis involves the intimate mixture of the liquid precursors (inorganic, organic and alcoholic solutions) at a molecular level in order to obtain a homogeneous solution at the atomic level which by precipitation will originate a solid precursor. Solution techniques include among others the precipitation and co-precipitation, hydrothermal synthesis, sol-gel, emulsion process, molten salt synthesis and spray pyrolisis. In each of these techniques the nucleation and growth of the solid phase occurs through a reaction in the liquid phase. Due to the high level of atomic and/or molecular homogeneity attained in solution these techniques give rise to high chemical homogeneous solid products, with a high purity and controlled particle morphology and size (<1 mm) allowing the formation of the desirable phases and the sintering of the ceramic at lower temperatures, without stoichiometric variations. Ceramics of BT, PT, PZT and PMN are currently being manufactured using powders synthesised by chemical solution methods [61]. The powders prepared from solution techniques must be separated from the solution media and dried as well as thermally decomposed to obtain the desired crystalline precursor. Depending on the systems and processing conditions it is also possible to obtain the desired crystalline phase directly from the solution [70]. The drying and calcination steps often lead to powder agglomeration and aggregation. The final characteristics of the powders greatly depend on experimental variables, such as concentration, pH, temperature, pressure, stabilizers, chelating agents, stirring and solvent removal conditions (evaporation, spray drying, spray pyrolisis and freeze drying). Extensive literature on the topic can be found in [61]. Vapour phase techniques refer to the nucleation of the crystalline phase from a gaseous phase and include: vapour-vapour reactions, vapour-liquid reaction and vapoursolid reaction. Vapour phase techniques imply the evaporation or sublimation of the precursors and a decomposition or reaction at high temperatures followed by a condensation with a rapid cooling. These experimental conditions give rise to an extensive nucleation and to a controlled growth and the obtained particles are very fine and de-aglomerated. These are not suitable techniques for multicomponents systems, therefore not so frequently used for the preparation of functional materials. Vapour phases techniques are mainly used for the preparation of materials with high sintering temperatures. The sintering is the step after the powder consolidation. In general the sintering of functional oxides should be carried out in an oxidizing atmosphere or in air. The sintering cycle should be optimized to achieve the maximum densification, although avoiding the abnormal grain growth and the loss of volatile elements (Pb, Bi). In the fabrication of ceramic functional materials two main sintering processes can be distinguished: conventional sintering, normally used for densification of BT (1350 ºC

23

for 3 h in air), PZT (1250 ºC for 5 h in oxygen) and PFW (970 ºC for 2h in air) ceramics; and hot pressing (HP) or hot isostatic pressing (HIP) used for processing transparent PLZT ceramics (1250 ºC for 16 h with an applied pressure of 14 MPa). For polar ceramics due to the random orientation of the ferroelectric domains inside the ceramic grains the macroscopic polarization is null after sintering. In order to pole the material a direct current (dc) electric field with a strength larger than the coercive field strength at a high temperature below TC should be applied. Generally the functional properties of ceramics are inferior to those of single crystals, mainly due to an average effect that results from the fact that in ceramics each grain has a different crystallographic orientation. Single crystals of perovskite PZN-PT and PMN-PT have been reported to exhibit extraordinary piezoelectric properties compared to polycrystalline ceramics. Because such crystals are difficult to produce without defects, in convenient sizes and by a cost effective process, recently Templated Grain Growth (TGG) emerged as a comparatively less costly technique for producing textured ceramics with single crystal-like properties. To attain the ultimate goal of TGG, which is to maximize the fraction of grains with a desirable orientation (texture), the nucleation and growth of the crystalline structure occurs on aligned single crystal template particles. Textured ceramics with a high fraction of the piezoelectric properties (strain and piezoelectric coefficient) of single crystals have been reported. Details of this technique can be found in the works of G. L. Messing group, among others [71-7371]. Current applications require functional materials either in a bulk (polycrystalline ceramics, texturized ceramics and single crystals) or in a film form (thin and thick films). Moreover among each technology the specific application will also define the details of the integration of the functional material into the device The increasing functionality, speed and portability have been the driving force to decrease the size of electronic devices. In this context functional materials films become particularly relevant. The ability to fabricate thin and thick films is associated with the development of advanced deposition techniques that permit a wide variety of high quality films with different thicknesses (thin films with less than one micron and thick films with dozens of micron) on different substrates (silicon, platinised silicon, sapphire, magnesia, zirconia, galium arsenide, lithium niobate, metallic alloys, glass, etc). The various techniques currently available to fabricate thin and thick films are listed in table 1. Film fabrication techniques can be divided into two general classes: physical vapor deposition (PVD) techniques and chemical deposition techniques, which include chemical vapor deposition (CVD) and chemical solution deposition (CSD). In the former, atoms from a source are transferred in a continuous and controlled manner under a vacuum atmosphere (> 10-5 Torr) to the substrate, in which the nucleation and growth of the film occur atomistically. Depending on how the particles (atoms or ions) are removed from the target, the following PVD techniques are considered: rf sputtering, ion beam sputtering, electron beam evaporation and laser ablation, among others. The former allows for careful control of film thickness and orientation and compatibility with the semiconductor integrated circuit processing.

24 TABLE I. Thin and thick film deposition techniques (adapted form Haertling [18].)

Thin Film Techniques Physical Vapour Deposition Sputtering (rf magnetron, dc, ion beam) Evaporation (e-beam, resistance, molecular beam epitaxy) Laser Ablation

Thick Films Techniques Tape casting Screen printing Electrophoretic deposition Hybrid sol-gel technique

Chemical Deposition Chemical Vapour Deposition MOCVD (Metal-organic CVD) PECVD (plasma-enhanced CVD) LPCVD (low pressure CVD) Chemical Solution Deposition Sol-gel (solution gelation) MOD (metallorganic deposition)

The difficulty in controlling the stoichiometry of multicomponent films, the slow rates of deposition (normally around 1 Å/s), the need for high-temperature postdeposition crystallization annealing and the high cost related with equipment acquisition and maintenance are the main disadvantages of these methods. For more details on the PVD methods the reader is referred to several text books [71]. Chemical methods allow higher deposition rates, good stoichiometry control, and the production of large area defect-free films and have lower equipment-related costs. Chemical vapour deposition (CVD) is very attractive for industrial manufacturing of functional films. However, the limited availability and toxicity of sources off precursors for functional materials restricts the use of this technology. A comparison between PVD and metalorganic chemical vapour deposition (MOCVD) for the processing of ferroelectric thin films and heterostructures can be found in [75]. On the other hand, chemical solution deposition methods, specially sol-gel, have been increasingly used for the preparation of films of functional materials. Chemical techniques does not require vacuum ambience, are cheaper and faster, allow for a good stoichiometry control and production of large area defect-free films and often produce films with better properties, although the texture degree of the film is inferior. Wet chemical methods entail the preparation of the solution, the deposition of the solution onto the substrate by dip- or spin-coating and the subsequent thermal treatment of the deposited layer to remove the organics and to achieve crystallization and densification of the coatings. Wet processes comprise solgel, metalorganic decomposition (MOD), electrochemical reaction and hydrothermal routes. Comprehensive review texts on solution deposition of piezo- and ferroelecrtic materials can be found in the literature [76, 77-81]. The described methods are mostly suitable for thin films (1 to 5 µm) preparation. The preparation of thicker films (>5 µm) using these techniques is possible although the process becomes time consuming and cost-ineffective. Also the probability of creating defects (cracks, pores, and inclusions) in the films increases with the number of layers. Hence, the preparation of thicker films requires different methodologies, as indicated in table 1. Thick films technologies are mostly based on the densification of powder films. Films with thickness in the range 5-500 µm can be prepared by these methods [82, 83]. A suspension of small powder particles (slurry) is deposited by tape casting, screen printing, jet printing or electrophoretic deposition onto the substrate and dense films are

25

attained after sintering. As the liquid phase is removed by evaporation the particles rearrange and the film shrinks. The final density is attained after sintering which is a critical step in the slurry-based technologies. The temperatures t required to densify lead based functional materials, above 850 ºC, can cause losses of volatile elements (Pb), densification problems and chemical partition of the composition. Usually sintering additives (lead based glass frit or lead borosilicate) are necessary although the final properties of the film might be deteriorated [84-87]. Engineered processes to produce dense thick films at low temperatures are then needed. Tape casting is an ordinary method to fabricate laminated thick layers (in the range of 10-500 µm) in multilayer structures, such as multilayer capacitors and actuators [88-91]. However, the method is not easily compatible with the deposition onto rigid substrates and the suspension and firing without deflection are very difficult. The capability of screen-printing functional films on a variety of flexible or rigid substrates (ceramic, metallic, polymeric) is an important advantage over the tape casting method. Screen-printing method is very well suited to prepare functional thick films with thickness ranging from 10 to 30 µm [9294]. In this technique the interactions between adhesion and sintering promoters, film material and substrate are important, especially for Si-based devices, and might limit the final properties of the device. Electrophoretic deposition (EPD) is another slurry-based coating process to fabricate dense thick films. In EPD, colloidal, charged particles deposit from a stable suspension onto an oppositely charged electrode upon the application of a dc electric t field. Comprehensive reviews on EPD can be found in [9597]. An important advantage of EPD is the possibility of using nanosized powders well dispersed in the suspension, which allow low sintering temperature processes and compatibility with several substrates, making EPD an appropriate process to fabricate lead based functional materials thick layers on silicon based and other substrates. Several works report the EPD preparation of BaTiO3 [98, 99] and PZT thick films [100103]. Almost no investigations have been reported yet on alternative lead free compositions. A further alternative methodology to prepare dense thick coatings compatible with Si technology has emerged as a low- temperature process, named composite (or hybrid) sol-gel technique [104]. It combines the sol-gel processing with fine powder particles in which the amorphous gel is used as the “cement” to glue the sintered piezoelectric powder. The composite suspension is then coated onto the substrate using spin-, dip- or spray-coating techniques. The main advantages over the classical slurry-based approach include [83]: (i) the reduction of the film m shrinkage during firing and crystallization which reduces the tendency to crack formation; (ii) the increase of the viscosity of the deposits which allows relatively thick individual layers to be deposited; (iii) the promotion of the crystallization of the sol-gel matrix due to the nucleation aids role of the nanopowder particles. This allows thick films to be fired at reduced temperatures. The drawback of this technique is the inevitable a porosity. Hence modifications of the hydrid sol gel process have been undertaken. The inclusion of infiltration steps in which the sol is infiltrated between the layers was reported for the preparation of PZT thick coatings on Si platinised substrates [105]. A different approach refers the sedimentation of the powder layer by centrifugation combined with the infiltration of the sol-gel solution. With this technique PZT and PMN-PT thick films with enhanced piezo- and ferroelectric properties were fabricate [106, 107].

26

5. Functional Materials Applications The most important applications for the above mentioned functional materials are summarized in table II. The ample range of applications is related to their varied properties (ferro, piro- and piezoelectric, electrostrictive and electro-optical) and to the possibility of designing their properties and producing reliable devices. Some of the applications are more suited for bulk ceramics, while others require films. The increasing trend for device miniaturization has been accompanied by a growing demand of functional films, either thin or thick. Besides the reduction of the device dimension and compatibility with integrated circuit technology, the use of films offers additional advantages: lower operational voltages, higher velocities, possibility of fabrication of complex structures, low processing temperatures and compatibility with a varied range of materials (metals, ceramics, polymers). The final application of a material is directly related to its properties. Some important properties of selected functional materials were summarized by Haertling [18]. Ferroelectric materials are generally characterized by: i) high dielectric permittivity values (200 – 10000), ii) low dielectric loss (0,1-7%); iii) high resistivity (>1013 Ωcm); iv) high to moderate dielectric breakdown (100-120 kVcm-1 for ceramics and 500-800 kVcm-1 for thin films) and v) non-linear electric, elecromecanhical and electro-optic behaviour. Capacitors with great capacitance density as the multilayer ceramic capacitors (MLC) are based on ferroelectric materials with high εr. In MLC thin (~1 µm) layers (>100) of a high εr material are interspersed with thin layers of metallic electrodes, creating minimised associations of parallel capacitors of high capacitance. MLC are made by tape-casting. Firstly, a slurry of the dielectric powder with suitable additives is prepared. Thin green sheets of the ceramic are then tape-casted. On the top of each dielectric layer a metallic electrode (Pd, Ag-Pd, etc.) is screen printed. These steps are repeated until hundreds of sheets are stacked. After lamination the green sheets are diced with the right size. MLC are then sintered. To finish the fabrication cycle terminations for the internal electrodes are applied [12]. Alkaline earth titanates (BT based) were traditional utilised as the dielectric material, but due to the high sintering temperatures noble metals should be used as electrodes, increasing considerably the price of the capacitor. Alternatively relaxor based materials (such as PMN) are now being employed. Besides the high dielectric permittivity (>30000), a broad dielectric permittivity maxima, low dependence of the dielectric properties on the field lead based relaxors can be sintered at T < 1000 °C, thus allowing the use of cheaper metallic alloys as electrodes. The drawbacks of the relaxors formulations are associated with the higher dielectric losses, the higher frequency dependence of the dielectric permittivity and the difficulty in processing monophasic materials. One recent application also based on high εr values of ferroelectric materials are the Dynamic Random Access Memories (DRAMs). A conventional DRAM is composed of a SiO2 (εr~4-7) capacitor in association with transistors and resistors [46]. To increase the storage capacity and decrease the device size ferroelectric thin films with high εr are required. Ta2O5 (εr~22) has been used to fabricate 256 Mb DRAM. However the Gigabit generation entails higher dielectric permittivity materials. Using a high-permittivity

27

material such as BST (εr~200) the capacitor of the 256 Mb DRAM would be realized in a planar structure [46]. Besides BST other high permittivity materials should be considered. An example is the Ba(ZrTi)O3 (BZT), that with εr similar to BST one exhibits improved dielectric loss, leakage and resistance degradation [46]. Further studies on this family of materials are needed. A comprehensive review on DRAMs was recently published [46]. TABLE II. Applications of functional materials [adapted from 18]

BULK

BULK AND FILMS

FILMS

APPLICATIONS

APPLICATIONS

APPLICATIONS

ML Capacitors

Dielectric Capacitors

Non Volatile Memories

Piezo Generators

IR Sensors

Buffer Layers

Pizo Motors

Piezo Sensors and Actuators

Integrated Optics

Piezo Actuators

Electrooptic Shutters

AR Coatings

Electrostrictive Actuators

Electrooptic Displays

PTC Sensors

The above-mentioned applications are based on the dielectric permittivity and not on the ferroelectric response. For such uses a high dielectric permittivity value stable with the temperature is required. However the ferroelectric hysteresis is a unique characteristic that can also be explored from the practical point of view. A ferroelectric material with a square hysteresis loop has stable Pr values for small changes of E and the switching of polarization occurs for high applied field. These are ideal features for the binary code and non-volatile characteristics required for non-volatile ferroelectric random access memories (NVFeRAMs). In the fifties due to the raising computer industry memories with high storage capacity were required. At that time ferroelectrics were already considered as promising candidates, however lack of reliability, fatigue of the switching cycles, imprint, high operation voltages and leakage currents limited their practical implementation. Magnetic and later semiconductor memories were used [108]. More recently due to the ability to prepare high quality films (epitaxially grown, defect free and with controlled stoichiometry) a renewed interest in ferroelectric memories appear. A FeRAM incorporates a ferroelectric thin film as a capacitor to store the data in a non-volatile state, allowing the date to be rewritten fast and frequently [109]. PZT and SrBi2Ta2O7 (SBT) are the materials under consideration for FeRAM applications. For PZT films the oxygen vacancies and the charge injection at the interface ferroelectric/electrode, considered to be responsible for the fatigue of the switching

28

cycles, can be minimized if oxide electrodes are used. For SBT films the degradation is controlled by the (micro-) structure t (specially the Bi layer). From the fatigue point of view SBT has been considered the most appropriated material. However, PZT can be processed at lower temperatures (500 ºC) than SBT, being more suited for Si based technology. Applications of non-volatile memories include a panoply of highly consumable multimedia equipment (digital cameras, video cameras and digital audio) and portable products (mobile phones, notebooks, PalmPCs, among others) [109]. A recent FeRAM application is the rf-operated Smart Card. A comprehensive review on FeRAMS can be found in [109]. Pyroelectricity is the polarization produced due to a small change in temperature as defined in section 3 of this paper. The pyroelectric response of ferroelectric materials is technologically important for thermal detectors, namely infrared detectors, used for the detection and prevention of fires, night vision, security systems, etc. [110]. Single crystals of triglycine sulfate (TGS), LiTaO3, and (Sr,Ba)Nb2O6 are widely used for heat sensing applications. The use of thin films of ferroelectric materials in pyroelectric devices allow, besides the miniaturization and the compatibility with the IC technology already indicated for FeRAMS, the operation at room temperature that constitutes an important technological step further. The use of ferroelectric thin films for pyroelectric devices is also advantageous due to the high cost of growing single crystals. However, the sensibility of the devices should be improved through the utilization of highly oriented films. PbTiO3, (Pb,La)TiO3 and PZT thin films have been used for pyroelectric sensing applications [110]. The high values of kp, d33 and d31 piezoelectric coefficients off ferroelectrics, namely PZT and PLZT account for the enormous number of piezoelectric applications for these materials, such as: nano- , micro- and macro-actuators, micropositioners, ultrasonic motors, dampers, microphones, gas igniters, accelerometers, pressure sensors, among several others. Piezoelectrics are also involved in the fabrication of microelectromechanical (MEMS) and nanoelectromechanical (NEMS) systems, that have an important impact on medicine and bioengineering (DNA and genetic code analysis and synthesis, drug delivery, diagnostics and imaging), bio- and information technologies, avionics and aerospace (nano- and microscaled actuators and sensors, smart reconfigurable geometry wings), automotive systems and transportation (transducers and accelerometers), etc. [111]. On the other hand, the actual interest in electrostrictive devices acting as tunable piezoelectric components is related to the high values of electrostriction characteristic of some ferroelectric relaxors (PMN-PT and PLZT).

6. Future trends in Functional Materials “Nothing is harder to predict than the future t of science and technology. Remember former IBM president Thomas J. Watson's 1943 remark that there was a worldwide market for "about five computers"? And then there was Bill Gates's 1981 prediction that 640 kilobytes of computer memory "ought to be enough for anybody." Why do even brilliant technologists like Watson and Gates have such trouble reading the future? New technologies don't always arise in a linear fashion. When cutting-edge fields of

29

knowledge come into contact, new disciplines can be spawned, and progress can go zooming off in unexpected directions” – in Untangling the Future - By Paul Saffo, Business 2.0 [112]. If history is any guide, the miniaturization and greater functionality will continue to drive the development of functional materials. New functional materials are expected to be developed trough Molecular Engineering with far above performance in comparison with actual ones (see part I of this book by A.I. Kingon). However for traditional functional materials, as those described in this paper, the future developments will look for: (i) tunable devices, implying the use of materials with very low loss at the microwave frequency range; (ii) deep understanding of the size effects in functional materials; (iii) establishment of the relationships between the nanoscale structure with the nano- and macroscale properties; (iv) very low processing temperatures for easy integration with different materials, (v) development of environmetal friendly materials with optimised properties and (vi) development of heterostructures with maximized properties.

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32 77. Schwartz, R.W., Boyle, T.J., Lockwood, S.J., Sinclair, M.B., Dimos, D., and Buchheit, C.D. (1995) SolGel Processing of PZT Thin-Films – A Review of the State-of-the-Art and Process Optimization Strategies, Integr. Ferroelectr. 7, 259-277. 78. Brinker C.J., Hurd A.J., Schunk P.R., Frye G.C., Ashley C.S., (1992) Review of Sol-Gel Thin-Film Formation, J. Non-Cryst. Solids 147, 424-436. 79. Reaney, I.M., Taylor, D.V., and Brooks, K.G. (1998) Ferroelectric PZT thin films by sol-gel deposition, J. Sol-Gel Sci. Techn. 13, 813-820. 80. Brinker, C.J. and Scherer, G.W. (1990) Sol – gel science: the physics and chemistry of sol-gel processing, Academic Press, New York. 81. Tuttle, B.A. and Schwartz, R.W. (1996) Solution deposition of ferroelectric thin films, MRS Bulletin 21, 49-54. 82. Prudenziati, M. (1991) Thick film technology, Sensor Actuat. A-Phys. 25-27, 227-234. 83. Kholkin, A.L., Wu, A. and Vilarinho, P.M. (2004) Piezoelectric Thick Film Composites: Processing and Applications, in Recent Research Developments in Materials Science, Research Sign Post, 5, pp. 1-24. 84. Akiyama, Y., Yamanaka, K., Fujisawa, E., and Kowata, Y. (1999) Development of lead zirconate titanate family thick films on various substrates, Jpn. J. Appl. Phys. 38, 5524-5527. 85. Jeon, Y., Kim, D.G., No, K., Kim, S.J., and Chung, J., (2000) Residual stress analysis of Pt bottom electrodes on ZrO2/SiO2/Si and SiO2/Si substrates for Pb(ZrTi)O3 thick films, Jpn. J. Appl. Phys. 39, 2705-2709. 86. Kubota, T., Tanaka, K., Sakabe, Y. (1999) Formation of Pb(Zr,Ti)O3-Pb(Zn,Nb)O3 system piezoelectric thick films in low-temperature firing process, Jpn. J. Appl. Phys. 38, 5535-5538. 87. Glynne-Jones, P., Beeby, S.P., Dargie, P., Papakostas, T., and White, N.M., (2000) An investigation into the effect of modified firing profiles on the piezoelectric properties of thick-film PZT layers on silicon, Meas. Sci. Technol. 11, 526-531. 88. Lubitz, K., Schuh, C., Steinkopff, T., and Wolff, A. (2002) Materials aspects for reliability and life time of PZT multilayer actuators, Piezoelectric Materials for the end user, Conference notes, Polecer Meeting, Interlaken, February 2002. 89. Nieto, E., Fernandez, J.F., Moure, C., and Duran, P. (1996) Multilayer piezoelectric devices based on PZT, J. Mater. Sci: Mater. Electron. 7, 55-60. 90. Galassi, C., Roncari, E., Capiani, C., and Pinasco, P. (1997) PZT-based suspensions for tape casting, J. Eur. Ceram. Soc. 17, 367-371. 91. Raeder, H., Simon, C., Chartier, T., and Toftegaard, H.L. (1994) Tape casting of zirconia for ionconducting membranes: a study of dispersants, J. Eur. Ceram. Soc. 13, 485-491. 92. Zhang, H.Z., Leppavuori, S., Uusimaki, A., Karjaleinen, P., and Rautioaho, R. (1994) Compositional and structural behaviour of screen-printed PZT thick films during rapid sintering, Ferroelectrics 154, 277282. 93. Fernandez, J.F., Nieto, E., Moure, C., Duran, P., and Newnham, R.E. (1995) Processing and microstructure of porous and dense PZT thick films on Al2O3, J. Mater. Sci. 30, 5399-5404. 94. Tanaka, K., Kubota, T., Sakabe, Y. (2002) Preparation of piezoelectric Pb(Zr,Ti)O3-Pb(Zn1/3Nb2/3)O3 thick films on ZrO2 substrates using low-temperature firing, Sensor Actuat. A-Phys. 96, 179-183. 95. Sarkar, P. and Nicholson, P.S., (1996) Electrophoretic deposition (EPD): mechanisms, kinetics, and applications to ceramics, J. Am. Ceram. Soc. 79, 1987-2002. 96. Van de Biest, O.O. and Vandeperre, L.J. (1999) Electrophoretic deposition of materials, Annu. Rev. Mater. Sci. 29, 327-352. 97. Boccaccini A.R. and Zhitomirsky, I. (2002) Application of electrophoretic and electrolytic deposition techniques in ceramics processing, Curr. Opin. Solid St. M. 6, 251-260. 98. Ngai, M., Yamashita, K., Umegaki, T., and Takuma, Y. (1993) Electrophoretic deposition of ferroelectric barium titanate thick films and their dielectrical properties, J. Am. Ceram. Soc. 76, 253-255. 99. Zhang, J. and Lee, B.I. (2000) Electrophoretic deposition and characterization of micrometer-scale BaTiO3 based X/R dielectric thick films, J. Am. Ceram. Soc. 83, 2417-2422. 100.Van Tassel, J. and Randall, C.A. (1999) Electrophoretic deposition and sintering of thin/thick PZT films, J. Eur. Ceram. Soc. 19, 955-958. 101.Su, B., Ponton C.B. and Button, T.W. (2001) Hydrothermal and electrophoretic deposition of lead zirconate tinate (PZT) films, J. Eur. Ceram. Soc. 21, 1539-1542. 102.Zhang, R.F., Ma, J., and Kong, L.B. (2002) Lead zirconate titanate thick film prepared by electrophoretic deposition from oxide mixture, J. Mat. Res. 17, 933-935. 103.Wu, A., Vilarinho, P.M., and Kingon, A.I. (2004) Electrophoretic deposition of lead zirconate titanate films on metal foils for embedded components, submitted to J. Am. Ceram. Soc.

33 104.Barrow, D.A., Petroff, T.E., and Sayer, M., (1996) US Patent 5,585,136. 105.Kholkine, A.L., Yarmarkin, V., Wu, A., Vilarinho, P.M., and Baptista, J.L. (2000) Thick piezoelectric coatings via modified sol-gel technique, Integr. Ferroelectr. 30, 245-259. 106. Kholkin, A.L., Yarmarkin, V.K., Wu, A., Avdeev, M., Vilarinho, P.M., and Baptista, J.L. (2001) PZT based thik film composites via a modified sol-gel route, J. Europ. Ceram. Soc. 21, 1535-1538. 107.Vilarinho, P.M., Wu, A., Kholkin, A. (2003) Method for the production of ceramic composites thick films by sedimentation and infiltration of sol-gel solutions, Portuguese patent pending n.º 102 909. 108.Auciello, O., Scott, J.F., and Ramesh, R. (1998) The Physics Of Ferroelectric Memories, Physics Today 51, 22-27. 109.Bottger, U., and Summerfelt, S.R. (2003) Ferroelectric Random Access Memories, in R. Waser (ed.) Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices, Willey-VCH, Weinheim, pp. 567-588. 110.Whatmore, R.W., Patel, A., Shorrocks, N.M., and Ainger, F.W. (1990) Ferroelectric Materials for Thermal IR Sensors: State of Art and Perspectives, Ferroelectrics 104, 269-275. 111.Lyshevski, S.E. (2002) MEMS and NEMS: systems, devices, and structures, CRC Press, Boca Raton, USA. 112.Saffo, P. (2002) Untangling the Future, Business 2.0.

SCALING OF SILICON-BASED DEVICES TO SUBMICRON DIMENSIONS

A.I. KINGON Department of Materials Science and Engineering North Carolina State University, Raleigh, NC 27695-7919, USA

Contents 1. 2. 3. 4. 5. 6.

Introduction Scaling of silicon-based devices 2.1. Trends 2.2. Roadblocks at the end of the silicon scaling era Integration of new materials with silicon 3.1. High permittivity gate oxides 3.2. Advanced dielectrics for DRAMs Integration of new functionality to silicon devices 4.1. Ferroelectric random access memories 4.2. Ferroelectric field effect transistors Where silicon meets molecular electronics Conclusions

1. Introduction The purpose of this paper, within the context of the NATO ASI proceedings, is twofold: a) To describe the competition that advanced functional materials, such as molecular devices, face from existing silicon technology. The new materials and devices must compete with devices fabricated using entrenched t semiconductor technology, especially silicon technology. The major problem is that silicon technology is not stationary, but progresses with a relentless momentum. This paper describes the progress in silicon technology from the perspective of scaling to submicron devices, and the expected performance at the end of the ‘silicon scaling era.’ It is at the end of this scaling era that new molecular electronic devices, such as those described by Kelly, and Sagiv and Cohen, are expected to become commercially viable. These molecular devices must outperform the silicon devices of thatt era, not the present generation. b) To describe difficulties and obstacles being faced by silicon electronics as the end of scaling is approached, and to show how new, functional materials are being considered for integration with silicon. These new materials are being incorporated in 35 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 35-50. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

36

order overcome some of the scaling obstacles, or alternatively to provide new functionality to silicon-based devices. The objectives of the paper are ambitious, and in reality the paper cannot cover all of the developments. As a result, some topics are mentioned only briefly, with references provided to recommended papers that represent either good review material, or represent important breakthroughs. Keywords: Scaling, silicon-based microelectronics, nanoelectronics, functional electronics, new materials. 2. Scaling of Silicon-based Devices 2.1. TRENDS The well-known trend of increasing number of devices per silicon chip is known as Moore’s Law [1]. As shown in Figure 1, the density has been increasing at an exponential rate (doubling every 18 months) for an amazing length of time, more than 30 years. The increasing device density has resulted from a regular decrease in the minimum feature size (along with a small increase in the overall chip dimensions). The decreasing feature size is also the origin of a number of related effects. It is the origin of the decreasing cost per function (storage bit or computational operation), the increasing microprocessor clock rate, and the decreasing power per logic or storage operation (leading to longer battery lifetimes in mobile devices). Scaling is also the origin of the dramatically decreasing size of electronic devices.

Figure 1. Diagram showing the exponential growth of the number of cells (logic or memory) per chip, as well as the decrease in the minimum feature size. (Original data from reference 2, figure adapted from reference 3).

This is the historical perspective. But what lies ahead? Since 1992, the Semiconductor Industry Association has been publishing ‘roadmaps,’ predicting the

37

main trends in the semiconductor industry 15 years into the future [2]. These roadmaps have provided a valuable source of guidance for the industry over the years, providing guidance for equipment and materials suppliers, and targets for researchers to provide solutions for upcoming years. An interesting side-note is that the competition bred by the roadmaps has resulted in semiconductor manufacturers frequently ‘beating’ the roadmap predictions, with individual firms working under the assumption that achieving the targets ahead of the roadmap would result in industry leadership. Table 1 compares important characteristics of past, present and future devices, showing the impact of incremental process innovation. The term ‘technology node’ relates to the minimum feature length allowed by the lithographic processes. Of particular note are the goals projected to be achievable by 2013, in particular the characteristic logic device gate lengths (13 nm), processor clock speeds, the sub-onevolt drive voltages, and the 3.1 billion transistors per chip. These can be contrasted with the 1993 values, showing the dramatic projected progress in a short 20 years. Also interesting is the fact that the year 2003 is the year in which the semiconductor industry entered the ‘nanoscale’ technology era, at 100 nm or below. Modern electronics is now nanoelectronics! TABLE I. Projections of the International Roadmap for Semiconductors (2003) Year of Production

2003

2005

2007

2009

2011

2013

2015

2017

100 nm 80 nm 65 nm 50 nm 40 nm 32 nm 25 nm 20 nm Physical Gate Length MPU/ASIC (nm)

45

32

25

20

16

13

10

8.0

DRAM Pitch (nm)

100

80

65

50

40

32

25

20

Equivalent physical Oxide Thickness Tox(nm) m2) High Performance

1.3

1.1

0.9

0.8

0.7

0.6

0.6

0.5

220

520

930

1200

2100

7700 10000 21000

307

487

773

1227

1948

3092

4908

7791

5.0 65

8.6 45

14.9 32

17.2 25

20

109 16

118 13

10

1.6

1.4

1.2

1.0

0.9

0.8

0.8

0.7

transistors) Unmanaged Gate Leakage Power (W/chip) Physical Gate Length low operating power (nm) EOT for low operating power Tox (nm)

0.51 2.22 5.21 6.07 11.7 20.8 25.6 100.0 m2) LOP Note: There are two types of transistors shown - the high performance logic, and the low operating power devices which are used for mobile applications.

The major message of this paper is to researchers involved in the development of new functional devices – both electronics and other functional devices. This message is that if the new devices are competing with Si-enabled devices, then they need to offer entirely new functionality, orr alternatively need to outperform the Si devices of the same generation. Thus, if one is developing molecular electronics, (for example, using the building blocks being developed by Sagiv and Cohen, see Chapter III of these proceedings), then the new molecular electronic devices must outperform the Si-based logic or memory in terms all the critical system performance parameters. Alternatively it must offer dramatically reduced cost or processing advantages, or offer new functionality currently not offered by scaled Si devices. These requirements provide

38

tremendous challenges for those of us involved in the development of new functional materials. The scaling of Si logic devices is mirrored in the scaling of Si-based memory devices, with dynamic random access memories (DRAMs) being the technology leader. Roadmap projections for DRAMs are also shown in Table 1. 2.2. ROADBLOCKS AT THE END OF THE SILICON SCALING ERA

Figure 2. Schematic cross-section of a field effect transistor (FET) drawn to scale. Note the very small thickness dimension of the gate oxide. The channel corresponds to the region in which the electronic carrier concentration is modulated by charging or discharging of the gate oxide capacitor. By modulating this concentration, the conductivity across this region (i.e., between the source and drain) is changed, hence the 'valve' type action. The source and drain regions correspond to the highly doped sections of the wafer at which two of the contacts are made (the third contact to this three-terminal device corresponds to the gate electrode). (The figure is adapted from reference 3).

Having pointed out the powerful capabilities projected for Si-based devices, we must hasten to add that there are major technical obstacles in the way of the achievement of the projected performance goals [3, 4]. Some of these are readily apparent in Table 1. Besides the difficulty in achieving the required feature resolution through lithographic techniques, there are a number of issues associated with the scaling of the gate dimensions, in particular the gate dielectric thickness. Figure 2 shows a schematic diagram of the CMOS transistor, drawn approximately to scale. As the areal dimensions are scaled, it is necessary to simultaneously scale the thickness of the gate dielectric in order to achieve a constant capacitance density to modulate the carriers in the channel to perform the transistor action. The traditional gate dielectric is a thermally grown amorphous silicon dioxide. However, the thickness dimension of the gate dielectric has dramatically decreased, and it is currently down to a few atomic layers thick (1.3 nm in 2003, Table 1). At these thicknesses, the leakage currents increase concomitantly, through an electron tunneling mechanism (Figure 3). In 2003, the gate leakage currents for logic devices can be as high as 220 A/cm2! By the 32 nm technology node of 2013, the leakage currents are projected to be as high as 7.7 x 103 A/cm2. As these represent

39

dissipative losses, the major implication of the high leakage current lies in the large amount of thermal power that must be dissipated (see Table 1). By the year 2013, logic chips are projected to dissipate about 450 W per chip under static conditions! Thermal management is going to become a major issue. Itt should be noted that at the 32 nm node of 2013, the physical thickness of the dielectric, if SiO2, is expected to be less than 0.6 nm. At this thickness, the SiO2 properties are no longer represented by bulk SiO2, as recently described by Muller et al [6].

Figure 3. Plots of the current densities flowing between gate contact and channel through an SiO2 dielectric, for various thicknesses of SiO2 dielectric, as a function of applied voltage (From reference 4). Although calculated and measured for an FET, the same results are relevant for DRAMs. The horizontal lines indicate maximum allowable current densities for the two cases.

Due to the gate leakage issues, over the past few years the silicon technology roadmaps have distinguished three types of product: high performance logic; low power; and low standby power devices. The last two are demanded by mobile consumer applications. These latter devices require lower leakage currents, and as a result the gate dielectric thickness will not scale as fast as the high performance devices. However, despite the lower scaling rate, it is for these low power devices that the issue of leakage current first becomes critical. The severe constraints imposed upon the gate dielectric and the gate dielectric stack (i.e. including the metal contact, Figure 2), has led to the expectation that the SiO2 dielectric will need to be replaced by an alternative, higher permittivity material. This higher permittivity will allow a thicker physical thickness for the same capacitance density. If a number of other requirements are met, then the alternative dielectric may have a lower corresponding leakage current density. This potential has led to a flurry of

40

research over the past few years into alternative materials for the gate stack of mainstream CMOS devices. In the next section we discuss briefly the progress in the development of alternative dielectrics for Si devices. However, the significance of this work should be noted in the context that the strength of the Si-based microelectronics industry has been based upon the very limited number of materials at the heart of the devices. Even the transition from Al wiring at the ‘back-end’ to Cu-based connections required a vast effort over many years. The materials at the ‘front-end,’ i.e. those associated with the heart of the transistor, have been sacrosanct for half a century. Replacing the SiO2 dielectric truly represents a paradigm shift within the industry. Similar roadblocks exist for DRAMs. Once again, the aggressive thickness scaling of the SiO2 dielectric leads to difficulties in meeting the required leakage current requirements, and there is an aggressive search for alternative dielectrics [3, 7-10].

3. Integration of new materials with silicon 3.1. HIGH PERMITTIVITY GATE OXIDES The substantially increasing leakage currents that result from the thickness scaling of SiO2 have two major negative outcomes [11]. First, it directly impacts the on-off characteristics of the transistor. Secondly, the large leakage currents result in extremely large power dissipation, with thermal management of the logic chips being of increasing concern. The need to solve the problem of the high leakage currents in the Si logic generations from approximately 2005 has resulted in a huge R&D effort in developing and incorporating alternative dielectrics with higher permittivities than SiO2. Simply put, the approach of utilizing a higher permittivity material will allow a dielectric with the same capacitance density as SiO2, but which is physically thicker. If certain rules are followed (see below) the higher physical thickness can reduce the leakage currents associated with direct electron tunneling. However, as one can imagine, the challenge of finding a suitable dielectric to replace thermal SiO2 is enormous. The quest may be divided into the following parts: • Selecting candidate dielectrics that are thermodynamically stable in contact with the doped Si channel, and under the subsequent processing conditions • Subsequently selecting candidates which have appropriate dielectric permittivities, band gaps, and band offsets from the Si conduction and valence bands • Selecting candidates that additionally result in acceptable transistor performance. We will discuss these issues in turn. Firstly, the need to ensure that there is no reaction between the alternative gate dielectric and silicon greatly limits the choice of materials, as discussed first by Hubbard and Schlom [12]. Simple materials with reasonable dielectric constants that were initially considered, such as TiO2 and Ta2O5, suffer from a thermodynamically favorable reduction, through the formation of the metal silicide and SiO2. This has resulted in investigations of simple oxides such as ZrO2, HfO2, Al2O3, La2O3, Y2O3, and Gd2O3, although their permittivities are lower than the two mentioned previously. Secondly, the candidate dielectrics t must have low leakage currents at the operating voltages. While there are other factors that may increase the leakage currents, a

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fundamental requirement is that there is an offset of greater than the operating voltages between the conduction and valence bands of the doped Si of the channel and those bands of the dielectric. Initially, it was assumed that if the optical band-gaps were sufficiently large, for example > 3 eV, then the conduction and valence band offsets would be appropriate. Calculations and experiments by Robertson [13], and subsequently others [14], showed that this simple assumption is inadequate, and that the number of candidates is further limited by this requirement. Furthermore, it has become clear that the band offsets are often not controlled t by the intrinsic properties of the materials, but can easily be modified by extrinsic factors that give charge transfer across the Si-dielectric interface. These processing-related issues are currently being investigated. Thirdly, and possibly most critically, there are many factors that can influence the carrier mobility in the Si channel, and thus the transistor performance, including charge at the interfaces, dipoles at the interface, and roughness at the interfaces, all of which can scatter the carriers. Additionally, it has recently emerged that phonon modes in the dielectric, which are responsible for the high permittivities, may also be reducing carrier mobility in the channel through remote phonon scattering [15, 16]. We now briefly present the current materials status. The preferred material at the present time is HfO2 for implementation at approximately the 65 nm technology node. Results for the closely related material, ZrO2, have been similar, but the community has leaned towards the former. HfO2 and ZrO2 have permittivities of approximately 20 - 25, in other words more than 5 times that of SiO2. The dielectrics are typically deposited in amorphous form. However, during post-deposition processing, two important phenomena occur. Firstly, crystallization typically begins as low as 400 ºC, and even very rapid annealing protocols are typically not successful in preventing crystallization. Secondly, if post processing in oxygen partial pressures greater than approximately 10–5 torr, oxygen from the atmosphere diffuses through the dielectric to the Si interface, and forms SiO2. The rate of SiO2 formation, or at least up to the first 0.5 to 1.0 nm, is extremely rapid. It occurs faster than Si oxidation in the absence of the dielectric, as shown by Garfunkel et al. The phenomenon is shown in Figure 4 [17]. The figure also shows the impact of processing at too low an oxygen partial pressure, namely the reduction of the dielectric to form a silicide [17, 18]. It is essential to avoid the reduction, and thus processing under some controlled t oxygen partial pressure is the norm. As a result, the gate stack does not consistt of a simple layer of high K dielectric (e.g. HfO2) directly on Si. Instead, the dielectric stack consists of Si with a thin interfacial layer of SiO2 (e.g. 0.6 nm thick), and with the HfO2 deposited upon that SiO2 layer. Typically, the HfO2 would be of 2-3 nm thickness. The stack therefore ends up with an effective permittivity corresponding to that of approximately 0.8 to 1.3 nm of SiO2. Figure 5 shows the status of various gate dielectrics, with the Equivalent Oxide Thickness (EOT, corresponding to the equivalent thickness of SiO2) plotted against the important parameter, gate leakage current density. It can be seen that the best alternative gate dielectrics are 2-3 orders of magnitude lower in leakage current density than the equivalent SiO2 gate stack.

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as-deposited Si

~ 26 Å

Ig (A/cm m2)

1000 °C - 10-55 Torr

10

3

10

1

-1

10

-3

10

-5

10

~ 28 Å

10-4

-7

10

10-3

-9

10

-3

-2

-1

0

1

2

3

Vg (V)

as-dep 1.6 10-5

10-4 1.2 10-3

1000 °C - 10-4 Torr

SiO2 ZrO 2

0.8 0.4 0 -3

~ 80 Å Si

1000 °C - 10-66 Torr conversion to ZrSi2

~ 55 Å -2

-1

0 1 2 3 extensive interface growth Vg (V) Figure 4. Composite of electrical and microstructural data for ZrO2-based dielectrics processed and different temperatures and oxygen partial pressures. The TEM of the as-deposited film shows 2.6nm physical thickness -5 of ZrO2, with little or no SiO2 apparent at the interface. High temperature annealing at 10 torr causes some SiO2 to form between ZrO2 dielectric and Si, by oxygen diffusion through the dielectric. Annealing at higher oxygen partial pressures results in more SiO2, and lower capacitance densities. On the other hand, annealing at too low an oxygen partial pressure causes reduction to form a silicide, with a resulting large increase in leakage currents [17, 18].

It must be mentioned that the interfacial SiO2 layer (around 0.5 to 1.0 nm in thickness) appears to play an extremely important role in the achievement of acceptable properties. The HfO2 is normally grown on the thin thermally grown SiO2 interface, and this implies that the interface closest to the channel can be processed to be of high quality, with low interface state defect densities. This approach relies upon the prior knowledge of the Si community to achieve the high quality interface. There are several complications that we have to mention. The first is that of crystallization. The gate stack is typically rapidly annealed to temperatures as high as 1100 ºC for a short period (for example – 5 seconds) in order to “activate” the dopants in the silicon. As mentioned previously, the crystallization occurs at temperatures substantially lower than this value, despite the rapid heating and cooling rates. At this point it is not yet known whether the presence of nanocrystalline grains of HfO2 are deleterious to the properties. Certainly, it does not appear that the grain boundaries impact the leakage currents. However, the crystallization is accompanied by some increase in roughness of the second (SiO2-HfO2) interface, and defects associated with the grain boundaries could easily be expected to act as charge traps, with either filling or emptying of the traps resulting in a negative impact upon transistor properties. To date, the identification of defects, and correlation with transistor properties, has not been accomplished. However, it does appear that attempts to thin or remove the SiO2

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interface results in poor transistor properties. This presents a major problem for scaling this system to equivalent oxide thicknesses of 0.5 nm or below, as predicted in the SIA Roadmap.

Figure 5. J vs EOT for some candidate dielectrics

The problem of crystallization may be addressed by alloying HfO2 with an oxide that retards crystallization, such as SiO2 or Al2O3. In the case of SiO2 alloy additions, the deposition of amorphous HfO2-SiO2 (or ZrO2-SiO2) does retard crystallization, but at the expense of permittivity [3]. Additionally, when crystallization does occur, the crystallization products are not the equilibrium products predicted by the binary oxide phase diagram, but instead they are the products of spinodal decomposition. Once again this is HfO2, surrounded by a SiO2-rich amorphous phase. It is nott yet clear whether the presence of the nanocrystalline phase is deleterious for transistor performance. Alloying with Al2O3 has successfully retarded crystallization, with a smaller penalty in permittivity than the SiO2 case [20], but unfortunately transistor properties have been unacceptable. Secondly, replacement of the dielectric also requires replacement of the gate electrode metal (see the transistor diagram in Figure 2), which is currently polysilicon (p-Si). This is primarily due to the loss off capacitance density associated with the additional SiO2 formation at this interface. Replacement of the p-Si must be by one or more metals with (once again) appropriate band offsets to the high permittivity dielectric, as well as thermodynamic stability in contact with the dielectric during

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subsequent processing. This presents an almost impossibly difficult problem, for which a limited number of solutions may be emerging [21, 22]. In summary, it appears that a high permittivity dielectric based upon HfO2 may be feasible, at least for one or two generations around the 65 nm technology node. However, no solutions have yet emerged for the technology nodes of 32 nm and below. Some research groups are investigating the M2O3 oxides, and M2O3-based alloys as potential gate dielectrics for the last technology nodes. Somewhat encouraging results, at least in terms of capacitor properties, have been shown for La2O3, Gd2O3, La2O3-SiO2, and LaAlO3, with some capacitor properties showing EOT values down to the 0.6 to 0.7 nm range, with leakage current densities 2-3 orders of magnitude lower than SiO2 at the same EOT [11, 17, 23]. The major problem faced is that of the interfacial SiO2 layer. In order to achieve the required EOT values around 0.5 nm, it is essential remove, or replace, this interfacial layer that is contributing about 0.5 nm to the total EOT. However, it is also this same interfacial layer that is allowing the best transistor properties to be achieved as the high K materials are incorporated. There is no obvious solution to this conundrum. It is important to note that the thermodynamic behavior of these M2O3 materials is different from that of HfO2 and ZrO2. Instead of phase separation, the M2O3 materials tend to react with SiO2 at the interface, consuming this material and forming an M2O3-SiO2 amorphous solid solution [17, 24, 25]. The case of amorphous LaAlO3 should also be mentioned. It has recently been shown that amorphous LaAlO3 can be deposited on bare Si, and that complete oxidation can be achieved without oxidation of the Si surface. Capacitor properties are encouraging in terms of EOT and critical current densities [11], although transistor properties have not yet been characterized. Finally, it should be noted that the Semiconductor Industry Association Roadmap suggests that the dielectrics required at the end of the silicon scaling era may well be multicomponent epitaxial oxides, rather than amorphous oxides. This represents a major challenge for the materials community. 3.2. ADVANCED DIELECTRICS FOR DRAMS There is a requirement for high permittivity dielectrics for DRAMs, analogous to that for gate stacks in logic devices. The 1T-IC DRAM cell contains a capacitor which acts as a simple charge storage device, with the presence or absence of the stored charge representing the binary information “1” or “0”. The transistor is simply a switch, which allows the information to be written or read. The capacitor has to be continuously rewritten, or ‘refreshed’, as the charge is lost through leakage. Once again, as DRAMs are scaled to smaller dimensions, the required capacitance remains approximately constant, set by the sense amplifier requirements. Thus, scaling requires an increase in either capacitance density, or alternatively an increase in capacitance dielectric area (as the footprint or area available for the DRAM cell inexorably reduces). Traditionally, the capacitor material has been SiO2, or nitrogen substituted SiO2 (SiON), and the dielectric area increased either by etching a large surface area ‘trench’ in the Si substrate, or by creating large surface area ‘built-up’ structures above the substrate (such as ‘crowns,’ ‘fins’ or multiple ‘discs’). At some point, the difficulty in creating these large area structures becomes sufficiently great that the incorporation of alternative, high permittivity dielectrics becomes a tenable alternative. References 7-10 represent comprehensive discussions of the problems, along with the materials solutions.

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All the DRAM manufacturers have extensive R&D programs investigating the intermediate permittivity dielectrics, such as Ta2O5, Al2O3 and HfO2. Ta2O5 has been studied as a DRAM and gate dielectric for over 10 years. It is envisaged that introduction will first occur in the form of metal/dielectric/silicon (MIS) capacitors, with the Ta2O5 deposited directly on Si, followed by later introduction of metal/insulator/metal (MIM) capacitors [26]. Introduction of MIS Ta2O5 capacitors has been much slower than expected, for the following reasons. Ta is generally deposited at low temperatures, with the resulting dielectric being amorphous or nanocrystalline. This microstructure needs to be annealed in an oxidizing atmosphere in order to increase the dielectric constant and reduce the leakage currents. As this is undertaken, oxygen diffusion through the dielectric results in the oxidation of the Si surface. The resultant low permittivity, series-connected SiO2 dielectric reduces the capacitance density and effective permittivity of the stack. Process integration studies have therefore had to find compromise solutions, including: rapid thermal annealing of the Si surface in N2 (RTN at 800 ºC) prior to dielectric deposition in order to increase the oxidation resistance of the surface; and annealing the Ta2O5 dielectric in UV-O3, followed by a rapid thermal anneal in O2. More effort has recently been devoted to Ta2O5-based MIM capacitors for DRAMs [26-32]. The MIM structure has the direct advantage of eliminating depletion effects associated with the Si interface, and also the problem of SiO2 formation at the interfaces. Attractive structures include TiN or Ru electrodes, or combinations thereof. A consortium of Fujitsu and Toshiba has developed a structure in which the electrode forms a high surface area, high aspect ratio cylinder, upon which the dielectric (in particular Ta2O5) can be deposited by chemical vapor deposition. A study of the mechanical stability of the electrode cylinder by the Fujitsu/Toshiba consortium suggests that this Ru/Ta2O5/Ru technology could be scaled beyond the 100 nm technology node. For example, the existing achievable cylinder aspect ratio of 8 (internal diameter to heightt ratio) would allow the 65 nm technology node (4 Gb) to be achieved [28]. Another dielectric that has received attention over the past few years is Al2O5 [3335]. This material may appear a surprising candidate, as it has a lower permittivity than Ta2O5, around 9 to 10. However, there are two factors favoring the material, namely its low leakage current density, and also the availability of high reliability layer-by-layer MOCVD growth (termed “atomic layer deposition” or ALD), along with the ALD equipment suitable for a manufacturing environment. Samsung have demonstrated a fully functional MIS 1 Gb DRAM using Al2O5 deposited by ALD on ‘rough’ Si with TiN plate (top) electrodes [34]. The low process temperature of 350 °C is attractive to minimize the formation of a low permittivity SiO2 layer at the Si interface. No predictions are yet being made regarding the scalability to further generations. However, it should be noted that the high quality conformal coverage makes the material attractive for high aspect ratio geometries, in particular deep trenches. This is demonstrated in a recent publication from Infineon, which demonstrates the use of ALD Al2O5 in trenches for sub-100 nm technology [36]. This work additionally uses rough polysilicon (HSG) in the trench, and uses a “bottle” geometry to maximize the surface area. Recently, DRAM manufacturers have been developing layered or ‘laminate’ dielectrics, in order to gain maximum advantage from each of two different dielectric materials. For example, Al2O5/HfO2 laminate structures have been demonstrated by Samsung [37]. The apparent advantage is that Al can be deposited with minimal

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accompanying growth of a deleterious SiO2 interfacial layer, while HfO2 has a higher dielectric constant (around 22). Looking beyond these simple oxides, towards the end of the Si scaling era, the silicon industry Roadmap suggests that DRAMs will need to incorporate the very high permittivity perovskite solid solution (Ba,Sr)TiO3 (or ‘BST’). This material was extensively studied during the decade of the 90’s [8-10]. 4. Integration of new functionality to silicon devices 4.1. FERROELECTRIC RANDOM ACCESS MEMORIES One of the important technological fields in which advanced materials have been integrated with Si integrated circuits in order to provide additional functionality is that of ferroelectric random access memories (FERAM) [38]. This memory device is analogous to a DRAM cell in that each cell consists of an access transistor and a capacitor. In this case, the capacitor dielectric is also a ferroelectric material (see Chapter 1). The access transistor allows a short pulse to be uniquely applied to the ferroelectric capacitor of the cell, writing (i.e. ‘poling’) the ferroelectric capacitor in one of two possible net polar orientations, corresponding to bit states ‘0’ or ‘1.’ The cell is read by again applying a voltage pulse to the capacitor, and monitoring the resultant current pulse through a sense amplifier. The current pulse corresponds to two possible cases. If no switching occurs, because the pulse is the same sign as the pulse that wrote the bit, then the current pulse corresponds to capacitor charging only. If, however, the read voltage pulse is of opposite sign to the write pulse, the resultant current pulse will contain the additional current corresponding to the polarization switching charge. The two cases can therefore be discriminated, i.e. the state of the cell can be read. It should be noted that this is a ‘destructive’ readout memory device. This is important, as both read and write cycles must therefore be included in determining the number of switching cycles that the memory must endure to achieve reliability and lifetime goals. The reason for the ongoing interest in ferroelectric memory lies in the unique combination of properties that it offers. In particular, the memory can in principle be as fast and as dense as the DRAM, but has the advantage of non-volatility. In comparison with other nonvolatile memories such as EEPROM or Flash, FERAM has shorter write times, and lower write voltages. The primary ferroelectric materials which are utilized in ferroelectric memories are the Pb(Zr,Ti)O3 (PZT) solid solution system, and modified SrBi2Ta2O9. These materials have been discussed in Chapter 1. The importance of scanning probe techniques for the characterization of the FERAM devices is discussed in the Chapter by Gruverman. The FERAM devices represent a case where complex, multifunctional oxides have been successfully integrated into a silicon integrated circuit. However, it should be noted that it has taken many years, almost 20 years, to get FERAM into commercial production. Furthermore, there are two important issues to point out. Firstly, these ferroelectric memories can be considered backend devices, rather than frontend. This means that the access transistors are processed first, followed by a relatively thick dielectric isolation layer, which protects the silicon frontend from potential contamination by elements from the ferroelectric. The ferroelectric layer is then deposited, and the ferroelectric capacitor stack defined. The ferroelectric stack can even

47

be processed in a portion of the facility separated from the main portion of the silicon fabrication process, in order to minimize contamination. Secondly, the properties of the ferroelectric memories are sufficiently unique that there is a niche market for low density devices, memories which a many generations behind in terms of technology node. If, as in the case of logic and DRAM devices, the oxides would have had to be integrated at the then-current generation, it is certain that the complexity of the materials and integration challenges would have doomed the project to failure. This provides a useful lesson for the integration of the new functional molecular materials with silicon substrates: the community should be aiming at devices that have substantially different, but useful properties, to those of current silicon semiconductor devices. These devices that will address unique applications, may have a market even at low density or low overall performance. 4.2. FERROELECTRIC FIELD EFFECT TRANSISTORS Another memory concept that has been discussed and developed for over 45 years is the ferroelectric field effect transistor (abbreviated FEFET or FEMFET). The concept is simple, replacing the gate dielectric of a field effect transistor by a ferroelectric material. The direction of polarization controls the flatband voltage of the capacitor, i.e. it gives two characteristic voltages at which the transistor can be turned on. This means the transistor can be used as a simple nonvolatile memory, with the added advantage that it has a non-destructive readout (NDRO), i.e. it does not need to be switched in order to read the bit state. The other major advantage is that it is a 1-transistor (1T) memory, and in principal it therefore is much smaller than any other memory type. The early work utilized bismuth titanate films, and uncovered a significant difficulty, namely the fact that the turn-on voltage, particularly in one orientation, changed with time. The origin of the phenomenon is clear – the polarization must be screened, and there are several competing sources of screening charge other than the desired carriers from the transistor channel, viz., charge which has leaked through the ferroelectric gate, or mobile charge from within the ferroelectric gate. The result is that the screening process occurs over a long time period (days and months), with a concomitant change in the turn-on voltage (i.e. the characteristic memory window). This is known as a retention problem. The problem is usually worse for one polarization, i.e. that direction for which screening requires minority carriers from the channel. Research by Westinghouse in the ‘80s and early nineties focused upon the problem of retention by addressing dielectric and interface quality. They moved from Bi4Ti3O12 to PZT and then to MBE-grown ferroelectric BaMgF4, but were unsuccessful in solving the retention problem [39]. More recently, research on the device type has renewed, particularly in Japan [40]. Approaches have included the incorporation of an additional insulator layer between ferroelectric and Si channel (MFIS-type), or even a floating gate (MFMIS-type); the matching of charge requirements at all interfaces; and minimization of leakage currents [40]. Retention of a few days has been achieved. The 1T ferroelectric memory thus remains tantalizing: the obstacles continue to loom large, but success would promise in a revolution in the microelectronics industry. A recent and interesting variation of a single transistor memory is the ferroelectric resistance tunnel junction that has been discussed by the group from Aachen in Germany [41].

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5. Where silicon meets molecular electronics An important question remains, which is whether the incorporation of the new materials will open up silicon technology to the further incorporation of new molecular functional materials directly into the Si chip, or subsequently to the adoption of Si-molecular material hybrid circuits. The major point of this paper is that it is important not to attempt to develop molecular materials which are the direct analogues of existing Si logic or memory devices – this is a monumental task which will not yield competitive devices without enormous resource allocation. This is particularly true for the case of three-terminal devices required for logic, and which also require some ‘gain’, i.e. the output power should be larger than the control power. This is proving extremely difficult to achieve with organic-based materials. Instead, in the short and medium term, the primary attention should be on investigating alternative molecular devices that offer new functionality, and open up new applications. By avoiding direct competition with the incumbents, the future of molecular materials will be bright. 6. Conclusions In this chapter we have emphasized the fact that Si-based devices continue to scale to smaller and smaller dimensions, in accordance with the semiconductor industry roadmap. With this scaling, chips become faster, cheaper, and more powerful, with more devices packed onto each chip. The scaling is at the point that, during 2003, the most advanced logic devices transitioned into the nanoelectronics era, with characteristic length dimensions less than 100 nm. However, obstacles associated with scaling have resulted in the unprecedented consideration of the replacement of the fundamental materials, in particular the replacement of the SiO2 gate oxide within the CMOS transistor. This is a trend that may result in many more multifunctional materials being integrated into mainstream silicon devices. Similarly, molecular materials may be integrated with Si semiconductors to yield hybrid devices, with new and unique functionality for as-yet un-thought-of applications. Acknowledgements The author would like to thank NSF and SRC for financial support for research in the topics described in this chapter. References 1. 2. 3.

Moore, G.E. (1975) Progress in digital integrated electronics, International Electron Devices Meeting 1975, Technical digest, pp. 11-13. International Technology Roadmap for Semiconductors, Semiconductor Industry Association, 1992, 1995, 1997, 1999, 2001, and 2003 editions. (url for 2001 edition is http://public.itrs.net) Kingon, A.I., Maria J.-P., and Streiffer, S.K. (2000) Alternative dielectrics to silicon dioxide for memory and logic devices, Nature, 406, 1032-1038.

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5. 6. 7. 8. 9. 10. 11.

12. 13. 14. 15. 16. 17.

18.

19. 20. 21. 22.

23. 24. 25. 26. 27.

28.

Lo, S.-H., Buchanan, D.A., Taur, Y., and Wang, W. (1997) Quantum-mechanical modeling of electron tunneling current from the inversion layer of ultra-thin-oxide nMOSFET’s, IEEE Electron Device Letters 18, 209-211. Data from the 2003 SIA Roadmap for Semiconductors. Muller, D.A., Sorsch, T., Moccio, S., Baumann, F.H., Evans-Lutterodt, K., and Timp, G. (1999) The electronic structure of the atomic scale of ultra-thin gate oxides, Nature 399, 758-761. Schroeder, H. and Kingon, A.I. (2003) High-Permittivity Materials for DRAMs, in R. Waser (ed.), Nanoelectronics and Information Technology, Wiley-VCH Verlag GmbH & Co., pp. 539-563. Summerfelt, S.R. (1997) (Ba,Sr)TiO3 Thin Films for DRAM's, in R. Ramesh (ed.), Thin Film Ferroelectric Materials and Devices, Kluwer Academic Publishers, Boston, pp. 1-42. Kotecki, D.E., (1997) A review of high dielectric materials for DRAM applications, Integr. Ferroel. 16, 1-19. Kotecki, D.E., Baniecki, J.D., Shen, H., et al. (1999) (Ba,Sr)TiO3 dielectrics for future stacked-capacitor DRAM, IBM J. Res. Develop. 43, 367-382. Osburn, C.M., Campbell, S.A., Eisenbraun, E., Garfunkel, E., Gustafson, T., Kingon, A., Kwong, D.-L., Lee, J., Lucovsky, G., Ma, T.P., Maria, J.P., Misra, V., Parsons, G., Schlom, D., and Stemmer, S. (2004) Materials and processes for high K gate stacks, to be published in IFST. Hubbard, K.J. and Schlom, D.G., (1996) Thermodynamic stability of binary oxides in contact with silicon, J. Mater. Res. 11, 2757–2776. Robertson, J. (2002) Electronic structure and band offsets of high-dielectric-constant gate oxides, Mater. Res. Bull. 27, 217-221. For example: Lucovsky, G. (2003) Electronic structure of transition metal/rare earth high-K gate dielectrics: interfacial band alignments and intrinsic defects, Microelectron. Reliab. 43, 1417-1426. Zhu, W., Han, J.-P., and Ma, T.P. (2004) Mobility measurement and degradation mechanisms of MOSFETs made with ultrathin high-k dielectrics, IEEE Trans. El. Dev. 51, 98-105. Fischetti, M., Neumayer, D., and Cartier, E. (2001) Effective electron mobility in Si inversion layers in MOS systems with a high-k insulator: the role of remote phonon scattering, J. Appl. Phus. 90, 4587-4608. Maria, J.-P., Wicaksana, D., Kingon, A.I., Busch, B., Schulte, H., Garfunkel E., and Gustafsson, T., (2001) High temperature stability in lanthanum and zirconium-based gate dielectrics, J. Appl. Phys. 90, 3476-3482. Stemmer, S., Chen, Z., Keding, R., Maria, J.-P., Wicaksana, D., and Kingon, A.I., (2002) Stability of ZrO2 layers on Si (001) during high temperature anneals under reduced oxygen partial pressures, J. Appl. Phys. 92, 82-86. Data compiled by C M Osburn, NCSU, and privately communicated. Chen, P.J., Cartier, E., Carter, R.J., et al. (2002) Thermal stability and scalability of Zr-aluminate-based high-k gate stacks, 2002 Symposium on VLSI Technology Digest of Technical Papers, pp. 192-193. Misra, V., Lucovsky, G., and Parsons, G. (2002) Issues in high-k gate stack interfaces, Mater. Res. Bull. 27, 212-216. Zhong, H., Hong, S.N., Suh, Y.-S., Lazar, H., Heuss, G., and Misra, V. (2001) Properties of Ru-Ta alloys as gate electrodes for NMOS and PMOS devices, 2001 Symposium on VLSI Technology, Digest of Technical Papers, pp. 49-53. Guha, S., Cartier, E., Gribelyuk, M.A., Bojarczuk N.A., and Copel, M.C., (2000) Atomic beam deposition of lanthanum- and yttrium-based oxide thin films for gate dielectrics, Appl. Phys. Lett. 77, 2710-2712. Stemmer, S., Maria, J.-P., and Kingon, A.I. (2001) Structure and stability of La2O3/SiO2 layers on Si(001),” Appl. Phys. Lett. 79, 102-104. Copel, M., Cartier, E., Narayanan, V., Reuter, M.C., Guha, S., and Bojarczuk, N. (2002) Characterization of silicate/Si(001) interfaces, Appl. Phys. Lett. 81, 4227-4229. Park Y. and Kim, K. (2001) COB stack DRAM cell technology beyond 100nm technology node, International Electron Devices Meeting 2000, Technical Digest, pp. 391-394. Hiratani, M., Hamada, T., Iijima, S., Ohji, Y., Asano, I., Nakanishi, N. and Kimura, S. (2001) A heteroepitaxial MIM-Ta2O5 capacitor with enhanced dielectric constant for DRAMS of G-bit generation and beyond, 2001 Symposium on VLSI Technology, Digest of Technical Papers, pp. 41-42. Fukuzumi, Y., Suzuki, T., Sato, A., Ishibashi, Y., Hatada, A., Nakamura, K., Tsunoda, K., Fukuda, M., Lin, J., Nakabayashi, M., Minakata, H., Shimada, A., Kurahashi, T., Tomita, H., Matsunaga, D., Hieda, K., Hashimoto, K., Nakamura, S. and Kohyama, Y. (2000) Liner-supported cylinder (LSC) technology to realize Ru/Ta2O5/Ru capacitor for future DRAMs, International Electron Devices Meeting 2000, Technical digest, pp. 793-796.

50 29. Lin, J., Suzuki, T., Minakata, H., Shimada, A., Tsunoda, K., Fukuda, M., Kurahashi, T., Fukuzumi, Y., Hatada, A., Sato, A., Sun, P.H., Ishibashi, Y., Tomita, H., Nishikawa, N., Ito, E., Liu, W.C., Chu, C.M., Suzuki, R., Nakabayashi, M., Matsunaga, D., Hieda, K., Hashimoto, K., Nakamura, S., Kohyama, Y., and Shiah, C.M. (2001) Backend process for cylindrical Ru/Ta2O5/Ru capacitor for future DRAM, Solid-State and Integrated-Circuit Technology, Proceedings, pp. 183-188. 30. Kim, W.D., Kim, J.W., Won, S.J., Nam, S.D., Nam, B.Y., Yoo, C.Y., Park, Y.W. Lee, S.I., and Lee, M.Y. (2000) Development of CVD-Ru/Ta2O5/CVD-TiN capacitor for multigigabit-scale DRAM generation, 2000 Symposium on VLSI Technology, Digest of Technical Papers, pp. 100-101. 31. Nakamura, Y., Asano, I., Hiratani, M., Saito, T., and Goto, H. (2001) Oxidation-resistant amorphous TaN barrier for MIM-Ta2O5 capacitors in giga-bit DRAMs, 2001 Symposium on VLSI Technology, Digest of Technical Papers, pp. 39-40. 32. Takeuchi, M., Inoue, K., Sakao, M., Ssakoh, T., Kitamura, C., Arai, S., Iizuka, T., Yamamoto, T., Shirai, H., Aoki, Y., Ijamada, M., Kubota, R., and Kishi, S. (2001) A 0.151 µm logic based embedded DRAM technology featuring 0.425 µm m2 stacked cell using MIM (Metal-Insulator-Metal) capacitor, 2001 Symposium on VLSI Technology, Digest of Technical Papers, pp. 29-30. 33. Kim, Y.K., Lee, S.H., Choi, S.J., Park, H.B., Seo, Y.D., Chin, K.H., Kim, D., Lim, J.S., Kim, W.D., Nam, K.J., Cho, M.-H., Hwang, K.H., Kim, Y.S., Kim, S.S., Park, Y.W., Moon, J.T., Lee, S.I., and Lee, M.Y., (2000) Novel capacitor technology for high density stand-alone and embedded DRAMs, International Electron Devices Meeting 2000, Technical digest, pp. 369-372. 34. Park, I.-S., Lee, B.T., Choi, S.J., Im, J.S., Lee, S.H., Park, K.Y., Lee, J.W., Hyung, Y.W., Kim, Y.K., Park, H.S., Park, Y.W., Leem, S.I., and Lee, M.Y. (2000) Novel MIS Al2O3 capacitor as a prospective technology for Gbit DRAMs, 2000 Symposium on VLSI Technology, Digest of Technical Papers, pp. 4243. 35. Kim, Y.K., Lee, S.M., Park, I.S., Park, C.S., Lee, S.I., and Lee, M.Y. (1998) Novel poly-Si/Al2O3/poly-Si for high density DRAMs, 1998 Symposium on VLSI Technology, Digest of Technical Papers, pp. 52-53. 36. Lutzen, J., Birner, A., Goldbach, M., Gutsche, M., Hecht, T., Jakschik, S., Orth, A. Sanger, A., Schroeder, U., Seidl, H., Sell, B., and Schumann, D. (2002) Integration of capacitor for sub-100-nm DRAM trench technology, 2002 Symposium on VLSI Technology Digest of Technical Papers, 178-179. 37. Lee, J.-H., Kim, Y.-S., Jung, H.-S., Lee, J.-N.-I., Kang, L.-K., and Suh, K.-P. (2002) Practical next generation solution for stand-alone and embedded DRAM capacitor, 2002 Symposium on VLSI Technology Digest of Technical Papers, 114-115. 38. Bottger, U. and Summerfelt, S. (2003) Ferroelectric Random Access Memories, in R. Waser (ed.), Nanoelectronics and Information Technology, Wiley-VCH Verlag GmbH & Co., pp. 565-588. 39. See for example: Sinharoy, S., Buhay, H., Francombe, m M.H., and Lampe, D.R. (1993) BaMgF4 thin film development and processing for ferroelectric FETs, Integr. Ferroelectr. 3, 217-223. 40. Ishiwara, H. (2001) Recent progress of FET-type ferroelectric memories, Integr. Ferroelectr. 34, 11-20. 41. Fitsilis M., Kohlstad, H. Waser, R., et al (2004) A new concept for using ferroelectric transistors in nonvolatile memories, Integr. Ferroelectr. 60, 45-58.

UNSOLVED PROBLEMS IN FERROELECTRICS FOR SCANNING PROBE MICROSCOPY J.F. SCOTT Symetrix Centre for Ferroics, Earth Sciences Department Cambridge University, Cambridge CB2 3EQ, U.K.

Contents 1.

2.

3.

4.

5.

6.

Introduction and deposition techniques 1.1. Nanophase deposition techniques 1.1.1. Electron-beam direct writing 1.1.2. Focussed-ion-beam processing 1.1.3. Self-assembly Topography of new films 2.1. Hafnia and zirconia 2.1.1. Hafnia HfO2 2.1.2. Zirconia ZrO2 2.2. Zircon ZrSiO4 Ferroelectrically filled porous Si and Al2O3 3.1. Porous silicon 3.2. Misted deposition 3.3. Strontium bismuth tantalate results Coherent nucleation of nano-domains 4.1. Gruverman-Shur data on lead germanate 4.2. E-field model (Shur) 4.3. Ripple model 4.4. Gross-Pitaevski model Perimeter effect 5.1. Fringing field model (Chu et al.) 5.2. Phase transition model (Tagantsev) 5.3. Lead zirconate-titanate data 5.4. Ballistic model (Dawber, Jung, and Scott) Ultra-thin polyvinylidene-trifuoroethylene (PVDF) films 6.1. Langmuir-Blodgett film data of Bune et al. 6.2. Kay-Dunn Theory 6.3. Inhomogeneous nucleation theory (Chandra et al.) 6.4. Screening corrections 6.4.1. Ku and Ullman 6.4.2. Simmons 6.4.3. Black and Welser 6.4.4. Dawber and Scott

51 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 51-73. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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7.

8.

6.4.5. 1/C versus thickness results 6.4.6. Relation to Tilley-Zeks theory Strontium titanate/barium titanate superlattices 7.1. Bowman, Gregg, et al. 7.2. BaTiO3 thin film results 7.3. Curie temperatures 7.4. Polarization directions 7.5. X-Ray results (Rios et al.) Conclusions

1. Introduction and deposition techniques Beginning in the 1950s every large US microelectronics company (Bell Labs, IBM, Ford, RCA, etc.) was involved in ferroelectrics t research. The main driving force was the idea that the +P polarization state and the –P polarization state of a ferroelectric could be used to encode the “1” and “0” of the Boolean algebra in which modern digital computers operate. At that time, however, ferroelectrics were available only as single crystals or rather thick ceramics. Since a typical coercive field for switching a ferroelectric from +P to –P (or vice versa) is ca. 40 kV/cm, a 1-mm thick device would have an operating voltage of 4000 Volts! Moreover, the devices were expensive. Therefore as silicon DRAM (dynamic random access memories) devices developed rapidly, ferroelectric RAMs were left on the back-burner as objects of mere academic novelty. This changed rapidly through the 1980s as silicon oxide films as thin as 20 nm were fabricated in pinhole-free 6” commercial wafer form. At that point the advantages of ferroelectric memories over Si DRAMs was recognized once again: They are nonvolatile (the memory does not need refreshing, like DRAMs, and does not forget if power is interrupted); they are radiation hard, no single event upset – SEU; and they are lighter in weight than Core magnetic memories, and 1000x faster to erase and rewrite than are EEPROMs – electrically erasable programmable read-only memories). The result has been a ferroelectrics renaissance. Ferroelectric RAMs are now used in smart debit cards at the 16 kbit and 64 kbit level and FRAMs up to 4 Mbit (Figs. 1-3); in SONY Playstation 2 (Fig. 4) and telecommunications. The highest density ferroelectric (FE) chips available are 4 Mbit from Samsung (using chemical solution deposition lead zirconate titanate – PZT – ceramics ca. 40 nm in grain size) and 4 Mbit from Panasonic (using strontium bismuth tantalate – SBT). A fully commercial 8 Mbit ferroelectric RAM is scheduled for production by Infineon (Japan) and Toshiba on 1 September 2003, using sputtered PZT. At present the road map for FRAM technology is well established: by 2008 the linewidth requirements are 0.1 microns; technology node is 70 nm; feature size F is 0.13 microns; 256 Mbit is the size; and complete cycle time is 16 ns. Therefore for this technology, nano-scale is not just a trendy buzz-word; it is a very strict imperative.

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Figure 1. Samsung 64 kbit FRAM.

Figure 2. Samsung 512 kbit FRAM block.

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Figure 3. Samsung 4Mbit FRAM cross-section.

As detailed below, many of the nano-scale ferroelectric systems below have yet to be investigated by scanning probe techniques. A primary aim of this book chapter is to focus attention on specific questions relating to them.

Figure 4. Sony Playstation 2 with Toshiba EEPROM and Fujitsu FRAM.

1.1. NANOPHASE DEPOSITION TECHNIQUES The three main techniques for 20 nm – 100 nm ferroelectric cells are: electron-beam direct writing (EBDW); focussed-ion-beam (FIB) deposition; and spontaneous selfpatterning.

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1.1.1. Electron-beam direct writing EBDW consists of the use of a cannibalized SEM electron microscope gun to cut out array patterns of ferroelectric capacitors. The results, illustrated in Figs. 5 and 6, are very impressive, but it must be emphasized that a single pattern, ca. 20 x 20 µm in size, takes about 24-72 hours to fabricate. Therefore this technique is not at present suitable for commercial production.

Figure 5. PZT nanoscale array produced by e-beam direct writing. Array on 1 micron scale (bar at lower right) (M. Alexe, private communication).

Figure 6. PZT single cell at 100 nm scale (M. Alexe, private communication).

These images may be contrasted with the results of focussed ion beam patterning (FIB) in Fig. 7 (PZT), and with self-patterning, which in bismuth-excess SBT and bismuth titanate (both PLD and CVD deposition), Fig. 8.

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Figure 7. PZT focussed ion beam array.

Figure 8. Bismuth oxide nano-electrodes self-patterned on bismuth titanate.

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1.1.2. Focussed-ion-beam processing The FIB processing of nanoscale ferroelectric capacitors is analogous to that of EBDW, except that an ion beam is rastered rather than an electron beam, as illustrated in Fig. 9. Some of the best results have been obtained1,2 at the University of Maryland by Aggarwal et al. (2000) and Ganpule et al. (1999). The resulting depth profile is shown schematically in Fig. 10. Note that lateral sizes as small as 20 nm on edge can be produced in this way. Fig. 11 shows actual devices fabricated in different diameters.

Figure 9. Schematic diagram of the focussed ion beam process (R. Ramesh, private communication).

Figure 10. (a) (left) Schematic cross section of typical FIB depth profile; (b) Integration into a nano-phase FRAM device.

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Figure 11. Top to bottom, FIB PZT devices of successively smaller lateral dimensions: 1.0 micron; 260 nm; 100 nm.

1.1.3. Self-assembly Spontaneous self-patterning of ferroelectrics was invented by3,4 Alexe et al. (1998) and Scott et al. (1998). The switching of these cells was developed by5 Alexe et al. (1999). Unfortunately no scanning probe measurements have been reported on them. The theory of such self-assembly was based upon the original work6 by Andreev (1981), which showed that islands forming on solid state surfaces would be mutually repulsive. This was developed into a full theory by Shchukin et al., originally in a short letter and later in a 1999 monograph.7 The predicted ordering in Shchukin’s work is an array of pyramids with {111} faces aligned along the [100] axes of the underlying Si single-crystal substrate. This is shown theoretically in Fig. 12 and confirmed for bismuth oxide in Fig. 13. Shchukin’s theory is for zero temperature; a finite-temperature thermodynamic model was produced8 by Williams et al. (2000). Important in Williams’ work is a distribution diagram, similar to a phase diagram. Three kinds of surface island structures are formed: small pyramids, larger domes (truncated pyramids), and very large “superdomes”. The number density of each depends upon annealing temperature

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and concentration of wetting material (bismuth in our case). The direct application of the Shchukin-Williams model to bismuth oxide nano-electrodes self-patterned onto SBT or bismuth titanate is underway by Dawber (2003).9 Scanning probe techniques have not been used on these systems yet.

Figure 12. Shchukin-Williams model for pyramid self-patterning

a

b Figure 13. (a). Plan view of spontaneous self-patterning of δ-Bi2O3 nanophase electrodes on the surface of PLD-deposited bismuth titanate. These are square pyramids with edges along the [100], [010] axes of the underlying silicon substrate, atop a metallic Bi wetting layer, and satisfy in detail the theory of Shchukin et 7 al. ; (b) Cross-section.

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2. Topography of new films 2.1. HAFNIA AND ZIRCONIA Hafnia HfO2 and zirconia ZrO2 are under active study for gate oxides in dynamic random access memories and related devices.10 In thin-film form they offer chemistry compatible with Si/SiO2 surfaces and very good conformal coverage. A good recent review is by Wilk et al.;10 see also Misra, Heuss and Zhong, and Lee, Jeon, and Hwang.10 No careful studies of film topography has been made in any of these systems, either by scanning probe spectroscopy or other techniques. In the present chapter we report only preliminary studies on the Hf- and Zr-butoxides. 2.1.1. Hafnia HfO2 We have produced thin film hafnia via mist deposition, using novel precursors: Hafnium and zirconium tertiary butoxides; a) hafnium tri-isopropoxy tetramethylheptanedionate, hafnium dimethylamide, and c) hafnium 2-ethylhexanote. Here we present preliminary results on HfO2 and ZrO2 films deposited using butoxide precursors, Hf(OtBu)4 and Zr(OtBu)4. The resulting film did not have the tetragonal phase often seen in hafnia films, but instead was roughly equal mixtures of orthorhombic, monoclinic, and amorphous, as shown by the XRD data in Fig. 14, from Morrison et al. (2003).11 Other recent work on HfO2 on Si is by Lin et al. (2002).12 The monoclinic and tetragonal phases of both hafnia and zirconia have been analyzed by Quintard et al. (2002).13

Figure 14. XRD of HfO2 film.

2.1.2. Zirconia ZrO2 XRD results for a Zr-deposited film heated at 800 °C for 30 min is shown in figure 6. A weak, broad peak is observed at ca. 2θ = 29.3° and is attributed to the 111 reflection of tetragonal ZrO2. It is clear that the film is not as crystalline as the similar Hf-deposited film, figure 15. This is unusual given the similar chemistries of Zr and Hf and requires

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further investigation. Recent studies of zirconia thin films are by Wang et al. (2002) and Chang and Lin (2001).14

Figure 15. XRD of zirconia film.

2.2. ZIRCON ZrSiO4 Zircon is of current interest as an encapsulation ceramic for plutonium reactor waste15 and other high-level radioactive spent-fuel disposal. XRD of our mist-deposited zircon films is shown in Fig. 16.

Figure 16. XRD of zircon film.

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3. Ferroelectrically filled porous Si and Al2O3 3.1. POROUS SILICON Silicon and alumina photonic crystals have been successfully fabricated and characterized for several years, usually by photolithography (etching of Si is greatly enhanced under illumination). A good review is by Birner et al. (2001).The extension of photonic structures from two-dimensional [2D] to three-dimensional [3D] was initiated by Schilling et al. (2001), using modulated pore diameters. The filling of Si pores with Si3N4 via conventional gas-phase CVD was discussed by Ottow et al. (1996).16 In our studies we replace CVD with a misted deposition system discussed elsewhere.17 This has significant advantages. 3.2. MISTED DEPOSITION Misted deposition is a kind of liquid-phase CVD in which submicron droplets of stoichiometric precursor solutions are delivered by a MHz atomiser onto a substrate. It was first reported17 by McMillan et al. (1992). For pore filling in silicon or alumina this provides a great advantage over CVD that harkens back to the days of Millikan and the Millikan oil-drop experiment. As students of physics will recall, fine droplets of liquids (including rain) are usually charged, with 1e or 2e or…5e per droplet. It appears that, for reasons yet unclear, that the internal walls of pores in Si are charged positively. Therefore the mist droplets are electrostatically attracted to coat these walls. Alternative models relying purely on capillary action and minimisation of surface energy are equally viable hypotheses at this stage. This produces uniform thickness (ca. 40 nm) coatings down the walls of ca. 100-micron pores, a remarkable result for pore aspect ratios used (>25). Results are shown in Figure 17 for SBT from Morrison et al. (2002).11

Figure 17. SEM cross-section of SBT nanotubes.

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3.3. STRONTIUM BISMUTH TANTALATE RESULTS SEM photos of porous Si filled with strontium bismuth tantalate are shown in Fig. 18. Here 4.3-micron outside diameter pores have been ffilled uniformly to a depth of 80 microns, with a resulting wall thickness for the SBT of ca. 40-60 nm. No scanning probe studies of these microstructures have been done yet; nor is it known whether the polarization direction is along the tube or through the tube wall, normal to the surface.

Figure 18. SBT nanotubes, plan view.

4. Coherent nucleation of nano-domains It was discovered in Sverdlovsk two decades ago by Gruverman (1983)18 that nanodomains nucleate coherently in front of macroscopic domain walls in ferroelectrics. This was initially observed in lead germanate, where domains are easily observable optically with high contrast. The key observation is that there is a critical field E0 above which this process is observed. The process has now been observed in several ferroelectrics other than lead germanate, including gadolynium molybdate and lithium niobate. 4.1. GRUVERMAN-SHUR DATA ON LEAD GERMANATE The initial data are summarised in Fig. 19, with scale of about 50 microns per cm. In the figure the large domain is moving downwards at a velocity of ca. 10 cm/s. This is a rather high velocity for a domain wall in a ferroelectric. Note in particular that the macroscopic domain wall is NOT atomically flat, nor even optically flat. It has a distinct wavelength λ.

Figure 19. Photograph of nanodomains nucleating in front of macroscopic domain wall.

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4.2. E-FIELD MODEL (SHUR) It has been suggested by Shur (2002)19 that this nanodomain nucleation requires a critical local field but not a critical domain wall velocity, and that the field will depend strongly upon electrode configurations and geometries. 4.3. RIPPLE MODEL I have proposed elsewhere20 that the data shown in Fig. 19 are due to the velocity (downwards in the figure) exceeding the ripple velocity of capillary waves in the domain wall. Under these conditions the domain wall will be strongly damped by creation of ripples of a precise wavelength. The ripple can be seen in Fig. 19 (moving horizontally) and its wavelength can be visually measured. The abrupt decay of domain wall energies at high fields has been measured recently by Zolotoyabko et al. (2002)21 but no mechanism was suggested by them. The mechanism I hypothesize is different from normal acoustic phonon drag, used by Dawber, Jung and Scott (2002)22 for the PZT perimeter effect, discussed below. It is closely analogous to Cerenkov radiation or “bow waves” from a ship: whenever the speed of an object through a continuous medium exceeds the velocity of waves in that medium, energy can be delivered into the waves. In our case, when the domain wall velocity exceeds the speed of domain wall ripples (dependent upon wavelength, which in turn is determined by other parameters, such as distance between pinning sites), a new relaxation process sets in. Since the ripple velocity in a domain wall is given by v = (Tk/ρ), where T is the surface energy of the domain (ca. 7 ergs/cm2 in most oxide ferroelectrics), and ρ is the density (ca. 7 gm/cc), there are no adjustable parameters in the model (k = 2π/λ is measured visually). For λ = 100 microns, as shown, v (critical) in Pb5Ge3O11 will be about 10 cm/sec, as measured experimentally by Gruverman (1983-6). No scanning probe techniques have been used to test these models or to image the nano-domains forming in front of an advancing macroscopic domain. It would be of greatt interest merely to measure the dependence of domain wall curvatures (e.g., wavelengths) upon applied field and/or as a function of velocity. 4.4. GROSS-PITAEVSKI MODEL Domain wall damping into acoustic phonons can be viewed as a particular example of the Gross-Pitaevski model for decay into a boson sea; in this case, the bosons are primarily large wave-vector acoustic phonons near the Brillouin zone boundary. This line of theory is developed by Frisch et al. (1992).23

5. Perimeter effect Dawber, Jung and Scott (2002) have found11 that PZT thin-film capacitors 180 microns to 0.5 microns on edge exhibit a dielectric loss peak with frequency at maximum given by f(max) = bp, (1)

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where p is the cell perimeter and b is a constant that depends on the material.. This holds true for square cells or for rectangular ones, so it is truly dependent upon perimeter and not cell area. 5.1. FRINGING FIELD MODEL (CHU ET Al.) Durkan, Chu et al. have shown24 (2000) that fringing fields in PZT films contribute to significantly to dielectric response but only for aspect ratios (lateral width to thickness) less than 5:1. Since the smallest aspect ratio employed in the present study is 1.1 microns/0.17 microns = ca. 6.5, this is nott important here, but for the new 0.5 x 0.5 micron 32 Mbit FRAMs from Samsung (173 nm thick), it needs to be considered. 5.2. PHASE TRANSITION MODEL (TAGANTSEV) Tagantsev (2002) has presented25 a rather different model to explain “doughnut-like” shapes of back-switching in PZT thin films. In his model there are two phases encountered for thin-film PZT capacitors on substrates, and it is the traversing of the phase boundary into one monoclinic phase that is responsible. While such a phase transition might introduce a large dielectric loss peak, as we measure in our PZT experiments, we can not relate the quantitative details of this model to our data. 5.3. LEAD ZIRCONATE-TITANATE DATA Data are shown in Fig. 20 and the cell structure in Fig. 21. Note that in these cells the top electrode and PZT layer are etched separately, so that a pedestal structure results. This may be important for the mechanism.

Figure 20. Dielectric data versus frequency for PZT cells of different perimeters.

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Figure 21. Capacitor structure for data shown in Fig. 20.

5.4. BALLISTIC MODEL (DAWBER, JUNG, AND SCOTT) Dawber et al. assume that the perimeter effectt results from domains nucleating along the stress-free edges of the PZT (there is a large lattice misfit stress in the interior of the cell) and propagates either towards the centre or around the perimeter. Because the ratio of cell perimeter to average radius is nearly the same (within 10%) for all rectangles, the two mechanisms are thus far indistinguishable. The model assumes that domain walls give up energy to pairs of large-k acoustic phonons, which are known in PZT to have a one-phonon density of states peak at 100 cm-1. This number agrees with quantitative calculations for a model in which the domain wall damping is acoustic phonon drag of form proportional to velocity squared. This is the accepted model for acoustic phonon gain (or loss) in semiconductors and also the model for damping of a mechanical object moving through a viscous continuum. No scanning probe techniques have been yet used to look for the domain motion in these PZT perimeters. 6. Ultra-thin polyvinylidene-trifuoroethylene (PVDF) films 6.1. LANGMUIR-BLODGETT FILM DATA OF BUNE ET AL. In 1998 Bune et al. reported26 a remarkable set of data on polyvinylidene difluoride copolymers with trifluoroethylene (PVDF-TFE). The observed ferroelectric switching in films as thin as 0.9 nm (two molecular layers). This thickness is sufficiently thin that many models of ferroelectrics (e.g., Batra and Silverman, 1973) predict27 that depolarization fields enter the films from the surfaces, destabilize the ferroelectricity, and thus prevent any switching or hysteresis. In addition to disproving such theories, the

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data of Bune and more recently of Ducharme et al. and Fridkin et al.26 showed two other things. First, the switching was extremely slow (seconds) in the thinnest films, compared with hundreds of microseconds in thin films of the same material; this was not readily understood nor had it been predicted. Second, there were two peaks in the dielectric response versus temperature, rather than the one peak at TC expected. Subsequent work by this Moscow-Nebraska group revealed that the dependence of coercive field Ec upon film thickness d was complicated and did not satisfy the KayDunn Law. 6.2. KAY-DUNN THEORY In 1962 Kay and Dunn published28 a model for Ec(d). It predicted that Ec(d) = a d-2/3. This law works surprisingly well for a great variety of ferroelectrics and consequently it has been used widely for 40 years. However, it is derived from assumptions that do not correspond to real materials: First, it assumes 100% homogeneous nucleation, whereas real ferroelectrics generally exhibit 100% inhomogeneous nucleation [as shown by Shur et al. via synchronized electrical t switching pulses and laser flash photography, the nucleation sites are always the same, so that homogeneous nucleation and/or spinodal decomposition is not involved]. Second, Kay and Dunn made a low-field expansion in E that can not be justified for thin films where E is very large even for small applied voltages V. Third, as admitted by Kay and Dunn in their paper, the activation energies extracted from fitting real data to their model are about two orders of magnitude larger than measured independently. 6.3. INHOMOGENEOUS NUCLEATION THEORY (CHANDRA ET AL.) Chandra et al. (2002) have rederived29 the Kay-Dunn Law from scaling arguments, assuming inhomogeneous nucleation and without the small-field assumption. This is a case where the underlying physics transcends the restrictions used in the original derivation (not uncommon in physics). 6.4. SCREENING CORRECTIONS In order to compare real switching data for ferroelectrics with the Kay-Dunn Law or any other law, it is first necessary to correct these data for screening in the metal electrodes. Although the screening length in a metal electrode such as Al, Au, or Pt is only about 0.05 nm, it can play a surprisingly large role. Depending upon whether the switched polarization 2P of the ferroelectric is large or small compared with the displacement vector D (and hence to the dielectric constant e), the effect of electrode screening can be of either sign; that is, it can increase or decrease the apparent coercive field measured. In the former case it simply occurs that a significant percentage of the voltage drop is in the metal and not across the ferroelectric film. The magnitude of the voltage drop percentage in the metal increases as the film thickness decreases. For this reason decreasing the ferroelectric film thickness to extremely small values is not a useful way to maximize capacitance for DRAM capacitors using PZT. Furthermore, using an oxide electrode such as SrRuO3 with long screening lengths, or a semiconductor electrode such as p+ Si will be very disadvantageous.

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Note that it is not necessary to use the Fermi-Thomas model of the metal screening length. More complex models can be used, and in particular for liquid electrodes (such as Hg or ITO) one should revert to the original double-layer models of Helmholtz (1894) or Gouy or Stern (1946). 6.4.1. Ku and Ullman The original theory of voltage drop and screening in the metal electrodes t of a dielectric capacitor were given by Ku and Ullman (1964).30 6.4.2. Simmons Simmons (1965) extended their work and recast it into a simpler analytic form.31 6.4.3. Black and Welser Black and Welser used the models of Ku and Ullman and of Simmons to explain their capacitance data on barium strontium titanate (BST) thin films for DRAM applications.32 However, they made an error, discussed below, of assuming the dielectric constant of the strontium ruthenate electrode is ca. 100. As discussed below, the Simmons model is a free-electron t model, and as such requires ε = 1 in the metal for self-consistency. Hence while the metal screening length enters the equations in an important way, the metal dielectric constant must be unity. 6.4.4. Dawber and Scott Dawqber and Scott (2001) applied these models successfully to tunnelling currents in ferroelectrics.33 Here the electrons must tunnel nott only through a barrier in the ferroelectric (BST, PZT or SBT) near the electrode, but it must tunnel through the depletion layer in the metal electrode as well. The experimental results on samples from Gregg and Bowman fit the screening correction model of Simmons. More recently Dawber and Scott have given a simple derivation of Simmons model which shows clearly why ε = 1 in the metal electrode.9 6.4.5. 1/C versus thickness results One of the classic tests of interface capacitance models is simply to plot reciprocal capacitance 1/C versus film thickness d. For a perfect capacitor on an ideal metal this gives a straight line with intercept through the origin. Many scientists have used this to test for interfacial “dead” layers. Our fitting of the PVDF-TFE data of Ducharme et al. gives a nonzero intercept numerically compatible with the Fermi-Thomas screening length of their aluminum electrodes. It does not permit a zero intercept. Similar results have been demonstrated for other ferroelectric films, most recently by Kingon et al. (2002).34 6.4.6. Relation to Tilley-Zeks theory The theory of polarization dependence P(z) upon depth z in a ferroelectric film was developed by Tilley and Zeks,35 and recently reviewed,36 and is based upon earlier work by Mills37 and by Lubensky and Rubin.38 It is a mean field theory that begins with the addition of polarization gradient terms in the free energy (similar to those used to describe incommensurate ferroelectrics). These gradient terms are phenomenological. In a real ferroelectric they may be dominated by oxygen vacancy gradients near the surfaces or electrodes. The resulting free energy is then minimized to find the

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equilibrium condition, resulting in two Euler-Lagrange equations. In general P(z) is not a constant throughout the ferroelectric film; as shown in Fig. 22, it either increases at the electrode interfaces (superpolarized surfaces, resulting in TC higher than in bulk) or it decreases (depolarized interfacial surfaces). These two cases are described by an extrapolation length δ, which is negative for depolarized surfaces and positive for superpolarized surfaces. Unfortunately the Tilley-Zeks theory yields neither the sign nor magnitude of δ. I have suggested elsewhere that in real systems d may be the FermiThomas (or other) screening length in the metal electrode. This would require a negative sign and give an exact numerical value 9, e.g. 0.04 nm for aluminum). This connection between the Tilley-Zeks theory and the theory of Ullman-Ku-Simmons is under study. As shown39 by Scott et al. (1988) and Duiker et al. (1990), for first-order phase transitions (as in PVDF-TFE) some values of δ result in separate phase transition temperatures for the interior off the films and for the region near their electrodes. Typically for this to occur δ must be approximately equal to or less than the polarization correlation length in the ferroelectrics, which is very small. This aspect of the extended Tilley-Zeks model seems to fit the two-peaked dielectric data of Bune et al. in PVDFTFE very well. We do NOT think thatt their data imply a domain-free “Landau” switching of the films; despite assertions to the contrary, such switching would occur at higher fields than they employ and be very fast.

Figure 22. Polarization versus depth in a depolarised thin film.

Note that none of the theories discussed in this section (Ku and Ullman; Simmons; Chandra et al.; Dawber and Scott; Tilley and Zeks) include interfacial misfit lattice strain; however, this has been incorporated analytically39 within the Tilley-Zeks model by Zhang, Yin, Zhang and Scott (2001). In real ferroelectric films the increase or decrease in Curie temperature is probably dominated by interface misfit strain and not by the effects described in the strain-free Tilley-Zeks model. This is best illustrated in BaTiO3 thin films, in which Tc can be increased by 300-500K above bulk on SrTiO3 substrates.40

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7. Strontium titanate/barium titanate superlattices 7.1. BOWMAN, GREGG, ET AL. Superlattices of many ferroelectrics have been produced, usually by molecular beam epitaxy, but also by other techniques; see especially the recent work of Bowman, Gregg et al. (Oneill 2000; Corbett 2001).41,42 The interest in these superlattices from a basic science point of view is in their Curie temperatures and their polarization directions. It would be especially useful to understand how these properties, especially TC, depend upon the superlattice periodicity. Here we denote periodicity by, for example, 4/4 or 10/10, where the first number is the number of unit cells of BaTiO3 and the second the number of SrTiO3 unit cells that make up the repeat units. Periodicities from 4/4 to ca. 100/100 have been studied in our work. See also the recent paper by Kim et al. (2002).43 7.2. BaTiO3 THIN FILM RESULTS Thin films of barium titanate exhibit very large upward shifts in Curie temperature if deposited on single-crystal strontium titanate substrates. The smaller lattice constant of strontium titanate compared with that of barium titanate shifts TC up by several hundred degrees, as shown by Li et al. (1999).40 7.3. CURIE TEMPERATURES Generally the Curie temperatures are not known as a function of periodicity. For barium titanate/strontium titanate Jiang et al. (2003)44 have found TC = 276 ºC for 10/10 superlattices and 326 ºC for 30/30 periods. 7.4. POLARIZATION DIRECTIONS Rather surprisingly, Jiang et al. find44 that not only are the strontium titanate layers ferroelectric at room temperature in barium titanate/strontium titanate superlattices of small periodicity (10/10, 30/30…) but that the polarization direction lies along [110] rather than the expected [001]. While this does not minimize the electrostatic ∇D term in the free energy, it apparently minimizes strain. 7.5. X-RAY RESULTS (RIOS ET AL.) Rios et al. (2002) have observed via XRD techniques45 a small 0.04% orthorhombic distortion from the expected tetragonal structure of strontium titanate layers in these superlattices. The lattice constants determined for the 30/30 superlattice are: a = 0.39366(1) nm; b = 0.39352(1) nm; c = 0.38566(2) nm. No scanning probe techniques have been used on these systems. 8. Conclusions In this paper I have tried to review seven different anomalies in ferroelectric thin films which have not yet been studied via scanning probe techniques. I hope that readers will be stimulated to try to elucidate some of them.

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References 1.

2. 3.

4. 5.

6. 7. 8. 9. 10.

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15. 16.

17. 18.

19.

Aggarwal, S., Ganpule, C.S., Jenkins, I.G., Nagaraj, B., Stanishevsky, A., Melngailis, J., Williams, E., and Ramesh, R. (2000) High density ferroelectric memories: Materials, processing and scaling High density ferroelectric memories: Materials, processing and scaling, Integr. Ferroelec. 29, 213-225. Ganpule, C.S., Stanishevsky, A., Su, Q., Aggarwal, S., Melngailis, J., Williams, E., and Ramesh, R. (1999) Scaling of ferroelectric properties in thin films, Appl. Phys. Lett. 75, 409-411. Alexe, M., Scott, J.F., Curran, C., Zakharov, N.D., Hesse, D., and Pignolet, A. (1998) Self-patterning nano-electrodes on ferroelectric thin films for gigabit memory applications, Appl. Phys. Lett. 73, 1592 1594. Scott, J.F., Alexe, M., Zakharov, N.D., Pignolet, A., Curran, C., and Hesse, D. (1998) Nano-phase SBTfamily ferroelectric memories, Integr. Ferroelec. 21, 1-14. Alexe, M., Harnagea, C., Hesse, D., and Goesele, U. (1999) Patterning and switching of nanosize ferroelectric memory cells, Appl. Phys. Lett. 75, 1793-1795; Schilling, J., Muller, F., Matthias, S., Wehrspohn, R.B., Gosele, U., and Busch, K. (2001) Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter, Appl. Phys. Lett. 78, 1180-1182. Andreev, A.F. (1981) JETP Lett. 53, 1063. Shchukin, V.A. and Bimberg, D. (1999) Spontaneous ordering of nanostructures on crystal surfaces, Rev. Mod. Phys. 71, 1125-1171. Williams, R.S., Medeiros-Ribeiro, G., Kamins, T.I., and Ohlberg D.A.A. (2000) Thermodynamics of the size and shape of nanocrystals: Epitaxial Ge on Si(001), Ann. Rev. Phys. Chem. 51, 527. Dawber, M. and Scott, J.F. (2001) Calculation of Schottky barrier height of platinum/lead zirconate titanate interface, Integr. Ferroelec., 38, 805-813. Wilk, G.D., Wallace, R.M., and Anthony, J.M. (2001) High-k gate dielectrics: Current status and materials properties considerations, J. Appl. Phys. 89, 5243-5275; see also Wallace, R.M. and Wilk, G.D. (2002) Alternative gate dielectrics for microelectronics, MRS Bull. 27, 186-187; Wallace, R.M. and Wilk, G.D. (2002) High-k Gate Dielectric Materials, MRS Bull. 27, 192-197; Lee, H., Jeon, S., and Hwang, H. (2001) Electrical characteristics of a Dy-doped HfO2 gate dielectric, Appl. Phys. Lett. 79, 2615-2617; Misra, V., Heuss, G.P., and Zhong, H. (2001) Use of metal-oxide-semiconductor capacitors to detect interactions of Hf and Zr gate electrodes with SiO2 and ZrO2, Appl. Phys. Lett. 78, 4166-4168. Morrison, F.D., Scott, J.F., Alexe, M., Leedham, T.J., Tatsuta, T., and Tsuji, O. (2002) Use of the 'mist' (liquid-source) deposition system to produce new high-dielectric devices: ferroelectric-filled photonic crystals and Hf-oxide and related buffer layers for ferroelectric-gate FETs, Microelectron. Eng. 66, 591599. Lin, Y.-S., Puthenkovilakam, R., and Chang, J.P. (2002) Dielectric property and thermal stability of HfO2 on silicon, Appl. Phys. Lett. 81, 2041-2043. Quintard, P.E., Barberis, P., Mirgorodsky, A.P., and Merle-Mejean, T. (2002) Comparative latticedynamical study of the Raman spectra of monoclinic and tetragonal phases of zirconia and hafnia, J. Am. Ceram. Soc. 85, 1745-1749. Wang, J. C., Chiao, S.H., Lee, C.L., Lei, T.F., Lin, Y.M., Wang, M.F., Chen, S.C., Yu, C.H., and Liang, M.S. (2002) A physical model for the hysteresis phenomenon of the ultrathin ZrO2 film, J. Appl. Phys. 92, 3936-3940; Chang, J. P. and Lin, Y.-S. (2001) Highly conformal ZrO2 deposition for dynamic random access memory application, J. Appl. Phys. 90, 2964-2969. Ewing, R.C. (2001) The design and evaluation off nuclear-waste forms: Clues from mineralogy, Canadian Mineralogist 39, 697-715. Ottow, S., Lehmann, V., and Foll, H. (1996) Development of three-dimensional microstructure processing using macroporous n-type silicon, Appl. Phys. A 63, 153-159; see also Smith, R.L. and Collins, S.D. (1992) Porous Silicon Formation Mechanisms, J. Appl. Phys. 71, R1-R22; as well as Birner, A., Wehrspohn, R.B., Gosele, U., and Busch, K. (2001) Silicon-based photonic crystals, Adv. Mater. 13, 377388. MacMillan, L.D., Paz De Araujo, C.A., Roberts, T., Cuchiaro, J., Scott, M.C., and Scott, J.F. (1992) Integr. Ferroelec. 2, 351. Gruverman, A. (1986) Ph.D. thesis, Univ. Urals, Sverdlovsk (Ekaterinburg), USSR; Shur, V.Ya., Gruverman, A., Kuminov, V.P., and Tonkachyova, N.A. (1990) Dynamics of Plane Domain-walls in Lead Germanate and Gadolinium Molybdate, Ferroelecrics. 111, 197-206. Shur, V.Ya., Baturin, I.S., Shishkin, E.I., and Belousova, M.V. (2003) New approach to analysis of the switching current data in ferroelectric thin films, Ferroelectrics 291, 27-35.

72 20. Scott, J.F. Dawber M, Jiang AQ, Morrison FD (2003) Ferroelectrics 286: 945-957; Scott, J.F. (2003) Domain wall kinetics: Nano-domain nucleation in lead germanate and Tilley-Zeks theory for PVDF Ferroelectrics 291, 205-215; Scott, J.F. (2003) New ferroelectric thin-film results: Electrode effects and photonic crystals, Ferroelectrics 293, 33-41. 21. Zolotoyabko, E., Quintana, J.P., Hoerman, B.H., and Wessels, B.W. (2002) Fast time-resolved x-ray diffraction in BaTiO3 films subjected to a strong high-frequency electric field, Appl. Phys. Lett. 80, 31593161. 22. Dawber, M., Jung, D.J., and Scott, J.F. (2002) Perimeter effect in very small ferroelectrics, Appl. Phys. Lett. 82, 436-438; see also Jung, D.J., Dawber, M., Ruediger, A., Scott, J.F., Kim, H.H., and Kim, K. (2002) Dielectric loss peak due to platinum electrode porosity in lead zirconate titanate thin-film capacitors, Appl. Phys. Lett. 81, 2436-2438. 23. Frisch, T., Pomeau, Y., and Rica, S. (1992) Transition to Dissipation in a Model of Superflow, Phys. Rev. Lett. 69, 1644-1647; see also Landau, L.D. and Lifshitz, E.M. (1987) Fluid Mechanics, Pergamon, Oxford. 24. Durkan, C., Welland, M.E., Chu, D.P., and Migliorato, P. (2000) Scaling of piezoelectric properties in nanometre to micrometre scale, Electron. Lett. 36, 1538-1539. 25. Astafiev, K., Sherman, V., Tagantsev, A., Setter, N., Rivkin, T., and Ginley, D. (2002) Investigation of electrical degradation effects in ferroelectric thin film based tunable microwave components, Integ. Ferroelec. 49, 103-112. 26. Bune, A.V., Fridkin, V.M., Ducharme, S., Blinov, L.M., Palto, S.P., Sorokin, A.V., Yudin, S.G., Zlatkin, A. (1998) Two-dimensional ferroelectric films, Nature 391, 874-877. 27. Batra, I.P. and Silverman, B.D. (1972) Thermodinamic Stability of Thin Ferroelectric Films, Solid State Comm. 11, 291. 28. Kay, H.F. and Dunn, J.W. (1962) Thickness Dependence of Nucleation Field of Triglycine Sulphate, Phil. Mag. 7, 2027. 29. Chandra, P., Dawber, M., Littlewood, P., and Scott, J.F. Nature Mater., in press. 30. Ku, H.Y. and Ullman, F.G. (1964) Capacitance of Thin Dielectric Structures, J. Appl. Phys. 35, 265; see also Mead, C.A. (1961) Anomalous Capacitence of Thin Dielectric Structures, Phys. Rev. Lett. 6, 545546. 31. Simmons, J.G. (1965) An Analytic from of Ku and Ullmans Equations (Electric Field Penetration of Tunnel Junction Electrodes - T), Appl. Phys. Lett. 6, 54; Simmons, J.G. (1967) Incorporation of ElectricField Penetration of Electrodes in Theory of Electron Tunneling Through a Dielectric Layer, Brit. J. Appl. Phys. 18, 269. 32. Black, C.T. and Welser, J.J. (1999) Electric-field penetration into metals: Consequences for highdielectric-constant capacitors IEEE T. Electron. Dev. 46, 776; see also Hwang, C.S. (2002) Thicknessdependent dielectric constants of (Ba,Sr)TiO3 thin films with Pt or conducting oxide electrodes, J. Appl. Phys. 92, 432-437. 33. Dawber, M., Sinnamon, L.J., Scott, J.F., and Gregg, J.M. (2002) Electrode field penetration: A new interpretation of tunneling currents in barium strontium titanate (BST) thin films, Ferroelectrics 268, 455460. 34. Kingon, A.I. (2002) Thickness, strain, and temperature-dependent properties of barium strontium titanate thin films, Proceedings of the 13th IEEE ISAF 2002, 151-154; see also part I of this book by A.I. Kingon. 35. Tilley, D.R. and Zeks, B. (1984) Landau Theory of Phase-Transitions in Thick-Films, Solid State Comm. 49, 823-827. 36. Zhong, W.L., Wang, Y.G., and Zhang, P.L. (1998) Ferroelec. Rev. 1, 131. 37. Mills, D.L. (1971) Surface Effects in Magnetic Crystals near the Ordering Temperature, Phys. Rev. B 3, 3887-3895. 38. Lubensky, T.C. and Rubin, M.H. (1975) Critical phenomena in semi-infinite systems. II. Mean-field theory, Phys. Rev. B 12, 3885-3901. 39. Scott, J.F., Duiker, H.M., Beale, P.D., Poulighy, B., Dimmler, K., Parris, M., Butler, D., and Eaton, S. (1988) Properties of Ceramic KNO3 Thin-Film Memories, Physica B 150, 160-167; Duiker, H.M., Beale, P.D., Scott, J.F., de Araujo, C.A.P., Melnick, B.M., Cuchiaro, J.D., McMillan, L.D. (1990) Fatigue and Switching in Ferroelectric Memories - Theory and Experiment, J. Appl. Phys. 68, 5783; Zhang, J., Yin, Z., Zhang, M.-S., and Scott, J.F. (2001) Size-driven phase transition in stress-induced ferroelectric thin films, Solid State Comm. 118, 241-246. 40. Li, C., Chen, Z., Cui, D., Zhou, Y., Lu, H., Dong, C., Wu, F., and Chen H. (1999) Phase transition behavior of BaTiO3 thin films using high-temperature x-ray diffraction, J. Appl. Phys. 86, 4555-4558.

73 41. O'Neill, D., Bowman, R.M., and Gregg, J.M. (2000) Dielectric enhancement and Maxwell-Wagner effects in ferroelectric superlattice structures, Appl. Phys. Lett. 77, 1520-1522. 42. Corbett, M.H., Bowman, R.M., Gregg, J.M., and Foord, D.T. (2001) Enhancement of dielectric constant and associated coupling of polarization behavior in thin film relaxor superlattices, Appl. Phys. Lett. 79, 815-817. 43. Kim, J., Kim, Y., Kim, Y.S., Lee, J., Kim, L., and Jung, D. (2002) Large nonlinear dielectric properties of artificial BaTiO3/SrTiO3 superlattices, Appl. Phys. Lett. 80, 3581-3583. 44. Jiang, A.Q., Scott, J.F., et al. (2002) J. Appl. Phys., in press. 45. Rios, S., Ruedger, A., Scott, J.F., et al. (2002) Appl. Phys. Lett., submitted.

Part II – Fundamentals of Scanning Probe Techniques

PRINCIPLES OF BASIC AND ADVANCED SCANNING PROBE MICROSCOPY

D.A. BONNELL1, R. SHAO Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut l ST Philadelphia, PA 19104 USA

Contents 1. 2.

Introduction Basic Concepts of Scanning Probe Microscopy 2.1. Electrostatic Force Microscopy 2.2. Magnetic Force Microscopy 3. Advanced Scanning Probe Microscopy: Exploiting Multiple Modulations 3.1. Scanning Spreading Resistance Microscopy and Scanning Capacitance Microscopy 3.2. Scanning Surface Potential Microscopy 3.3. Scanning Impedance Microscopy 3.4. Scanning Gate Microscopy 3.5. Piezoresponse Force Microscopy 3.6. Scanning Microwave and Dielectric Microscopy 4. Applications 4.1. Transport in Single Molecules and Nano Wire/Tubes 4.2. Domain Interactions in Ferroelectric Thin Films 5. Other Techniques and Future Directions

Abstract Understanding the behavior of complex materials such as organic self-assembled monolayers, molecular and nano wires, transition metal oxide thin films, is facilitated by probes of local properties. Recent extensions of scanning probe microscopy that extract electrical potential, capacitance, dielectric constant, electromechanical coupling coefficients and impedance, are described. In most cases, these complex properties are accessed by stimulations and/or response function detection with multiple frequency modulations. Several illustrative example include determination of the electronic

1

Corresponding author. Phone: (215)898-6231, Fax: (215)573-2128. Email address: [email protected] 77 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 77-101. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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structure of individual defects in a carbon nanotube, ferroelectric domain interactions in oxide thin films, and electric potential of an alkanethiol on metal. Keywords: Scanning probe microscopy, multiple modulation, spatial resolution, complex materials, molecular wires, ferroelectric domains.

1. Introduction The quest toward understanding the behavior of condensed matter has relied on measuring structure, bonding, and properties at increasingly local levels. This has driven advances in techniques that probe both soft and hard materials directly as well as indirectly. Examples include the suite of imaging and spectroscopy based on electron optics, spatially confined synchrotron radiation, optical spectroscopies such as ‘micro’ Raman and FTIR, etc. While structure and bonding based probes have accessed molecular and atomic scales for decades, local determination of properties was elusive. The emergence of scanning probes filled this gap to some extent. Technique AFM EFM MFM SSPM(KPM) SCM SCFM SSRM SGM SIM

NIM PFM NPFM SNDM NFMM

TABLE I. Properties and Modulated Operation Modes of Scanning Probes Mode Property References nc/ic, mech, [2-5] VdW interaction, topography phase/amp electrostatic force nc, mech, [2-5] phase/amp magnetic force, current flow nc, mech, [2-5] phase/amp nc, elec, 1st potential, work function, adsorbate [2-5, 27-44] harmonic enthalpy/entropy c, F, cap sensor capacitance, relative dopant density [2-12, 15-17, 1924] c, elec, 3rd dC/dV, dopant profile [26] harmonic c, F, dc current resistivity, relative dopant density [2-5, 12-14, 18] nc, elec, amp current flow, local band energy, contact [2-5,53-59] potential variation nc, elec, interface potential, capacitance time constant, [51, 53] phase/amp local band energy, potential, current flow (in comb. w/ SSPM) c,F, freq spectrum interface potential, capacitance, time constant, [55] dopant profiling c, elec, phase/amp d33 [2-5, 60-65] c, elec, 2nd switching dynamics [66] harmonic c, F, 1stt or 3rd dC/dV, dielectric constant [67, 68] harmonic c, F, phase microwave losses, d33 [69-71]

Mode: c= contact, nc = non contact, ic = intermittent contact, mech = cantilever is driven by a mechanical oscillation, elec = cantilever is driven or responds to an oscillating electrical signal, F = constant force feedback, phase = detection or feedback on phase, amp = detection of amplitude at preset frequency.

The utility of local probes is illustrated by the fact that only 10 years after commercial SPMs became available upwards of 1750 papers per year [1] are published

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that cite scanning probes as a key word. Several monographs have summarized the state of this field and various times and books are available that provide introduction to the field and general overviews [ 2 , 3 , 4 , 5 ]. Most applications utilize SPM as a straightforward qualitative mapping tool. Some researchers interested in complex behavior of solids have examined fundamental probe-surface interactions and extended SPM to probe local electronic transport, dielectric, ferroelectric, magnetic properties. It is convenient to categorize scanning probe techniques in terms of probe-sample contact, source of cantilever oscillation, and feedback function. Various scanning probe techniques are described in these terms in Table I, which also lists the properties that can be accessed with each. For example, conventional atomic force microscopy (AFM) can be a non-contact, mechanically driven oscillation with amplitude or phase based detection. Piezoelectric force microscopy (PFM) is a contact, electrically driven oscillation, with phase based detection. Combined with detection and/or feedback of not only 1stt harmonic response functions, but also 2ndd and 3rdd harmonic response functions, a wide range of properties can be accessed. An underlying theme of the newest developments is the use of multiple signal modulations or high order harmonics of modulated signals. This paper first summarizes the basic concepts that are needed in order to understand the more sophisticated uses of SPM presented in this volume. Several advanced techniques are described and a few examples are used to illustrate the applications. 2. Basic Concepts of Scanning Probe Microscopy SPM is based on the interaction of a probe tip and a surface, which for completeness are summarized here. A comprehensive treatment of surface and intermolecular forces can be found in an excellent book by J. Israelachevili [6]. The fundamental interaction at short distances is derived from van der Waals forces. At distances of a few nms, van der Waals forces are sufficiently strong to move macroscopic objects such as AFM cantilevers. Van der Waals interactions consist of three components: polarization, induction, and dispersion. Polarization refers to permanent dipole moments such as exist in water molecules or in BaTiO3. Induction refers to the contribution of induced dipoles. Dispersion is due to instantaneous fluctuations of electrons, which occur at the frequency of light causing optical dispersion, thus the name. A reasonable approximation of the interaction is obtained assuming that dispersion dominates and is isotropic, additive, and non-retarded. Under these assumptions the van der Waals potential between two planes is -A/12ρZ2, and between a sphere and a plane is -AR/6Z; in which Z is the distance between objects, b R is the radius of the sphere, and A is the Hamaker constant. The complete interaction must include the repulsive as well as attractive terms. The Hamaker constant is the term that characterizes the properties of the materials, including collective interactions and polarization if calculated from dielectric and optical properties. It is ª 3kT § ∈1 − ∈3 ·§ ∈2 − ∈3 · 3ηω « ¨ ¸ ¨ ¸ + A= 4 ¨© ∈1 + ∈3 ¸¹¨© ∈2 + ∈3 ¸¹ 8 2 «« ¬

(

)( 1

2

(

)(( ª ) «¬( 1

2

)

) +( 1

2

º » » 1 2º »¼ »¼

)

(1)

80

where k is the Boltzmann constant, T is temperature, ρ is the density, εi is the dielectric constant in medium i (i.e. sample (1), tip (2), or intervening material (3)), and ni is refractive index. The Hamaker constant is on the order of 10-19 J for most solids. In many situations long range forces act in n addition to short range forces between two surfaces. Examples of long range interactions include electrostatic attraction or repulsion, current induced or static magnetic interactions, and forces due to the surface energy of water condensed between the sample and tip. Very close to the surface these forces are much smaller than those due to van der Waals interactions and usually contribute little to the signal. Farther from the surface, the van der Waals interactions decay rapidly to the point of being negligible. In this regime long range forces are still significant. This difference in decay length provides a means to distinguish the two types of interactions. The general relations describing the force experienced by a tip above a homogeneous surface for electrostatic and magnetic interactions are described in Eqs. 3 and 4, where ∆V is the difference in potential between sample and tip, C is the tipsample capacitance as a function of separation (z), Bsample is the magnetic field emanating from the sample surface, and m is the magnetic dipole of the tip [7, 8]. Conducting and/or magnetic tips are obviously necessary to access electrical or magnetic fields: 1 (2) )2 ∂ C Felectrosta tic = − ( 2 ∂z (3) Fmagnetosta tic = ∇ m • B sample

(

)

These relations are oversimplifications but suffice to describe the operating principles of electrostatic force imaging (EFM) and magnetic force imaging (MFM). The underlying principle of AFM is that the interactions between the end of a probe tip that is mounted on a cantilever result in a response in the cantilever, notably a deflection. The mechanical resonant frequency off the cantilever is determined by the dimensions of the structure and the properties of materials from which it is made. This resonant is related to the cantilever spring constant according to Eq. 4, where the cantilever is conceptually treated as a classical, 1-dimensional, lightly loaded, “fixedfree” beam: (4) t E k ω

o

=

λ2

ρ

=

m

eff

The vibration amplitude, A, detected at a given frequency, ω, changes as a function of the force gradient as shown in Eq. 5. §ω A ( ω = ω o′ ) = a o Q ¨¨ o © ω o′

∂F § · ∂z ¸¸ ≈ a o Q ¨ 1 − ¨ 2k ¹ ©

· ¸ ¸ ¹

−1

(5)

where Q is the quality factor and k is the spring constant of the cantilever. Note that by measuring the change in amplitude both the magnitude and sign of the force gradient are determined. As shown in Fig. 1, SPM techniques detecting electrostatic or magnetic interactions are usually implemented in lift mode: typically, the topography is first obtained in contact mode after which the tip is separated a preset distance from the surface (chosen such that short range forces do not contribute to the electrostatic or magnetic forces of

81

interest). At this preset sample-tip separation long range interactions are measured, usually with an ac technique.

Surface Figure 1. Schematic of lift mode SPMs, e.g. EFM, SSPM, MFM, SIM, etc.

2.1. ELECTROSTATIC FORCE MICROSCOPY Electrostatic Force Microscopy (EFM) is commercially available and in terms of Table I is a noncontact tool with detection by y mechanical oscillation. While scanning at a constant tip/surface separation (usually 50~100nm), the cantilever is mechanically oscillated at its resonant frequency and constant amplitude. Under the attractive electrostatic interaction, the motion of the cantileverr can be approximated by a simple harmonic oscillator: (6) meff z + γz + kz = F (z ) where meff is effective mass of the tip, γ is damping coefficient. And electrostatic force F(z) can be further expanded: dF F ( z ) = F ( z 0 + dz ) = F ( z 0 ) + dz (7) dz z = z0

where z0 is the equilibrium position (approx. lift height) about which the cantilever is oscillating. The resonant frequency is shifted from that of a free cantilever (Eq. 4):

∆ω =

ω 0 dF 2k dz

(8)

The frequency shift results in phase and amplitude shifts relatively to a freely oscillating cantilever:

82

∆φ =

Q dF Q dF and ∆A A = CA0 k dz k dz

(9)

Thus imaging ∆φ or ∆A is equivalent to imaging the force gradient variation on the surface. In order to enhance the quality of imaging, a dc bias is usually applied to the cantilever. 2.2. MAGNETIC FORCE MICROSCOPY A ferromagnetic AFM tip can be used to sense the local magnetic field distribution. High resolution Magnetic Force Microscopy (MFM) has been developed to image ferromagnetic domain structures, study the quality of magnetic record media, superconducting current, as well as the integrity of microelectronic circuits. Similar to EFM, MFM is based on detecting dynamic response of a magnetized AFM cantilever to the magnetic force gradient. MFM is also realized in dual pass lift mode. In the first pass, the surface topography is acquired. In the second pass, the cantilever is mechanically driven, and during the scanning a constant separation with the surface is maintained. The magnetic force gradient results in a change in the cantilever resonant frequency, ∆ω =

Fm ω 0 dF 2k dz

, where Ȧ0 is the resonant frequency without external forces

and k the spring constant. The magnetic force Fm in the point probe model is given by Eq. 3. For more than a decade, MFM has been the primary tool of imaging magnetic domains. However, it is discovered that oftentimes with the strong magnetic field produced by the scanning probe can alter the domains in the sample. The result is a big difference between two consecutive images. Another major application of MFM is the imaging of current carrying microcircuits. Intensive study in the area has been done by R. Yongsunthon, E. D. Williams et al. [9, 10] In one of their works, current crowding effect was observed near the defects in a microfabricated connection, leading to further study of electromigration and circuit failure mechanism. One should keep in mind, however, when scanning across a biased device, electrostatic force also contributes to the cantilever oscillation (as in SSPM). To achieve quantitative magnetic interaction, MFM is further developed to include an electrostatic force correction mechanism, which is realized by combining conventional MFM with SSPM [11]. By adjusting a dc bias applied to the cantilever, the contribution from electrostatic force to the tip oscillation can be nullified.

3. Advanced Scanning Probe Microscopy: Exploiting Multiple Modulations

3.1. SCANNING SPREADING RESISTANCE MICROSCOPY AND SCANNING CAPACITANCE MICROSCOPY One of the first measurements to emerge from electrostatic force microscopy was motivated by the need to map dopant profiles in semiconductor devices with decreasing dimension. Two contact techniques, Scanning Spreading Resistance Microscopy

83

(SSRM) [12, 13, 14] and Scanning Capacitance Microscopy (SCM) [12, 15, 16, 17], were developed. Actually, both SSRM and SCM map carrier concentration from which dopant concentration is calculated. In SSRM a conducting tip is biased with respect to the sample and the current through the tip/surface contact is detected under force feedback control. The amount of current is determined by the local spreading resistance of the surface, which is related to the local conductivity ı and the contact radius a by 1 . As ı is a function of the carrier concentrations p, n and carrier mobilities µ , p R= 4 aσ µn: σ = q ( pµ p + nµ n ) , the concentration of the major carriers can be estimated. Because the native oxide layer on Si hinders tip/surface contact, carrier profiling usually requires a tip coated with a hard material (e.g. doped diamond) and a high spring constant cantilever to provide strong indentation forces (~20µN) [12, 18]. In SCM, by contrast, the carrier concentration is profiled via the detection of tipsurface capacitive coupling, and thus a good quality oxide surface layer is required. As the tip is scanned across the sample, a high frequency capacitance sensor detects the tipsample capacitance. An ac voltage applied to the tip induces the depletion and accumulation of carriers, resulting in a change in measured capacitance, ǻC. In a semiconductor, the depletion/accumulation width is inversely related to the carrier concentration, so mapping of ǻC/ǻV yields the carrier concentration profile. Difficulties in quantification arise if the dopant concentration is non-uniform, and when spatial resolution decreases due to low dopant concentrations. A recent modification incorporates an additional feedback that adjusts ǻV to maintain a constant ǻC during the scan, maintaining a constant depletion width. Analysis of SCM results are mathematically challenging, usually requiring 2-D or 3-D numerical approaches [19, 20, 21, 22]. Williams et al. were the first to map the capacitance distribution in a FET device, showing that the source, drain and gate are evident and the difference in majority carrier (n or p type) is indicated (Fig. 2). The device is 180 nm and capacitance gradients over tens of nm are clearly visible. H. Edwards et al. have imaged the capacitance variations at a pn junction in a MOS-FET with spatial resolution of ±30nm, on the same order as that of the Si depletion width [23]. The potential impact of the ability to determine local capacitance is obvious but not limited to conventional semiconductors. SCM, in conjunction with SSPM has also been used to characterize grain boundary properties in ceramics such as a CdTe film [24]. Both SSRM and SCM suffer from limitations in spatial resolution due to the need for high load tip contact and from limitations in capacitance inherent in the capacitance sensor. In addition there is an intrinsic trade off in that as contact area is reduced to increase spatial resolution, the signal to noise ratio deteriorates. Two approaches are currently being explored to solve this problem. One solution is to improve the sensitivity of the sensor [25]. An alternative proposed by Kobayashi et al. [26] is to eliminate the sensor entirely and apply an oscillating electric field to a conducting tip in contact. The third harmonic of this signal, if it can be detected, gives dC/dV directly. This technique is related to high order PFM and high order Scanning Nonlinear Dielectric Microscopy, discussed below.

84

Figure 2. Scanning Capacitance Microscopy of a 0.18 nm FET. Contrast in capacitance is related to local dopant concentration. Source, drain and gate are indicated, along with the channel. This data demonstrates that spatial resolution on the order of tens of nms is necessary to characterize variations in this device. (courtesy of C. C. Williams)

3.2. SCANNING SURFACE POTENTIAL MICROSCOPY Scanning Surface Potential Microscopy (SSPM), sometimes referred to as Kelvin Probe Microscopy (KFM), was developed to map the work function variation of a surface [27, 28]. In SSPM, the tip/surface separation is maintained constant (typically tens to 100 nanometers) with the actuator disengaged, so that the tip is no longer mechanically driven. In the meantime, a biasing voltage Vtip = Vdc + Vac cos(ωt ) is applied to the tip. Let the surface potential of the sample be Vs, the capacitive is given by

Fcap ( z ) =

1 ∂C (Vtip − Vs ) 2 2 ∂z

(10)

where C is the tip/surface. A lock-in amplifier picks the first harmonic of the tip oscillation signal under the capacitive force Fcap. By expanding equation (1), the first harmonic component (F F1Ȧ) of Fcap is obtained:

F1ω =

∂C (Vdc − Vs )Vac ∂z

(11)

By properly adjusting the dc bias component Vdc using a feedback loop, F1Ȧ can be nullified, i.e. F1Ȧ=0, which is satisfied when Vdc=V Vs. Because of its capability of resolving potential contrast down to several millivolts, this technique has found wide applications in studying electrically active interfaces, surface desorption phenomena, as well as self-assembled monolayers. The apparent ease with which potential variations

85

can be mapped belies the challenges in interpreting images on electrically [29, 30] and topographically [ 31 ] inhomogeneous surfaces. In the case of semiconductor and dielectric surfaces the electrostatic properties of a surface are not characterized solely by intrinsic potential and topography. SSPM images of these surfaces should be interpreted in terms of effective surface potential that includes capacitive interactions per se, along with contributions from surface and volume bound charges, double layers and remnant polarization [32, 33, 34, 35]. For semiconductor surfaces without Fermi level pinning, tip-bias induced band bending [ 36 ] can lead to a non-linear surface potential dependence on voltage [37], further complicating quantification of experimental results. Despite these challenges the obvious need to examine variations in local potential in electronic nano devices spurred efforts to overcome some of the obstacles with careful analytical treatments that determined limits in quantification, and allowed complex materials to be addressed. Progress was slow immediately after the introduction of the technique, but the late nineties saw SSPM applied to semiconductor [38, 39], organic [40] and ferroelectric [41, 42] surfaces, as well as to defects [43, 44], and photoinduced [45, 46] and thermal phenomena [47, 48] in these materials. An illustrative example is the attempt to determine what the surface potential of an organic self assembled monolayer (SAM) represents. Figure 3a shows how a pattern of two SAMs with dramatically different properties yields a clear difference in the surface potentials. The difference in potential for this particular comparison of dodecane thiol vs PETB is 80mV. The question arises as to what this value represents. At the limit of very short chain lengths the potential might be treated as a substrate work function modified by adsorbates. At the limit of very long chain lengths, it might be the work function presented by the polymer. In the intermediate range it must be a convolution of the substrate work function, the dipole in the molecule-metal bond, and the dipole of the molecule to which the end group (charged or uncharged) contributes. Eng at al began to address this problem with a comparison of potential as a function of chain length [49].

(a) Figure 3. (a) SSPM of a SAM pattern on Au (111) produced with two types of organic molecules. (courtesy of R. Alvarez) (b) A quantitative relationship between the alkane thiol chain length and surface potential (Courtesy of L. Eng reprinted with permission of the American Chemical Society)

Figure 3b shows a direct correlation between chain length and potential which indicates that the molecular dipole plays a large role. While most investigators assume that the metal/molecule bond is sufficiently screened so as not to contribute, Alvarez et al determined that substrates do influence the result [ 50 ]. And experimental

86

measurement and first principles calculations have not yet converged. It is fair to say that at this point that absolute values of potential can not be quantified, but variations in potential can be determined with energy resolution of 2-4 meV. It goes without saying that understanding potential variations in SAMs will be invaluable as complex molecules and patterning is explored. 3.3. SCANNING IMPEDANCE MICROSCOPY In order to explore mechanisms of transport in complex devices it is necessary to determine time and temperature dependence as well as voltage dependent response functions. In macroscopic systems this is done with frequency dependent perturbations or ultra fast probes of relaxation from excited states. The first introduction of frequency dependence in scanning probes is referred to as Scanning Impedance Microscopy (SIM) [51]. This is a noncontact, first harmonic detection in which the oscillating electrical signal is applied to the sample instead of the tip. In SIM, a lateral ac signal is applied to the sample and the tip is either grounded or dc biased. Same as in SSPM, the tip/sample separation is maintained constant with the mechanical actuator disabled. According to Eq. (1), the capacitive interaction is expressed as:

F=

1 ∂C 1 ∂C (Vdc − Vs ) 2 = [Vdc − Vs0 − Vac cos(ωt + ϕ L )]2 2 ∂z 2 ∂z

(12)

where Vs, and Vs0 are local surface potentials after and before the lateral bias is applied, Vac is the local local oscillation of the surface potential, and ĳL is the phase lag relative to the power source. The amplitude and the phase lag ĳc of the first harmonic cantilever response are

A1ω =

| F1ω | 1 m (ω − ω 0 ) 2 + γ 2ω 2

and

ϕ c = arctan(

γω ) ω − ω0

(13)

(14)

where | F1ω |= ∂C (Vddc − Vs0 )Vaac , is the amplitude of the first harmonic capacitive force, ∂zz m is the effective mass, Ȗ the damping coefficient. From (3), ĳc is independent of the location of the tip. The total phase lag of the cantilever oscillation relative to the driving source is ϕ = ϕ L + ϕ c . During the lift scan, A1Ȧ and ĳ are acquired simultaneously with the lock-in technique. Assuming SIM is used to image an electrical component (e.g. an 1 active interface) with an impedance of Z = =| Z | exp( j∆ϕ ) , as illustrated in 1 + jω C R Fig.4, ∆ϕ = ϕ 2 − ϕ1 , and

| Z | ∝ | A2 exp( jϕ 2 ) − A1 exp( jϕ 1 ) | ∝ | V2 − V1 | (15) The greatly enhance spatial resolution has enabled SIM as a quick tool to check the connection reliability of a ‘nano-circuit’ built from carbon nanotubes and/or nanowires.

87

In combination with other SPM techniques, SIM has revealed dielectric constant suppression at an oxide grain boundaries [52], mapped the rectifying behavior of a Schottky junction, and characterized defect mediated transport across a nanotube [53]. The application of this technique to interfaces f is treated in detail by Bonnell and Kalinin elsewhere in this volume [54].

ϕ2, A2

ϕ1, A1 Ri

R

R

Ci

Interface

V (a)

(b)

Figure 4. Principle of SIM: an electroactive interface can be modeled as a simple RC element. The phases (ĳ1, ( 1, A2) of tip oscillation on both sides of the interface are related by Eqs. (13), (14) and ĳ2) and amplitudes (A (15).

ș

|Z| 1

2

3

3

3 µm

(a)

2

1

(b)

2.0x10

5

1.5x10

5

1.0x10

5

5.0x10

4

2V 3V 5V

Zi(Ω)

(c)

0.0 0

1x10

5

2x10 Z r( Ω )

5

3x10

5

4x10

5

Figure 5. Contrast Mechanism Maps of PFM as a function of contact radius and indentation force. SI - strong indentation regime, CSI - contact limited strong indentation, LE - linear electrostatic regime, NE - nonlinear electrostatic regime, PD - plastic deformation. Dotted line delineates the region where stress-induced switching is possible. The maps are constructed for (a) good tip-surface contact (w = 0.1 nm) and (b) bad contact (w = 1 nm).

88

The second approach to accessing frequency dependent transport expands the frequency range to many orders of magnitude. Nano Impedance Spectroscopy (NIS) [55] is a contact probe with force feedback in which the oscillating signal is applied to the tip; phase and amplitude are detected at the sample. The frequency dependent measurement can be implemented in two terminal or three terminal configurations depending on the device geometry Figure 5 (c) illustrates the local impedance between a tip and lateral electrode, across a ZnO grain boundary. The electrode contact and grain boundary properties are distinguished as two semi circles in the impedance spectra, allowing the actual properties of the grain boundary to be characterized. The local boundary potential, capacitance, charge and depletion lengths can be extracted with spatial resolution on the order of tens of nms. In a configuration with an electrode under the sample, the impedance of individual grains can be mapped, Figure 5 (a) and (b). 3.4. SCANNING GATE MICROSCOPY A clever modification of EFM has been developed recently in order to characterize lateral transport in low dimensional systems. Electrodes are connected, for example by e-beam lithography, to the feature of interest, which might be a quantum well, nanotube, or molecular wire. The tip, which is scanned over the structure while current is flowing between the electrodes, perturbs the system acting as a local gate. The signal that is mapped as an image is the relative differences in current through this three terminal device as a function of the tip position. Some samples are amenable to configurations that also contain a back gate, in which case the tip gate and back gate can both be varied. This technique, referred to as Scanning Gate Microscopy, is a non contact, electrically driven probe system [53, 56, 57, 58, 59]. Due presumably to the geometric constraints of this configuration SGM has been applied most frequently to carbon nanotubes. An example is shown in section 3.1. The next generation of local transport measurement will utilize individually addressable multiple tip scanning probes to explore alternative configurations of 2, 3, and 4 point transport measurements at nm length scales. 3.5. PIEZORESPONSE FORCE MICROSCOPY As the ability to synthesize complex functional materials increases in sophistication, characterization of nonlinear properties such as piezoelectric, ferroelectric, and ferromagnetic responses at small scales is becoming important. Piezoelectric Force Microscopy (PFM) is a scanning probe that holds the promise of determining electromechanical coupling coefficients at local scales. PFM is a contact, electrically driven V0cos(Ȧ ( t) is probe technique with feedback based on phase lag. An ac voltage Vac=V applied upon the tip and ferroelectric surface junction. If the material is piezoelectric, the field results in a local deformation of the surface that oscillates the tip, i.e. piezoresponse [60, 61]: PR = A0 cos(ωt + δ ) , where A0 is the amplitude of PR, which is proportional to the electromechanical coefficients, and į is the phase difference between the driving signal and the piezoresponse, is determined by the orientation of the domain. For downward oriented domains, į = -180o and for upward oriented domains, į = 0o.

89

The phase therefore indicates the orientation of atomic polarization, while the amplitude gives the magnitude of the coupling coefficient. In reality, electrostatic interactions between the tip and the surface, as well as between the cantilever and the surface are not negligible, as shown by a variable temperature measurement done by Luo et al. A rigorous treatment of the imaging contrast includes simultaneous electrostatic and electromechanical interactions. The total contribution to the measured amplitude A should be (16) A = Ael + Apiezo + Anloc where Aell is from the tip-surface electrostatic force, Apiezo is from the electromechanical interaction and Anloc is the nonlocal canilever effect. Obviously, reliable piezoresponse results are obtained only if electrostatic interactions are minimized. Taking an approach familiar to materials scientists, the analytical solutions of these interactions can be presented as contrast mechanism maps (Fig. 6) that relate experimental conditions to the properties of the material and delineate the conditions under which quantitative measurements can be obtained [62]. This is critical since it has been shown that under some experimental conditions the response has no connection to local properties.

Figure 6. NIS imaging of a junction of ZnO grains (a) |Z| (b) θ; impedance spectrum shows two relaxation processes (c).

The dynamic switching of a domain is studied via the dc voltage dependence of PR, which is usually accomplished by simultaneously applying a slow periodical dc voltage to the bottom electrode and acquiring the PR signal with the probe staying at one point. By defining PR mathematically as (17) PR = A cos δ an electromechanical hysteresis loop can be constructed by plotting the PR versus the dc voltage, due to the back and forth switching of the domain by the dc voltage (Fig. 7). For the general case there is also an in-plane component to polarization that can be accessed by measuring lateral response of the tip to field variation [ 63 , 64 ]. Furthermore, the piezoelectric response is a tensorial function, the complexity of which depends on the symmetry of the compound and the orientation of the grain or crystal. Harnagea et al have shown that even for BaTiO3 with relatively high symmetry it is not

90

possible to deduce domain orientation from out of plane PFM alone [65]. Either the grain orientation or the in-plane component must also be known. In spite of these challenges, PFM has become the preferred method of characterizing ferroelectric thin films and exploring the physics of polarization dynamics. The relationship between higher order harmonics, 2ndd and 3rd, of the PR function and time dependence of domain switching is being developed into a probe of switching dynamics in Nonlinear Piezo Force Microscopy (NPFM) [66].

PR(a.u.)

0.3

0.0

-0.3 -12

-8

-4

0 Bias(Volt)

4

8

12

Figure 7. Electromechanical hysteresis loop acquired with PFM on PZT 20/80 thin film.

3.6. SCANNING MICROWAVE AND DIELECTRIC MICROSCOPY A complementary strategy to accessing linear and nonlinear dielectric properties is referred to as Scanning Nonlinear Dielectric Microscopy [ 67 , 68 ] and Near Field Microwave Microscopy (NFMM) [69, 70]. The approach utilizes a coaxial probe in which a sharp, center conductor ‘tip’ protrudes. The probe is actually the end of a transmission line resonator, which is coupled to a microwave source. In the configuration used in Anlage’s group the probe tip is held fixed, while the sample is supported by a spring-loaded cantilever applying a controlled normal force on the order of 50 µN between the probe tip and the sample. The concentration of the microwave fields at the tip changes the boundary condition of the resonator, and hence, the resonant frequency and quality factor. The magnitude of the perturbation depends on the dielectric properties of the sample. A simple model describes the probe and sample interaction as a circuit of the sample sheet resistance RX connected in series with the probe/sample capacitance CX. And collected frequency shift ∆f and quality factor Q are related to RX and CX according to standard microwave theory. The spatial resolution of the microscope in this mode of operation is about 1 µm. NFMM has shown promise in mapping dielectric constant variations in a number of complex oxides; i.e. ferroelectric and superconducting compounds. Anlage et al. have demonstrated that high order

91

harmonic powers acquired by NFMM can be used to spatially resolve the local nonlinearity. In their work, the grain boundary area of superconducting YBCO thin film deposited on a SrTiO3 bicrystal was spatially resolved from the ratio of the second and the third power [71]. In the early version of NFMM, the probe is scanned in contact with the sample. The damage to the probe due to the large contact force severely impairs the spatial resolution. Recently, NFMM has been developed to include an STM feedback enabling a noncontact scanning with a separation of about 1nm. The improvement in spatial resolution was significant [72]. The sensitivity of this new NFMM technique to physical properties such as dielectric loss has been demonstrated on a boron doped silicon (Fig. 8). The difference in sheet resistance RX in doped and undoped regions were resolved by ∆f and Q images.

1 µm

350

413

475

538

600

Topography in Angstroms

364

368

371

375

378

Resonator Quality Factor

100

75

50

25

0

Frequency shift (kHz)

Figure 8. Images of a boron doped silicon sample (a) STM topography; (b) Quality factor; and (c) frequency shift images. (Courtesy of S. M. Anlage and reprinted with permission of Elsvier B. V.)

4. Applications

The expanding toolbox of local probes of complex properties can provide insight regarding local phenomena in two distinct contexts. It can be used to quantify properties of structures that are so small as to exhibit quantum mechanical or continuum based size dependent behavior. It can be used to probe local variations in larger systems in which these variations influence global behavior. An example of each follows. 4.1. TRANSPORT IN SINGLE MOLECULES AND NANO WIRE/TUBES Transport in reduced dimensions is becoming increasingly important as developments in nanostructured materials enable device elements to be made of organic and biological molecules, nanotubes, nanowires, quantum dots, etc. The ultimate goal of basing device function on molecules raises the challenge of isolating and characterizing the behavior single molecules or wires. Of course it is possible, and in fact has often been accomplished, to distribute nanostructures across a suitable substrate and examine them ‘top down’ with any of the scanning probes. In some cases this provides new insight, as for example in the STM analyses of carbon nanotubes which related local density of

92

states to atomic structure [73, 74]. It must be noted that in this configuration the tipnanostructure-substrate properties, rather than the lateral properties of the structure, are measured. The simplest conceptual approach to accessing lateral transport properties of a molecule or nanowire is to connect electrodes to molecules/wires that are distributed on a surface and measure from remote connections. One of the first wires to be characterized in this manner was a single phthalene molecule [75]. Transport in DNA has been examined, as well [76, 77]. The most extensive use of this strategy has been on carbon nanotubes. Both the Dekker group and the McEuen group have used SGM or simple transport measurements in this configuration. These results provide evidence that some carbon nanotubes act as real quantum wires. The low dimensionality is expected to result in strong electron–electron, so it has been suggested that electrons in nanotubes form a correlated ground state known as a Luttinger liquid. Some low temperature measurements provide evidence for this, while some points to coherent backscattering processes. Transport in semiconductor nanotubes is even less well understood. Electrode contact potential, chemical adsorption defects [78], and nanotubes/substrate interface contacts impact properties [79]. Johnson et al. [79] and Furher et al. [80] have used local probes to demonstrate a potential for defects at nanotubes to be memory bits. (a)

600 Spot diameter (nm)

500 400

Defect 1 Defect 2 Defect 3 Defect 4

4

(b)

3

300

2

200 100 0

(c) 0

2

4 6 Tip bias (V)

8

1

Figure 9. Scanning Impedance Microscopy of a single walled carbon nanotube acquired with increasing tip voltage from left to right (a). Contrast maxima indicate regions where the p type tube is depleted of carriers. Defects are labeled in the SGM image (b). The voltage dependence of this contrast can be used to extract the valence band energy at the defect (c).

93

Adding the frequency dependence of SIM to a configuration that isolates a single wire has been used to determine the effect of defects on transport and the local electronic structure of an individual defect. For the case of a carbon nanotube, the tip is used as a local gate to drive individual defects into carrier depletion. The consequent increase in the resistance of the tube is registered as contrast variation in SGM and SIM images as shown in Figure 9(a) and (b). A relatively straight forward calculation shows that the voltage dependence of the contrast is related to the valence band energy at each defect. The tip voltage required to cause the defect to become a scattering center is the energy difference between the local valence band and the Fermi energy. This is illustrated in Figure 9 (c), which also compares the spatial resolution of SGM and SIM on a nanotubes. This approach can be generalized to all classes of molecular wires. 4.2. DOMAIN INTERACTIONS IN FERROELECTRIC THIN FILMS Complex transition metal oxides, as exemplified by the perovskite family of compounds, offer wide ranging and intricate property combinations. Compounds in this class can be insulating or superconducting, optically active or transparent, ferroelectric or ferromagnetic. Some exhibit non intuitive combinations of properties; transparent and conducting, ferroelectric and ferromagnetic, etc. Understanding behavior in these systems requires a combination of electrostatic and dielectric probes. For the case of thin films, in which grain sizes and domain sizes can be less than 100 nm, local probes are a necessity. First observations of ferroelectric domains were based on SSPM [81, 82, 83, 84, 85]. Motivated by the concept of high density ferroelectric memory, many groups used a conductive tip of a SPM to induce local domain orientation and imaged the result with SSPM. An interesting observation was that the domains appeared not be to stable. Since the fundamental limit of domain stability was under some debate this result was accepted. However it was shortly realized that atomic polarization is compensated at a surface that is exposed to ambient. The SSPM measurements reflect the sum of surface charge due to polarization and compensation charge due to adsorbates. In most cases the sign of the surface charge is that of the compensating species, i.e. opposite that of the domain polarization. Nevertheless, SSPM was used to examine domain wall motion and ferroelectric/paraelectric phase transitions. The advent of PFM, which is not sensitive to the compensation charge, promised to eliminate ambiguity; however, first measurements were not consistent. Luo et all found that the temperature dependence of PFM contrast of triglycine sulphate near the Curie temperature was similar to that of the spontaneous polarization rather than the piezoelectric coefficient [48]. The gradual change in potential was attributed to the dominance of electrostatic interactions due to the charged surface [ 86 ], since the electromechanical response based on the piezoelectric coefficient would diverge in the vicinity of the Curie temperature. Contrasting behavior was observed in the existence of a lateral PFM signal which could not result from surface charge alone [64, 87, 88], the absence of relaxation behavior that is characteristic of compensation charge [32, 89], as well as numerous observations using both EFM/SSPM and PFM [90, 91] that clearly pointed to a significant electromechanical contribution to PFM contrast. The discrepancies can be resolved with reference to Figure 4. Experiments done under

94

conditions in which the sample/tip interaction was influenced by electrostatic forces as well as piezoelectric deformation obtained different results than those with conditions squarely in SI regime where the signal is directly related to the piezoelectric coefficient. In many cases, topological information on domain structure and orientation obtained from SPM images is sufficient and numerous observations of local domain dynamics as related to polarization switching processes [92, 93, 94], ferroelectric fatigue [95, 96, 97, 98], phase transitions [48, 99, 100, 101], mechanical stresses [102], etc. have been made. However, the detailed analysis of local ferroelectric properties including hysteresis measurements [103], stress effects in thin films [104], size dependence of ferroelectric properties [105, 106], etc. requires quantitative interpretation of the SPM interaction. Many of the articles in this volume will treat various aspects of these issues.

5. Other Techniques and Future Directions

These few examples illustrate the tremendous advances that are being made in understanding linear and non linear properties of complex systems at the nanometer scale. In some cases the complexity is due to size, in others the presence of interfaces, boundaries, and domain structures. The ability to localize the measurement to nms and to access properties more involved than linear electromagnetic responses is critical to understanding these systems. The former is facilitated by using scanning probes, the latter by utilizing multiple modulation schemes. The length constraints of a single article have precluded a comprehensive overview of all techniques. The selection presented here was driven in part by the topics treated in the associated conference and by the content of the other papers in this volume. One obvious omission is the class of measurements based on magnetic interactions. For example Scanning Squid Microscopy and local Magnetic Resonance Microscopy continue to be exciting. Similarly, near field optical probes, advanced tunneling microscopies, and the suite of local mechanical property techniques are developing simultaneously. The subset of the scanning probe field presented here is very dynamic right now, perhaps being driven by the increasing interest in a wider range of complex materials. The next few years will witness another leap in understanding as the multiple modulation probes are combined with the atomic resolution capabilities of non contact AFM.

Acknowledgements

We are grateful for continued support by the Department of Energy and the National Science Foundation for that part of the work done in our labs. Clayton Williams, Charlie Johnson, Lukas Eng and Steve Anlage have graciously provided figures. We have benefited from extensive discussions with Sergei Kalinin, Lukas Eng, and Alexei Gruverman.

95

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NANOSCALE PROBING OF PHYSICAL AND CHEMICAL FUNCTIONALITY WITH NEAR-FIELD OPTICAL MICROSCOPY

L.M. ENG Institute of Applied Photophysics, Department of Physics University of Technology Dresden, D-01062 Dresden, Germany [email protected]

Contents 1. 2.

3.

4.

5.

Introduction Optical Far-field Properties 2.1. Optical Polarisation 2.2. Optical Absorption 2.3. Fluorescence 2.4. Raman spectroscopy 2.5. Interference and coherence 2.6. Optical resolution: the Abbe limit The Optical Near-field Concept 3.1. Principle of optical near and far field 3.2. Aperture type optical near-field microscopy (A-SNOM) 3.3. Scattering type optical near-field microscopy (s-SNOM) Application of Optical Near-field Microscopy to Probe Functionality 4.1. Contrast by fluorescence and photoluminescence 4.2. Near-field optical polarisation contrast 4.3. Absorption contrast in A-SNOM 4.4. Nano-Raman 4.5. Near-field optical modification and manipulation Conclusion

Abstract Near-field optical microscopy provides clue advantages for the future nanoscale inspection of organic and inorganic materials providing ultra-short time resolution and improved spatial confinement. Starting from m basic properties of optical waves, this contribution summarises what chemical and physical information may be collected when performing such (near-field) optical experiments resulting in specific and functional properties of the material under consideration. Also near-field optical microscopy (SNOM) is discussed both from is theoretical and experimental point of 103 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 103-118. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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view, directly leading to the modern type of scattering near-field optical microscopy (sSNOM). That type of near-field method will definitely lead to the expected realm and revival for local optical detection and tracking of functional systems on the 10 nm scale.

1. Introduction Inspecting optical properties of solid and soft matter materials turns out to be of ultrahigh importance in the 21stt century when gaining information on the physico-chemical behaviour and dynamics of functional devices. Not only has the optical lateral resolution to be pushed down to the 1 nm range, but time resolved experiments using modern type femto-second lasers and coherence imaging is of clue importance when gaining an understanding of the nanoscopic properties in clusters, molecules, and correspondingly at interfaces. Much of that driving force stems from industrial applications pushing the structure size of the features of interest below the magic 100 nm border: mass production with 93 nm fab-lines are just popping up, and the impact of extreme ultraviolet photolithographic for large scale manufacturing has been recognised and established in research. Applications such as storage devices, nanoscale electronics, and supramolecular assembly all demand these steps and would considerably profit when having possibilities in tracking surface and bulk functionality at a 10 nm resolution and beyond, or directly applying optical methods for structuring and initiating functionality on the same scale.

Figure 1. Development of the data storage density in optical discs. Shown are the needs for developing optical near-field applications. (with courtesy of Thomson Muti Media.)

Figure 1 shows an example of needing developments in the near-field area for instance for storage applications [1]. In few years already will far field optical microscopy be limited in size and resolution to read and address such memories, and

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novel ways like the optical near-field and other nanooptical issues have to be established in order to take over that task. The contribution presented here now is devoted to summarise the most important optical properties being responsible for the recognition and signal generation when probing such functional systems. Most of such state-of-the-art properties are based on far-field experiments recording the optical response of an ensemble, for instance in optical absorption, fluorescence, or Raman spectroscopy. Hence both the question of optical coherence and resolution ultimately have to be discussed. It is thus important to understand such influences before then dropping into a discussing of scanning near-field optical microscopy (SNOM) which aims at gaining even much more insight on the very local scale. In contrast to far-field experiments where propagating waves are collected, the optical near-field arises only in the vicinity of a scattering or diffracting object and has to be collected in close proximity being on the order of less than half the optical wavelength λ in use [2]. From the historical and widely used approach of aperture type near-field microscopy (a-SNOM), today’s development heads towards the scattering type y set-up (s-SNOM) allowing both a higher optical throughput and better resolution. We show that in principle the optical resolution is given by the electric field confinement only and may be pushed down to below 10 nm for small confined scatterers. Therefore, for both microscopical and sensoric applications in functional systems, a big effort has to be spentt on developing such nanoscale scatterers, i.e. clusters of special optical functionality.

2. Optical Far-field Properties As mentioned above, today’s optical methods in microscopy and spectroscopy integrate methodologies where the optical average of an ensemble is detected. This drawback stems from the resolution both in space and time, and generally results in the incoherent superposition of events. Hence it is difficult to judge on the microscopic or atomic origin and behaviour of individual chromophores of functional elements since all information on the local phase and polarisation mainly is lost. Nevertheless, on the atomic or molecular scale, all systems optically respond to the stimulus by exhibiting their characteristic and indicative optical transitions; note, however, that this information is washed out in due experiments resulting in an averaged response only. One way out though, mostly practised in biological and biomedical research, is to track such functional systems (molecules) by literally dispersing them in an appropriate medium. This is not possible for solids or sample surfaces, since they always offer their functional property as a whole. Furthermore, the packing density and arrangement of atoms and molecules may even favour one or the other functionality, which means, that dispersing like in biology would not be appropriate at all, yet killing all desired functionality. We thus face the problem that we have to develop ways and methods in order to track functional groups at surfaces in their actual state and conformation. This needs methods which may reach single atomic resolution and beyond. Scattering methods like X-ray diffraction or neutron scattering right offer this sub-atomic resolution, however, at

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the expense of needing laterally largely extended assemblies of uniform property. As a result, we again obtain an integral information only, not yielding insight on the behaviour of just one functional group within the “sea” of all other units. Scanning probe microscopy, on the other side, has the potential to address only one molecule or atom, at least for scanning tunnelling microscopy (STM) and scanning force microscopy (SFM) under UHV conditions. Measuring an optical information from such individual species using near-field optical microscopy, however, still counts to one of the major challenges in experimental physics, and is not routinely applicable. This may though drastically change following all the good news in this contribution when reporting on the scattering-type SNOM. 2.1. OPTICAL POLARISATION

G

By definition, the optical polarisation is aligned parallel to the electric field vector Ei G of a plane optical wave with frequency ω, propagation direction ki = 2π and initial phase ϕ i :

λ

{(

)}

GG G G Ei = Ei,o ⋅ exp i ki r − ωt + ϕ i . (1) Any state of polarisation may be regarded as the superposition of elementary G G polarisation states. As an example, we superimpose E1 and E2 having different kvectors and phases, but equal frequency. The resulting wave then reads as: G2 G G G 2 G 2 G G ( I = E = E ⋅ E * = E1 + E2 + 2 E1E2 ⋅ cos . (2) G Note that the polarisation in E dramatically depends on the beating term in equ. (2); while the magnitude is sensitive to the cos(x) term, the polarisation is influenced by the G G G G scalar product E1 ⋅ E2 . Assuming the two plane waves E1 and E2 to be denoted in the G G ªE º complex Jones- matrix [3] description E = « G1 » allows a very simple and instructive «¬ E2 »¼ differentiation of all possible states of optical polarisation: G ° E real → linear polarization °° G G G G G G Im E = ex E1 ± e y E2 = ® E complex, = 1 → circular polarization Re °G ° E complex, Im ≠ 1 → elliptical polarization °¯ Re This differentiation holds for both the optical near and far field, and allows many ways of experimentally investigate the polarisation properties.

[(

)

]

2.2. OPTICAL ABSORPTION Similar to affecting the optical polarisation via the dipolar character of materials, optical absorption is based on the elastic response of the electron-core system to an external

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G

time varying electric field E described in the so-called Lorentz model (Lorentz, 1907). The induced dipole moment G P=

Ne 2

G m ⋅E (3) ω o2 − ω 2 − iωγ depends on the number of electrons N involved, the electronic mass m and charge e, the with K the elastic force actual and effective resonance frequencies ω and ω o = K m constant binding the electron to the nucleus, and γ denoting a frictional damping force of the electron motion. As shown in Fig. 2, different processes attribute to γ affecting the dielectric constant in ordinary dielectrics in different frequency regimes, such as atomic polarisation in the UV, displacement polarisation in the infrared, and orientation polarisation at ultra-high frequencies. Note that the complex index of refraction n is

connected to the real and imaginary dielectric constant

(

)2 = ε r' + i ⋅ ε r'' ,

ε r'

and

ε r''

via

with κ the extinction index of the medium. Note that the

absorption coefficient 2α of that same medium connects to κ through α = ω ⋅ κ with c c the speed of light.

Figure 2. Spectral dependence of the dielectric constant in ordinary dielectrics respecting atomic polarisation, displacement polarisation , and orientation polarisation, respectively.

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2.3. FLUORESCENCE Fluorescent emission is typical to organic and biological molecules. Populating higher electronic levels allows to monitor their decay either from singulett or triplett levels, as shown in Fig. 3a). Note that the probability of singulett emission is much larger due too shorter live times (some nano-seconds) and the larger cross section (see Fig. 3b), compared to triplett emission. Fluorescent photons emit into 3D space and thus give rise too blurring when inspecting materials under an optical microscope. Sophisticated techniques such as stimulated depletion emission quenches the spatial spreading allowing for unprecedented optical resolution in far-field optical fluorescence microscopy of ~ 50 nm [4].

Figure 3. a) Optical fluorescence energy diagram showing singulett S and triplett T emission; b) spectral dependence of the optical cross section for absorption (σa), fluorescent singulett (σe), and triplett (σT) emission for Rhodamin 6G.

2.4. RAMAN SPECTROSCOPY Unless fluorescence emission, Raman spectroscopy absorbs photons into a virtual electronic state finally being sensitive to the decay of this excited photon into one of the vibrational ground levels. Depending on whether the emitted photon has smaller, equal, or larger energy than the incident photon we differentiate between Stokes, Rayleigh, and Anti-Stokes Raman scattering, respectively, as shown in Fig. 4. Note that Raman emission from a virtual level thatt coincides with a higher absorptive molecular state (as shown above for fluorescence) is also possible; we then speak of resonant Raman scattering. In any case, the spectral signal probed allows inspection of atomic bond energies by simply stimulating these electrons t forming the bond, similar to a spring mass model. Hence, Raman scattering is highly directional and needs special 3D setups.

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Fig. 5 shows an example when investigating barium titanante (BaTiO3) single crystals with both polarisation microscopy and Raman spectroscopy [5].

Figure 4. Principle of Raman spectroscopy; the decay from a virtual electronic level into the ground state vibrational levels results in a fingerprint of the local bonding.

Figure 5. a) Bright field optical transmission microscopy, b) polarisation imaging, and c) µ-Raman spectroscopy of ferroelectric BaTiO3. The Raman spectra in c- and a-type domains are obtained from locations C and A/B in b), respectively [5].

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2.5. INTERFERENCE AND COHERENCE The superposition of two photons as described by equ. (2) may be mathematically rearranged into G G ) I = I1 + I 2 + 2 E1E2 ⋅ cos +( G G* (4) = I1 + I 2 + 2 ⋅ Re E1E2 = I1 + I 2 + 2 ⋅ Γ112 (τ ),

[(

)

]

G G with Γ112 (τ ) = E1(t ) E2* (t + τ ) the cross-correlation function.

Equ. (4) is important whenever two or more photons are collected simultaneously, which is inherently the case when treating macroscopic objects. Hence the time delay τ in equ. (4) may arise from both an effective temporal delay when one and the same atom or molecule emits the two photons consecutively, or what is more probable, from temporally synchronised, spatially separated emitters thus revealing a spatial coherence. This question is of fundamental interest when either the light source or the detector employed in the experiment becomes nanoscopic in dimension. Therefore time or space correlation is of an extremely high and fundamental interest in near-field optical microscopy (SNOM) 2.6. OPTICAL RESOLUTION: THE ABBE LIMIT As mentioned above, new physical insightt may be expected from nanoscale optical experiments of functional systems. Focussing optical waves with conventional optical components, however, still results in a relatively large optical spot, the size of which is given by Abbe’s diffraction limit [6] 1.22 ⋅ λ Φ= (5) N . A. with N.A. the numerical aperture of the objective in use. Fig. 6 shows such an experimental approach using a circular aperture. The resulting Fraunhofer diffraction pattern concentrates most energy in the central peak suppressing the side wings drastically.

Figure 6. Optical far-field resolution given by the Fraunhofer diffraction limit of a circular aperture; a) cross-section, and b) top view.

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3. The Optical Near-field Concept 3.1. PRINCIPLE OF OPTICAL NEAR AND FAR FIELD

∆X

As mentioned above, far-field optical propagation is limited by diffraction given by the resolution criteria of Abbe. To downpass this optical resolution, one of the most promising concepts bases on the near-field optical or evanescent properties accompanying diffraction and scattering for any object.

Tip

Near-field

φ Synge (1928), ∆X << λ Figure 7. Comparison of a) optical far and b) optical near-field principle.

Fig. 7 illustrates this behaviour by comparing the optical far and near field in the following way: An object given by the diffractive aperture of width 2dd at position z = 0 G diffracts the incident plane wave with amplitude Eo into the far field (at z = Z much larger than λ) where we detect the Fraunhofer pattern as given in chapter II.6. Introducing, however, a second aperture (of diameter φ) at distance z = ε much closer than λ allows the fast decaying evanescent waves to be collected and scattered into the far-field. Note that φ has to be as small as possible in order to be able to collect most spatial frequencies diffracted into the near-field from our object under investigation. This is shown in Fig. 8, where the amount of signal scattered into the far-field is plotted λ/5 and φ = λ λ/25 in for an object wave number K = π d and two probing apertures φ = λ Fig. 8a) and b), respectively. As shown the larger signal stems from case b). From that reasoning result 4 important consequences: • The contribution of a certain spatial frequency K depends on the distance z and decays exponentially. The near-field signal is zero for z → ∞ and maximised for z →0. • The spatial distribution of the optical near field for z << λ is very characteristic and can be measured by scattering or diffracting the near field into the far field [7].

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• The smaller φ , the larger the contribution of a spatial frequency component K (see Fig. 8). • The measured quantity in the far field is proportional to the grey shaded area in Fig. 8 enclosed between −2π λ and +2π λ . This signal approaches zero for K → ∞ .

Figure 8. Optical near-field transmission for an object wave number K= π/d d and two aperture diameters of a) λ/5 and b) λ /25. Note the larger signal amount scattered into the far-field for the smaller aperture b). λ

a)

b)

sample c)

L

sample

tip φ

aperture-SNOM

d)

L

tip φ

scattering-SNOM

Figure 9. Set-ups for probing the optical near field; shown are a) diffracting tip and sample, b) diffracting sample, scattering tip, c) diffracting tip, scattering sample, and d) scattering tip and sample. Note that only c) and d) are technically realised.

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The above discussion on the fundamental principle of SNOM can be further extended in that the aperture type object and collecting probe in Fig. 7 may be differentiated as being either a diffracting aperture t or a scatterer of size L. This is shown in Fig. 9 where inherently the for cases shown have to be confounded: a) diffracting tip and sample, b) diffracting sample, scattering tip, c) diffracting tip, scattering sample, and d) scattering tip and sample. 3.2. APERTURE TYPE OPTICAL NEAR-FIELD MICROSCOPY (A-SNOM) While historically proposed as early as 1928 [8] and realised in 1984 [2], the aperture type SNOM (Fig. 9c) suffers from the factt that no reproducible way of preparing aperture tips are known to date. From the different methods proposed so far such as fibre pulling, fibre etching, truncation by y focused ion beam, aperture opening by an Efield or a solid electrolyte etching, fibre apertures with Quartz caps, tetraeder tips, or integrated Si-cantilever probes, none has resulted in fulfilling the criteria of reproducibility, low cost, and high throughput. Hence the principle of A-SNOM, although theoretically very elaborate, seems to lack from experimentally achievable realisation. 3.3. SCATTERING TYPE OPTICAL NEAR-FIELD MICROSCOPY (S-SNOM) As mentioned above, any particle or cluster may be used to realise the s-SNOM set-up as schematically sketched in Fig. 9d). Although experimentally introduced in the 90’s [9], s-SNOM experiences a fast grow due to its ease and comparability to conventional scanning force technology; in fact, the Si-based AFM tip may be directly used as the scattering centre for s-SNOM. Note, however, that the optical contrast can be improved dramatically by considering the optical field enhancement of confined nanostructures exhibiting electronic Plasmon resonances at optical frequencies, as well as due to the lightning rod effect experienced by non-symmetrical scatterers [7]. Figure 10 displays the local field enhancement of a spherical Au nanoparticle of radius a as a function of optical wavelength λ. Note the large field enhancement of more than a factor of 10 for particles below a 30 nm radius and close to the UV regime. Figure 11 finally illustrates the calculated optical enhancement for a realistic 3D structure consisting of a silver tip with tip diameter 30 nm above a glass sample. Under evanescent illumination with λ = 633 nm, the field enhancement is very prominent; as shown confinement of the enhanced field is proved to occur only under the tip. Hence improving the enhancement with smaller tips while obtaining an even better resolution than the 30 nm shown here is evident. To do so, we propose to use small functional clusters possessing any type of anisotropy, either geometrical or optical. This allows reproducible scatterers to be manufactured and allowing for the routine optical inspection on the 10 nm scale, for instance by nano-Raman spectroscopy [10] and others.

114

air glass

E2=55*E02

50 nm Ei Figure 10. Optical field enhancement of metallic nanoparticles of radius a. Note the spectral dependence.

k

Figure 11. Optical near-field enhancement in sSNOM using evanescent illumi-nation of a solid silver tip of 30 nm tip diameter. Note the prominent enhancement even for the large tipsample system treated.

4. Application of Optical Near-field Microscopy to Probe Functionality Finally we briefly discuss near-field optical applications when probing functionality by means of different optical signals. 4.1. CONTRAST BY FLUORESCENCE AND PHOTOLUMINESCENCE Xie and Dunn [11] have shown for the first time that near-field optical resolution of single dispersed molecules is possible. As stated in the introduction their approach based on isolating individual molecules on a surface rather than probing a single molecule embedded within a solid matrix. They achieved a sub 50 nm resolution using fibre optical probes implementedd in an A-SNOM type set-up. 4.2. NEAR-FIELD OPTICAL POLARISATION CONTRAST Figure 12 displays the contrast obtained with polarisation sensitive A-SNOM [12]. Rotating the direction of the polarisation analyser while collecting the near-field light intensity allows to detect the polarisation orientation for each Rhodamin nanocrystal. Note that this technique has sever impactt for any birefringent nanosystem such as ferroelectrics [13], biological samples, or in magnetooptics [14].

115

Figure 12. Near-field optical polarisation contrast of Rhodamin nanocrystals; frame size: 10 µm (with courtesy of H. Heinzelmann).

0.03 0.02 0.01

T/T 0.00 ∆

-0.01 -0.02

(a)

-0.03 400 450 500 550 600 650 700

750

Wavelength (nm) 0.04 0.03 0.02

T/T 0.01 ∆

0.00

-0.01 -0.02 400 450

(b) 500 550

600 650 700

750

Wavelength (nm)

Figure 13. Optical absorption of individual Au-nanoparticles displayed as a function of wavelength. Note the spectral differences when measuring a) beside and b) on top of the Au cluster. The relative ∆T/T at 500 nm in b) is even larger than 0 dB.

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4.3. ABSORPTION CONTRAST IN A-SNOM Using a white light spectrum for illumination, Seidel et al. [15] recently proved that ASNOM is also able to resolve individual clusters, butt furthermore to shed light on internal conversion mechanisms by analysing the spectral response from such nanosystems. In their work, Au clusters were deposited from a tip by the dip-pen technique an their individual optical response spectrally analysed by A-SNOM. When measuring beside (see Fig. 13a) and on top (Fig. 13b) of such a cluster the optical absorption changes dramatically. For λ = 500 nm for instance and positioning the aperture tip above the cluster, the relative optical transmission ∆T/T is even larger than 100% (larger than 0 dB in the plotted scale) indicating internal conversion from higher energy levels into the 500 nm regime. 4.4. NANO-RAMAN One of the first examples using the scattering type SNOM involved nano-Raman spectroscopy [10]. In this mode, a conventional AFM cantilever was gold coated and positioned in the illuminated area from an inverted optical microscope. Operating the cantilever in the lift-mode allows differentiation between near-field and far-field optical components. Hence chemical differences displayed in the Raman spectra combined with high spatial selectivity due to the local field enhancement a at the tip end were obtained. 4.5. NEAR-FIELD OPTICAL MODIFICATION AND MANIPULATION A-SNOM was used to probe both the photophysical and photochemical properties of functional polymer films [16]. In this approach, the near-field absorption properties of an ultra thin polymer film of ~ 50 nm thickness was first recorded, showing large absorption around 337 nm. This frequency was attributed to the -N=N- bonding that was subsequently cracked by suitable laser pulses. SNOM -tip

DNA-STRAND

Laser 50nm 5 nm m

ion exchange / metallisation

Laser

SO3Na N2 SO3Na

SO3Na

N2

N2

SO3Na N2

SO3Na

SO3Na

SO3Na

SO3Na

N2

N2

N2

N2

SO3Na N2

SO3Na N2

SO3Na N2

SO3Na

SO3Na

SO3Na

N2

N2

N2

SO3Na N2

z.B.: Ag, Pd, Pt, Au

Figure 14. Principle of optical nanostructuring of photolabile polymers using the optical near field.

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As shown in Fig. 14, this procedure was used to functionalise both positive [17] and negative [18] polymer resist films on the nanometer scale that were used to deprotect or bleach the functional end group, respectively. Fig. 15 finally shows an example where this area selective UV imaging by A-SNOM was applied to a photolabile (positive) amine polymer thin film. Shown in that figure are the changes in optical density after UV laser irradiation at 325 nm. As indicated it is possible to vary the local functionality which then shows up in a varied optical spectrum or transmission. Bright areas thus no longer absorb at 325 nm while grey areas still do.

Figure 15. Area selective UV imaging of a photolabile (positive) amine polymer thin film. Shown are the changes in optical density after UV laser irradiation at 325 nm. Frame size: 76 µm, z-scale denotes increase in optical transmittance.

5. Conclusion In conclusion, we reported here on the possibility to probe functionality with unprecedented resolution by optically tracking absorptive, refractive, fluorescent, polarisation, or Raman properties in the optical near-field. To overcome the low signal intensities inherently stemming from the close tip-sample approach, the novel type of near-field optical microscope (SNOM) implying scattering from an optical tip being a functional nanocluster is discussed. The lighting rod effect as well as Plasmon enhancement are the convincing physical parameters that allow to track optical functionality even down to the 10 nm regime.

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Acknowledgement The author kindly thanks F. Braun, S. Grafström, Ch. Loppacher, S. Trogisch, and B. Voit for helpful discussion. Financial support by the German Federal Research Society (DFG), the BMBF, and the Fonds of the German Industry is gratefully acknowledged. References 1. 2. 3. 4. 5.

6.

7.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18.

Deutsche Agenda: Optische Technologien für das 21. Jahrhundert, VDI Technologiezentrum, Düsseldorf, (2000), ISBN 3-00-006083-9. Pohl, D., Denk, W., and Lanz, M. (1984) Optical stethoscopy: Image recording with resolution Ȝ /20, Appl. Phys. Lett. 44, 651-653. Fowles, G.R. (1989) Introduction to Modern Optics, Dover Publishing, New York. Klar, T.A., Dyba, M., and Hell, S.W. (2001) Stimulated emission depletion microscopy with an offset depleting beam, Appl. Phys. Lett. 78, 393-395. Tarrach, G., Lagos, P.L., Hermans, R.Z., Loppacher, Ch., Schlaphof, F., and Eng, L.M. (2001) Highresolution spot allocation for Raman spectroscopy on ferroelectrics by polarization and piezoresponse force microscopy, Appl. Phys. Lett. 79, 3152-3154. Abbe, E. (1873) Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung, M. Schutze's Archiv für mikroskopische Anatomie IX 413; Abbe, E. (1982) The Relation of Aperture and Power in the Microsope, J. Royal Soc. II, 300; Abbe, E. (1982) The Relation of Aperture and Power in the Microsope, J. Royal Soc. III, 790; Abbe, E. (1904) Gesammelte Abhandlungen, Verlag Gustav Fischer, Jena. Renger, J., Deckert, V., Hellmann, I., Grafström, S., and Eng, L.M. J. (2004) Evanescent wave scattering and local electric field enhancement at ellipsoidal silver particles in the proximity of a glass surface sharp noble metal tips, Opt. Soc. Am. A 21, in press. Synge, E.H. (1928) A Suggested Method for extending Microscopic Resolution into the UltraMicroscopic Region, Philos. Mag. 6, 356-362. Zenhäusern, F., O´Boyle, M.P., and Wickramasinghe, H.K. (1994) Apertureless near-field optical microscope, Appl. Phys. Lett. 65, 1623-1625. Stöckle, R.M., Suh, Y.D., Deckert, V., and Zenobi, R. (2000) Nanoscale chemical analysis by tipenhanced Raman spectroscopy, Chem. Phys. Lett. 318, 131-136. Xie, X.S. and Dunn, R.C. (1994) Probing Single Molecule Dynamics, Science 265, 361-364. Heinzelmann, H. (1996) Ph.D. thesis, University of Basel. Eng, L.M. and Güntherodt, H.-J. (2000) Scanning Force Microscopy and Near-Field Optical Microscopy of Ferroelectric and Ferroelastic Domain Walls, Ferroelectrics 236, 35-46. Betzig, E., Trautmann, J.K., Wolfe, R., Gyorgy, E.M., Finn, P.L., Kryder, M.H., and Chang, C.-H. (1992) Near-field magneto-optics and high density data storage, Appl. Phys. Lett. 61, 142-144. Seidel, J., Grafström, S., Loppacher, Ch., Trogisch, S. Schlaphof, F., and Eng, L.M. (2001) Near-Field Spectroscopy with White-Light Illumination, Appl. Phys. Lett. 79, 2291-2293. Voit, B., Braun, F., Loppacher, Ch., Trogisch, S., and Eng, L.M. (2002) Photolabile Ultrathin Polymer Films for Spatially Defined Attachment of Nanoobjects, Poly. Mater.: Sci. Eng. 87, 407-408. Braun, F., Eng, L., Trogisch, S., and Voit, B. (2003) Novel Labile Protected Amine Terpolymers for the Preparation of Structured Functionalized Surfaces: Synthesis and Characterization, Macromol. Chem. Phys. 204, 1486-1496. Loppacher, Ch., Trogisch, S., Braun, F., Zherebov, A., Grafström, S., Eng, L.M., and Voit, B. (2002) Metal Salt Complexation of Spin-coated Ultrathin Diazosulfonate Terpolymer Films, Macromolecules 35, 1936-1946; Braun, F., Eng, L.M., Loppacher, Ch. Trogisch, S., and Voit, B. (2002) Novel Diazosulfonate-terpolymers for the preparation of structured functionalized surfaces - synthesis and characterization, Macromol. Chem. Phys. 203, 1781-1790.

NANOSCALE ELECTRONIC MEASUREMENTS OF SEMICONDUCTORS USING KELVIN PROBE FORCE MICROSCOPY

Y. ROSENWAKS and R. SHIKLER Department of Physical Electronics, t Faculty of Engineering, Tel-Aviv University, Ramat-Aviv 69978, Israel

Contents 1.

2.

3.

4.

5.

1 Kelvin probe force microscopy 1.1. Introduction 1.2. The Kelvin probe 1.3. Kelvin probe force microscopy experimental setup Measurements of operating semiconductor devices 2.1. Equilibrium measurements 2.2. Measurements under operating conditions Minority carrier diffusion length t measurements using Kelvin probe force microscopy 3.1. Diffusion length measurements in pn junctions 3.1.1. The KPFM based Method 3.1.2. Analysis 3.1.3. Measurements on p-n Junctions 3.1.4. Measurements at GaP/Metal Junctions 3.2. Measurements at GaP/metal junctions Sensitivity and spatial resolution in Kelvin probe force microscopy 4.1. Introduction: tip-sample electrostatic interaction 4.2. Electrostatic screening in semiconductors 4.3. Numerical analysis of the tip-semiconductor electrostatic force 4.4. Comparison with experimental results Conclusions

Abstract As characteristic dimensions of semiconductor devices continue to shrink, the ability to characterize structure and electronic properties in such devices at the nanometer scale has come to be of outstanding importance. The Kelvin probe force microscopy technique has already been demonstrated as a powerful tool for measuring electrostatic forces and electric potential distribution with nanometer resolution. In this review, we demonstrate several recent applications of this 119 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 119-151. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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technique. We begin by reviewing the basics of the method and presenting the basic experimental setup. Section 2 presents measurements conducted on operating GaP light emitting diode. The operating device surface band structure was imaged with nanometer resolution, and it was shown that the surface band structure is governed by absorption of the internal light emission. We then demonstrate how the Kelvin probe force microscopy can be used for measuring minority-carrier diffusion length in semiconductors. It is shown that this method could be very useful in measuring very short diffusion lengths (< 1 µm). The last section focuses on the sensitivity and spatial resolution in semiconductor measurements. We present a framework that allows extracting the real surface potential taking into account the tip-sample electrostatic interaction. The model is compared to ultra high vacuum Kelvin probe force microscopy measurements of atomic steps on GaP.

1. Kelvin Probe Force Microscopy 1.1. INTRODUCTION Scanning probe microscopy has opened new opportunities to image semiconductor surfaces with unprecedented spatial resolution. Perhaps the most widely used scanning probe instrument is the atomic force microscope (AFM), which provides direct surface topographic images, as well as information on other tip/sample forces like friction, magnetic, and electrostatic. The Kelvin probe force microscopy (KPFM) technique has already been demonstrated as a powerful tool for measuring electrostatic forces and electric potential distribution with nanometer resolution. Due to its promise of highspatial-resolution surface potential measurements, the KPFM has found many diverse applications in recent years. The technique has been applied to materials science applications such as: work function mapping1, and ordering in III-V compound semiconductors2. Kikukawa et al. have conducted surface potential measurements of silicon pn junctions3, and Vatel et al. have demonstrated potential measurements of resistors4, and n-i-p-i heterostructures5. KPFM has also proved to be effective in electrical characterization of submicron devices like high electron mobility transistors (HEMT’s)6, and light emitting diodes7. In addition, several groups have used the technique for two-dimensional surface dopant profiling8, and were able to distinguish relative changes in dopant concentration with lateral resolution of less than 100 nm. 1.2. THE KELVIN PROBE The Contact Potential Difference (CPD) between two materials, for example between an AFM tip and a sample, is defined as:

VCPD =

φtip − φ sample −q

(1)

where φ1 and φ2 are the work functions of the tip and the sample, respectively, and q is the elementary charge. Therefore, if an AFM tip and a semiconductor with different work functions are held in close proximity to each other a force will be developed

121

between them, due to the potential difference VCPD; this is schematically described in Figure 1. When the two materials are not connected their local vacuum levels are aligned but there is a difference in their Fermi levels. Upon electrical connection, electrons flow from the material with the lower work function to the one with a higher work function (in this case from the semiconductor to the tip) as shown in

Figure 1. Definition and basic measurement setup of contact potential difference (CPD)

Figure 1 (a). This process continues until the Fermi levels are aligned; the two materials are now charged and there is a difference in their local vacuum levels. Due to the charging of the tip and the sample, an electrostatic force develops as shown in Figure 1 (b). This force can be nullified by applying an external bias between the tip and the sample. The magnitude of this bias is the contact potential difference and its sign depends whether it is applied to the sample or to the tip as seen in Figure 1 (c). This will be explained in more detail after we presentt the basic equations for the tip-sample electrostatic force.

122

A typical KPFM measurement is conducted in the following way. An AC bias at a frequency ω is applied between the tip and the sample. It can be shown9 that the force component at this frequency is proportional to the CPD and therefore, can be nullified using a feedback loop whose input is the component m of the electrostatic force at a frequency of ω. The most naï˪ï˪ve way to derive this force is to treat the tip-sample system as a parallel plate capacitor with one plate being the tip apex, and the other the sample underneath it8. Under this assumption the force which is just the derivative of the electrostatic energy with respect to the tip-sample separation, z, is given by:

F = −

∂U ∂Z

= − Q

1 V 2

2

∂C 1 V α ∂Z 2 Z

2 2

(2)

where the electrostatic energy U is given for a parallel plate capacitor configuration by U = 1 CV 2 with C the tip sample capacitance, and V the potential difference between the 2

AFM tip and the sample. Using the following expression for the potential difference: V= Vdc ± VCPD + Vacsin((ωt) where VDCC is a nullifying voltage applied in order to measure the CPD and inserting it in Eq. (2) gives :

1 [( V CPD − V DC ) 2 + 2 (V CPD − V DC )V ac sin( ω t ) 2 2Z 2 + V ac sin 2 (ω t )] F ∝

(3)

and as expected the force at a frequency ω is proportional to the CPD. Hence, based on Eq.

(3) the sign of VCPD will be different if the nullifying voltage P

is applied to the tip or to the sample. The posteriori DC voltage difference VCPD is thus given for the two cases as: P VCCPD =−

P VCCPD =−

φ tip

· § φ sample − ¨¨ + Veext ¸¸ = VCCPD − Veext e © −e ¹

φ tip e

−

φ sample

(4)

+ Veext = VCCPD + Veext −e (4b) are for the cases of voltage applied to the

where equations (4a) and sample and to the tip respectively. Following the nullifying procedure, i.e. when

P VCCPD = 0 , we obtain Veext = ±VCCPD where the '+' and '-' refer to the external bias

applied to the sample and the tip respectively.

123

Figure 2 shows CPD measurements of a cleaved pn junction as described in detail in the next section. It shows two potential line scans across the pn junction when the feedback (nullifying) potential is applied to (a) the sample surface and (b) to the AFM tip. As explained above, the external voltage equals the CPD when it is applied to the sample; this is shown by curve (a) of Fig. 2. This is supported by the fact that the CPD of the p side of a pn homojunction is always higher than that of the n side of the junction.

Figure 2. pn junction potential measured by applying the feedback voltage (a) to the tip, and (b) to the sample. The curves represent (a) the correct, and (b) incorrect CPD values, respectively.

The above analysis is based on three basic assumptions whose validity will be closely examined in section 4. These are: 1) The electrostatic interaction is only between the tip apex and the sample directly underneath it; 2) The assumption of a / and 3) The capacitance (in both the energy and parallel plates capacitor, i.e., C α 1/z hence in the force terms) is voltage independent.

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1.3. KELVIN PROBE FORCE MICROSCOPY EXPERIMENTAL SETUP Figure 3 shows a schematic diagram of the KPFM measurement setup. It is based on a commercial AFM (Autoprobe CP, Veeco, Inc.) operating in non-contact mode. For topographic imaging, the cantilever, heavily doped silicon with sharpened tip ((R<20 nm), was driven by a piezoelectric bimorph at a frequency (typically 80-100 kHz) slightly above resonance. An alternating voltage Vacsin((ωt) at a frequency of around 20 kHzz was applied to the cantilever in order to induce an electrostatic force between the tip and the sample. The CPD between the tip and the sample surface was measured in the conventional way1 by nullifying the output signal of a Lock-in amplifier (LIA) that measures the electrostatic force at the frequency ω.

Figure 3. Schematic diagram of the KPFM measurement setup using Autoprobe CP, Veeco Inc. The topography part is the solid line and the CPD part is the dashed line.

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The sensitivity of the surface potential measurements was evaluated by applying an external square wave voltage to the sample and measuring the CPD between the tip and the sample without scanning. The sensitivity, which we define as the smallest measurable CPD, VCPD,min, and which we have calculated as the root mean square (rms) was found to be less then 5mV. The theoretical VCPD,min is given by1:

VCPD , min =

· 2kTKB § d ¨¨ ¸ 3 π Qff res © ε 0V AC R ¸¹

where k is the Boltzman constant, T is the temperature, and

(5)

ε0

the vacuum permittivity.

For the silicon force sensor used in our experiments with a resonance frequency (f (fress) of 80 kHz, spring constant (K (K) of ~3 N/m, an experimental bandwidth (B) of 1 Hz, Quality factor (Q) of around 500, distance between tip and sample (d) d of 20 nm, we obtain VCPD,min of around 0.15 mV. Considering the fact that Eq. (5) does not take into account instrumental noise sources and that the alternating voltage frequency, Vac, is largely removed from fres our VCPD, min is close to the theoretical limit.

2. Measurements of Operating Semiconductor Devices 2.1. EQUILIBRIUM MEASUREMENTS The shrinkage of semiconductor devices to the sub micrometer level has led to the need for the direct measurement of two-dimensional (2-D) potential profiles with nanometer resolution. The information given by such measurements is useful for understanding the relations between the device performance and surface band structure. The surface band structure has a large effect on physical device properties like carrier recombination10, and breakdown phenomena. Therefore, KPFM measurements can lead to improved understanding of the performance of surface rich devices like light emitting diodes (LED’s) and semiconductor lasers. In this section, measurements of 2D potential distribution of operating GaP light emitting diodes (LED’s) at equilibrium and under applied bias are reported. Measurements conducted at equilibrium (when the external bias is zero) enabled us to extract the location of the metallurgical junction of the s

device. When forward bias is applied, the junction built-in voltage at the surface, Vbbi , decreases with increasing applied forward bias up to flat-band conditions, and then inverted. Additional measurements, including surface photovoltage spectroscopy (SPS), show that the potential distribution is governed by self-absorption of the sub-bandgap light emission from the device.

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The GaP samples (Elma Inc.) were grown by liquid phase epitaxy. They consisted of a 10 micron thick Zn doped (p~5x1017 cm-3) GaP layer on top of a 40 micron thick ntype layer grown on a GaP substrate; the peak emission was at a wavelength of 565 nm. Ohmic contacts were formed using evaporation of Ni/Ge/Au/Ni/Au to the n-type substrate, and Pd/Zn/Pd for the top p-layer. The samples were cleaved in air, and then placed in a specially designed holder for the KFM measurements. The bias to the LED was applied in the way shown in Figure 4. Figure 5 shows (a) the CPD and (b) the topographic images of the GaP LED in equilibrium, i.e., with no applied external voltage. The figure shows three main results: 1) The potential in the direction perpendicular to the junction is homogeneous throughout the scanning range (5µm); 2) There is no correlation between the CPD and topography images; this is an indication that there is no cross talk between the s

topography and potential measurements; 3) The built-in potential on the surface, Vbbi is around 1.1 V V; this voltage is much smaller than the value in the bulk which was b

calculated to be Vbbi = 2 V V. This difference is due to surface band bending effects as will be explained in more detail below.

Figure 4. Schematic of the cleaved GaP sample measurement setup under external forward bias.

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Figure 5. CPD (a) and topography (b) images of a cleaved GaP pn junction under equilibrium conditions.

Figure 6 (a) shows one potential line scan across the LED pn junction. An analysis of an abrupt pn junction shows that the junction built-in electric field, E = -∂V//∂x , has an extremum at the metallurgical junction between the p- and the n-type regions. Figure 6 (b) shows the derivative of the measured potential with respect to the x-axis; the x direction is perpendicular to the junction, i.e., parallel to the surface, as shown in the figure. It is observed that the metallurgical junction can be located with an error of less than 50 nm. The width of the junction can also be estimated from Figure 6 (b) to be ~0.5 µm. This calculated width is around an order of magnitude larger compared with that calculated based on the bulk doping concentration. This inconsistencyy is related to the difference between the built-in voltage on the surface and in the bulk and to the convolution effect of the measuring AFM tip. The former is explained below and the s

b

later is discussed in details in chapter 4. The lower Vbbi (compared with Vbbi ) is most probably due to two main reasons: semiconductor surface states, and/or external charge on the sample surface. Surface states (due to imperfect cleavage and/or oxides on the air exposed sample) can trap holes (electrons) on the cleaved surfaces of the p (n) sides of the junction, creating depletion-type band bending opposite in sign on each side of the junction. Thus, the bands will bend up in the n-doped region and down in the p-doped s

region, with the net result being a reduction of Vbbi . The reduction of the built-in voltage on the surface may be used to derive the surface band bending and/or the surface charge on the cleaved crystal. However, the surface states distribution on the cleaved junction surface is not known and therefore, the band bending can only be estimated as described below.

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Figure 6. Measured junction potential (a) and its first derivative (b) with respect to the x-axis. The first derivative is the calculated junction electric field.

Figure 7 shows the 2D potential distribution calculated using Poisson’s equation of the following form: · §V · § V ·· (6) q §¨ §¨ ¸ ¸ ∆V =

n exp¨¨ ¸¸ − exp¨¨ − ¸¸ ¸ − D ¸ © φT ¹ © φT ¹ ¹ ¹

i ε s ¨© ¨©

where V is the electrostatic potential, εs is the permittivity of GaP, D is the net concentration of the ionized impurities (dopants). The following boundary conditions were used to solve Eq. (2.7): for the x-axis, Newmann boundary conditions of the form ∂V//∂x = 0 were used. The Newmann boundary conditions are justified far from the junction (at a distance of more than 1 µm) because the potential is constant in the direction perpendicular to the junction. The value of V on the cleaved surface and at the bulk was used for the two remaining boundary conditions in the perpendicular y-axis. The potential in the bulk was calculated using a one-dimensional Poisson’s equation with the appropriate doping values. For the surface potential (the fourth boundary condition), we have used the measured CPD data. However, these data represent the distribution of the contact potential difference between the tip and the sample surface. Hence, the value of V at the surface is known up to an arbitrary constant. For the calculation shown in Figure 7, we assumed that the band bending at the surface was of the same magnitude (and opposite sign) for both the n-type and p-type sides. The Poisson equation was solved using an algorithm used by Mayergoyz11. The result shown s

b

in Figure 7 demonstrates that the low Vbbi (~1.1 V ) relative to Vbbi (~ 2 V ) is due to surface band bending effects as explained above. In addition, the width of the space charge region (SCR) can be obtained. Figure 7 shows that the width of the SCR in the bulk is on the order of 30 nm. This value does not change much even if the band bending at the surface is not of the same magnitude for the p and n sides and therefore, can be assumed to be the correct value. In summary, surface band bending effects cause s

b

to the difference in the magnitude of Vbbi relative to Vbbi .

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Figure 7. Calculation of 2D potential distribution assuming symmetric depletion at the p- and n-type surface. The figure demonstrates the reduced surface built-in voltage,

Vbbis , relative to that in the bulk.

2.2. MEASUREMENTS UNDER FORWARD BIASFigure 8 shows CPD measurements conducted under different applied forward bias to the LED contacts from 0 to 1.78 V. The CPD measured at biases of 0, 1.54, 1.62, 1.66, and 1.78V are presented in Figure 8 (a), (c),(e), and (g), respectively. Figure 8 (a), (c), (e), and (g) are CPD images, while Figure 8 (b), (f), (h) are the Topography images. The topographic images (b), (f), and (h) demonstrate that there is no cross talk between the topography and the electrostatic measurements. Figure 8 (a), (b), (e), (f), (g), and (h) show that the CPD and the topography images are uncorrelated also under applied bias. The topographic images for the biases (c) and (d) are identical in these images. The most surprising phenomenon is the junction inversion obtained under forward bias of 1.72 V presented in Figure 8 (g); this is clearly a surface effect which cannot take place in the bulk. This surface inversion implies that the junction on the surface is under reverse bias and hence, the s surface current flows in opposite direction to that in the bulk. The dependence of Vbbi on the applied bias is summarized in Figure 9. The figure shows nine CPD line scans s measured in the range of 1.5-1.78 V external applied bias. At biases below 1.5 V, Vbbi does not change substantially; this is because there are voltage drops on the imperfect ohmic contacts. In the 1.56 V line scan, there is a small ”valley” that does not appear in the higher voltage line scans; this is probably an indication of surface states that change the measured CPD at this location.

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It was also found that the width of the pn junction does not change with decreasing surface built-in voltage. This indicates that the depletion regions width cannot be calculated based on a one-dimensional analysis; this is because the pn junction is measured at the surface and a two-dimensional analysis (as shown above) is required. s However, the insensitivity of the junction width at the surface to Vbbi can be explained using the following semi-quantitative argument. In the one-dimensional case, the pn s

junction width depends on the ratio between the built-in voltage, Vbbi , and the doping concentration, D. As will be shown in the next paragraph, there is a depletion type band bending at the pn junction surface. This band bending is due to surface charge opposite in sign to the ionized dopants in the two p and n space charge regions; thus the net s

charge at the surface is reduced. Therefore, the ratio between Vbbi and De (the ”effective doping”at the surface) is approximately constant. Since the depletion region width in the one-dimensional approximation is proportional to

Vbbis

De

, it does not change with

s

increased external applied bias. The magnitude of Vbbi changes by about 1.1 V in the bias range between 1.5 and 1.78 V. This large change is unexpected based on the theory of pn junctions; this theory shows that Vbi in the bulk should decrease linearly with a s

proportionality factor of 1 with increasing forward bias. In principle, a change in Vbbi which is much larger than the external applied bias can be due to two reasons: 1) Reabsorption of light emitted inside the device, and 2) Charging or discharging of s surface states. Changes in Vbbi resulting from light absorption were studied using surface photovoltage spectroscopy (SPS). The SPS technique is based on the following principle: illumination of a semiconductor surface or interface by monochromatic light results in charge exchange between the bands and local states within the band gap. This change will be accompanied by a change in the surface potential and therefore, will change the CPD between the sample and the measuring probe. By measuring the CPD as a function of the incident light energy, a surface photovoltage spectrum like the one shown in Figure 10 is obtained.

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Figure 8. CPD and topography images of the cleaved LED. Structure measured in equilibrium (a)-(b),under applied biases of (c)1.54 V,(d)1.62 V,(e)–(f)1.66V, and(g)-(h)1.78V. The topographic images (b),(f),and (h)demonstrate that there is no crosstalk between the van der Walls and the electrostatic forces.

132

Figure 9. Potential distribution across the pn junction under nine different applied forward bias.

Figure 10. Surface photovoltage spectrum (SPS) of the p-type Gap surface. The measurement was conducted using the standard Kelvin probe method. The vertical line represents the LED emission energy.

133

The figure shows SPS measurements conducted on the surface of the p-GaP layer. Two main transitions at 2.19 and 2.4 eV V are observed. The first is a decrease of the surface photovoltage (SPV) and is due to an electron transfer from a shallow state located at an energy of Et =2.19 eV V below the conduction band minimum,(Ec), to the conduction band (E Ec-Et =2.16 eV, V the peak of LED emission energy). Such a transition increases the band bending at the p-layer surface (due to an increase of the free electron s

concentration in the conduction band), thus, decreasing Vbbi as explained earlier. The second feature is the increase in the SPV signal at an energy around the Eg energy (~ 2.4 eV). This increase in the CPD is due to band-to-band transition and indicates that the layer is p type as expected.

3 Minority carrier diffusion length measurements using Kelvin Probe Force Microscopy 3.1. DIFFUSION LENGTH MEASUREMENTS IN PN JUNCTIONS In this section we present a novel application of the KPFM technique: measurement of minority carrier diffusion length (L ( ) in semiconductors. Despite the fact that the study of carrier transport and diffusion in semiconductors is a mature subject, recently several scanning probe techniques have been used to measure L with high resolution.12 The method presented here is based on measuring the surface photovoltage between the tip of an atomic force microscope and the surface of an illuminated semiconductor junction. The photogenerated carriers diffuse to the junction and change the contact potential difference between the tip and the sample, as a function of the distance from the junction. The diffusion length, L, is then obtained by fitting the measured contact potential difference using the minority carrier continuity equation. The method is applied to measurements of electron and hole diffusion lengths in GaP epilayers. 3.1.1. The KPFM based Method Our method is based on measuring the SPV between the tip of a Kelvin force microscope (KPFM) and the surface of a uniformly illuminated semiconductor junction. The method is schematically described in Figure 11. It is based on the KPFM setup described above. The GaP samples were cleaved in air, and then placed in a specially designed holder for the KPFM measurements. The cleaved or cross-sectioned semiconductor junction is uniformly illuminated from the top using a laser beam (λ= 488 nm) passing through an optical fiber brought to a distance of about 100 µm from the AFM tip. The distance between the fiber and the sample surface (which is a few nanometers underneath the tip in the non-contact operation mode) is adjusted in order to create a laser spot size much larger than the measured carriers diffusion length. In the measurements reported here a spot size of about 50 µm in diameter was used. The photogenerated minority carriers change the CPD between the tip and sample by changing the surface band bending. The induced SPV (defined here as |CPDlight – CPDdark|) is a function of the excess minority carriers concentration. Therefore the SPV

134

will be the smallest at the edge of the junction (due to a depletion of the minority carriers) and will increase with the distance from the junction due to diffusion of the minority carriers towards t e junction. This is demonstrated in Figure 12 which shows two CPD images (5x5 µm) of a p-n junction measured in the dark (a), and under superbandgap illumination (b). It is observed that the junction built-in voltage in (b) is greatly reduced due to the photovoltaic effect. In addition there are two regions in (b) where the SPV changes exponentially with the distance from the junction edges; this is due to minority carrier diffusion to the two junction-edges. The bumps in the CPD image measured in the dark (Figure 12, (a)) may be due to surface states on the cleaved crystal surface.

Figure 11. Schematic diagram of the diffusion length measurement setup. The inset shows the pn junction bands diagram under illumination, and the minority carrier diffusion to the junction.

3.1.2. Analysis The calculation of the minority carriers diffusion length from the SPV data is as follows. The dependence of SPV on ¨nSCR (the excess minority carrier concentration at the edge of the cleaved surface space charge region (SCR), i.e. ¨n (x,y=w) where w is the width of the cleaved surface SCR) is obtained by measuring the SPV as a function of the exciting light intensity, II. The SPV is then fitted to: SPV = C[ln [ (1+I/IIo)] (7) which is the equation frequently used to relate the SPV to super bandgap illumination intensity.13 Io is an arbitrary light intensity used for normalization, and C is a constant needed for units conversion. Since ¨nSCR is linear with the exciting light intensity (I (I)13, Eq. (7) represents the dependence of SPV on ¨nSCR. Thus, the SPV can now be obtained by calculating ¨nSCR using the minority carrier continuity equation, and substituting it in Eq. (7) above. Figure 13 shows the SPV measured under different light intensities; each symbol set represents measurements conducted at a different position on the cleaved surface, i.e. at a different distance from the edge of the p-n depletion region ((x=0 in Figure 12 (b)). The figure shows that the dependence of SPV on ¨nSCR does not change

135

with distance from the p-n junction; this justifies the use of Eq. (7) at all distances from the junction. A non-linear fit to this data gives the value of the constant C in Eq. (7).

Figure 12. Two-dimensional CPD images of the cleaved GaP p-n junction in the dark (a), and under super bandgap (λ= 488 nm) illumination (b). The minority carrier diffusion on both sides of the p-n junction can be clearly observed in (b).

Figure 13. Surface photovoltage measured under different light intensities; each line represents measurements conducted at a different position on the cleaved surface, i.e. at a different distance from the edge of the p-n depletion region.

136

The steady state continuity equation for electrons in one dimension (the x-axis in Figure 11), assuming uniform excitation (which is a very good assumption as long as the exciting spot size >> L) can be written as:

d 2 ∆ n SCR ( x ) ∆ n SCR ( x ) g − = − 2 2 Dn dx Ln

(8)

where Dn is the electrons diffusion constant, and g is the generation function. The electric field is neglected in Eq. (8) because ¨nSCR is calculated (by definition, for the yaxis) only outside the space charge regions. (This also holds for the y direction (perpendicular to the cleaved surface, see Figure 11)), which means that our calculation is valid only outside the SCR, i.e. att a distance of about 50 nm below the cleaved surface. Diffusion in the y direction is neglected because GaP absorption depth (~20 µm) >> Ln for the laser wavelength used in our measurements. The solution to Eq. (8) subjected to the boundary conditions:

d∆ ∆nSCR dx

= x =0

S d∆ ∆nSCR ∆nSCR ( x = 0) ; D dx

=0

(9)

x →∞

is:

∆nSCR ( x) = A exp(− x / L) + gτ

(10)

Where τ is the effective electron bulk recombination lifetime, and A is a function of the electron velocity at the edge of the p-n junction, S, given by:

A= By substituting Eq. (7), we obtain:

−S S+D

gτ

(11)

L (11), in Eq. (10), and then in Eq.

SPV ( x) = C ⋅ ln[1 + ( exp(− / ) + gτ ) / ∆

0

]

(12)

where ∆no is a normalization factor. 3.1.3. Measurements on p-n Junctions Figure 14 shows experimental (solid lines) and calculated (dashed lines) SPV line scans measured under three different light intensities of: (a) 0.41, (b) 1.3, and (c) 4.1 µW at the output of the optical fiber. The coordinate x=0 corresponds to the edge of the depletion region, see Figure 12(b). The highest light intensity is estimated to be not more than a few µW/cm2 exciting the sample surface under the tip. This corresponds to ¨n< 1x1012 cm-3, which means that all our measurements are conducted under very low injection levels. A nonlinear fit of the data to Eq. ) with D =3 cm2/s, gives L of 0.85±0.01, 2.1±0.02, and 2±0.02 µm, and S of 1.7⋅105, 2.5⋅105, and 1.3⋅105 cm/sec for (a), (b), and (c) respectively. Two advantages of this newly proposed method are that the measured diffusion lengths are independent of the surface recombination velocity on the cleaved surface, and of the minority carrier velocity, at the junction edges-S. The surface recombination on the cleaved surface will affect the value of ¨nSCR(x); the larger the surface recombination, the smaller is the SPV. S will change the value of the constant A in Eq.

137

(11), but not the decay profile of SPV(x) which is governed by L. In addition, the fits in Fig. Figure 14 show that: 1) The values of L are not very sensitive to the carrier injection levels , 2) The value lue of S can be obtained from the measurements, and 3) The diffusion lengths are in excellent agreement with literature reported values for GaP; these vary between 0.5-5 µm depending upon doping and growth methods.

Figure 14. Experimental (solid lines), and calculated (dashed lines) SPV profiles as a function of the distance from the edge of the p-n junction (x=0), for three different light intensities of: (a) 0.41, (b) 1.3, and (c) 4.1 µW at the output of the optical fiber. The theoretical fits based on Eq. (12) gave electron diffusion lengths of: 0.85±0.01, 2.1±0.02, and 2±0.02 µm for (a), (b), and (c) respectively.

3.1.4. Measurements at GaP/Metal Junctions / GaP junction measured in Figure 15 shows two CPD images (12x12µm) of a metal/pthe dark (a), and under super-bandgap illumination (b). It is observed that the junction built-in voltage is greatly reduced due to the photovoltaic effect, but in addition there is an exponential region in the SPV image on the semiconductor side of the junction due to the carriers diffusion as in the p-n junction. The sharp and big potential increase observed at the position x > 12 micron, is due to the metal barrier. Figure 16 shows experimental (solid lines) and calculated (dashed lines) SPV line scans measured under three different light intensities of: (a) 1.6, (b) 0.9 , and (c) 0.71 µW at the output of the optical fiber. The coordinate x=0 corresponds to the edge of the p-type semiconductor depletion region, see Figure 15 (b). The largest light intensity is estimated to be not more than a few µW/cm2 exciting the sample surface under the tip. This corresponds to ¨n< 1x1012 cm-3, which means that all our measurements are conducted under very low injection levels. A nonlinear fit of the data to Eq. (12) with D =3 cm2/s, gives L of 1.77±0.02, 1.66±0.02, and 1.87±0.02 µm, and S of 4.5⋅104, 4.2⋅104, and 3.9⋅104 cm/sec for (a), (b), and (c) respectively. These results are in excellent agreement with the results obtained for the p-n junctions (Figure 14).

138

Figure 15. Two dimensional CPD images of the cleaved GaP/metal junction in the dark (a), and under super bandgap (λ= 488 nm) illumination (b). The minority carrier diffusion can be clearly observed in (b).

Figure 16. Experimental (solid lines), and calculated (dashed lines) SPV profiles as a function of the distance from the edge of the junction (x=0), for three different light intensities of : (a) 1.6, (b) 0.9 , and (c) 0.71 µW at the output of the optical fiber. The theoretical fits based on Eq. (12) gave electron diffusion lengths of : 1.77±0.02, 1.66±0.02, and 1.87±0.02 µm for (a), (b), and (c) respectively.

139

In summary, we have presented a new method based on Kelvin probe force microscopy for measuring minority carriers diffusion length in semiconductors. The method is based on measuring the surface photovoltage between the tip of an atomic force microscope and the surface of an illuminated semiconductor junction. It was shown that the KPFM proposed method can be very useful in measuring very short diffusion lengths (≤ 2 microns). The EBIC method is impractical for such cases, because of the volume in which the excess carriers are generated. The resolution of the KPFM technique can be below 50 nm, depending mainly on the shape of the AFM tip used in the measurements. This sets the lowest limit for diffusion lengths measurements using this method. In practice, this lower limit may be much larger (by a factor of 3 or more) depending on the photovoltage response of the measured sample. The main disadvantage of the KPMF method is that it does not work well with narrow or medium bandgap semiconductors (≤ 1 eV). This is because the SPV of a semiconductor is exponential with the bandgap energy18. However, since the technological importance of wide bandgap semiconductors is increasing in recent years (and in most cases their diffusion lengths are very short) we believe that the KPFM method proposed here may prove to be very important.

4. Sensitivity and spatial resolution in Kelvin probe force microscopy 4.1. INTRODUCTION: TIP-SAMPLE ELECTROSTATIC INTERACTION It is accepted that the finite tip size in scanning probe-microscopies can have a profound effect on the obtained topographic image. Deconvolution of the tip shape from the measured image can then be used to restore the true surface topography from the measurement14. The KPFM method 'suffers' from similar convolution effects to those taking place in topography images but of different nature. The basic equation of the KPFM technique (Eq. (2)) is based on the assumptionn that the interaction is only between the tip apeex and the sample area directly underneath it. This assumption might be a good approximation for short- range forces like Van der Walls (the dominant forces in topography measurements) or for tunneling currents in STM measurements. The KPFM M however is based on measuring electrostatic forces , which have an infinite range; therefore, the entire tip-sample interaction has to be considered. The deconvolution the real potential distribution from the measured KPFM image is thus of a great importance and was considered by several authors. One of the simplest models was suggested by Hochwitz et. al.15 where the tip was replaced by a series of (staircase) parallel plate capacitors. The real CPD at every point i on the sample surface is different from the measured one and is calculated as follows. Starting from Eq. (3) we replace the ω term of the force by:

Fω ∝ V AAC sin (ω

)¦ i

∂C i ∂zz i

(

)

(13)

where the index i correspond to all the parallel plate capacitors and to all the sample regions which form the other plates of the capacitors (see Figure 17 ), and V D DC is the tip (or sample) bias that nullifies the electrostatic force between the AFM tip and the

140

sample. The above equations can be inverted to give the CPD as function of the measured V D DC 's:

∂C i

V DDC =

¦ ∂z i

VCCPD

i

i

∂C ¦i ∂z i i

A further simplification is introduced by setting C i =

(14)

1 . A schematic description zi

of this model is shown in Figure 17 where the division of the tip into the small parallel plate capacitors is shown. The advantage of this simple model is its easy implementation and calculation. However, the assumptions underlying this 'staircase' model are questionable as explained below.

Figure 17. A schematic model for the division of the AFM tip into small parallel plates capacitors. The two plates of the capacitors are indicated the one on the tip and the one on the sample surface.

The tip area is underestimated because its half cone-opening angle is very small

~ 6 ο .The total area of the sample interacting with the tip is very small due to the high aspect ratio of the tip and due to the factt that only sample regions directly underneath the tip are considered. Moreover the expression for the parallel plate capacitor, C ∝ 1 , z is valid only when the plates area is much larger than their separation. A typical capacitor in the staircase model has an area of 20x20 nm. Therefore, capacitors that are situated above a height of few tens of nanometers violate this approximation. In addition, the capacitance used for each capacitor is voltage independent. This is based on the assumption that the sample 'capacitor' (the capacitance of the depletion region) is much larger then the tip-air-sample surface capacitor and therefore the presence of the tip do not change the sample surface potential. To date, all the models used to analyze three-dimensional tip-sample electrostatic interaction in KPFM replace the semiconductor sample by a surface with a fixed or

141

variable potential. This is only true for the case of a weakly interacting tip-sample system; this assumption will be examined in details in the following section. We begin by studying the effect of electrostatic screening in semiconductors in three dimensions. We then present the framework in which the magnitude of the tip-sample interaction is calculated. We end this section by comparing our model to surface potential measurements on atomic steps of a cleaved GaP. 4.2. ELECTROSTATIC SCREENING IN SEMICONDUCTORS Electrostatic screening is a well-known phenomenon in which charges of one type rearrange themselves around charge of the opposite type in order to minimize the total electrostatic energy. Three-dimensional screening in semiconductors cannot be calculated analytically, and the use of a numerical simulation is required. Since the KPFM measures the CPD between the tip and the semiconductor surface, we have calculated the local surface potential resulting from a charged defect located at different distances from the semiconductor surface, i.e. the defect screening length. A silicon sample with a background doping of 1017 cm -3 that has an average band bending of 0.12 V at the surface was used in the calculations. We have solved the Laplace and Poisson equations for the 3D tip-air-sample system for different positions of an electronic defect ( )3 having a total charge of one elementary charge, q relative to the surface. At the semiconductor-air interface, the following boundary condition: (15) n ε

semi

E semi − ε 0 E air = Q ss = −

ss

§ E − E 1 + exp ¨¨ ss φT ©

F

· ¸¸ ¹

were used. E is the electric field, n ss is the density of surface states, and E ss is the energy of an acceptor like surface states. For all the other boundaries we have used the Neumann boundary conditions, i.e. ∇ nV = 0 where ∇ n is the derivative normal to the surface. The equations were discretisized using a finite difference model.16 We then solved the equation using the fixed point iteration method combined with successive over relaxation.17 This method solves at each grid point the difference equation resulting from the discretization process. When the difference equations are nonlinear, a NewtonRaphson scheme is used, while for the linear case a simple successive over relaxation method is used. The surface potential calculated using the above formalism for defects located at three different distances (of 2, 4, and 12 nm) below the surface is shown in Figure 18. The Figure shows that when the defect is positioned 2 nm below the surface the local change in the band bending at the surface is ~100 mV; however if the defect is positioned 12 nm below the surface, the local band bending at the surface is only around 5 mV which is the typical sensitivity of the KPFM method7. In summary, it is found that the KPFM method is sensitive to defects located up to a distance of few nanometers from the semiconductor surface, and that their average density has to be >1018 cm-3 in order for the band bending to be larger then a few mV.

142

Figure 18. Position of

EF

relative to the intrinsic Fermi level (local band bending) at the surface of a silicon

sample due to a charged defect located at varying distances from the surface.

4.3. NUMERICAL ANALYSIS OF THE TIP-SEMICONDUCTOR ELECTROSTATIC FORCE As mentioned in section 1 above, the KPFM feedback loop ideally nullifies the force component at the frequency ω , therefore a calculation of the KPFM signal amounts to find the tip voltage, Vtip , that minimizes the total electrostatic force, V DC in Eq. (3). The calculation of the electrostatic force, F , can be accomplished in two different ways: the first by calculating the total electrostatic energy for two closely separated tip heights, and then calculate the derivative with respect to the tip sample distance as:

F =−

∂U ∂ 1 2 = − ³ E dV ∂z ∂z V 8π

(16)

where E is the electric field and the integral is taken over the entire volume of the tip and sample. The same result can be obtained by calculating the Maxwell stress that acts on the tip surface. Because the tip is assumed to be a perfect conductor, the Maxwell stress is a vector (rather then a tensor) that is perpendicular to the tip surface. The electrostatic force can then be calculated by integrating the Maxwell stress over the entire tip surface:

143

F =−

∂U 1 =− ∂z 2ε s

³E

2

dS Sˆ ⋅ zˆ

(17)

S

where dSˆ is a tip surface element, and zˆ is a unit vector in the z direction. In both cases the electric field is calculated from the solution of the Poisson equation of the tipsample system; both methods gave identical results. The KPFM method uses AC C modulated tip bias and the nullifying procedure is done on the ω component of the force. However, the force and as a consequence, the Poisson equation, are solved for steady state conditions. This is justified based on the following argument. It is assumed (and this was also verified experimentally) that the frequency ω is large enough that the semiconductor band edges cannot follow the AC voltage changes. Therefore, Eq. (3) can be solved for a given DC C bias. Following Hudlet et. al.18 the force at a frequency ω can be expanded in a Taylor series see from the DC C force to give:

F(

p

(ω ))

( ) + ∂FF

DC

∂Vtip

p

VAC sin(ω ) +

∂ 2 FDC 2 ∂Vtip

(

AC

(ω ))2

(18)

where FDC is the calculated DC C force and Vttip is the DC C bias applied to the tip or to

the sample by the external voltage source. The force at a frequency ω is the second term on the r.h.s. of Eq.

F(

p

(ω ))

( ) + ∂FF

DC

p

∂Vtip

VAC sin(ω ) +

∂ 2 FDC 2 ∂Vtip

(

AC

and can be neglected. The measured value VCCPD is the value Vttip electrostatic force (the analogous to V DDC , in Eq.

(ω ))2 (18) that minimizes the

(3)).

The same approach was applied in the past for a metallic sample where the sample surface potential was assumed constant.19 Here the force is calculated as the derivative of the total energy including the energy required to bend the semiconductor bands; this energy can be due to the presence of surface states and/or due to tip induced band bending. Figure 19 shows the potential distribution calculated according to the above formalism for a defect (with a total charge q) located 2 nm below the sample surface. The tip bias is 0.3 V below the potential of the intrinsic Fermi level at the semiconductor surface, i.e., Vtip =

φs q

− 0.3 .

One of the most important issues in KPFM is whether the presence of the tip has any significant effect on the semiconductor SCR, i.e. is there any tip-induced band bending at the semiconductor surface. Hudlet et. al.18 showed that at least in the one-dimensional case, the tip sample system can be modeled as two capacitors in series. They have also shown, that when the distance between the sample and the tip is reduced, the sample capacitance cannot be neglected and it changes the force acting on the tip. In order to check this effect in the three-dimensional case, we have calculated the surface band

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bending (E F

Eis ) for a tip located 5 nm above a semiconductor surface and having a

potential of 0.6 Volt higher then the sample. The result is shown in Figure 20. The figure clearly shows that the local changes in the sample band bending induced by the biased tip are very small (less than 40 mV). This means that the change in the semiconductor SCR capacitance due to the biased tip is negligible, and that the tipsample electrostatic force is governed by the 'air capacitor'. A similar calculation (including the calculation of the electrostatic energy and the electrostatic force) was conducted for a silicon sample having surface states density of n SS = 3 ⋅ 10 11 cm -2 but with varying doping concentration, and a tip-sample bias of 0.5 V.

Figure 19. Potential distribution for the near surface defect with tip-sample bias of 0.3 V; the defect is indicated by the oval under the tip.

145

Figure 20. Local band bending ( E F

− Eis ) for a semiconductor that has no surface states and for tip-

sample distance of 5 nm and an applied bias of Vttip = 0.6 V

The results shown in Figure 21 demonstrate that the electrostatic energy increases with decreasing doping density because the energy required for the formation of the depletion region increases; this can be explained as follows. The electrostatic energy is due to the tip-air-semiconductor surface capacitor, which is in series with the SCR capacitor. In the one-dimensional case the sample SCR capacitance decreases with increasing doping level, therefore the total energy increases with the increase in doping. However, in the 3D case the energy of the air capacitor can be neglected due to the tip shape. The energy of the semiconductor SCR is proportional to the voltage square over the depletion region length, and the latter increases as the square root of the voltage. Therefore, the total energy increases with decreasing doping level as shown in Figure 21.

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Figure 21. Electrostatic energy as function of tip-sample m distance for varying doping concentration.

All the curves in Figure 21 have the same dependence on the tip-sample distance and they differ only by a constant. This means that the electrostatic force, which is the derivative of the energy, should be the same for all the doping concentrations. This is shown in Figure 22 which shows the electrostatic force (as a function of tip-sample distance) calculated from the electrostatic energy using: F =

∂U . ∂Z Q

It must be reemphasized that in KPFM measurements the potential difference between the tip and the sample m is nullified, so typically the voltage difference between any point on the tip and the sample surface is much lower then the 0.5 Volt used in the calculations above. In summary, we have found that the dominant contribution to the tip-sample electrostatic force is from the tip-air-sample surface capacitor and the SCR capacitance can be neglected. Thus, the assumption used by Hochwitz et. al.15, Hudlet et. al.9, and Jacobs et. al.19 is correct. Furthermore, the above conclusion simplifies tremendously the simulation of semiconductors KPFM images. This is because it requires solving only the Laplace equation using fixed (potential independent) boundary conditions at the sample surface.

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Figure 22. The absolute value of the electrostatic force as a function of tip-sample distance for all the doping concentrations shown in Figure 21.

4.4. COMPARISON WITH EXPERIMENTAL RESULTS Considerable effort, both experimental and theoretical, has been devoted to the understanding of the properties of atomic steps formed during epitaxial growth of semiconductors.20 In particular, reconstructions of step edges can locally change the electronic properties and lead to charged states in the gap; such charges have a pronounced influence on the physics of the microscopic mechanisms of diffusion and sticking of charged adatoms21 and vacancies at the step edges. Therefore, knowledge of the existence of charges along steps is important m for the optimization of growth parameters and interface properties. Measurements conducted by Sommerhalter et al.22 have shown that the atomic steps present at the GaAs(110) surface show local changes in band bending due to the presence of charged surface states. KPFM measurements across atomic steps are an ideal system to compare to our simulation since both the width of the defect and its location (right at the surface) are very well defined. Figure 23 shows a KPFM measurement (dots) conducted under ultra high vacuum (UHV) conditions of an atomic step on a cleaved GaP (110) surface.23 The CPD calculation (solid line) was carried out in the following way. First we have calculated the CPD resulting from a Gaussian potential distribution 0.1 V high, and 50 nm (standard deviation) wide.

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Figure 23. KPFM measurement on UHV cleaved p-GaP (110) (dotted line) together with the calculated CPD (solid line) for a tip height of 6 nm.

The results are shown in Figure 24 for seven different tip-sample distances. The figure shows that for a tip height of 5 nm (the experimental scanning height in the UHV KPFM measurements) the CPD signal is reduced by a factor of around 2.5, and its width is increased by a factor of 2 relative to the theoretical surface potential represented by the top curve. The surface charge density at the step was extracted by fitting the measured CPD to the calculated surface potential, based on two main assumptions: 1) The surface states induced by the atomic steps are positioned only at the sample surface; 2) Average surface states densities are assumed (and not quantum mechanical distributions(, therefore, we assumed that the surface states are distributed in a width of 2 nm (the lower limit for the validity of the Poisson equation) The above assumptions reduce the number of unknown (‘fitting’) parameters to two: the surface charge density at the atomic step, and the background surface charge density. The calculation is conducted by assuming two initial values for these two surface charge densities, and then the 3D semiconductor surface potential distribution is calculated using Eq. (6). We then calculate the measured CPD in the presence of the tip and compare the result with the measurement; this procedure is repeated, by changing both the background surface charge, and the charge at a step until a good visual fit like the one shown in Figure 23 is obtained. This fit was obtained using a background and defect surface charge densities, of and nssbackground = (6 ± 2) ⋅1011 cm -2

nssstep = (6 ± 1) ⋅1012 cm-2 respectively. Such a reasonable fit could not be achieved using other combinations of charge densities. This is due to the fact that the width of the Gaussian CPD profile at the step is much more sensitive to the background charge

149

density (screening effect), while its magnitude is more sensitive to the charge density at the step itself. In addition these results are in a good agreement with measurements of s

the surface built-in potential, Vbi (see 2.1 above)~ 1.2 eV, V of a GaP pn junction measured

n

background ss

on

the

same sample. A surface charge density of -2 corresponds to band bending of eV on both the p≅ 0.4 = (6 ± 2) ⋅10 cm 11

s

and n-sides of the junction thus giving a Vbi of around 1.3 eV.

Figure 24. Calculated CPD for a Gaussian surface potential distribution for seven different tip heights.

In summary, we have presented a method for obtaining the real potential distribution from KPFM measurement. It was demonstrated that this method could be used to extract the charge density at a local defect (atomic step) and under certain conditions, the background surface charge density. The latter is critical information necessary for the development of two dimensional doping measurement methods.

5. Conclusions This review described the use of the KPFM technique to image potential distribution across semiconductor surfaces and devices. The important contribution of this work can be divided into three main parts: a) Measurement of operating semiconductor devices. b) Development of the KPFM technique to measure minority carrier diffusion length in semiconductors.

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c) Development of a general methodology for calculating tip-semiconductor electrostatic interaction, which can be used for extracting real CPD images from KPFM data. This work serves just as a starting point for the reconstruction of the real potential distribution on semiconductor surfaces. Faster calculation schemes should be developed, since the present computation time is a major obstacle for a practical usage of this methodology. The relation between the sample physical parameters and the surface potential distribution should be improved. For example, the charge term (the right hand-side) of the Poisson equation (Eq. (6)) is given using average charge distribution. This is not valid for very small scales (< 2 nm) and have to be replaced with charge density calculated using the Schrödinger equation. In addition, for the simulation of measurements under ambient conditions, the model must incorporate a water layer on top of the semiconductor surface.

6. Acknowledgement This research was supported by the Israel Science foundation administered by the Israel Academy of Sciences and Humanities-Recanati and IDB group foundation, and by grant 9701 of the Israel Ministry of Sciences. R. S. was supported by Eshkol special scholarship of Israel Ministry of Sciences. The authors acknoweledge the collaboration with Th. Glatzel, and S. Sadewasser from the Hahn Mietner Institute (Berlin) in the UHV KPFM measurements.

References 1. Nonenmacher, M., O’Boyle, M.P,. and Wickramasing H.K. (1991) Kelvin probe force microscopy, Appl. Phys. Lett. 58, 2921-2923. 2. Leng, Y., Williams, C.C., Su, L.C., and Stringfellow G.B. (1995) Atomic ordering of GaInP studied by Kelvin probe force microscopy, Appl. Phys. Lett. 66, 1264-1267. 3. Kikukawa, A., Hosaka, S., and Imura R. (1995) Silicon pn junction imaging and characterizations using sensitivity enhanced Kelvin probe force microscopy, Appl. Phys. Lett. 66, 3510-3512. 4. Vatel, O.and Tanimoto M. (1995) Kelvin probe force microscopy for potential distribution measurement of semiconductor devices J. Appl. Phys. 77, 2358 -2362. 5. Chavez-Pirson, A., Vatel, O., Tanimoto, M., Ando, H., Iwamura, H., and Kanbe H. (1995) Nanometer-scale imaging of potential profiles in optically excited n-i-p-i heterostructure using Kelvin probe force microscopy, Appl. Phys. Lett. 67, 3069-3071. 6. Mizutani, T., Arakawa, M., and Kishimoto, S. (1997) Two-dimensional potential profile measurement of GaAs HEMT’s by Kelvin probe force microscopy, IEEE Elec. Dev. Lett. 18, 423-425; Arakawa, M., Kishimoto, S., and Mizutani, T. (1997) Kelvin probe force microscopy for potential distribution measurements of cleaved surface of GaAs devices, Jpn. J. Appl. Phys. 36, 1826-1829. 7. Shikler, R., Fried, N., Meoded, T., and Rosenwaks, Y. (1999) Potential Imaging of Operating Light Emitting Devices using Kelvin Force Microscopy, Appl. Phys. Lett. 74, 2972-2974; Shikler, R., Meoded, T., Fried, N., Mishori, B., and Rosenwaks, Y. (1999) Two Dimensional Surface Band Structure of Operating Semiconductor Devices, J. Appl. Phys. 86, 107-113. 8. Henning, A.K., Hochwitz, T., Slinkman, J., Never, J., Hoffman, S., Kaszuba, P., and Daghlian, C. (1995) Two-dimensional surface dopant profiling in silicon using scanning Kelvin probe microscopy, J. Appl. Phys. 77, 1888-1896.

151 9. Hudlet, S., Jean, M.S., Roulet, B., Berger, J., and Guthmann, C. (1995) Electrostatic forces between metallic tip and semiconductor surfaces, J. Appl. Phys. 59, 3308-3314. 10. Sandroff, C.J., Nottenburg, R.N., Bischoff, J.C., and Bhat, R. (1987) Dramatic enhancement in the gain of a GaAs/AlGaAs heterostructure bipolar transistor by surface chemical passivation, Appl. Phys. Lett. 51, 3335. 11. Mayergoyz, I.D. (1986) Solution of the nonlinear Poisson equation of semiconductor device theory, J. Appl. Phys. 59, 195-199. 12. Gustafsson, A., Pistol, M.E., Montelius, L., and Samuelson, L. (1998) Local probe techniques for luminescence studies of low-dimensional semiconductor structures, J. Appl. Phys. 84, 1715-1775; Vertikov, A., Ozden, I., and Nurmiko A.V. (1999) Investigation of excess carrier diffusion in nitride semiconductors with near-field optical microscopy, Appl. Phys. Lett. 74, 850-852. 13. Goodman, M. (1961) A method for the measurement of short minority carrier diffusion lengths in semicondutors, J. Appl. Phys. 32, 2550-2552. 14. Markiewicz, P., and Goh, M.C. (1994) Atomic force microscopy probe tip visualization and improvement of images using a simple deconvolution procedure, Langmuir 10, 5-7. 15. Hochowitz, T., Henning, A.K., Levey, C., Daghlian, C., and Slinkman, J. (1996) Capacitive effects on quantitative dopant profiling with scanned electrostatic force microscopes, J. Vac. Sci. Technol. B 14, 457464. 16. Mayergoyz, I.D. (1986) Solution of the nonlinear Poisson equation of semiconductor device theory, J. Appl. Phys. 59, 195-199. 17. Korman, C.E., and Mayergoyz, I.D. (1990) A globally convergent algorithm for the solution of the steady-state semiconductor device equations, J. Appl. Phys., 68, 1324-1334. 18. Hudlet, S., Saint Jean, M., Roulet, B., Berger, J., and Guthmann, C. (1995) Electrostatic forces between metallic tip and semiconductor surfaces, J. Appl. Phys. 77, 3308 -3314. 19. Jacobs, H.O., Knapps, H.F., Muller, S., and Stemmer, A. (1997) Surface potential mapping: A qualitative material contrast in SPM, Ultramicroscopy 69, 39-49; Belaidi, S., Lebon, F., Girard, P., Leveque, G., and Pagano, S. (1998) Finite element simulations of the resolution in electrostatic force microscopy, Appl. Phys. A 66, S239-S243. 20. Heinrich, M., Domke, C., Ebert, Ph., and Urban, K. (1996) Phys. Rev. B 53, 10894. 21. Doi T., and Ichikawa, M. (1995) Direct Observation of Electron Charge of Si Atoms on a Si(001) Surface, Jpn. J. Appl. Phys. 34, 25-29. 22. Sommerhalter, Ch., Matthes, Th.W., Glatzel, Th., Jäger-Waldau, A., and Lux-Steiner, M.Ch. (1999) High-sensitivity quantitative Kelvin probe microscopy by noncontact ultra-high-vacuum atomic force microscopy, Appl. Phys. Lett. 75, 286-288. 23. Glatzel, Th., Sadewasser, S., Shikler, R., Rosenwaks, Y., and Lux-Steiner, M.Ch. (2003) Kelvin Probe Force Microscopy on III-V Semiconductors: The Effect of Surface Defects on the Local Work Function, Materials Sci. and Eng. B 102, 138-142.

EXPANDING THE CAPABILITIES OF THE SCANNING TUNNELING MICROSCOPE

K.F. KELLY,* Z.J. DONHAUSER, B.A. MANTOOTH, and P.S. WEISS Departments of Chemistry and Physics, The Pennsylvania State University 152 Davey Laboratory, University Park, PA 16802-6300, USA

Contents 1. 2.

Introduction Alternating Current Coupled to the STM 2.1. Introduction 2.2. Experimental setup 3. Dopant-profiling with ACSTM 3.1. Theory 3.2. Characterization of bulk silicon 3.3. Atomic scale imaging of pn junctions 4. Feature Tracking in STM 4.1. Cross-correlation 4.2. Pixel roundoff correction 5. Application of the Feature Tracking Algorithm 5.1. Single molecule switching 5.2. Diffusion of benzene on Ag{110} 6. Conclusions

Abstract Scanning probe microscopes allow unprecedented views of surfaces and the site-specific interactions and dynamics of adsorbates. Our efforts to identify and to characterize atoms and molecules on surfaces and how it is that the scanning tunneling microscope images these surfaces and adsorbates will be discussed. We have extended the capabilities of scanning probe microscopes in several ways; two in particular will be highlighted. In the first section, recent advances in tunable microwave frequency scanning tunneling microscopy (STM) allow dopant profiling at unprecedented resolution will be presented. We apply nonlinear tunable microwave frequency scanning tunneling microscopy and spectroscopy to profiling dopants at ultrahigh resolution in *

Present Address: Department of Electrical Engineering, Rice University, Houston, TX 77251, USA

153 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 153-171. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

154

semiconductors that is sensitive to both dopantt type and density. We are then able to use a spectroscopic imaging mode to map the dopant density at the atomic scale. In the second part of this chapter, advanced image processing techniques that extend the scientific capabilities of STM will be presented. A digital image tracking algorithm based on Fourier-transform crosscorrelation has been developed to correct for instrumental drift in scanning tunneling microscope images. This tracking algorithm was used to monitor conductance changes associated with different conformations in conjugated switching molecules and to trace the diffusion of individual benzene molecules on silver.

1. Introduction With its ability to image and to manipulate single molecules and atoms, the scanning tunneling microscope has produced many new discoveries in physics, chemistry, and engineering. However, two drawbacks to this instrument are its restriction to a serial, point-by-point mode of data acquisition and the inevitable convolution of the electronic information that it acquires with surface topography. In this chapter, we discuss in detail two separate modifications to the operation of the scanning tunneling microscope to overcome both these challenges to obtain capacitive and dynamic information.

2. Alternating Current Coupled to the STM 2.1. INTRODUCTION The alternating current scanning tunneling microscope (ACSTM) extends the capabilities of the STM from a simple atomic-scale topographic and local density of states (LDOS) probe to a spectroscopic probe capable of measuring local variations in chemical, dielectric, and magnetic properties [1-10]. Spectroscopic contrast has already been observed on several surfaces [5, 6], but its interpretation is not resolved. In addition, the ACSTM extends the capabilities of the tunneling microscope beyond conducting substrates to enable imaging and local spectroscopy on insulators [1-10]. Kochanski first demonstrated ACSTM operation on insulators and semiconductors by detecting the third harmonic of the applied bias frequency in a cavity resonant at the detection frequency [1]. This scheme has since been applied by others to study substrates ranging from metals to insulatorr [2, 3] and to measure doping profiles in silicon [6]. In our previous work, we have avoided the use of a resonant cavity in favor of retaining broadband frequency response [4, 7-10]. The ACSTM is conceptually very similar to conventional STM. The sample is scanned by a piezoelectrically driven probe tip controlled by a feedback signal sensitive to the probe tip-sample gap distance. In ACSTM, high (typically microwave) frequency bias is applied to the probe tip. As described below, we can apply a bias at any frequency from dc to 20 GHz, an additional variable with which to interrogate the surface under study. The response that can be expected varies from quasi-static at low frequencies to dispersive at high frequencies. In the quasi-static limit the ACSTM can be treated as a conventional STM experiment with a time-varying dc bias. In this limit

155

there is no extra information in the frequency domain. At sufficiently high frequencies, the tunnel junction response becomes dispersive. This deviation from quasi-static behavior is due to the inability of the system to follow the rapidly oscillating ac field. By mapping the frequency and amplitude dependence of this response, we can determine the origin(s) of these effects and use this information to elucidate the local chemical, electronic, and/or structural properties of the substrate surface [8, 10]. Only a small fraction of the power incident on the ACSTM probe tip is expected to interact with the tunneling junction, therefore the response signal due to the tunneling junction will be small compared to the total incident power at the fundamental frequency. Further complications arise from non-local interactions of the probe with its surroundings, which can dominate the ACSTM response at the fundamental frequency; these non-local interactions can affect the microwave energy in the tunneling junction, thus complicating the interpretation of the local nonlinear signal as well. Minimizing the non-local interactions is desirable for any ACSTM detection scheme and is the focus of this report. 2.2. EXPERIMENTAL SETUP The STM is a well-established surface probe that is routinely capable of spatial resolution on the atomic scale. Our goal has been to incorporate the unparalleled imaging capability of the STM with an accurate dopant profiling system. The instrument is based on a custom-built alternating current scanning tunneling microscope (ACSTM) [4, 5, 7]. The instrument we have developed is tunable over a wide frequency range and has the ability to introduce up to three frequencies to the tunneling junction simultaneously. Our instrument detection system m is capable of detecting transmitted and reflected, fundamental and nonlinear alternating current signals, and can determine phase as well as magnitude information. This allows us local access to the frequency dependence, energy, and position of electronic t responses of doped semiconductors. Introducing multiple frequencies to the STM probe tip allows us to generate a difference frequency signal that is produced due to the nonlinear nature of the STM tunnel junction. Data acquisition was accomplished using a difference frequency mixing strategy. A schematic of the instrument configuration is shown in Figure 1. In addition to the conventional DC bias applied to the tunnel junction, two frequencies are introduced from tunable waveform generators. The frequencies are offset by a small amount (typically 5 kHz) that becomes the detected frequency (ω1 − ω2 = ∆ω). The mixing product (∆ω) occurs at low frequency, so it is conveniently extracted and detected using a lock-in amplifier. A reference signal for the lock-in is created by splitting off a portion of the applied AC signals prior to the tunnel junction in a directional coupler, and sending them through a diode to generate the desired difference frequency.

156

Figure 1. Schematic of the difference frequency detection scheme. Two frequencies, ω1 and ω2 are generated and combined. A portion of the mixed signal is sent through at diode, which creates the nonlinear difference frequency reference signal, ∆ωreff for the lock-in amplifier. The remainder of the mixed signal is combined with the DC bias voltage and sent to the STM tip. The nonlinear nature of the STM tunnel junction and of the sample creates the difference frequency signal, ∆ωsignal. This is extracted from the tunnel current and sent to the lock-in amplifier for comparison with ∆ωref.

3. Dopant-profiling with ACSTM 3.1. THEORY Scanning probe microscopes are extremely important for characterizing semiconductors with very high spatial resolution. According to the 2001 International Technology Roadmap for Semiconductors [11], there was already an unmet critical need to be able to determine 2-D dopant profiles with 3 nm resolution in 1999, and 1 nm spatial resolution will be required by 2008. Much of the recent work in this field has focused on the development of the scanning capacitance microscope (SCM) [12-18]. These instruments have shown high sensitivity towards dopant density and type, and have accurately imaged devices on semiconductor surfaces with resolution as high as 10 nm [12, 13]. However, the lateral resolution when using capacitance detection is limited by the probe tip geometry and dopant level [12, 14, 15]. Improving spatial resolution may require the development of new scanning probe techniques. To address these and related issues, we have developed a novel dopant profiling tool based on the alternating current scanning tunneling microscope (ACSTM). We have already used this method to probe the electronic properties of self-assembled monolayers and single molecules [19-21]. The present work extends the technique to semiconductor dopant profiling. As shown below, the nonlinear AC signal is sensitive to dopant type and density, giving us a convenient means to integrate a dopant profiling system with the high-resolution STM. In this work, we first characterize the frequency and voltage response of our technique, and then use it to image patterns on doped semiconductor substrates to determine both dopant density and dopant type.

157

The tip-sample distance is precisely controlled using the DC tunneling current for feedback; this prevents the metal tip from contacting the silicon substrate. This tip-airsilicon arrangement resembles a metal-insulator-semiconductor (MIS) structure. Signals resulting from an MIS structure will consist of both capacitive C(V) and conductive G(V) terms. C(V) originates from the capacitances of the air gap and silicon depletion layer, while G(V) describes losses in the AC signal from effects such as the STM tunneling current, series resistance in the silicon substrate, and sample and tip local density of states. The difference frequency detection strategy makes use of the capacitive characteristics of the doped silicon, which vary according to dopant density and type. Additionally, it allows us to tune the instrument over a range of fundamental frequencies, from 0-20 GHz, while the output signal detected remains at a constant frequency. A similar two-frequency mixing strategy designed to image p-n junctions using a microwave frequency compatible AFM has been previously reported by Schmidt et al. [22]. These particular AFM experiments used the sum and third harmonic frequencies as nonlinear mixing product signals. It was found that the sum frequency V2, signal and the third harmonic signal are proportional to dC/dV and d2C/dV respectively. We expect the difference frequency signal to be analogous to the sum frequency signal, and be proportional to dC/dV. V A complete discussion of the nature of the mixing products can be found in references 22 and 23.

Figure 2. (A) Model capacitance curves of a metal-insulator-semiconductor structure for both a p- and n-type semiconductor. (B) Corresponding dC/dV V curves, determined numerically.

Typical capacitance versus voltage curves for a MIS structure are shown in Figure 2 (A). The numerical differentials are shown in Figure 2 (B). If we consider the ACSTM tip-gap-semiconductor a MIS structure, the precise shape and magnitude of these curves would be determined by a variety of factors, including the dopant concentration, the distance of the tip from the sample (the insulator thickness), the magnitude of the tunneling current, and the probe tip geometry. Although they only model our system, we can use the curves in Figure 2 to understand qualitatively the difference frequency signal observed in images at different biases. Because we expect the magnitude and phase of the signal to be related to the differential capacitance [22, 23], we expect that the largest signals would occur at bias voltages near 0 volts, and that the signal would decrease as the magnitude of the bias increases. Additionally, we expect an 180o relative phase shift between n- and p-type regions on the semiconductor surface. While our system is significantly more complicated than a simple fixed-geometry MIS capacitor,

158

the dC/dV V model is a first-order approximation for the contrast observed in difference frequency images obtained at different bias voltages. 3.2. CHARACTERIZATION OF BULK SILICON For the initial characterization experiments on uniformly doped Si, we purchased p- and n-type silicon samples from Virginia Semiconductors, Inc, Fredricksburg, VA 22401, USA. Samples were prepared by annealing at 950 oC for one hour, and then the surfaces were cleaned with a 1:1 H2O2:HCl solution. Immediately prior to all measurements with the ACSTM, we dipped the test samples in a 48% HF solution for ~2 minutes to remove the surface oxide. The experiments were performed in a custom-built tunable ACSTM, described above. All measurements were carried outt at ambient temperature and pressure. The cleaned, doped Si substrates were used to map out the frequency and voltage response as a function of dopant type and concentration. t In Figure 3, the magnitude of the difference frequency signal is plotted as a function of applied frequency and voltage, for both p- and n-type Si. The difference frequency signal is strongly dependent on the fundamental frequency.

Figure 3. Difference frequency signal magnitude for Si(100) as a function of fundamental modulation frequency and bias for (A) 0.001 ohm-cm boron-doped and (B) 1-3 ohm-cm phosphorus-doped silicon.

Figure 3 (A) shows data for highly doped p-type Si (0.001 Ω-cm boron-doped). A wide peak is centered at -0.7 V sample bias. Figure 3 (B) shows data for lightly doped n-type Si (1-3 Ω-cm phosphorous-doped). The peak for phosphorous occurs close to 0 V bias voltage. For both n- and p- type Si, the lower applied frequencies provide the largest signals. This can be attributed to attenuation of high frequency signals through the transmission lines leading into the ACSTM. Reflections of the high frequency signals can occur at transmission line connectors and in coupling to the STM tip. This results in more loss at high frequency, and less signal generated in the tunnel junction for frequencies greater than several hundred MHz. Fortunately, a large nonlinear effect is seen at low frequencies providing the difference frequency signal necessary for semiconductor characterization. It is important to note that the data displayed is the magnitude of the difference frequency signal; all phase information is neglected. Because changes in tip size and shape as well as the precise sample orientation can

159

affect the phase of the difference frequency signal, between the n- and p-type Si it is difficult to compare phase information. As described below, we expect a phase difference when n- and p-type Si are compared on the same substrate. 3.3. ATOMIC-SCALE IMAGING OF pn JUNCTIONS To fabricate patterned substrates, we photolithographically prepared a stripe pattern with a 2 µm pitch. Both boron doped p-type and phosphorus doped n-type bulk silicon with concentrations of 1 x 1015 cm-3 were used as the base substrates. We implanted both n- and p-type bulk substrates with boron doses ranging from 1x1011 cm-2 to 2x1014 cm-2 or phosphorus doses ranging from 1x1011 cm-2 to 3x1014 cm-2. All boron implants were done at 35 keV and all phosphorus implants were done at 50 keV. The samples discussed below are bulk n-type Si doped with a 1x1011 cm-2 dose of boron, and bulk ptype Si doped with a 2x1013 cm-2 dose of boron. The final samples consisted of implanted 0.5 µm stripes spaced by 1.5 µm of unimplanted substrate. We then activated all implants by rapid thermal annealing at 1040 oC for 40 seconds.

Figure 4. 1.2 µm x 1.2 µm difference frequency images of a 1x10 cm boron implant stripe in a 1x10 cm phosphorus doped Si(100) substrate at varying biases. The implant stripes were defined photolithographically to have a width of 0.5 µm. Corresponding topographic images are inset. Colorbars indicate signal magnitude. 15

-3

15

-3

A series of bias dependent images demonstrate the trends described above. Figures 4 (A-D) are difference frequency images of an n-type substrate doped with boron. The

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sample was prepared to have 0.5 µm p-type (with a nominal concentration of 1015 cm-3) stripes, with a background of 1.5 µm n-type stripes (1015 cm-3). After locating the pattern, difference frequency images were acquired at voltages ranging from -1.5 V to +1.5 V. There is a strong bias dependence observed in the difference frequency images. Between all of the images, the largest signals are seen at +0.5 V and -0.5 V. This is expected for values near zero, based on the model differential capacitance curves. The stripe feature is still evident at higher bias voltages, but the magnitude of the difference frequency signal has greatly diminished. The expected 180o phase shift between n- and p-type silicon is observed in the images acquired at high voltage, confirming our assignment of the different regions. However, the images at lower applied bias do not exhibit this phase shift. This may be due to convolution of the dC/dV V signal with contributions from the STM tunneling current or contributions of higher-order V2). The corresponding topographic images are inset capacitive products (such as d2C/dV in Figures 4 (A-D). The stripe feature is evident in all of these images. This may be an artifact of STM imaging that is due to differences in conductivity of the different regions, or it may be a physical artifact of the substrate processing steps, such as implant swelling.

Figure 5. A 1.2 µm x 1.2 µm difference frequency image of a 1x10 cm boron implant stripe in a 1x10 -3 cm boron doped Si(100) substrate. The implant stripe was defined photolithographically to have a width of 0.5 µm. The corresponding topographic image is inset. 18

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We have also demonstrated the ability of the ACSTM to distinguish between areas of differing dopant concentration for the same dopant type. Figure 5 is an image of a 1015 cm-3 p-type Si substrate nominally doped with stripes of 1018 cm-3 boron. Again, the area of higher concentration was implanted as 0.5 µm stripes with a pitch of 2 µm. In this case, the stripe feature is completely absent from the inset topographic image, yet shows up clearly in the corresponding difference frequency image. From these and related results, we ascertain that the magnitude of the difference frequency signal depends strongly on the local dopant density, and not solely on dopant type. The results

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also demonstrate the ability of the ACSTM to differentiate between areas of high and low concentration using difference frequency detection. This capability is important for imaging patterned substrates. The results and discussion presented above are a preliminary demonstration of the ability of the ACSTM to characterize semiconductor dopants using difference frequency detection. We have successfully shown the ability to distinguish between n- and p-type silicon on the nanometer scale. In addition, we have demonstrated the sensitivity of the ACSTM to dopant concentration. Future experiments with the ACSTM are underway that will determine the concentration detection limits, the maximum spatial-resolution, and will image functional semiconductor devices. 4. Feature Tracking in STM A common problem with many scanning probe microscope (SPM) techniques is drift caused by the relative motion of the sample and the probe. In applications using piezoelectric crystals for raster scanning such as most SPMs, nonlinear responses such as hysteresis and creep [24, 25] can cause the probe to drift across the surface [26]. When attempting long-term temporal analysis (i.e., many hours), the drift can be severe enough to cause the scan window to drift beyond the original region of interest. In an effort to compensate for this drift, we have developed a fast image cross-correlation (XC) technique that is used for post acquisition drift elimination to enable several types of temporal data analyses, including temporal topographic analysis and diffusion of individual molecules. This method of drift elimination is a computational solution; others have implemented instrumentation-based solutions such as tracking tunneling microscopy [27] where the tip is moved in a circle laterally (x,y ( ) and the x and y topographic gradients are measured to keep the tip located over one molecule. This method has been used to track diffusion [28, 29] and rotation [30] of individual molecules on surfaces. While instrumentation-based tracking has the capability of measuring events on the millisecond time scale, it is limited in that it can track only one molecule at a time. In contrast, tracking diffusion or other t events in an image allows monitoring of many molecules with the disadvantage of a slower time scale limited by the image acquisition rate. However, the use of fast scanning instruments (up to 20 frames/s) [31] can bring image tracking close to the time scale of instrumentation-based tracking. One of our interests is in monitoring topographic changes, such as the change in apparent height or even disappearance of a protrusion. In this latter case, the instrumentation-based tracking method, which would fail as a protrusion (or depression) is required for tracking. With XC tracking, the entire image is tracked such that the behavior of individual molecules (topographic or spatial changes) does not play a major role in the overall tracking algorithm; these features are extracted and analyzed after tracking. Image tracking is a vital factor in video compression [32] and machine vision, and as such, is currently an area of intense research [33-36]. Several algorithms have recently been developed to track three-dimensional (3D), two-dimensional (2D), and rotational motions for various microscopies [37-40]. In this work, we assume that SPM techniques will produce image sequences of constant image size and resolution. Because of the orthogonal geometry of mostt scanning probe actuators, such as the beetle-style STM

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[41], only lateral, non-rotational drift should occur. Therefore, a simple XC approach can be used to find the best alignment, and thus the drift between successive images. The maximum of the 2D XC represents the best alignment, also referred to as registration, of two images. The deviation of this maximum from the center of the image represents the drift (in pixels) between the two images. By determining the drift from a sequence of images, we have been able to select and to extract specific regions from these images for further analysis. In this article, we discuss methods to resolve temporally the conductance behavior of conjugated molecular switches inserted into alkanethiol self-assembled monolayers [42] and to analyze the diffusion of individual benzene molecules adsorbed on Ag{110} [43]. Through these analyses, statistical information on conformational switching and hopping distances, respectively, are obtained. 4.1. CROSS-CORRELATION The real-space cross-correlation C(x ( ,y , ) for two digital images, a1(I (I,JJ) and a2(I (I,JJ), can be calculated from a comparison of the subsets of each image [a1(i,j , ) and a2(i,j , )] at multiple offsets (x ( and y) specified by [44, 45]

Variations on this technique have been used previously for several applications including molecular tagging velocimetry [45], stability measurements of STMs [46], and atomic force microscopy (AFM) image alignment [39]. While this approach yields the desired XC, large images can present an exceptionally demanding computational load. In addition, this technique is limited in the available search window (limits on x and y), determined by the size of the subset images such that i + x
where n is the frame number, C is the XC image, denotes the Fourier-transform operator [48], -1 denotes the inverse Fourier-transform operator, A is the Fourier domain image, A* denotes the complex conjugate of the Fourier domain image, h is a Hanning window [49], and a is the original image. In performing the Fourier domain XC, we found that a 2D Hanning window function was required to obtain the true XC maximum as the non-windowed Fourier transform generates a white-noise response along the horizontal and vertical center of the image resulting from the lack of

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periodicity at the image edges. This generates an overwhelming peak in the center of the XC image not related to the registration of the two images. An example XC image is shown in Fig. 7 where (A) and (B) are the images to be cross correlated and the maximum in Fig. 7(C) represents the best alignment of the two images.

Figure 6. Dimensions for real-space calculation using Eq. (1). I and J are the number of pixels in the image, i and j are the number of pixels in the subset image, Sx and Sy determine the size of the search window. The location of the subset image at point A (dotted line) corresponds to the offset positions x = - Sx/2, y = Sy/2, and the location of the subset image at point B (dashed line) corresponds to offset positions x = y = 0.

Figure 7. STM images of the conjugated oligomers inserted into a host SAM of dodecanethiol on Au{111}, frame 1 (A) and frame 15 (B). The cross-correlation of these two images resulsts in (C) where, the maxima represents best alignment of images.

Using Fourier domain XC maximum tracking, van Noort et al. were able to track the diffusion of DNA in sequential AFM images [38]. While our interests are in tracking adsorbates similar to this experiment, compensation for lateral tip-sample drift [26] must

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be performed before adsorbate analysis can be accomplished. The drift between each image is obtained by recording the deviation of the XC maxima pixel coordinates from the center of the image. We apply this procedure to track the relative movement of the surface and the probe tip to generate a drift track. The drift track is used to calculate the location and to extract a specific region from a sequence of images for further analysis. While individual adsorbates could be used as the tracking images, this has the disadvantages that the adsorbate could change over time and lead to poor tracking, and potentially the XC calculation would have to be computed for each adsorbate. For these reasons, we calculate the XC for an entire image where large stationary features such as step edges and other surface defects act as the major alignment features. The drift track calculated from a full image should be applicable to all adsorbates, assuming no midimage tip jumps occur in the image sequence. A method to correct for mid-image tip jumps is discussed below. Purely periodic surfaces such as well-resolved atomic lattices would be difficult to track with the Fourier transform (or any other) XC method because the periodic lattices would generate manyy XC maxima. However, the presence of any nonperiodic features such as defects or step edges eliminates this problem.

Figure 8. Drift tracks analyzed with several key frame intervals k. The track is relative to frame 1 which starts at (0,0). Each data point thereafter represents the pixel offset relative to frame 1.

All of our calculations were implementedd in Matlab [40]. Image sizes ranged from 256x256 to 400x400 pixels. While this calculation was done serially, the XC calculations are independent from frame to frame; therefore, a parallel implementation could be used for large-scale calculations. The computational expense of real-space convolution of an image of size N2 and search window of size M2 (SSx = Sy = M M) yields approximately N2(M – N + 1)2 integer multiplications and the same number of integer additions. Whereas the Fourier domain method uses approximately 12M M2 log2M floating 2 point multiplications and 18M M log2M floating point additions [34]. When M is much larger than N, the spatial correlation is more computationally m advantageous. For our drift track calculations, the Fourier domain method is the most efficient.

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4.2. PIXEL ROUNDOFF CORRECTION After using a drift track to determine the region of interest to extract for a given adsorbate, we found that there was a cumulative error in our tracking algorithm such that as more images were tracked, the track became less accurate. For example, when a single stationary molecule was extracted with the calculated drift track, it should appear stationary in the extracted images; however, in this case, the molecule would appear to move or even to drift out of the extraction region. We attribute this error to fractional pixel drift. Because successive frames are compared and the Fourier-transform technique is limited to 1 pixel resolution, non-integer pixel drift cannot be detected. As each successive correlation is performed, the error propagation is additive. While this problem could be addressed with the more computationally expensive method of increased resolution via image interpolation [39], or the seventh-order polynomial fit to the XC peak used by Zheng and Klewicki [45], we have developed a key frame technique that has no impact on the computational load. A key frame is an image with a frame number (n + 1) that is a multiple of the key frame interval (k). k The concept of key frames is that successive images are correlated, with the exception that every key frame is correlated with the previous key frame, thus altering Eq. (2) to Cn(I (I,JJ) = -1[A [ n - k(I (I,J) J)An*(I (I,JJ)] for key frames only. The effect of key frame interval size can be seen in Fig. 8, where k = 1 represents no key frames (sequential XC), and k = 5 would compare frame 2 to 1, 3 to 2, 4 to 3, 5 to 4, 6 to 1, and then 7 to 6. The circles in Fig. 8 representt the ‘‘real’’ track, calculated by methods discussed in Sec. IV. The error with and withoutt key frames can be seen by comparing the drift track for k = 1 and the real drift track in Fig. 8, where the k = 1 track differs from the real track by 5 pixels for the last frame. For this series of images, k = 5 agrees well with the real track in the last frame and appears to give the optimal fit. To determine the optimal key frame interval, a simulated image of a Gaussian peak was positioned on a flat background with a specified orthogonal velocity (pixels/frame) and tracked with this algorithm. Because the drift is known, a track error can be calculated. For integer velocities all values of k yielded a perfect track; however, for noninteger velocities the optimal k was found to be the inverse of the fractional component of the velocity, the number of frames required for the fractional component to propagate a full pixel of drift. For example, the optimal key frame interval for drift velocities of 0.2, 1.2, or 2.2 pixels/frame was k = 5. While this would imply that selection of k relies on knowing the drift, we have found that slower drifts (0–1 pixels/frame) track better with larger k values (2–10), and most all tracks are more accurate for k > 2. As a future improvement to this algorithm, an average velocity could be monitored to adjust k as the tracking progresses. Correlating all images to the first image was not done because subsequent images may have enough drift or change over time to the extent that they do not resemble the initial image.

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5. Application of the Feature Tracking Algorithm 5.1. SINGLE MOLECULE SWITCHING It has been observed that a family of conjugated oligomers, based on 4,4’di(ethynylphenyl)-1-benzenethiol, referred to henceforth as ‘‘switch’’ molecules, exhibit reversible conductance switching. Previously, these molecules have been used in nanopore experiments where they have been shown to exhibit negative differential resistance and bi-stable conductance states that can be reversibly switched from high conductance (ON) to low conductance (OFF) states under applied electric t fields [51-53]. To understand the physical processes governing this behavior on an individual-molecule basis, we studied these molecules using the STM as a local probe [42]. Using an insertion process described in detail in the following chapter, single switch molecules are inserted at defect sites in self-assembled monolayers (SAMs) of ndodecanethiolate, such as step edges and substrate vacancies, resulting in a low density of isolated switch molecules adsorbed on the surface (Figs. 7 and 9). When imaged, switches would spontaneously switch from their on state, appearing in STM images as a 4–5 Å protrusion, to their off state appearing as a slight protrusion out of the SAM [26, 42]. Persistence times of both states range from fractions of seconds to many hours.

Figure 9. Topographic analysis of switch molecules. (A) and (B) are frames 1 and 60, respectively, from a movie. The white protrusions are individual switch molecules, the darker large spots are substrate vacancies or SAM domain boundaries. The white boxes represent the extracted region for one switch. Imaging conditions: 2 Vsample = -1.0 V, I = 0.8 pA, 1000x1000 Å , 256x256 pixels, frame acquisition = 2.07 min/frame, delay between frames 556 s. (C) Using the real track from Fig. 3, a region was extracted from 60 frames of a movie, bicubicly interpolated (for improved display, height calculations do not use interpolated data) to twice the original pixel density and median filtered. The 60 frames displayed were extracted from a 200 frame movie acquired over 10 h; further switching was not observed after the displayed frames by this particular switch. Note that each frame has been rotated by 90° relative to (A) in the frame view. (D) The calculated height of the molecule above the SAM.

Constant-current STM images representt the convolution of topography and electronic state (conductivity) of the surface. Therefore, a change in either or both will result in an apparent change in height. To measure this change in height, a movie spanning several hours of data acquisition would be tracked. Using the drift track, individual switch molecules are extracted and processed to calculate the apparent height

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of a switch molecule above the SAM surface throughout the course of the movie (Fig. 4). Large scan areas on the order of 1500 x 1500 to 2500 x 2500 Å2 were acquired over a period of up to 25 h (400 images) to observe as many molecules and switching events as possible. While this tracking algorithm may be implemented in the acquisition software, we have currently used it only as a post acquisition tool to extract and to monitor the topography of each single switch. The topographic height of a switch is obtained by extracting a 16 x 16 pixel region from each image, and calculating the difference of the median of the 9 highest pixels in the extracted region and the median of the lowest fourth of the points from the extracted region. This method was used because of the different adsorption sites in which each switch could reside, such as in or beside a substrate vacancy, or on or next to a step edge. We found that this method gave reproducible topographic heights for most of the molecules analyzed, independent of the insertion site. An example of the time-resolved switching can be seen in Fig. 9(C) and the corresponding calculatedd topographic height difference in Fig. 9(D). A consequence of this method is that an apparent height of zero will occur only if the image were flat and featureless. Because our images have corrugation from the superlattice molecules and noise, the minimum calculated height of a switch molecule is typically 2 Å. In addition, this method works best for well-isolated molecules; if adjacent switch molecules are inside of the extracted region, their topographic height can influence the calculated apparent height of the switch molecule of interest, especially in the case of measuring a switch in an off state. Another complication for the height calculation is that the difference in height between the SAM and the switch can be sufficient to drive the STM feedback mechanism to overcompensate and ‘‘overshoot’’ the real topographic height of the molecule and possibly to oscillate while scanning over the molecule, yielding falsely large apparent heights. To minimize these problems, the extracted region is median filtered before the height calculation to eliminate any noise spikes or gross overcompensation of the feedback mechanism. To characterize the reversible conductance switching, a statistical analysis of the calculated height distributions was performed, as seen in Fig. 3 in Ref. 19. The distribution shows the bimodal characteristic of the switches and the on/off ratios of the molecules. From these data we were able to conclude that the switching observed by the STM was induced by a change in molecular conformation [42]. 5.2. DIFFUSION OF BENZENE ON Ag{110} Another application for this tracking algorithm is to record molecular adsorbate motion across surfaces. The adsorbed molecule’s motion in two dimensions over the anisotropic surface potential is of great importance in understanding chemical reactions on surfaces. Of particular interest is the study of molecular motion and binding with respect to lattice orientation, step edges, and surface defects. A model system for the investigation of substrate-adsorbate interactions is the adsorption of benzene on metal surfaces, due to benzene’s relative structural simplicity, high symmetry, and the high contrast with which it appears in STM images. Jackiw et al. have observed that benzene molecules tend to diffuse along the closepacked rows of the [101] direction for Cu{110}, and along the [001] direction for

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Ag{110} [43, 54]. In these experiments, benzene was deposited on the Cu or Ag surface at 4 K, where it adsorbed randomly on the terraces. Repeated cycles of Ar+ sputtering and annealing were used to clean the surface before exposure to the benzene molecules. STM measurements were carried out in a low temperature, ultrahigh-vacuum STM [55] with the capability of raising the temperature in a controlled manner up to 80 K [56]. Instead of calculating the height of a molecule as in the previous case, here the location of the molecule in each extracted image is calculated. This is accomplished by selecting the area in which a molecule diffuses during the STM movie [white box in Figs. 10(A) and 10(B), enlarged in Fig. 10(D)]. The object to be tracked is then selected [white box in Fig. 10(D), also shown in Fig. 10(E)]. The extracted images [Figs. 10(D) and 10(E)] are then cross-correlated to generate the XC image, Fig. 10(F). In this case, the extracted images are relatively small and the search window the full image size of Fig. 10(D) is larger than the adsorbate image Fig. 10(E), therefore it is more advantageous to calculate the diffusion track with the real space XC similar to Eq. (1). For the diffusion track XC we used the built-in Matlab XC function (xcorr2) that returns the normalized cross-correlation with an extended search window as described in Ref. 44. The maximum of Fig. 10(F) corresponds to the adsorbate location and can be tracked to monitor the diffusion of the molecule Fig. 10(G), henceforth referred to as a diffusion track. Because the adsorbate is user selected, this method can be used to track protrusions or depressions of any shape. However, the diffusion tracking, just like the drift tracking algorithm, uses the maximum of the XC image for detecting motion; in the event that another molecule diffuses into the extracted area the maxima may correspond to the new molecule rather than the desired molecule, leading to a false diffusion track.

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Figure 10. Diffusion analysis of benzene on Ag{110}. (A) and (B) are frames 1 and 19 (280 x 280 Å ), respectively, from a 64 frame movie. The white protrusions are individual benzene molecules adsorbed on Ag{110}. The white boxes represent the user selected region for a molecule. Imaging conditions: Vsample = 0.100 V, I = 0.1 nA. (C) The extracted images of the drift area, 64 frames acquired over 52 min. (D) Frame 1 of the extracted images; the white box illustrates the region extracted for (E). (F) The real space XC of (D) and (E). (G) The location track of the benzene molecule calculated from the maxima of the real space XC (F) of each extracted image.

Because this analysis involves the detection of small motions and precise positions, all drift must be completely eliminated. While this algorithm can track general diffusion as seen in Fig. 8, it does not provide the precision to eliminate all of the drift completely. When the drift track is used on a stationary object such as a step edge or an

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immobile adsorbate, the diffusion track of the object should exhibit no movement, however, deviations of <2 pixels were observed. The accuracy of the drift track can be analyzed by the diffusion track of a stationary object. To calculate the real track, as shown in Fig. 8, for the elimination of all drift, the diffusion track of the stationary object is used as an error signal and subtracted from the drift track to provide a corrected drift track. For image sequences that have mid-image tip jumps, this correction method can be applied to stationary objects on both t sides of the tip jump. Although few conclusions have been drawn yet, we envision that the combination of this drift tracking algorithm and a variable-temperature STM will be useful in obtaining energies of diffusion barriers, average hopping distance, and adsorbate–adsorbate interactions [2831, 57-60].

6. Conclusions In this chapter, we have demonstrated two methods for extending the capabilities of the scanning tunneling microscope. In the first example, a hardware modification that allows direct coupling of microwaves to the STM junction was described. We exploited this capability to gain capacitive as well as conductive information about the sample, utilizing it to examine dopant distributions in semiconductors. The second half of this chapter illustrated software modifications and image analysis that extended STM from a static probe of molecules on surfaces to a dynamic mapping of the interface. This algorithm was used to track both motion of molecules across surfaces as well as conformational motion in a stationary molecule. These two examples illustrate only two of many of the variations on tunneling microscopy that have been developed since its invention over 20 years ago. In relation to the dopant-profiling work the authors gratefully acknowledge useful discussions with Joe Kopanski, Steve Stranick, Greg McCarty and Lloyd Bumm. The authors would also like to thank H.-P. Rust and J. I. Pascual at the Fritz-Haber-Institut der Max-Plank-Gesellschaft and J. J. Jackiw for the use of their benzene on Ag{110} data and helpful discussions. The continuing support of the Army Research Office, the Defense Advanced Research Projects Agency, the National Science Foundation, the Office of Naval Research, and Atolytics, Inc. are most gratefully acknowledged.

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171 33. Stiller, C. and Konrad, J. (1999) Estimating Motion in Image Sequences - A Tutorial on Modelling and Computation of 2D Motion, IEEE Signal Process. Mag. 16, 70-91. 34. Lewis, J.P., Industrial Light & Magic, http://www.idiom.com/;zilla/Papers/nvisionInterface/nip.html 35. Barnea, D.I. and Silverman, H.F. (1972) IEEE Trans. Comput. 21, 179. 36. Handbook of Image and Video Processingg (2000), edited by A. Bovik Academic, San Diego, CA. 37. Lockwood, W.D. and Reynolds, A.P. (1999) Use and Verification of Digital Image Correlation for Automated 3-D Surface Characterization in the Scanning Electron Microscope, Mater. Charact. 42, 123134. 38. van Noort, S.J.T., van der Werf, K.O., de Grooth, B.G., and Greve, J. (1999) High Speed Atomic Force Microscopy of Biomolecules by Image Tracking, Biophys. J. J 77, 2295-2303. 39. Romer, J., Plaschke, M., and Kim, J.I. (2000) Alignment of AFM Images Using an Iterative Mathematical Procedure 85, 99-105. 40. Rosolen, G.C. and King, W.D. (1998) An Automated Image Alignment System for the Scanning Electron Microscope, Scanning 20, 495-500. 41. Bumm, L.A. and Weiss, P.S. (1995) Small Cavity Nonresonant Tunable Microwave-Frequency Alternating-Current Scanning Tunneling Microscope, Rev. Sci. Instrum. 66, 4140-4145. 42. Donhauser, Z.J., Mantooth, B.A., Kelly, K.F., Bumm, L.A., Monnell, J.D., Stapleton, J.J., Allara, D.L., Tour, J.M., and Weiss, P.S. (2001) Conductance Switching in Single Molecules through Conformational Changes, Science 292, 2303-2307. 43. Jackiw, J.J., Pascual, J.I., Mantooth, B.A, Weiss, P.S., and Rust, H.P. (in preparation). 44. Russ, J.C (1995) The Image Processing Handbook, 2nd ed., Chemical Rubber, Ann Arbor. 45. Zheng, Q.X. and Klewicki, J.C. (2000) A Fast Data Reduction Algorithm for Molecular Tagging Velocimetry: The Decoupled Spatial Correlation Technique, Meas. Sci. Technol. 11, 1282-1288. 46. Huang, W.H., Wang, W.W., Xia, A.D., Jin, N., and Hu, Z.Q.J. (2000) Time-Stability Measurement and Compensation of a Scanning Probe Microscope Instrument, Vac. Sci. Technol. B 18, 2027-2029. 47. Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1986) Numerical Recipes, the Art of Scientific Computing, Cambridge University, Cambridge. 48. Fast Fourier transform libraries often return a Fourier domain image where the dc peak is in the corners of the image; for this calculation the dc peak must be shifted to the center of the image. In addition, note that the multiplication of Fourier domain images is elemental, and not matrix multiplication. When computing the inverse Fourier transform, the correlation image is flattened into only real numbers by calculating the absolute value of the real and imaginary (resulting from rounding errors) components returned by a Fourier transform. 49. Oppenheim, A.V. and Schafer, R.W. (1989) Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, pp. 63–67, 447, 746–747, 839–842. 50. The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098. 51. Chen, J., Reed, M.A., Rawlett, A.M., and Tour, J.M. (1999) Large On-Off Ratios and Negative Differential Resistance in a Molecular Electronic Device, Science 286, 1550-1552. 52. Chen, J., Wang, W., Reed, M.A., Rawlett, A.M., Price, D.W., and Tour, J.M. (2000) Room-Temperature Negative Differential Resistance in Nanoscale Molecular Junctions, Appl. Phys. Lett. 77, 1224-1226. 53. Reed, M.A., Chen, J., Rawlett, A.M., Price, D.W., and Tour, J.M. (2001) Molecular Random Access Memory Cell, Appl. Phys. Lett. 78, 3735-3737. 54. Jackiw, J.J. (2001) Ph.D. Thesis Exploration of Nanoscale Structures and Properties, Pennsylvania State University. 55. Rust, H. P., Buisset, J., Schweizer, E.K., and Cramer, L. (1997) High Precision Mechanical Approach Mechanism for a Low Temperature Scanning Tunneling Microscope, Rev. Sci. Instrum. 68, 129-132. 56. Briner, B. G., Doering, M., Rust, H. P., and Bradshaw, A. M. (1997) Microscopic Molecular Diffusion Enhanced by Adsorbate Interactions, Science 278, 257-260. 57. Repp, J., Moresco, F., Meyer, G., Rieder, K.-H., Hyldgaard, P., and Persson, M. (2000) Substrate Mediated Long-Range Oscillatory Interaction Between Adatoms: Cu/Cu(111), Phys. Rev. Lett. 85, 29812984. 58. Pedersen, M.O., Osterlund, L., Mortensen, J.J., Mavrikakis, M., Hansen, L.B., Stensgaard, I., Laegsgaard, E., Norskov, J.K., and Besenbacher, F. (2000) Diffusion of N Adatoms on the Fe(100) Surface, Phys. Rev. Lett. 84, 4898-4901. 59. Osterlund, L., Pedersen, M.O., Stensgaard, I., Laegsgaard, E., and Besenbacher, F. (1999) Quantitative Determination of Adsorbate-Adsorbate Interactions, Phys. Rev. Lett. 83, 4812-4815. 60. Qin, X.R., Swartzentruber, B.S., and Lagally, M.G. (2000) Diffusional Kinetics of SiGe Dimers on Si(100) Using Atom-Tracking Scanning Tunneling Microscopy, Phys. Rev. Lett. 85, 3660-3663.

FUNCTIONS OF NC-AFM ON ATOMIC SCALE

S. MORITA1,2, N. OYABU1, T. NISHIMOTO1, R. NISHI1, O. CUSTANCE1,2, I. YI1,2 and Y. SUGAWARA2,3 1 Department of Electronic Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871, JAPAN 2 Handai Frontier Research Center, Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871, JAPAN 3 Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871, JAPAN

Contents 1. 2. 3. 4. 5.

6. 7. 8.

Introduction Noncontact Atomic Force Microscope (NC-AFM) System 2.1. Frequency modulation (FM) detection method Guidelines for the Achievementt of True Atomic Resolution with NC-AFM Spatial Resolution in High Performance NC-AFM Functions of NC-AFM on an Atomic Scale 5.1. Three-dimentional mapping of atomic force 5.2. Discrimination of atomic force mechanisms and atom species 5.3. Control of atomic force and atom position Thermal Fluctuation of Atom Investigated by Low Temperature NC-AFM Mechanical Atom Manipulation Based on NC-AFM Method 7.1. Mechanical vertical manipulation of individual Si adatom Conclusion

Abstract Using the noncontact atomic force microscope (NC-AFM), we investigated functions of NC-AFM. As a result, we found that the NC-AFM works not only the atomic resolution microscope but also novel atomic tools based on a mechanical method such as a three-dimensional mapping tool of atomic force between the tip and sample atoms, a discrimination tool of atomic force mechanisms between the tip and sample atoms, a discrimination tool of atom species on the sample surface, a control tool of atomic force between the tip and sample atoms, a control tool of atom position on the sample 173 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 173-195. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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surface, and an atom manipulation tool. 1. Introduction The atomic force microscope (AFM) invented in 1986 is a unique microscope based on a mechanical method, which has the following characteristics; (1) it has true atomic resolution, (2) it can measure atomic force (so-called atomic force spectroscopy), (3) it can observe even insulators, and (4) it can measure mechanical responses such as elastic deformation. However, usual contact mode imaging is rather t destructive [1] and cannot routinely achieve observation of an atomic defectt [2], although the periodic lattice structure can be imaged [3]. On the other hand, the noncontact atomic force microscope (NC-AFM) utilizing a frequency modulation (FM) detection method achieved true atomic resolution in 1995 for Si(111)7x7 [4-5] and InP(110) [6]. After that, various kinds of sample surfaces such as Si(100)2x1 [7], GaAs(110) [8], NaCl(100) [9], TiO2(110) [10], Si(111)л3xл3-Ag [11], Ag(111) [12], graphite(0001) [13], NiO(100) [14], C60 [15], Si(100)2x1:H[16], HCOO㧙/ TiO2(110) [10], and self-assembled monolayer of adenine base [17] have been observed with atomic resolution. Very recently, the latest results in the NC-AFM field have been published in a book [18]. The present review article deals with the experimental demonstrations of NC-AFM functions on an atomic scale such as the three-dimensional (3D) mapping of atomic force (so-called atomic force spectroscopy) between the tip and sample atoms, discrimination of atomic force mechanisms between the tip and sample atoms, discrimination of atom species on sample surfaces, control of atomic force between the tip and sample atoms, control of atom position on sample surfaces, and mechanical atom manipulation based on the NC-AFM method. 2. Noncontact Atomic Force Microscope (NC-AFM) System 2.1. FREQUENCY MODULATION (FM) DETECTION METHOD In the NC-AFM measurement, the force interaction acting on the probe tip is detected Ʀ of the mechanical resonant oscillation of the cantilever as as a frequency shift Ʀν shown in Fig. 1. Here, ν0, ν and A0 are the mechanically free oscillation frequency, the mechanical oscillation frequency of the cantilever under attractive force and oscillation amplitude, respectively. Figure 2 shows a schematic diagram of the NC-AFM. The displacement of the cantilever due to the force interaction was detected with a fiber- optic interferometer or optical beam deflection as a frequency shift of the mechanical oscillation of the cantilever utilizing a frequency modulation (FM) detection method [19]. This system has three feedback loops. One with an automatic gain control (AGC) circuit which is used to maintain the oscillation amplitude constant (switch 1 is “ON”) in the constantoscillation mode, while the excitation voltage supplied u to the piezoelectric tube scanner is maintained constant in the constant-excitation mode (switch 2 is “ON”) [20]. In the present experiment, we mainly used the latter mode to weaken the damage due to the sudden contact between the tip and the sample surface. The frequency shift of the

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Oscillation Amplitude

cantilever shown in Fig. 1 was detected by a tunable analog FM demodulator in Fig. 2.

Frequency Shift

Ǎ Ǎν

A0

ν

ν0

Oscillation Frequency of Cantilever Figure1. Oscillation amplitude A as a function of mechanical oscillation frequency of the cantilever.. Schematic model of the frequency shift

FM Demodulator

Fiber-Optic Interferometer 1 2

∆ν Frequency Shift Image

AGC Circuit

∆ν Feedback Loop Phase Shifter

Z+δ Z X,Y

Cantilever

δZ Feedback and Scan Circuits

∆Z

Topography

Sample

Ʀν Ʀ Figure 2. Schematic diagram of the NC-AFM using the FM detection method. This system has three feedback loops.

3. Guidelines for the Achievement of True Atomic Resolution with NC-AFM Spatial resolution as shown in Table I is a very y fundamental value that determines the basic performance of the NC-AFM. Here, we will simply show approximated equations of the vertical and lateral resolutions of the NC-AFM [21]. By assuming that the value f(z) measured with the NC-AFM is proportional to exp(-z/L), where z and L are the tip-sample distance and the decay length of the measured value, respectively, and that the signal(S)-to-noise(N) ratio of f(z) is k=S/N

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Ҍ1, the equation of vertical resolutionǬz is approximately given by įz = L/k. (1) By assuming that the radius R of tip curvature is much larger than the tip-sample distance z, i.e., R » z » įz, the lateral resolutionǬx is approximately given by įx = [2Rįz]1/2. (2) By assuming that the radius of tip curvature is much smaller than the tip-sample distance z, i.e., įz « R « z, the lateral resolutionǬx is approximately given by įx = [2zįz]1/2. (3) By assuming tip-sample distance dependence of frequency shift as f(z) = A/zn (n;integer, A;constant) and įz « z0, the decay length is approximately given by L = z0/n. (4) From Eqs. (1)-(4), guidelines for the achievement of true atomic resolution with the NC-AFM [21-22] will be given by good signal-to-noise ratio (large k), small decay length (small L), small radius of tip curvature (small R), small tip-sample distance (small z) and large n. In the present experiment, to obtain the clean Si tip, both contamination and native oxide on the virgin Si tip (the spring constant; 27-41 N/m, the mechanical resonant frequency; 151-172 kHz, the nominal radius of the tip apex; 5-10 nm, and the Q factor of the cantilever; 38,000 in UHV) were removed by in situ Ar-ion sputtering. Besides, to obtain the small decay length and also small tip-sample distance, the NC-AFM image was obtained under the noncontact or near contact region just before the contact point [22]. TABLE I. Spatial resolution of high performance NC-AFM

Resolution

Application

Vertical

Lateral

Commercial NC-AFM

10 pm rms 0.1 Å rms

100 pm rms 1 Å rms

Semiconductor Atom, Ionic Atom

Home-built NC-AFM

1 pm rms 0.01 Å rms One hundredth of atom size

10 pm rms 0.1 Å rms One tenth of atom size i

Observation of Metal Atom, 3D-Measurement and Control of Atomic Force

Developing Homebuilt NC-AFM

100 fm rms 0.1 pm rms 0.001 Å rms

1 pm rms 0.01 Å rms One hundredth off atom size i

Atom and Molecule Manipulation?

4. Spatial Resolution in High Performance NC-AFM Here, we will demonstrate spatial resolutions obtained with our home-built NC-AFM. Table Σ roughly summarizes vertical and lateral resolutions of high performance NC-AFM for commercial, home-built and developing home-built NC-AFMs,

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respectively. Our home-built NC-AFM has vertical resolution of roughly 1 pm (one hundredth of atom size) and lateral resolution of 10 pm (one tenth of atom size) as follows.

(a)

2.0nmx2.0nm

(b)

0.03nm

(c)

0.28µ0.01nm

0 0

4.1nm

(a) NC-AFM image with two Ag(111) terraces separated with an atomic step. Scan area is 2 nmx2 nm. (b) NC-AFM image of the atomically flat surface of Ag(111). (c) Cross-sectional line profile obtained along the white line of (b) clearly shows lattice spacing off 0.28±0.01 nm of Ag(111) surface.

Figure 3 (a) shows a high-resolution NC-AFM image [12] with two Ag(111) terraces separated by an atomic step of Ag(111) film evaporated on Si(111)7×7 surface. Figure 3 (b) shows an NC-AFM image of the atomically flat surface of Ag(111) [12]. The

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cross-sectional line profile of Fig. 3 (c) obtained along the white line in Fig. 3 (b) clearly shows lattice spacing of 0.28±0.01 nm of Ag(111) surface. Thus we canobserve even metal atoms using atomic force, in spite of the nearly homogeneous and hence siteindependent surface on atomic force due to free-electron screening. The cross-sectional line-profile of Fig. 3 (c) shows nearly 10 pm (= 0.01 nm) corrugation. Therefore, our home- built NC-AFM has nearly 1 pm vertical resolution.

A 0.32±0.01nm

Figure 4. NC-AFM image of Si(100)2×1surface. Thin broken lines indicate centerlines of dimers along the dimer bond. “A” shows a missing dimer defect. Rectangle shows a 2×1 unit cell.

Next we measured the NC-AFM images of a Si(100)2×1 clean surface. Figure 4 shows the atomic resolution image of Si(100)2×1 surface [16]. Paired bright spots (imaged dimer) constituting rows with a 2×1 symmetry were clearly observed. Further, the distance between paired bright spots was 0.32±0.01 nm. So our home-built NC-AFM can measure the distances between paired bright spots with an accuracy of ±0.01 nm (= 10 pm). This result roughly shows that our home-built NC-AFM has nearly 10 pm lateral resolution. In the case of hydrogen terminated Si(100)2×1:H monohydride surface, the distance between paired bright spots was 0.35±0.01 nm [16], which approximately agrees with the distance between hydrogen atoms on monohydride surface, i.e., 0.352 nm. Thus, our home-built NC-AFM can measure 30 pm change of the distance between paired bright spots due to hydrogen termination [16]. Thin broken lines in Fig. 4 indicate the centerlines of the dimers. By careful investigation, we found that the lateral position of the dimer was displaced toward the missing-dimer defect

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along the dimer row. The first and second dimers adjacent to the missing-dimer defects such as “A” in Fig. 4 are displaced by ca.80 pm and ca.40 pm, respectively. The third and fourth dimers are displaced only within the experimental error (±0.01 nm). In contrast, even the first and second dimers adjacent to missing-dimer defects in the Si(100)2×1:H monohydride surface are not displaced [18].

5. Functions of NC-AFM on an Atomic Scale As confirmed by functions and measured samples listed in Table II, the NC-AFM works not only the atomic resolution microscope but also novel atomic tools based on a mechanical method such as a three-dimensional (3D) mapping tool of atomic force between the tip and sample atoms, a discrimination tool of atomic force mechanisms between the tip and sample atoms, a discrimination tool of atom species on the sample surface, a control tool of atomic force between the tip and sample atoms, a control tool of atom position on the sample surface, and an atom manipulation tool. Here, we will introduce several examples of functions of NC-AFM on an atomic scale. TABLE II. Confirmed functions of high performance NC-AFM Measured Samples by NC-AFM (*collaboration with JRCAT) InP(110) Si(111)7x7 Ag(111) Si(100)2x1:H Adenine* Observation (Atom/ Molecule) GaAs(110) Si(100)2x1 TiO2* Cu(111)* Thymine* Si(111)7x7 3D-Mapping of Atomic Force Oxygen Adsorbed Si(111)7x7 Si(111)¥ ¥3x¥ ¥3-Ag Si(111)7x7 Si(111)5¥ ¥3x5¥ ¥3-Sb Discrimination of Atomic Force Si(111)¥ ¥3x¥ ¥3-Ag Oxygen Adsorbed Si(111)7x7 Si(111)5¥ ¥3x5¥ ¥3-Sb Si(111)7x7-Ge Si(111)7x7-Sn Discrimination of Atom Species Oxygen Adsorbed Si(111)7x7 Si(100)2x1-Ge Si(111)7x7-Al Oxidation of Si Tip Si(100)1x1:2H Control of Atomic Force Ag or Sb Adsorbed Si Tip Si(100)1x1:2D Si(100)1x1:2H Si(100)1x1:2D Si(111)7x7 Si(111)5¥ ¥3x5¥ ¥3-Sb Si(111)¥ ¥3x¥ ¥3-Ag Point Charge Imaging n+-GaAs(110) Si(111)7x7

Si(111)5¥ ¥3x5¥ ¥3-Sb

As shown in Table II, our NC-AFM can map a atomic force three-dimensionally. There are two methods for three-dimensional mapping of atomic force. One method measures the tip–sample distance dependence of the NC-AFM images. This kind of three-dimensional (3D) mapping of atomic force on an atomic scale was achieved on Si(111)√3×√3-Ag surface [11] and on oxygen adsorbed Si(111)7×7 surface [23]. The other method measures the site dependence of frequency shift curves. This kind of three-dimensional mapping of atomic force on an atomic scale was achieved on Si(111)7×7 surface [24]. Figure 5 shows one example of three-dimensional mapping of atomic force obtained by measuring the tip–sample distance dependence of the NC-AFM images on oxygen adsorbed Si(111)7×7 surface. At relatively far distance,

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only several bright spots indicated by white open circles can be seen clearly as shown in Fig. 5 (a). It should be noted that at this distance, Si adatoms, i.e., the 7×7 structure, cannot be observed clearly. On the other hand, at near distance, the 7×7 structure can be seen clearly as shown in Fig. 5 (b). These results suggest that the NC-AFM can develop into a kind of spectroscopic tool, i.e., atomic force spectroscopy, which can measure the three-dimensional force-related map with true atomic resolution.

Relatively Far Distance

O2: 0.03L at RT = -10Hz

= -13Hz

Near Distance

O 7×7

15nm

(a)

Si

15nm

(b)

Figure 5. NC-AFM images of oxygen adsorbed Si(111)7×7 at (a) relatively far distance and at (b) near distance. Scan areas are 15 nm ×15 nm.

5.2. DISCRIMINATION OF ATOMIC FORCE MECHANISMS AND ATOM SPECIES As listed in Table III, we succeeded in discrimination of Si (column IV) atom from other atom species such as oxygen (column VI), Sb (column V), Al (column III), Ge (column IV) and Sn (column IV) atoms. Here, we will introduce several examples. From three-dimensional mapping of atomic force such as Figs. 5 (a) and (b), we can conclude that two force mechanisms work between the Si tip and oxygen adsorbed Si(111)7×7 surface. One is a kind of long-range force, which works well even at relatively far distance. The other is a kind of short-range force, which works strongly only at near distance. The short-range force contributes t to NC-AFM imaging of the 7×7 structure, that is, Si adatoms, as shown in Fig. 5 (b). Hence the short-range force is the covalent bonding force between dangling bonds of Si adatoms and the tip apex Si atom, and has a critical distance dc, below which the covalent bonding force works strongly as shown in Figs. 5 (a) and (b). On the other hand, at relatively far distance, different atoms from Si adatoms seem to be imaged by the long-range force. Oxygen adsorbed Si(111)7×7 surface has only two kinds of atoms, that is, Si atoms and oxygen atoms. Therefore, we conjectured that, at relatively far distance, oxygen atoms (or molecules) were imaged by the long-range force. Oxygen atoms will be charged negatively,

181

because of its high electronegativity and n-type silicon substrate. Therefore, the origin of the long-range force may be electrostatic force between negatively charged O atom (or O2 molecule) and Si tip. Thus using three-dimensional mapping of atomic force, we can discriminate mechanisms of atomic forces between the tip and the sample surface, and also we can discriminate atom species on the sample surface. TABLE III. Discrimination of atom species using NC-AFM

High Performance NC-AFM Atom Species

Atoms with Different Properties

Principles

Long Range and Short Range Forces

Different Same Column Column Atoms Atoms Difference of Covalent Bonding Force Strength Difference of Difference of Bond Covalent Bond Order Energy/Length

Elements of Column III and V (ex. Si Measured Oxygen Adsorbed atom and Sb atom) Samples Si(111) Surface Elements of Column (Atoms) IV and III (ex. Si atom and Al atom)

Si atom and Ge atom (Elements of Column IV) Si atom and Sn atom (Elements of Column IV)

KPFM/NCAFM Different Column Atoms Contact Potential Difference (CPD) Elements of Column IV and V (ex. Si atom and Sb atom)

Ge Atoms

Ge:0.06ML/1×1

(a)

Ge:0.29ML/1×1

(b)

Ge:0.52ML/1×1

(c)

Figure 6. NC-AFM images of Si(111)7×7-Ge intermixed surfaces obtained for Ge depositions of (a) 0.06 ML/1×1, (b) 0.29 ML/1×1 and (c) 0.52 ML/1×1.

Next, we will show another example of discrimination of atom species. We fabricated Si(111)7×7-Ge intermixed surface as shown in Fig. 6. On this surface, Si adatoms and Ge adatoms coexist. As a result, using the clean Si tip, covalent bonding force works between the Si tip apex atom and adatoms of Si and Ge. We found two kinds of bright spots forming a 7×7 structure as shown in Fig. 6. One kind of bright

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spots is brighter than the other kind of bright spots. These two kinds of bright spots seem to correspond to Si adatoms and Ge adatoms. Then, by increasing Ge atoms from 0.06 ML, 0.29 ML and 0.52 ML, we found that the number of brighter spots decreases, as shown in Figs. 6 (a), (b) and (c). Hence, we attributed the brighter spots to Si adatoms and the dim spots to Ge adatoms. Covalent bond energies of Si-Si bond and Si-Ge bond are 2.32 eV and 2.12 eV, respectively. Therefore, the covalent bonding force for Si adatoms will be larger than that of Ge adatoms. This speculation qualitatively agrees with the experimental results. Thus, our home-built NC-AFM can clearly discriminate Si adatoms and Ge adatoms, although the difference of covalent bond energies for Si–Si bond and Si-Ge bond is only ca. 10%. Here, covalent bond radiuses of Si and Ge adatoms are 117 pm and 122 pm (-4% difference), respectively, so that difference of covalent bond radiuses, i.e., difference of corrugations, will play a minor role in this system. TABLE IV. Bond order of Si(111) 5√3×5√3-Sb surface measured with Si and Sb tip

Si tip (dangling bond) Sb tip (lone pair) Si adatom (dangling bond) Sb adatom (lone pair)

Topography (Si Tip)

nb=2 na=0 n=1 nb=2 na=1 n=0.5

Topography (Sb Tip)

nb=2 na=1 n=0.5 nb=2 na=2 n=0

CPD Image (Si Tip)

A: Brighter Atom (Si)

A: Bright Atom (Si)

A Atom: Dark Spot (Si)

B: Dim Atom (Sb)

B: Unresolved (Sb)

B Atom: Dim Spot (Sb)

(a)

(b) A: Si B:Sb

(c)

Figure 7. NC-AFM images of Si(111)5√3×5√3-Sb surface obtained with (a) Si tip and (b) Sb tip. (c) CPD image obtained with Si tip. These NC-AFM images were obtained at the same area.

We also succeeded in discriminating the difference of strength of the covalent bonding force for Si adatoms with a dangling bond and for Sb adatoms with a lone pair on Si(111)5√3×5√3 -Sb surface using a clean Si tip with a dangling bond. Such difference of strengths of the covalent bonding force F(Z) = (nb-na)dƦ d E(Z)/dZ depends

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on the bond order n = (nb-na)/2 and enables us to discriminate Si adatoms and Sb adatoms. Here, nb and na are number of electrons thatt will enter the bonding and antibonding orbitals, respectively. ƦE(Z) is the covalent bonding energy. By the difference of bond order listed in Table IV, using clean Si tip with a dangling bond, Si adatoms were imaged brighter than Sb adatoms as shown in Fig. 7 (a). Here, brighter spots, i.e., Si adatoms, were encircled by white open circles. Besides, using Sb adsorbed Si tip, only Si adatoms were selectively imaged as bright spots as indicated by open circles in Fig. 7 (b). We constructed high performance Kelvin probe force microscope combined with NC-AFM (KPFM/ NC-AFM). Figure 8 shows the schematic model of KPFM/ NC-AFM with atomic resolution [25]. It should be noted that the operation of this system is very difficult, because this system has four feedback loops. Using developed high performance KPFM/NC-AFM, we simultaneously imaged NC-AFM topography and contact potential difference (CPD) image with a clean Si tip as shown in Figs.7 (a) and (c). Then we found that Sb adatoms appeared as dark spots as indicated by open circles in Fig. 7 (c). Thus, we discriminated Si adatoms from Sb adatoms on Si(111)5√3×5√3-Sb by CPD imaging [26]. As a result, we succeeded in discrimination of Si adatoms from Sb adatoms on Si(111)5√3×5√3-Sb surface using three different methods at the same area as shown in Fig. 7. displacement detector

FM demodulator

detects force from frequency shift (∆f )

KPFM circuits optical fiber

oscillates at resonance frequency ((ff0)

automatic gain controller

cantilever sample e tip-sample distance control PI feedback (PIF) 1 tube scanner topography topograph Figure 8. Schematic model of Kelvin probe force microscope combined with NC-AFM (KPFM/NC-AFM). This system has four feedback loops.

5.3. CONTROL OF ATOMIC FORCE AND ATOM POSITION By placing a suitable atom at the tip apex, we can control atomic force and force mechanism between the tip apex atom and the surface atom. This kind of atomic force control was demonstrated on Si(111)7×7 surface by using an oxidized Si tip instead of

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the clean Si tip [27], on Si(111) √3×√3-Ag surface by picking up an Ag atom on the Si tip [28], and on Si(111)5√3×5√3-Sb surface by picking up an Sb atom on the Si tip as shown in Figs.7 (a) and (b) [18, 26]. By moving the tip apex toward the sample surface, we can increase the strength of the attractive force and we can pull up the surface atom. This is another kind of atomic force control, which also enables us to control atom position. This kind of atomic force control was demonstrated on Si(100)1×1:2H dihydride surface [29-30], and on Si(100)1×1:2D dideuteride surface with a clean Si tip. Here, we will introduce several examples. We investigated frequency-shift curves between a Si(111)7x7 surface and the oxidized Si tip, and also a corresponding NC-AFM image of a Si(111)7x7 surface measured by the oxidized Si tip. Here, to obtain the inactive Si tip without a dangling bond, the virgin Si tip with both contamination and native oxide was used without in situ Ar-ion sputtering [27]. As a result, frequency-shift curve measured by the oxidized Si tip did not show a discontinuity but showed only a continuous smooth curve. On the other hand, frequency-shift curves measured by the clean Si tip clearly showed a discontinuous jump above Si adatoms. Further, t the NC-AFM images measured by the oxidized Si tip became unclear compared with those measured by the clean Si tip. Therefore, we concluded that the strong interaction force, i.e., the discontinuity in the frequency-shift curve, due to the onset of the covalent bond between dangling bonds of the clean active Si tip and a Si(111)7x7 sample surface was suppressed by replacing the clean active Si tip apex with the oxidized inactive Si tip apex. We also concluded that the force interaction mechanism between a Si(111)7x7 sample surface and the oxidized Si tip was mainly the van der Waals force and/or the Coulomb force. This result suggests that we can control interaction force between the tip and sample atoms on an atomic scale by placing a suitable atom m on the tip apex. It should be noted that current experimental results qualitatively agree with the calculated results [31-32], and also agree with the recent experimental results by Lantz et al. [33] who carefully investigated the tip-sample distance dependence of line sections at the low temperature. In case of Si(100)1×1:2H surface or Si(100)1×1:2D surface, a repulsive force works between adjacent hydrogen or deuterium atoms due to the proximity effect and originates a 1×1 canted structure which increases the distance between adjacent hydrogen or deuterium atoms, i.e., reduces the repulsive force strength. Figs. 9 (a), (b) and (c) show NC-AFM images of Si(100)1×1:2D surface obtained using a clean Si tip and decreasing the tip-sample distance from (a) 0.12 nm, through (b) 0.09 nm, to (c) 0.07 nm before the contact point. At the relatively far distance of Fig. 9 (a), the NC-AFM showed a 1×1 pattern. But at the near distance of Fig. 9 (b), the NC-AFM showed a 2×1 pattern. Moreover, at the close distance of Fig. 9 (c), the NC-AFM again showed a 1×1 pattern. Thus, the NC-AFM on Si(100)1×1:2D surface showed a pattern change from 1×1, through 2×1, to 1×1 similar to Si(100)1×1:2H surface [29] by decreasing clean Si tip-sample distance. To explain such tip–sample distance dependence of NC-AFM image, we considered the effect of attractive force between the tip apex atom and the nearest deuterium atom on the surface structure. At the relatively far distance, the magnitude of the attractive force between the tip apex atom and the nearest deuterium atom is smaller than that of the repulsive force between adjacent deuterium atoms. In this case, the original 1×1 canted structure is stable even under

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NC-AFM measurement. Then NC-AFM will observe the original 1×1 canted structure at the relatively far distance as shown in Fig. 9 (a). However, at the near distance, the magnitude of the attractive force becomes nearly equivalent to that of the repulsive force. As a result, the attractive force will pull up the nearest deuterium atom, and will play the role of trigger to induce self-organized 2×1 novel structure. Thus NC-AFM will observe the tip-induced self-organized 2×1 novel structure as shown in Fig. 9 (b). At near distance, we observed various kinds of 2×1 novel structures as shown in Figs. 9 (b), (d) and (e). Further, at the close distance, the magnitude of the attractive force becomes larger than that of the repulsive force. As a result, the attractive force will pull up the nearest deuterium atoms one by one. This vertical r motion of each deuterium atom due to pulling up seems large enough compared with the corrugation of the self-organized 2×1 novel structure, and hence tip-induced 1×1 novel structure will be observed by the NC-AFM. It should be noted that, by retracting the tip, 1×1 at the close distance changed to 2×1 at the near distance, but 1×1 at the relatively far distance did not appear as shown in Fig. 10. However, by retracting tip further and then approaching again, 1x1 at the relatively far distance was occasionally observed.Thus NC-AFM can control atomic force and atom position by moving the tip apex toward the sample surface atom. Tip-Sample Distance d

Relativelyy Far

3.7nm

Close

(b)

(a) ǻǵ ǵ= -24Hz

(c)

d = 0.12nm ǻǵ= -26Hz

d = 0.09nm

2×1

d = 0.07nm

1×1

2.8nm

1×1

ǻǵ= -28Hz 28H

(d)

(e)

Figure 9. Tip–sample distance dependence of the NC-AFM image on Si(100)1×1:2D obtained using a clean Si tip and decreasing the tip–sample distance from (a) 0.12 nm, through (b) 0.09 nm, to (c) 0.07 nm. (d) and (e) show typical examples of 2×1 NC-AFM images.

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Tip-Sample Distance d

Relatively Far

5.6 nm

Near

(a)

(b)

ǻǵ= -59Hz

(c)

ǻǵ= -53Hz

ǻǵ= -44Hz

Figure 10. Tip–sample distance dependence of the NC-AFM image on Si(100)1×1:2D obtained using a clean Si tip and retracting the tip–sample distance from (a), (b) and (c).

6. Thermal Fluctuation of Atom Investigated by Low Temperature NC-AFM At room temperature (RT), surface atoms may thermally fluctuate between several stable states. Hence, the RT-NC-AFM as well as RT-STM will observe time-averaged image of such thermally fluctuated atoms. On the other hand, at low temperature (LT), thermal fluctuation will freeze out. Hence, the LT-NC-AFM will observe atomic image localized under one stable state. Here, we will introduce several examples.

Asymmetric Dimer Si(100)Ideal Surface

(a)

Symmetric Dimer

(e)

(c) Top View

Top View

0.384nm 0.384

0.768nm 0.768 Attractive Force Dangling Bond

(b)

(d) Side View

Si(100)1x1

(f) Si S Si

Side View w

Si(100)2x1

Si(100)C(4x2)

Figure 11. Schematic models of Si(100)1x1-ideal surface [(a) and (b)], Si(100)2x1-clean surface with symmetric dimers [(c) and (d)], and Si(100)C(4x2)-clean surface with asymmetric dimers, i.e., buckling structure [(e) and (f)]. Hatched regions in (a), (c) and (e) show each unit cell.

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In the case of an ideal surface, each Si atom at the first layer on Si(100)1×1 surface has two dangling bonds as shown in Figs. 11 (b) and (a), respectively. Then to decrease the number of dangling bonds, adjacent Si atoms forms Si dimer and Si(100) surface constitutes self-organized 2×1 dimer row structure as shown in Figs. 11 (d) and (c), respectively. Moreover, Si(100)2×1 surface forms the buckling structure due to the charge transfer to decrease the surface energy further as shown in Figs. 11 (f) and (e). But the thermally activated flip-flop motion occurs between two equivalent buckling structures at RT. Hence, a 2×1 symmetric dimer structure such as Fig. 4 was observed on Si(100)2×1 clean surface at RT using NC-AFM because of the time averaging effect during NC-AFM measurement. On the other hand, the thermally activated flip-flop motion will freeze out at low enough temperature and Si(100)2×1 surface constitutes C(4×2) the structure shown in Fig. 11 (e). Fig. 12 shows the low temperature LT-NC-AFM image of Si(100) surface obtained at 5K [34]. This NC-AFM image clearly shows zigzag lines due to the alternating buckling and mainly C(4×2) pattern made of quasi-hexagonal rings. Thus, our home built LT-NC-AFM has atomic resolution and can clearly image the Si(100)C(4×2) structure at 5k.

Figure 12. Low-temperature NC-AFM image of Si(100)C(4×2) surface at 5 K. Scan area was 9.4 nm×9.4 nm. Open rectangle formed by white solid lines shows a C(4×2) unit cell.

Next, we will introduce another example on thermal fluctuation. The honeycomb-

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chained trimer (HCT) model has been accepted as the appropriate model for Si(111)√3×√3-Ag surface. In this model, the surface contains Ag trimer at the first layer 0.075nm above the Si trimer at the second layer. The distance between the centers of Ag trimers forming the honeycomb m arrangement is 0.384nm. At RT, bright spots in NC-AFM image constituted hexagonal rings forming a honeycomb structure as shown in Fig. 13 (a) at the relatively far distance (Z=0.2-0.3nm from the contact point) [11]. By comparing the bright spot pattern of hexagonal rings and ca.0.39nm spacing of bright spots in Fig. 13 (a) with the HCT model, we concluded that the center of Ag trimers was imaged as bright spots at the relatively far distance. Recently, Sasaki et al. [35] clarified thatt thermal fluctuation between inequivalent-triangle (IET) structure at RT and the pinning effect of the thermal fluctuation of Si(111)√3×√3-Ag surface by the tip will deduce the experimental image of Fig. 13 (a). They also predicted that, at LT, IET structure, i.e., inequivalent Ag trimer structure, can be directly observed by NC-AFM because of the freeze out of thermal fluctuation. Hence, we tried to observe Si(111)√3×√3-Ag surface at LT using LT-NC-AFM. Figure 13 (b) clearly shows the presence of two inequivalent Ag trimer structures at LT, i.e., white (ca. 0.39 nm) and black (ca.0.33nm) triangles in Fig. 13 (b) predicted by them theoretically [34].

RT(Room Temperature)

LT(Low Temperature)

6K

_ [112]

1nm

(a)

4.3nm×4.3nm

(b)

Figure 13. (a) Room-temperature (RT) and (b) low-temperature (LT) NC-AFM images of Si(111)√3×√3-Ag surface.

7. Mechanical Atom Manipulation Based on NC-AFM Method STM is the first generation of the individual atom manipulation tool. However, STM is a microscope based on the electric method that measures the tunneling current between the tip apex atom and surface atom. Therefore the STM has inherent limitations such as STM cannot observe an insulator surface, cannot manipulate individual atoms and molecules on insulator surfaces, and cannot directly measure atomic force or force related information. On the other hand, AFM is the microscope based on the mechanical method that measures the atomic force or force related information between the tip apex

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atom and the surface atom, and has potentials of insulator surface imaging with atomic resolution, manipulation of individual atoms and molecules on insulator surface, and measurement of atomic force or force related information on an atomic scale.

Step 1 NC-AFM imaging mag g

Step 2 Step 3 Mechanical cal contact c NC-AFM imaging imag ag

Z signa signal igna g gn gna

Feedback Controller

Z piezo

(a)

(b)

Feedback Controller

(c)

Figure 14. (b) Atom extraction by mechanical contact between the tip and sample surface atoms. NC-AFM imaging (a) before and (c) after mechanical contact.

7.1. MECHANICAL VERTICAL MANIPULATION OF INDIVIDUAL Si ADATOM NC-AFM succeeded in a kind of atom manipulation even at RT such as extraction of a single Ag atom from Si(111)√3×√3-Ag sample surface [36], and extraction of Sb atoms from Si(111)5√3×5√3-Sb sample surface [26]. We also tried extraction of a single Si atom from Si(111)7×7 using LT-NC-AFM as shown in Fig. 14. After NC-AFM imaging such as in Fig. 14 (a), we mechanically moved the Si(111)7×7 sample surface toward the tip apex Si atom up to some distance z to induce mechanical contact such as in Fig. 14 (b). Then by retracting the sample surface down to the initial distance, we again imaged the sample surface using NC-AFM such as in Fig. 14 (c). When we could not observe signs of atom extraction, we again moved the sample surface toward the tip apex Si atom further. By repeating this procedure, we succeeded in extracting a single Si adatom on the Si(111)7×7 surface mechanically. Figures 15 (a) and (b) are NC-AFMimages before extraction and after extraction, respectively. White open circles show a missing Si adatom, which is a marker of the same site. By comparing Fig. 15 (b) with (a), it is clear that a corner Si adatom indicated by white arrows was mechanically extracted. In the case of Ag extraction, a tip apex Si atom with a dangling bond will cut an Ag-Si covalent bond and will pick up the Ag atom from the Si(111)√3×√3-Ag sample surface. This is a kind of rearrangement of the Ag-Si covalent bond and the number of the dangling bonds does not change. On the other hand, in the case of Si adatom extraction, the tip apex Si atom with a dangling bond will cut the three Si-Si covalent bonds between the Si adatom and the lower three Si atoms. Hence, the extraction process will increase the number of dangling bonds. Thus the Si extraction process seems to be rather complicated. One possible explanation is that the cutting of three Si-Si covalent bonds occurred under the repulsive force. This means that the Si adatom was not extracted due to the pull-up process as in Fig. 16 (a), but due to the push-out

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process as in Fig. 16 (b). In this process, mechanical energy due to atomic indentation under weak repulsive force will increase the atom potential, and may finally cut the three Si-Si covalent bonds and push out a single Si adatom. Then, the pushed out Si atom may adsorb at the top of the tip apex, the side of the tip or on the sample surface.

Si(111)7x7

Before extraction

After extraction

(a)

(b)

Figure 15. NC-AFM images of Si(111)7×7 at 9.3 K (a) before Si and (b) after Si adatom extraction by mechanical h i l contact. t t

(a)

(b)

Pull Up

Push Out

Strong Attractive Force

Weak Repulsive Force

Figure 16. Elementally processes of vertical atom manipulation by mechanical contact. (a) Pull up process under strong attractive force and (b) push out process under weak attractive force.

We also succeeded in sequential atom extractions up to 5 Si adatoms on Si(111)7×7 surface as shown in NC-AFM images [left side] and 7 ×7 unit models [right side] in Fig. 17. In Fig. 17 (d), we can see the deposited atom at the right down side of the white dotted rhombus. This may be the extracted Si adatom. This atom moved after the next extraction as shown in Fig. 17 (e). After extractions, as shown in Figs.17 (c) and (f), we occasionally found laterally moved Si adatoms indicated by white spheres in 7×7 unit models. We also succeeded in the reverse atom manipulation, i.e., atom deposition from the tip to the missing Si adatom defect, by mechanical contact as shown in NC-AFM images of Fig. 18 (a)[before atom deposition] and Fig. 18 (b) [after atom deposition]. This is a kind of repair of atom defect. We also succeeded in the lateral atom

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manipulation as shown in Fig. 19 (a) [before lateral atom manipulation] and Fig. 19 (b) [after lateral atom manipulation].

Number of Missing Si adatoms

3

0 (a)

(d)

DB 19

1

(b)

4

(e)

DB 21

2

(c)

DB 25

DB 27

5

(f)

DB 23

DB 29

Sequential Si adatom extraction by mechanical contact. NC-AFM images [left side] (a) before and after mechanical extractions of (b) one, (c) two, (d) three, (e) four, and (f) five Si adatoms. 7×7 unit models [right side] show schematic models of Si adatoms in the unit cell marked by white dotted rhombuses in NC-AFM images. At (c) and (f), we can find laterally moved Si adatom indicated by white spheres in 7×7 unit models. Temperature is 8.6K. Scan area is 9.2nmÈ9.2nm

(a)

(b)

Figure 18. NC-AFM images of (a) before mechanical repair of missing Si adatom defect indicated by the

white arrow and (b) after repair of Si adatom missing defect on Si(111)7×7 at 78 K

192

(a)

(b)

Figure 19. NC-AFM images of Si(111)7×7 at 8.6 K and models of 7x7 struxture (a) before and (b) after mechanical lateral manipulation of Si adatom. Scan areas are 9.2 nm×9.2 nm.

Vertical Manipulation

Lateral Manipulation

Cutting of Covalent Bond

Formation of Covalent Bond

Cutting and Formation of Covalent Bond

Atom Removal

Atom Deposition

Atom Transfer

Si Tip Apex

Si Tip Apex

Si Tip Apex

Top of Tip Apex

Approach Bond Break Sample Surface Si(111)7x7 (a)

Bond Break and Formation Bond Formation Sample Surface (b)

Sample Surface (c)

Figure 20. Schematic models of elementally processes of (a) atom extraction, (b) atom deposition, and (c) lateral manipulation of Si adatom on Si(111)7×7 sample by mechanical contact.

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Thus, we succeeded in three types of atom manipulations by mechanical contact as shown in Figs. 20 (a), (b) and (c). The atom extraction process includes the cutting of three covalent bonds of extracted Si adatom with the Si substrate as shown in Fig. 20 (a). The atom deposition process includes the formation of three covalent bonds at the deposited missing defect site on Si(111)7× 7 sample surface as shown in Fig. 20 (b). The lateral atom manipulation process includes the cutting of three covalent bonds at the site before the manipulation, and then the formation of three covalent bonds at the site after the manipulation as shown in Fig. 20 (c).

8. Conclusion Our home-built NC-AFM has a vertical resolution of roughly 1 pm and a lateral resolution of 10 pm. Using this NC-AFM, now, we can observe even metal atoms and we can measure atomic forces three-dimensionally on an atomic scale. Besides, we can discriminate mechanisms of atomic force such as long range and short range forces, and we can discriminate Si (column IV) atom from other atom species such as oxygen (column VI), Sb (column V), Al (column III), Ge (column IV) and Sn (column IV) atoms. Further, we can control atomic force by replacing a Si atom on the tip apex with a suitable atom such as Ag and Sb atoms, and we can control atom position by approaching the tip apex atom toward the sample atom. We also succeeded in atomically resolved imaging of atomic point charge and screening electron clouds using electrostatic force microscope (EFM) combined with NC-AFM, and also in atomically resolved imaging of contact potential difference (CPD) and Z derivative of capacitance using Kelvin probe force microscope (KPFM) combined with NC-AFM. These results were partly introduced in another chapter. Moreover, we recently succeeded in manipulation of a single atom by mechanical contact, i.e., a kind of atomic indentation. In the atom extraction process, mechanical energy due to atomic indentation under weak repulsive force will increase the atom potential and may finally push out a single atom. We also succeeded in sequential atom extractions up to 5 atoms, atom deposition and lateral atom manipulation by mechanical contact. We should explore near contact and close contact phenomena in more detail. Then this will enable us to assembly atom by atom, which may lead to construction of novel nanomaterials and nanodevices a by combining mechanical atom manipulation technique with atom discrimination technique.

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25.

26.

(1995) Atomically resolved image of cleaved surfaces of compound semiconductors observed with an ultrahigh vacuum atomic force microscope, J. Vac. Sci. Technol. B 13, 1265-1267. Giessibl, F.J. (1995) Atomic Resolution of the Silicon (111)-(7x7) Surface by Atomic Force Microscopy, Science 267, 68-71. Kitamura, S. and Iwatsuki, M. (1995) Observation of 7x7 Reconstructed r Structure on the Silicon (111) Surface using Ultrahigh Vacuum Noncontact Atomic Force Microscopy, Jpn. J. Appl. Phys. 34, L145-L148. Sugawara, Y., Ohta, M., Ueyama, H., and Morita, S. (1995) Defect Motion on an InP(110) Surface Observed with Noncontact Atomic Force Microscopy, Science 270, 1646-1648. Uchihashi, T., Sugawara, Y., Tsukamoto, T., Minobe, T., Orisaka, S., Okada, T., and Morita, S. (1999) Imaging of chemical reactivity and buckled dimmers on Si(100)2x1 reconstructed surface with noncontact AFM, Appl. Surf. Sci. 140, 304-308. Sugawara, Y., Uchihashi, T., Abe, M., and Morita, S. (1999) True atomic resolution imaging of surface structure and surface charge on the GaAs(110), Appl. Surf. Sci. 140, 371-375. Bammerlin, M., Lüthi, R., Meyer, E., Baratoff, A., Lü, J., Guggisberg, M., Gerber, Ch., Howald, L., and Güntherodt, H.-J. (1997) True Atomic Resolution on the Surface of an Insulator via Ultrahigh Vacuum Dynamic Force Microscopy, Probe Microscopy 1, 3-9. Fukui, K., Onishi, H., and Iwasawa, Y. (1999) Imaging of atomic-scale structure of oxide surface and adsorbed molecules by noncontact atomic force microscopy, Appl. Surf. Sci. 140, 259-264. Minobe, T., Uchihashi, T., Tsukamoto, T., Orisaka, S., Sugawara, Y., and Morita, S. (1999) Distance dependence of noncontact-AFM image constrast on Si(111)л3xл3-Ag structure, Appl. Surf. Sci. 140, 298-303. Orisaka, S., Minobe, T., Uchihashi, T., Sugawara, Y., and Morita, S. (1999) The atomic resolution imaging of metallic Ag(111) surface by noncontact atomic force microscope, Appl. Surf. Sci. 140, 243-246. Allers, W., Schwarz, A., Schwarz, U.D., and Wiesendanger, R. (1999) Dynamic scanning force microscopy at low temperatures on a van der Waals surface: graphite (0001), Appl. Surf. Sci. 140, 247-252. Hosoi, H., Sueoka, K., Hayakawa, K., and Mukasa, K. (2000) Atomic resolved imaging of cleaved NiO(100) surfaces by NC-AFM, Appl. Surf. Sci. 157, 218-221. Kobayashi, K., Yamada, H., Horiuchi, T., and Matsushige, K. (1999) Investigations of C60 molecules deposited on Si(111) by noncontact atomic force microscopy, Appl. Surf. Sci. 140, 281-286. Yokoyama, K., Ochi, T., Yoshimoto, A., Sugawara, Y., and Morita, S. (2000) Atomic Resolution Imaging on Si(100)2x1 and Si(100)2x1:H Surfaces with Noncontact Atomic Force Microscopy, Jpn. J. Appl. Phys. 39, L113-L115. Uchihashi, T., Okada, T., Sugawara, Y., Yokoyama, K., and Morita, S. (1999) Self-assembled monolayer of adenine base on graphite studied by noncontact atomic force microscopy, Phys. Rev. B 60, 8309-8313. Morita, S., Wiesendanger, R., and Meyer, E. (Eds.) (2002) Noncontact Atomic Force Microscopy, Springer, Berlin Heidelberg. Albrecht, T.R., Grütter, P., Horne, D., and Rugar, D. (1991) Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity, J. Appl. Phys. 69, 668-673. Ueyama, H., Sugawara, Y., and Morita, S. (1998) Stable operation mode for dynamic noncontact atomic force microscopy, Appl. Phys. A 66, S295-S297. Morita, S. and Sugawara, Y. (1999) Guidelines for the achievement of true atomic resolution with noncontact atomic force microscopy, Appl. Sur. Sci. 140, 406-410. Morita, S., Sugawara, Y., Yokoyama, K., and Uchihashi, T. (2001) Atomic Scale Origins of Force Interaction, in B. Bhushan (ed.), Fundamentals of Tribology and Bridging the Gap between the Macroand Micro/Nanoscales, Kluwer Academic Publishers, Dordrecht, pp. 103-120. Nishi, R., Araragi, S., Shirai, K., Sugawara, Y., and Morita, S. (2003) Atom Selective Imaging by NC-AFM: Case of Oxygen Adsorbed on a Si(111)7×7 Surface, Appl. Surf. Sci., in press. Morita, S., Sugawara, Y., Yokoyama, K., and Uchihashi, T. (2000) Correlation of frequency shift discontinuity to atomic positions on a Si(111)7x7 surface by noncontact atomic force microscopy, Nanotechnology 11, 120-123. Okamoto, K., Sugawara, Y., and Morita, S. (2002) The elimination of the ‘artifact’ in the electrostatic force measurement using a novel noncontact atomic force microscope/electrostatic force microscope, Appl. Surf. Sci. 188, 381-385. Okamoto, K., Yoshimoto, K., Sugawara, Y., and Morita, S. (2003) KPFM Imaging of Si(111)

195 5√3×5√3-Sb Surface for Atom Distinction Using NC-AFM, Appl. Surf. Sci., in press. 27. Uchihashi, T., Sugawara, Y., Tsukamoto, T., Ohta, M., Morita, S., and Suzuki, M. (1997) Role of a covalent bonding interaction in noncontact-mode atomic-force microscopy on Si(111)7x7, Phys. Rev. B 56, 9834-9840. 28. Yokoyama, K., Ochi, T., Sugawara, Y., and Morita, S. (1999) Atomically Resolved Silver Imaging on the Si(111)-(л3xл3)-Ag Surface Using a Noncontact Atomic Force Microscope, Phys. Rev. Lett. 83, 5023-5026. 29. Araragi, S., Yoshimoto, A., Nakata, N., Sugawara, Y, and Morita, S. (2002) Atomic resolution imaging of Si(100)1×1:2H dihydride surface with noncontact atomic force microscopy (NC-AFM), Appl. Surf. Sci. 188, 272-278. 30. Morita, S. and Sugawara, Y. (2002) Atomically Resolved Imaging of Si(100)2×1, 2×1:H and 1×1:2H Surfaces with Noncontact Atomic Force Microscopy, Jpn. J. Appl. Phys. 41, 4857-4862. 31. Pérez, R., Payne, M.C., Stich, I., and Terakura, K. (1997) Role of Covalent Tip-Surface Interactions in Noncontact Atomic Force Microscopy on Reactive Surfaces, Phys. Rev. Lett. 78, 678-681. 32. Sasaki, N. and Tsukada, M. (1999) Theory for the effect of the tip-surface interaction potential on atomic resolution in forced vibration system of noncontact AFM, Appl. Surf. Sci. 140, 339-343. 33. Lantz, M.A., Hug, H.J., van Schendel, A., Hoffmann, R., Martin, S., Baratoff, A., Abdurixit, A., Güntherodt, H.-J., and Gerber, Ch. (2000) Low Temperature Scanning Force Microscopy of the Si(111)7x7 Surface, Phys. Rev. Lett. 84, 2642-2645. 34. Uozumi, T., Tomiyoshi, Y., Suehira, N., Sugawara, Y., and Morita, S. (2002) Observation of Si(100) surface with noncontact atomic force microscope at 5K, Appl. Surf. Sci. 188, 279-284. 35. Sasaki, N., Watanabe, S., and Tsukada, M. (2002) Visualization of Thermally Fluctuating Surface Structure in Noncontact Atomic-Force Microscopy and Tip Effects on Fluctuation: Theoretical Study of Si(111)- (√3×√3)-Ag Surface, Phys. Rev. Lett. 88, 046106. 36. Yokoyama, K., Ochi, T., Sugawara, Y., and Morita, S. (1999) Atomically Resolved Silver Imaging on the Si(111)-(л3xл3)-Ag Surface Using a Noncontact Atomic Force Microscope, Phys. Rev. Lett. 83, 5023-5026.

Part III – Application of Scanning Techniques to Functional Materials

SCANNING PROBE MICROSCOPY OF PIEZOELECTRIC AND TRANSPORT PHENOMENA IN ELECTROCERAMIC MATERIALS

S.V. KALININ* and D.A. BONNELL** Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 *** Department of Materials Science and Engineering, The University of Pennsylvania, 3231 Walnut St, t Philadelphia, PA 19104 *

Contents 1. 2.

3.

4.

5.

Introduction Transport measurements by Scanning Probe Microscopy 2.1. DC transport by Scanning Surface Potential Microscopy 2.2. AC transport properties by Scanning Impedance Microscopy 2.3. Current based SPM transport measurements Properties of individual interfaces 3.1. Surface potential and interface screening 3.2. DC transport at grain Boundaries 3.2.1. Potential probe: SSPM 3.2.2. Current probe: Conductive AFM 3.3. Impedance and interface trap states Local phenomena in polycrystalline oxides 4.1. Grain boundary mediated transport in ZnO 4.2. Temperature dependent transport: BaTiO3 4.3. Domain wall mediated transport: BiFeO3 4.3.1. Piezoresponse Force Microscopy of BiFeO3 4.3.2. DC transport in BiFeO3 4.3.3. Grain boundaries and AC transport in BiFeO3 Conclusions

1. Introduction A wide range of electric, electromechanical and magnetic properties of polycrystalline oxides enables their multiple applications as electronic ceramic materials.1,2,3 The two large classes of electroceramic materials are semiconducting oxides and ferroelectric and piezoelectric materials. The macroscopic transport properties of polycrystalline semiconducting oxides are largely determined by the microstructure, particularly by grain boundary structure and topology. Depending on the properties and the fabrication route, the grain boundaries are associated with various degrees of structural and 199 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 199-222. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

200

compositional disorder. The enthalpy of defect formation at the grain boundaries is typically smaller than in the bulk; grain boundaries therefore act as sinks for dopant atoms and oxygen vacancies, resulting in the large composition and carrier concentration gradients.4 In extreme cases, grain boundaries can be associated with the impurity phase wetting layers. Often grain boundaries enable useful behavior, such as low-field magnetoresistance,5,6,7 grain boundary Josephson junctions,8 positive temperature coefficient of resistivity (PTCR)9,10 and varistor behavior.11 In other cases, grain boundaries limit the performance of the material, e.g. critical current density in high temperature superconductors. In mostt cases, grain boundary transport phenomena are governed by the interface charge, i.e. the electronic properties of the interface, even though more subtle effects associated with magnetic disorder and strain are possible. Another class of electrically active oxide materials is formed by ferroelectric and piezoelectric materials. Strong electromechanical coupling in ferroelectrics enables applications for microelectromechanical systems (MEMS), sensors and actuators.12,13,14 In bulk ferroelectrics, depolarization energy and strain limits the maximum domain size, giving rise to complex domain patterns. The immediate implication of domains is that experimentally accessible properties of a ferroelectric crystal, and especially ceramics, are averaged over multiple domains. Domain structure significantly influences many physical properties, such as piezoelectricity, electrooptical properties, hysteresis and switching behavior. Despite the outstanding technological and scientific relevance of interface and ferroelectric phenomena, experimental opportunities for the fundamental studies are limited. Ferroelectric domain size is usually small, ranging from nanometers in ferroelectric thin films to tens of microns in single crystals and ceramics, precluding macroscopic studies of polarization dependent properties. The vastt majority of transport measurements are performed on polycrystalline materials; thus, no relationship between the structure and properties of individual interface can be established. The key to understanding the structure-property relationship in electroceramic materials is the ability to perform local studies of structure and electrical phenomena. The development of scanning probe microscopy techniques in the last two decades for the first time allowed local property measurements on the nanoscale level. Here we summarize some of the scanning probe techniques that for the characterization of transport and ferroelectric properties in the polycrystalline oxides. 2. Transport Measurements by Scanning Probe Microscopy 2.1. DC TRANSPORT BY SCANNING SURFACE POTENTIAL MICROSCOPY Scanning Surface Potential Microscopy (SSPM) is a well-established SPM technique that allows the local potential to be determined with submicron resolution. Principles of SSPM are discussed in Chapter [Shao and Bonnell]. SSPM has been successfully used to detect stray fields over Schottky double barriers in electroceramics and semiconductors and to image potential drops at laterally biased grain boundaries. Particularly of interest are applications of SSPM for spatially resolved dc transport imaging at electroactive interfaces and in polycrystalline materials. In these applications, SPM tips acts as a moving voltage probe similarly to 4 probe resistance measurements, giving the advantage of spatial resolution.

201

In a SSPM transport experiment, a biased interface is connected to a voltage source in series with current limiting resistors to prevent accidental current flow to the tip.15 For a system with a single electroactive interface, the total resistivity of the sample RΣ, is (1) RȈ = 2 R + R gb V ggb

( )

where Vgb is the potential across the interface, Rgb(V Vgb) is the voltage dependent resistivity of the interface and R is the resistivity of the current limiting resistors. The applied bias dependence of the potential drop at the interface is directly assessable by SSPM and is referred to as the voltage characteristics of the interface. In general Vgb), can be reconstructed as case, interface current-voltage characteristics, Igb(V (2) I gb V gb = V − V gb 2 R

( ) (

)

provided the values of current limiting resistors are known. Variation of current limiting resistors, R, can be used to determine the presence of stray resistances in the circuit (e.g. contact and bulk resistances). Alternatively, the current, Igb, can be measured directly using current-voltage converter. SSPM metrology of laterally biased devices is limited by a significant cantilever contribution to the measured potential, minimization of which requires imaging at small tip-surface separations.16 To compensate for potential variations due to differences in local work function, images under applied lateral bias should be corrected by the grounded surface potential values. Similar analysis can be performed for the transport in the multiple interface systems.17 Assuming the series arrangement of the grains, total resistance of the sample, RΣ, can be written as )R gb + Rrc (3) RȈ = Rlc + NR gi + ( where Rlc is the resistance of the left contact, Rrc is the resistance of the right contact, Rgb is the grain boundary resistance, Rgi is the resistance of grain interior and N = n+m+1 is the number of the grains, n and m being the number of grains to the right and left of the investigated grain. Eq. (3) can be interpreted in terms of the brick-layer model, where RΣ Sgrain, where Rsample is sample resistance, Sgrain is average grain size and Ssample is Rsample Ssample/S is sample cross-section area. The potential drop at the individual grain boundary, ǻVgb = V1 − V2 , is ǻVgb =

Rgb RȈ

(4)

V

where V is the lateral dc bias. The potential drop within the grain, ǻVgi = V2 − V3 , can be determined as ǻV gi =

R gi RΣ

V=

dV l dx

(5)

where dV dx is the experimentally determined potential gradient along the grain and l is the grain size. Therefore, the ratio of the potential drop at the grain boundary and in the grain interior, α, is equal to the ratio of the grain boundary and grain interior resistivities ǻV ggb R gb = =α (6) ǻV ggi R gi

202

Provided that the electrode resistance is small, Rrc+Rlc<
(

)

( )

equivalent circuit in Figure 1d tan (

)=

ωCd Rd2 2 2 2 d ) + Rω C d Rd

(

The voltage oscillation amplitude ratio, A1 A2 = β

β −2 =

{(

)

−1

(8)

, is

} +ω C ) 2

2

2 4 d Rd

(9) 2 R2 High and low frequency limiting behavior for Eqs. (8, 9) is summarized in Table 1. In the high frequency limit phase shift at the interface is determined by interface capacitance and circuit termination only. Thus, SIM phase imaging at frequencies above −1 −1 C gb , provides a quantitative measure the interface relaxation frequency, ω >> ω r = R gb

(

of interface capacitance. Quantitative determination of interface C-V curve for metalsemiconductor interface using combination of SIM in the high frequency regime and SSPM was reported elsewhere.18

203

Vtip = V dc + V ac cos (

)

Vttip = V ddc

Current 1 Current 2 Vlat = V dc + V ac cos (

Vllat = V ddc

(a)

Rl

ϕ1, A1

V2

V1 Rgb

)

ϕ2, A2

Rgb g

Rr

Zl

V Rc

Cgb

Rl

V

V

Rr

(f)

(d)

(b)

Rgb

Figure 1. Experimental set-up for dc transport measurements by Scanning Surface Potential Microscopy (a), ac transport measurements by Scanning Impedance Microscopy (c) and two-terminal conductive AFM (e) and corresponding equivalent circuits (b, d, f). TABLE I. Frequency dependence of interface phase shift and amplitude ratio. Frequency, Low frequency limit,

High frequency limit,

Phase shift,

ω << ω r

ω << ω r

ωC gb

(

2 R gb g

)

R gb

2 R

(

g

Amplitude ratio,

A1 A2

R + R gb R 1

1 ωC gb R

Crossover frequency, −1 −1 ω r = R gb C gb 1 + R gb R

( )

tan ϕ gb

)

R + R gb R

Similarly to conventional impedance spectroscopy [Ref. 19], interface phase shift and the amplitude ratio can be used simultaneously to determine the interface transport properties. For frequency independent Rgb, Cgb (Model 1), experimental phase shift – frequency (Model 1a), amplitude ratio-frequency (Model 1b) or both dependencies simultaneously (Model 1c) can be fitted to Eqs. (8, 9), where Cgb and Rgb are now fitting parameters. For models 1a and b, the second observable provides independent verification of the results. Alternatively, frequency dependent interface resistance and capacitance Rgb(Ȧ), Cgb(Ȧ) (Model 2) can be calculated at each frequency from the experimental phase shift and amplitude ratio. Such data are expected to be particularly important for the characterization of the interfaces with large frequency dispersion of interface transport properties, e.g. due to the interface states or deep traps at semiconductor grain boundaries20 or several relaxation processes in ionic conductors,

204

for which interpretation of conventional impedance spectroscopy results is not straightforward. In polycrystalline materials, the direct application of SIM allows quantitative measurements of phase changes within the grain and grain boundaries as well as delineation of the resistive vs. capacitive behavior of individual microstructural elements. Assuming the series arrangement of the grains as illustrated in Figure 1b, the total impedance of the sample, ZΣ, is: (10) Z Ȉ = Z lc + N Z gb + Z gi + Z rc

(

)

where Zlc is the impedance of the left contact, Zrc is the impedance of the right contact, Zgb is the grain boundary impedance, Zgi is the impedance of grain interior and N = n+m+1 is the number of the grains. Grain boundary and grain interior impedances are modeled by capacitive and resistive elements in parallel, 1 1 , Z gi = (11a, b) Z gb = 1 / Rgb + i 2πffC gb 1 / R gi + i 2πffC gi where f is frequency, Rgb and Cgb are the grain boundary resistance and capacitance and Rgi and Cgi are the grain interior resistance and capacitance. As for the DC transport, Eq. (10) can be interpreted in terms of the brick-layer model, where measured grain boundary and bulk resistances and capacitances for the sample are scaled linearly and reciprocally by the number of grains in the cross-section of the sample. The phase change at the grain boundary is calculated from the ratio of impedances between the region to the left and to the right of grain boundary and the ground: )Z gi + Z rc nZ gb + ( β= (12) ( ) g g + Z rc

( )

as tan ϕ gb = Im(

)

( )

(

)

(impedance divider effect). The ratio of voltage oscillation

amplitudes on the left and on the right is A2 A1 = β similarly to single-interface case. Similar analysis for the grain interior and electrodes is straightforward. It should be noted that Eqs. (3) and (10) are directly interpretable in terms of the brick-layer model. Indeed, the grain boundary and bulk impedances scale reciprocally with cross-section area; therefore, impedance ratios defined in Eqs. (4) and (12) do not depend on sample area. The quantitative analysis of SIM imaging of polycrystalline materials indicates that imaging of polycrystalline ceramics will exhibit phase shifts on the interface and phase shifts of the opposite sign in the grain interior.17 The presence of the resistive circuit termination suppresses the latter for frequencies above the resonant frequency. At the same time, below the resonant frequency the amplitude drops at the interfaces and exhibits uniform behavior within the grains similarly to the dc potential behavior. Above the resonant frequency there is no amplitude change at the interfaces, while there is an amplitude drop within the grain that can be determined as a uniform slope. 2.3. CURRENT BASED SPM TRANSPORT MEASUREMENTS The alternative approach for transport measurements by SPM is based on current probes as described in Chapter [Shao and Bonnell]. Techniques such as Scanning Spreading Resistance Microscopy (SSRM), conductive AFM (c-AFM) and Scanning Capacitance

205

Microscopy (SCM) are ultimately sensitive to the transport phenomena at the tip-surface junction. An alternative approach for local transport measurements using c-AFM employs two-terminal configuration as illustrated in Figure 1e.21 In two-terminal cAFM, measured is the current on the left contact, Il, and right contact, Ir, induced by current, It, injected from the biased tip. From charge conservation, It = Il + Ir. From the equivalent circuit in Figure 1f for symmetric crystal (Rl = Rr = R), currents are R gb + R R I l = Vttip 2 , I r = Vttip 2 (13a, b) R + R gb Rts + R g R + R gb Rts + R g

(

(

)

)

(

)

For good tip-surface contact, Rts << Rgb, Eqs. (13a, b) are simplified as I l = Vtip R , and

(

)

I l = Vttip R + R gb . From Eq. (13a, b), the ratio of currents on the left and right are

independent on tip-surface contact resistance and can be calculated as Il R . = I r R + R gb

(14)

Thus, Eq. (14) can be used to determine grain boundary resistance and bulk resistances from the two-terminal c-AFM data. Noteworthy, the current ratio in Eq. (14) is independent of the absolute value of tip-surface resistance. Hence two-terminal cAFM can be used for quantitative measurements of grain boundary resistances provided that Rts doesn’t change across the interface. Additional insight into interface properties can be obtained using c-AFM at high tip voltages. In this regime, high-energy electrons injected from the tip can result in the formation of electron-hole pairs, splitting of which in the internal field at the interface will give rise to the position dependent current similar to the Remote Electron Beam Induced Current (REBIC) in electron microscopy. However, this imaging regime can be best realized under ultra high vacuum conditions when the surface recombination and contamination effects can be minimized. Similar approached can be extended to the ac current measurements using singleand two-terminal NanoImpedance Microscopy.22 Particularly of interest are applications of nanoimpedance spectroscopy, in which impedance is measured as a function of frequency and dc bias on the tip. The frequency analysis of impedance data allows establishing the major elements of the equivalent circuit and determination of corresponding parameters. Combined with the precise control of tip position on the surface, it opens multiple new opportunities for the nanoscale characterization of transport properties of materials. 3. Properties of Individual Interfaces In this Section, we use SPM based techniques for the direct spatially resolved imaging of interface properties on the grounded and biased surfaces. The techniques described in the previous section are demonstrated on a well-defined example of an electroactive grain boundary in metallic SrTiO3.

206

3.1. SURFACE POTENTIAL AND INTERFACE SCREENING In order to relate the grain boundary properties to atomic configuration, an interface with a known structure was used. Nb-doped Σ5 SrTiO3 bicrystals (0.5 wt%) were produced by diffusion bonding. Numerous high-resolution transmission electron microscopy studies on similar bicrystals have shown that the interfaces are atomically abrupt, with no impurity segregation.23 A 10x10x0.5 mm crystal, dark-blue due to the donor doping, is sectioned such that the grain boundary is perpendicular to the (100) surface. The grain boundary can be easily detected by means of transmission optical microscopy as a dark blue (almost black) line on the lighter background perpendicular to the edge of the crystal. Topographic features were used as markers to determine the position of grain boundaries in the EFM and SSPM measurements; very often, a wedgelike divot is associated with the grain boundary-crystal edge junction. Prior to imaging the crystal was repeatedly washed with ethanol, acetone and distilled water. The AFM, EFM and SSPM measurements were performed on a commercial instrument (Digital Instruments Dimension 3000 NS-III) with Co/Cr coated tips (l ≈ 225 µm, resonant frequency ~ 70 kHz). SSPM measurements were performed from ~10 nm to 1.5 µm above the surface; EFM measurements were performed from 20 to 200 nm above the surface. The scan rate varied from 0.2 Hz to 0.5 Hz. The driving voltage dependence of surface potential observed by SSPM saturates at driving voltage ~ 1-2 V for the lift heights of interest; therefore, Vac, was chosen to be > 5 V. To reduce the effect of drift the images were acquired with the grain boundary oriented along the slow scan axis. Topographic and EFM images were processed by line flattening.24 SSPM images were processed only by a constant background subtraction. Force gradient and potential profiles were obtained by averaging the flattened EFM and unprocessed SSPM images along the slow scan axis. The use of low dc bias voltages contributes to higher image stability. In addition, detection in SSPM implies much smaller tip oscillation amplitude than that in topographic or EFM imaging. From a direct comparison of the signal from the photodiode in the main scan line and non-contact scan line the characteristic oscillation amplitude during potential detection is < 1 nm depending on feedback circuit parameters. Thus, for flat surfaces imaging is possible at very small tip-surface separation. To perform SIM measurements, the microscope was augmented by external electronics as described elsewhere.15 The surface topography and surface potential are compared in Figure 2. The surface is extremely flat with RMS roughness less then 1 nm and a number of spots due to contaminates. Pores with diameters of ~100-200 nm are distributed non-uniformly along the interface. This observation suggests that the pores exist in the bulk as well and contribute to the optical contrast of the grain boundary. Similar observations of pores at SrTiO3 bicrystal interfaces are reported by other groups.25 The surface potential measured 50 nm above the surface exhibits a sharp protrusion associated with the grain boundary. The half-width of the broad potential feature is ~700 nm. The detailed analysis of the SSPM image formation mechanism on the grounded surface was reported by Kalinin and Bonnell.26 It was found that within the crystal the potential is almost constant, decreasing only to κ/(κ+1) of its bulk value at the surfaceinterface junction for ideal termination, where κ = 300 is dielectric constant of SrTiO3. Potential decreases rapidly in air and the analytical model for the quantification of grain boundary potential from the SSPM and Electrostatic Force Microscopy (EFM) data was developed. Quantification of both the EFM and SSPM results lead to a depletion width of dsc ≈ 200 nm and a potential of φgb ≈ 30 mV for the grain boundary, i.e. close to the

207

values measured directly. This potential value is significantly smaller than expected for typical SrTiO3 interface (~ 0.5 V). The width of the observed grain boundary contrast (~ 700 nm) was found to be larger than the depletion width obtained from distance dependencies (~ 400 nm) and significantly larger than the bulk depletion width expected in heavily doped SrTiO3 (~10-50 nm) or determined from capacitance measurements (15 nm). This behavior was attributed to the surface damage and charge accumulation at the surface-interface junction; however, no evidence supporting this model was reported. Strikingly, the sign of the grain boundary potential feature as observed by SSPM is positive. In the n-doped material, this corresponds to the accumulation type grain boundary, which can account for the small value of grain boundary potential limited by the separation between the donor levels and the bottom of conductions band. However,

(a)

(b)

(c)

(d)

Figure 2. Surface topography (a), surface potential of the grounded SrTiO3 bicrystal surface (b) (large scan size) and surface pot ential for forward (c) and reverse (d) bias. Scale is 40 meV (b) and 0.4 V (c, d).

using SSPM imaging under applied bias the grain boundary is unambiguously associated with potential barrier as illustrated in Figure 2c, d and, therefore, is depletion type and must be charged negatively. In order to rationalize these observations, we introduce a screening model for the surface interface junction as shown in Figure 3. In this model, accumulation of charged adsorbates at the surface-interface junction results in the widening of the grain boundary potential feature and, most notably, in the sign inversion. To verify this hypothesis, we attempted to remove the screening charges. Application of lateral bias across the interface results in the high lateral field in the interface region (~107 V/m). The electrostatic forces induced by the field swipes the screening charges from the surface-interface junction area. After the bias is switched

208

off, the true sign of the grain boundary is observed, as illustrated in Figure 4 b. This potential distribution is metastable and the accumulation of screening charges reduces the magnitude of the negative feature with subsequent sign reversal. Corresponding relaxation times are large (30 min - several hours) and strongly depend on the surface treatment prior to the experiment. It can be argued that this effect can be attributed to the charge trapping at the interface; however, characteristic retention time is much larger than can be expected for typical interface states. Moreover, such relaxation process would be observed in the impedance spectroscopy data, contrary to the experimental observations.27 It must be noticed that while mobile charge redistribution during electrical SPM imaging was reported previously [Ref. 28], such drastic change in the observed interface properties is highly unusual. These results illustrate that in ambient the screening charges preclude reliable measurements of the grain boundary potential barrier and depletion width. Even though the potential on the surface-interface junction can be determined reliably from the distance dependence of grain boundary potential contrast, it is no longer simply related

V0 Vgb

(a)

5 µm

(c)

V0 Time

Veff

Bias off Bias on

(d)

Figure 3. (a) Equilibrium surface potential at SrTiO3 bicrystal grain boundary. (b) Grain boundary potential evolution in the turn-off experiment. The arrow indicates time direction. Charge and potential distributions at pristine (c) and screened (d) grain boundary-surface junction.

to the potential of the grain boundary in the bulk. In fact, even the sign of the potential can be determined erroneously. The depletion width measured by SSPM in this case corresponds to the Debye length of the screening charges on the surface and the observed potential profile width (~700 nm) roughly corresponds to the measured surface depletion width (2d ≈ 400 nm) with the tip smearing effect (~200 nm)29 taken into account. Interestingly, similar behavior was observed recently for ferroelectric surfaces, on which the equilibrium surface potential as observed by SSPM has the sign of the

209

screening charge rather than polarization charge.16,30 These observations suggest that surface screening is a universal feature of oxide surfaces in air and great care should be taken in the direct interpretation of the results of ambient electrostatic force sensitive SPMs. To access interface potential data UHV conditions are required, under which external screening is negligible. 3.2. DC TRANSPORT AT GRAIN BOUNDARIES

10

-1

1.0 0.5

10

-2

10

-3

2.45

0.0 -0.5 -1.0 -10

-5

0 5 Lateral bias, V

2.35 2.30

2.20

10

2.15 -2

-1

10 Bias, V

(b)

10

-4

0

-1

-2

(d)

3

4

10 Frequency, q y Hz

10

4

2.4 2.2

-7

2.0

1.5

1.0 10

-2 0 2 Lateral bias, V

(c)

2.5

0

130 nm

2.25

Capacitance, 10 F

10

-5

Amplitude ratio

tan(φgb)

10 1

10 10

(a)

10

10

-4

GB position, µ m

2.40

Current, A

Grain boundary potential, V

3.2.1. Potential probe: SSPM To study the dc transport in SrTiO3 grain boundary, Nb-doped Σ5 SrTiO3 bicrystals (1 at.%) was soldered by indium to copper contact pads. Surface topography, potential on the grounded and biased surface is illustrated in Figure 2. Note that on applying the bias the potential drop develops at the grain boundary, clearly illustrating its resistive nature. To quantitatively study interface transport properties, a slow triangular ramp (0.002 Hz) is applied across the bicrystal during SSPM imaging. Collected was the SSPM image in which each line corresponds to different lateral bias conditions, i.e. potential profile across the interface; the second image stores the actual lateral bias. The voltage characteristics of the interface for different current limiting resistors are shown in Figure 4a. The voltage drop across the interface is almost linear for small lateral biases and then saturates, illustrating the decrease of the interface resistance with bias. The maximum observed potential drop across the interface is ~ 1 V; application of higher biases or the use of smaller circuit termination resistors resulted in the current flow to the tip and the destruction of the latter. Using the formalism developed in Section II, the I-V V curve reconstructed from the potential data is shown in Figure 4b. The I-V V curves

5

10

(e)

3

4

10 Frequency, Hz

10

5

2.0 1.8 1.6 1.4 0.0

(f)

0.2 0.4 Interface bias, V

Figure 4. Interface potential drop at the as a function of external lateral bias for different current limiting resistors (a) and I-V curve reconstruction from SSPM data (b). (c) Bias dependence of grain boundary position. Frequency dependence of interface phase shift (d). Solid lines are fits by Eq. (14). (e) Frequency dependence of amplitude ratio compared to calculated values using interface parameters from Table 2. (f) bias dependence of interface capacitance from SIM data compared with C-V curve measured at the same modulation signal.

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for different circuit terminations coincide with each other and coincide with the I-V curve obtained by direct two probe measurements between the contacts. These results indicate that the bulk and contact contribution to the material resistance is negligibly small compared to the grain boundary resistance, which is thus the dominant resistive element of the circuit. Therefore, in the subsequent analysis of the ac and dc transport properties of grain boundary bulk and resistive contributions can be neglected. Additional information on grain boundary properties can be obtained from the structure of potential profile under applied bias. Biasing the grain boundary is accompanied by the displacement of the center of mass of the depletion region. This displacement from negative to positive breakdown voltage is equal to depletion width. To analyze the grain boundary position, 256 potential profiles at different biases were extracted and fitted by the Boltzmann function. Bias sweep was performed several times to ensure the absence of the drift. Shown in Figure 4c is the position of the potential profile as a function of external bias and from these data the displacement is estimated as ~130 nm. This value is also very similar to the depletion width determined from the force gradient-distance and force - distance analysis. However, based on data on the surface screening, this value pertains to the characteristic Debye length of the screening charges rather than intrinsic depletion width. 3.2.2. Current probe: Conductive AFM The presence of the screening charges at the surface-interface junction limits the applicability of the ambient non-contact SPM techniques for grain boundary studies. To obtain additional information on the interface properties, we used the single- and twoterminal variants of conductive AFM as discussed in Section II.C. Single-terminal c-AFM current image the grounded bicrystal surface and corresponding profile perpendicular to the grain boundary are shown in Figure 5a, b. The grain boundary is clearly associated with low conductivity region, as can be expected from the SIM/SSPM data. The width of the profile in c-AFM is determined by the depletion width of the grain boundary and imaging conditions such as the rise time of the current amplifier and tip-surface contact area. The former effect can be minimized by scanning at smaller areas; however, for yet unclear reasons (most likely, contamination build-up or tip oxidation) the signal was repeatedly lost for small scan sizes and small tip velocities. The average tip-surface current far from the grain boundary is strongly tip and bias polarity dependent and for the probe used was 1.34 mA at tip bias of 1 V. Using the resistivity value ρ = 0.017 Ohm·cm [Ref. 31], the contact radius can be estimated as 18 nm. The width of the grain boundary feature is ~ 100 nm, the conductivity is suppressed by ~18% compared to the bulk value. The observed interface width and magnitude are weighted average of interface and the bulk due to the instrumental broadening. If the conductance in the GB region is much smaller than in the bulk and the interface current is zero, the intrinsic depletion width can be estimated as ~18 nm. This value is close to the value estimated from the measured grain boundary capacitance (dd = 22 nm). Illustrated in Figure 5c-f are the results of two terminal measurements of the same interface. Note the formation of the sharp current step when the tip traverses the grain boundary. The magnitude of the current step is determined by the voltage divider ratio formed by the grain boundary resistance and circuit termination resistance, Eq. (14).The relative current drop at the interface agrees well with that expected from the ratio of

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grain boundary resistance and the total resistance (0.81 for current 1, 0.73 for current 2, 0.76 expected for Rgb = 600 Ohm and R = 1480 Ohm). These results illustrate huge potential of the c-AFM for the interface characterization. Here, the surface charge effect on the measurements is minimal; therefore, interface properties can be characterized reliably. However, these measurements are complicated by the nature of the tip-surface contact, which, until now, has limited the number of successful experiments. 3.3. IMPEDANCE AND INTERFACE TRAP STATES The ac transport properties of the interface were studied using the Scanning Impedance Microscopy. Shown in Figure 4d, e are the frequency dependence of the interface phase shift and amplitude ratio for different circuit terminations. At the first step of analysis,

Total current

1 µm

(a)

Current 1 Current 1

(c)

Current 2

4 µm Current 2

(e)

4 µm

Figure 5. Current images and current profiles across the SrTiO3 grain boundary in the single terminal (a, b) and two-terminal set-up (c-f). Insets show the schematic of single-terminal (a) and two-terminal (c, e) current measurements.

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phase shift data was fitted by Eq. (8) for frequency independent Rgb, Cgb (Model 1) and the fitting results are summarized in Table 2. TABLE II. Grain boundary properties by Model 1 R, Ohm 148 520 1480 4700 IS

Rgb, Ohm 243.7 ± 3.5 387.8 ± 4.5 510.1 ± 3.0 666.3 ± 7.0 533± 0.4

-7

Cgb, 10 F 2.14 ± 0.04 2.15 ± 0.04 2.25 ± 0.03 2.21 ± 0.04 2.94 ± 0.01

Note that the interface capacitance is virtually independent on circuit termination resistance, while interface resistance is smaller for small circuit termination resistances. This behavior is ascribed to the large driving amplitude used in this experiment (1 Vpp), which results in the decrease of effective interface resistance due to the non-linear I-V characteristic of the grain boundary. The effective oscillation amplitude is larger for small R, resulting in smaller Rgb. In the future, care must be taken to ensure imaging in the small signal regime using cantilevers with higher sensitivity. To check the consistency of obtained interface parameters, the frequency dependence of amplitude ratios for different circuit termination resistors are calculated using Eq. (9) and data in Table 2 as shown in Figure 4e. Note the excellent agreement between the measured and calculated values despite the absence of free parameters. At the second step, we studied the frequency dependence of interface resistance and capacitance. In this case, Eqs. (8, 9) are solved at each frequency for Rgb, Cgb. Thus determined capacitance values are relatively frequency independent, while the interface resistance rapidly decreases in the high frequency region. This behavior is because the amplitude ratio is close to unity for high frequencies and small errors in the amplitude ratio and surface potential required for bias correction [Eq. in Chapter Shao and Bonnell] result in large errors in calculated resistance and capacitance. Thus, interface resistance can be most reliably determined in the low frequency regime, whereas interface capacitance can be determined both in the low frequency regime (Model 1 and 2) and in the high frequency regime using Model 1 for phase data and known circuit termination. The SIM capacitance-voltage behavior is illustrated in Figure 4f. Here, the phase and amplitude data are measured as a function of tip bias at 5 kHz, i.e. in the region where the reliable determination of Rgb, Cgb is possible. The phase shift-bias dependence is symmetric as a function of bias. For the amplitude data, the correction for tip bias and surface bias variation is introduced and the symmetric shape of the amplitude-bias curve is indicative of the adequate correction. The grain boundary capacitance calculated from these data for different circuit terminations (Model 2) are shown in Figure 4f. The interface capacitance exhibits weak bias dependence, which is attributed to the aforementioned errors in the experimentally measured amplitude ratio. Also shown in Figure 4f is the bias dependence of interface capacitance measured at 10 kHz and same modulation amplitude as in SIM experiment, illustrating the good agreement between the local SIM measurements and C-V measurements in the large modulation signal regime. It can be conjectured that extrapolation of SIM for small signal amplitudes will allow exact determination of interface parameters.

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These results illustrate that application of the SSPM and SIM for the quantification of the interface transport properties is remarkably similar to conventional C-V and 4 probe impedance spectroscopy measurements. In both cases, care must be taken to minimize the amplitude of the probing voltage to minimize its effect on measured properties. As it can be expected, conventional current-based transport measurements allow significantly higher sensitivity and precision and are capable of measurements in the larger (1 mHz - 100 MHz) frequency range. In conventional SIM, the frequency range is limited by the bandwidth of the optical detector to ~1 MHz; better performance can be expected using alternative detection schemes. Using calibration and correction procedures described above, SIM and SSPM can provide transport information within ~10% error, this value being primarily determined by the cantilever contribution to measured signal. The primary advantage of SIM and SSPM is that these techniques allow spatial localization of microstructural elements with resistive and capacitive behavior, which can be then compared to AFM, optical or electron microscopy images. It can be expected that the SIM/SSPM will provide best results in conjunction with current based transport measurements, in which global frequency dependent impedance of the system and local behavior of the individual structural element are determined simultaneously. Again, the sensitivity and spatial resolution of SIM/SSPM can be significantly improved if the measurements are performed under UHV conditions. 4. Local Phenomena in Polycrystalline Oxides After an understanding of grain boundary phenomena in single interface systems by SPM was achieved, this approach was extended to polycrystalline oxide materials. In these materials, the transport properties result from the interplay of electronic, magnetic and ferroelectric behavior. Correspondingly, depending on the nature of the material, local potential and transport studies can be complemented by high-resolution magnetic32 and ferroelectric domain imaging. Combined with potential for variable temperature measurements, SPM provide the powerful for the imaging and quantification of electric, magnetic, transport and ferroelectric phenomena as summarized below. 4.1. GRAIN BOUNDARY MEDIATED TRANSPORT IN ZnO Polycrystalline ZnO is widely used as a prominent electroceramic material due to nonlinear current voltage characteristics, which enable its application in varistors and surge protectors. This material was extensively studied by conventional impedance, I-V V and C-V V techniques on the bulk samples and microimpedance measurements using fabricated contact arrays on sample surface. However, the former access only averaged interface properties in the polycrystalline samples, while the latter are typically

214

(a)

20 µm (c)

20 µm

(g)

(b)

5 µm (d)

5 µm

(h)

Figure 6. Surface topography (a,b) and surface potential for grounded (c,d), forward (e,f) and reverse (g,h) biased ZnO varistor surface. Current map reconstruction for forward and reverse biased varistor is superimposed on (e,g). High resolution images (f,h) clearly indicate the presence of rectifying grain boundaries.

associated with the non-uniform currentt distribution in the sample, thus hindering the quantitative interpretation of the I-V V and impedance data. Here, we illustrate the applicability and limitations of SPM transport measurements for the analysis of transport phenomena in such materials. In the three-terminal set-up, SPM tip acts a moving voltage probe, while the current is induced by the macroscopic external electrodes. Therefore, current in the sample is macroscopically uniform precluding current crowding effects, while potential drop at each interface can be quantified. Shown in Figure 6 are surface topography and surface potential on a polycrystalline ZnO surface under different bias conditions. The topographic image exhibits a number of spots due to contaminants and depressions due to inter- and intragranular pores. The surface potential of the grounded ZnO surface is essentially uniform over ZnO grains and exhibits well-defined contrast due to the chemical inhomogeneity of the surface. Small potential depressions in the center of the image are associated with second phase (Bi-based spinel phase) inclusions thatt can be clearly observed using electron microscopy. On application of 5 V lateral bias potential drops at the grain boundaries become evident (Figure 6e). The contrast inverts on application of bias of opposite polarity (Figure 6f). Note that the potential depression on the second phase inclusion is independent of applied bias. Some grain boundaries demonstrated rectifying behavior. Shown in Figure 6 b, d, f, h is surface topography and surface potential of the central part of image. Grain boundaries are now seen as depressions on topographic image, probably due to the selective polishing. The surface potential of the unbiased surface exhibits potential depressions att grain boundaries. Unlike SrTiO3 bicrystal, the origins

215

of the interface potential variations are traced to the presence of a second Bi-rich phase as shown by SEM imaging in the backscattering regime. Application of a direct bias clearly delineates three large grains within the image (Figure 6f), and reversal of the bias indicates that at least two of the grain boundaries exhibit rectifying behavior (Figure 6h). The individual grain boundaries typically exhibit asymmetric voltage characteristics and a number of rectifying grain boundaries was observed. This behavior was attributed recently to the piezoelectric effect on grain boundary potential barriers;33 however, attempts to perform simultaneous piezoresponse and potential imaging in ZnO were unsuccessful, probably due to the high surafce conductivity. SSPM of polycrystalline samples can be further extended to reconstruct the current distribution through a complex microstructure. The ohmic behavior of the grain gives rise to a potential gradient in the current direction. Hence, a general pattern of current distribution can be obtained by differentiating the surface potential map along x- and ydirections and averaging the derivative maps over the individual grains. Average x- and y- derivatives of potential are proportional to the x- and y- components of the current in the grain and hence the direction of the current can be determined. The reconstructed current distribution is superimposed on potential map in Figure 6e, g. It should be noted that the magnitude of the current couldn't be obtained solely from the SPM image; additional information on the total current through the sample, specific conductivity of the grains or multiple SPM measurements with different circuit termination resistors would be required. Further progress in this field is expected if the local SIM and SSPM studies are combined numerical modeling similar to Fleig and Maier.34,35 Scanning Impedance Microscopy of polycrystalline ZnO has shown that even for the highest experimentally accessible frequencies (100 kHz as limited by the lock-in amplifier used) the interfaces are in the low-frequency regime. Both amplitude and

(a)

(b)

3 µm

(c)

(d)

1 µm

(e)

16 µm

(f)

Figure 7. Surface topography (a,c,e) and current (b,d,f) images of etched (a-c) and non-etched ZnO surface. Imaging is made is the single terminal (a-c) and two-terminal (e,f) configuration.

216

phase images exhibit abrupt changes of signal at the interfaces (not shown) similar to the dc potential. Further progress can be achieved by higher-frequency SIM measurements; in particular, such measurements can establish the origins of the frequency dispersion of interface capacitance and determine whether it is generic for individual grain boundaries or collective phenomena due to the variation of grain boundary properties in the sample. Conductive AFM imaging in single-terminal and two-terminal configurations on ZnO is illustrated in Figure 7. The current image on the etched surface closely resembles the sample topography, probably due to the topographic artifacts (tip does not penetrate the grooves between the protrusions on the surface). In the two-terminal configuration, the grain contrast is determined by the separation from the macroscopic electrodes, illustrating the potential for the spatially resolved characterization of single interfaces. Similar approach can be extended for frequency dependent transport measurement as summarized in Chapter [Shao and Bonnell].

(a)

(c)

(e)

(b)

(d)

(f)

10 µm

Figure 8. Surface potential of forward biased (a,b) and grounded (c,d) PTCR BaTiO3 compared to the corresponding piezoresponse image (e,f) at room temperature (a,c,e) and at 35°C (b,d,f). The decrease of ferroelectric polarization results in the formation of resistive barriers at the interfaces.

4.2. TEMPERATURE DEPENDENT TRANSPORT: BaTiO3 An interesting example for SPM studies is polycrystalline semiconducting BaTiO3 with positive temperature coefficient of resistance (PTCR). In this material, below ferroelectric Curie temperature the interface charge is compensated by the spontaneous polarization. On increasing the temperature, polarization decreases and the interface potential barrier develop, resulting in the drastic increase of interface resistance. Illustrated in Figure 8 is surface potential on the grounded, forward and reverse biased PTCR surface room temperature. The grain boundaries are clearly conductive. On increasing the temperature, potential barriers at grain boundaries on the laterally

217

biased sample become visible. Ferroelectric activity of BaTiO3 can be accessed locally by piezoresponse force microscopy (PFM). Shown in Figure 8e are piezoresponse and surface potential images of PTCR surface at room temperature. The fact that individual grains consist of single domain with an absence of surface potential variations on the grounded surface (not shown) is consistent with a high carrier concentration in semiconducting BaTiO3 that screens spontaneous polarization and stabilizes a single domain structure. From PFM image, the individual grains are clearly in the single domain state. On increasing the temperature, the piezoelectric activity decreases as illustrated in Figure 8f. Resistive barriers do not exist at the grain boundaries at room temperature; however, SSPM indicates the development of resistive barriers below the nominal transition temperature (50 °C). Simultaneous piezoresponse imaging confirms the localization of potential drop att the grain boundaries. PFM contrast does not disappear well above the onset of PTCR behavior in agreement with broad transition observed in the impedance spectroscopy measurements performed both on the macroscopic device and between micropatterned electrodes. The variation of PFM and SSPM signals within the image provide quantitative measures of grain boundary resistivity and piezoresponse activity and indicate the concurrent increase in resistivity and decrease of piezoresponse with temperature. To summarize, a combination of variable temperature SSPM under external lateral bias and piezoresponse imaging allows real space imaging of grain boundary PTCR behavior. At room temperature, most of the grains are in the single domain state, consistent with high conductivity of the material. Piezoresponse activity decreases with temperature along with the increase of the resistivity of grain boundary regions. The formation of resistive grain boundary barriers begins below the nominal transition temperature, while piezoresponse activity is observed in the PTCR region. These results indicate the gradual nature of the transition, which is a direct consequence of large dispersion of grain boundary properties. Further progress in this direction is expected for PTCR samples with larger grain sizes facilitating the quantitative observations of interface potential behavior under variable temperature conditions. 4.3. DOMAIN WALL MEDIATED TRANSPORT: BiFeO3 Bismuth ferrite BiFeO3 simultaneously exhibits both ferroelectric (TC = 830 oC) and long range antiferromagnetic G-type ordering (TN = 370 oC).36 Because of this magnetoelectric coupling, it has been proposed that BiFeO3 ceramics systems could be used to develop novel memory device applications. Extensive structural, magnetic, and electric studies of various BiFeO3 solid solutions systems have been reported.37,38,39 The electric and dielectric properties of BiFeO3, which could be strongly affected by small amounts of impurities and ferroelectric behavior, have been inadequately investigated. It was suggested that the impurity segregation on grain boundaries could lead to complex impedance behavior and grain boundary barrier layer (GBBL) dielectric effects. Here, electrical SPM is used to study piezoresponse and microscopic ac and dc transport in polycrystalline BiFeO3, thus facilitating the understanding of the macroscopic impedance and dielectric properties. 4.3.1. Piezoresponse Force Microscopy off BiFeO3 It was long known that BiFeO3 exhibits ferroelectric properties. However, experimental measurements of electromechanical properties are hindered by relatively high

218

conductivity of this material. Due to the lack of transparency in the visible range, optical observation of domain structure is also impossible. Here we attempted local studies of piezoelectric activity of BiFeO3 by piezoresponse force microscopy. In these experiments, the modulating bias is applied to the sample, while variation of tip bias allowed recording local hysteresis loops and studying local switching behavior. Shown in Figure 9 are surface topography and piezoresponse phase and amplitude images of polished BiFeO3 surface. PFM images exhibits clear domain structure, in which the amplitude is constant for the antiparallel domain and the phase changes by 180°. The maximum response amplitude depends on grain orientation and some grains

(a)

5 µm

(c)

(e)

(b)

2 µm

(d)

(f)

Figure 9. Surface topography (a,b), piezoresponse phase (c,d) and amplitude (e,f) of BiFeO3 surface at different magnifications. Note that extremely clear PFM contrast is observable despite relatively high (~100 kOhm) conductivity of the sample.

are characterized by virtually zero amplitude. A number of such grains are located at the junctions and can be interpreted as impurity inclusions, similarly to previous analysis of phase distribution in Li2O-Nb2O5-TiO2 system.40 4.3.2. DC Transport in BiFeO3 The surface topography and surface potential at a BiFeO3 surface under different bias conditions are shown in Figure 10. The topographic image exhibits a number of spots due to contaminants and depressions due to inter- and intragranular pores. Grain boundaries can be seen due to selective polishing of grains with different orientations. The surface potential of the grounded BiFeO3 surface exhibits large-scale potential variations due to ferroelectric domains and surface contaminants. On application of a 10 V lateral bias, the potential drops at the grain boundaries become evident (Figure 10c). The contrast inverts on application of a bias of opposite polarity (Figure 10d). Note that the potential features related to ferroelectric polarization are independent of the applied bias. Ramping the dc bias across the sample has shown that the potential drop at the interface is linear in external bias and the grain boundaries exhibit ohmic behavior for small interface biases (∆V Vgb < 50 mV)).

219

4.3.3. Grain boundaries and ac transport in BiFeO3 The surface topography, SIM phase and amplitude images at 70 kHz of the same region are shown in Figure 10a, e, f. Note that the phase images exhibit well-defined phase shifts at the grain boundaries, while the amplitude image shows a uniform decrease of amplitude across the surface. Positive phase shifts at the grain boundary and a negative phase shift in the bulk are clearly observed in agreement with theoretical arguments. For higher frequencies phase shifts in the grain interior are not observed due to the resistive component in the experimental circuit. At the same time, the amplitude decreases linearly in the direction of current flow indicating that the experimental frequency range (10-100kHz) is above the relaxation frequency of the interface. To quantify the frequency dependence of the grain boundary phase shift, the latter was determined for a series of images collected at 10kHz steps. The analysis in the vicinity of the resonant frequency of the cantilever (60 kHz) is complex due to a force-gradient induced resonant frequency shift and associated non-linear phase behavior. To relate the SIM phase shift to the material properties, the latter were independently determined by impedance spectroscopy and the corresponding spectra are shown in Figure 11. From the impedance spectroscopy data, the average grain boundary resistivity and capacitance are estimated as Rgb = 116 kOhm cm and Cgb = 7.6 nF/cm, while the grain interior resistivity and capacitance are Rgi = 812 Ohm cm and Cgi = 7 pF/cm. It should be noted that two RC elements provide a relatively poor description of the high frequency region of the experimental impedance spectra; the properties of the grain boundary component are well defined, whereas bulk properties can be determined only approximately. Figure

(a)

(c)

(d)

(d)

(f)

5 µm

(b)

Figure 10. Surface topography (a), surface potential of the grounded surface (b), and surface under lateral bias of 10 V (c) and –10 V (d). Scale is 200 nm (a), 50 mV (b,c,d). SIM phase (e) and amplitude (f) images of the same region at 70 kHz. Scale is 0.2° (e).

220

10b shows the calculated grain boundary phase shift vs. frequency dependence as compared to experimental SIM data. The only free parameter in the calculations is the effective grain number. The best fit is obtained for n = 210 grains, which is comparable with grain number N ~ 70 estimated from the grain size (~ 20-30 µm) and the distance between measurement point and left contact (~ 1-2 mm). The discrepancy between the two is due to the uncertainty in the bulk resistance and variation in grain boundary properties and orientation. Note the excellent agreement between phase angle frequency 0.15

Z'' [kOhm cm]

100 180 Hz

50 0.05

0

(a)

0.10

0

50 100 Z [kOhm cm] Z'

10

(b)

Frequency [kHz]

100

Figure 11. (a) Cole-Cole plots of as prepared BiFeO3 pellets () and the rectangular sample (S) used for scanning probe microscopy studies. (b) Experimental SIM phase shift across the interface and theoretical curve calculated from the impedance data.

dependences obtained from local measurements and impedance spectroscopy. To summarize, ferroelectric domain structures in BiFeO3 can be observed and local hysteresis loops can be obtained by PFM despite the high conductivity of the material. Both ferroelectric domain structure and local chemical composition can be modified by PFM. The fingerprints of the domain structure can be observed in surface potential images as well. Grain boundaries are shown to be associated with resistive barriers by SSPM. It is shown that ferroelectric domain boundaries do not contribute to the SIM image, thus allowing unambiguous correlation of impedance spectra with electroactive grain boundaries. For BiFeO3 ceramics excellent agreement between local SIM measurements and impedance spectroscopy data was found. 5. Conclusions In this Chapter, Scanning Probe Microscopy techniques were used for the characterization of electric, ferroelectric and transport phenomena in a number of singleand multiple interface oxide systems. Transport properties of Σ5 grain boundary in Nbdoped SrTiO3 bicrystal were characterized and compared to the conventional measurements. This behavior is shown to be due to screening at a surface-interface junction by mobile adsorbates. SPM based dc and ac current measurements were shown to be relatively insensitive to the presence of the screening charge due to the large relaxation times of the latter. Combination of SSPM on the laterally biased surface and SIM is used to determine I-V characteristic and interface resistance and capacitance, elucidating the contributions of the interface, the bulk and contacts to the device

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properties. Several models for the quantitative analysis of SIM data were suggested and the results obtained were found to be in a good agreement with conventional transport measurements. Two-terminal conductive AFM was used to directly image the depletion barrier associated with the grain boundary and determine grain boundary resistance. Polarization-mediated local transportt behavior was studied in a number of piezoelectric and ferroelectric polycrystalline oxides. In polycrystalline ZnO a number of grain boundaries with asymmetric I-V characteristics were observed; however, attempts to perform simultaneous piezoresponse and potential imaging were unsuccessful. In polycrystalline BaTiO3, high electromechanical activity allowed combination of variable temperature SSPM and piezoresponse imaging of grain boundary PTCR behavior. The formation of resistive grain boundary barriers was observed below the nominal transition temperature, while piezoresponse activity was observed in the PTCR region. These results indicate the gradual nature of the transition, which is a direct consequence of large dispersion of grain boundary properties. In polycrystalline BiFeO3, ferroelectric domain structure was observed and local hysteresis loops were obtained by PFM, unambiguously proving it's ferroelectric nature. Grain boundaries, rather than ferroelectric domain walls, are shown to be responsible for lowfrequency dielectric behavior. Excellent agreement between SIM and impedance spectroscopy was found. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Hench, L.L. and West, J.K., Eds. (1990) Principles of electronic ceramics, Wiley Interscience, New York. Buchanan, R., Ed. (1991) Ceramic materials for electronics, Marcel Dekker Inc., New York. Levinson, L.M., Ed. (1988) Electronic Ceramics: Properties, Devices and Applications, Marcel Dekker Inc., New York. Sutton, A.P. and Ballufi, R.A. (1995) Interfaces in Crystalline Materials, Oxford University Press, Oxford. Balcells, L.L., Fontcuberta, J., Martinez, B., and Obradors, X. (1998) Magnetic surface effects and lowtemperature magnetoresistance in manganese perovskites, J. Phys. C 10, 1883-1890. Ziese, M. (2002) Extrinsic magnetotransport phenomena in ferromagnetic oxides, Rep. Prog. Phys. 65, 143-249. Sun, J.Z. and Gupta, A. (1998) Spin-dependent transport and low-field magnetoresistance in doped manganites, Annu. Rev. Mat. Sci. 28, 45-78. Hilgenkamp, H. and Mannhart, J. (2002) Grain boundaries in high-T-c superconductors, Rev. Mod. Phys. 74, 485-549. Huybrechts, B., Ishizaki, K., and Takata, M. (1995) The positive-temperature coefficient of resistivity in barium-titanate, J. Mat. Sci. 30, 2463-2474. Amin, A., and Newnham, R.E. (1992) Thermistors, Key Eng. Mater. 66&67, 339-373. Desu, S.B. (1992) Interfacial effects in perovskites, Key. Eng. Mater. 66&67, 375-420. Lines, M.E. and Glass, A.M. (1977) Principles and Applications of Ferroelectric and Related Materials, Clarendon Press, Oxford. Setter, N. and Colla, E.L., Eds. (1993) Ferroelectric Ceramics, Birkhauser Verlag, Basel. Jaffe, B. Cook Jr., W.R., and Jaffe, H. (1971) Piezoelectric Ceramics, Academic Press, New York. Kalinin, S.V. and Bonnell, D.A. (2001) Scanning impedance microscopy of electroactive interfaces, Appl. Phys. Lett. 78, 1306-1308. Kalinin, S.V. and Bonnell, D.A. (2001) Local potential and polarization screening on ferroelectric surfaces, Phys. Rev. B 63, 125411. Kalinin, S.V., Suchomel, M.R., Davies, P.K., and Bonnell, D.A. (2002) Potential and impedance Imaging of polycrystalline BiFeO3 ceramics, J. Am. Ceram. Soc. 85, 3011-3017. Kalinin, S.V. and Bonnell, D.A. (2002) Scanning impedance microscopy of an active Schottky barrier diode, J. Appl. Phys. 91, 832-839.

222 19. Macdonald, J.R., Ed. (1987) Impedance Microscopy: Emphasizing Solid Materials and Systems, John Wiley, New York. 20. Blatter, G. and Greuter, F. (1986) Carrierr Transport Through Grain-Boundaries in Semiconductors, Phys. Rev. B 33, 3952-3966. 21. Kalinin, S.V. (2002) Nanoscale Electric Phenomena at Oxide Surfaces and Interfaces by Scanning Probe Microscopy, Ph.D. Thesis, University of Pennsylvania, Philadelphia. 22. Shao, R., Kalinin, S.V., and Bonnell, D.A. (2003) Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy, Appl. Phys. Lett. 82, 1869-1871. 23. Browning, N.D., Buban, J.P., Moltaji, H.O., Pennycook, S.J., Duscher, G., Johnson, K.D., Rodrigues, R.P., and Dravid, V.P. (1999) The influence of atomic structure on the formation of electrical barriers at grain boundaries in SrTiO3, Appl. Phys. Lett. 74, 2638-2640. 24. Command reference manual, Digital Instruments (1997). 25. McDaniel, E.B., McClain, S.C., and Hsu, J.W. P. (1988) Nanometer scale polarimetry studies using a near-field scanning optical microscope, Appl. Optics 37, 84-92. 26. Kalinin, S.V. and Bonnell, D.A. (2000) Surface potential at surface-interface junctions in SrTiO3 bicrystals, Phys. Rev. B 62, 10419-10430. 27. Kalinin, S.V., Duscher, G., and Bonnell, D.A. to be published. 28. Domansky, K., Leng, Y., Williams, C.C., Janata, J., and Petelenz, D. (1993) Mapping of Mobile Charges on Insulator Surfaces with the Electrostatic Force Microscope, Appl. Phys. Lett. 63, 1513-1515. 29. Kalinin, S.V., Freitag, M. Johnson, A.T., and Bonnell, D.A. (2002) Carbon r nanotubes as a tip calibration standard for electrostatic scanning probe microscopies, Appl. Phys. Lett. 81, 754-756. 30. Kalinin, S.V., Johnson, C.Y., and Bonnell, D.A. (2002) Domain polarity and temperature induced potential inversion on the BaTiO3(100) surface, J. Appl. Phys. 91, 3816-3823. 31. Johnson, K.D. and Dravid, V.P. (2000) Static and dynamic electron holography of electrically active grain boundaries in SrTiO3, Interface Science 8, 189-198. 32. Popov, G., Kalinin, S.V., Alvarez, T., Emge, T.J., Greenblatt, M., and Bonnell, D.A. (2002) Micromagnetic and magnetoresistance studies of ferromagnetic La0.83Sr0.13MnO2.98 crystals, Phys. Rev. B 65, 064426. 33. Verghese, P.M. and Clarke, D.R. (2000) Piezoelectric contributions to the electrical behavior of ZnO varistors, J. Appl. Phys. 87, 4430-4438. 34. Fleig, J. (2002) The grain boundary impedance of random microstructures: numerical simulations and implications for the analysis of experimental data, Solid State Ionics 150, 181-193. 35. Rodewald, S., Fleig, J., and Maier, J. (2001) The distribution of grain boundary resistivities in SrTiO3 polycrystals: a comparison between spatially resolved and macroscopic measurements, J. Eur. Ceram. Soc. 21, 1749-1752. 36. Fischer, P., Polomska, M., Sosnowska, I., and Szymanski, M. (1980) Temperature Dependence of the Crystal and Magnetic Structures of BiFeO3, J. Phys. C 13, 1931-1940. 37. Mahesh Kumar, M., Srinivas, A., Suryanarayana, S.V., and Bhimasankaram, T. (1988) Dielectric and impedance studies on BiFeO3-BaTiO3 solid solutions, Phys. Stat. Sol. A 165, 317-326. 38. Polomska, M., Kaczmarek, W., and Pajak, Z. (1974) Electric and Magnetic Properties of Bi1-xLaxFeO3 Solid Solutions, Phys. Stat. Sol. A 23, 567-574. 39. MacChesney, J.B., Jetzt, J.J., Potter, J.F., Williams, H.J., and Sherwood, R.C. (1966) Electrical and Magnetic Properties of System SrFeO3 – BiFeO3, J. Am. Ceram. Soc. 49, 644. 40. Borisevich, A.Y., Kalinin, S.V., Bonnell, D.A., and Davies, P.K. (2001) Analysis of phase distributions in the Li2O-Nb2O5-TiO2 system by piezoresponse imaging, J. Mater. Res. 16, 329-332.

SFM-BASED METHODS FOR FERROELECTRIC STUDIES

A. GRUVERMAN North Carolina State University Raleigh, NC 27695-7920

Contents 1. 2. 3. 4.

5.

6.

Introduction Ferroelectric domain imaging in SFM Non-contact domain imaging 3.1. Electrostatic Force Microscopy 3.2. Scanning Surface Potential Microscopy Contact domain imaging 4.1. Domain imaging via polarization-dependent friction 4.2. Domain imaging via surface topography 4.3. Domain imaging via nonlinear dielectric response 4.4. Domain imaging via static piezoresponse 4.5. Domain imaging via dynamic piezoresponse - Piezoresponse Force Microscopy Piezoresponse Force Microscopy of ferroelectric domains: static and dynamic properties 5.1. Characterization 5.2. Domain control 5.3. Fabrication Conclusion

1. Introduction Rapid development of electronic devices based on ferroelectric thin films generated a strong need for studies of ferroelectric t properties at the nanoscale. Fortunately, this need appeared at the same time as new techniques for nanoscale characterization of materials became available. Specifically, scanning force microscopy (SFM) has emerged as a powerful tool for high-resolution characterization of virtually all types of materials, such as metals, semiconductors, dielectrics, polymers and biomolecules. A number of papers and books on scanning probe methods have already been published, which can be used as an introduction to the principles of scanning force microscopy [1, 2, 3, 4, 5]. In the field of ferroelectricity, the application of the SFM technique resulted in a real breakthrough providing an opportunity for nondestructive nanoscale visualization of domain structures in ferroelectric thin films. The employment of SFM 223 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 223-249. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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made possible nanoscale mapping of the surface potential, evaluation of local electromechanical properties and dielectric constant measurements. In other words, characterization by means of SFM provides crucial information on the dielectric properties of ferroelectrics with unprecedented spatial resolution. Another promising development related to SFM is modification of the ferroelectric properties at the nanoscale via local polarization reversal induced by a conductive SFM tip. An increasing number of papers indicates a growing importance of SFM in the field of ferroelectricity (Fig. 1). Research groups in the US, Europe and Asia are actively using SFM for high-resolution characterization of ferroelectric materials both in bulk and thin layer forms. 2. Ferroelectric domain imaging in SFM Scanning force microscopy can be considered as a combination of a surface force apparatus and a surface profilometer as it is based on local monitoring of the interaction forces between a probing tip and a sample. The forces acting on the tip after it has approached the sample surface cause a deflection of the cantilever according g to Hooke's law. This deflection can be detected optically or electrically with sub-Ångström accuracy and is controlled by a feedback device, which regulates the vertical position of the tip as it scans the sample surface. Scanning is realized by placing the sample on a piezoelectric scanner, which allows for lateral and vertical positioning of the sample relative to the tip with nanometer precision. By keeping the cantilever deflection constant during scanning, a three-dimensional map of the surface topography can be obtained. Besides this method, called the constant force mode, many other modes have been developed. The response of the cantilever to the externally modulated force (for example, due to an applied ac bias) can be used to map such physical properties as mechanical stiffness, friction, electric fields, density of electronic states, and so forth. Depending on the type of tip-sample force interaction - attracting or repelling - the SFM can operate in two different regimes: non-contact or contact, respectively. In the noncontact regime, the tip is scanned over the surface at a distance of 10-100 nm, which is controlled, for example, by monitoring the resonant frequency of the cantilever [6]. The tip-sample interaction in this regime is dominated by the long-range polarization and electrostatic forces. Because of this feature, non-contact SFM can be used for ferroelectric domain imaging by detecting the electrostatic field of the surface polarization charges. This mode of SFM is called electrostatic force microscopy (EFM) [7]. Quantitative information on local surface potential related to spontaneous polarization can be obtained by means of scanning surface potential microscopy (SSPM), or Kelvin probe force microscopy (KPFM) [8, 9, 10] a technique complementary to EFM. General disadvantages of non-contact methods include susceptibility to screening effects, sensitivity to sample surface conditions and low resolution in ambient air. In the contact regime, the probing tip is in mechanical contact with the sample surface and senses repulsive short-range forces. The difference in mechanical, structural, electrochemical, dielectric and piezoelectric properties of opposite ferroelectric domains can provide domain contrast in the SFM contact regime. Contact SFM methods of domain imaging include a topographic mode of atomic force

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microscopy (AFM), lateral (friction) force microscopy (LFM), piezoresponse force microscopy (PFM) and scanning nonlinear dielectric microscopy (SNDM).

Figure 1. Number of publications on SFM studies of ferroelectrics per year.

3. Non-contact domain imaging 3.1. ELECTROSTATIC FORCE MICROSCOPY Imaging of ferroelectric domains in the non-contact mode is based on the detection of the modulated electrostatic interaction force between the probing tip and polarization charges. Using this approach, a pioneering work on SFM domain imaging has been performed by Saurenbach and Terris in a single crystal of gadolinium molybdate [11]. In EFM, the cantilever is made to oscillate near its resonant frequency using a piezoelectric bimorph. When the tip is brought close to the surface, the attractive force gradient acting on the tip alters the force constant k0 of the cantilever as k'= k0 − ∂F /∂z . This in turn leads to the change in the resonant frequency and in the vibration amplitude. A feedback loop adjusts the tip-sample distance so as to maintain the amplitude of oscillation constant. Obviously, in the case of the ferroelectric sample, there is an electrostatic contribution to the attractive force due to the Coulomb interaction between a surface polarization charge and an image charge Qt in the probing tip. As the tip crosses the wall, it experiences a change in the force gradient and the feedback loop alters the tip-sample distance so as to keep the gradient and the vibration amplitude constant. This produces a variation of contrast in the feedback signal image, which can be interpreted as an image of the domain wall [12, 13]. Since the Coulomb force is proportional to the product of the polarization and image charges,

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the force gradient signal provides information only on the polarization magnitude, and not the sign. This implies that the contrast of opposite 180º domains will be the same and that only domain walls will be visible due to the spatial variation of the charge density in the vicinity of a 180º domain boundary. A rather wide image of the domain wall (about 10 µm while the actual wall thickness is of the order of several lattice constants) obtained by Saurenbach and Terris had been attributed to the tip-sample separation and the finite size of the tip, which broadened any sharp changes in the force gradients. Later works of Luthi et all [14, 15, 16] and Eng et all [17, 18, 19] demonstrated that lateral resolution in EFM can be significantly improved: in single crystals with cleaved polar surfaces, such as GASH and TGS, the width of the walls measured in EFM was in the range from 8 to 80 nm. However, this method of domain imaging may suffer from the cross-talk with other sources of the force gradient, such as, for example, van der Waals forces. As a result, the force gradient image is usually a superposition of domain and surface topographic features. In the case of domains of irregular shape and complex surface topography, the interpretation of the EFM images could be quite difficult. One of the ways to alleviate this problem is to use a lift-mode technique, which combines the contact and noncontact modes. In this approach, the tip scans each line twice: first, recording the topography in the contact regime, and second, retracing t the topographic line at the predetermined height while detecting the variations in the vibration amplitude. In this case, since the tip-sample distance is keptt constant during the second scan, the force gradient is related to the surface charge. Another method to circumvent the cross-talk effect is by using a dual modulation scheme, developed for the detection of static surface charges [20, 21]. In this approach, also used by Saurenbach and Terris, the cantilever is additionally modulated by an ac voltage Vt = Vac cossωt applied between the probing tip and the bottom electrode. The frequency of the electrostatic modulation is chosen so that it is well below the frequency of mechanical modulation to avoid any resonance effect. In this case, an additional capacitance component will be introduced to the force acting on the tip, which can be written as:

F = Fcap + Fcoul =

1 ∂C 2 QQ V + s t2 2 ∂z 4πε 0 z

(1)

where C is the tip-surface capacitance and z is the tip-surface separation. The total charge induced in the tip will be Q t = −(Q s + Q e ) = −(Q s + CV Vt ) . The force gradient can be expressed as: 2 2 2 2 Qs º» Qs Vac cossωt ª C 1 ∂C º Vac ∂F ª«Vac ∂ C ∂ C = + cos2 2ωt + « − »+ 2 2 2 « » ¬ z 2 ∂z ¼ 4 ∂z 2 ∂z ¬ 4 ∂z 2πε 0 z ¼ 2πε 0 z

(2)

Three terms in Eq. (2) represents a dc component and first and second harmonics of the force gradient. In the absence of net polarization (Qs = 0), the only oscillating signal that can be measured is the signal oscillating at 2ω . For electrically polarized samples (Qs • 0), the first harmonic is non-zero and can be used to obtain information on the surface charge distribution. This method of domain imaging, which has been used by a number of groups [22, 23, 24, 25, 26, 27, 28, 29, 30, 31] is sensitive to the charge only and allows determination of its sign by monitoring the phase of the first harmonic signal with a lock-in.

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Figure 2 illustrates an application of this technique to domain imaging in a tetragonal Pb(Zr,Ti)O3 (PZT) film. Prior to the imaging, a small part of the film was polarized by scanning with a positively biased tip and two lines were written across this area with a tip under a negative bias. The positively and negatively polarized domains appear as bright and dark areas, respectively, due to uncompensated polarization charges of newly switched domains. At the same time, this image illustrates one of the limitations of the EFM method. Namely, an unwritten area shows only slight variation of the contrast, although it contains as-grown domains with polarization normal to the film surface, which was confirmed by another SFM method. Furthermore, the contrast of the written structure gradually fades and almost disappears within several hours. This behavior is due to the accumulation of surface charge on the film surface, which neutralizes polarization charges and causes a uniform contrast over the surface due to zero net charge. Therefore, although the EFM charge detection mode has the advantage of distinguishing between topographic features and the electrostatic signal, the domain contrast in this mode can be easily obscured. In addition, a surface contamination layer always present on the sample surface under ambient conditions can change or even conceal the image of real domain structure. Conducting experiments in vacuum or in inert atmosphere can eliminate these detrimental effects and make possible detailed investigation of the spatial distribution of polarization charges and stray electric fields at ferroelectric surfaces. Another problem is that quantification of the EFM signal is problematic since the tip-sample capacitance is difficult to measure accurately.

Figure 2. EFM charge image of a PZT film. Bright and dark areas correspond to positively and negatively 2 poled regions, respectively. The scanning area is 10x10 µm [79].

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3.2. SCANNING SURFACE POTENTIAL MICROSCOPY A method closely related to EFM is the SSPM method of domain imaging based on detection of a surface potential associated with spontaneous polarization. In the presence of a surface potential, the electrostatic force acting on the tip depends on the tip-sample potential difference Vs:

F=

1 ∂C Q s Q t (Vt − Vs )2 + ∂z 4 πε 0 z 2 2

(3)

The absolute value of the surface potential can be measured using the so-called nulling method [28]. In this approach, the probing tip is additionally biased by a dc voltage, so that Vt = Vdc + Vac cossωt . In the case of complete screening of polarization charges by adsorbed surfaces charges (Qs = 0), the three components of the electrostatic force can be written as:

1 1 ∂C Fdc = ((Vdc − Vs )2 + Vac2 ) ∂z 2 2 ∂C F1ω = (Vdc − Vs )Vac cosωt ∂z 1 ∂C F2 w = Vac2 cos2ωt 4 ∂z

(4) (5) (6)

The first harmonic of the electrostatic force is then nullified by adjusting the constant bias on the tip so that Vdc = Vs . By detecting the nullifying Vdc value during scanning, a surface potential image can be obtained. This approach has been extensively used by Kalinin and Bonnell to study polarization screening processes in ferroelectrics [32, 33, 34]. Figure 3 shows schematic diagrams of domain structure, surface topography, and surface potential in a single crystal of barium titanate. Corrugated surface topography is an indication of a- and c-domain regions (with in-plane and outof-plane spontaneous polarization, respectively). SSPM image provides additional information on the domain structure: inverted potential contrast within the c-domain region indicates the presence of antiparallel c-domains. The low value of the surface potential change across the 180º domain boundaries (of the order 150 mV) is due to almost complete screening of polarization by surface charges. The SSPM approach has been also used for nanometer detection of two-dimensional potential profiles at the semiconductor interfaces [35]. 4. Contact domain imaging Contact domain imaging can be divided into static and dynamic, or voltage-modulated, methods. Static imaging methods, such as a topographic mode of AFM and lateral force microscopy, make use of the surface domain-dependent properties of ferroelectrics, such as surface corrugations associated with the presence of different domains, difference in structure of polar faces of opposite domains, variations in friction forces and so on. Dynamic methods, which include PFM and SNDM, are based on voltage modulation and detection of the electrical and mechanical response of opposite ferroelectric domains to the applied ac voltage. The contact SFM imaging methods provide significant advantages, such as high lateral resolution (well below 10 nm), a

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possibility of the 3-dimensional reconstruction of domain structure and effective control of nanodomains. However, interpretation of the domain images could be complicated by cross-talk between different mechanisms involved in the domain contrast formation.

Figure 3. SSPM imaging of the barium titanate surface: (a) schematic diagrams of domain structure; (b) surface topography; (c) a-domain region with c-domain wedges [32].

4.1. DOMAIN IMAGING VIA POLARIZATION-DEPENDENT FRICTION The first imaging of antiparallel domains via polarization-dependentt friction has been performed by Luthi et all [12, 14]. Using this approach, domain structure has been revealed on freshly cleaved surfaces of single crystals of GASH and TGS [17, 19, 36, 37, 38]. In most of the papers, the imaging mechanism is attributed to the permanent charging of the probing tip by a ferroelectric surface. Electrostatic tip-sample interaction causes an additional contribution to the lateral force acting on the tip and results in different torsion of the cantilever when the tip is scanning surfaces of opposite

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180º domains. Consequently, electrostatic interaction results in different lateral forces acting on the tip from opposite 180º domains. The lateral resolution has been reported to be less than 8 nm. The image contrast depends on the scanning direction and can be reversed by switching from forward to backward scan, which is an indication of the tribological effect rather than of the surface morphology (Fig. 4).

Figure 4. Friction force image of a GASH cleavage surface. An imbedded domain exhibits opposite contrast compared to the surrounding due to the difference in tip-surface friction forces. Scan direction: (a) left to right; (b) right to left.

A complementary mechanism of the domain contrast in LFM can be the difference in surface structure of opposite domains which gives rise to different friction coefficients of the regions occupied by these domains [39, 40]. One of the greatest limitations of this method is that it is extremely sensitive to the surface conditions affecting sample tribological properties: adhesion layers, interfacial wetting, contamination, roughness. As a result, its application is mainly limited to crystals with atomically flat surfaces of cleavage planes, such as GASH and TGS. On atomically flat terraces of the freshly cleaved surfaces, even small variations in the friction forces can be easily detected. However, even in these crystals, friction images exhibit a wide diversity and should be interpreted with caution. For example, due to the different orientation of molecules on the chemically homogeneous terraces comprising the surface of individual domains, frictional contrast can occur not only between opposite domains, but also inside individual domains [40]. Long exposure to ambient environment could lead to deterioration of surface quality and to degradation of the domain contrast. 4.2. DOMAIN IMAGING VIA SURFACE TOPOGRAPHY The conventional topography mode of SFM has been used for domain studies via investigation of the domain-related surface morphology of ferroelectrics. There are several mechanisms which can provide morphological contrastt of ferroelectric domains: (1) topographic steps at domain boundaries due to the structural difference between positive and negative ends of domains [41]; (2) inclination of the cleaved d surfaces according to the polarity of domains and the direction of cleavage propagation [41, 42,

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43]; (3) surface corrugation at the junction of a- and c-domains in perovskite ferroelectrics [12, 17, 44, 45, 46, 47, 48, 49, 50, 51, 52]. The topographic steps of several Ångströms in height have been observed at the 180º domain boundaries on the cleaved surface of TGS crystals by Bluhm et al [39] and Eng et all [25, 53]. This effect was explained by the relative shift of atom positions in opposite domains. An additional factor, which can affect the surface topography and reveal domain structure, is the different etching behavior of positive and negative domains. Selective etching with subsequentt topographic imaging has been used to reveal nanoscale domains in LiNbO3 crystals [29, 54]. For hydrophilic materials such as TGS and GASH, exposing a sample to humid atmosphere can reveal domains due to selective surface etching by the water vapor. Topographic imaging of the etched surface can be used for identification of domain polarity [15, 37, 39]. At the same time, this feature of TGS could be a complicating factor: fine morphological structures of ferroelectric domains on opposite cleavage faces of TGS vary strongly even for domains of equal polarity. Etching of positive domains can result both in etch hole formation and recrystallization of islands from the saturated solution at the surface, depending on which molecular layer is exposed to ambient air after the cleavage. Etch patterns can be easily confused with domain structure. Another mechanism, which can lead to domain topographic contrast, is surface corrugation at the 90º domain walls separating domains with in-plane polarization (adomains) and out-of-plane polarization (c-domains). Using this approach, a-c-domain structure has been observed in BaTiO3 and PbTiO3 crystals and PZT thin films [12, 4552]. A difference between a and c lattice constants of the tetragonal cell produces a lattice distortion at the junction of a- and c-domains and surface inclination with a characteristic angle determined as θ = π 2 − 2 arctan(a / c ) (Fig. 5). Domain structures consisting of alternating a- and c-domains arise to reduce elastic energy in mechanically strained ferroelectric samples, such as epitaxial thin films [55, 56, 57, 58, 59]. SFM can provide a simple and nondestructive method for studying domain patterns in epitaxial ferroelectric films by topographic imaging of their surfaces. Figure 5 shows a topographic image of an epitaxial Pb(Zr0.20,Ti0.80)O3 film. The a-c-domain arrangement appears as a rectangular structure with heightt variations in the range of 1.5-3.5 nm, occurring as a result of twinning between a- and c-domains. A value of surface tilting of approximately 2º was measured at the 90º domain boundaries, which is consistent with the c/a ratio of the unit cell of the film at room temperature. Considering that the tetragonality of a PZT film with Zr/Ti ratio of 20/80 is about 4%, the 90º-domain wall should stand at an angle of 43º44′ to the polar direction. The relative tilt between the surfaces of two adjacent a- and c-domains, therefore, will be 2º32′, which fits fairly well with the value obtained from the SFM measurements. There are obvious limitations on the applicability of the SFM topographic mode for domain imaging. Any treatment of the surface during sample preparation inevitably eliminates the fine structure of morphological steps associated with domain patterns. Therefore, only crystals with cleavage planes, like TGS and GASH, are suitable for SFM topographic studies. Also, since formation of 180° domain walls does not influence the surface topography, this method is not applicable for imaging of domain structure consisting of antiparallel c-domains, which is of direct interest for investigation of the polarization reversal processes in ferroelectrics. In some limited cases, the topographic mode can be used for visualization of opposite 180º domains via

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detection of the static piezoelectric sample deformation induced by an external dc bias [60] as will be discussed in one of the following sections.

Figure 5. (a) Topographic image of an epitaxial PZT film showing a rectangular structure of a and c domains. (b) Lattice matching at the 90º-domain wall through the formation of a strained unit cell. Twinning occurs on the (101) plane. Arrows indicate the polarization vectors [49].

4.3. DOMAIN IMAGING VIA NONLINEAR DIELECTRIC RESPONSE Recently, Cho et all have developed a pure electrical dynamic method of domain delineation [61, 62, 63, 64]. This method, termed scanning nonlinear dielectric microscopy (SNDM), is based on the detection of the capacitance variation with an alternating electric field. To measure the capacitance variation, Cho et all developed a special lumped constant resonator probe using an electrolytically polished tungsten needle and a LC resonance circuit operating in the microwave frequency range. Application of the modulation voltage E (in the range of 100 Hz to 1000 Hz) across the sample leads to the oscillating change ∆Cs in the capacitance between the needle and the bottom electrode due to the nonlinear dielectric response of the sample with the first harmonic component proportional to the nonlinear dielectric constant ε 333 :

∆C Cs ε 333 = E cossωt Cs ε 33

(7)

where Cs and ε 33 are a static capacitance and a linear dielectric constant, respectively. The change in the capacitance is measured by detecting the modulated high-frequency signal (around 1.3 GHz) of the oscillator using a demodulator and a lock-in amplifier. The sign of an even rank tensor, such as the linear dielectric constant, does not depend on the polarization direction. On the other hand, the lowest order of the nonlinear dielectric constant ε 333 is a third-rank tensor, similar to the piezoelectric constant, so the sign of ε 333 changes with inversion of the spontaneous polarization. Therefore, a polarization map can be obtained by point-to-point detection of the field-induced changes in the nonlinear dielectric constant. This method, as it is designed, allows nanoscale detection of antiparallel 180º domains in the surface layer with a thickness much smaller than the probe size (< 10 nm). According to Ref. [65] sub-nanometer lateral resolution can be obtained by detecting the higher order nonlinear dielectric constants. However, in this case the imaged region will become even shallower.

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Figure 6. (a) Probe configuration in SNDM, (b) a sketch and (c) two-dimensional image of the 90° a–c domain structure in a BaTiO3 single crystal [62].

Figure 6 shows a two-dimensional SNDM image of a-c-domain structure in barium titanate single crystal. The sign of ε 333 in the +c domain is negative, whereas it is positive in the -c domain. Furthermore, the magnitude of ε111 is zero in the a-domain. It is possible to measure ferroelectric polarization parallel to the sample surface by detecting ε 311 constant using different configuration of electrodes, which makes SNDM suitable for three-dimensional domain structure reconstruction. Since in SNDM the probing tip is in contact with the sample surface, nanoscale domain dots can be switched by applying a relatively low dc bias to the probe, which in combination with high spatial resolution can be used for ultrahigh-density data storage [63]. Closely related near-field scanning microwave techniques have been used for domain imaging and dielectric t constant measurements in single crystals of LiNbO3, BaTiO3, and deuterated triglycine sulfate and thin films of Ba0.6Sr0.4TiO3 [66, 67, 68, 69]. However, the lateral resolution has been just below 1 µm due to the size of the inner probe of the resonator. 4.4. DOMAIN IMAGING VIA STATIC PIEZORESPONSE The next domain imaging method makes use of the piezoelectric properties of ferroelectrics and therefore is often referred to as piezoresponse. It is based on the detection of local piezoelectric deformation of the ferroelectric sample induced by an external electric field. Since all ferroelectrics exhibit piezoelectric properties, application of an external voltage results in the deformation of a ferroelectric sample. Depending on the relative orientations of the applied field and the polarization vector, sample deformation can be in the form of elongation, contraction or shear. For the converse piezoelectric effect, the field-induced strain S j can be expressed as [70]:

S j = dij Ei where dij is the piezoelectric coefficient and Ei is the applied field.

(8)

On the other hand, using the thermodynamic approach it can be shown that the piezoelectric coefficientt relates to the spontaneous polarization Ps via the following expression [71, 72]:

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dij = ε im Q jmk Psk (9) is the dielectric constant and Q jmk is the electrostriction coefficient. For a

where ε im single domain ferroelectric of tetragonal symmetry, the relation between the piezoelectric coefficients and the polarization in the reduced matrix notation can be written as: d33 = 2ε 33Q33 Ps 3 (10) The d33 , or longitudinal piezoelectric coefficient, represents an expansion or contraction of the sample along the polar direction when the applied field is parallel to it. The d31 , or transverse piezoelectric coefficient, represents an expansion or contraction of the sample in the direction perpendicular to the applied field. The d15 coefficient describes shear deformation of the ferroelectric sample. The linear coupling between the piezoelectric and ferroelectric constants infers that the domain polarity can be determined from the sign of the field-induced strain. Application of the electric field along the polar direction results in the elongation of the domain with polarization parallel to the applied field and in the contraction of the domain with opposite polarization. The field-induced strain in this case can be written as:

S=

∆L L

= ±d ± 33 E

(11)

where ∆L is the sample deformation and L is the sample thickness. Equation (4) can be rewritten as: ∆ = ±d ∆L ± 33V (12) where V is an applied voltage. The ± sign reflects the opposite piezoelectric coefficients for antiparallel domains. Therefore, opposite domains can be visualized by monitoring their voltage-induced surface displacement. Due to its extremely high vertical sensitivity, nanoscale topography variations can be routinely measured in SFM. However, domain imaging based on detecting the static piezoelectric deformation is difficult to implement unless a sample has a very smooth surface. In a sample with an average surface roughness of several nanometers per square q micron, the static cantilever deflection due to the ppiezoelectric deformation (typically of the order of several Ångströms) will be superimposed on the much larger deflection signal due to the surface roughness which will make domain imaging very problematical. From Eq. (12) it follows that increasing the imaging voltage can infinitely enhance the contrast between opposite c-domains. However, there is a strict limitation imposed on this parameter: to perform nondestructive visualization of domain structure, the imaging voltage should be kept below the coercive voltage of the ferroelectric sample. In addition, a high imaging voltage will lead to an increased contribution of the electrostatic signal to the tip-sample interaction, which in some cases can obscure the domain image. Given that a typical value of the coercive field in a 200 nm thick Pb(Zr,Ti)O3 ferroelectric film is approximately 50 kV/cm, the imaging voltage should not exceed 1 V, otherwise the imaging process will change the domain structure by inducing the polarization reversal. In a PZT film with a d33 constant of about 200 pm/V the surface displacement induced by an external voltage of 1 V will be only 0.2 nm. Obviously, such a displacement could not be reliably detected in ferroelectric films

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where topographic features can be of the order of several nanometers. The static approach can be applied in some limited cases, for example to ferroelectric samples with relatively high values of piezoelectric constants and coercive fields. Wang et al [60] used this approach to delineate domains in a doped crystal of Sr0.61Ba0.39Nb2O6 (SBN) known for a high concentration of the pinning centers which gives rise to increased local coercive fields. Due to this feature of the SBN sample, even under an applied voltage of 200 V there exist non-switched c-domains antiparallel to the external field. At the same time, this voltage is high enough to produce surface indentation of about 2 nm due to contraction and elongation of opposite domains, which makes them discernible in the topographic mode. Another interesting observation reported in Ref. [60] includes the photostimulated nanoscale topographic changes due to the piezoelectric effect by an internal electric field. 4.5. DOMAIN IMAGING VIA DYNAMIC PIEZORESPONSE - PIEZORESPONSE FORCE MICROSCOPY A problem of low sensitivity of a static piezoresponse mode has been circumvented by employing a dynamic piezoresponse imaging method based on the voltage-modulation approach, which increases sensitivity by three orders of magnitude. In this approach, known as piezoresponse force microscopy (PFM), an ac modulation (imaging) voltage V = V0 cossωt is applied to the ferroelectric sample and surface displacement is measured using a standard lock-in technique by detecting the vertical vibration of the cantilever, which follows sample surface oscillation. A domain map can be obtained by scanning the surface while detecting the first harmonic component of the normal surface vibration (vertical piezoresponse): ∆ =∆ ∆L ∆L0 cos((ωt + ϕ ) (13) where ∆L ∆ 0 = d33V0 is a vibration amplitude and ϕ is a phase difference between the imaging voltage and piezoresponse, which provides information on the polarization direction. With the modulation voltage applied to the probing tip, positive domains (polarization vector oriented downward) will vibrate in phase with the applied voltage so that ϕ(+) = 0º, while vibration of negative domains (polarization vector oriented upward) will occur in counter phase: ϕ(− ) = 180º. The dynamic piezoresponse mode has been developed for detection of polarized regions in ferroelectric copolymer films of vinylidene fluoride and trifluoroethylene [73] and quickly became one of the most widely used methods for nanoscale characterization of ferroelectrics. The pioneering studies performed by Franke et al. [74], Gruverman et al [36, 75] and Hidaka et al [76] demonstrated the applicability of PFM for high-resolution visualization and modification of domain structure in PZT thin films. One of the significant advantages of the PFM method is that it also allows delineation of domains with polarization parallel to the sample surface (a-domains) [51, 77, 78]. In the lateral PFM approach, developed by Eng [77], a-domains are visualized by detecting the torsional vibration of the cantilever. Application of the modulation voltage across the sample generates sample vibration in the direction parallel to its surface due to the piezoelectric shear deformation. This surface vibration, translated via the friction forces to the torsional movement of the cantilever, can be detected in the

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same way as the normal cantilever oscillation in vertical PFM. The amplitude of the inplane oscillation (lateral piezoresponse) is given by: ∆ 0 = d15 V0 ∆X (14) while the polarization direction can be determined from the phase signal since oscillation phases of opposite a-domains differ by 180º. It should be noted that Eq. (14) could be used only when the in-plane polarization vector is perpendicular to the physical axis of the cantilever. However, in the general case the in-plane polarization vector can be oriented arbitrary with respect to the cantilever. Therefore, to obtain a complete picture of the in-plane distribution of polarization, X and Y components of the lateral piezoresponse image should be recorded by physically rotating the sample by 90º. Although quantitative analysis of the lateral piezoresponse signal is rather difficult due to the complexity of the friction mechanism involved, it can readily provide valuable information on in-plane distribution of polarization facilitating the 3dimesional reconstruction of the nanoscale domain arrangement. Figure 7 presents experimental results on simultaneous acquisition of vertical and lateral piezoresponse images as well as topography of a PbTiO3 film. Grains in the central part of the topographic image (Fig. 7(a)) are characterized by a strong vertical piezoresponse signal (bright contrastt in Fig. 7(b)), while their lateral piezoresponse signal is rather weak (gray contrast in Fig. 7(c)), suggesting predominantly out-of-plane orientation of the polarization vector. On the other hand, grains in the lower part of the topographic image exhibit gray contrast in Fig. 7(b) and bright contrast in Fig. 7(c), which is an indication of in-plane polarization.

Figure 7. Topographic (a), vertical piezoresponse (b) and lateral piezoresponse (c) images of the lead titanate film. Grains in the center have bright contrast in (b) and gray contrast in (c) suggesting out-of-plane polarization. Grains in the lower part of the image exhibit gray contrast in (b) and black-white contrast in (c), 2 which is an indication of the in-plane polarization. The scanning area is 0.9x0.9 µm (Image by B. Rodriguez).

In terms of exciting the piezoelectric vibration of the sample, there are two main approaches in PFM. In one approach, the vibration is generated locally by applying a modulation voltage between the bottom electrode and the conductive SFM tip, which scans the bare surface of the film without a deposited top electrode. A great advantage of this approach is a possibility of establishing correlation between domain configurations and film microstructure. In addition, this method can be used for nanoscale domain writing and direct investigation of domain wall interaction with microstructural features, such as defects and grain boundaries, for local spectroscopy measurements and investigation of electrical and mechanical coupling between adjacent

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grains. Furthermore, this approach offers extremely high resolution, potentially allowing investigation of the microscopic mechanism of the domain wall motion. However, the electric field generated by the SFM tip in this configuration is highly inhomogeneous, which makes quantitative analysis of the field dependent parameters difficult. This problem is exacerbated by the likely presence of a contamination layer at the film surface, which increases the resistance of the tip-sample electric contact. As a result, an increased time constant of the electric circuitry makes it difficult to extend the experiments on switching behavior to the micro- and nanosecond range, which is of direct application interest. In an alternative PFM approach, domain structure can be visualized through the top electrode of a ferroelectric capacitor. In this case the piezoelectric vibration is generated in a film region underneath the deposited top electrode which is much larger that the tip-sample contact area. The modulation voltage can be applied either by using an external wire attached to the top electrode or, in the case of a micrometer size electrode, directly through the conductive SFM tip. In both cases the piezoelectric displacement is probed locally by the SFM tip. In such a configuration, a homogeneous electric field is generated throughout the ferroelectric film, which allows quantitative treatment of domain wall dynamics and investigation of polarization reversal mechanism in ferroelectric capacitors. Due to the reduced time constant, fast pulse switching and transient current measurements can be accomplished in submicron capacitors, thus making PFM suitable for memory device testing. Combined PFM studies of the ferroelectric t films and capacitors bring about complementary information and provide direct assessment of the effect of the electrical and mechanical boundary conditions on domain stability and polarization reversal. It is generally accepted that the PFM method is the most suitable technique for investigation of the domain structure in ferroelectric materials, particularly in thin films [79]. This view is based on several key features of PFM, such as (1) high lateral resolution (better than 10 nm [80, 81]), (2) a possibility of 3-dimensional reconstruction of domain structure [51, 77, 82, 83], (3) effective manipulation and control of nanosize domains [74-76, 84, 85, 86, 87], (4) nanoscale hysteresis loop measurements [79, 88, 89, 90, 91, 92, 93, 94]. In addition, the applicability of PFM to nanoscale characterization of capacitor structures [95, 96, 97, 98,99, 100, 101] is of direct application relevance since it can be used for testing ferroelectric memory devices. In spite of the apparent simplicity of the PFM method, quantification of the PFM data, particularly in the case of thin films, is nontrivial due to the complexity of the tipsample interaction. Experimental conditions, such as driving voltage, frequency, loading force, cantilever force constant, tip apex radius, ambient environment, as well as physical properties of the samples (thickness, dielectric constants, orientation, defect structure, crystallinity, electrode material) should be taken into account to avoid misinterpretation of the PFM results [102]. Despite of this difficulty, PFM has become one of the main tools for high-resolution characterization of ferroelectric crystals and thin films. PFM can provide crucial information on correlation between domain configurations and microstructural features, basic mechanisms of polarization reversal, the scaling effect and intrinsic variability of properties at nanoscale. One of the examples of the recent breakthrough results made possible due to PFM is characterization of the switching behavior of 0.04 µm2 ferroelectric capacitors [103].

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5. Piezoresponse force microscopy of ferroelectric domains: static and dynamic properties Application of scanning force microscopy to ferroelectric materials opened new possibilities for their characterization, control of ferroelectric properties at the nanoscale and fabrication of regular nanodomain patterns for use in functional devices. 5.1. CHARACTERIZATION Over the last 10 years SFM has proved to be an indispensable tool capable of dielectric, surface potentiometric and electromechanical characterization of ferroelectrics at the micro- and nanoscale level. Application of SFM has rendered direct information on local surface potential and charge distribution, nanoscale domain arrangement with defects and domain kinetics during phase transition t [17, 23, 32, 34, 37, 48, 104]. SFM has been successfully applied to high-resolution studies of static and dynamic properties of domains in ferroelectric thin films and capacitors [74-103]. Recent achievements facilitated by the SFM approach include manipulation of domains as small as 20 nm in diameter [63, 79], direct study of domain nucleation and growth during polarization reversal [96], investigation of the mechanisms of polarization decay and ferroelectric fatigue at the sub-grain level [75, 80, 86, 89], evaluation of the switching behavior of individual nanocapacitors via hysteresis loop measurements [97-102] and investigation of the dielectric breakdown mechanism [105]. Application of PFM made possible directt investigation of the microscopic mechanisms of the degradation effects, such as fatigue, imprint and retention loss, in ferroelectric thin films. These studies have been performed both in thin films without top electrodes and in capacitor structures. One of the first attempts of studying the fatigue effect in PZT thin film capacitors by PFM had been undertaken by Colla et al [106]. They found that the polarization suppression was due to the "region by region" or "grain by grain" freezing of polarization. This finding is consistent with the data obtained by Gruverman et al [107] who performed measurements on the free film surface. This approach allowed visualization of individual grains with frozen polarization. The most likely mechanism was considered to be charge entrapment at the film interfaces. Another degradation effect the mechanism of which was uncovered by PFM was retention loss [75, 80,108,109]. It has been shown that the loss of polarization occurs as a result of spontaneous backswitching. However, reports on the retention properties observed using SFM-based methods have been inconsistent. For example, authors of Ref. [76] reported a retention time of about 70 years for 90-110 nm domains formed in Pb(Zr,Ti)O3 (PZT) thin films. On the other hand, retention loss within the time range of several days has been observed in [75]. There is also no consensus on the time dependence of retention loss. While some groups have reported a log linear time dependent decay of polarization suggesting a broad distribution of relaxation times [110], other researchers have deduced stretched exponential retention behavior suggesting a random walk type mechanism of retention loss in PZT films [75]. The backswitching mechanism also varies depending on type initial domain structure and film crystallinity. In polycrystalline films it proceeds via the motion of a single 180º domain wall which leads to complete polarization backswitching in an individual grain.

239

On the other hand, in epitaxial films the mechanism of backswitching is nucleation of 180º domains. Other studies indicate that retention characteristics vary widely depending on various parameters such as film thickness, domain size, poling time and voltage. 5.2. DOMAIN CONTROL Scanning force microscopy provides a unique opportunity for controlling the ferroelectric properties at the nanoscale and direct studies of the domain structure evolution under an external electric field, which cannot be matched by previously available techniques. A conductive probing tip can be used not only for domain visualization but also for modification of the initial domain structure. Application of a small dc voltage between the tip and bottom electrode generates an electric field of several hundred kilovolts per centimeter, which is higher than the coercive voltage of most of ferroelectrics, thus inducing local polarization reversal. When an electric field is applied opposite to the polarization direction of a singledomain ferroelectric, the switching mechanism involves several steps [111]. First, new domains with the reverse polarization direction nucleate, mainly at the surface, and then grow through the sample thickness (forward growth). Second, the grown domains expand sidewise as new domains continue to form. Finally, the growing domains coalesce to complete the polarization reversal of a ferroelectric. The contribution of the forward and sidewise growth mechanisms is a function of the applied field and the electrodes and to a large extent determines the switching time. Until recently, observation of domain dynamics during switching in thin films has not been performed due to the absence of an appropriate experimental technique. It has become possible with the help of the PFM method. This approach allows direct studies of the mechanism of polarization reversal, measurements of the key parameters of domain dynamics such as nucleation rate, domain wall velocity, spatial distribution of nucleation sites, etc. However, a poor time resolution, which is determined by the time required for image acquisition makes the in situ measurements of domain dynamics during fast switching processes difficult. While SFM can be readily used to investigate slow polarization relaxation processes with characteristic times of the order of minutes and above, it is a challenge to deduce the mechanism of domain transformation when polarization reversal occurs in a matter of microseconds and faster. This problem is usually circumvented by studying domain structure dynamics in a quasi-static regime using step-by-step switching. This method has been previously used at the macroscopic level in classical switching experiments on correlating the domain structure evolution and transient current in ferroelectric crystals [111] and later was applied to thin films [112, 113]. In this approach, partial reversal of polarization is generated by applying a voltage pulse shorter than the total switching time with subsequent piezoresponse imaging of the resulting domain pattern. By applying a sequence of voltage pulses of successively increasing duration and acquiring piezoresponse images after each pulse a consistent picture of time dependent behavior of domain structure can be obtained providing information on the domain wall velocity, its spatial anisotropy and its field dependence. To avoid data misinterpretation due to spontaneous backswitching between the pulses, stability of the produced intermediate patterns should be checked by acquiring domain images at different time intervals after single pulse application. To describe the sidewise expansion of the domain it is

240

necessary to take into account the field dependence of the domain wall velocity and the spatial distribution of the electric field generated by the probing tip [114]. A similar approach has been used by Hong et al [96] to investigate the domain nucleation and growth during polarization reversal in PZT film capacitors - the first study of this kind for thin films. In their study, domain imaging had been performed with an imaging ac bias superimposed with a dc bias that was incrementally increased from zero to a value above the macroscopic coercive voltage. At a given dc bias an intermediate step of polarization reversal had been recorded. It was found that nucleation and forward growth of the nuclei initially occurred at some preferential sites at the fields below the coercive one. At the higher fields, the number of nuclei increased significantly. Important point is that the sidewise expansion of the grown nuclei played little role in the polarization reversal, suggesting the forward domain growth being the rate-limiting mechanism in PZT capacitors. 5.3. FABRICATION SFM capability of domain control creates a possibility of developing ferroelectrics with specifically designed nanoscale domain patterns, which can find application in novel electronic devices. For example, Hidaka et all [76] and Cho et all [63] proposed to use SFM as a basis for high-density data storage with a ferroelectric layer as a recording medium and nanoscale domains as data bits. Recently, a pioneering work by Kalinin et all [115] has demonstrated the feasibility of practical application of ordered domain structures for fabrication of nanostructures. Manipulation of polarization of ferroelectric substrates in SFM opens a new way to assembly nanostructures consisting of oxide substrates, metal nanoparticles, and organic/biological molecules. The idea of using ferroelectric templates for nanofabrication is based on utilizing the local surface electronic properties and surface chemical reactivity, which can be controlled by switching the direction of spontaneous polarization. On the surface of a ferroelectric, an abrupt change in the normal component of the spontaneous polarization results in the bound polarization charges and in the appearance of a depolarizing field [116]. Energy consideration requires that this field must vanish outside the ferroelectric, i.e. it must be compensated. In a ferroelectric capacitor, this field can be completely compensated (screened) by the charges on the electrodes. In addition, screening by charge absorption at the surface can be accompanied by accumulation of the free carriers in the ferroelectric sample just near its surface. Surface potential, determined by the relative contribution of the external (surface charges) and internal (non-equilibrium carriers) screening mechanisms, is a crucial parameter for assembling molecular structures. Therefore, investigation of the interface properties and deconvolution of the external and internal screening in ferroelectrics is critical for developing new nanofabrication methods using domain patterned ferroelectric templates. Several groups reported generation of the regular domain patterns with nanoscale periodicity using SFM [36, 63, 76, 113, 117, 118]. Nanodomain patterns can be successfully fabricated not only in thin films but also in bulk crystals in spite of the fact that the tip-generated electric field quickly decreases with distance to the bulk of the sample [52, 117]. Examples of SFM-fabricated nanodomain patterns in BaTiO3 and Sr0.61Ba0.39Nb2O6 single crystals are shown in Fig. 8.

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Figure 8. SFM-generated nanoscale domain patterns in (a) BaTiO3 and (b) Sr0.61Ba0.39Nb2O6 [118] single crystals.

6. Conclusion t devices generated a strong need for extensive Rapid development of ferroelectric-based investigation of the nanoscale properties of ferroelectric materials. Application of scanning force microscopy to ferroelectrics opened new possibilities not only for their high-resolution characterization, butt also for control of ferroelectric properties at the nanoscale. This paper presented a review of the recent advances in this field. It would not be an exaggeration to say that SFM had allowed a breakthrough in studying such problems as the basic mechanism of polarization reversal in ferroelectric films, mechanisms of degradation effects, reconstruction of domain structure in ferroelectric films at the sub-grain level and other problems of fundamental and technological importance. SFM of ferroelectrics has a very strong potential in fabrication of functional nanostructures.

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SCANNING TUNNELING SPECTROSCOPY Local density of states and spin distribution of interacting electron systems

M. MORGENSTERN Inst. of Applied Physics, Hamburg University, Jungiusstr. 11, D-20355 Hamburg, Germany e-mail: [email protected]

Contents 1. 2. 3.

4.

5. 6.

Introduction Scanning Tunneling Spectroscopy 2.1. Spin-polarized Scanning Tunneling Spectroscopy Experimental setup 3.1. Measurements on InAs 3.2. Measurements on Fe-islands Experimental results on InAs 4.1. B = 0 T 4.2. B = 6 T 4.3. Conclusions Experimental results on Fe-islands Summary

Abstract Scanning tunneling spectroscopy (STS) and its extension, the spin-polarized scanning tunneling spectroscopy (SPSTS), reveal basic information on the spatial distribution of electron systems. STS measures the local density of states given by the sum over squared single-particle wave functions at a chosen energy, while SPSTS detects the spatial distribution of the spin at the same energy. The application of these techniques on electron systems, which are not spatially uniform, is of particular interest. Here, we discuss two examples. First, the paradigmatic electron system located in the quasiparabolic conduction band of InAs is investigated and different types of electron phases are identified depending on the dimension of the system and the applied magnetic field. Second, the spin-polarized technique is used to determine the domain configuration of ferromagnetic particles at different heights. Keywords: scanning tunneling spectroscopy, electron systems in InAs, domains in ferromagnetic particles. 251 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 251-273. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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1. Introduction The development of low-temperature scanning tunneling spectroscopy (STS) provides the opportunity to measure the local density of states (LDOS ( S) with high spatial and energy resolution [1, 2]. As long as a single particle description is adequate, the LDOS is simply defined as: G G LDOS ( E , r ) = ¦ | Ψi ( E , r ) | 2 (1) ∆ ∆E G with Ψi being the single particle wave functions at energy E as a function of position r and ∆E ∆E being the energy resolution of the experiment. Obviously, the LDOS S is straightforwardly linked to the Schrödinger equation and is, thus, a basic property of each electron system. Working at low temperature reduces ∆E ∆ , which means that less wave functions contribute to the signal. In many electron systems the wave functions are spin-degenerate and the information given by the LDOSS is rather complete. However, in particular, in interacting electron systems the spin-degeneracy is lifted and a distinction between the different spin channels is necessary. The recent development of spin-polarized scanning tunneling spectroscopy (SPSTS) allows this distinction by using ferromagnetic tips causing different tunneling probabilities for different spin channels [3, 4]. The understanding of interacting electron systems is a major challenge in solid state physics. Often the interacting systems are not spatially uniform and a local technique like STS can give additional insight into the behaviour of the system [5-14]. It is well known that a rather systematic study t of interaction effects can be performed on degenerately doped III-V semiconductors [15, 16]. Here, one deals with only one band exhibiting a nearly parabolic dispersion and the influence of the interaction parameters like dimension, potential disorder, electron density and magnetic field can be varied systematically. Ionized dopants provide the potential disorder, i.e. deviations from the periodicity of the crystal potential. A low electron density, tuned t e.g. by a gate, increases the importance of electron-electron interactions. Finally, the magnetic field can be used to quench the kinetic energy (Bloch wave energy). This can lead to systems which are largely determined by the interaction of the electrons with the potential disorder and/or mutual electron-electron interactions [17]. Many different electron phases have been identified leading to a variety of physical effects such as metal-insulator transitions [18], quantum Hall transitions [19], composite fermion phases [20], Wigner crystals [21] or Luttinger liquids [22]. Even quantum Hall ferromagnets [23] and quantum Hall superconductors [24] have been found. Such electron phases are intensively studied by macroscopic means like transport, magnetization and optical spectroscopy [25]. On the other hand, the microscopic properties have barely been probed. The latter is rather important, since detailed predictions exist from theory (see e.g. [26-28]). It is, thus, straightforward to apply scanning probe methods which allow the study t of microscopic properties on a nm-scale [29-31]. Here, we summarize the first systematic STS study of a III-V-semiconductor (InAs) varying magnetic fields and dimensions [32-39]. Although the spin distribution was not measured on the InAs samples, it is well known that the spin is also an important quantity in such systems. The rather new technique of SPSTS would be adequate to measure it. However, so far SPSTS is only

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applied to ferromagnetic materials [3, 4, 40], where the LDOSS is spatially uniform and the distinction between spin-related and LDOS-related contributions to the signal is straightforward. In the second part of this article, we will show some more recent examples revealing different domain patterns on Fe-islands of different size. In particular, it will be shown that the high spatial resolution is necessary to probe details of the domain configuration like the core size in a magnetic vortex structure [41].

2. Scanning Tunneling Spectroscopy In scanning tunneling microscopy (STM), a metallic tip is positioned close to a sample surface and the tip is moved parallel to the surface. One detects the tunneling current I as a function of applied voltage V and lateral position of the tip with respect to the surface ((x,y) [1]. For elastic tunneling, which is the major tunneling channel in usual STM/STS experiments [42], and z-distances, where tip LDOSS and sample LDOSS are mutually not influenced, a matrix approach developed byy Bardeen is appropriate to describe I [43]. Since the resulting expression is still complicated, Tersoff and Hamann introduced the additional assumption that the tip exhibits a DOS consisting of s-like states [44,45]. That lead to the expression: eV I (V , x, y , z ) ∝ ³ ρ t (eV − E ) ⋅ ρ s ( E , x, y ) ⋅ T ( E , V , z ( x, y )) dE (2) 0 Here ρt(E) is the tip LDOSS at the end of the tip, ρs(E,x,y) is the sample LDOSS at the surface and T(E,V,z(x,y)) is a transmission coefficient basically describing the spatial overlap of states from sample and tip. The integral covers the region of energetically overlapping occupied and unoccupied states. To extract the sample LDOS ρs from the data, T(E,eV,z) has to be known. One can

ˆ , where Φ ˆ is measure it using I(V,z) ∝ T(E=eV,V,z), which is valid as long as V << Φ the effective barrier height at V = 0 mV [46]. Measuring I(U,z) usually confirms the assumed exponential shape ˆ − e | V | / 2) ⋅ z ) T ( E = eV , V , z ) ∝ exp(− A ⋅ (Φ

(3)

ˆ depends with A = 8m / η (m: electron mass, η : Planck's constant). As expected Φ on the tip. It is mostly found to be smaller than the work functions of the tip and the ˆ is not completely clear, but it is sample [47,48]. The reason for the small values of Φ ˆ is regarded as a likely that image charge effects playy an important role. In this work, Φ measurable quantity, i.e. I(U,z) curves are recorded for each set of measurements to ˆ . Mostly, Φ ˆ ≈ 1.4 eV is found on InAs(110) [46]. determine the actual Φ Direct access to the LDOSS is given by the differential conductivity dI/dV, V i.e.

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dI (V , x, y, z ) ∝ ρt (0) ⋅ ρ s (eV , x, y ) ⋅ T ( E = eV ,V , z ) dV eV

+ ³ ρt (eV − E ) ⋅ ρ s ( E , x, y ) ⋅ 0 eV dρ (eV − E ) t

+ ³

0

dV

dT ( E ,V , z ) dE dV

(4)

⋅ ρ s ( E , x, y ) ⋅ T ( E ,V , z ) dE

ˆ and can then be neglected. A The second and third term are small if V << Φ quantitative estimate shows that they contribute less than 10 % to dI/dV V as long as ˆ ≤ 0.1 [46]. Thus, at low V the lateral distribution of dI/dV(x,y) would directly V /Φ reflect the sample LDOSS at the corresponding energy E, if z is constant. However, since images are usually obtained by stabilizing the tip at each ((x,y)-point, z(x,y) can fluctuate. By recording z(x,y) in parallel to dI/dV(x,y) and measuring the I(z)-dependence of the corresponding tip at V V, one can compensate this error resulting in [38]

LDOS ( E = eV , x, y ) = ρ s (eV , x, y ) ∝

dI / dV (V , x, y ) I (V , z ( x, y ))

(5)

Thus, the lateral dependence of the LDOSS can be directly measured. Often it is not necessary to use eq. (5), but sufficient to assume LDOS(eV,x,y) ∝ dI/dV(V,x,y). This has the advantage that one does not introduce additional noise to the original dI/dV V data by the division. As a rule of thumb, one can keep in mind that corrugations in dI/dV(x,y) of less than 10 % have to be normalized according to eq. (5), while larger corrugations are not sensitive to a changing z(x,y). Assumptions. The assumptions of the above derivation are the following: First, T T=0 K has been assumed, but temperature is easily included by introducing the corresponding Fermi functions. At low T T, temperature basically restricts the energy resolution ∆E ∆E of the experiment, which is additionally influenced by the modulation voltage Vmodd (rms-value) used to detect dI/dV V by lock-in technique. This results in 2 ∆E E = (3.3 ⋅ kT ) 2 + (2.5 ⋅ Vm mod )

(6)

Second, possible tip-surface interactions have to be considered. It is rather settled, that they are not relevant at tunneling resistances above 100 MΩ corresponding to tipsurface distances of about 5 Å [49]. Third, and most important, the restriction to s-like tip states is questionable. Chen has shown that tip states of higher orbital momentum would lead to a replacement of ρsample by its spatial derivative in eq. (2) and (4) [50]. In particular, for px-, py- or pz-parts of the tip state the first derivative along x, y or z should be used. For d-states, one needs the corresponding second derivatives, and so on. Since tunneling into higher orbital tip states requires a strong orientation of the states towards the surface, i.e. along z, one usually detects a derivative of ρsample along z. Anyway, at large enough tip-surface distances the z-dependence of the LDOSS is largely described by e −α z . In case of higher orbital tip states this mainly leads to an additional numerical constant in eq. (2) and (4), if α does not depend on (x,y). The latter is indeed evidenced on the larger length

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scales mainly studied in this work by measuring the spatial dependence of I(z). Consequently, large scale dI/dV-images V represent the LDOSS even if the tip orbital is not s-like. In contrast, atomic scale images are influenced by the derivative effect. There, the apparent corrugation is largely a consequence of a laterally changing α. Chen has shown that using higher orbital tip states generally leads to an increase in corrugation on the atomic scale with respect to the LDOSS [50]. Finally, a word is in order with respect to the interpretation of dI/dV(V)-curves. Being influenced by the LDOS(E), they are influenced by two other effects. First, T(E,V,z) depends on V V. From equation (1.3) one sees that T(E,V,z) gets larger for increasing |V|. V Thus, one should keep in mind that an increase of dI/dV V with increasing |V| V is larger than the corresponding increase of the LDOS(E). Between |V| V = 0 mV and |V| V = 100 mV, this effect can be estimated to be below 25 %. Second, strong features in the DOS(E) of the tip, ρtip(E), can change the appearance of dI/dV-curves. V These features can usually be identified, if one has some knowledge of the sample DOS. Such tips should not be used for measurements. Images and curves presented in this work are either normalized to adequately represent the LDOS(E,x,y) or it has been checked that this normalization is not relevant for the conclusions taken from the data. 2.1. SPIN-POLARIZED SCANNING TUNNELING SPECTROSCOPY In spin polarized scanning tunneling spectroscopy (SPSTS), one uses a ferromagnetic tip. Therefore, the LDOSS of the tip ρt is not identical for the two spin channels ↑ and ↓ [51]. Since the tunneling process is largely spin-conserving, equation (1.4) has to be rewritten using two additive parts for each term. In one part, one replaces ρs and ρt by ρs(↑) and ρt(↑) and in the other one one uses ρs(↓) and ρt(↓). If ρs(↓) = ρs(↑), that does not change anything, since the addition can be performed straightforwardly. However, if this is not the case, one gets access to the local spin polarization of the sample SS(E,x,y) defined as

S s ( E , x, y ) :=

ρ s (↑)( E , x, y ) − ρ s (↓)( E , x, y ) ρ s (↑)( E , x, y ) + ρ s (↓)( E , x, y )

(7)

To see that we start with the spin polarized version of equation (1.4), neglecting the integral terms and assuming that the transmission coefficient T(E=eV,V,z) does not depend on the spin, which results in:

dI (V , x, y, z ) ∝ ( ρt (↑)(0) ⋅ ρ s (↑)(eV , x, y ) + ρt (↓)(0) ⋅ ρ s (↓)(eV , x, y )) (8) dV ⋅T ( E = eV ,V , z ) If one now switches the magnetization direction of the tip by an external field from positive to negative, one interchanges the meaning of ρt(↑) and ρt(↓). After some algebra that leads to:

dI / dV V+ − dI / dV V− (V , x, y , z ) = S s (eV , x, y ) ⋅ S t (0) dI / dV V+ + dI / dV V−

(9)

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with dI / dV+ and dI / dV− being the dI/dV-signal V measured with positive and negative magnetization direction of the tip and St being analogously defined to Ss. Thus, the variation of spin polarization with position can be measured. When spin averaged LDOSS of the sample ρs(E,x,y) does not depend on position, but the spin polarization Ss(E,x,y) does depend on position, it is not necessary to perform the two measurements. Ferromagnetic metals often exhibit such a spatially constant LDOS. Then, one can rewrite equation (1.8) [51]:

dI (V , x, y, z ) ∝ ρ s (eV ) ⋅ ρ t (0) ⋅ (1 + S s (eV , x, y ) ⋅ S t (0)) ⋅ T (eV , V , z ) (10) dV Thus, any contrast in dI/dV(x,y) is caused by local variations of the sample spin polarization, again if z is spatially constant. Finally, one has to consider the fact thatt the spin axis in the above derivation has been fixed by the preferential orientation of spins inside the tip, i.e. the orientation of tip

G

magnetization M t . However, the preferential axis inside the sample could be different exhibiting an angle α with respect to the tip axis. Then one has to include a cos(α)-term. If one investigates domain structures in simple ferromagnets, the preferential axis of the

G

sample M s ( x, y ) spatially varies, while the spin polarization with respect to that axis Sss(E) is spatially constant. Then one rewrites equation (1.10) into:

dI (V , x, y, z ) ∝ ρ s (eV ) ⋅ ρ t (0) ⋅ dV G G (1 + S ss (eV ) ⋅ S t (0) ⋅ cos( M s ( x, y ), M t )) ⋅ T (eV , V , z )

(11)

In that case, one measures the relative orientation of tip magnetization and sample magnetization as a function of position.

3. Experimental Setup 3.1. MEASUREMENTS ON InAs The measurements on InAs are performed with a UHV low-temperature scanning tunneling microscope (STM) working at T = 6 K and in magnetic fields up to B = 6 T perpendicular to the sample surface [52]. Degenerate n-InAs ((N ND = 1.1 (1.8)⋅1016 cm-3) -8 is used. After in-situ cleavage at a base pressure below 1⋅ 10 Pa, the InAs-sample is transferred into the STM and moved down into the cryostat. The procedure results in a clean InAs(110)-surface with an STM-detectable adsorbate density of about 10-7/Å2, an even lower surface vacancy density and a step density well below 1/µm [46]. The adsorbate density does not increase within weeks. The as-cleaved samples are used for the 3DES, 1DES and 0DES measurements. To induce the 2DES, Fe is deposited from an e-beam evaporator. The coverage is determined by counting the atoms and given with respect to the unit cell of InAs(110) [53]. An ex-situ etched W-tip is prepared in-situ by field emission and voltage pulses between the tip and a W(110)-sample.

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Constant-current images are recorded with the voltage V applied to the sample. The differential conductivity dI/dV V is recorded by lock-in technique (f = 1.5 kHz, V modd = 0.420 mVrms). The dI/dV(V)-curves are measured at fixed tip position with respect to the surface stabilized at a current I stab and a voltage Vstab. Maps of the LDOS(E) result either from ((x,y)-arrays of adequately normalized dI/dV(V)-values or from so called dI/dVV images measured directly in constant-current mode at the corresponding V. V V is identified with E-E EF. For better comparison, partly Ekin is given, which is the energy with respect to the known bulk conduction band minimum of InAs. 3.2. MEASUREMENTS ON Fe-ISLANDS The measurements on Fe-islands are performed with a UHV low-temperature scanning tunneling microscope working at T = 14 ± 1 K and in magnetic fields up to B = 2 T [54]. The Fe-islands are prepared in-situ by depositing 7-10 ML of Fe on a stepped W(110) substrate. Either the Fe is deposited at room temperature and subsequently annealed to T = 800 K or directly deposited at T = 700 K. Both lead to asymmetric Fe-islands elongated into the [ 1 1 0 ]-direction. The first procedure leads to smaller lateral extensions of about 4⋅104 nm2 and a larger height (8-9 nm), while the latter procedure produces thinner (4-5 nm) and more extended islands (≈ 8⋅104 nm2). The areas between the islands are covered with a single pseudomorphic ML of Fe [55]. For spin-polarized measurements the ex-situ etched W-tip is flashed in-situ to T = 2300 K before a coating of Cr or Fe is deposited at room temperature. Finally the coating is annealed at T = 550 K. Most of the measurements are performed with the Cr coating minimizing the influence of stray fields of the tip on the sample [56]. It turned out that the magnetization of Cr tips with thickness below 40 ML is preferentially oriented perpendicular to the surface, while thicker coatings usually lead to a parallel orientation [41]. Thus, the former tips are sensitive to the out-of-plane component of the spin, while the latter are sensitive to the in-plane component. It has been checked that the LDOS S of the Fe-islands is laterally homogeneous by recording dI/dV-images V with an uncoated Wtip. Moreover, the identical LDOSS is found on different islands.

4. Experimental Results on InAs The InAs(110) surface is particularly suited for the investigation of the paradigmatic parabolic conduction band of III-V materials by STS. The main reason is that surface states on InAs(110) are about 1 eV away from m the band edges [57]. Thus, measuring at low V exclusively probes the nearly parabolic bulk band of InAs. The band structure of InAs(110) calculated within the Local Density Approximation (LDA) is shown in Fig. 1 [58]. Surface states identified either by their relative intensity in vacuum or by their relative intensity in the surface layer are marked as grey open symbols. Obviously, there are no surface states around 0 eV. Instead, the positive energy region close to EF is dominated by bulk states showing a nearly parabolic dispersion around the Γ -point. The Bloch states of this bulk conduction band marked in Fig. 1 are the subject of this study.

E-EF [eV]

258

bulk cond. band

In-db

k [BZ-units] Figure 1. Calculated band structure of InAs projected on the (110) surface [58]: the LDA calculation uses the FLAPW basis set and periodic boundary conditions in (x,y ( ); a film of nine atomic layers is used in z including the (110)-surface; the reconstruction of the surface is found in agreement with experiments by optimizing the total energy; letters at the kk-axis mark the edges of the surface Brillouin zone (BZ); small closed circles are calculated states and open, grey symbols additionally mark identified surface states; the bulk conduction band investigated in this study and the states corresponding to the In dangling bond (In-db) are indicated.

Another advantage of InAs is its low effective mass mefff=0.023⋅ me and its high gfactor g=14.3. This leads to a large Landau level separation ∆E ∆ELL = ƫeB/mefff and a large spin level separation ∆E ∆ s = gµBB. Thus, the magnetic field B has a large influence on the system. Finally, we found out that the InAs(110) surface can be used to modify the dimension of the parabolic band. On the as-cleaved surface, one probes the usual threedimensional band [38]. Depositing adsorbates on the surface leads to a confinement of the band perpendicular to the surface resulting in a two-dimensional system [53]. A onedimensional system has been found below positively charged step edges [35] and finally, a zero-dimensional system could be induced by using work function differences between the tip and the sample [32]. Figure 2 summarizes the main results by showing the LDOSS in different dimensionality with and without magnetic field. All images are obtained at a similar kinetic energy (voltage) and it has been shown that the electron systems are subject to a similar potential disorder [33,35,36]. Moreover all systems are part of the nearly parabolic conduction band of InAs. To a minor extent, the slightly different electron densities play a role for the LDOS. The main differences are, however, the dimensionality and the magnetic field. Obviously, the LDOSS patterns are rather different.

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3D

1D

2D

0D

100 nm

EF dI/dV [arb.units]

100 nm

5Å

a

100 nm

d

b

-150 -100 -50

c

0

sample voltage [mV]

dI/dV [arb. units]

100 nm

Exp. Fit

h e

f

g

0 10 20 30 40 50 60 70

sample voltage [mV]

Figure 2. LDOSS of the InAs conduction band: (a) 3DES at B = 0 T, Ekin= 50 meV; ring structures are Bloch waves scattered at ionized impurities [38]. Inset: atomically periodic part of the Bloch states with brighter (less bright) bumps corresponding to As (In) atoms [58]; atomic structure does not change with dimensionality or magnetic field; (b) 2DES at B = 0 T, Ekin= 60 meV [36]; (c) 1DES at B = 0 T, Ekin= 0/5/15/20/25/35/45/50/55/60/65/75 meV from left to right [35]; (d) dI/dV-spectrum V of 0DES at B = 0 T; peaks corresponding to confined states are marked by vertical lines [32]; (e) 3DES at B = 6 T, Ekin= 60 meV [39]; (f) V 2DES at B = 6 T, Ekin= 60 meV [37]; (g) 1DES at B = 6 T, Ekin= 5/15/25/35/45/55/65/75 meV; (h) dI/dVspectrum of 0DES at B = 6 T; spin states, as deduced from the shown fit curve consisting of 6 Gaussians are marked by up and down arrows; the spin states of the 0DES are used to probe the sensitivity of the exchange interaction on potential disorder [33].

4.1. B = 0 T In 3D at B = 0 T, circular wave patterns centred t around individual dopants are observed [38]. They result from the scattering of the Bloch waves at the attractive potential of the charged donors. The different appearance of the circular patterns is due to the different depth of the donors below the surface (0-25 nm). Changing the energy of the LDOSimages simply changes the wave length of the patterns in accordance with the dispersion of the nearly parabolic bulk conduction band of InAs. A zoom into the LDOS S is shown in the inset of Fig. 2a. It reveals that the scattered states are indeed Bloch states exhibiting a periodicity corresponding to the unit cell of InAs. The appearance of this periodicity can be reproduced by LDA-calculations [58]. It turns out that the brighter dots are centered at the As atoms, while the fainter dots are centered at the In atoms. This atomic part of the Bloch waves is not changed in different dimensions and at different magnetic fields. Reducing the dimensionality from 3D to 2D leads to a more complicated wave pattern (Fig. 2b). The wave length is rather the same as in 3D and again can be changed by changing the energy in accordance with the dispersion of the bulk conduction band [36]. However, the patterns are not centered around special points of the sample, but

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exhibit a rather homogeneous corrugation consisting of plane wave and circular wave parts. Moreover, the corrugation Cmeas defined as

C meas =

LDOS mean − LDOS min LDOS mean

(12)

with LDOSSmean being the average value of the LDOSS within an image and LDOS Smin being the smallest value, is much larger in 2D. Cmeas amounts to 3 % in Fig. 2a (3D), but is close to 60 % in Fig. 2b (2D). These two differences between 2D and 3D, - larger corrugation and more complicated patterns in 2D -, can be related to the large influence of potential disorder on 2D systems. It is well known that electron systems in dimensions ≤ 2 tend to weakly localize [59]. The reason is that a scattering path of an electron within a 2D system is always closed. Due to the time reversal symmetry within the system, each closed path is possible in both directions (clock-wise and counterclockwise). The corresponding paths can interfere constructively leading to the observed wave pattern (standing waves). In contrast, a closed path in 3D is rather improbable and mainly caused by retroreflection at a certain scatterer. Thus, the interference patterns observed in 3D originate that only from the rare events that an electron is retroreflected at a dopant leading to a faint circular pattern around each dopant. In contrast, in 2D complicated interference patterns corresponding to the complicated closed paths are the main cause of interference and more complicated patterns are observed. Indeed the wave patterns observed in 2D can be largely reproduced by solving the corresponding single-particle Schrödinger equation taking the potential disorder into account but neglecting electron-electron interactions [36].

Figure 3. Histograms of LDOS values observed in the images of Fig. 2: (a) 3DES at B = 0 T, Ekin= 50 meV; (b) 2DES at B = 0 T, Ekin= 60 meV; (c) 1DES at B = 0 T, Ekin= 40 meV; (d) 3DES at B = 6 T, Ekin= 60 meV; (e) 2DES at B = 6 T, Ekin= 60 meV; (f) 1DES at B = 6 T, Ekin= 40 meV; the resulting corrugation Cmeas defined in equation (1.12) is indicated; LDOS Sminn and LDOSSmean are marked in (d).

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Of course, a single weakly localized state would exhibit a corrugation of 100 %, which is larger than the observed LDOSS corrugation of 60 %. Two origins of this reduction in Cmeas are identified. First, the LDOSS is an overlap of several wave functions due to the limited energy resolution ∆E ∆ of the experiment (see eq. (6)). For example, at least N = 30 different wave functions contribute to the image area A displayed in Fig. 2b as calculated by N = DOS ( E ) ⋅ ∆E ⋅ A [36]. Note that, if the extension of the states is larger than the image area, even more states would contribute with part of its intensity distribution. Thus, a single LDOS-value of zero necessary for Cmeas=100 % requires positions within the image area, where all contributing states have zero intensity. The calculations of the LDOSS mentioned above show that this is rather improbable. Instead a corrugation of only 70 % is found within the calculation [36]. The remaining discrepancy of 10 % to the experimental value is due to the finite phase coherence at T = 6 K, which destroys part of the interference patterns in the experiment. Obviously, the measured corrugation Cmeas is an important quantity describing the LDOS. Fig. 3 shows the distribution curves of LDOS-values obtained in different dimensions and at different magnetic fields. The resulting Cmeas is indicated. A strong corrugation is observed in 2D and 1D at B = 0 T in accordance with the prediction that weak localization is relevant in dimensions ≤ 2 [59]. But also the magnetic field increases the corrugation in 3D and 2D as discussed below. In contrast, in 1D, Cmeas is reduced by the B-field. In 1D, we find LDOSS patterns looking like pearl chains (Fig. 2c) [35]. Again the wave length is reduced with increasing energy in accordance with the dispersion of the InAs bulk conduction band. This is demonstrated in Fig. 4a showing the Fourrier k transformation of the real space data. The Fourrier transformation represents the k-space distribution of waves contributing to the LDOSS patterns. For comparison, the expected dispersion of the two 1DES-subbands is marked. Obviously, there is a dominating intensity around these values, but additional intensity mainly at smaller wave vectors. This additional intensity is a consequence of the interaction of the electron waves with the potential disorder. To show this, we again solve the single-particle Schrödinger equation considering the potential disorder, but neglecting electron-electron interactions. The resulting Fourrier transformation is shown in Fig. 4b. Although the patterns are not exactly identical, they appear very similar. Thus, we conclude that our LDOSS patterns can again be largely described by the interaction of the electrons with the potential disorder [35]. To add further evidence to this conclusion, Fig. 4c and d show the measured and calculated Fourrier transformation of another 1DES confined below another step and exhibiting only one subband. The same conclusions can be drawn from these images. The result, that electron-disorder interaction is sufficient to describe the data, is rather surprising, because it is known from theory that clean 1D systems can not be described by single-particle states at all [60]. Instead, the excitations of a 1D system are charge and spin density waves exhibiting different dispersion [22, 60]. Thus, our STS experiment must couple to these excitations. Since, we do not distinguish different spins using an uncoated W-tip, we couple to the charge density wave. However, its dispersion starting from EF should be modified by the electron-electron interaction. The steepness should be increased by the inverse of the so called g-factor defined as

262

g = (1 + ECoul / 2 Ekkin ) −1 / 2 [25,60]. Since the corresponding energies are known for the two systems in Fig. 4, the g-factor can be calculated to be 0.8 and 0.71 for Fig. 4a and c, respectively [35]. The resulting slopes are indicated and we do not find any preferential intensity along these slopes. One might argue that the reason is the influence of the disorder on the system. However, one finds in both systems ECoul > Ekin > Edisorder >> kT , i.e. the electron-electron interaction is the dominating energy scale about a factor of two larger than the energy scale describing the interaction with the potential disorder [35]. Basically, this strange behaviour of a 1DES is not understood so far.

Fourrier transformation (FT) of the LDOS S images in the 1DES; each voltage V corresponds to a different LDOS S image: (a) FT of the images of Fig. 2c; (b) FT of calculated LDOSS images corresponding to Fig. 2c; (c) FT of the LDOSS images of another 1DES; (d) FT of corresponding calculated LDOSS images; calculations only consider electron-disorder interaction, but not electron-electron interaction; curved lines mark the unperturbed single-particle dispersion of the 1DES subbands; straight lines show the expected deviation due to electron-electron interaction [35].

The zero-dimensional system called the tip-induced quantum dot (QD) is described only shortly. Fig. 4d shows a dI/dV-curve V of the QD. The peaks are the quantized states [32]. They are partly degenerate leading to up to 100 electrons within the QD. Since the QD is coupled to the tip, the lateral distribution of the states can not be measured. Instead, the QD is moved with the tip. This can be used to study the influence of potential disorder on the quantized states [32]. Most importantly, it has been found that the lowest energy QD state, - centered in the QD -, directly follows the potential disorder of the sample. The local energy of the lowest peak, thus, indicates the local potential. This can be used to measure potential landscapes as present e.g. in a 2DES. It

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has been exploited to get the input for solving the single-particle Schrödinger equation as described above [36]. 4.2. B = 6 T Next, the data at B = 6 T will be discussed in reversed order. In 0D, the peaks shown in Fig. 2h are split into doublets. The splitting is compatible with the exchange enhanced spin-splitting within the QD as calculated by Hartree-Fock calculations [61]. The enhancement factor found in the calculation as well as in the experiment varies between 1 and 2 depending on the occupation of the QD. More exactly, it depends on the total spin S within the QD which varies between S = 0 and S = 1 depending on the local disorder potential of the sample: the larger S, the larger the enhancement factor. Importantly, one can directly show that the enhancement factor does not correlate with the potential in the center off the QD. Measuring the potential shows that the total energy of the doublets is directly linked to this center potential, while the spin splitting is not [33]. Obviously, the spin splitting is a less local property, which is due to the complicated mixing of occupied levels within the exchange term. In other words, the experiment is a visualization of the nonlocality of the exchange interaction [33]. S data obtained at B = 0 T and B = In 1D, little difference is found between the LDOS 6 T (Fig. 2c and g). Only a slight energy offset of 7.5 meV is observed, which can be traced back to the so-called magneto-confinement [25], i.e. parabolic confinement energies being En = ( n + 1 / 2) ⋅ =ω 0 become magnetoconfinement energies

En = (n + 1 / 2) ⋅ = ω 0 2 + ω c 2 with ωc = eB/mefff being the cyclotron frequency. The small influence of the magnetic field is due to the large ƫω0 ≈ 60-100 meV with respect to ƫωc ≈ 30 meV. Moreover, the corrugation Cmeas is slightly decreased (Fig. 3c and f), which can be straightforwardly explained by the continous destruction of weak localization in magnetic field [25]. More dramatic changes are found in 2D and 3D. Instead of the wave patterns observed at B = 0 T, serpentine structures running irregularly across the image area are observed [37, 39, 62]. In 2D, such structures have indeed been predicted and used to explain the quantum-Hall transitions [26]. They are called drift states. Conservatively estimated, the requirements to observe driftt states are twofold and compare properties of the potential disorder V(x.y) with ƫωc and the magnetic length l B = = / eB :

Vmax ( x, y ) − Vmin ( x, y ) ≤ =ω c 2) ∇V ( x, y ) << =ω c / l B at all (x,y ( ) 1)

Thus, potential fluctuations should not be larger than the Landau level separation and the potential must be smooth on the length scale of lB. Fig.1.5a shows a 2DES potential landscape measured with the help of the tip-induced QD [32, 36]. It fluctuates by about ± 20 meV, which is slightly larger than ƫωc ≈ 30 meV at B = 6 T. Indeed, the V shown in Fig. 5b exhibit Landau levels in magnetic spatially averaged dI/dV-curves field, which are not completely separated. Moreover, the steepest areas in the potential landscape of Fig. 5a exhibit ∇V ≈ 1.5 meV/nm in comparison with ƫωc/llB ≈ 3 meV/nm. Thus, we are close to the conditions required for the observation of drift states.

264

6T

+

B

≈ 2λB(20 nm)

50 nm

50 nm

dI/dV [arb. units]

2.7 % Fe-n/InAs(110)

hωc

6T hωc

5T 0T

E0

E1 EF

-100 -50

0

50

sample voltage [mV]

50 nm

Figure 5. (a) 2DES potential landscape measured with the help of the tip induced quantum dot [32,36]; the potential fluctuates between -20 meV and 20 meV; (b) spatially averaged dI/dV-curves V of the Fe-induced 2DES [37]; B-fields, subband energies E0, E1 of the 2DES, and expected Landau level splittings ƫωc are marked; (c) classical path of an electron around a potential hill of height 20 meV at B = 6 T, lB is indicated; (d)-(i) LDOS-images of the 2DES at B = 6 T recorded at the same position: (d) V V=-82.6 mV, (e) -85.6 mV, (f) -88.6 mV, (g) -91.6 mV, (h) -94.6 mV, (i) -97.6 mV; (j)-(l) LDOS-images at B = 6 T recorded at the same V=-82.6 mV; (k) -85.6 mV, (l) -88.6 mV, (m) -91.6 mV [37]. position: (j) V

Figure 5c visualizes the origin of drift states within a simplified model. A classical electron path is drawn within a potential landscape of similar strength and smoothness as the one in Fig. 5a. The electron moves on a cycloid path around the hill, i.e. the fast circular motion expected in the absence of potential disorder is accompanied by a drift motion along an equipotential line of the hill. The mean energy of such a path corresponds to the cyclotron energy plus the energy of the probed equipotential line. Very similar states are found in a quantum m mechanical calculation [63]. Ando was the

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first to show that drift states running along equipotential lines and having a FWHM of about lB are the solutions of a single-particle 2D Schrödinger equation in sufficiently high magnetic field [64]. Indeed, the states visible in Fig. 2f have a FWHM of 10.6 ± 0.3 nm, very close to lB = 10.5 nm at B = 6 T [37]. The energy dependence of the drift states is shown for two cases in Fig. 5d-i and j-m, respectively. In both cases, the drift states increase in diameter with decreasing energy indicating that the corresponding electrons drift around a potential hill. Note that the appearance of drift states provides a very natural explanation for the metal-insulator transitions accompanying the well-known quantum-Hall-transitions [19]. Since nearly all equipotential lines are closed, nearly all drift states are localized and the sample is nearly always an insulator. However, in the center of the potential landscape, there is one line which transverses the whole potential landscape. This leads to metallic behaviour exactly if the Fermi level crosses that state. At that magnetic field, the transition between different Hall plateaus takes place.

(a) B-field dependence of 3DES corrugation Cmeas at Ekin= 5 meV, the transition to the extreme quantum limit (EQL) is marked [62]; (b) single dI/dV-curves V of the 3DES recorded at the B-fields indicated; an offset, which spatially varies, is subtracted; an ideal V 2-curve is added for comparison (dashed line) [67].

The 3D data in magnetic field also exhibit serpentine structures (Fig. 2e). The width of these structures is again about lB and they show the same energy dependence as the 2D data, i. e. they are also drift states. However, drift states are usually not expected in 3D. The reason is that the drift motion displayed in Fig. 5c requires a restriction of the motion perpendicular to the B-field. 3D electrons can escape from a certain equipotential line due to their motion parallel to the magnetic field [65]. Indeed, the drift states are not observed in 3D below a certain B-threshold, which turns out to be given by the extreme quantum limit (EQL). Only if all electrons are located in the lowest spinpolarized Landau level, drift states are observed [39]. Moreover, the corrugation Cmeas increases with the magnetic field above the EQL as shown in Fig. 6a. The increase in Cmeas is caused by the appearance of an increasing number m of drift states [62]. Since Cmeas is always lower than the corrugation in the 2D system, we conclude that only part of the 3D states are transformed into drift states. A reasonable scenario is based on the fact that the average kinetic energy Ekin of the electrons in 3D is quenched above the

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EQL according to Ekin ∝ B −2 , a consequence of the increasing degeneracy of the Landau level [65]. The electrons t get slower in the direction parallel to B and their probability to be scattered increases. Some electrons become confined in their motion along z. The corresponding states are quasi-two dimensional and can exhibit drift states. The higher the B-field, the more electrons are confined and the more drift states appear. The localization of electrons can also be directly seen in dI/dV-curves. V Theory predicts that localized electrons interacting by their Coulomb potential exhibit a Coulomb gap in the DOSS at EF [66]. In 3D, the gap should be parabolic. Such a gap is indeed found as shown in Fig. 6b [67]. 4.3. CONCLUSIONS Several different LDOSS patterns have been observed in the paradigmatic case of the occupied quasi-parabolic conduction band of InAs. Dimensionality and B-field were tuned systematically and the origin of the different patterns have been identified. However, the investigation of the phase diagram of quasi-free electrons on the local scale is far from complete. As known from m transport measurements, many different phases caused by the electron-electron interaction appear, if one proceeds to lower temperature and lower potential disorder. Thus, a major issue of the future will be to proceed in that direction in order to identify other and partly new electron phases on the local scale.

5. Experimental Results on Fe-Islands Nanoscale ferromagnetic islands are ideally suited for SPSTS investigations, since equation (1.11) can be applied and the obtained dI/dV-signal V is directly proportional to

G G cos( M s ( x, y ), M t ) . Consequently, domain configu-rations can be imaged by SPSTS.

A large contrast is obtained, if SSS(E) ⋅ St(0) is large. Typically, one tries to optimize the contrast by tuning the applied voltage [68]. Moreover, the magnetic domain structure t in nanoscale islands is nowadays of enormous technological interest with respect to magnetic recording, e.g. within the socalled magnetic random access memory [69]. Also developments within spintronics, a proposed new electronics using the spin instead of the charge as the information unit, needs ferromagnetic islands as spin injectors [70]. The exact knowledge of the domain configuration of the ferromagnetic islands is a basic requirement for these technological applications. Fe-islands of different size can be easily prepared on W(110) by depositing Fe at different temperatures. The lateral size of the islands is several 100 nm, while the height varies between 3.5 nm and 10 nm [41]. The domain configuration of such islands is principally governed by three quantities [71]. The exchange stiffness favours a parallel alignment of neighbouring spins and, thus, tries to avoid the formation of several domains within an island. Its main counterpartt is the stray field energy, which is reduced by the formation of domains within an island. The optimal reduction of stray field energy would lead to an alignment of all spins parallel to the edges of the island.

267

For the thin islands investigated here, this strongly favours an in-plane orientation of the spins. But also the in-plane orientation is forced to circulate around the centre in order to be parallel to the lateral edges. The third parameter is a consequence of the spin-orbitinteraction and is called magnetocrystalline anisotropy. It favours certain orientations of magnetic domains with respect to others. The favoured orientation is called easy axis. For the investigated Fe islands, also the magnetocrystalline anisotropy favours an inplane orientation. However, the favoured in-plane direction is different for the Fe atoms within the bulk of the island, i.e.[ 001 ], than for the Fe-atoms on the surface and at the interface Fe/W(110), where it is [ 1 1 0 ] [72]. Consequently, the monolayer covering the W-substrate is always oriented along [ 1 1 0 ]. Also very thin islands are preferentially oriented along [ 1 1 0 ], while the preference of the magnetocrystalline anisotropy for thicker islands is [ 001 ] [72]. In between, both orientations are similar in energy. Which domain pattern is realized now depends on the interplay between the three quantities. Generally, the following rules apply for thin islands [71, 73]: 1) The thicker the island, the more probable is a multidomain state. 2) If the magnetocrystalline anisotropy is large, all domains are oriented along the easy axis. 3) If the magnetocrystalline anisotropy is small, the domains are oriented preferentially parallel to the island edges. The resulting circulating spin configuration is called a vortex. 4) In very asymmetric islands (length/width), t two vortices can be realized. These general rules are indeed found as shown in Fig. 7. The thinnest island exhibits no contrast in the SPSTS experiment, i.e. it is a monodomain island (Fig. 7a). A slightly thicker island shows two domains (Fig. 7b). Here the magnetocrystalline anisotropy of the surface dominates and both domains are oriented along [ 1 1 0 ]. Even thicker islands show four domains and a detailed analysis of the spin orientation of the tip reveals that the four domains are oriented along the edges of the island as marked by arrows in Fig. 7c [41]. Finally, an island of similar height, but larger extension along [ 001 ] shows a different pattern (Fig. 7d). This pattern is compatible m with the double vortex structure sketched in Fig. 7f. The latter is calculated using a micromagnetic simulation of the island, which takes the details of the island size into account [76]. Fig. 7e shows the

G

expected contrast of such a configuration, if M t is oriented along the sketched direction. Obviously, the calculated contrast in Fig. 7e reproduces the observed one in Fig. 7d. Of particular interest is the spin orientation within the vortex structure of Fig. 7c. As discussed above, the vortex structure avoids stray field energy, but costs exchange energy, since the spins are nott oriented in parallel within the vortex. The largest cost in exchange energy obviously appears in the centre of the vortex. To avoid this cost theory predicted already in 1964 that the spin in the centre of a vortex must turn out of plane [74]. Only recently, this out-of-plane component was verified experimentally by magnetic force microscopy [75]. However, only SPSTS was able to resolve the length scale of the area with deviations from m the in-plane orientation [41].

268

h=3.5 nm

h=4 nm h=9 nm

50 nm [001] 100 nm

100 nm [110]

100 nm

h=8 nm

100 nm

h=8 nm

100 nm

h=8 nm

Figure 7. SPSTS results on Fe-islands deposited on W(110): (a) monodomain island; (b) double domain island; (c) island with four domains in flux closure configuration; (d) island with two flux closure configurations; heights h of the different islands are indicated; arrows mark the tentative domain orientations on the islands (note that only the relative orientation of different domains can be unambiguously determined by SPSTS [41]); (e) simulation of the SPSTS contrast resulting from the spin configuration displayed in (f); to G calculate the SPSTS contrast, M t was assumed to be oriented in the indicated direction; (f) spin configuration of the island measured in (d) as resulting from a micromagnetic simulation [76].

269

Fig. 8a and b show two SPSTS images of the centre region of an island in the vortex state. One is measured with a tip being sensitive to the in-plane component and the contrast around the core varies in a cos(Θ)-fashion as expected from a continuous curling of the in-plane spin around the core (see equation (1.11)). The cos(Θ)-shape is indeed evidenced by the line scan on the circle marked in Fig. 8a and displayed in Fig. 8c. The other image (Fig. 8b) is measured with a tip being sensitive to the out-of-plane component and shows only a bright spot in the centre of the core. An angularly averaged line scan away from the spot is shown in Fig. 8d and compared with the result of a micromagnetic simulation [76]. The agreement is nearly perfect evidencing that the width of the core is only determined by two parameters, the exchange stiffness and the stray field energy of the core region. The former tries to increase the size of the vortex core, while the latter tries to decrease it.

Figure 8. SPSTS results of a vortex core: (a) inner area of an island as the one shown in Fig. 7c measured with G a tip being sensitive to the in-plane component of sample magnetization M s ( x, y ) ; (b) similar area measured

G

with a tip being sensitive to the out-of-plane component of M s ( x, y ) ; (c) line scan along the circle marked in (a) (black) in comparison with a cos(Θ)-function (grey); (d) angularly averaged line scan away from the centre as marked in (b) (grey line) in comparison with the result of a micromagnetic simulation (black points) [41].

6. Summary In this article, measurements using scanning tunneling spectroscopy (STS) and spinpolarized scanning tunneling spectroscopy (SPSTS) at low temperature are described. A basic derivation of the physical content of the results of such measurements is followed

270

by two examples, where the techniques are applied. First, STS results on paradigmatic electron systems being part of the quasi-parabolic conduction band of InAs are shown. Different dimensions and magnetic fields lead to largely different distributions of the measured local density of states, which partly could be understood by the basic knowledge on interacting electron systems, but partly lead to surprising results. SPSTS results are presented on nanoscale ferromagnetic islands, where the contrast can be straightforwardly interpreted as a domain contrast. Four different domain patterns are identified and a particular feature of the so-called vortex configuration is investigated on the nm-scale giving a nice confirmation of a 40-year old theory [74].

Acknowledgement It is a pleasure to acknowledge a number of people involved in the work presented. The experimental results have been contributed by A. Wachowiak, J. Wiebe, J. Klijn, C. Meyer, D. Haude, C. Wittneven, R. Dombrowski and M. Bode. Theoretical calculations have been performed by V. Gudmundsson, R. Römer, L. Sacharov, S. Blügel, and A. Kubetzka. Moreover, I like to thank R. Wiesendanger, U. Merkt, T. Matsuyama, D. Weiss, W. Hansen, L. Schweitzer, F. Evers, and S. Kettemann for helpful discussions and support. Financial support by the Deutsche Forschungsgemeinschaft (SFB-508/B4 and Wi 1277/15-2) and the BMBF (13N7647) is gratefully acknowledged.

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NANOINSPECTION OF DIELECTRIC AND POLARIZATION PROPERTIES AT INNER AND OUTER INTERFACES IN FUNCTIONAL FERROELECTRIC PZT THIN FILMS L.M. ENG Institute of Applied Photophysics, Department of Physics University of Technology Dresden, D-01062 Dresden, Germany [email protected]

Contents 1. 2.

3. 4.

5.

Introduction Methods 2.1. Piezoresponse Force Microscopy (PFM) 2.2. Kelvin Probe Force Microscopy (KPFM) 2.3. Pull-off Force Spectroscopy (PFS) Materials Results 4.1. Polarization profile across the PZT film 4.2. Relaxation dynamics within the PZT film 4.3. Local dielectric constant at the PZT surface Conclusion

Abstract We report on novel approaches using scanning force methods [i.e. piezoresponse force microscopy (PFM), Kelvin probe force microscopy (KPFM) and pull-off force spectroscopy (PFS)] in order to deduce the local dielectric and polarization properties on functional ferroelectric PZT thin films both at outer and inner interfaces with a lateral resolution of better than 50 nm. We show that the polarization profile into the depth of the PZT sample varies dramatically being built up at the bottom Pt electrode over a transition layer of more than 200 nm in thickness. Also this interfacial area shows a different relaxation behavior upon switching. The results are explained both in the view of negatively charged defects pinned at the PZT/Pt interface as well as the possible variation in the local dielectric properties across the film thickness. Investigating the latter made the quantitative deduction of values such as the effective dielectric polarization Pz, the deposited charge density σ, and the surface dielectric constant εsurface in thin ferroelectric PZT films necessary. We illustrate that such measurements in

275 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 275-287. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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fact are possible on the nanometer scale revealing quantitative data when combining PFM and PFS.

1. Introduction Ferroelectric thin films have gained considerably interest in the last couple of years due to their functionality and potential being employed for instance in molecular adsorption [1] and nonvolatile random-access-memory devices (FeRAM) [2]. Among potential candidates, Pb(ZrxTi1-x)O3 (PZT) is one of the most promising materials because of its large remanent polarization and low coercive field. However, PZT is also well known for its poor fatigue behavior on metal electrodes [3, 4] and occurrence of size effects [57] which are good due to the ferroelectric/electrode interface properties [3-7]. Hence the functionality driven by surface charges and local electric fields becomes difficult to control. However, addressing the inspection of internal interfaces, for example, the ferroelectric film / metal electrode interface, has been so far mostly restricted to research using transmission electron microscopy (TEM) [8, 9]. On the other hand, the influence of preparation conditions on the nanoscopic properties of as-prepared cross sections for TEM may be debated, in conjunction with how the electron beam alters the local electronic and physical constitution. Therefore we propose here an alternative route to inspect the local dielectric and polarization properties using non-destructive and non-invasive methods derived from scanning force microscopy (SFM). Simultaneously, these techniques offer a high resolution in real space being extended down to the atomic scale when inspecting ferroelectric systems under ultra-high vacuum (UHV) conditions [10, 11]. Under ambient conditions in air, though, the resolution is limited due to the relatively large capillary forces resulting in worn tips after a few scan lines. Nevertheless, when accurately controlling the tip-sample interaction force (zero force point) the resolution even on ferroelectrics approaches 1 nm in topography and ~ 5 nm for sub-surface information [12] deduced for instance with piezoresponse force microscopy (PFM).

2. Methods 2.1. PIEZORESPONSE FORCE MICROSCOPY (PFM) Fig. 1 presents such high resolution imaging of an individual PZT grain. The method applied is PFM the details of which are described elsewhere [10, 13]. In principle an AC signal is applied to the tip which consequently, when contacting the sample, activates 3dimensional local sample vibrations due to the inverse piezoelectric effect. We developed sensitive measurement set-ups in order to deduce the tensorial properties of the piezoelectric constant and hence the three dimensional polarization G P = ( Px , Py , Pz ) , for instance for single crystals [14-18], ceramics [19-21], thin films [12, 22-27], etc. down to a 5 nm resolution. Using a highly doped Si cantilever with 70 kHz resonance frequency, it is possible to apply an AC voltage of 2 Vp-p in the range

277

between 10 - 25 kHz (12 kHz in the actual experiment) while still being far from mechanical resonances of the coupled lever/sample system.

Figure 1. Domain pattern in an individual PZT grain: (a) sample topography (total z-scale 10 nm), (b) reconstruction of the domain pattern, (c) out-of-plane polarization (OPP) components, and (d) in-plane polarization (IPP) components. Lamellar 90° domain patterns are clearly visible in (c) also revealing domain inversion well inside the grain.

Basically, PFM measurements result in deducing the AC contribution SACC of both the polarization and mobile charge which possibly might be accumulated at the sample surface (compensation charge for instance resulting from switching experiments). Differentiation between the two contributions on the nanometer scale, though, so far seemed to be impossible. In fact PFM is sensitive to a signal given by [26] S AC = Pz − γ ⋅ σ , (1) with Pz showing the effective contribution of dielectric polarization along the zdirection, and σ being the surface charge density due to charge deposition from the tip. Both contributions Pz and σ can be seen to influence the measurement at the same time.

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The proportionality factor γ is so far unknown and has to be deduced theoretically or during the experiment. Note the subtractive behavior of the two contributions since electrostatic interaction of the tip with the deposited charge is always repulsive while the inverse piezoelectric effect in PFM acts in the opposite way. As previously shown [28, 29] γ covers the regime between 0 < γ < 1. Thus the inverse piezoelectric effect always dominates the overall interaction in PFM. Therefore, PFM effectively reveals the local polarization distribution close to the sample surface [13, 23, 24, 30, 31]. 2.2. KELVIN PROBE FORCE MICROSCOPY (KPFM) For KPFM the same AC voltage is applied to the cantilever which is now kept strictly away from the sample surface in true non-contact mode [32, 33]. The oscillation amplitude is kept to below 10 nm mp-p in order to improve the force resolution and avoiding elastic tip sample interaction due to tapping. The additional AC field exerted by the tip modulates the force and allows the minimization of all electrostatic interactions by sensing the force minimum [34] due to ∂C (∆Φ ) 2 , F=1 (2) 2 ∂z with C the tip-sample capacitance and z the mean tip sample distance. As indicated in equ. 2, both a negative and positive potential difference ∆Φ Φ between tip and sample surface affect our measurements similarly (always resulting in an attractive force) showing the quadratic behavior of Coulomb forces. In ordinary non-contact SFM though, both the tip and sample surface potential are electrically not controlled. Moreover when investigating ferroelectrics having a bound surface charge density, any arbitrary tip potential being different from the local sample surface potential directly leads to an additional force term in our non-contact interaction (equ. 2). The interpretation of data recorded by EFM or non-contact SFM therefore always suffers from this point, specifically when Coulomb forces dominate the local force contribution. KPFM, however, enables the most accurate surface potential measurements since all extra forces arising via equ. 2 are directly balanced at the tip. 2.3. PULL-OFF FORCE SPECTROSCOPY (PFS) In contrast to PFM, PFS measurements do not allow the two contributions Pz and σ to be separated from their sign, which therefore results in summing over the two signals rather than building the difference as shown in equ. 1 [26]. Since pull-off force experiments are performed with a DC voltage applied to the conducting tip while retracting the tip from the sample surface, we write correspondingly: S DC = Pz + δ ⋅ σ . (3) The positive sign directly results from electrostatic forces always being attractive between tip and (any) sample independent of whether electrons or holes are the majority carriers. The proportionality factor δ is larger than one since the surface charge density σ clearly dominates the polarization induced force on the tip. In order to separate Pz and σ we therefore have to determine γ and δ either theoretically or in our experiment.

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3. Materials

450nm PZT

Ps

5µ

m

100nm Pt 500nm SiO2 Si

Angle: 6°

surface

Figure 2. Schematic view of the sample system (top), and scanning electron micrograph of the as-polished PZT structure, giving access to all interfaces (bottom).

We used two different types of PZT as functional sample surfaces. For studying the internal interface properties, an RF sputtered 450 nm thick (111)-oriented Pb(Zr0.25Ti0.75)O3 film deposited onto a Pt(111)/SiO2/Si substrate was used. Such samples are ideal for applications in pyroelectric sensors [35] showing self-polarization with the normal component pointing from the bottom Pt electrode to the top surface [36]. In fact ellipsometry measurements indicate that self-polarization gradually

280

increases over the first 300 nm [35]. Therefore, such ferroelectric samples were polished under different small angles ranging between 1-6° (see Fig. 2). This greatly enlarges the cross section of the film making both the surface and inner interface accessible to SFM. For example the 450 nm thick film is enlarged to ~5 µm as shown in Fig. 2. The PZT/Pt interface was scanned with the cantilever aligned parallel to the layers. The scan range was large enough (> 8 µm) to include both the intact PZT film of 450 nm nominal thickness as well as the SiO2 section thus providing good reference marks both for potential and topography measurements. By scanning the tip from left to right over the wedge, the information from different positions on the PZT film corresponding to different thicknesses was directly deduced. The second sample was selected with a Pb(Zr0.53Ti0.47)O3 concentration having a thickness of 600 nm. Details of sample preparation are given in [37]. The transition layer for the second type of samples is much smaller allowing the preparation of thinner films (down to 20 nm thickness only) and their integration in high-density FeRAM applications.

4. Results 4.1. POLARIZATION PROFILE ACROSS THE PZT FILM Piezoresponse force microscopy (PFM) [13] and Kelvin probe force microscopy (KPFM) [11] were applied to deduce the polarization and local electric potential distribution over the whole cross section of the PZT sample (see Fig. 3 and 4) under static conditions as well as after switching. The details of our setup are described elsewhere [11, 13]. Fig. 3 depicts the piezoresponse signal (red curve) and the sample topography (black curve) taken across the wedged sample. Note the different sample regions deduced from the topography profile. From left to right, they are the PZT native surface, the polished PZT wedge, the Pt bottom electrode, and the SiO2 (not shown). In our setup, the direction of self-polarization results in a negative response for the PFM signal. We clearly see that on the PZT wedge away from the Pt electrode, the absolute value of the piezoresponse signal first increases gradually with increasing film thickness before then saturating at a distance of 2.2 µm from the Pt, which corresponds to a critical film thickness tc ≈ 240 nm. The existence of such a thick transition layer clearly resembles the ellipsometry measurements reported in the literature [35]. The overall sign of the polarization is still negative, as expected. Similar experiments were performed with the tip now scanning in non-contact mode. Such KPFM measurements are sensitive to the electrical potential variations induced by charges located both at the surface and within the interior of the film. Fig. 4 shows a full image scan over the wedged sample area. Due to the built-in polarization of the PZT film the top surface is positively charged while being negatively compensated thus forming a Helmholtz double layer [38]. This is reflected in Fig. 4 by the negative absolute potential value. Taking into accountt that long-ranging electrostatic forces tend to smear out the experimental potential distribution [39], the observed profile is in good

281

out-of-palne piezoresponse signal [a.u.]

agreement with the transition layer thickness of 240 nm found by PFM and reported in Fig. 3. 0

2

4

6

8

film thickness 240nm 2.2 2µm

0

-1

-2

-3

-4

PZT 0

PZT polished

2

4

6

Pt 8

Distance [µm] Figure 3. PFM (red) and topographic cross-section (black) of the PZT wedge sample. Note that the PFM signal saturates when the sample exceeds a thickness of ~240 nm although the sample still increases in thickness.

Pt

PZT slope voltage (V)

Y [µm]

PZT

X [µm]

Transition layer

Figure 4. KPFM image showing the build-up of the surface potential for an increasing film thickness (from right to left). Note the relative negative value of the surface potential when reaching the nominal sample thickness of 450 nm (@ x = ~ 4µm).

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To date many models have been proposed that would accurately explain the effects reported above for the PZT/Pt interface [6, 40-43]. Most of them are related to the charge carrier concentration in conjunction with the Schottky barrier built up at the ferroelectric/metal interface, among which the electron injection scenario [42, 43] seems to be the most appropriate in our case. For ferroelectric films an interface layer usually forms close to the substrate. The band bending in the PZT at the interface leads to a significant lowering of the Schottky barrier [40] between PZT and Ptt so that electrons may inject from the Pt electrode into the semiconductor then becoming trapped in the PZT film to form negatively charged defects, for instance Ti3+, or lead vacancies (VPb2-) [44]. Thus an internal electric field is built up resulting in a permanent poling of the film. The above described scenario represents one of the most important origins of selfpolarization. In order to clarify the existence of such a transition layer, it is necessary also to investigate both the dynamic behavior of the interfacial layer as well as the dielectric properties of the sample, specifically at interfaces. 4.2. RELAXATION DYNAMICS WITHIN THE PZT FILM

Y (µm)

voltage (V)

To clarify the switching properties we applied a DC voltage of +20 V to the tip in contact mode while scanning the tip over the wedge at a constant speed of 2 µm/s. The scanning range was chosen to cover the whole PZT slope leaving only a small gap for the Pt electrode to avoid anyy short circuit (see Fig. 5). Mapping both the PFM (see Fig. 5) and KPFM signals directly after switching shows the two signals decay with a time constant τ being in the order of several hours [25]. The decay is slowest at the center of the switched region (center of the PZT slope) and becomes faster near its borders. This behavior is reasonable since the driving force for back switching is expected to be larger at the edge than at the inner part. Further details are discussed in [25].

PZT Pt slope

PZT

X (µm) Figure 5. Switching dynamics probed across the wedge sample with PFM. Note that the tip did not touch the Pt electrode for switching in order to avoid tip-sample short circuit.

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4.3. LOCAL DIELECTRIC CONSTANT AT THE PZT SURFACE From equs. 1 and 3, it follows that both Pz and σ depend on SACC and SDC in the following way: Pz =

γ ⋅ S DC δ , γ +δ δ

S AC +

(4)

and − S AC S σ = DC . γ +δ

(5)

Both SACC and SDC may be deduced from force measurements as denoted by equs. 1 and 3. In PFS we measure the overall force acting on the tip when pulling the tip back from the surface. Thus such a DC force may be written as: FDC = ADC (ε , U ) ⋅ U 2 + S DC ( Pz , σ ) ⋅ U + C , (6) where ADC specifies the induced dielectric force component (proportional to U2), and SDC the force contributions due to polarization and/or mobile charges depending linearly in U. U C represents any additional DC force contribution as stems for instance from the capillary force affecting the tip-sample interaction. The coefficient ADC in equ. 6 denotes the dielectric properties thus containing information on the tip-sample capacitance. For the geometry chosen in our experiment, the top electrode is our conductive tip while the bottom electrode is laterally extended. In fact one could therefore calculate the field distribution between t tip and sample to be that of a point charge in front of an extended dielectric half space having a counter electrode that merges to infinity. For the sake of simplicity, however, and because the PZT film thickness used in this experiment was rather low, we still model the tip-sample system in our experiment as a plate capacitor resulting in: ADC = − 1 ε o ε (U ) ⋅ a . (7) 2 In equ. 7, a specifies the geometry while ε(U) now denotes the field dependent local dielectric constant probed with the tip.

284

Experimentally, both PFM and PFS measurements are now performed at one and the same surface spot in a spectroscopic, and an absolute matching of the two curves is intended using a polynomial fitting. Such an approach is reasonable since it is both Pz and σ which contribute to the AC and DC force terms via equs. 4 and 5. Our experiment [26] then allows the following results to be deduced: 1.) PFM probes the piezoelectric properties even for tip-sample voltages up to ±10 V. 2.) Only for larger fields exceeding 10 V in reversed polarization direction will mobile surface charges contribute to the overall signal SACC in PFM (deposited upon switching). In contact experiments, however, such mobile charges are directly eliminated via the conductive tip. 3.) From an absolute matching of PFM and PFS we find εsurface to measure ~140, much smaller than the bulk ε value determined from dielectric spectroscopy (εBulk =~ 500). These results suggest, that also the top PZT surface has different properties compared to the bulk values. In fact, various theoretical models already suggested the existence of a pure dielectric surface layer [40] to be present on PZT thin films. Here, for the first time, we have given experimental evidence that this is true for both the inner and outer interfaces in PZT on the nanometer scale.

5. Conclusion In conclusion, we reported the investigation of functional surfaces like the inner and outer interfaces in PZT in order to quantify both the amount of effective ferroelectric polarization and change in dielectric properties. With PFM and KPFM we find a transition layer occurring at the Pt/PZT interface within which the polarization builds up reaching its saturation value for film thicknesses exceeding 240 nm. Its presence was also tested under dynamic switching conditions suggesting that the observed temporal behavior may tentatively be attributed to the influence of negatively charged defects accumulated at that inner surface. Furthermore, for the voltage regimes used here, no evidence was found that PFM measurements should lack mobile charge deposition upon switching. In contrast, we prove that the PFM signal purely reflects the measured piezoelectric displacement which hence may be compared to the local polarization distribution. In addition, the dielectric constant at the PZT top surface was found to be dramatically reduced compared to the bulk value. Our measurements therefore suggest a dead layer to be present. Similar experiments deducing the local dielectric constant are now necessary for the inner interface.

285

Acknowledgement The author kindly thanks H. Chaib, K. Franke, G. Gerlach, S. Grafström, Ch. Loppacher, X. M. Lu, F. Schlaphof, and G. Suchaneck for helpful discussion. Financial support by the German Federal Research Society (DFG) in the Graduate College „Sensorics“, Dresden and under grant no. EN 434/2-3 is gratefully acknowledged.

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MICROSCALE CONTACT CHARGING ON A SILICON OXIDE

S. MORITA1, T. UCHIHASHI2, K. OKAMOTO1, M. ABE1 and Y. SUGAWARA3 1 Department of Electronic t Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871, JAPAN 2 SFI Physics Department,The University of Dublin, Trinity College,Dublin 2, Ireland 3 Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871, JAPAN

Contents 1. 2.

3.

4.

5.

6.

Introduction Reproducible and controllable contact charging 2.1. Characteristics and problems of usual macroscopic contact charging 2.2. Characteristics and merits of novel microscopic contact charging Reproducible and controllable contact charging on a thin silicon oxide using an Atomic Force Microscope (AFM) with a single-asperity conductive tip 3.1. How to deposit charge by microscopic contact with AFM-tip 3.2. How to image microscopic charge distribution with AFM-tip Elementally processes of microscopic contact charging and dissipation 4.1. Time evolution of electrostatic force due to deposited charge 4.2. Contact voltage and dissipation time dependences of peak values of electrostatic force 4.3. Dissipation processes and charge sites of deposited charge 4.4. Phase Transition of densely deposited negative charge 4.5. Spatial distribution of densely deposited negative charge 4.6. Contact voltage and contact time dependence of initial electrostatic force and FWHM in air and in a vacuum Atomically resolved imaging of point charge and contact potential difference 5.1. Atomically resolved imaging of point charge 5.2. Atomically resolved contact potential difference Conclusion

289 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 289-308. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

290

Abstract In this study, we investigated contact charging and its dissipation on a silicon oxide surface using a reproducible and controllable contact charging method. As a result, we found that negative charge has three stages of both contact charging and charge dissipation, while positive charge has only one stage. By keeping on contact charging further, negative charge became high density, i.e., a solid phase of charges, on the silicon oxide surface even at room temperature in air. Further, we imaged point charge and charge distribution of free electrons on n+-GaAs(110) cleaved surface with atomic resolution using an electrostatic force microscope (EFM) combined with a noncontact atomic force microscope (NC-AFM). Moreover, we also imaged contact potential difference on Si(111)7x7 and Si(111)5√3×5√3-Sb with atomic resolution using a Kelvin probe force microscope (KPFM) combined m with NC-AFM.

1. Introduction Contact charging of insulators [1-2] and charge dissipation on and in insulators [3-4] are among the most important phenomena in surface physics and also surface engineering. If it were possible to investigate elementary processes of contact charging and its dissipation, deeper understanding of charge transfer phenomena on and in insulators would be obtained. However, contactt electrification of insulators and charge dissipation on and in insulators in air are still unresolved problems in physics, in spite of its long history of study from the time of the ancient Greeks. In this review paper, we will first explain how to achieve reproducible and controllable contact charging and dissipation on a thin silicon oxide (SiO2) surface at room temperature in air and in a vacuum. Next, we will introduce experimental results of reproducible and controllable contact charging and dissipation. Here, we will make clear elementary processes of microscopic contactt charging and charge dissipation on and in a thin silicon oxide. Then, by combining electrostatic force microscope (EFM) with noncontact atomic force microscope (NC-AFM), we will image point charge and charge distribution of free electrons on n+-GaAs(110) cleaved surface with atomic resolution. Further, by combining Kelvin probe force microscope (KPFM) with NCAFM, we will image contact potential difference on Si(111) 7x7 and Si(111)5√3×5√3Sb with atomic resolution.

2. Reproducible and Controllable Contact Charging 2.1. CHARACTERISTICS AND PROBLEMS OF USUAL MACROSCOPIC CONTACT CHARGING In the case of metal-insulator and insulator-insulator contacts, usual macroscopic contact charging has the problem of bad reproducibility, because of (1) multi-contacts due to multi-asperities, (2) back flow of residual charge at the second contact, (3) electric discharge due to large voltage induced by residual charge Q as shown in Fig. 1.

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Another problem is that usual contact charging induced byy contact potential difference (CPD) cannot change and hence cannot control the polarity of deposited charge because of the fixed CPD polarity. But, back flow of residual charge induces opposite charge deposition at the second contact. As a result, in case of double- or multicontacts, charge deposition with both polarities will occur [1]. On the other hand, in case of single-contact, polarity of deposited charge will alternately change during sequential contacts [2]. Before back flow off residual charge, by retracting or separating two bodies, distance A between two bodies will increase and hence bias voltage between two bodies will also increase because of capacitive relation as shown in Fig. 1. This increase of bias voltage will induce electric discharge between two bodies. (1) Multi-contacts due to Multi-asperities Contact Charging

Multicontacts

Side View (2) Back Flow due to Residual Charge Back flow occurs at the second contact

(1) Single Asperity

Single Asperity Insulator

(2) Control of Residual Charge Charge control at the metal apex (3) Suppression of Electric Discharge

Electric Potential Control of Charge

r

1 Large

Residual Charge

Q=CV=(ǭ Q=CV=( ǭS/ S/AA8

(3) Electric Discharge due to Large V Large Q=CV=(ǭ Q=CV=( ǭS/ S/AA8

2 Small Constant electric potential (4) Forced Charging due to Electric Potential 8

2 Large

Constant Charge (4) Charging due to Contact Potential Difference(CPD) Figure 1. Characteristics and problems of usual macroscopic contact charging.

Insulator

Figure 2. Characteristics and merits of novel microscopic contact charging.

2.2. CHARACTERISTICS AND MERITS OF NOVEL MICROSCOPIC CONTACT CHARGING To achieve reproducible and controllable contact charging on a thin SiO2 surface, we used (1) single asperity metal tip, (2) electrically controlled residual charge, (3) electrically suppressed electric discharge and (4) used forced charging due to external bias potential [5] as shown in Fig. 2. Magnitude of residual charge was controlled by external bias voltage using capacitive charging effect. In this case, bias voltage in capacitive relation becomes constant. Then, by increasing A between tip apex and sample surface, capacitive charge will decrease and hence electric discharge will be suppressed. It should be noted that this external voltage will induce forced charging due to external electric potential and that it enables us to control even polarity of deposited charge.

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3. Reproducible and controllable contact charging on a thin silicon oxide using an atomic force microscope (AFM) with a single-asperity conductive tip 3.1. HOW TO DEPOSIT CHARGE BY MICROSCOPIC CONTACT WITH AFM-TIP Figure 3 shows schematic models of contact charging [5]. As shown in Figs. 3 (a) and (b), when a thin silicon oxide layer with an electrically grounded substrate was brought into contact with an AFM tip of a conductive cantilever biased by a contact voltage VC during a certain contact time t0, contact-electrified charges QS were controllably deposited by electric force. Then, the polarity of deposited charge depended on the polarity of VC because of the forced charging. Here, absolute magnitude of VC was set lower than the threshold voltages of dielectric breakdown for air and the oxide layer [6, 7]. As the conductive cantilever, we used a microfabricated Si3N4 cantilever with a pyramidal Si3N4 tip coated with 1.5nm-thick Cr and 50nm-thick Au films. Nominal values of the spring constant, mechanical resonant frequency and tip radius were k = (0.16-0.18) N/m, fR = 27 kHz and 25 nm, respectively. We chose a thin silicon oxide as the insulating film because of its homogeneity, flatness and small trap sites. Further, the thin silicon oxide enables us to apply a strong electric field with a rather small voltage. The silicon oxide layers with (3.8-5.7) nm thickness were formed on p-type single crystal Si(100) wafers with a resistivity of 10-20 ȍcm. Contact charging on the silicon oxide surface was performed at room temperature in air under ambient conditions. Negative Charge Contact Single Asperity Conductive Cantilever

ltage Measurement Voltage Voltag Vs<0

/C<0 =Vs/C<0

SiO2

SiO2 ++++++++++++

Contact Voltage

Silico Silicon

Silicon

C

C

Contact ha Charging Cha

ltage Measurement Voltage Voltag

Attractive

Positive Charge

/C>0 =Vs/C>0

Single Asperity Conductive Cantilever

iO2 SiO

ilicon Silico Silicon

SiO2

Contact Voltage

D

Silicon

D Figure 3. Schematic models for microscopic contact charging of (a) negative charge and (b) positive charge.

+O CIG(QTEG CIG(QTEG ( T ( TV E3U TV HQT 8U Figure 4. Schematic models for microscopic electrostatic force measurement of negative charge using (a) negative and (b) positive measurement voltage VS.

293

3.2. HOW TO IMAGE MICROSCOPIC CHARGE DISTRIBUTION WITH AFM-TIP

Figure 4 shows schematic models of electrostatic force measurement of deposited negative charge [5]. After contact charging, the oxide layer was subsequently withdrawn to a distance Z from the tip apex as shown in Fig. 4. Then, deposited charge QS at the distance Z was imaged as an electrostatic force f(t), which exerted on the tip apex of the conductive cantilever biased by a measurement voltage VS. The electrostatic force f(t) in Fig. 4 is generally given by f(t) = aVS2 + bVSQS(t) + cQS(t)2, (1) 2 2 (a[N/V ], b[N/VC], c[N/C ]: constant) [8], where t is the dissipation time after the contact charging. The units are Newton (N) for the electrostatic force f(t), Volt (V) for the measurement voltage VS, Coulomb (C) for the deposited charges QS and second (s) for the dissipation time t. Here, the first term on the right-hand is a dominant attractive force due to the capacitive force but it was subtracted to image site- and timedependence of deposited charge, because the capacitive force contributes to uniform background independent of time and location. In the present experiment, the absolute value of the VS is usually set enough large to satisfy the condition |bVSQS(t)| » |cQS(t)2|. Therefore, the measured spatial change of the electrostatic force F(t) is approximated as F(t) = f(t) - aVS2 = bVSQS(t). (2) Thus, the time dependence of the deposit charges QS(t) is proportional to the value of the measured electrostatic force F(t) that can be deduced as the product of the spring constant k and the displacement ǻZ of the cantilever as shown in Figs. 4 (a) and (b). The electrostatic force measurements on the silicon oxide surface were performed at room temperature in air under ambient conditions.

4. Elementally Processes of Microscopic Contact Charging and Dissipation 4.1. TIME EVOLUTION OF ELECTROSTATIC T FORCE DUE TO DEPOSITED CHARGE After contact charging under the contact voltage of VC = -4V during the contact time of t0 = 20 s on the silicon oxide with 3.8 ± 0.3 nm thickness, we measured the time evolution of electrostatic force due to deposited charge as shown in Figs. 5 (a) and (b). Here, we observed the spatial change of the electrostatic force only for the X-scan but the time evolution along the Y-axis [5]. The upward and downward directions of the Zaxis correspond to the increase of the repulsive and attractive forces, respectively. Figures 5 (a) and (b) were obtained under the measurement voltages of VS = -4 V and +4 V at Z = 53 nm, respectively. From Eq. (2), the repulsive force peak for VS = -4 V and the attractive force peak for VS = +4 V imply that both charges deposited under the contact voltage VC = -4 V had negative sign. Next, after contact charging under the contact voltage of VC = +4 V during the contact time of t0 = 20 s, Figures 6 (a) and (b) were obtained under the measurement voltages of VS = -4 V at Z = 60 nm and +4 V at Z = 52 nm, respectively. From Eq. (2), the attractive fforce peak for VS = -4 V and the repulsive force peak for VS = +4 V imply that both charges deposited under the contact voltage VC = +4 V had positive sign. Further, as shown in Figs. 5 and 6, absolute peak values of the initial repulsive and attractive forces were nearly the same irrespective of

294

the sign of the measurement voltage VS in the case of the same contact voltage VC. This result makes clear the reproducibility of the voltage controllable contact charging.

In Air asurement V VS=-4V

VC=-4V t0=20sec

M Z=52.7nm

VS=+4V

In Air

Z=52.7nm

VC=+4V t0=20sec

urement Vol VS=-4V

VS=+4V Z=51.9nm

due to negative charge under the measurement voltages of (a) VS = -4 V and (b) VS = +4 V. The oxide thickness is 3.8 ± 0.3 nm.

Figure 6. Time evolution of the electrostatic force due to positive charge under the measurement voltages of (a) VS = -4 V and (b) VS = +4 V. The oxide thickness is 3.8 ± 0.3 nm.

4.2. CONTACT VOLTAGE AND DISSIPATION TIME DEPENDENCES OF PEAK VALUES OF ELECTROSTATIC FORCE By comparing Fig. 5 with Fig. 6, we found that the initial peak value of the electrostatic force Fi = 280 pN due to negative charge was several times larger than that due to positive charge Fi = 60 pN, although the absolute values of the contact voltage VC, contact time t0, measurement voltage VS and tip-sample distance Z were nearly the same. Therefore, we investigated the contact voltage dependence of Fi as shown in Fig. 7. Here, the Fi was measured attractively in all cases. The contact time of 20 s was selected from the trade-off between the stronger electrostatic force and the narrower FWHM by investigating the contact time dependence of the electrostatic force and FWHM. Small open circles show experimental results, while the number in the large open circles shows the measured sequence. Continuous VC dependence of the Fi in spite of random sequence for VC value supports that we achieved reproducible and controllable contact charging using a voltage controllable contact charging structure shown in Figs. 1 (a) and (b). From Fig. 7, we found that the contact potential difference (CPD) between the silicon oxide and the Au film on the tip apex is nearly +2V, because the Fi becomes nearly zero at VC = -2 V. When the CPD is positive, the positive charge deposition should be preferred rather than the negative one in contrast to the

295

experimental result around VC = -4 V compared with that around VC = +4 V as shown in Figs. 5 and 6. Thus, Figure 7 clearly shows that the preference of the negative charge deposition is not induced by the CPD but should be attributed to the strong VC dependence. Such VC dependence shown in Fig. 7 suggests the difference of the contact charging and/or dissipation mechanisms between the positive and negative charges. In order to investigate the contact charging and dissipation mechanisms, we performed measurements on contact charging and dissipation with various VC. Here, the contact time t0, the measurement voltage VS and the tip-sample distance Z were maintained to be nearly constant. Figure 8 shows plots of the peak values of the electrostatic force Fp(t) as a function of time after the contact charging. Contact charging was performed with the contact voltage from VC = -2 V to –5 V for the negative charge and from VC = +2 V to +6 V for the positive charge, respectively. The contact time and the tip-sample distance were t0 = 20 s and Z = (50-60) nm, respectively. As shown in Fig. 8, time evolution and VC dependence of Fp(t) for the positive charge were very simple, so that both contact charging and dissipation mechanisms seem to be only one stage.

In Air Negative Charge

In Air Positive Charge

tSiO2=5.4 nm

Figure 7. Initial peak values of the electrostatic force due to the deposited charge as a function of contact voltage VC. The oxide thickness is 5.4 ± 0.1 nm.

Figure 8. Dissipation time dependence of peak values of electrostatic force due to deposited negative and positive charges after the contact charging with various contact voltages VC. The oxide thickness is 5.4 ± 0.1 nm.

On the other hand, as shown in Fig. 8, both time evolution and VC dependence of Fp(t) for the negative charge were clearly divided into three stages. That is, in the case of the low contact voltage region (VC = -2 V), only the slow decay process appears. As the VC decreases, initial decay process becomes more rapid in the medium contact voltage region (VC = -2.5 V), and then another slow decay process appears in the lower contact voltage region (VC -3 V). Each decay process corresponds to a different dissipation process of the deposited negative charge. The decrease in VC at the

296

cantilever side means the increase of the charging state energy at the silicon oxide side. Thus, there are three charging states for the negative charges on the oxide layer, and these charging processes occur from the lower energy state to the higher one in sequence (IIIĺIIĺI) as shown in Fig. 8. Here, these charging processes are referred to as stages I, II and III for VC -3 V, VC = -2.5 V and VC = -2 V, respectively. In contrast, the dissipation process of the deposited negative charges occurs in the opposite sequence to that of the charging process, that is, from a high-energy charging state to a lower one (IĺIIĺIII). The transition of the first stage I to the second one II occurred around the critical force of FC = 200-250 pN [9]. 4.3. DISSIPATION PROCESSES AND CHARGE SITES OF DEPOSITED CHARGE As shown in Fig. 9, when charge is deposited on a thin SiO2 film, there are two dissipation processes. One is the surface diffusion on a thin SiO2 film, the other is the recombination process through a thin SiO2 film with hole in p-type Si substrate. To discriminate these two processes, we investigated time dependence of total charge by spatially integrating electrostatic force distribution. In case of surface diffusion process, total charge will be conserved irrespective of the decrease of peak value of electrostatic force, while, in case of recombination process, total charge will decrease depending on the decrease of peak value of electrostatic force. Negative Charge

In Air

tSiO2=5.4nm

Figure 9. Schematic model of two dissipation processes on a thin silicon oxide.

Figure 10. Time evolution of peak value and spatially integrated value (total charge) of electrostatic force distribution induced by deposited negative charge.

In case of positive charge, the spatially integrated value of electrostatic force F(t) was nearly independent of time so that the number of charge was conserved [9-10]. This result suggests that the positive charge will be deposited on a thin SiO2 surface and will dissipate only by surface diffusion process. On the other hand, in case of negative charge, as shown in Fig. 10, during stages II and III both integrated and peak values decrease, although during stage I the integrated value seems to be nearly

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constant. Besides, during stage III both integrated and peak values seem to have the same decay constant, while during stage II integrated value has a longer decay time. From these results, we concluded that the negative charge will dissipate only by surface diffusion process during stage I, only by recombination process during stage III, and by both diffusion processes during stage II. The deposition process in the stage III seems to correspond to the lowest energy state because it appears even at low contact voltage VC as shown in Fig. 8. This lowest energy state seems to relate to the positively charged trap sites in the oxide layer which trap negative charges, i.e., the process 1 in Figs. 11 (a) and (b). The trap sites have a large capture cross-section on the order of 10-12-10-14 cm2 for the negative charge [11]. From the electrostatic force measurement, we estimated the trap site charge density as ca. 1.5x10-7 C/cm2 [12], which nearly agreed with the typical value of ca. 8x10-8 C/cm2 obtained from the C-V measurement in the MOS capacitor with p-type silicon substrate [13]. The energy level of the trap site seems to be deep in the energy gap of the oxide layer, and it will locate near the interface between the oxide layer and the Si substrate as shown in Fig. 11. Thus, the dissipation in the stage III occurs toward the silicon substrate, i.e., the process 3 in Figs. 11 (b) and (c), and has a long decay constant. On the other hand, the deposition processes in the stages I and II seem to correspond to higher energy states because they appear at lower contact voltage VC. Since the positively charged trap sites are already occupied by the negative charges, excess contact charge seems to be deposited on the oxide surface [9]. Thus, the charge sites in the stages I and II seem to be the neutral sites on the oxide surface with shallow energy levels in the energy gap of the oxide layer because the energy level of the neutral site on the oxide surface is higher than that of the positively charged trap site. 4.4. PHASE TRANSITION OF DENSELY DEPOSITED NEGATIVE CHARGE Figure 12 shows peak values and full widths at half-maximum (FWHMs) for the electrostatic force after the contact charging of negative charge as a function of the dissipation time. Here, the contact charging was performed under VC = -4 V and t0 = 20 s, and the attractive force measurement (VS = +4 V) was compared with the repulsive one (VS = -4 V) at Z = 55 nm [15]. We can see that both measurements show three stages of dissipation processes with respect to the time t. That is, the decay of the peak values is rather slow in the first stage I (0 s < t < 75 s), but becomes fast in the second stage II (75 s < t < 95 s), and then again becomes slow in the third stage III (95 s < t). The transition of the first stage to the second one occurred around the critical force of FC = 200 pN. In the first stage I, the peak values under the attractive force measurement nearly agreed with those under the repulsive one, while, in the second stage II, the peak values under the attractive force measurement decayed faster than those under the repulsive one. In the third stage III, both peak values decayed at nearly the same rate. Thus, the first stage I seems to be stable state where its decay rate is independent of attractive or repulsive force measurement, while the second stage II seems to be unstable state where its decay rate depends on attractive or repulsive force measurement. On the other hand, the FWHMs for the electrostatic force show considerably different tendencies as a function of time t. Under the repulsive force measurement, the

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FWHM monotonously increased, while, under the attractive one, the FWHM clearly showed three stages similar to the peak values. That is, the FWHM slightly decreased at the first stage I (0 s < t < 75 s), but rapidly increased in the second stage II (75 s < t < 95 s), and remained almost constant in the third stage III (95 s < t). Thus, in the first stage, the FWHM increased under the repulsive force measurement, while it conversely decreased under the attractive one. In the second stage, the FWHM under the attractive one increased much faster than that under the repulsive one. In the third stage, the difference of both FWHMs gradually became small.

Negative Charge

Contact ontact Voltage Vc = -4 V C

II

tSiO2 = 5.4 nm

Figure 11. Schematic models of charge sites for contact charging of negative charge. (a) electron capture by positively charged trap sites (stage III), contact charging on the oxide surface (b) with low charge density (stage II) and (c) with high charge density (stage I).

Figure 12. Dissipation time dependence of peak values and full widths at half-maximum of electrostatic force due to deposited negative charges compared between the repulsive and attractive force measurements. The oxide thickness is 5.4±0.1 nm.

At first, we will discuss the transition of peak value of electrostatic force from the first stage I to the second stage II. This transition cannot be explained by a simple model with two different decay constants, because the first stage I with a longer decay constant appears at first and then disappears when the second stage with a shorter decay constant appears. As shown in Fig. 13 (a), in case of a simple model with two different decay constants, a stage with a shorter decay constant appears at first and then disappears when another stage with a longer decay constant appears. Therefore, this transition is a kind of phase transition such as from stable state to unstable state as shown in Fig. 13 (b). In the deposition process of the stage I, the peak value of the electrostatic force just after the contact charging tends to saturate as shown in Fig. 8. This result indicates that the density of the deposited negative charge in the central region is limited by the Coulomb repulsive force between the deposited negative

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charge on the oxide surface, i.e., the process 4 in Fig. 11 (c). Thus, the deposited negative charges in the stage I seem to be veryy dense [14, 15] and slowly dissipate as shown in Fig. 8. We calculated the number of the deposited negative charges at the central region with a sphere-plane model under the point-charge approximation. Then the charge density was obtained by dividing the number of the deposited charge by the effective area where the electrostatic force microscope (EFM) detected. We assumed that the radius of the effective area was equal to that of the curvature of the EFM tip apex, and that the density of the negative charges was uniform within the effective detected area. As a result, the charge density was roughly estimated as about 3.0x1013 charges cm-2, where the mean distance and the potential between the nearest neighbor charges were about 2 nm and 0.7 eV/electron, respectively. Using the so-called parameter ī that is the ratio of the Coulomb potential UCoulomb and the kinetic energy Um [16], we can investigate the phase of deposited charge as shown in Fig. 14. From the saturated peak value FC = 250 pN of electrostatic force, we estimated the value of the parameter ī = 24-44. This value is enough larger than ī = 1 so that the stable stage I seems to be in the solid phase of charge [9]. However, in the deposition process of the unstable stage II, the electrostatic force is weaker than that in the stable stage I as shown in Fig. 8. Thus the deposited negative charge seem to have lower charge density than that in the stage I, i.e., the liquid orr gas phase of charge, and rapidly dissipate as shown in Fig. 8. We attributed the stage II to the process 2 in Figs. 11 (b) and (c) [12].

Two Decay Constant Model

Gas Phase II

Liquid Phase

I

Solid Phase Phase Transition Model Figure 13. Schematic model of time evolution from stage I to stage II (a). Superposition model of two different decay time constant states and (b) phase transition model.

Figure 14. Schematic model of charge state of the deposited negative charge, which is classified into three phases depending on the magnitude of the parameter ī. ī

300

4.5. SPATIAL DISTRIBUTION OF DENSELY DEPOSITED NEGATIVE CHARGE To make clear the origin of the time dependence of peak values and FWHMs shown in Fig. 8 in more detail, we compared the spatial distributions of the electrostatic force under the repulsive force measurement with those under the attractive one at A, B, C, D and E in Fig. 8 [9]. The thin and thick curves in Fig. 15 correspond to the spatial distribution of the electrostatic forces under the attractive and repulsive force measurements, respectively. Here, the spatial distribution labeled A and B were measured in the stage I, C was measured at the boundary between the stage I and II, D was measured at the boundary between the stage II and III, and E was measured in the stage III. During the stage I (A and B), the spatial distributions measured attractively coincided with those measured repulsively in the central region, whereas they did not coincide in the surrounding region. These results indicate that the deposited negative charges are more sensitive to the applied electric field in the surrounding region than in the central region of the spatial distribution during the stage I. Therefore, we conjectured that the deposited negative charge in the central region were in the high density state on the oxide surface, i.e., the solid phase of charge, but those in the surrounding region were in the low density state on the oxide surface or were captured by the positively charged trap sites. Further, during the stages II and III (C, D and E), the difference between the spatial distributions measured attractively and repulsively became larger and larger even in the central region. Here, all deposited negative charge seem to be in the low density state on the oxide surface, i.e., the liquid or gas phase of charge, or to be captured by the positively charged trap sites.

Negative Charge Repulsive Force ti

r

VC = -4 V t0 = 20 s

VS=+4V(Attractive)

VS=-4V(Repulsive)

Figure 15. Typical spatial distribution of the electrostatic force due to deposited negative charge. Attractively (thin line) and repulsively (thick line) measured electrostatic forces are superimposed. The oxide thickness is 5.4 ± 0.1 nm.

As shown in Figs. 12 and 15, in the second stage II, the peak values under the attractive force measurement decayed faster than those under the repulsive one. Simultaneously measured FWHM under the attractive one increased rapidly than those under the repulsive one. These results suggest that the attractive force measurement

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accelerates the diffusion of the charge in the second stage II, i.e., the liquid or gas phase of charges, on the oxide surface because of the action-reaction effect due to the attractive force measurement, while the repulsive force measurement disturbs the charge diffusion [9]. 4.6. CONTACT VOLTAGE AND CONTACT TIME DEPENDENCE OF INITIAL ELECTROSTATIC FORCE AND FWHM IN AIR AND IN A VACUUM In order to study the spatial distributions and the charging states of deposited negative charges in more detail, we investigated the contact voltage VC and the contact time t0 dependences of the initial spatial distribution at about 8 s after the contact charging at Z=50 nm [17]. Here, we measured the electrostatic force under VS=0 V so that the measured spatial change is given by F(t) = cQS(t)2. (3) At first, we investigated contact voltage and contact time dependences of initial peak value of electrostatic force in air. In the case of the VC dependence measurement, we set t0 = 20 s, while, in the case of t0 dependence measurement, we set VC = -4 V. Figure 16 shows the initial peak value of electrostatic force as functions of VC and t0. The peak values clearly saturate to FiC = 260 pN. This saturation was explained by the density saturation of negative charge by the process 4 in Fig. 11 [18]. Here, the saturation density of the deposited negative charge was determined by the Coulomb repulsive force between the negative charge, and the negative charge fell in the stable state, i.e., a solid phase of charge [9]. Vs=0V

Z = 50nm

In Air

d

In Air

d

d s

In Vacuum

Figure 16. Contact voltage and contact time dependences of the initial peak value of the electrostatic force just after the contact charging in air.

Figure 17. Contact voltage and contact time dependences of the initial FWHM of the electrostatic force just after the contact charging in air and in a vacuum.

Figure 17 shows the initial FWHM of the electrostatic force distributions, in air (closed triangles and circles) and in a vacuum (open triangles and circles), plotted as functions of VC (circles) and t0 (triangles). In air, since the FWHM increases with

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increase in VC and t0, the deposited negative charge seem to diffuse with increase in the deposited charge. The diffusion rates of deposited negative charge in VC and t0 dependences are estimated to be about 8.7 nm/V and 0.075 nm/s, respectively. Therefore, by keeping on the contact charging, the negative charge will be deposited incessantly because of the diffusion of deposited negative charge towards the surrounding region. As a result, in the case of dense contact charging of negative charge in air, the charge density and hence the electrostatic force at the central region will remain to be constant as shown in Fig. 15. It should be noted that, in the case of VC dependence, the diffusion rate increases by about 8.7 nm/V as a function of the contact voltage VC to maintain the charge density constant and hence saturate the peak value of electrostatic force at the central region in air. On the other hand, in a vacuum, as shown in Fig. 17, the FWHM is nearly independent of VC and t0. This result means that deposited negative charge does not diffuse f in a vacuum [19]. It should be noted that the diffusion rate of deposited negative charge in air strongly depends on humidity. Negative Charge

In Air

P-Si(100)

In Vacuum

In Vacuum

P-Si(100) Figure 18. Contact voltage and contact time dependences of the initial peak value of the electrostatic force just after the contact charging in a vacuum.

Figure 19. Schematic models for the dense contact charging of negative charge on SiO2 thin film in air and in a vacuum with AFM tip.

Figure 18 shows the initial peak value of the electrostatic force just after the contact charging in a vacuum as functions of VC and t0. In the t0 dependence, the peak value of the electrostatic force saturate at around 150 pN for t0γγ200 s. Thus, the charge density at the central region also seems to saturate in a vacuum. However, in the measurement of the VC dependence, the peak value increased monotonically with increase in the contact voltage VC in spite of the long t0 = 1000 s, which means the saturation of the contact time dependence. In particular, as shown in the inset of Fig. 18, the square root of peak value plotted as a function of VC agreed well with a solid straight line whose relationship was denoted by F1/2 = aVC + b (a, b: constants). So the saturated density in a vacuum seems to be determined only by the value of VC. From eq. (3), this result

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means that the number of deposited negative charge QS is proportional to the contact voltage VC. The constant term b may be attributed to the contact charging due to the contact potential difference Vcpd. Hence, this result agrees qualitatively with the capacitive relationship QS = C(VC + Vcpd). We propose the Coulomb repulsive force models for the dense contact charging of negative charge in air and in a vacuum as shown in Figs. 19 (a) and (b), respectively. In the case of the contact charging of negative charge in air, as shown in Fig. 19 (a), the densely deposited charge density at the central region saturates nearly to a constant value independent of VC and t0, because of the surface diffusion due to the strong Coulomb repulsive force. Then the FWHM of the spatial distribution increases as a function of VC and t0. On the other hand, in the case of the contact charging of negative charge in a vacuum, as shown in Fig. 19 (b), the densely deposited charge density at the central region saturates nearly to a constant value independent of t0, but increases proportionally to VC, because of the capacitive charging. In a vacuum, surface diffusion does not occur so that the capacitive charging will cease after the long contact time because of the strong Coulomb repulsive force.

5. Atomically Resolved Imaging of Point Charge and Contact Potential Difference 5.1. ATOMICALLY RESOLVED IMAGING OF POINT CHARGE In this experiment, we tried to image point charge [20-21] by combining electrostatic force microscope (EFM) with noncontact atomic force microscope (NC-AFM) [22]. Here, we eliminated the electrostatic force contribution in the topography of n+GaAs(110) cleaved surface with EFM/NC-AFM, as shown in Figs. 20 and 21, by applying the sample voltage of VDC= -0.375 V, which compensated the averaged contact potential difference (CPD) between the Si tip and n+-GaAs(110) cleaved surface. On the other hand, by applying a large positive sample voltage of VDC = 0.625 V or a large negative sample voltage of VDC = -1.234 V, we enhanced the electrostatic force between tip and sample surface. To separate the contribution of the electrostatic force to NC-AFM, we applied sample voltages of VDC= -0.375 V and 0.625 V (or 1.234 V), alternately. Then, to image the NC-AFM, we closed the feedback loop to maintain the constant frequency shift under the sample voltage of VDC = -0.375 V and imaged the feedback voltage by scanning the tip. On the other hand, for the EFM imaging, we opened the feedback loop under the sample voltage of VDC = 0.625 V (or 1.234 V) and imaged change of the frequency shift between two alternate sample voltages by scanning the tip [20-21]. The NC-AFM topographies of Figs. 20 (a) and (b) clearly show several atomic point defects as well as periodic lattice structure. Atomic point defects appear as depressions (dark contrast). By comparing the NC-AFM topography a of Fig. 20 (a) with that of Fig. 20 (b) imaged at 8 min. later, we found that atomic point defects moved even at RT as shown by relative positions of defects A and B. We also found that the atomic point defect A appears as a large and deep depression, while others such as defect B appear as small and shallow depressions. In EFM images of Figs. 20 (a) and (b), only the large and deep defect A clearly

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changed its contrast from protrusion t (bright contrast) at VDC = 0.625 V to depression (dark contrast) at VDC = -1.234 V as shown in cross-sectional line profiles along white lines indicated in EFM images. Bright contrast suggests that the point charge of the atomic point defect A has positive sign, because negative charge on the tip of cantilever induced by the sample voltage of VDC = 0.625 V detects attractive force from the point charge [20-21]. Similarly, dark contrast also suggests that the point charge of the atomic point defect A has positive sign, because positive charge on the tip of cantilever induced by the sample voltage of VDC = -1.234 V detects repulsive force from the point charge. Small and shallow defects and periodic lattice structure in EFM images did not change vague contrast from bright to dark (or vice versa) by changing the sample voltage from VDC = 0.625 V to VDC = -1.234 V. Therefore, we conjectured that small and shallow defects and periodic lattice structure have not charge or have only small charge, and that those vague contrasts in EFM images are ghosts perhaps due to the cross talk between the NC-AFM topography and the EFM image. nc-AFM Topography

Electrostatic Force Image

nc-AFM Topography

VDC= - 0.375V

VDC=0.625V 6

VDC=-0.375V

Electrostatic Force Image +Qs + +Q Q

VDC=0.625V

A

A

C

+Qs

C D

ThomashomasThomas T Fermii ing Screening

E

in 8 min later

0Hz 5.0Hz A

A

44H Hzz 4Hz

0 09 m 0.09nm

0.07nm

B

+Qs

!

0

!

42

0

42 2

(a)

VDC= - 0. 0.375V .

VDCC= -1.234V 2334V

+Qs

DC VDC

A A

C

+Qs

D

ThomasT Fermi Screening

E B

0.07nm 00.07 07

B

0 11 m 0.11nm

2.88 (b) 2.8Hz A

Area! 15nm ×15nm Scan Area !1 5 × 15nm

0 A

+Qs

Figure 20. Simultaneously obtained NC-AFM topography and electrostatic force microscope (EFM) image. Cross-sectional line profiles are obtained along white solid lines indicated in images. (a) and (b) are successively measured images with interval time of 8 min. Scan area is 15nmx15nm.

C

2Hz 2H

C

Q 0

2

(b)

+Qs 422

Area! 4 ×40nm Scan Area !40nm × 40nm

Figure 21. Simultaneously obtained NC-AFM topography and EFM image. Cross-sectional line profiles are obtained along white solid lines indicated in images. (a) and (b) are successively measured images with interval time of 8 min. Scan area is 40nmx40nm.

Figures 21 (a) and (b) show wide area images of NC-AFM topography and EFM. The NC-AFM topographies show many atomic point defects, although the periodic lattice structure became vague. Only three atomic point defects C, D and E of Figs. 21 (a) and (b) changed those contrasts of EFM images from protrusion to depression by changing the sample voltage from VDC = 0.625 V to VDC = -1.234 V as shown in crosssectional line profiles along lines indicated by arrows in EFM images. Therefore, only three atomic point defects C, D and E have positive charge. As shown by white solid circles in EFM image of Fig. 21 (a), we found dark

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regions surrounding bright spots corresponding to atomic point defects with positive charge. As shown by white solid circles in EFM image of Fig. 21 (b), these dark regions became bright by changing the sample voltage from VDC = 0.625 V to VDC = 1.234 V. Dark contrast suggests that the charge of dark regions on the sample surface has negative sign, because negative charge on the tip of cantilever induced by the sample voltage of VDC = 0.625 V detects repulsive force from the dark region. Similarly, bright contrast also suggests that the charge of bright regions on the sample surface has negative sign, because positive charge on the tip of cantilever induced by the sample voltage of VDC = -1.234 V detects attractive force from the bright region. It should be noted that white solid circles show the calculated Thomas-Fermi screening length and well agree with extent of dark and bright regions. Thus, h we concluded that, in these regions, free electrons are screening positive point charges. Further, as shown by white broken circles in EFM images of Figs. 21 (a) and (b), we found similar regions which changed its contrastt from dark to bright by changing the sample voltage from VDC = 0.625 V to VDC = -1.234 V, although these regions have not positive point charge at its center. We conjectured that these regions also made from the free electrons that screen positive point charges located below the sample surface. It suggests that positive point charges located below the sample surface will not be observed because of the electron screening, although the screening electron clouds will appear on the sample surface. The number of defects without positive point charge seems to exceed the number of Si impurity density, while that with positive point charge roughly agrees with the number of Si impurity m density. Therefore, Si ionized donor may be the origin of defects with positive point charge. However, it appears as large and deep depressions in the NC-AFM topography. This result suggests that positive point charge locally changes the contact potential difference (CPD). Hence, positive point charge will exerts the repulsive force toward the tip of cantilever with the positive charge induced by the sample voltage of VDC = -0.375 V. This repulsive force may show Si ionized donor as a large and deep depression. Thus, it should be noted that to obtain true topography and hence quantitative EFM image, we should compensate the CPD on an atomic scale. 5.2. ATOMICALLY RESOLVED CONTACT POTENTIAL DIFFERENCE To compensate the contact potential difference (CPD) on an atomic scale, we combined Kelvin probe force microscope (KPFM) with NC-AFM [23]. KPFM measures capacitive force (dC/dz)(V - φ)2/2 in addition to the usual atomic force Ftopo. Here, C, φ and V are capacitance, contact potential difference (CPD) and external bias voltage between tip and sample, respectively. By applying the DC and AC voltages V = VDC + VACsinωt, ω the ω and 2ω terms in the total force become (dC/dz)VAC(VDC φ)sinωt ω and -(dC/dz)VAC2cos2ωt/4, ω respectively. To measure CPD φ, we used the feedback circuit to control the ω term zero by changing VDC, so that VDC satisfies the ω term is proportional to dC/dz. relation VDC = φ. Here, the 2ω As shown in Fig. 22, we simultaneously measured the NC-AFM topography, the CPD and the dC/dz of Si(111)7x7 sample surface. As a result, we achieved atomically resolved imaging of the CPD and the dC/dz of Si(111)7x7 as well as the NC-AFM topography [23].

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Using developed high performance KPFM/NC-AFM [23], we simultaneously imaged the NC-AFM topography and the CPD of Si(111)5√3×5√3-Sb as shown in Fig. 23. As a result, we succeeded in discriminating Sb adatoms and Si adatoms on Si(111)5√3×5√3-Sb from the CPD image [24].

CPD Image (Si Tip) Si Atom: Dark Spot (a)

Sb Atom: Dim Spot 353

imag CPD image (mV)

imag KFM image

Topography (Si Tip)

VDC φ (b)

292

i h Spot Si A Atom: Brighter i l Dim i Spot Sb Atom: A Little

1 376 1.376

(Hz)

Si adatom Sb adatom

1 360 1.360

Simultaneously obtained images of (a) NC-AFM topography, (b) CPD and (c) dC/dz of Si(111)7x7. Scan area is 10.2nmx6.6nm.

Figure 23. Simultaneously obtained images of (a) NC-AFM topography, (b) CPD of Si(111) 5√3×5√3-Sb. Scan area is 10.1nmx8.5nm.

6. Conclusion In this study, we investigated the elementary processes of contact charging and its dissipation on a silicon oxide surface using a reproducible and controllable contact charging method. As a result, we found that negative charge show three stages of both contact charging and charge dissipation, while positive charge shows only one stage. By keeping on contact charging further, negative charge became stable state with high density, i.e., a solid phase of charges, on the silicon oxide surface even at room temperature in air. Although we cannot introduce in this review chapter, we also investigated (1) stability of densely deposited charge [25], (2) dissipation of densely deposited negative charge on various dielectric t films [26-27], and (3) correlation between deposited charge groups [28-29]. Next, to investigate charge distribution and also charge dissipation in more detail, we developed electrostatic force microscope (EFM) combined with noncontact atomic force microscope (NC-AFM). As a result, we succeeded in imaging point charge and charge distribution of free electrons on n+-GaAs(110) cleaved surface with atomic resolution using EFM/NC-AFM. However, we found that, to obtain true topography and hence quantitative EFM image, we should compensate the CPD on an atomic scale. Therefore, to compensate the CPD on an atomic scale, we developed Kelvin probe force microscope (KPFM) combined with NC-AFM and then imaged contact potential difference (CPD) of Si(111)7x7 on an atomic scale. Using this novel high-resolution

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KPFM, we succeeded in discriminating Sb adatoms and Si adatoms on Si(111)5√3×5√3-Sb.

References 1. Terris, B.D., Stern, J.E., Rugar, D., and Mamin, H.J. (1989) Contact Electrification Using Force Microscopy, Phys. Rev. Lett. 63, 2669-2672. 2. Schönenberger, C. (1992) Charge flow during metal-insulator contact, Phys. Rev. B 45, 3861-3864. 3. Stern, J.E., Terris, B.D., Mamin, H.J., and Rugar, D. (1988) Deposition and imaging of localized charge on insulator surfaces using a force microscope, Appl. Phys. Lett. 53, 2717-2719. 4. Schönenberger, C., and Alvarado, S.F. (1990) Observation of Single Charge Carriers by Force Microscopy, Phys. Rev. Lett. 65, 3162-3164. 5. Morita, S., Fukano, Y., Uchihashi, T., Okusako, T., Sugawara, Y., Yamanishi, Y., and Oasa, T., (1993) Reproducible and Controllable Contact Electrification on a Thin Insulator, Jpn. J. Appl. Phys. 32, L1701L1703. 6. Morita, S., Sugawara, Y., and Fukano, Y. (1993) Atomic Force Microscope Combined with Scanning Tunneling Microscope [AFM/STM], Jpn. J. Appl. Phys. 32, 2983-2988. 7. Fukano, Y., Hontani, K., Uchihashi, T., Okusako, T., Chayahara, A., Sugawara, Y., Yamanishi, Y., Oasa, T., and Morita, S. (1994) Time Dependent Dielectric Breakdown of Thin Silicon Oxide Using Dense Contact Electrification, Jpn. J. Appl. Phys. 33, 3756-3760. 8. Sugawara, Y., Morita, S., Fukano, Y., Uchihashi, T., Okusako, T., Chayahara, A., Yamanishi, Y., and Oasa, T. (1995) Time Dependence and its Spatial Distribution of Densely Contact-Electricfied Electrons on a Thin Silicon Oxide, in H.-J.Güntherodt, D.Anselmetti and E.Meyer (eds.), Force in Scanning Pribe Methods, NATO ASI Series E: Applied Sciences-Vol.286, Kluwer Academic Publishers, Dordrecht,, pp. 501-506. 9. Fukano, Y., Sugawara, Y., Uchihashi, T., Okusako, T., Morita, S., Yamanishi, Y., and Oasa, T. (1996) Phase Transition of Contact-Electrified Negative Charges on a Thin Silicon Oxide in Air, Jpn. J. Appl. Phys. 35, 2394-2401. 10. Morita, S., Uchihashi, T., Okusako, T., Yamanishi, Y., Oasa, T., and Sugawara, Y. (1996) Stability of Densely Contact-Electrified Charges on Thin Silicon Oxide in Air, Jpn. J. Appl. Phys. 35, 5811-5814. 11. Nicollian, E.H., and Brews, J.R. (1981), MOS (Metal Oxide Semiconductor) Physics and Technology John Wiley & Sons, New York, 1981, p. 314. 12. Fukano, Y., Okusako, T., Uchihashi, T., Sugawara, Y., Yamanishi, Y., Oasa, T., and Morita, S. (1994) Observation of Positively Charged Trap Site in Silicon Oxide Layer with an Atomic Force Microscope, Extended Abstracts of the 1994 International Conference on Solid State Devices and Materals, Yokohama, pp. 37-39. 13. Furukawa, S. (1982), Handotai Device (in Japanese), Corona-sha, Tokyo, p. 153. 14. Morita, S., Sugawara, Y., Fukano, Y., Uchihashi, T., Okusako, T., Chayahara, A., Yamanishi, Y., and Oasa, T. (1993) Stable-Unstable Phase Transition of Densely Contact-Electrified Electrons on Thin Silicon Oxide, Jpn. J. Appl. Phys. 32, L1852-L1854. 15. Sugawara, Y., Morita, S., Fukano, Y., Uchihashi, T., Okusako, T., Chayahara, A., Yamanishi, Y., and Oasa, T. (1994) Spatial Distribution and Its Phase Transition of Densely Contact-Electrified Electrons on a Thin Silicon Oxide, Jpn. J. Appl. Phys. 33, L70-L73. 16. Grimes, C.C., and Adams, G. (1979) Evidence for a Liquid-to-Crystal Phase Transition in a Classical, Two-Dimensional Sheet of Electrons, Phys. Rev. Lett. 42, 795-798. 17. Sugawara, Y., Tsuyuguchi, T., Uchihashi, T., Okusako, T., Fukano, Y., Yamanishi, Y., Oasa, T., and Morita, S. (1996) Density saturation of densely contact-electrified negative charges on a thin silicon oxide sample due to the Coulomb repulsive force, Philos. Mag. A 74, 1339-1346. 18. Morita, S., and Sugawara, Y. (2001) Microscopic contact charging and dissipation, Thin Solid Films 393, 310-318. 19. Tsuyuguchi, T., Uchihashi, T., Okusako, T., Sugawara, Y., Morita, S., Yamanishi, Y., and Oasa, T. (1994) Contact Electrification on Thin Silicon Oxide in Vacuum, Jpn. J. Appl. Phys. 33, L1046-L1048. 20. Sugawara, Y., Uchihashi, T., Abe, M., and Morita, S. (1999) True atomic resolution imaging of surface structure and surface charge on the GaAs(110), Appl. Surf. Sci. 140, 371-375. 21. Morita, S., Abe, M., Yokoyama, K., and Sugawara, Y. (2000) Defects and their charge imaging on semiconductor surfaces by noncontact atomic force microscopy and spectroscopy, J. Cryst. Growth 210,

308 408-415. 22. Morita, S., Wiesendanger, R., and Meyer, E. (Eds.) (2002) Noncontact Atomic Force Microscopy, Springer, Berlin Heidelberg. 23. Okamoto, K., Sugawara, Y., and Morita, S. (2002) The elimination of the ‘artifact’ in the electrostatic force measurement using a novel noncontact atomic force microscope/electrostatic force microscope, Appl. Surf. Sci. 188, 381-385. 24. Okamoto, K., Yoshimoto, K., Sugawara, Y., and Morita, S. (2003) KPFM Imaging of Si(111) 5√3×5√3Sb Surface for Atom Distinction Using NC-AFM, Appl. Surf. Sci., in press. 25. Morita, S., Uchihashi, T., Okusako, T., Yamanishi, Y., Oasa, T., and Sugawara, Y. (1996) Stability of Densely Contact-Electrified Charges on Thin Silicon Oxide in Air, Jpn. J. Appl. Phys. 35, 5811-5814. 26. Okusako, T., Uchihashi, T., Nakano, A., Ida, T., Sugawara, Y., and Morita, S. (1994) Dissipation of Contact Electrified Electrons on Dielectric Thin Films with Silicon Substrate, Jpn. J. Appl. Phys. 33, L959L961. 27. Uchihashi, T., Okusako, T., Tsuyuguchi, T., Sugawara, Y., Igarashi, M., Kaneko, R., and Morita, S. (1994) Charge Storage on Thin SrTiO3 Film by Contact Electrification, Jpn. J. Appl. Phys. 33, L959-L961. 28. Uchihashi, T., Okusako, T., Sugawara, Y., Yamanishi, Y., Oasa, T., and Morita, S. (1996) Correlation between contact-electrified charge groups on a thin silicon oxide, J. Vac. Sci. Technol. B 14, 1055-1059. 29. Uchihashi, T., Okusako, T., Sugawara, Y., Yamanishi, Y., Oasa, T., and Morita, S. (1996) Proximity effects of negative charge groups contact-electrified on thin silicon oxide in air, J. Appl. Phys. 79, 4174-4177.

CONSTRUCTIVE NANOLITHOGRAPHY

S.R. COHEN, R. MAOZ, and J. SAGIV Weizmann Institute of Science P.O.B. 26, Rehovot, ISRAEL 76100

Contents 1. 2. 3.

4.

5. 6.

Introduction Silane-based Self-Assembled Monolayers (SAMs) – preparation and chemistry SPM-based nanolithography 3.1. Anodic oxidation of silicon 3.2. Constructive nanolithography - chemical, physical, and analytical basis 3.2.1. Oxidative processes 3.2.2. Reductive processes 3.2.3. In-situ chemical generation and import of prefabricated inorganic species by Ligand exchange 3.2.4. “Macro-Nano” approach Analytical techniques 4.1. Macroscopic analytical techniques 4.2. SPM-based techniques Experimental considerations for optimization of writing Future directions and applications

1. Introduction The subject of this volume, Scanning Probe Microscopy, by its nature brings us to the molecular or atomic realm, or minimally into nanometer-scale phenomena. This chapter deals with the fabrication of small features on solid surfaces, aided by the scanning probe microscope (SPM) tip. Whereas lithography was developed to create small structures, and is continually undergoing improvements to reduce the size scale and improve fidelity, reproducibility, and speed, most lithographic procedures treat the surface as a formable mold, into which features are etched or grown with spatial resolution aided by the blocking properties of a resist. The procedures described here use the surface as template for subsequently grown structures – the surface is built upon rather than carved into. Further, in contrastt to conventional lithographic processes, this can essentially be thought of as resistless lithography, since the organic coating on the silicon substrate is not used to “block” chemical access to the silicon, but rather serves as a template for the growth of surface structures, by chemical specificity of subsequent reactions. In this case, the organic coating consists of a self-assembled monolayer 309 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 309-331. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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(SAM) film. The wide range of surface chemical modifications that can be controllably performed on such films lends flexibility to this technique that is not available with other lithographic processes. In order to provide a sound overview of this field, brief discussions of the principle ingredients will be made - silane-based SAMs, and scanned-probe based anodic oxidation at a silicon surface. Subsequently, several examples of the application of this technique will be given, in order to give a feeling for the extent of different possibilities, and to demonstrate the philosophy of the approach. Particular care will be given to the experimental aspects of the work, such as the non-trivial problem of performing surface analytical chemistry at the nanoscale. The goal of this chapter is thus to present the scientific basis behind a new approach for performing surface chemistry at the nanoscale, rather than to propose a technologically sophisticated lithographic procedure.

2. Silane-Based Self-Assembled Monolayers (SAMs) – Preparation and Chemistry Monolayer films of long chain hydrocarbons can form well-ordered, close-packed films on a variety of surfaces. For a general treatment of monomolecular surface films, the reader is referred to ref. 1. Zisman and coworkers first investigated the spontaneous adsorption of such monomolecular films onto polar surfaces from organic solutions over half a century ago.2 Silane-based monolayers were heavily investigated from the late 1970s onward. Such monolayer films are extremely stable due to their capability to , undergo chemical adsorption at the surface through the strong Si-O bond.3 4 Furthermore, lateral covalent bonding between adjacent adsorbate molecules results in an extremely robust monolayer that can be subjected to rigorous chemical treatments without perturbation of the structure of the layer itself, or of the underlying substrate. Based on these properties, numerous chemical modifications of the monolayer surfaces were demonstrated, which also led to chemical assembly of multilayers.5,6,7,8 Following quantitative oxidation of such surfaces by chemical means, observed by SPM, we were intrigued by the idea of performing the oxidation with fine spatial resolution, by using the SPM tip in a spontaneously formed nano-electrochemical cell.9 The silane monolayers used in this work were prepared by well-documented 79 procedures, , starting from organotrichlorosilanes (NTS, OTS, or mixtures thereof, see Figure 1). NTS was generously supplied by K. Ogawa, Matsushita Electric Ind. Co., Ltd.10 OTS used was “For Synthesis” grade (Merk-Schuchardt). Substrates were doublepolished silicon wafers (<100>, Semiconductor Processing Co.), typically p-type (resistivity 8-11 ohm-cm). The wafers were cleaned by high-power microwave treatment.11 Monolayers were assembled by twice immersing pieces of the clean Si into a 5 mM solution of the appropriate silane in pure bicyclohexyl for approximately 30 s, and then sonicating in analytical grade toluene. The hydrophobic monolayer is completely dry upon removal from this rinse. Monolayer quality was checked by Fourier Transform Infra-Red Spectroscopy (FTIR) and contact angle measurements. Using the initial starting surface consisting of OTS, NTS, or a mixture thereof, a large variety of surface modifications could be made, provided that the initial monolayer is closely packed and strongly adsorbed. UV/vis and FTIR spectroscopies were used to verify that all chemical transformations modified the outer functionality only, leaving

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the anchoring of the monolayer and its configuration on the surface intact. NTS was modified in a variety of ways:

Figure 1. Schematic of the starting molecules, in free and surface-bound form (A) OTS; (B) NTS.

Oxidation was affected with KMnO4 crown ether complex (dicyclohexano-18-crown-6). The NTS monolayer was treated in a 5 mM solution of the complex in analytical grade benzene for 2 days in a closed vessel with an atmosphere of saturated benzene, followed by multiple rinses with benzene, 2 minutes sonication in benzene, 30 minutes soaking in 5% aqueous HCl, followed by thorough rinse in a purified water stream. Thiol-top sulfur functionality was formed by irradiation at 254 nm for 20 minutes under an atmosphere of H2S diluted in Ar. This was typically performed on a mixed monolayer, formed by adsorption from a 1:1 mixture of OTS:NTS in order to maintain a low energy surface which ensures sample cleanliness and confinement of the water meniscus (vide infra). Surface metal salts such as the silver and cadmium thiolates were formed by ion exchange onto the thiolated surface from aqueous solutions of the respective acetates. 3. SPM-Based Nanolithography In the quest for production of ever-smaller devices, miniaturization has turned to SPM for both formation, and testing of small features and devices on surfaces. This direction was driven by the realization that conventional lithography technology could not meet the ever-increasing demands, and indeed physical limitations seemed to point to this route as a dead-end path. Despite the largest disadvantages of SPM-based techniques – slow read and write times due to the mechanical motion of a probe tip, there were hopes that multiple tip-writing, such as in the “millipede” device,12 would bring the speed/size characteristics into a range which allowed competition with the other, intrinsically parallel techniques. Subsequently, new variations of the conventional lithography techniques (“soft-lithography”,13 SCALPEL,14 extreme UV photolithography,15,16 and others) have somewhat altered the pessimistic predictions for those parallel techniques, and pushed back for some time the necessity of implementing SPM – based lithography. On the other hand, the efforts invested into SPM-based techniques have born fruit, and brought this concept to the stage of a feasible product within a decade of its conception,

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which compares favorably with the time-line for concept-to-product of other technologies. Initial tests of the utility of proximal probe lithography were made already in the early years of SPM work.17,18 Various mechanical manipulations of surface layers were performed by SPM,19 ordering of atoms by STM was demonstrated in 1990,20 small features were written by melting a metallic glass in 1988,21and formation of structures , directly on Si was first shown in 1990.22 23,24 The promotion of SPM, and other alternative techniques to achieve miniaturization goals was soon found to be limited by steps other than the writing tool used: Pattern broadening originating in exposure and development steps of the resist material remained a significant factor in ultimate size achieved. For instance, e-beam pattern broadening due to electron scattering within the resist layer has been addressed by going to ever-thinner resist layers, the ultimate being an ordered, monomolecular layer film.25 Thus, SAMs were seen as an ultimate replacement for polymer resists, due to their molecular thickness, robustness, and diverse functionality. This previous work established that SAM resists, combined with SPM exposure and modifications of development techniques could lead to excellent patterning resolution. 3.1. ANODIC OXIDATION OF SILICON As the field developed, it became clear that SPM could be used as a tool to build up structures and devices on a surface, rather than for exposing thin resists by destroying them. Early works showed that reproducible structures could be formed on either Hpassivated Si or Si with a native oxide layer while controlling the size and shape of silicon oxide growth. However, the mechanism of the oxide growth, depicted schematically in Figure 2 was only later elucidated through a number of works.26,27,28,29 The process is essentially an electrochemical one, requiring the presence of a small water bridge between tip and surface which will develop spontaneously in ambient environment. The formation of the liquid droplet on silicon is dependent on several factors. Growth of an oxide dot under voltage bias depends strongly on the relative humidity in the working environment. Typical laboratory conditions with relative humidity of 50% were generally sufficient to produce the effect. By varying the magnitude and duration of the voltage pulses, it was possible to demonstrate that the voltage pulse itself has a key role in development of a water bridge.28 It was shown that the magnitude, rather than duration of the pulse is the parameter that controls formation of the bridge. Below a critical voltage, no water bridge and hence no writing could occur. The critical voltage was proposed to induce a polarization of the water, which led to formation of the water bridge. The presence of the water bridge could be detected independently by observing the mechanical behavior of the oscillating cantilever. In analogy to other film growth processes where ionic transport is required, the magnitude of the electric field was indicated for governing the ultimate feature size. Thus, the presence of a water bridge over which the field remains constant would lead to significant broadening of the features. This broadening was observed both for the growing film, and for the depleted silicon volume.26

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Figure 2. Schematic of SPM-Based oxidation of Si, showing growing SiO2 dot, and relevant processes.

The process depicted in Figure 2 begins with formation of the water droplet, followed by electrochemical formation of the oxyanion inside this droplet at the negative electrode. Migration of the oxyanion to the silicon surface is initially rapid, but slows as the oxide film thickness increases. The kinetic influence of the different steps has been addressed for this system. The rate-limiting step is not likely the oxyanion formation (which includes hole transport to the surface, since the doping type (p or n) does not strongly influence the rate.29 Thus, either oxyanion formation, or its migration to and reaction with the surface must control the reaction rate. The Cabrera-Mott model predicts such a fall off due to the effect of the field on the barrier for ion transport. However, dependence on both voltage and field were found, and the rate of fall off did not fit the exponential dependence predicted by this model. Both mismatch between the growing oxide and underlying silicon,26 and negative charge buildup in the growth region22 have been linked to the rate fall-off. Tight control of the oxide size and shape was necessary to form the small structures desired, and successes in this direction were carried to other common device substrates such as GaAs. This work led directly to creation of sub-10 nm device formation.30 As a final note, using probes in the noncontactt mode rather than contact mode introduces another parameter for smooth variation of the electric field applied and reducing the tip wear.31 3.2. CONSTRUCTIVE NANOLITHOGRAPHY- CHEMICAL, PHYSICAL, AND ANALYTICAL BASIS Despite the fine control and remarkable achievements of the approaches described above, they could not address the question of building up complex, multilayer structures on a surface, or allow access to the rich chemistry available on SAMs which have been

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demonstrated by wet-chemical processes.6,7 The robust nature of silane-based SAMs enables a large repertoire of chemical transformations on these films without compromising their ordered, close-packed surface configuration. This feature is central to their application in nanolithography since one key function of the monolayer film is to provide an ordered template for the structures grown upon it. Furthermore, the presence of the organosilane film serves as a protective barrier on the surface and prevents further reactions of the silicon substrate, water condensation, and can serve as a boundary lubricant in preventing wear for cases where mechanical abrasion is of concern. Tip-induced chemical transformations on SAMs were initially designed to mimic the well-studied wet-chemical reactions described above. The unique configuration of the proximal probe lithography proves to be necessary in carrying out such analogous reactions. Thus, the small aqueous droplet, which spontaneously forms by capillary condensation between tip and surface, provides a nano-reaction cell in which familiar wet-chemical processes can proceed. These reactions are more varied and versatile than the oxidative reaction shown on silicon. Furthermore, we should expect differences in the mechanism for the monolayer reaction as compared with silicon. As was mentioned in section 3.1, oxyanion migration through the growing SiO2 zone is required for anodic oxidation on silicon. 3.2.1. Oxidative Processes For reactions on the SAM outer functionality, the oxyanion migration step is excluded from the process, since all reactions occur at the exposed outer surface, and there is not an infinite reservoir of reactant rising from the bulk. For the fundamental oxidation reaction on a pristine SAM, such as oxidation of OTS, the following reaction steps are proposed: At the negative tip: (1) 2H2O + 2e- → H2 + 2OHAt the positive surface: R-CH3 + 2OH- +2h+ → RCOOH +2H2 (2) Leading to the overall surface reaction: (3) R-CH3 + 2H2O → RCOOH + 3H2 Thus, the reaction ultimately involves transport of charge through the organic molecular bridge from the surface carriers. Electron transport through molecules has been studied intensively in recent years due to its importance for molecular-based electronics.32 In general, transport rates decline exponentially with the molecule length, and in addition vary vastly between different molecules with different functionalities.33 Of major concern in such studies is the barriers formed between molecule and surface, and between upper electrode and molecule, viz. at the tip/molecule interface. Chemical binding at such an interface will lower the barrier for electron transport. As the SPM tip does not chemically bind to the surface, this barrier is potentially a large one. A number of conducting tips have been used for SPM nanolithography, and we may expect that the efficiency of the writing will be strongly dependent on the type of tip used. The second barrier, at the surface, is intrinsically large since the molecule is chemically bound to the insulating native oxide growing on the silicon.

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Figure 3. Topography (left) and Friction (right) images after step 1 (A) and step 2 (B) , scheme X. Further writing under the same conditions shows how the writing conditions which oxidize the monolayer leave the bilayer unchanged (C,D). 3D view of final structure with cross-sections shown in (E).published with permission from Advanced Materials, ref. 9, Figure 5.

The oxidative scheme outlined in Eqs. 1-3 indicates an oxidation of the outer surface functionality whereby the oxyanion formed in electrolysis of water reacts with the organic moiety, aided by influx of holes from the surface to form the oxidized surface species. This reaction has been performed on both NTS and OTS. Figure 3 shows the possibility of bilayer buildup using such a scheme, and highlights the influence of film thickness on the effectiveness of the writing step. An OTS surface was also electrochemically oxidized on a large scale by applying the bias through a fine-mesh copper grid placed in intimate contact with the surface. The substantial surface area which was reacted could then be investigated using FTIR surface spectroscopy, as shown in Figure 4. Small electronic devices structures will likely be heterogeneous, involving both organic and metallic components. Oxidative nanolithographic schemes can be used to form small metal oxide surface structures.34 For this, we can either start with a Agmodified surface as described in section 2.3, or use a silver tip, and deposit the metal directly onto the surface. Depending on the environmental conditions, this can result in formation of the silver oxide, or direct transfer of Ag metal on the tip to Ag oxide on the silver-free surface in “fountain-pen” fashion.(An analogous inverse process whereby material pre-coated on the tip is transferred without chemical change to the surface has

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been termed “dip-pen” lithography).35 To form the oxide, we have at the (positively biased tip): 2Ago + H2O → Ag2O + 2H+ +2e(4) And at the negatively biased surface 2H2O + 2e- → H2 + 2OH(5) Giving an overall Process: 2Ago + H2O → Ag2O + H2 (6) The pattern formed under these writing conditions (positively-biased Ag tip, humid air) was clearly observed in topography, but did not lead to build-up of Ag metal upon exposure to the Ag enhancing solution, which eliminated the possibility that it was elemental Ag. On the other hand, by minor modification of the operating conditions, elemental silver could be formed.

Figure 4. Quantitative Brewster angle FTIR spectra of: dotted line, OTS/Si monolayer self-assembled on silicon substrate; full line, after contact for about 2 min with a 3000 mesh copper grid to which an electrical bias of -13 V was applied relative to the silicon substrate, followed by exposure to aqueous HCl (5%) for 2 h; dashed line (1900 - 1300 cm-1 spectral region only ), after exposure of the acid-treated surface for 0.5 min to a solution of octadecylamine in BCH . All curves represent net spectra of the organic coating, after mathematical subtraction of the spectral contributions of the bare Si substrate Reprinted by permission from ref 36, Figure 3.

3.2.2. Reductive Processes The above process was observed in humid air. It is interesting to note that under an atmosphere of dry nitrogen, Ag metal is deposited directly onto the surface, presumably by the following steps: At the positively biased tip:

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Ago

→ Ag+ + e-

(7)

At the surface: R-SH + Ag+ + e- → R-SH + Ago (8) with overall process of transfer of metallic silver from tip to surface. These different results under dry or humid air were conveniently distinguished by applying the Ag enhancing developer solution. The pattern obtained under humid air did not develop further, whereas that produced under dry nitrogen did. Metallic patterns can be created using the surface as a reservoir rather than the tip, as indicated in Figure 5. Preparation of the Ag ion –loaded surface is done by photolysis of an NTS surface under H2S atmosphere, leading to the “thiol-top-functionalized silane monolayer” (TFSM). Exposure to a solution of silver salt results in a chemisorbed outer layer of Ag ions. Reduction of this ionic silver will then occur under positive tip bias: At the negative surface, (9) 4R-S-Ag+ + 4e- + 4H2O → 4R-SH +4Ago + 4OHAt the positive tip 2H2O → O2 + 4H+ + 4e(10) Overall process: 4R-S-Ag+ + 2H2O → 4R-SH + 4Ago + O2 (11) Although Ag can be deposited from a Ag tip under positive tip bias, these conditions do not yield surface Ag for a conductive, non-Ag tip on the Ag –ion loaded surface. This further confirms that the tip-induced reduction of surface-bound silver is a watermediated Faradaic process.

Figure 5. Scheme for Reduction of metal ions on surface. Published with permission from Advanced Materials, ref. [34], Figure 1.

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3.2.3. In-situ Chemical Generation and Import of Prefabricated Inorganic Species by Ligand Exchange We now consider post-lithographic schemes whereby the chemical transformations as outlined above serve as “active sites” for spontaneous organization and the deposition occurs by different means than those outlined above. The bilayer buildup shown in Figure 3 is an example of the first stage of such a design, whereby the OTS molecules spontaneously assemble from solution onto the bound oxidized NTS molecules. The additional concept introduced here is to perform surface chemistry on the structures formed, as precursor for continued surface build-up entailing yet another type of interaction. Here, we consider both in-situ chemical generation, and import of prefabricated nanoparticles via ligand exchange. In order to allow the possibility to perform chemical transformations that involve harsh reactants, it is necessary to use an inert surface as a template. For this reason, OTS is the monolayer template of choice, in its unmodified form being inert to strong oxidants and low energy UV photolysis. We have explored these two different schemes for formation of hybrid inorganic/organic structures., Figure 6 shows a generic scheme for in-situ generation. In both the upper and lower pathways, a reactive layer results from the initial processing.36 The initial nanoelectrochemical patterning on OTS is followed by buildup of a second layer of the (relatively) reactive NTS. The NTS can be outer functionalized to form a TFSM, or alternatively an oxidized organic film. These bilayer templates can now serve as sites for further assembly. Exposure of the TFSM to a Cadmium salt leads to the formation of surface-sulfur-bound Cadmium. Subsequent exposure to H2S will rejuvenate the TFSM whereby the monolayer of the CdS remains attached to it. An arbitrarily number of layers of CdS can be formed in this way.36, 37 We have demonstrated cycling this Cd addition up to 7 times, to form three dimensional CdS layers.36

Figure 6. Generic scheme for in-situ chemical generation on the surface through a thiol linkage. Published with permission from Advanced Materials, ref. [36 ], Figure 1.

Ligand exchange was employed in a scheme which allows chemical binding of water-soluble, ligand capped Au nanospheres [Au55(Ph2PC6H4SO3Na)12Cl6] to a TFSM.38 Small metal particles, strategically placed on a surface with respect to current-carrying leads, represent one formulation of a single electron device in which electron transport

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occurs in quanta. In this case, the strong affinity of the thiol for the Au is the driving force for ligand exchange and subsequent binding. XPS spectra t indicate that the ligand coating is only partially removed. 3.2.4. “Macro-Nano” Approach Although a strong repertoire of surface tools has been developed for the characterization of monolayer films before and after surface transformations,1 these techniques are not well suited for the nanometer-sized features produced in SPM Nanolithography. For instance, XPS is sensitive to surface species down to the level of about 1%, with spatial resolution in state-of-the art equipment limited to 1-2 microns. FTIR spectroscopy can provide resolution at the 10-micron level and here only by application of an FTIR microscope, and is generally also insensitive to coverage significantly less than a monolayer. Contact angle measurements are inherently ambiguous for mixed surface species, although some efforts have been made to model the behavior based on relative surface energy contributions.39 Nonetheless, this technique has neither spatial resolution nor sensitivity for the small structures developed here. For this reason, we have developed a battery of protocols that allow confirmation of the intended surface reaction at the nanoscale. One such protocol involves comparison and correlation of well-established surface techniques for investigation of macroscopic surface regions with SPM measurements on the same samples at the nano-scale. Having established these correlations, SPM characterization of the small features is then sufficient. This approach exploits the chemical transformations described in section 2, which can be carried out over macroscopic surface regions. These surface transformations can be limited to well-defined regions on the surface, by only exposing part of the sample surface to the reactant solution. SPM measurements made on either side of the border can then be used to determine the expected contrast for analogous features produced by SPM Nanolithography. An example of this is shown in Figure 7 (a, b) where a clear border between oxidized and unoxidized NTS is observed by the SPM friction image (although not accompanied by any topographic change). In this case, the microscopic border shown here separates two macroscopic regions, which were well-characterized by FTIR spectroscopy t and contact angle measurement. The higher friction region can be directly assigned to the oxidized species. This correlation having been established, higher friction contrast is then use as identification of the oxidized species at the nanoscale. Figure 7 (c, d) points to another clear means for monitoring the lithographic action, which is the buildup of the second layer. Dipping the sample into an adsorption solution containing OTS leads to formation of a bilayer – OTS/NTSox. SPM measurements provide direct evidence of the indicated reaction, as seen by the higher topography and lower friction on the oxidized bilayer as compared with the bare NTSox. Whereas this experiment was performed by partial dipping of the oxidized surface into the OTS adsorption solution, it is in fact a selective chemical reaction: As the silane linkage can only occur at an oxide surface, a second layer will assemble on the oxidized region, whereas no reaction will occur on the inert nascent NTS region. SPM topography and lateral force images can then be used to distinguish these features on the nanoscale, as is demonstrated in section 4.1.

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Figure 7. (a), (b) Topography and friction mappings of chemically-patterned borderline (KMnO4 oxidation) on NTS, showing higher friction of the oxidized region to right. (c), (d) Borderline between NTSox/OTS (bilayer) demonstrating the lower friction and higher topography of OTS-coated region to right. Reprinted with permission from Advanced Materials [ref. 9], Figure 4.

The ability to induce the surface reactions by two parallel routes, one macroscopic/wet-chemical and the other nanolithographic/SPM-induced is therefore central to the Macro/Nano approach. These two parallel tracks are shown schematically in Figure 5 for the formation of metallic surface features. It was realized that the nanotopological change involved in reduction of a surface ionic species to produce the reduced metal could not be predicted. Further, frictional contrast t is problematic since these loosely-bound species are easily swept away in the contact-mode imaging required for friction measurement. A first step therefore entailed performing the wet-chemical reduction on a large surface region (Fig. 5, bottom scheme), then monitoring the change by UV-visible spectroscopy, and X-ray Photoelectron Spectroscopy, with confirmation by AFM imaging. Further verification of the chemical transformation exploited selective chemical reaction on the reduced species, resulting in a topographic feature

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observable on the surface. This was performed with a commercial silver developing solution, which deposits metallic Ag only on those regions where Ag nanoparticles already exist, leaving the ionic Ag unchanged.40 4. Analytical Techniques 4.1. MACROSCOPIC ANALYTICAL TECHNIQUES A number of macroscopic techniques have become accepted for testing monolayer quality and integrity. Despite the drawbacks mentioned above, these techniques are essential for proper characterization of a monolayer film. Most commonly used in our laboratories are FTIR spectroscopy, UV/visible spectroscopy, contact angle measurement, x-ray diffraction/reflection, and x-ray photoelectron spectroscopy (XPS). These techniques are termed macroscopic since they average information from large lateral expanses on the surface, up to 2-3 mm across. On the other hand, they are sensitive to small nuances of molecular orientation and coverage, and extremely surface-sensitive, capable of detecting a fraction of a monolayer. Accordingly, they can provide an indication of the average molecular state and orientation on the surface. Contact angles give a quick and qualitative estimate of the film quality. Often, a good test for a hydrophilic surface or completely reacted monolayer surface is simply observing a thorough wetting of the surface by water. Surface roughness can also influence the contact angle,41 though this should not be relevant for well-prepared monolayers on smooth substrates. For oriented trans-hydrocarbon chains exposing close-packed methyl groups, a contact angle of the order of 115 degrees for water, and 55 degrees for BCH should be obtained. For high quality monolayers, there is no measurable hysteresis between advancing and receding contact angle values. Contact angles of even a few degrees below these values and exhibiting hysteresis are indicative of poorly organized or sparsely packed monolayers. Contact angle values are shown in Table I. When only dispersion forces are involved, the contact angle can directly yield the interfacial energy between a liquid droplet and the surface, hence for liquids of known properties will probe the surface free energy. When there is a polar component to the interaction, a series of test liquids (minimum two) must be used to resolve the polar and dispersion components of the interaction.42,43 TABLE I. Contact angles of monolayer films (degrees ±1) Water

HD

BCH

OTS

115

52

55

NTS

103

50

52

NTS(ox)

0

0

0

FTIR spectroscopy, by measuring the energy (wavelength) and intensity of bands associated with particular vibration modes can identify specific functional groups on the surface, give a rough quantitative estimate of surface coverage, and under certain measurement conditions can identify the average molecular orientation on the surface.

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This is demonstrated clearly in Figure 4. The strong CH2- symmetric and antisymmetric peaks are seen at 2850 cm-1 and 2917 cm-1. Further, the CH3 antisymmetric stretch appears at 2964 cm-1, arising from the terminal methyl group in the OTS. The C=O stretch at 1713 cm-1 appears upon oxidation of the terminal CH3 of OTS to COOH. UV/vis spectroscopy is sensitive to the electronic transition assigned to certain chemical species, and in particular can return quantitatively the coverage of a metallic surface species. XPS can correlate the energy of a photoelectron to a particular nucleus, and thus examines not only the chemical surface make-up, but also the chemical environment. Further, by adjusting take-off angle, highly-resolved depth profiles can be made. However, the monolayer is easily damaged by the secondary electrons excited by the incident x-rays. This damage depends on type of binding to substrate, and appears to be enhanced for specific functional groups.44 Due caution must be exercised in these analyses – mainly reducing exposure times which can be accomplished by a small-spot x-ray irradiation being continually moved to fresh sample regions. Despite these caveats, the power of XPS for detecting small concentrations of surface species (1%), depth profiling, and functional group differentiation make it an essential tool. Recently, time of flight secondary ion mass spectroscopy (TOF-SIMS) has been applied to correlate lithographic changes on the surface as observed by SPM with the presence of different chemical species.45 By patterning large surface patches of 100 microns, it was possible to extract SIMS data for patterned vs. nonpatterned regions. Interestingly, not only CxHyO species were observed, but also CxHyN moieties when the carrier for the water vapor was rich in nitrogen. Additionally, a linear correlation was found between concentration of CxHyO and CxHyN. X-ray grazing incidence angle diffraction (GID), and reflectivity measurements provide additional structural information on monolayer and multilayer films.46 By using synchrotron radiation, sufficiently strong signals can be obtained even from monolayer films. 4.2. SPM-BASED TECHNIQUES Topographical imaging can be roughly broken down into two different techniques: contact mode imaging, and dynamic mode imaging. Contact mode imaging, where the tip tracks the surface similar to the operation of a profilometer, can be performed simultaneously with friction mapping. Although the forces in SPM are low, on the order of nanoNewtons, the contact pressures are actually quite high due to the small contact area. Soft, and loosely bound surface structures can be easily deformed or pushed aside in this mode. The dynamic mode, which monitors changes in amplitude or frequency of an oscillating tip due to interaction with the surface, can be operated in a range of interaction regimes, from true noncontact, to “bouncing” on the surface with each oscillation cycle. Lateral forces cannot be directly measured in this mode, however the phase shift between the excitation and tip response can. This phase shift carries information on the mechanical characteristics of the surface, much as the friction signal does. Here, we consider the different information that can be garnered from these different modes, the artifacts that can be encountered, and how these considerations apply to the systems under study in this paper. We have seen that the friction contrast t provides a convenient measure of the lithographic transformations induced by the tip. Friction, in general, is related to true area of contact between the tip asperity and surface (as opposed to projected or apparent area). Thus, changes in the tip-surface adhesion due to changing chemical nature of the

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surface can lead to friction contrast. This follows directly from the adhesion-based model of friction developed by Bowden and Tabor.47 In SFM, the intrinsic adhesion forces which can arise from van der Waals, capillary, and electrostatic forces, can often far exceed the magnitude of the instrumentally applied contact forces, controlled by the setpoint. These phenomenal will then give rise to higher friction as can be seen in the equation for adhesion-based friction:47 (12) F =µ a

[

]

where µ is a friction coefficient, W the applied load, A the contact area and Pa the adhesion mediated contact pressure. Thin organic films may, however, present a special case of boundary lubrication. In this case, the organic film serves as a thin lubricating layer, one molecule thick, and its effectiveness in reducing friction depends on how robust it is relative to the applied pressure. The friction is then equal to the shear resistance of the substrate and that of the film, multiplied by the relative fraction of exposure they express at the tip. (13) F = αAss + α As f

[

]

Here, A is total contact area, the fraction which pokes through to the substrate, and Ss, Sf the shear strengths of surface and film, respectively. In either case, we can see that the mechanical characteristics of the film, governed by its degree of packing, rigidity, and exposed functionality, will control the measured friction. Quantitative evaluation of frictional characteristics are, however confounded by the artifacts which can occur due to unwanted bending and buckling of the cantilever, even on flat surfaces, or influence of surface topography when it is significant.48 As mentioned, the dynamic modes can minimize the surface damage, which commonly occurs in contact mode. For instance, in evaluation of the small metallic Ag nanoclusters formed as result of surface reduction, it was necessary to apply dynamic mode imaging, as the small particles were easily swept away in the contact mode (a complication which disappeared after application of the developing solution – the resulting large Ag structures were stable under contact mode scanning). Since materialsspecific contrast from friction is not available here, one can attempt to obtain similar information from the phase contrast images. Since the phase shift is strongly influenced by viscoelastic energy loss during the contactt period of the cycle, various claims have been made for deducing from such images information about the surface elasticity, adhesion, etc. However, some artifacts can arise in this mode also. By assuming a simple Herzian model, and considering the surface deformation expected for various values of surface and tip characteristics, Spatz et al showed that significant deformation of the surface can occur under ordinary operating conditions.49 Conversely, when attractive forces are considered, one expects an instability under certain operating conditions that causes the feedback-controlled topography to give a false measure of sample heights.50 For these reasons, due care should be used in measurement of feature heights, and assignment of their identity by phase or friction mappings. Careful working procedures can minimize the possibility of artifacts. We typically used frequency values slightly below the cantilever resonance, and worked at a setpoint as close to that of the free amplitude value which still gives stable feedback. In addition, care was taken to avoid assigning heights based on narrow structures whose dimensions approached those of the tip. When stronger adhesive forces existed between tip and surface, nitrogen purge can sometimes reduce those due to capillary condensation. Finally, the correlation

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between heights measured from SFM topographies and evidence from the other experimental work was always considered. 5. Experimental Considerations for Optimization of Writing Whereas the function of the SAM in this work is not to serve as a sacrificial layer, it has been demonstrated in other works that under appropriate conditions, the monolayer can be efficiently removed or destroyed, exposing the silicon substrate to chemical attack.51 It is then clear that application of overly harsh conditions will result in a damaged, disordered, or removed film and subsequent steps requiring an ordered template film will not be possible. On the other hand, if the writing conditions are too mild, no reaction will occur. Considering the fundamental differences between writing on silicon and on the monolayer film, we do not expect the influencing factors discussed in section 3.1 for silicon to apply in precisely the same way here. Five factors were found to influence the writing step: 1) Voltage applied 2) “Dwell time” (tip velocity, pulse length) 3) Humidity 4) Nature of the tip 5) Type of substrate used (Si n/p). The appropriate voltage lies within a certain range of values, whose magnitude is set by the other conditions. For instance, typical threshold voltage for initiating oxidation of NTS was 4-5 volts (negative tip). Damage to the film as evidenced by topographic growth of silicon oxide was typically observed above 9 volts. These values are general guidelines as they are strongly affected by all of the other conditions. Writing was performed in two different modes: vector and raster action. For the former mode the tip only scans the specific regions to be modified, while applying a bias. The features seen in Figure 3 were made in this fashion. Typically, the bias was applied continuously during this step, so thatt tip velocity (generally a few microns/sec) determines the dwell time. When scanning single lines, the written features were fainter than when scanning under identical conditions over a solid area, such as a square. This is presumably due to overlap of the electrochemically active region to previous and subsequent scan lines, due to the size of the water meniscus. Under raster scanning, the tip traverses the entire scan area, and voltage pulses are applied at specific pixels only. Pulse length used was on the order of milliseconds. This mode can be used to copy a picture, designed off-line by any means, onto the surface.

325

Figure 8. Set-up for controlling humidity in SFM chamber.

Humidity and environment control were achieved by applying the set-up shown in Figure 8. With exception of those lithography schemes that do not require water, removal of water will inhibit the writing step. This is demonstrated in Figure 9. Formation of a water meniscus by capillary condensation at the tip-surface interface is a relatively well-understood phenomenon, but the influence of a hydrophobic film on the surface can only be estimated qualitatively at this point. By consideration of measured contact angles and spreading tendency on such films relative to clean silicon or silicon oxide, the meniscus size should be reduced. This will directly influence the size of the written features. The minimum linewidth observed by us for oxidation of the NTS surface was 9 nm. This influence must be weighed against the other factors determining feature size such as tip size, and availability of reactant in the vicinity. Formation of nanometallic clusters in the Ag reduction is evidence for the latter, since the size of these clusters must be regulated by the “reservoir” of available Ag ions within the relevant diffusion length on the surface. Repeat experiments in the same region gave indication that writing a Ag feature diminishes the possibility to form another such feature in the near vicinity (fraction of a micron), thus supporting this conjecture. Several types of tips were used for writing, highly doped silicon tips and silicon tips coated with various conductive coatings: Boron-doped CVD diamond; refractory metals (TiN, W2C, TiO); and noble metals (Au, Pt, Pd.). Each tip material has its advantages and disadvantages. The CVD diamond tip is inert, hard, and durable. Once it became contaminated, it could be cleaned by performing coarse scans on a sample of CVD diamond. These tips, however, were quite large, > 100 nm tip radius. On the other

326

extreme is the highly doped Si, which can be extremely sharp, < 10 nm tip radius. Using such tips, we were able to write lines with diameter 9 nm. This tip is, however, easily broken, oxidized, or contaminated. The metal-coated tips have varying degrees of sharpness and conductivity. Poor conductivity leads to a large voltage drop at tipsurface interface, which makes the effective bias voltage used in the writing step significantly smaller. These coatings eventually wear off or become contaminated. Electromigration, one mode of the unwanted removal of the tip coating, should be lower for higher melting refractory metals, thus they should be more durable. This was not necessarily born out in practice. Presumably due to lack of control in the production process, wide variations in writing efficiency are observed not only between the different tip types, but within a given tip type. Tips with reproducible characteristics (size, conductivity, reactivity) would be a significant breakthrough in this respect. Preliminary results using carbon nanotubes indicate that they may meet these requirements.52

Figure 9. Lateral force images of tip-inscribed lines on NTS. Writing conditions: -9 volts on tip, 38 passes at 7 microns/sec. (A) ambient humidity (B) after 10 minutes purging with dry nitrogen. (C) return to ambient humidity. Arrows show start and end points of each line. This series of experiments shows that the writing efficiency can be tempered by reducing the water vapor concentration, and that the efficiency returns upon reestablishing higher humidity. This Figure, and Figure 11 prepared using WSxM©; http://www.nanotec.es.

With respect to the type of surface, several variables exist. Firstly, the doping of the Si substrate, n or p, was observed to strongly affect the ease of writing. Using p-Si with a varying doping density (variations up to 3x in resistivity) showed good correlation with lithographic patterning, with the lower resistivity substrates being easier to write structures on. n-Si was also used: although the lithographic step could be performed with both doping types, p-Si gave better results. Another surface factor that could be varied was the extent of monolayer coverage. In principle, the surface coverage can be continuously varied from bare silicon to close-packed monolayer. Previous work, mentioned in section 3.1, and work in our lab has established that large mounds of SiO2, tens of nm high, can be readily written on the bare silicon surface at relatively low biases, under 5 V. This response was never observed on the good monolayer surfaces. However, Figure 10 shows the effect of writing on a partial NTS monolayer, where the monolayer appears as distinct islands with exposed silicon between them. Close inspection of the friction image shows that for the lower voltages (5.5 volts), and smaller dwell times, the writing occurs only on the silicon, leaving the friction contrast of the NTS islands unchanged. As voltage and dwell time are increased, the NTS islands eventually reach the same friction signal as the oxidized silicon. It is interesting to note

327

that even for higher voltages and longer dwell times, the growth of the SiO2 regions was limited and never exceeded the height of the NTS islands.

Figure 10. Writing features in friction mapping on a partial NTS monolayer.

6. Future Directions and Applications A sampling of the variety of nanostructures which can be formed using Constructive Nanolithography have been presented here. This sett is by no means exhaustive, but demonstrates the possibilities available for precise formation of complex surface structures using a relatively simple experimental set-up. The resolution attainable is limited by the extent of the water meniscus. Increasing the hydrophobic nature of the surface limits the meniscus size which in turn reduces the ultimate line width. As we have seen, availability of neighboring metal ions forming metal nanoclusters will limit their size. The ratio of different components in a mixed monolayer is one way to control those very properties. Thus, we expect to see greater selectivity and size control as the role of the surface properties is understood qualitatively. Examples have been presented of organic, metallic, and semiconducting surface nanostructures. Hybrid structures, for instance, consisting of metallic nanoparticles connected by unique bridging molecular species could be conceived. A first step in this direction is the chemical attachment of gold nanoparticles to a surface in an ordered pattern that was formed by nanolithography techniques.38 These efforts could clearly lead to functioning molecular-level devices. Finally, fast, proximal probe storage protocols could be conceived using the principles demonstrated here. Multiple arrays of cantilevers are being incorporated into storage devices of high density and reasonable high writing rate involving thermomechanical writing.12 Whereas the lithographic writing step has been presented here as the precursor to further transformations for building a 3-dimensional structure,

328

this writing step itself has potential for data storage devices. By encoding surface bits as regions of high friction (oxidized NTS or OTS), rather than depressions in a polymer film, one could reduce the resolution and read times significantly over the technique of substrate melting. Stability, resolution, and speed of writing could lend importance to this proposal. Since resolutions under 9 nm have been achieved for this process without optimizing conditions, we expect that even narrower structures could be formed. Reliability and durability of the written bits is essential. Figure 11 shows a sample where a patterned OTS sample was heated to 100 C in an attempt to accelerate any deterioration of the oxidized sample thatt may occur. The contrast is actually improved after heating and the signal-noise ratio grew by approximately 2 orders of magnitude as can be seen in the cross-sections. Since this exposure was performed on the inert SAM surface, minimal tip wear is expected, and high writing speeds could be obtained.

Figure 11. Friction mappings of oxidized surface before (left) and after (right) heating to 100 C for 1 hour. Cross sections below each friction map show the relative signal to noise in each image.

329

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330 26. Avouris, P., Hertel, T. and Martel, R. (1997) Atomic force microscope tip-induced local oxidation of silicon: kinetics, mechanism, and nanofabrication, Appl. Phys. Lett. 71, 285-287. 27. Dagata, J.A., (1998) Understanding scanned probe oxidation of silicon, Appl. Phys. Lett. 73, 271-273. 28. Garcia, Calleja, Perez-Murano (1998) Local oxidation of silicon surfaces by dynamic force microscopy: Nanofabrication and water bridge formation, Appl. Phys. Lett. 72, 2295-2297. 29. Snow, E.S. and Campbell, P.M. (1994) Fabrication of Si nanostructures with an atomic force microscope, Appl. Phys. Lett. 64, 1932-1934. 30. Snow, E.S. and Campbell, P.M. (1995) AFM fabrication of sub-10-nanometer metal-oxide devices with in- situ control of electrical properties, Science 270, 1639-1641. 31. Pérez-Murano, F., Abadal, G., Barniol, N., Servat, J. Gorostiza, P., and Sanz, F. (1995) Nanometer-scale oxidation of Si(100) surfaces by tapping mode atomic force microscopy, J. App. Phys. 78, 6797-99;Wang, D., Tsau, L. and Wang, K.L. (1994) Nanometer-structure writing on Si(100) surfaces using a non-contactmode atomic force microscope, Appl. Phys. Lett. 65, 1415-1417. 32. See, for instance, Chemical Physics 281 issues 2-3 (2002). 33. Holmlin, R.E., Haag, R., Chabinye, M.L., Ismagilov, R.F., Cohen, A.E., Terfort, A., Rampi, M.A., and Whitesides, G.M., J. Am. Chem. Soc. (2001) Electron transport through thin organic films in metalinsulator-metal junctions based on self-assembled monolayers, 123, 5075-5085. 34. Maoz, R., Frydman, E. Sagiv, J., Cohen, S.R. (2000) “Constructive nanolithography”: site-defined silver self-assembly on nanoelectrochemically patteerned monolayer templates, Adv. Mater. 6, 725-731. 35. Piner, R.D., Zhu, J., Xu, F., Hong. S.and Mirkin, C.A. (1999) “Dip-Pen nanolithography” Science 283, 661-663. 36. Maoz, R., Frydman, E., Cohen, S.R.,and Sagiv, J. (2000) Constructive nanolithography: inert monolayers as patternable templates for in-situ nanofabrication of metal-semiconductor-organic surface structures – a generic approach, Adv. Mater. 12, 725-731. 37. Höppener, S., Maoz, R., Cohen, S.R., Chi, L.F., Fuchs, H. and Sagiv, J. (2002) Metal nanoparticles, nanowires and contact electrodes self-assembled on patterned monolayer templates – a bottom-up chemical approach, Adv. Mater. 14, 1036-1041. 38. Liu, S., Maoz, R., Schmid, G., and Sagiv, J. (2002) Template guided self assembly of [Au55] clusters on nanolithographically defined monolayer patterns, Nanoletters 2, 1055-1060. 39. Ederth, T. and Liedberg, B. (2000) Influence of wetting properties on the long-range hydrophobic interaction between self-assembled alkylthiolate monolayers, Langmuir 16 2177-84. 40. Maoz, R., Frydman, E. Sagiv, J., Cohen, S.R. (2000) “Constructive nanolithography”: site-defined silver self-assembly on nanoelectrochemically patteerned monolayer templates, Adv. Mater. 6, 725-731. 41. Adamson, A.W. (1990) Physical Chemistry of Surfaces John Wiley and Sons, Toronto. 42. Good, R.J. (1993) Contact angle, wetting, and adhesion: a critical review in Mittal, K.L. ed., Contact Angle, Wettability and Adhesion VSP, Utrecht, The Netherlands pp 3-37. 43. Owens, D.K. (1969) Estimation of the surface free energy of polymers, J. Appl. Pol. Sci. 13, 1741-1747. 44. Frydman, E., Cohen, H. Maoz, R. and Sagiv, J. (1997) Monolayer damage in XPS measurements as evaluated by independent methods, Langmuir 13, 5089-5106. 45. Pignataro, B., Licciardello, A., Cataldo, S.and Marletta, G. (2003) SPM and TOF-SIMS investigation of the physical and chemical modification induced by tip writing of self-assembled monolayers, Mat. Sci. Eng. C 23, 7-12. 46. Baptiste, A., Gibaud, A., Bardeau, J.F., Wen, K., Moaz, R. Sagiv, J., and Ocko, B.M. (2002) X-ray, micro-Raman, and infrared spectroscopy structural characterization of self-assembled multilayer silane films with variable numbers of stacked layers Langmuir 18, 3916-3922. 47. Bowden, F.P., Moore, A.J.W., and Tabor, D., (1943) The ploughing and adhesion of sliding metals J. Appl. Phys. 11, 80-91. 48. Warmack, R.J., Zheng, X.-Y., Thunday, T. and Allison, D.P. (1993) Friction effects in the deflection of atomic force microscope cantilevers, Rev. Sci. Instrum. 65, 394-399; 49. Grafstrom, S., Neitzert, M., Hagen, T., Ackermann, J., Neumann, R., Probst, O., and Wörtge, M., The role of topography and friction for the image contrast in lateral force microscopy, Nanotechnology 4, 143-151. 50. Spatz, J. P.; Sheiko, S.; Moller, M.; Winkler, R. G.; Reineker, P.; Marti, O. (1997) Tapping scanning force microscopy in air-theory and experiment, Langmuir 13, 4699-4703. 51. Kühle, A., Sørensen, A.H., and Bohrl, J. (1997) Role of attractive forces in tapping tip force microscopy, J. Appl. Phys. 81, 6562-6569.

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NANOMETER-SCALE ELECTRONICS AND STORAGE

K.F. KELLY,* Z.J. DONHAUSER, P.A. LEWIS, R.K. SMITH, and P.S. WEISS Departments of Chemistry and Physics, The Pennsylvania State University 152 Davey Laboratory, University Park, PA 16802-6300, USA

Contents 1. 2.

3.

4.

Introduction Self-assembled monolayers 2.1. Phase separation driven by terminal functionality 2.2. Phase separation driven by internal functionality 2.3. Separation driven by post-adsorbtion processing Single molecule conductance switching 3.1. Isolation of individual molecules 3.2. Vapor-phase annealing 3.3. Results and discussion of the switching mechanism Conclusions

Abstract The ability to control the placement off molecules is essential for the patterning and fabrication of nanoscale electronic devices. We apply selective chemistry and selfassembly in combination with conventional nanolithographic techniques to reach higher resolution, greater precision, and chemical versatility in the nanostructures that we create. We illustrate three successful approaches: (1) phase separation of selfassembled monolayers (SAMs) by terminal and internal functionalization, (2) phase separation of SAMs induced by post-adsorption processing and (3) control of molecular placement by insertion into a self-assembled monolayer. These methods demonstrate the possibilities of patterning films by exploiting the intrinsic properties of the molecules. We then employ these self-assembled monolayers as a means to isolate molecules with electronic function to determine the mechanisms of function, and the relationships between molecular structure, environment, connection, coupling, and function. Using self-assembly techniques in combination with scanning tunneling microscopy (STM) we are able to study candidate molecular switches individually and *

Present Address: Department of Electrical Engineering, Rice University, Houston, TX 77251, USA

333 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 333-354. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

334

in small bundles. Alkanethiolate SAMs onn gold are used as a host two-dimensional matrix to isolate and to insulate electrically the molecular switches. We then individually address and electronically probe each molecule using STM. The conjugated molecules exhibit reversible conductance switching, manifested as a change in the topographic height in the STM images. The origins of switching and the relevant aspects of the molecular structure and environment required will be discussed.

1. Introduction Control and stabilization of molecular assemblies at the nanometer scale are crucial steps in the fabrication of molecular-scale devices. Current techniques such as photolithography or electron beam lithography [1] and ‘soft lithography’ [2, 3] are limited in their resolution and cannot reproducibly achieve patterns with dimensions at the nanometer scale. At the other end of the spectrum, single molecule manipulation has been successfully demonstrated using scanning probe microscopy, but is unable to produce devices in parallel and is still too time consuming to be practical as a fabrication technique [4-8]. We anticipate the need to combine the speed and versatility of lithographic techniques with the resolution of single-molecule control in order to construct commercially viable molecular devices.

2. Self-assembled monolayers We and others have developed and utilized methods that exploit the inherent chemical, physical and thermodynamic properties of molecules for facile means to pattern surfaces at the molecular level using self-assembly techniques in order to investigate molecularbased electronic devices. Self-assembly is a natural a phenomenon that can be observed in many biological, chemical and physical processes [9, 10]. This method has been explored recently as a means to produce supramolecular assemblies in a straightforward manner [9-14]. The most commonly studied and best characterized systems are alkanethiolate SAMs on Au{111} [15, 16]. Alkanethiolate SAMs form spontaneously on Au{111} through chemisorption of the S head group to the Au surface. The monolayers interact on the surface through van der Waals forces that occur amongst adjacent alkyl chains. The origin of the stability of SAMs is thus twofold, due to the covalent S–Au bond and the attractive van der Waals forces between the methylene groups. As a result of the attractive interactions imparting stability and order to these systems, SAMs are known to have a low defectt density and resist degradation in air. The process of self-assembly lends itself naturally to controlling the local placement of molecules. In particular, SAMs have been used as model systems for fabricating structures with controlled geometries [3, 17-21], as well as essential components in the actual device structure [22-25]. Multi-component SAMs formed by co-deposition of two or more adsorbates from solution have been investigated for their patterning potential [13, 14, 26-31]. When more than one adsorbate is considered, it is necessary to account for the interactions between the different adsorbates and whether these will favor mixing or separation.

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Whitesides and co-workers studied multi-component SAMs co-deposited from solution using contact angle measurements and x-ray photoelectron spectroscopy (XPS) to examine possible phase separation [28]. It was concluded from this study that SAMs adsorbed from a solution at equilibrium containing a long-chain and a short-chain alkanethiolate will not separate into discrete domains but rather randomly intermix on the surface. Other studies conducted by Bain and Whitesides using SAMs coadsorbed from alkanethiolates possessing different terminal functionality produced similar conclusions [26, 27]. However, these analyses involved analytical methods that are ensemble-averaging techniques (e.g. XPS, infrared spectroscopy, ellipsometry and wettability measurements), which determine averaged, ‘macroscopic’ properties of the sample. Insofar as molecular level patterning is concerned, where the size regime for structures at the nanometer scale is desired, it is necessary to use techniques that are able to distinguish molecular level characteristics. With the development of scanning probe microscopies, such as scanning tunneling microscopy (STM) [32] and atomic force microscopy (AFM) [33], it is possible to gain local information at the atomic scale and obtain real-space images of surfaces [34-36]. This has proven to be enormously beneficial in studies of patterning such as phase separation of SAMs, where previous analytical methods were able to measure only ensemble averages. We are concerned with the design and control of systems such as these, and have been successful in demonstrating various methods for patterning SAMs using selfassembly to form the structures and STM (along with ensemble-averaging techniques) to determine the success of the method. This paper outlines recent research conducted by our group involving patterning of SAMs, namely phase separation due to terminal and internal functionality, phase separation induced by post-adsorption processing and controlled placement of individual molecules by insertion. 2.1. PHASE SEPARATION DRIVEN BY TERMINAL FUNCTIONALITY Stranick et all [30] conducted an extensive study of the phase separation of multicomponent SAMs. The components in the SAMs were –S(CH2)15CH3 and – S(CH2)15OCOCH3, which are similar in length and chemical activity and differ only in their terminal functional groups. STM was used to obtain real-space images of the phase-separated domains. Although it was possible to characterize the average film composition using ensemble techniques (e.g. XPS, IR spectroscopy and ellipsometry), the imaging capability of a scanning probe method was useful in determining whether the system phase separated on the nanometer scale. Figure 1 is an STM image of phaseseparated domains of these two components in the SAM. The topographically higher areas (shown as brighter) were assigned as the methyl-ester-terminated alkanethiolate domains whereas the lower areas are the hexadecanethiolate domains. The STM topographic height difference between the areas corresponds to <1 Å with the methylester-terminated molecules appearing higher. In this instance, the domains were small (nanometers), such that in previous ensemble averaged measurements the films would have appeared to be randomly mixed. However, the STM images indicate that phase separation is occurring with no external modification necessary.

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To understand phase separation, the enthalpic and entropic contributions must be considered. Since entropy favors a mixing when two or more components are involved, the formation of discrete domains indicates that the enthalpic contributions of the system must outweigh the entropic contributions. Also, it is commonly thought that adsorption from solution is reversible, with exchange processes between the molecules on the surface and those in solution continuously occurring [28]. Therefore, as the system approaches equilibrium, the formation of domains indicates that this is a lowerenergy state as compared to random intermixing. In addition to this, the prospect of surface diffusion must also be considered. In this paper, coalescence of hexadecanethiolate domains was shown to occur over a period of less than 1 h as illustrated in Figure 1. Additionally, the divergence of one large domain into two smaller ones was not observed. This indicates that there is some degree of lateral motion on the surface. Although this diffusion is slow with respectt to adsorption from the solution, it can be hypothesized from these observations that the lateral motion is working toward formation of segregated domains. Thus, we infer that both exchange processes in solution and lateral surface diffusion after removal from solution are important in SAMs that form phase-separated domains.

Figure 1. Two sequential STM images of a 50 nm x 31 nm area taken 37 minutes apart showing a SAM containing islands of hexadecanethiolate (darker area) surrounded by methyl-ester-terminated alkanethiolate (brighter areas). Domain coalesence is observed at this timescale (indicated by the two areas). The reverse process was not observed. Imaging conditions Vtip = -1 V, I = 1 nA.

As the domains were found to coalesce slowly and to reduce their curvature over time [30], we conclude that the system had not reached equilibrium. Keeping these films from reaching equilibrium by controlling the rates of motion and exchange has since become a cornerstone in our strategy for controlling nanometer-scale structure [37]. Although the tail groups in these molecules are only weakly interacting, this driving force is enough to induce separation at the molecular level. This contradicts earlier studies of multi-component SAMs in which it was inferred from averaging measurement techniques that random mixing of the two components in a SAM accurately represented the surface composition. Studies involving other mixtures of molecules differing only in the end group (i.e. –CH3, –CO2CH3, –OH and –CN) were also performed [31]. These ffilms also separated into different domains to some degree, with the exception of the –OH and –CN terminated systems. Since the basis for separation in these systems is the interaction between end groups, it follows that the degree of end group polarity will drive the separation process. It is thus possible to

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control the phase separation of molecules by selecting end groups with large differences in polarity. 2.2. PHASE SEPARATION DRIVEN BY INTERNAL FUNCTIONALITY Phase separation can also be influenced by the internal functionalization of the molecules in a multi-component SAM. Recently, we have conducted research on amidecontaining alkanethiolate SAMs (e.g. 3-mercapto-N-nonylpropionamid N e, or 1ATC9) codeposited with a non-functionalized alkanethiolate (e.g. decanethiolate) [29]. A schematic diagram of the family of amide-containing molecules is shown in Figure 2. Because of the internal amide functional group, adjacent molecules can form stabilizing hydrogen bonds between the carbonyl and amino moieties that will direct their interactions on the surface. Hutchison and co-workers have demonstrated the formation of stable monolayers of amide-containing alkanethiolates t using XPS, contact angle goniometry, IR spectroscopy and electrochemical methods [38-40]. It was concluded that hydrogen bonding between the amide functional groups and van der Waals interactions of the alkyl chains play an equally important role in determining whether the SAMs will be well ordered. In monolayers of amide-containing alkanethiolates with alkyl chains containing fewer than 15 methylene units, the SAMs were disordered; however, it was shown that the underlying amide layer still appeared well ordered.

Figure 2. Schematic diagram of molecules used in the amide-alkanethiolate studies. Left to right: 1ATC9, 2ATC6, and 3ATC3.

Figure 3. (A) STM image of a 100 nm x 100 nm area of a phaseseparated SAM co-adsorbed from 1:1: solution of 1ATC9 (brighter areas) and decanethiol (darker areas). An enlarged view (25 nm x 25 nm) of the boxed area in (a) is shown in (b). Imaged with Vtip = -1 V, I 1 A

These systems were subsequently studied using STM to gain an understanding of the ordering of the monolayers at the nanometer scale [29]. Upon co-deposition with decanethiol, phase separation occurred spontaneously at room temperature. Figure 3 is an STM image of a film co-adsorbed from a 1:1 solution of 1ATC9 and decanethiolate on Au{111}. The 1ATC9 molecules are physically higher than decanethiolate molecules by <3.3 Å when adsorbed on the surface. These regions show up in the STM images as topographically higher (brighter areas). Both h the 1ATC9 and decanethiolate domains are highly ordered and adopt (¥3 × ¥3)R 3 30° lattice structures. Phase separation was observed over varying molar ratios of 1ATC9 and decanethiol solution (1/99%, / 5/95%, / 25/75%, / 50//50%, 75//25%, 95//5%, 99/1% 1ATC9/decanethiol) [41]. In films adsorbed

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from solutions containing a lower concentration t of 1ATC9 molecules (i.e. 1%, 5%, 25% 1ATC9), the 1ATC9 domains appear to be forming at domain boundaries and substrate defects since these nucleation sites are areas in the film that are accessible to the 1ATC9 molecules. Additionally, the films are stable in air. Thus the placement and number of molecules adsorbed on the surface can be controlled by monitoring the defect density as well as the concentration of and exposure to the deposition solution. Unlike the studies performed by Hutchison and coworkers, the monolayers in these films are well ordered independent of the length of the alkyl chains (eight methylene units). However, it is important to note that both the substrates and the analytical methods used in each study were different andd are likely responsible for the apparent discrepancy between the two studies. The substrates used for the IR studies performed by Hutchison and co-workers were Au/Cr/SiO2 as compared to the more ordered Au on mica for the STM studies. The disorder seen in the IR samples with fewer than 15 methylene units may be a result of the polycrystalline Au/Cr/SiO2 substrate and not of the inherent ordering of the system. Hydrogen bonding is a logical explanation for the observed phase separation since these interactions would be much more favorable than interactions between the polar amide group and nonpolar alkyl chains of the decanethiolate molecules that would occur in random mixing of the two species. Also, van der Waals interactions of the alkyl chain overlayer in the 1ATC9 molecules provides additional stabilization to the molecules. In SAMs coadsorbed from solutions containing 3-mercapto-N-( N (N-nhexylacetamido)propionamide (referred to as 2ATC6) and decanethiol, phase separation was also noted [41]. However, STM measurements of mixed SAMs of a 3-mercapto-NN (N-((N-n-propylacetamido)acetamido)propionamide (referred to as 3ATC3) and (N decanethiol showed that monolayers were not ordered, despite the 3ATC3 molecules having six opportunities for hydrogen bonding with their nearest 3ATC3 neighbors (two per amide functional group). As the number of methylene units in the alkanethiolates decreases, the SAMs require longer adsorption times to form ordered monolayers because of the absence of stabilizing van der Waals forces [15]. Therefore, it follows that the flexible alkyl chains play an integral role in ordering the SAM; phase-separated domains result from the substantially different interaction strengths available via multiple hydrogen bonds between adjacent amide-containing alkanethiolate molecules versus the smaller van der Waals contributions of the n-alkanethiolates. These mixed SAMs prepared from amide-containing alkanethiolates and nalkanethiolates show potential for patterning, as in a platform m for adsorbing other molecules. Although the SAMs possess the same exposed functionality at the surface of the film, the differing underlying layers lead to different desorption characteristics, sticking coefficients and domain stability. Because the alkanethiolate domains are held on the surface less strongly, they will desorb more readily than the amide-containing molecular domains. Thus, patterning can be achieved this way, with the ability to control the desorption of part of the monolayer in order to replace it with another component onto the surface.

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2.3. SEPARATION DRIVEN BY POST-ADSORPTION PROCESSING Along with spontaneous separation of SAMs into molecular domains, post-adsorption processing of monolayers can also be used in directing the assembly process. Bumm et al [37] focused on thermal annealing of a dodecanethiolate SAM followed by adsorption of decanethiol to produce a separated binary component SAM. It was initially demonstrated that these two alkanethiolates were similar enough in chain length that they were miscible on a surface and are randomly mixed when codeposited from a 95% decanethiol/5% dodecanethiol solution as shown in Figure 4. In this figure, the protruding features are attributed to dodecanethiolate molecules. It is important to note that the longer dodecanethiolate molecules are not adsorbing at domain boundaries or near substrate defects in the films, as was observed with the amide-containing alkanethiolate SAMs studies. In contrast, there appears to be true randomness in the monolayers as to where the dodecanethiolate molecules are adsorbing. To ascertain the effect of annealing of the SAMs, Bumm et al formed a singlecomponent SAM of dodecanethiolate on Au{111}. This was then annealed at 78 oC in ethanol for 1 h, which succeeded in partially desorbing the monolayer as seen in Fig. 5. Annealing also decreased the defect density and structural domain boundaries which are normally found in alkanethiolate SAMs. Thus, ‘clean’ SAMs of dodecanethiolate could be produced with this process. It is well known that alkanethiolate molecules undergo significant desorption at 60 o C [42]. Therefore, dry annealing processes that had been previously used to increase the domain size of alkanethiolate SAMs also introduced defects within the monolayer domains [36]. Since the annealing process is performed f in solution, it is expected that as the SAM is heated, adsorbate molecules in the solution will undergo exchange processes more readily with the desorbing molecules due to the raised temperature. Also, increased temperatures will support lateral diffusion on the surface. Therefore, a situation that approaches equilibrium more closely than traditional SAMs formed at room temperature will occur.

Figure 4. STM image of a 25 nm x 25 nm area of a SAM adsorbed from a 95:5 solution of decanethiol:dodecanethiol. The higher areas correspond to dodecanethiolate molecules randomly interspersed throughout a matrix of decanethiol. Imaged at Vtip = +1 V, I = 10 pA.

Figure 5. STM image of a 500 nm x 500 nm area showing both the reduced defect density and partial monolayer desorption after thermal annealing in neat ethanol. The inset is an apparent tunneling barrier height image. Imaging with Vtip = +1 V, I = 10 pA.

After partial desorption of the initial single-component monolayer, the substrate was immersed in a 1 mM ethanolic solution of decanethiol for 6 h at room temperature as

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shown in Figure 6. This resulted in virtually defect-free islands of dodecanethiolate molecules surrounded by domains of decanethiolate molecules in which the defect density and structural domain boundaries were typical for SAMs adsorbed at room temperature. As discussed later in this article, these film preparations proved useful in quantifying the contributions of the molecules to electron transportt as a function of chain length [43-45]. Along with the separation that is achieved using this annealing process, molecularly sharp domain boundaries are also apparent in Figure 7. The lattice structure between the regions of decanethiolate and dodecanethiolate is continuous; that is, there is no chain twisting nor distinct physical defects at the domain boundaries. These boundaries are stable in air at room temperature. In contrast, domain boundaries between different regions of decanethiolate from the unprocessed SAM adsorption are distinct and indicate chain twist that is typical of domain boundaries in alkanethiolate SAMs, an example of which can be seen in Fig. 6(c). At the defect-free boundaries between decanethiolate and dodecanethiolate domains, the steps between the molecular terraces, the longer dodecanethiolate molecules are more accessible and thus can expose unique functionality on the film surface, possibly enabling selective deposition or reaction at such topologically one-dimensional sites like those in Fig. 6(a). Therefore, another level of patterning can be realized in which the exposed longer-chain functional groups at the boundaries can be manipulated to undergo reactions at those specific sites. Postadsorption processing (i.e. annealing and controlled exposure) of SAMs proves useful as a way to control the type and density of defects in SAMs so that patterning following adsorption can be accurately controlled.

Figure 6. STM image of a 50 nm x 50 nm area of a decanethiol/dodecanethiol SAM after post-adsorption backfill processing. The lettered arrows identify three variations of the SAM boundary. Imaged at Vtip = +1 V, I = 5 pA.

Figure 7. STM image of a 25 nm x 25 nm area showing molecularly sharp boundaries at the edges of areas covered by dodecanthiolate and decanethiolate. Imaged at Vtip = +1 V, I = 10 pA.

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3. Single molecule conductance switching Microelectronics technology has focused on producing ever smaller and faster devices, which has led to formidable technological challenges in fabricating and characterizing devices at the nanometer and sub-nanometer scales. If miniaturization of electronic components and devices is to reach its ultimate limits, new methods and strategies will need to be developed. One promising alternative to conventional technology is molecular electronics [46], where single molecules may be used as active components in electronic devices. Although the field is still in its infancy, there have been demonstrations of functional single molecule electronics. Two-terminal devices have been constructed that examine the viability of individual and bundled molecules as wires [47-49], switches [50-53], and diodes [54, 55]. Conjugated phenylene-ethynylene oligomers have been identified as a family of molecules with favorable characteristics for molecular electronic design; they are rigid, fully conjugated, and have tunable functionality [46, 48, 53-60]. Nanopore experiments have demonstrated the viability of these molecules as electronic devices. In these experiments, a monolayer of molecules was sandwiched between two evaporated gold electrodes in a small pore, < 30 nm in diameter. The nanopore devices were used to test groups of thousands of these molecules, elucidating interesting and functional properties including negative differential resistance (NDR), two persistent conductance states, and controlled switching under electric field [53-55]. As a complement to the nanopore work, theoretical studies have suggested a variety of mechanisms that produce switching effects. These mechanisms range from reduction and conformational twisting of the molecules [56] to rotation of substituents [61]. We seek experimental evidence that will determine the factors that play important roles in the switching of these molecules; we study molecules in this family on an individual or collective basis using STM [47, 48, 51]. Unlike the aforementioned nanopore experiments, here the molecules are bound only to one gold electrode, and the STM tip acts as the second electrode that can individually address each molecule to determine its electronic and structural properties. Systems for study must be carefully designed, as precise control at the single molecule level is often a difficult venture. To this end, we utilize self-assembly to control the placement, orientation, and local environment of single molecules. 3.1. ISOLATION OF INDIVIDUAL MOLECULES Whereas codeposition of a multi-component SAM has been demonstrated in controlling the formation of nanometer-scale domains, it is also possible to control the insertion of individual molecules into an alkanethiolate matrix. We have previously shown that monolayers of alkanethiolates are well suited for the two-dimensional matrix isolation of individual molecules [47, 48, 51]. The monolayers are well understood as discussed above, so they are easily manipulated to serve as host matrices for the insertion of molecules of interest. The host monolayers contain a variety of defect sites, including domain boundaries, step edges, and substrate vacancy islands. At these locations, guest molecules have access to the underlying gold, and may be able to bind to the substrate via a sulfur head group. Varying the deposition and processing conditions of the host matrix film can manipulate the densities of these defects [37]. Due to the limited space

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in the defect sites of the SAM matrix, the guest molecules are forced to stand up from the gold surface, and a portion of the conjugated molecules will then protrude from the host matrix. This arrangement allows us to locate the molecules with the STM, and to probe the molecules end-to-end. In our configuration, the STM tip serves as one electrode and the gold substrate serves as the other. Because STM images are a convolution of the tip and surface structure, it is not always possible to distinguish individual from bundled molecules. For surface features with low corrugation, such as the molecular lattice of the matrix, STM images are good representations of the surface structure. Details of features with higher aspect ratios, such as the protruding switch molecules, can be more difficult to resolve with the STM, and thus more difficult to interpret. As in our earlier work, we are able to infer that many of the similar protruding features at structural domain boundaries on substrate terraces, where access for insertion is limited, are individual molecules [47, 48]. When codeposited films of molecular wire candidates and alkanethiolates were prepared, they were found to be highly disordered compared to pure alkanethiolate films. Even at low concentrations of the molecular wire in solution (11%), no crystalline order was observed. It was concluded that the molecular wires disturb the ordering process during deposition. However, the insertion process allows us to produce well ordered SAMs before exposure to the molecular wires in solution. Prior to and immediately following insertion, the crystalline order of the dodecanethiolate matrix could easily be observed. Substrate defects and domain boundaries that are indicative of alkanethiolate SAMs also remain before and after insertion. After insertion, the films are interspersed with protrusions appearing <4–6 Å higher than the film in STM images. These were attributed to the molecular wires, as they were not present in the films imaged immediately before insertion. The molecular wires insert at domain boundaries, substrate defects and step edges. It is thus assumed that the molecular wire candidates are chemisorbing to the Au surface through a S–Au bond at sites that are particularly accessible to the molecules. This same insertion strategy has been used to bind tethers designed and synthesized by Weck and Grubbs to serve as the anchor and initiation points for ring-opening metathesis polymerization (ROMP) [62, 63]. By controlling the initial SAM defect density, we controlled the number of inserted tethers and their separation. Polymerization from these norbornene-terminated phenylene-ethynylene thiolates then resulted in individual, isolated polymer chains in the low-SAM-defect limit, or micronswide polymer brushes where large defects had been opened to allow substantial insertion. Since ROMP yields a living polymer, the chain length could be controlled via monomer supply and polymerization time. The insertion process is an effective way to measure single molecules. Further control over the placement of the molecules can be achieved by controlling the substrate defect density as in solution annealing (detailed in the above section), or by carefully selecting the matrix molecule to control the uniformity of the environment of the inserted molecules [64]. In our more recent work, we have compared molecules (shown in Fig. 8) that have shown switching behavior 2ƍ and 3ƍ in nanopore experiments and in calculations, with those that have not 1ƍ [6]. We have found that all three of these molecules exhibit stochastic switching between at least two conductance states, as do oligothiophene

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thiols [65]. The amount of switching directly correlates to the amount of order in the insertion matrix, leading us to conclude that the mechanism of conductance switching is mainly due to motions of the molecules. Additionally, we later describe vapor annealing, a novel technique for modification of the local structure of SAMs [66]. For these experiments SAM matrices were prepared on commercially obtained Au{111} on mica [67]. The Au substrates were annealed and cleaned using a hydrogen flame immediately prior to film preparation. SAMs for the host matrices were deposited from a 1 mM solution of dodecanethiol in ethanol. Three types of SAMs were made: 1) SAMs were adsorbed by exposing the gold surface to the alkanethiol solution for 24 h; 2) SAMs were adsorbed for 5 min deposition time, to allow less time for self-assembly of the matrix and to leave more and larger defect sites for insertion; 3) following the insertion step (described below), typical (deposited from solution for 24 h) SAMs were annealed in dodecanethiol vapor at 80 °C for 2 h in a sealed vial. The third type of SAM processing was utilized to improve SAM quality, and reduce defect density. This process allows us to add matrix molecules from m the gas phase, while reducing exchange processes that are inevitable during solution phase annealing [66]. Following all SAM depositions, the substrates were rinsed in ethanol and dried with nitrogen.

Figure 8. Phenylene-ethynylene oligomers (1, 2, 3) that were inserted into alkanethiolate matrices. The scheme for base-promoted hydrolysis is show beneath each molecule.

To insert guest molecules into the host SAM matrices, solutions were prepared containing 0.1 µM of 1, 2, or 3 (defined in Fig. 8) in dry tetrahydrofuran. Aqueous ammonia was added to hydrolyze the thioacetyl t protecting group, generating the thiol in situ to adsorb as the thiolate 1ƍ, 2ƍ, or 3ƍ on the surface. The SAMs were exposed to this solution for times ranging from 0.5 to 3 h. After rinsing and drying, the samples were stored at room temperature in a desiccator until imaging. Figure 9(a) is a STM image obtained under ambient conditions off a single molecule of 3ƍ inserted in a dodecanethiolate monolayer, located at a domain boundary. Although the host matrix is generally very stable over long periods of time, inserted molecules are observed to change conductance state frequently over time, or to move within the site. The inserted molecules have at least two states that differ in their apparent height in STM topography by <3 Å. Since topographic STM images represent a convolution of the electronic and topographic structure of the surface, the apparent height change

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observed in the STM images can be due to a change in physical height of the molecule, a change in the conductance of the molecule, or both. We refer to the more conductive state (greater apparent height) as ON (Fig. 9(a)), and the less conductive state as OFF (Fig. 9(b)). The molecule in the OFF state is still visible as a smaller protrusion, indicating that it is still present in the same defect site. The conductance state switching observed between Figs. 9(a) and 9(b) occurs spontaneously during STM imaging.

Figure 9. STM images of a 5 nm x 5 nm area showing a single molecule of 3• protruding from a matrix of dodecanethiolate, in the ON and OFF states (a 0.3 nm height difference). Imaged at Vsample = -1.0 V, I = 1 pA.

Figure 10. Four representative images from a time-lapse series of images. Each 77 nm x 77 nm image was acquired at Vsample = -1.0 V, I = 1 pA. The three molecules labelled A-C are found to switch conductance states several times between the four images.

Stochastic switching between the ON and OFF states is reversible. Time-lapse series of images acquired over several (up to 26) hours recorded the temporal behavior of the molecules. Drift arising from thermal fluctuations and creep in the STM piezoelectric

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imaging mechanism makes it difficult to observe a single small feature on the surface for long times so relatively large scan areas ([1000 to 2500 Å]2) were used to ensure that several molecules of interest remained in the area sampled for the full duration of imaging. Additionally, large-scan areas allowed us to monitor several molecules simultaneously, enabling statistical analysis of the multiple switching events. Figure 10 shows a series of four images selected from a larger series of time-lapse images, taken over a span of < 10 hours. Four substrate terraces are visible in each 770 Å × 770 Å image, separated in height by about 2.4 Å. The host matrix monolayer contains a variety of defect sites, including domain boundaries and substrate vacancy islands. These defect sites served as adsorption sites for the inserted molecules of 2ƍ, which are visible as 3 Å protrusions in the images. Using an automated digital tracking and extraction algorithm discussed in the earlier chapter, the three molecules labeled A–C in Fig. 10 were individually monitored for a complete series of 98 images. For each image in the sequence, a smaller image of each molecule was extracted, and assembled into the sequences in Figs. 11(a)–11(c). Because each frame contains only a single molecule, the molecular height above the SAM can be automatically measured for each frame, generating the height versus time plots shown in Figs. 12(a)–12(c) [68]. Molecule A was relatively active in switching between the ON and OFF states during the first 220 minutes of acquisition, butt then stabilized in the ON state for the remainder of the images. Molecule B exists predominantly in the ON state for the first 300 minutes, before switching predominantly into the OFF state for the last half of the sequence. Molecule C switched OFF after just two images, and remained mainly in the OFF state for the rest of the images. Several important observations can be made from these three representative molecules: 1) In all cases, switching between states is reversible. 2) Both the ON and the OFF states can persist for hours, or can change rapidly, persisting for just one image. 3) In the OFF state, the molecules still appear to protrude slightly from the host film, indicating that they remain bound to the same defect site, and that they do not desorb or diffuse out of the imaging area.

Figure 11. Extracted areas around each molecule labelled A-C in Fig. 10 for the full time-lapse series of images. These images were used to calculate the height profiles shown in Fig. 12.

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Figure 12. The height versus time profiles for the molecules shown in Figs. 10 and 11. The heights were calculated as described in ref. 68.

While the molecules shown in Figs. 10 and 11 are all 2ƍ, analogous switching behavior was also observed for 1ƍ inserted into matrices off dodecanethiolate. Additionally, we have determined that switching is not unique to phenylene ethynylene oligomers. We have also analyzed SAM matrices with oligothiophenes inserted. Like the phenylene ethynylenes, the thiophene molecules are fully conjugated, and consist of three or four thiophene units. However, they y are not completely rigid and have more possible conformations. The oligothiophenes exhibit similar two-state reversible switching [65], demonstrating that the switching we observe may not depend on the specific functionality of the phenylene ethynylene oligomers. 3.2. VAPOR-PHASE ANNEALING While the functionality of the oligomer may not be essential for stochastic switching, the insertion matrix plays a critical role in controlling the guest molecules. By changing the defect density and film quality, we changed the rates and numbers of molecules that switched. As described in the experimental section, we compared three methods for controlling the defect density of our matrices: vapor annealing to decrease defect density, typical SAM deposition (24 h), and decreased deposition time to increase defect density (5 min). Vapor-phase annealing was shown to be an effective means to fill defects in the monolayer [66]. If insertion of guest molecules is done prior to vapor-phase annealing, the vapor molecules have the opportunity to “backfill” around inserted molecules, as they cannot desorb into solution. It is assumed that desorption of the chemisorbed molecules from the film into the vapor a will be significantly reduced at 80 oC, thus allowing us to tailor the local surrounding of inserted molecules. To demonstrate the viability of the vapor annealing process, a decanethiolate film was prepared, and molecules of 2ƍ were inserted. This film was then annealed in

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dodecanethiol vapor. Introduction of dodecanethiol t from the vapor phase allows us to place these molecules selectively at monolayer defect sites, domain boundaries and substrate step edges. The apparent difference in height of the dodecanethiolate and decanethiolate molecules is < 1.1 Å as observed with STM [43], making it easy to distinguish between the two molecules. This type of mixed monolayer provides a convenient method to assess the effectiveness of the vapor annealing process. An image of the inserted decanethiolate film vapor, annealed in dodecanethiol, is shown in Fig. 13. The vapor-phase molecules have adsorbed along existing monolayer domain boundaries, as evidenced by the networked structure of the dodecanethiolate domains. Additionally, dodecanethiolate molecules (topographically higher areas) occupy most of the space along the step edges and around substrate vacancy islands. An inserted molecule is visible on the lower substrate terrace (shown in greater detail in the inset). Dodecanethiolate molecules supplied from the vapor are located around this molecule. Surrounding the guest molecule with vapor phase molecules may restrict its movement, if dodecanethiolate molecules occupy lattice sites previously unoccupied by the host matrix. This ability to “backfill” the host monolayer with vapor molecules is confirmation of our ability to tailor the local environment of inserted molecules in an attempt to regulate their behavior.

Figure 13. STM image of an 80 nm x 80 nm area of a decanethiolate (darker regions) monolayer with 2• inserted and vapor annealed in dodecanethiol (brighter regions). Inset is a 13 x 13 nm image of the same molecule. Both images acquired at Vsample = -1 V, I = 1 pA.

Vapor annealing is used to reduce defect density; the converse method is the use of a short deposition time. With a 5-minute SAM deposition, the monolayer is chemically attached, essentially complete, but not fully organized. However, slower adsorption processes that serve to increase order in the film have not yet completed. This is because initial monolayer formation occurs rapidly, but film restructuring and further ordering

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occurs over long times during exposure to the alkanethiol solution. The result of the shorter adsorption time is a generally ordered film with high defect density. 3.3. RESULTS AND DISCUSSION OF THE SWITCHING MECHANISM To test the ability of the matrix to affect switching, a pure dodecanethiolate vapor annealed film with 1ƍ inserted was compared to an unannealed SAM with 1ƍ inserted. Similarly, 2ƍ inserted in a SAM prepared over 5 min was compared to a SAM produced from the standard 24 h solution deposition. The results of these experiments are summarized in Fig. 14 and Table I.

Figure 14. Height distributions of 1• (C and D) and 2• (A and B). All data was digitally extracted from series of images acquired over 20 h.

Each histogram in Fig. 14 shows the distribution of heights for a representative sample of molecules extracted from a sequence of 200 images taken over 20 h (summarized in Table I). The apparent heights were calculated in the same fashion as for Fig. 11(a)–11(c). The bimodal distribution observed for the molecular heights in each sample is caused by bistability of the conductances of the inserted molecules; the peak at lower apparent height results from molecules in the OFF state, while the other peak corresponds to the ON state. Figures 14(a) and 14(b) show the distributions for 2ƍ in the (more ordered) SAM deposited for 24 h and in the (more defective) SAM deposited for 5 min, respectively. The apparent height difference between the ON and the OFF states is approximately the same, regardless of the host matrix order. However, the fraction of molecules in the OFF state increases dramatically in the less-ordered film. Gaussian fits to the peaks reveal ON/OFF ratios of 12.3 for the more ordered SAM and 2.1 for the less ordered SAM (Table I). The low ratio in the less ordered SAM is a direct result of increased switching activity in this sample. The high ratio in the SAM adsorbed for 24 h may be caused by undersampling of molecules in the OFF state, caused by the less frequent switching in the more ordered films; there are not necessarily fewer molecules in the OFF state. This undersampling problem arises because molecules continually in the OFF state are difficult to locate in large STM images, allowing us to overlook switches that remain OFF through the many hours of data acquisition. Another

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result of the shorter SAM deposition time is an increased coverage of inserted molecules. The measured coverage of the inserted molecules in the less ordered film was found to be 2.6 times that of the more ordered film. The higher coverage is likely caused by the higher defect density of the less ordered film, f as there are more sites for insertion. Not only are there more defects, but some are likely larger, allowing more freedom of movement for the inserted molecules. This, in turn, leads to a higher switching activity. The results presented in Figs. 14(c) and 14(d) demonstrate that vapor annealing of the host monolayer also affects switching. The number of molecules observed in the OFF state decreased in the vapor-annealed film (Fig. 14(d)) when compared m with the standard film (Fig. 14(c)). ON/OFF ratios were 5.2 for the unannealed film versus 9.2 for the vapor annealed film (Table I). Again, the higher ratio in the vapor annealed film is indicative of lower switching activity. Thus, the host matrix can hinder switching when it is very well ordered, by obstructing motion of in the guest molecules. Details of the mechanism of the switching observed here are not yet fully understood. However, based on our observations and the data of others, we can make some inferences regarding the origins of switching. The results for 1ƍ and 2ƍ demonstrate that the molecules are very similar in their switching behavior; switching of both molecules does not appear to depend on the specific chemical nature of the molecule, but is strongly correlated to the order of the host matrix. While the data presented in Table I may imply that 1ƍ has a higher switching activity, a full analysis of several data sets (not presented here) suggests that there is not a significant difference between 1ƍ and 2ƍ in their stochastic switching activity. This result eliminates the possibility that rotation off functional groups, such as the nitro group in 2ƍ [61], is responsible for the switching we observe. We conclude that the nitro functionality plays little role in the stochastic switching observed here, while the local environment plays a much more critical role in mediating stochastic switching. As mentioned above, further evidence of the non-specificity of the molecular functionality to switching is that we have also observed reversible switching for other families of molecules, including oligothiophenes [65].

It has been suggested that large conductance changes in molecular films of 2ƍ and 3ƍ may be due to an internal twist in the molecule that alters the conjugation n of the molecule and thus change the conductance of the molecule [56]. For analogous systems, it has been calculated that the phenyl planes can freely rotate with respect to each other at temperatures as low as 30K [57]. However, our experiments were performed at room temperature, and the states we observe can persist for several hours. It is unlikely that an unrestricted molecule would be able to maintain a static twisted or planar conformation for these time periods. For this mechanism to contribute significantly to the stochastic

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switching that we observe, it would be necessary for the host matrix to inhibit intramolecular rotation enough to stabilize each state. The viability of this mechanism requires the ability of the matrix to be somewhat fluid (or at least more conformationally relaxed) at defect sites where active molecules reside. They would have to be large enough to permit initial adsorption, but small enough to hinder intramolecular rotations. To examine the possibility of an electronic or electrochemical mechanism for switching, we have studied this system over a range of voltages and currents. The magnitude of the tunneling current determines the number of electrons that are available to interact with local electronic states to induce such phenomena as local heating, electron charging, or electrolytic cleavage of chemical bonds [69]. The applied voltage creates large local electric fields that can interact with molecular or induced dipoles to produce molecular motion [70]. Time-lapse series of STM images have been acquired at bias voltages ranging from -1.4 to +1.4 V (with magnitudes as low as 250 mV), and at tunneling currents ranging from 0.1 to 4.0 pA. In this range of tunneling conditions, we have not observed significant correlation with the amount of switching. This observation diminishes the possibility off an electrochemical mechanism, in which changes in conductance of the molecules may be caused d by a twist in the molecules that is induced by reduction of the molecules [56]. Because such charging effects are intimately related to the applied voltages and magnitude of tunneling currents in STM experiments, it is difficult to reconcile our observations with a mechanism that is dominated by electronic effects such as reduction or charging. It is possible that the switching observed here is a tilting of the inserted molecules or a change in the orientation of the molecule with respect to the STM tip. This type of motion can cause a change in the physical heightt of the molecule above the host matrix, which would result in a change in the apparent height of the molecule as observed with STM. This type of motion of the molecule can result from a change in the angle of the gold-sulfur-molecule bonding geometry. Experimental [71] and theoretical [72] studies have suggested two energetically similar geometries for thiolate monolayers bound to gold, due to varying hybridization of the sulfur atom (sp vs. sp3). A concerted motion involving attached substrate atoms is also quite possible. The energy barrier for the transition between these two states may be as low as 2.5 kcal/mol [72]; switching between these states is feasible for molecules at room temperature. The speed of such a switching mechanism would be limited byy the rotational frequencies of the molecules involved to a few GHz. Physical changes such as tilting can also result in large changes in molecular conductance. A change in the molecular orientation with respect to the electrodes (the substrate and the STM tip) can cause a variation in the effective conductance of the molecule by two orders of magnitude [73]. This effect is caused by a change in the overlap of the ʌ molecular orbitals with the orbitals of the metal electrodes. Of course, a tilting mechanism would require a large defect site in the matrix to allow significant movement of the molecule. Additionally, because there are only two observed states for these molecules, this implies m that there are just two preferred tilts of the molecule, independentt of defect type and size. As to the roles of the functionality in 2ƍ and 3ƍ, we speculate that the permanent dipole in the molecules caused by the functional groups may be useful in deliberately switching the molecules [51, 53]. Large electric fields applied with the STM tip or in

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nanopores may interact with these dipoles, providing a “handle” for applying torque and changing the tilt of the inserted molecules. As a final note, we have recently observed switching behavior in these systems using a UHV STM, operating at room temperature. Conducting the experiments in vacuum enables us to confirm that the switching is not related to interactions with surface contaminants or the ambient atmosphere. In future experiments we will use higher biases and low temperature to examine their effects on stochastic switching as well as controlled switching between t conductance states.

4. Conclusions Organic monolayers can be patterned through phase separation due to terminal and internal functionalities, as well as by post-adsorption processing leading to separation and controlled placement of individual molecules through insertion. The key to each of these processes is controlling intermolecular interactions and defect type and density so as to control the film dynamics. Ongoing research in our group includes studying possible phase separation due to differing head groups and substantial differences in chain lengths of the alkanethiolate molecules. The methods detailed here have been applied to control the placement of molecules. However, for these to be useful, it will be necessary to dictate precisely where individual molecules are placed. By simultaneously controlling substrate, film and their subsequent reactivity, this may become possible. We have used our control over monolayer formation to observe switching of single molecules with STM, manifested as a change in the apparent height of molecules inserted into host matrices of alkanethiols. We have demonstrated that the nature of defects in the host films can control the motion of inserted molecules and affect the amount of switching. We have also shown that the local environment plays an extremely important role in determining the behavior of single molecules, and may be an essential consideration for single molecule electronic design. We would like to acknowledge the contributions to this work by our highly productive and stimulating collaborators: Profs. Dave Allara, Bob Grubbs, Jim Hutchison, Jim Tour and Marcus Weck and their research groups. We also thank Lloyd Bumm, Tom Pearl, Beth Anderson, Brent Mantooth, Arrelaine Dameron, Sanjini Nanayakkara, and Jason Monnell for their experimental assistance. The continuing support of the Army Research Office, Defense Advanced Research Projects Agency, National Institutes of Standards and Technology, National Science Foundation, Office of Naval Research, and the Semiconductorr Research Corporation is gratefully acknowledged.

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Part IV – Contributed papers

STM TIPS FABRICATION FOR CRITICAL DIMENSION MEASUREMENTS

A. PASQUINI, G.B. PICOTTO, M. PISANI CNR-Istituto di Metrologia “G.Colonnetti” Strada delle Cacce 73, 10135 Torino, Italy

Abstract In this contribution a method is described for sharpening Tungsten (W) tips through a two-step electrochemical etching. In the first step, under strong reaction conditions, we obtain a long hyperbolic cone, while in the second with a micropositioner we bring only the apex of the first cone in contact with a thin film of etchant. In this way, controlling the meniscus height with an optical microscope, only the very end of the tip is etched. Some processing parameters such as the rate of the electrochemical reaction of erosion of the W wire, related to the electrolyte concentration and to the applied voltage, the length of the wire immersed in the solution and the shape of the meniscus have been investigated. Both direct current (DC) and alternating current (AC) were tested, observing two different ways of W wire erosion. The fabrication process provides very sharp tips, tips with radius of curvature below 10 nm and cone angle aperture within 30° have been obtained in some cases. Further improvements are in progress, namely to extend the tip-shape repeatability as given by the two-step process. Some promising STM images of diffraction gratings have been obtained using tips fabricated with this process.

1. Introduction The needs of critical dimension measurements (linewidth, lineshape, steps-height and orthogonality of 2-D structure) of patterned surfaces, gratings and 2-D grids in the submicrometer range with uncertainty smaller than 1 nm are increasing with the latest nanotechnology developments. Scanning Tunnelling Microscopy is a very useful metrological tool for high resolution three-dimensional (3D) imaging of nanostructure surface topography. STM provides atomic resolution of highly-oriented structures, while nanometric level resolution may be achieved with patterned surfaces in a non-destructive way and for a wide range of materials. STM exceeds the limits of conventional methods for topographic investigation as Scanning Electron Microscope (SEM), stylus profiling, optical interferometry both in resolution as well as in sample contamination problems. High sharpness of the tip is necessary for STM image resolution and accuracy of the topographic profile. Radius of curvature and cone angle of the tip have to be small relative to the critical dimensions of the structure to be imaged. 357 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 357-362. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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The electrochemical etching methods for sharpening STM tips have been deeply investigated in literature [1-5 and references therein]. A survey of the procedures based on both one-step and multiple-step electrochemical processes is given in [1, 2]. The etching of W and Pt/Ir wires to fabricate tips of various shape, using a two-step method, has been described in [2]. In addition, a four-step electrochemical reaction described by Libioulle et al. [3] provides very sharp and stable to oxidation Pt and Pt/Ir tips. In this paper, a two-step electrochemical-based method developed for sharpening Wtip is described. Promising results were obtained with this relatively simple process. From a preliminary investigation we obtained about 40% of the etched tips with radius of curvature below 30nm. The W-tips have been used to image a UV holographic grating fabricated on InP substrate. The grating , shadow gold coated, has a nearly rectangular profile with a pitch of about 480nm.

2. Tip Fabrication The electrochemical process of erosion of a tungsten wire involves the anodic dissolution of the metal in aqueous-base solution by a Standard Redox Potential (SRP) of –2.48 V and the reduction of water to form H2 bubbles and Hydroxide anions to the cathode through a Standard Oxidation Potential (SOP) of +1.05 V. The tungsten oxide anions are produced once the potential exceeds -1.43 V. SRP = -2.48 V (1) Cathode: 6H2O +6e- → 3H2(g) + 6OH−2

Anode: W(s) + 8OH- → WO 4 - + 4H2O + 6eSOP =+1.05 V (2) 0 2W(s) + 2OH + 2H2O → WO4 + 3H2(g) E = -1.43 V (3) Etching occurs at the air/electrolyte interface when a positive voltage is applied to the wire. The surface tension of the aqueous solution produces a meniscus around the wire. The shape of meniscus determines the aspect ratio and the final shape of the tip. The rate of etching reaction at the top of the meniscus is slower than at the bottom due to a concentration gradient caused by diffusion of OH- anions to the anode. The part of the tip under the meniscus is normally etched away, but a flow of a denser tungsten oxide, falling down into the solution, protects the end of the tip. So the rate of the reaction in the lower part of the wire is smaller than the reaction in the meniscus. The electrical resistance of the W increases as the sectional area of the wire decreases. Due to the OH- anions consumption during the reaction, NaOH solution has to be changed periodically. The etching process planned by us consists of two different steps: in the first one, we immerse vertically for about 2 mm a tungsten wire of 0.25 mm diameter in a NaOH 1M electrolytic solution (Fig. 1). The counter electrode is a C rod. With a micropositioning system and an optical microscope we control the length of the tip immersed in the solution. Although DC-based etching produces vigorous bubbling of hydrogen around the tipelectrolyte meniscus, DC supply voltage is used in the first step of the etching because it provides a sharp narrow tip cone with hyperbolic shape. The reaction, driven by a 25 V DC supply, ends in a few seconds. This tip is further etched in a second step: the long narrow cone is immersed by means of a precise positioning system of a few micrometers inside a NaOH 0.1M electrolyte ffilm, held by the Ptt ring counter electrode

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(Fig 2). Even if etching by means of AC voltages produces a tip with a cone angle larger than with the DC supply voltage, the second step is based on an AC voltage, by which a precise control of the reaction rate and of the meniscus shape around the tip is obtained. The set-up allows etching to be confined to the end of the tip obtained in the first step. In this step the reaction, driven by 20 V AC, is very quick, 1-2 seconds. Sharp tips are obtained with the highest possible electrochemical reaction rate; nevertheless, this may cause strong bubbling and consequent instability of the meniscus level. The rate of the electrochemical reaction is therefore optimized by the applied voltage and electrolyte concentration. The two-step etching process provides W tips with two subsequent cones of different aperture at the tip end.

Figure 1-2. First and second step set-up of the etching process. In the second step a film of NaOH electrolyte is kept by a Pt ring, working as counterr electrode. The tip is immersed in the film only for few micrometers through a micropositionig system and under an optical microscope. The reaction, driven by 20 V AC in the second step, ends in 1-2 seconds, providing tips with a cone of two different apertures.

3. Tip images Optical microscope images at low magnification (200x, Fig. 3) show double cone tips, results of the two-step etching procedure. The cone angle of the fabricated tips has been estimated to be, in most cases, lower than 30°.

⎯ 100 µm

⎯ 100 µm

⎯ 100 µm

Figure 3. Optical microscope images of three etched tips: the double cone is the result of the two-step etching process. The terminal cone angle appears lower than 30°.

Transmission Electron Microscope images (TEM, Fig. 4), provide important information on the quality of the tip: radius of curvature of the fabricated tips has been

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measured at high magnification showing values smaller than 50nm, and in some cases also smaller than 10 nm.

Figure 4. TEM images show radii of curvature of the apex from 50nm to less than 10nm

4. Diffraction grating The W tips have been used to characterize the surface topography of a diffraction grating used for optical laser communication. The grating was fabricated using holographic lithography on a n-doped InP semiconductor. The grating structure has a rectangular profile with flat surfaces and nearly vertical walls of the trenches, as shown in Scanning Electronic Microscope (SEM) images published elsewhere [5]. The average pitch (∼480nm) of the grating has been precisely measured by optical diffractometry. For STM imaging, the grating was shadow coated with a thin layer of electron gunevaporated gold. 5. STM imaging We used a home-made microscope set on a table with passive antivibration system in a room under ambient conditions. The instrument operates with the electronic system of a commercial microscope (Nanoscope II). STM imaging in air of most semiconductors is not easy, because surface contamination and oxidation can affect tunneling current and image formation. The oxide leads chemical nonhomogeneity to the surface which can result in roughness. All the STM images were recorded in constant current mode with a tunneling current of 1nA and a bias voltage of 100mV m at scan frequencies below 0.35 Hz. Four STM images taken at different sampling points of the grating, are shown in Fig. 5. The images (a, b, c) have been taken with the same tip while the image (d) with a different one. The influence of the tip shape is visible comparing the images (c) and (d), namely the profile of the trenches appears larger and steeper in the image (d). The image (c) shows a trapezoidal profile and a smaller width of the trenches. Local roughness of the walls/trenches are visible in all the images. In some cases, small distortions due to noise are present as well. The image (d) shows a nearly rectangular profile in agreement with those obtained from SEM images of the trenches [5]. Therefore, the rectangular surface profile is well reconstructed with some tips, others give some visible reconstruction errors due to the tip shape. To give some consistency to

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that, we analyzed the existing methods to deconvolute the tip shape from the STM images. Nevertheless, the reconstruction algorithms need to be further investigated, a good repeatability of the methods has been obtained only in few cases. We have also noticed a progressive tip degradation with time. TEM images of used tips confirmed this observation showing large radius of curvature. Maybe surface contamination and W wire oxidation have a decisive role to modified geometry and conductivity of the tip after some time. Therefore, fresh tips should be used for best resolution.

(a)

(b)

(c)

(d)

Figure 5. STM images of a UV holographic grating. The images were taken with two home-made W tips at different sampling points of the grating surface. Images of 3µm (a), 2µm (b), and 1µm (c, d) scan sizes are shown.

6. Discussion The two-step etching technique seems promising for repeatable fabrication of W tips having a final cone angle lower than 30° and radii of curvature smaller than 50nm. The DC-based etching used in the first step has a determining role in the process because it provides tips with a long hyperbolic cone. This is necessary to control the meniscus level when the apex of the tip is carefully immersed in the electrolyte kept by the Pt ring, for the second step process. In addition, the AC-based etching allows a better control of the reaction speed in the second step. In this way, the etching is limited to the tip apex, and a small aperture cone is obtained at the end.

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The fabricated tips show a repeatable double-cone shape which ends in a small aperture cone with a radius of curvature sometimes down to 10 nm. The good resolution of the tips is confirmed by a number of STM images taken with a UV holographic grating. Further activities are in progress, namely to extend the tip-shape repeatability as given by the two-step process, and to test some deconvolution methods for compensating the error due to finite tip-shape.

7. References 1. 2. 3. 4. 5. 6.

Fotino, M. (1993) Tip sharpening by normal and reverse electrochemical etching, Rev.Sci.Instrum. 64, 159-167. Melmed, A.J. (1991) The art r and science and other aspects of making sharp tips, J Vac.Sci.Technol.B 9, 601-608. Libioulle, L., Houbion, Y., and Giles, J. M. (1995) Very sharp platinum tips for scanning tunneling microscopy, Review of Scientific Instrument 66, 97-100. Ekvall, I., Wahlström, E., Claesson, D., Olin, H., and Olsson, E. (1999) Preparation and characterization of electrochemically etched W tips for STM, Meas.Sci.Technol. 10, 11-18. Musselman, H., Petereson, P.A., and Russell, P.E. (1990) Fabrication of tips with controlled geometry for scanning tunnelling microscopy, Precision Engineering 12, 3-6. Meneghini, G., Picotto, G.B., Gentili, M., and Grella, L. (1994) STM Characterization of InP Gratings for DFB Laser Fabrication, Surface and Interface analysis 22, 296-299.

SCANNING PROBE MICROSCOPY CHARACTERIZATION OF FERROELECTRICS DOMAINS AND DOMAINS WALLS IN KTiOPO4

C. CANALIAS‡, R. CLEMENS, J. HELLSTRÖM, F. LAURELL Department of Laser Physics and Quantum Optics, Royal Institute of Technology, 10691 Stockholm, Sweden J. WITTBORN∗ Department of Material Science, Royal Institute of Technology, 10044 Stockholm, Sweden H. KARLSSON Cobolt A.B., Lindstedtsvägen 24, 100 44 Stockholm, Sweden

Abstract We use the inverse piezoelectric effect to image artificially made ferroelectric domains of periodically poled KTiOPO4 crystals and KTiOPO4 waveguides using scanning probe microscopy. On applying a high-frequency AC electric field between a gold-coated scanning probe microscope tip in contact with the crystal surface and an electrode below the ferroelectric crystal, the crystal surface oscillates at the frequency of the applied electric field due to the inverse piezoelectric effect. With this technique, and by monitoring the vertical deflection of an AFM tip, which gives contrast between the domains, while the lateral deflection of the tip gives contrast at the domain walls, we determine the apparent domain wall width of the ferroelectric domains to be approximately 20-80 nm for the KTiOPO4. The lateral resolution of this imaging technique is estimated to be about 1 nm.

1. Introduction Engineered periodic domain microstructures r in ferroelectric crystals such as KTiOPO4 (KTP) and LiNbO3 (LN) are of great interest for fabrication of non-linear optical devices. The so called quasi-phase matching approach, in which a periodically modulated nonlinearity is utilized, allows versatile and efficient frequency conversion in the whole transparency region of the material. In this method a periodic structure of reversed domains is created in the crystal by electric field poling. The periods for frequency conversion range typically from around 40 µm in the infrared regime down to 3 µm for the blue to ultraviolet wavelength region. In order to obtain a high conversion ‡ ∗

e-mail: [email protected] Present address: Ericsson Microelectronics, 16481 Kista, Sweden.

363 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 363-369. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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efficiency of the laser light a high quality poling is of utmost importance. Accurate duty-cycles, minimum domain size variations and homogeneous poling all through the crystal, as well as minimal mechanical stress induced at the domain boundaries become crucial factors for the fabrication. The narrower the domains are, the higher is the influence of the domain wall width. Thus, it is important both from a fundamental and a technological point of view to understand as well as control the formation of inverted domains. Methods such as electrostatic t force microscopy (EFM)[1], and near-field scanning optical microscopy (NSOM) [2, 3], and second harmonic generation imaging [4] have been developed in order to visualize the domain structure of ferroelectric materials in a non-destructive way. In this paper, a method [5] that uses atomic force microscopy (AFM) to characterize domain walls in periodically poled KTP (PPKTP) and in KTP waveguides is presented. The surface oscillations caused by the inverse piezoelectric effect have been detected using atomic force microscopy (AFM), making possible the study of the ferroelectric structure of a crystal. This method has been applied to several ferroelectric materials [6, 7, 8, 9]. AFM was used by applying an ac voltage between a gold-coated AFM-tip, and an electrode placed underneath the crystal. By monitoring the vertical deflection of the tip, caused by surface oscillations, contrast between different polarized areas was observed. Contrast at the domain walls was obtained through the lateral deflection signal of the tip.

2. Experimental For our studies we used z-cut, 1 mm thick KTP samples that were periodically patterned with conventional photolithography on the c+ face. A metal layer was deposited after developing the resist. Domain inversion under the metal was performed by applying short electric pulses and using liquid electrodes [10]. Two atomic force microscopes were used for these studies: an ARIS-3300 from Burleigh Instruments and a Dimension 3100 from Digital Instruments. In both cases, a function generator was connected between the tip and the conductive sample holder, and a lock-in amplifier band-pass filtered the signal from light-detector to the AFMcontroller in order to image the domains. The setup t is presented in Fig. 1. Application of an a.c. voltage of 25 Vpp, ω = 90 kHz between the electrode on the bottom surface of the crystal and the grounded Au-coated silicon tip caused surface oscillations, due to the inverse piezoelectric effect. The electromechanical response was detected by scanning with the AFM tip in contact mode in combination with the lock-in amplifier to follow both the amplitude and the phase of the crystal oscillations at the fundamental frequency ω, and at 2ω.

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Figure 1. Experimental setup for the AFM. An a.c. voltage is applied between the Au-coated tip and the bottom electrode of the crystal. The crystal oscillations are detected by scanning in contact mode, in combination with a lock-in amplifier.

3. Results and Discussion Signals from the vertical and lateral deflections of the tip were recorded. Vertical deflection indicates contrast between opposite domains. It is a widely accepted approach [6, 7, 8, 9] that the response of the sample measured at the first harmonic, i.e., at the frequency ω, is related to the inverse piezoelectric effect. The phase shift of the response at ω characterises the sign of the polarization vector, while the amplitude is related to the magnitude of the polarization vector. The response at the second harmonic is related to the electrostrictive response of the sample. Both sides of the crystal were studied in order to check the uniformity of the poling. The topography of the c- face of a flux-grown PPKTP crystal is shown in Fig. 2a, where no evidence of ferroelectric domains can be appreciated. In Fig. 2b the phase of the first harmonic ω is shown. The alternating phase contrast of 180° corresponds to domains with opposing spontaneous polarization. A similar, but weaker response at the amplitude in the first harmonic ω was found. This response represents a difference in the magnitude of polarization in opposite domains [11], which may be due to the presence of a built-in internal electric field, which creates an asymmetry in the hysteresis loop. It should be noted that the curvature of the images is due to an artifact from the non-linearity of the piezoelectric tube scanner of the AFM used, and does not reflect the true geometry of the domains. The second harmonic response of the vertical deflection showed a weak, domain dependent response, with some enhancement of the response near the domain wall, suggesting some electrostrictive dependence of the polarization direction, and a local minimum in electrostriction at the domain wall.

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Figure 2. AFM images: (a) Topographic image of the –c face of a PPKTP sample. (b) Phase of the vertical deflection at the first harmonic showing contrast between domains with opposite directions of polarization. Both micrographs were taken over an area of 20 × 20 µm2.

Contrast at the domain walls was given by y the lateral deflection of the tip, as shown in Fig. 3. The tip was pushed sideways, giving contrast at the domain walls where adjacent domains were oscillating in opposite directions. At the first harmonic, the contrast caused by the amplitude was weaker than the phase shift contrast. The brightness-darkness contrast depends in both cases on the scanning direction, i.e., on the relative angle between cantilever and domain walls. The largest contrast was obtained when the relative angle between the cantilever and the domains was 45°. At 90° the contrast nearly disappeared, and at 0°, some domain walls became invisible because lateral deviation of the tip att those angles was not detectable.

Figure 3. Phase of the lateral deflection at the first harmonic showing contrast at the domains walls. The micrographs show an area of 20 × 20 µm2.

The apparent domain wall width was studied with both types of detection. Fig. 4. shows a micrograph of 600 nm × 600 nm of the phase response of (a) the vertical deflection and (c) the lateral deflection att the first harmonic. The profiles of these pictures are shown in Fig. 4b. and 4d. The apparent domain wall width measured in Fig. 4b. is approximately 54 nm. The width has been defined as the length from 25% to 75% of the full transition. In Fig. 4d., the measured domain wall width at FWHM of the full transition is around 66 nm. Different PPKTP samples have been studied, and the apparent domain wall width appeared to be between 20 and 80 nm, depending on the previous poling procedure applied to the sample. Waveguides on KTP were also studied with this technique. They were fabricated by ion-exchange of Rb/Ba for K ions in a periodic array in a periodic array of rectangular segments, which then defines an optical waveguide [12]. The ion-exchanged areas are

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domain reversed due to the way that the large Rb and Ba ions are accommodated in the crystallographic lattice [13]. The exchanged-regions are usually 5-10 µm deep.

Figure 4. Micrographs over an area of 600 × 600 nm2 at a domain wall in a PPKTP crystal. (a)The phase response of the vertical deflection at the first harmonic is shown. (b) A line profile across the domain wall; the domain wall width appears to be ~40 nm. (c) The phase response of the lateral deflection at the first harmonic of the same domain wall as in (a). (d) A line profile across the domain wall; the domain wall width measured at FWHM is ~66 nm.

Fig. 5 shows (a) the topography of the exchanged segments, the phase response of (b) the vertical deflection and, (c) the lateral deflection at the first harmonic. The apparent domain wall for these domains was measured to be 26 nm.

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(a)

(b)

Figure 5. AFM images: (a) Topographic image of a Rb/Ba-exchanged waveguide on the c- face of a KTP crystal. (b) Phase of the vertical deflection at the first harmonic showing contrast between domains with opposite directions of polarization. (c) Phase of the lateral deflection at the first harmonic showing contrast at the domains walls. The micrographs show an area of 20 × 20 µm2.

Compared to non-contact SPM techniques such as EFM the technique for domain and domain wall imaging described in this report gives at least one order of magnitude better resolution. The reason for this is that since the tip is in contact with the sample surface, the interaction between tip and sample is spatially limited to the very apex of the tip. The lateral resolution is thus limited only by the width of the tip-sample contact area. For non-contact methods on the other hand the interaction between tip and sample will be integrated over an area of the sample depending on the distance between tip and sample, and the active volume of the tip in a rather complex manner depending on the type of interaction.

4. Conclusion In conclusion, we show that a suitably modified AFM technique is a very effective and informative tool to investigate the domain structure in PPKTP crystals and in KTP waveguides. The method is non-destructive and the lateral resolution is of the same order as for normal contact mode SPM, i.e., ~1 nm. Using this method the apparent domain wall width of crystals is found to be in the range 20-80 nm.

References 1. 2.

Bluhm, H., Wadas, A., Wiesendanger, R., Roshko, A., Aust, J.A., and Nam, D. (1997) Imaging of domain invertedgratings in LiNbO3 by electrostatic force microscopy, Appl. Phys. Lett. 71, 146-148. Yang, T.J., Mohideen, U., and Gupta, M.C. (1997) Near-field scanning optical microscopy of ferroelectric domain walls, Appl. Phys. Lett. 71, 1960-1962.

369 3. 4. 5.

6. 7.

8.

9. 10. 11. 12. 13.

Orlik, X.K., Labardi, M., and Allegrini, M. (2000) Nanometer-scale observation of ferroelectric domains using an apertureless near-field optical microscope, Appl. Phys. Lett. 77, 2042-2044. Bozhevolnyi S.I., et al., (1998) Second-harmonic imaging of ferroelectric domain walls, Appl. Phys. Lett. 73, 1814-1816. Wittborn, J., Canalias, C., Rao, K.V., Clemens, R., Karlsson, H., Laurell. F. (2002) Nanoscale imaging of domains and domain walls in periodically poled ferroelectrics using atomic force microscopy, Appl. Phys. Lett. 80, 1622-1624. Gruverman, A., Auciello, O., and Tokumoto, H. (1996) Nanoscale investigation of fatigue effects in Pb(Zr,Ti)O3 films, Appl. Phys. Lett. 69, 3191-3193. Tybell, T., Ahn, C.H., and Triscone, J.M. (1998) Control and imaging of ferroelectric domains over large areas with nanometer resolution in atomically smooth epitaxial Pb(Zr0.2Ti0.8)O3 thin films, Appl. Phys. Lett. 72, 1454-1456. Tyunina, M., Wittborn, J., Rao, K.V., Levoska, J., Leppävuori, S. and Sternberg, A. (1999) Domain configuration in pulsed laser deposited films of rhombohedral PbZr0.65Ti0.35O3, Appl. Phys. Lett. 74, 31913193. Kolosov, O., Gruverman, A., Hatano, J., Takahashi, K., and Tkumoto, H. (1995) Nanoscale Visualization and Control of Ferroelectric Domains by Atomic Force Microscopy, Phys. Rev. Lett. 74, 4309-4312. Karlsson H. and Laurell, F. (1997) Electric field poling of flux grown KTiOPO4, Appl. Phys. Lett. 71, 3474-3476. Gopalan, V. and Gupta, M.C. (1996) Observation of internal field in LiTaO3 single crystals: Its origin and time-temperature dependence, Appl. Phys. Lett. 68, 888-890. v.d. Poel, C.J., Bierlein, J.D., Brown, J.B., and Colak, S. (1990) Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides, Appl. Phys. Lett. 57, 2074-2076. Thomas, P.A., and Glazer, A.M. (1991) Potassium titanyl phosphate, KTiOPO4. II. Structural interpretation of twinning, ion exchange and domain inversion, J. Appl. Cryst. 24, 968-971.

IMAGING LOCAL DIELECTRIC AND MECHANICAL RESPONSES WITH DYNAMIC HETERODYNED ELECTROSTATIC FORCE MICROSCOPY

D.R. OLIVER*, K.M. CHENG, A. PU, D.J. THOMSON, G.E. BRIDGES Electrical and Computer Engineering, University of Manitoba Winnipeg, Manitoba, Canada R3T 5V6.

Abstract A scanning probe microscopy based technique has been developed for mapping variations in the polarizability of materials. A number of experiments illustrating the potential of this technique are presented. These include the image of a grating sample with alternating regions of materials with different dielectric constants. Next, the technique is used to study mechanical resonances and dynamics in microelectromechanical (MEM) structures. Finally, a stroboscopic image of an operating 434 MHz surface acoustic wave device shows that the instrument can detect dipoles at frequencies four orders of magnitude of the resonance frequency of the sensing cantilever. In this experiment the dipoles imaged result from the mechanical action of the surface acoustic wave on the piezoelectric substrate. The technique may be employed to produce images that display the local polarizability of materials as a function of frequency and we expect this technique to be useable at frequencies into the millimeter wave region. Keywords: scanning probe microscopy, electrostatic force microscopy, polarization dynamics, nanotechnology, micro-electro-mechanical systems. 1. Introduction Mapping local dielectric and mechanical properties of materials on a microscopic scale is important for a number of scientific f and technological applications.1 This paper discusses a scanning probe microscopy based technique that has been developed for mapping variations in the concentration of locally induced dipoles. Electric fields in dielectric materials induce dipoles related to the polarizability of the material. In this technique the polarization is induced by a modulated signal applied to a conducting probe in the vicinity of the sample. Induced polarization dipoles in the surface of the material generate an electrostatic attraction between the probe and the dielectric material. Using techniques common in non-contact force microscopy these forces can easily be sensed.2,3 Remarkably, this measurement technique can be extended to frequencies well above the mechanical resonant frequency of the probe cantilever by utilizing amplitude modulation heterodyning. By rastering the probe over the surface an *

Author to whom correspondence should be addressed: [email protected].

371 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 371-385. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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image of the dielectric properties of the surface can be produced. Several experiments that illustrate potential fields of application for this technique are described below

2. Experimental The goal of this work is to develop an instrument that can detect local, dynamic polarization responses where "local" is similar in scale to the tip dimensions of the probe used. The apparatus illustrated in Fig. 1 is based on an established technique for electrostatic force probing of operating integrated circuits and devices where an electrical signal is applied to a non-contacting SPM cantilever and probe.2,3 Highfrequency potentials may be measured by applying a high-frequency signal to the probe and modulating this at the mechanical resonant frequency of the cantilever. Commercially microfabricated cantilevers (MikroMasch NT-MDT CSC12) with a W2C conductive surface coating have been used. In Fig. 1, the signal of experimental interest is at the frequency ωRF.

Figure 1. Diagram of the experimental setup showing the beam-bounce detection system used to detect topographic data (contact mode) and the dynamic electrostatic response (lift mode). The sample is grounded and the activation signal is applied via the probe. The apparatus is placed in a vacuum chamber to improve the sensitivity of the probe.

A laser beam reflected from the upper surface of the cantilever is detected by a split photodetector, characterizing cantilever deflections (∆z). Limited by thermal noise, this system can detect sub-nanometre deflections. The RF signal (ω ωRF) is generated by a RF source (Rohde & Schwarz SMT 03) and is amplitude modulated at half the mechanical

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resonance of the cantilever (ωm = 0.5ωr). A modulating signal, at a fundamental ωm, is employed and is generated using a signal generator (Stanford Research SR345). A highspeed switch (Mini-Circuits MSWT-4-20) is used as the modulator. As discussed below, due to the V2 dependence of the force, the signal extracted by the lock-in amplifier (SRS Model 830) is obtained at ωr. The vertical component of the electrostatic force Fz on the probe due to a localized point (x,y) on the sample being studied (as shown in Fig. 1) may be described as

1 § ∂C · 2 Fz (x, y ) = ¨ ts ¸[Vt − Vs ] 2 © ∂z ¹

.

(1)

Cts is the total capacitance between the probe tip and the potential sample. For square wave modulation Vt can be written as

ª º ∞ «1 2 1 » Vt = « + ¦ coskω m t»VRF cosω RF t , 2 π k=1 k «¬ »¼ odd with the terms in the square brackets due to the square wave modulation at ωm. When the sample is grounded, Vs = 0 in (1), and substituting Vt into (1) yields

·2 §ª º ∞ ¸ » 1 § ∂C ·¨« 1 2 1 Fz = ¨ ts ¸¨« + ¦ cos kω m t»VRF cosω RF t ¸ 2 © ∂z ¹¨ 2 π k=1 k ¸ »¼ odd ¹ ©«¬ 1 § ∂C ·§ V 2 V2 · = ¨ ts ¸¨ RF cos2ω RF t + RF ¸ × 2 © ∂z ¹© 2 2 ¹

(2)

ª § § · · « 1 4 ¨ ∞ 1 ª1 cos2kω m t º¸ 2 ¨ ∞ 1 ¸ + ¨¦ cos kω m t ¸ + » « 4 + π 2 ¨ ¦ k 2 «¬2 + ¸ ¼¸ π ¨ k=1 k 2 ¨ k=1 ¸ «¬ © odd © odd ¹ ¹ § ·º ∞ ∞ ·¸» §1 ·§ 1 4 ¨ ¦ ¦¨ cos kω m t¸¹¨© j cos jω m t ¸¹¸» π 2 ¨¨ k=1 j=1 © k ¸» © odd odd ¹¼

.

The resulting 2ωm (= ωr) term in the force Fz is

ª§ º · ∞ «¨ » 1 § ∂Cts · 2 1 ¸ Fz(2ω m ) = 2 ¨ ¸VRF (1+ cos2ω RF t )«¨1+ ¦ ¸ cos2ω m t» . 2π © ∂z ¹ k(k + 2) ¸ «¬¨© k=1 »¼ odd ¹

(3)

The geometry of the electrostatic interaction between probe and sample as well as the dielectric constant of the sample are contained within the capacitance derivative term in (3). The deflection amplitude ∆z of the probing cantilever at twice the

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modulation frequency is measured. The amplitude of the deflection when 2ωm = ωr is at the cantilever resonance, thus

∆zω m ≈

Q F , k z(2ω m )

(4)

where Q is the quality factor off the mechanical resonance (~104 in vacuo) and k ~0.6 Nm-1 is the spring constant of the cantilever. The following section describes experiments that show the application of this technique in three different situations.

3. Results 3.1 GRATING SAMPLE 5 µm

5 µm Si

4

4

3

3

2

2

1

1 0

1

2

3

4

5 µm

(b) 0

1

2

3

4

5 µm

Figure 2. (a) Topography of the 3 µm Si/SiO2 grating sample, (b) electrostatic force response in lift mode measured at 120 nm above the surface with fRFF = 10 MHz and (c) a comparison between the data from the dashed lines in (a) and (b). As is evident in (c), the variation in the electrostatic data is the inverse of the topography, this difference as expected the relative dielectric constants of the two regions.

The results discussed in this section were obtained from a commercially microfabricated grating (NT-MDT TGZ02) normally used for calibrating the XYZ PZT. The grating has a pitch of 3 µm and comprises 104 nm SiO2 steps fabricated on a silicon substrate. The entire structure has a 10 nm coating of Si3N4 to prevent oxidation of the grating.4 With

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the instrument operating in lift mode and a probing cantilever with 22ffm = fr = 70.7 kHz, the topography and electrostatic response images shown in Fig. 2 were obtained. The electrostatic response data in Fig. 2 shows there is a larger electrostatic response when the probe is above regions of the sample with higher dielectric constant (polarizability) and results from differences in the •Cts/•z in (1). The alternating Si (εr = 11.9) and SiO2 (εr = 3.9) regions of grating provide a useful illustration of this principle, although the Si3N4 coating (εr = 4.2) will modify the contrast. 3.2 ELECTROSTATIC ACTIVATION AND DETECTION OF CANTILEVER RESONANCE MODES There is considerable interest in the possibility of using micro-electro-mechanical (MEM) elements incorporated in system-on chip devices as filters, mixers and MHz frequency references.5 Using resonant mechanical structures in this fashion shows promise for lower power than comparable electrical or piezoelectric devices. The designs for these elements are based on combinations of vibrating beams and/or cantilevers. Such structures have very small vibration amplitudes (especially at MHz frequencies) and few methods can characterize the performance of these elements independently of the fabricated structure and its external connections. The instrument can be used as a dynamic probe of the mechanical responses of MEM structures, providing the material of the MEM element is electrostatically responsive.

Figure 3. The instrument configured to activate resonance modes in the test cantilever.

In this work a conducting cantilever induces motion through electrostatic force and the induced motion is detected using the heterodyne techniques discussed above. A

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Optical (µV/¥Hz)

Deflection signal (a.u.)

probing cantilever with a relatively low resonant frequency ((ffr ~ 14 kHz) and spring constant (k ~ 0.03 Nm-1) was used. The “sample” or “test” cantilever had a higher resonant frequency ((ffr ~ 80 kHz) and spring constant (k ~ 0.6 Nm-1). The resonant frequencies of both the probe and test cantilever can be easily characterized from their thermal resonance peak which can be recorded independently using the same optical beam-bounce system. (a)

Frequency (kHz) Deflection signal (a.u.)

(b)

Frequency (kHz) Figure 4. (a) Test cantilever thermal resonance in air and in vacuo characterized optically using the beam bounce system. The electrostatic detection of the cantilever resonance is also shown in terms of the ∆z signal at the lock-in amplifier. The quality factor (Q) values were calculated using the full-width at half maximum power (3dB) bandwidth. The apparently (very) large Q in the electrostatic data is discussed below. (b) Detail of the electrostatic response data in (a).

The probe cantilever was manually positioned to within a few µm of the test cantilever. The manual approach was observed through an optical microscope with long working distance objectives. Sweeping the RF source frequency, ωRF, in the range of the test cantilever resonance yielded an electrostatic t force response close to the resonance point that was obtained from the thermal peak using the beam-bounce system. Fig. 4

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shows a comparison between the thermal resonance peaks obtained optically and the fundamental resonance of the test cantilever observed by sweeping ωRF. The optically characterized thermal peaks exhibit the expected increase in Q (narrowing of the spectrum) due to the absence of (air) damping in vacuo. The slight shift in resonant frequency from 77.6 kHz to 77.9 kHz can also be attributed to this. The offset observed in the electrostatic result cannot be attributed to an increase in Q as the vacuum is the same (on the order of milliTorr) and appears therefore to result from the electrostatic interaction. A DC charge buildup on either probe in addition to the signal Vt on the probe (as discussed earlier) would contribute directly to this, however further measurements where the DC potential of the “test” cantilever was varied between –5V and +5V did not affect the position of the observed resonance. As seen in Fig. 4b, the overall bandwidth of the resonance curve obtained electrostatically is on the order of 10 Hz. This is, comparable to the 3dB bandwidth (11.7 Hz) of the thermal peak obtained in vacuo using the beam-bounce system. The apparently “split-peak” nature of the electrostatic response gives a clue to the result in Fig. 4b. A spectrum analyzer, connected to the output of the deflection sensor, was used to obtain the raw ∆z signal. Four data sets are shown in Fig. 5. The signal in Fig. 5 is then fed into the lock-in amplifier.

”

Figure 5. Raw ∆z data for four values of fRFF near the resonance (fres) of the test cantilever.

The lock-in amplifier effectively “measures” the magnitude and phase in a very narrow bandwidth centered at 2ωm = 2π(14.456) kHz, the resonance of the probing cantilever. As indicated in Fig. 5, Within 10 Hz of the resonance fres of the test cantilever, the “near” and “far” peaks have completely separated outt from the central resonance. Correspondingly, the amplitude of the central peak, and thus the signal measured by the lock-in, drops by almost an order of magnitude. The “split-peak” in Fig. 4b can be directly attributed to very slight asymmetries in the spacing of the “near” and “far” peaks on either side of the probing cantilever resonance (2ωm). The “near” and “far” peaks appear to be due to beating artifacts in the test cantilever mixed with terms in the Fourier expansion in Vt due to the switch.

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Resonance points were determined by adjusting ωRF until the beat frequency was almost eliminated (50 mHz – 100 mHz could easily be achieved). The variations in separation of these two pairs of peaks as a function of the distance from the resonance of the test cantilever fres are shown in Fig. 6.

Peak Separation (Hz)

500

400

“•••” •••••

300

••∆f ∆ ••∆f ∆

200

100

0 -120

−2∆f ∆ “near”

-90

+2∆f ∆ “near”

-60

-30

0

30

60

90

120

∆f = fRF – fres (Hz) ∆f Figure 6. Response of “near” and “far” peak separation (see Fig. 5) to the difference between applied frequency ωRF (f (fRF) and the mechanical resonance ((ffres) of the test cantilever.

An additional feature of the signal mixing due to the Vt2 term in (1) is the capacity to excite the mechanical resonances in the system. As a consequence of the Vt2 term, it is intuitive to see that setting ωRF = 0.5ωres will successfully excite the mechanical resonance in the test cantilever. Experimentally, it has been found that the other resonances at frequencies, ωRF = (ωres + ωm) and ωRF = (0.5ωres + ωm) can also be excited. Of great interest is the potential for this technique to activate and measure higher modes than just the fundamental. The frequencies of these modes can be predicted from the optical measurement using standard eigenvalue solutions for the modes of a vibrating cantilever using the following relations:6,7

ω n +1 = ϕ n2 ωn . π ϕ n = [1.194 ,2.988,5,7,. , (2n −1)]

(5)

2

Using these eigenvalues, the higher mode frequencies can be predicted and they are compared to those found experimentally in Fig. 7.

379 7000

Slope = 1

6000

5000

4000

3000

2000

1000

0 0

1000

2000

3000

4000

5000

6000

7000

Predicted from thermal fundamental (kHz)

Figure 7. The first six mode frequencies of the test cantilever. Predicted values calculated from the in vacuo optical determination of the fundamental mode and (4), measured values obtained using the electrostatic technique discussed.

It is worth noting that at higher modes the effective spring constant is much higher and the vibration amplitude is correspondingly smaller. The effective spring constant at the fourth mode (k4) has been calculated by Rast et all to be k4 ~ 3650k1 (where k1 is the spring constant at the fundamental mode).8 The ability of this technique to activate mechanical resonances modes into the MHz range makes it an attractive candidate for the analysis of more complicated micro-electro-mechanical structures. However, the complexity of the interaction illustrated in the seemingly simple case of a cantilever reported here illustrates that such analyses may not be straightforward. 3.3 STROBOSCOPIC IMAGING OF A TRAVELING SURFACE ACOUSTIC WAVE Surface acoustic wave (SAW) devices are widely used as resonators and filters in radiofrequency (RF) applications such as mobile communications. In a SAW device, subnanometre displacement acoustic waves are propagated along the surface of a crystalline material. In the case of piezoelectric materials the deformations produced by the SAW result in localized polarization. The SAW is generally introduced into the surface layers via an interdigital transducer (IDT) comprising a series of electrodes patterned onto the surface of the piezoelectric material. SAW propagation was first described by Rayleigh9 and the body of literature has grown to include monographs describing the general properties of SAW propagation in a variety of media10,11 and the design of filters.12 However, explicitly imaging a propagating SAW remains a challenging problem as the displacements at the surface of the material are very small (sub-nanometre), typical SAW velocities are in the range 103-104 ms-1 and SAW frequencies range from 100 MHz to 5 GHz depending on the material. Attempts to image SAWs using optical reflection13 and scanning acoustic force microscopy (SAFM)14,15,16 have been limited by the bandwidth of the detection apparatus or require an interference pattern from which the high-frequency behaviour of the SAW

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can be recovered. A recent report describes a scanning tunneling microscopy technique for the study of SAW propagation, although design considerations limit this technique to frequencies less than 1 GHz.17 An attempt to explicitly image SAW propagation using a scanning electron microscope has been reported,18 however distortions of the image due to charging effects limited this study to low accelerating voltages and probe currents. We demonstrate how the heterodyne electrostatic force technique can be utilized to explicitly image the polarization due to a propagating SAW. In this experiment a microfabricated cantilever with a W2C conductive surface coating (MikroMasch NT-MDT CSC12) and resonant frequency ~60 kHz was used. The measurement system used is show in Fig. 8 (this is different that the system described in Fig. 1).

Figure 8. Diagram of the experimental setup showing the beam-bounce detection system used to detect topographic data (contact mode) and the dynamic electrostatic response (lift mode). The cantilever is shown above the exposed substrate between the interdigital transducers (IDTs) across which the surface acoustic wave travels.

Assuming that the distance between the probe and the surface is small compared to the wavelength of the SAW (on the order of 1 µm – 10 µm for RF devices), the vertical component of the electrostatic force Fz on the probe due a localized point (x,y) on the device being studied may be described, similarly to (1), as

1 § ∂C · 2 Fz (x, y ) = ¨ ts ¸[Vt − Vs ] + ³ E tp ρ t ⋅ zˆds tip 2 © ∂z ¹ 1 § ∂Cts · 2 ≈ ¨ ¸[Vt ] + E tp (z)qt 2 © ∂z ¹

(5)

The electric field Etp is due to any surface charge on the device. Here Cts is the total (constant) capacitance between the probe tip and the SAW device substrate and ρt is the total charge density at the probe. Vs is any potential applied to the substrate of the SAW device and is assumed to be grounded. The signal applied to the probe is,

381

ª º ∞ «1 2 1 » Vt = « + ¦ coskω m t»VRF cos(ω RF t + φt ) 2 π k=1 k «¬ »¼ odd

(6)

Again, a Mini-Circuits MSWT-4-20 driven at ωm is used as the modulator. Typically the substrate is mounted in a package that is grounded (Vs = 0 as indicated in (5)). Surface charge density variations are created due to the mechanical action of the passing SAW on the piezoelectric substrate.11 When the probe-sample distance is much less than the SAW wavelength, the electric field Etp due to the charge at the surface can be approximated to the product of the field in the z direction, Etp(z) = σ/2ε0, where the planar ωRFt + φp). In (5), the total surface charge distribution σp due to the SAW is σ = σPcos(ω charge on the probe can be approximated as qt = -0.5σ + CtsVt. Substituting the above and using (2) to extract the appropriate term from [Vt]2, the ωm terms (not including DC, higher order ωm and RF components) in the force are

§ 1 § ∂C · 2 σ CV Fz(ω m ) = ¨ ¨ ts ¸VRF 1+ cos2(ω RF t + φ t ))+ p ts RF cos(φ p − φ t )+ ( 4ε0 © 2π © ∂z ¹ · σ p CtsVRF cos(2ω RF t + φ p + φ t )¸[cos ω m t ] . 4ε0 ¹

(7)

The signal extracted at ωm by the lock-in amplifier is

∆ ωm ≈ ∆z

· §C · Q QV VRF §§ ∂Cts · Fz(ω m ) = ¨¨ ¸VRF + ¨ ts ¸σ p cos(φ p − φ t )¸[cosω m t ] . k 2πk ©© ∂z ¹ © ε0 ¹ ¹

(8)

where Q is the quality factor off the mechanical resonance (~104 in vacuo) and k ~0.6 Nm-1 is the spring constant of the cantilever. Equation 8 shows that as the probe is rastered across the substrate at a constant height from the sample, the variation in the deflection signal with position (x,y) will be a function of the amplitude of the local surface charge σp(x,y) and the local relative phase of the surface charge φp(x,y) a the frequency ωRF. The first term in (8) contributes to a constant DC offset. For a travelling SAW, the amplitude will be a constant with position. However, the phase term cos(φp - φt) will exhibit the same spatial periodicity in (x,y) as the travelling SAW in the surface of the substrate. A SAW device (Panasonic Model QR 434C) was mounted on a matched transmission line connected between the RF source and a 50Ω terminator. This assembly was held in a piezoceramic tube (PZT) positioner underneath the probe/cantilever. This PZT governed XYZ motion in the instrument. The topography and structure of the SAW device was characterized using the instrument in contact AFM mode showing that the IDT electrodes had a periodicity of 3 µm and a height of 100 nm. This IDT electrode region is quite distinct from the flat substrate between the electrodes across which the SAW propagates. During operation, each line of the raster is traced twice, firstly in contact to obtain topographic data and secondly to obtain the electrostatic response. The topography of various regions of the sample is shown in Fig. 9.

382

6 5

6 µm

4

1

0

Figure 9. (a) Topography of IDT electrodes showing a pitch of 3 microns. This measurement corresponds reasonably with the wavelength obtained from the stroboscopic image of the SAW. (b) Topography of the exposed substrate between the IDT electrodes (where the SAW image was obtained). Images such as this were obtained at the same time as the polarization image. The surface features are on the order of 10 nm.

In contact mode the probe is held against the surface with a constant force, which is monitored using the deflection of the laser beam. Perturbations to the PZT z-position required to maintain constant ∆z signal (force) are recorded as a topographic trace. Returning to the start of the scan line, the PZT is retracted a set distance (600 nm) and the probe is re-traced along the scan line, but now at a constant height above the surface. During this, the controller records the electrostatic signal obtained from the lock-in amplifier. The lock-in amplifier enables the magnitude or the phase of the electrostatic deflection signal ∆z to be recorded. The electrostatic force image shown in Fig. 10 is a 256 line scan of the exposed substrate. The spatial period (wavelength) of the SAW in Fig. 10 is 4.8 µm, yielding a propagation velocity for the 434 MHz SAW of 2100 ms-1. An example of the ∆z magnitude is shown exhibiting the expected periodic variation of cos(φp - φt) from (7).19

Figure 10. 22.5 µm x 22.5 µm image of the polarization due to a propagating SAW on the substrate surface of the device. The stroboscopic nature of the electrostatic force image results from the phase relationship at every point in the scan between the probe and the surface. The image was obtained in lift mode 600 nm above the substrate with 0.5 mW power applied to the probe and 2.5 mW power applied to the SAW device. The "missing" wavefront in the upper corner corresponds to the location of an IDT electrode.

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Fig. 11 is a topographic image of the same region as in Fig. 10. The non-linearity of the PZT is evident in the corresponding topographic image as a slight "bowing" of the topography. The IDT electrode is also visible in the Fig. 11.

Figure 11. 22.5 µm x 22.5 µm topographic image of the SAW device region obtained simultaneously with the dynamic image (Fig. 10). The slight curvature of the surface is due to the non-linearity of the piezo (automatically corrected in Fig. 10). An IDT electrode can be seen in the upper right-hand corner of the image. The topography data recorded along the dashed line are shown above.

As the technique presented in this work can explicitly image a traveling SAW, it may be possible to use it to study interference and scattering effects due to surface features. Fig. 12 illustrates how a the traveling SAW is visible on either side of a damaged region of the surface, and how local damage to the first pair of IDT electrodes doesn’t entirely impede the operation of the device.

0µ

10

5

20 µm

10 0

5

0

Figure 12. (a) Topographic image of a damaged region of the device substrate showing a scratch and damage to nearby IDT electrodes. (b) Corresponding electrostatic response image (lift height 900 nm) showing the SAW propagating on either side of the damaged region. Note too that the grounded (alternate) IDT electrodes appear to be missing from the electrostatic response image.

4. Summary Dynamic heterodyne electrostatic imaging has been shown to generate images of a grating sample. This demonstrates the capability of this technique to distinguish

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between regions with different dielectric constants. The technique has been adapted to activate mechanical resonances above 6 MHz. These observed resonances were in agreement with the predicted values, and although t this experiment demonstrates that the instrument may be useful in characterizing micro-electro-mechanical elements, it also provides useful information about the interaction between probe and sample. Finally, the instrument has imaged the polarization due to a propagating 434 MHz SAW on the surface of an operating SAW device. The technique has been developed such that the signal inducing the polarization at the sample surface can be introduced via the probe demonstrating that electrical properties of materials can be dynamically imaged at frequencies significantly greater than the mechanical resonant frequency of the probe cantilever used in the SPM system. Acknowledgments This work was supported by the Canadian Institute for Advanced Research (CIAR) Nanoelectronics Initiative, the Natural Sciences and Engineering Research Council of t Corporation (CMC), Micronet (The Canada (NSERC), the Canadian Microelectronics Microelectronics National Center of Excellence) and the Canadian Foundation for Innovation (CFI). References 1.

Stern, J.E., Terris, B.D., Mamin H.J., and Rugar, D. (1988) Deposition and imaging of localized charge on insulator surfaces using a force microscope, Appl. Phys. Lett. 53, 2717-2719. Terris, B.D., Stern, J.E., Rugar, D., and Mamin, H.J. (1989) Contact electrification using force microscopy, Phys. Rev. Lett. 63, 2669-2672. Terris, B.D., Stern, J.E., Rugar, D., and Mamin, H.J. (1990) Localized charge force microscopy, J. Vac. Sci. Technol. A 8, 374-377. Weaver, J.M.R. and Abraham, D.W. (1991) High resolution atomic force microscopy potentiometry, J. Vac. Sci. Technol. B 9, 1559-1561. Nonnenmacher, M., O’Boyle, M.P., and Wickramasinghe, H.K. (1991) Kelvin probe force microscopy, Appl. Phys. Lett. 58, 2921-2923. Yokoyama, H.and Inoue, T. (1994) Scanning Maxwell stress microscope for nanmetre-scale surface electrostatic imaging of thin films, Thin Solid Films 242, 33-39. 2. Bridges, G.E., Said, R.A., and Thomson, D.J. (1993) Heterodyne electrostatic force microscopy for noncontact high frequency integrated circuit measurement, Electron. Lett., 29, 1448-1449. 3. Said, R., Mittal, M., Bridges, G.E., and Thomson, D.J. (1994) High frequency potential probe using electrostatic force microscopy, J. Vac. Sci Technol A 12, 2591-2594. 4. Malyshkin, P. Private Communication (July 2002) MikroMasch/NT-MDT, Tallinn, Estonia. 5. Bannon III, F.D., Clark, J.R., and Nguyen, C.T.-C. (2000) High-Q HF microelectronic filters, IEEE J. Solid-State Circuits 35, 512-526. 6. Stowe, T.D. (2000) PhD Thesis, Stanford University CA, USA 7. Kinsler, L.E., Frey, A.R., Coppens, A.B., and Sanders, J.V. (1982) Fundamentals of Acoustics 3/e, John Wiley & Sons NY, USA. 8. Rast, S., Wattinger, C., Gysin, U., and Meyer, E. (2000) The noise of cantilevers, Nanotechnology, 11, 169-172. 9. (Lord) Rayleigh (1885) On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4-11. 10. Acoustic Surface Waves (1978) in A. Oliner, (ed.), Topics in Applied Physics Vol. 24, Springer, Berlin. 11. Biryukov, S.V., et al (1995) Surface Acoustic Waves in Inhomogeneous Media, Springer Series on Wave Phenomena Vol. 20, Springer, Berlin. 12. Matthews, H. (ed.) (1977) Surface Wave Filters: Design, Construction and Use, Wiley, New York.

385 13. Gualtieri, J.G. and Kosinski, J.A. (1996) Large-area, real-time imaging system for surface acoustic wave devices, IEEE Trans. Instrum. Meas., 45, 872-878. 14. Hesjedal, T. and Behme, G. (2001) High-resolution imaging of surface acoustic wave scattering, Appl. Phys. Lett. 78, 1948-1950. 15. Behme, G. and Hesjedal, T. (2001) Influence of surface acoustic waves on lateral forces in scanning force microscopies, J. Appl. Phys., 89, 4850-4856. 16. Hesjedal, T. and Behme, G. (2001) High-resolution imaging of a single circular surface acoustic wave source: Effects of crystal anisotropy, Appl. Phys. Lett. 79, 1054-1056. 17. Voigt, P.U., Krauß, S., Chilla, E., and Koch, R. (2001) Surface acoustic wave investigation by ultrahigh vacuum scanning tunneling microscopy, J. Vac. Sci. Technol A 19, 1817-1821. 18. Roshchupkin, D.V. and Brunel, M. (1994) Scanning electron microscopy observation of surface acoustic wave propagation in the LiNbO3 crystals with regular domain structures, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 41, 512-517. 19. Oliver, D.R., Pu, A., Thomson, D.J., and Bridges, G.E. (2001) Heterodyne electrostatic imaging of polarization due to a surface acoustic wave, Appl. Phys. Lett. 79, 3729-3731.

AFM PATTERNING OF SrTiO3-δδ THIN FILMS AND DEVICE APPLICATIONS

L. PELLEGRINO INFM-LAMIA, Dipartimento di Fisica Via Dodecaneso 33, 16146 Genova, Italy

Abstract SrTiO3 (STO) is commonly known as a high-εr dielectric compound (εr =300 @ 300K), but it shows also a metal-insulator transition due to cation substitutions (i.e. La:STO, Nb:STO) or by introducing oxygen vacancies (SrTiO3-δ). The carrier concentration needed to turn into the conducting state (1018 e/cm3) is pretty low among perovskite oxides. Additionally, conducting STO presents high bulk mobility (104 cm2/Vs @ 4.2K). We think STO can be used as a functional conducting element in the developing oxide electronics. In this work we modify on submicron scale conducting SrTiO3-δ thin films grown on insulating LaAlO3 (LAO) substrates by simply applying a negative voltage to the conducting tip of an Atomic Force Microscope (AFM). Modified regions show different electrical and structural properties with respect to the as-grown films which can be exploited to realize submicrometric STO electrical circuits. After discussing the mechanisms of the process, we present the fabrication of a SrTiO3-δ based side gate field effect transistor. 1. Introduction Due to its interesting dielectric properties associatedd with a high dielectric constant (εr=300 @300K), strontium titanate (STO) is one the best candidate to sustain a role as a functional dielectric element in the field of oxide electronics [1, 2, 3, 4, 5]. In the stoichiometric state STO is a band insulator with a band gap of 3.2 eV, but upon chemical substitutions on its cation sites, like (La,Sr)TiO3 or Sr(Ti,Nb)O3, or by introducing oxygen vacancies (SrTiO3-δ), strontium titanate undergoes a metal-insulator transition [6]. With respect to other perovskite oxides, conduction in STO takes place just with a carrier density of the order of 1018 cm-3 [6], showing n-type semiconducting behavior and metallic conduction if the doping level increases. In its metallic state STO presents a high residual resistivity ratio R(300K)/R(4.2K)) of approximately 3000 [6] and exhibits superconductivity in the milliKelvin regime [7]. 387 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 387-398. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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STO conducting properties have been exploited by several authors [8, 9, 10]. In particular, due to the quite low density of carriers needed to switch into the conducting state, STO has been also considered as a functional semiconductor in field effect heterostructures [11]. In this work we apply the local probe oxidation technique to conducting STO thin films. Within this technique we will present a novel approach to pattern STO thin films which will be exploited to the fabrication of a STO-based side gate field effect transistor. Scanned probe oxidation was introduced in the 90s by Dagata and coworkers [12], who oxidized a silicon surface using a Scanning Tunneling Microscope (STM). Later on, the more versatile AFM was employed to local oxidize thin films of simple metals such as titanium [13, 14], aluminum [15] , chromium [16] and semiconductors like GaAs [17], allowing the fabrication of very y narrow wires down to tenths of nanometers [18] and nanometric devices such as side gate field effect transistors [19], single electron transistors [20], SQUIDs [21] , quantum rings [22]. During local oxidation, the conducting tip of the AFM is biased with a voltage and the electric field around the tip triggers chemical transformations on sample surface. Indeed, operating in air, a water meniscus appears spontaneously in the region between tip and sample where a nano-electrochemical cell is formed and sample surface is directly affected. There are a lot of studies in literature about the role of the experimental parameters involved in these local chemical transformations (magnitude and waveform of applied voltage, air humidity, tip speed, AFM operation mode) [23, 24, 25, 26]. For silicon and metal surfaces, the process has been explained in terms of either a simple electrochemical oxidation or a chemical reaction induced by the intense current density flowing through the tip. In the case of perovskite oxides, we expect more complicated processes due to the number of secondary phases which may form [27, 28, 29].

2. Experimental Oxygen deficient SrTiO3 thin films are deposited from single crystal targets on (100) LaAlO3 substrates by Pulsed Laser Ablation. Finite size effect and low angle X -ray reflectivity measurements allowed calibrating film thickness in the 10-60nm range (Fig.1a). X-ray analysis reveals also a high structural quality of the films and epitaxial growth (Fig.1b). AFM morphology measurements performed on as-grown films show atomic roughness of about 0.2 nm. Samples deposited above 650 °C in UHV or low oxygen pressure (10-9÷10-6 mbar) grow epitaxially and have slightly metallic or semiconducting behavior with carrier densities in the range 1020÷1018 cm-3 depending on oxygen deposition pressure (Fig. 2a). Films 10-60 nm thick are processed by standard optical lithography and chemical etched in 10% HF solution in ultrasonic bath, obtaining conducting channels of ~20 µm width with resistivities in the 0.03 – 1 Ωcm range (see inset Fig.2a). AFM experiments were performed by a Park Scientific Autoprobe CP5® microscope in contact mode and in a controlled atmosphere with a variable humidity percentage. A

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negative DC voltage was applied to the conducting tip (W2C coated Si tips having a force constant 0.12 N/m), while the sample is electrically connected to an external acquisition system, which allows to perform electrical measurements during AFM operations (Fig 2b).

Figure 1. (a) Finite size effect around the 002 peak showing the good crystalline quality of the films. (b) X-ray φ scan of a SrTiO3 thin film on LAO (100) substrate showing epitaxial growth.

Figure 2. (a) R vs T diagram of a STO film showing semiconducting behavior. (Inset) Diagram of the optically lithographed samples. (b) Configuration for the real time measurement of channel resistivity during AFM operations.

3. Results and Discussion We performed different line scans at the same speed in two different air humidity concentrations, biasing the AFM tip with increasing negative voltages. After the line

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scans, a topographic image of the whole region is taken with the same tip connected electrically to ground (Fig. 3). When the biasing voltage exceeds typically -6V, we observe overgrowth of lines on the surface of the STO film.

Figure 3. AFM topography of several lines obtained by scanning the conducting tip biased with different applied voltages in low (left) and high (right) humidity concentrations.

Figure 4. Self limiting of the process after application of a high bias voltage to the tip in high humidity, showing the micrometric dimensions of the modified regions in the xy plane and the limited vertical growth.

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These lines are stable in time as images taken after few days reveal the same structures. By increasing the magnitude of the applied voltage, the width and height of the lines increase, but while the width can increase to several microns, the height does not exceed few tens of nm. We note that for a given film thickness, there exist a maximum height of the order of the film thickness after which, increasing tip voltage or air humidity produces only a widening of lines and no further vertical growth (Fig.4). The voltage bias is the key parameter in controlling the process, while tip speed seems to be less critical, at least in the range 0.05 µm/s – 5 µm/s. Air humidity and tip wear have a significant effect on this mechanism. In particular, the voltage bias needed to observe this overgrowth is decreased by higher humidity and increased by tip wearing. Unfortunately, the resolution is worsened by high humidity and tip wearing. So far, our line resolution is about 100 nm. The regions affected by the biased tip differ from the rest of the film surface in morphology, structure and likely chemical composition. Morphological studies shows a granular structure of the modified regions associated with an increased surface roughness (1.7 nm r.m.s., see Fig. 5) with respect to atomically flat STO films.

Figure 5. Morphology of a modified region, showing a granular structure with r.m.s. roughness of 1.7 nm

Surprisingly, after a few seconds dip in HCl solution, overgrown lines disappear and leave grooves underneath which extend below the surface of the film down to a depth proportional to the height of the preexisting lines. This fact demonstrates that the AFM induced reactions extend beneath the film surface. In Figure 6a we show topography of lines written with different voltages and the corresponding grooves obtained after the HCl etching (Fig. 6b).

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Figure 6. (a) As-grown lines obtained with different bias voltages and (b) AFM image of the same region after few seconds in HCl solution. A voltage controlled etching of the film is clearly visible. (From left to right, -12 V, -16 V, -12 V, -8 V).

In Table I is reported a statistics on this image, where it appears that line resolution depends on the tip voltage and the groove depth t equals approximately the line height. TABLE I. Statistics of lines and grooves reported in Figure 6

Voltage [V]

-8

-12

-16

-12

Height [nm]

5

11

12

10

Depth [nm]

4

10

12.5

12.5

Width [nm]

125

335

520

290

By this technique it is so possible to develop a local etching of the STO films which can be controlled in efficiency by the magnitude of the tip voltage. Further studies will be directed to understanding the surface properties of the regions affected by the etching with the aim to perform successive depositions of other epitaxial oxides on AFM fabricated STO templates. STO films seem not to be removed by immersion in the HCl solution. In some cases dipping in HCl slightly increases the resistivity of the film, probably because of the etching of few STO unit cells or the depletion of surface carriers due to impurities at surface.

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Concerning the chemical nature of the modified regions, due to surface overgrowth, it seems unlikely that a simple local oxidation of SrTiO3-δ into SrTiO3 is occurring, because it would not explain the large volume expansion of the modified part. We argue the process we are studying may be instead explained in terms of a surface chemical reaction triggered by the tip electric field. This phenomenon was observed in YBCO [30, 31] thin films where a water mediated local electrochemical decomposition of YBCO in the field of the STM tip was reported. In our case, a phase transformation of SrTiO3 into carbonates, hydroxides and other oxides is likely to occur [27]. Anyway, the formation of amorphous and poorly dense SrTiO3 with a high etching selectivity with respect to epitaxial STO films cannot be excluded at this stage. To distinguish the nature of this process XPS and Auger analyses are underway. Modified regions have insulating behavior [32]. In Figure 7 it is reported a plot of the conductance of a 15 nm thick and 15 µm wide channel while the biased tip scans the channel transversely from edge to edge. The decrease of the conductance is consistent with the progressive narrowing of the conducting channel so demonstrating the insulating nature of the modified lines.

Figure 7. (a) 20 µm x 20 µm topography of a 15 nm thick optically lithographed channel after a transverse scan with the biased tip (Vtip = -25 V, scan speed 0.5 µm/sec). (b) Plot of the channel conductance while the biased tip approaches the edge.

To test the insulating quality of the written lines, we performed I vs V characteristics of the insulating barriers before and after the chemical etching. In Figure 8a we report electrical measurements of the as-grown line performed by measuring the current flowing through the barrier after biasing the channel with a voltage. We may see that the curve exhibits a non linear behavior presenting a resistivity of about 105 Ωcm for field of 100 kV/cm, at which point leakage begins to increase. After HCl etching the insulating line is removed, leaving a groove and the insulation of the barrier increases. In this last case, the resistivity of the air gap barrier exceeds 109 Ωcm for fields up to 1MV/cm.

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Figure 8. (a) I vs V characteristics of the AFM-defined insulating barrier. (b) I vs V characteristics of an HCl etched barrier reflecting an improvement of the insulation with respect to the as-grown lines.

The possibility to selectively remove conducting STO regions with a submicrometric resolution allows the fabrication of STO based nanodevices.

Figure 9. AFM image of a Side Gate Field Effect Transistorr fabricated on a 15 nm thick conducting STO film on a LAO substrate, showing the active channel, the Gate and the Ground pads.

In Figure 9 we report a 3D image of a Side Gate Field Effect Transistor fabricated by patterning a conducting STO film.

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A 15 nm thick STO film is patterned by the AFM in order to create a 700 nm wide and 3 µm long STO conducting channel which is directly connected to Drain and Source pads. The Source-Drain channel is electrically disconnected from the two STO regions which constitute the Gate and the Ground pads by means of AFM defined grooves. By applying a voltage to the Gate pads, electrostatic coupling to the Source-Drain channel and accumulation or depletion of electrons onsets, so modulating channel conductivity. As the surface charge density is fixed by the Gate voltage and by the capacitance between the Gate pad and the channel itself, the modulation of the SourceDrain resistance increases as the active channel width diminishes. In the case of a semiconducting sample, the charge induced region extends into the channel by approximately the Debye length, which is approximately 20 nm, for a conducting STO film with about 1018 e/cm3 .

Figure 10. (a) Zoom of the active channel. (b) Time evolution of the Source-Drain resistance during a square wave gate voltage (amplitude ± 10 V, 20 s period).

We achieved the fabrication of a 15 nm thick, 150 nm wide and 200 nm long active channel (see zoom in Figure 10a) by narrowing with the biased tip the 700 nm wide Source-Drain channel and controlling at the same time the channel width by measuring the Source-Drain resistance. At the end the sample was dipped in HCl solution in order to etch away the modified regions. In Figure 10b is reported the time behavior of the Source-Drain resistance during a square wave gate voltage with amplitude ±10 V and 20 seconds period. Resistance measurements were performed both in DC with different Source-Drain currents and in AC technique with a lock-in amplifier. All measurements confirm the electrostatic origin of resistance modulation, which is approximately 1 % with a gate electric field of about 125 kV/cm. Measurements up to 50 V shows linear modulation of the channel resistance with the Gate field. This modulation is approximately four times the effect presented with a different geometry [32]. Modeling of the capacitive coupling of the side gate in relation with the geometry of the device and the physical properties of the channel will be attempted.

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As observed also in the other device [32], upon application of high gate fields, together with electrostatic modulations, the channel resistance slowly drifts in the same direction of the field effect. We believe this process to be determined by the progressive charging and releasing of traps at channel edges. Also oxygen vacancies migration in the channel triggered by the gate fields cannot be excluded at this stage. We plan to apply this technique also to the fabrication of other type of devices. As a preview on future developments we present a prototype realization of STO islands 200 nm X 200 nm and 8 nm thick on insulating LAO. We think a weak electrical coupling between islands could be realized by leaving thin conducting barriers through defining shallow grooves by controlling the tip voltage. In Figure 11 is presented a topographical image of the performed three fundamental steps.

Figure 11. Fabrication of 200 nm x 200 nm STO islands on an insulating LAO substrate. (a) Writing of thin wires. (b) Fabrication of shallow transverse barriers. (c) Topography of the islands after HCl etching. The thinner barriers between the islands are realized by controlling the etching depth of the STO film with the bias voltage of the tip.

4. Conclusions In conclusion, we applied the local probe oxidation technique to conducting SrTiO3 thin films for the first time. The voltage biased tip of an atomic force microscope determined local chemical transformations at the surface of the film which resulted in a local overgrowth of the surface itself. Modified regions have different structure, morphology and transport properties with respect to oxygen reduced strontium titanate and may be etched away by a simple dip in HCl, leaving grooves underneath into the STO film. We showed a way to control STO etching depth and to realize in-plane line patterns with a resolution of about 100 nm. An example of side gate field effectt transistor with an active channel 150 nm wide and 200 nm m long was reported, showing a resistance

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modulation of 1% with gate voltages of 10 V (125 kV/cm). In future perspective we plan to realize real control of oxygen content in reduced SrTiO3-δ without involving any surface chemical reaction. Further studies will be also directed to increase the resolution and to apply this technique to other perovskite systems.

Acknowledgments This work was done in collaboration with E. Bellingeri, D. Marré, I. Pallecchi and A.S. Siri with the financial support of CARIGE foundation. The authors wish to thank Renato Buzio and Daniele Pergolesi for useful discussions.

References 1. 2. 3. 4. 5.

6. 7. 8. 9.

10. 11. 12.

13. 14. 15. 16.

17.

Newns, D.M., Misewich, J.A., Tsuei, C.C., Gupta, A., Scott, B.A., and Schrott, A. (1998) Mott transition field effect transistor, Appl. Phys. Lett. 73, 780-782. Fuchs, D., Schneider, C.W., Schneider, R., and Rietschel, H. (1999) High dielectric constant and tunability of epitaxial SrTiO3 thin film capacitors, J. Appl. Phys. 85, 7362-7369. Katsu, H., Tanaka, H., and Kawai, T. (2001) Dependence of carrier doping level on the photo control of (La, Sr)MnO3/SrTiO3 functional heterojunction, J. Appl. Phys. 90, 4578-4582. Watanabe, Y. and Okano, M. (2001) Photodiode properties of epitaxial Pb(Ti, Zr)O3/SrTiO3 ferroelectric heterostructures, Appl. Phys. Lett. 78, 1906-1908. Sugiura, M., Uragou, K. , Tachiki, M. and Kobayashi, T. (2001) Estimation of trap levels in SrTiO3 epitaxial films from measurement of (LaSr)MnO3/SrTiO3/(LaSr)TiO3 p-i-n diode characteristics, J. Appl. Phys. 90, 187-191. Tufte, O.N. and Chapman, P.W. (1967) Electron Mobility in Semiconducting Strontium Titanate, Phys. Rev. 155, 796-802. Koonce, C.S., Cohen, M.L., Schooley, J.F., Hosler, W.R., and Pfeiffer, E.R. (1967) Superconducting Transition Temperatures of Semiconducting SrTiO3, Phys. Rev. 163, 380-390. Zhang, J., Tanaka, H., and Kawai, T. (2002) Rectifying characteristic in all-perovskite oxide film p-n junction with room temperature ferromagnetism, Appl. Phys. Lett. 80, 4378-4380. Watanabe, Y., Bednorz, J.G., Bietsch, A., Gerber, Ch., Widmer, D. and Beck, A. (2001) Current-driven insulator–conductor transition and nonvolatile memory in chromium-doped SrTiO3 single crystals, Appl. Phys. Lett. 78, 3738-3740. Shimizu, T. and Okushi, H. (1999) Intrinsic electrical properties of Au/SrTiO3 Schottky junctions, J. Appl. Phys. 85, 7244-7251. Pallecchi, I., Grassano, G., Marré, D., Pellegrino, L., Putti, M., and Siri, A.S. (2001) SrTiO3-based metal– insulator–semiconductor heterostructures, Appl. Phys. Lett. 78, 2244-2246. Dagata, J.A., Schneir, J., Harary, H.H., Evans, C.J., Postek, M.T., and Bennett, J. (1990) Modification of hydrogen-passivated silicon by a scanning tunneling microscope operating in air, Appl. Phys. Lett. 56, 2001-2003. Snow, E.S. and Campbell, P.M. (1995) AFM Fabrication of Sub-10-Nanometer Metal-Oxide Devices with in Situ Control of Electrical Properties, Science 270, 1639-1641. Irmer, B., Kehrle, M., Lorenz, H., and Kotthaus, J.P. (1997) Fabrication of Ti/TiOx tunneling barriers by tapping mode atomic force microscopy induced local oxidation, Appl. Phys. Lett. 71, 1733-1735. Snow, E.S., Park, D., and Campell, D.M. (1996) Single-atom point contact devices fabricated with an atomic force microscope, Appl. Phys. Lett. 69, 269-271. Wang, D., Tsau, L., Wang, K.L., and Chow, P. (1995) Nanofabrication of thin chromium film deposited on Si(100) surfaces by tip induced anodization in atomic force microscopy, Appl. Phys. Lett. 67, 12951297. Heinzel, T., Held, R., Lüscher, S., Ensslin, K., Wegscheidre, W. and Bichler, M. (2001) Electronic properties of nanostructures defined in Ga[Al]As heterostructures by local oxidation, Physica E 9, 84-93.

398 18. Legrand, B. and Stievenard, D. (1999) Nanooxidation of silicon with an atomic force microscope: A pulsed voltage technique, Appl. Phys. Lett. 74, 4049-4051. 19. Campbell, P.M., Snow, E.S., and McMarr, P.J. (1995) Fabrication of nanometer-scale side-gated silicon field effect transistors with an atomic force microscope, Appl. Phys. Lett. 66, 1388-1390. 20. Matsumoto, K., Ishii, M., Segawa, K., Oka, Y., Vertanian, B.J., and Harris, J.S. (1996) Room temperature operation of a single electron transistor made by the scanning tunneling microscope nanooxidation process for the TiOx/Ti system, Appl. Phys. Lett. 68, 34-36. 21. Bouchiat, V., Faucher, M., Thirion, C., Wernsdorfer, W., Fournier, T., and Pannetier, B. (2001) Josephson junctions and superconducting quantum interference devices made by local oxidation of niobium ultrathin films, Appl. Phys. Lett. 79, 123-125. 22. Fuhrer, A., Lüscher, S., Ihn, T., Heinzel, T., Esslin, K., Wegscheider, W., and Bichler, M. (2001) Energy spectra of quantum rings, Nature 413, 822-825. 23. Avouris, P., Hertel, T. and Martel, R. (1997) Atomic force microscope tip-induced local oxidation of silicon: kinetics, mechanism, and nanofabrication, Appl. Phys. Lett. 71, 285-287. 24. Tello, M. and Garcia, R. (2001) Nano-oxidation of silicon surfaces: Comparison of noncontact and contact atomic-force microscopy methods, Appl. Phys. Lett. 79, 424-426. 25. Bloeß, H., Staikov, G., and Schulyze, J.W. (2001) AFM induced formation of SiO2 structures in the electrochemical nanocell, Electrochim. Acta 47, 335-344. 26. Abadal, G., Pérez-Murano, F., Barniol, N., and Aymeric, X. (1998) Field induced oxidation of silicon by SPM: study of the mechanism at negative sample voltage by STM, ESTM and AFM, Appl. Phys. A 66, S791-S795. 27. Szot, K. and Speier, W. (1999) Surfaces of reduced and oxidized SrTiO3 from atomic force microscopy Phys. Rev. B 60, 5909-5926. 28. Szot, K., Speier, W., Herion, J., and Freiburg, C.H. (1997) Restructuring of the Surface Region in SrTiO3, Appl. Phys. A 64, 55-59. 29. Szot, K., Pawelczyk, M., Herion, J., Freiburg, CH., Albers, J., Waser, R., Hulliger, J., Kwapulinski, J., and Dec, J. (1996) Nature of the Surface Layer in ABO3-type Perovskites at Elevated Temperatures, Appl. Phys. A 62, 335-343. 30. Bertsche, G., Clauss, W., Prins, F.E., and Kern, D.P. (1998) Modification of YBa2Cu3O7 –δ wires using a scanning tunneling microscope: Process and electrical transport effects J.Vac. Sci. Technol. B 16(6), 3883-3886. 31. Bertsche, G., Clauss, W., and Kern, D.P. (1996) Nanometer-scale surface modifications of YBa2Cu3O7 –δ thin films using a scanning tunneling microscope, Appl.Phys.Lett. 68, 3632-3634. 32. Pellegrino, L., Pallecchi, I., Marré, D., Bellingeri, E., and Siri, A.S. (2002) Fabrication of submicron-scale SrTiO3- δ devices by an atomic force microscope, Appl.Phys.Lett. 81, 3849-3851.

NANOSCALE INVESTIGATION OF A RAYLEIGH WAVE ON LiNbO3

J. YANG*, R. KOCH Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, D10117 Berlin * Corresponding author: e-mail: [email protected]

Abstract The scanning tunneling microscope (STM) after sophisticated modification is a powerful technique to investigate surface acoustic waves (SAWs) with high spatial resolution. Using our ultra high vacuum SAW-STM, a Rayleigh wave propagating in LiNbO3 has been characterized. In accordance with a previous model, the amplitude and phase signals extracted from the modulated tunneling current depend on the surface inclination and the eccentricity β of the SAW. From comparison with simulated amplitude and phase images a value for β = 35−40° is obtained in good agreement with the theoretical eccentricity of the Rayleigh wave. Keywords: Surface acoustic waves, elastic properties of solid, scanning tunneling microscope.

1. Introduction Surface acoustic waves (SAWs) are widely employed for high frequency (HF) filtering and signal processing in technological applications, such as mobile phone and satellite telecommunication. Furtheremore, since the dynamics of surface motion contains important information on surface and subsurface elastic properties and material structure, SAWs are also a standard probe in materials science [1]. Commonly, the elastic constants of bulk and thin films are determined by optical methods, which measure the propagation time of the SAW over a distance of many wavelengths, thus yielding the phase velocity averaged over the propagation path [2]. The spatial resolution of optical techniques is limited byy the laser beam size. Employing lock-in and mixing techniques, Chilla and coworkers [3, 4] demonstrated that scanning probe techniques – despite their large response times – are sensitive to HF surface acoustic wave fields (~ 10 MHz → GHz) as well. In particular, the unique spatial resolution of the scanning tunneling microscope (STM) can be utilized to investigate amplitude and phase of SAWs [5] and furthermore to determine locally the elastic constants and other material properties, which are related to amplitude and phase of SAWs. Here we report on recent results of a Rayleigh wave propagating on a piezoelectric LiNbO3 single crystal surface obtained with our ultra high vacuum (UHV) SAW-STM [6]. Our investigation shows that – in agreement with the model of Chilla et al. [3, 7] – 399 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 399-404. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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the amplitude and phase information extracted from m the tunneling current is modified by the morphology of the thin Au film, which serves as a conducting layer for the SAWSTM experiments. By comparing the experimental findings with simulated amplitude and phase images we quantitatively determine the eccentricity of the SAW oscillation ellipse on surface areas with dimensions much smaller than the wavelength of the SAW.

2. Experimental The experiments presented here were performed in a UHV system consisting of separate chambers for sample preparation and SAW-STM investigation (base pressure < 2 × 1010 mPa). The UHV SAW-STM − developed recently in our group [6] − is based on a commercial Omicron STM-1 and has been modified by adding a UHV-compatible highfrequency wiring system for SAW-excitation and signal detection for frequencies up to 1 GHz. The substrate is a piezoelectric single crystal, Y-cut LiNbO3, carrying a lithographically fabricated interdigital transducer (IDT) for exciting Rayleigh wave at a resonance frequency of 246 MHz. It is mounted onto the sample holder, which allows for versatile sample transfer into and within the UHV system. When the sample holder is inserted into the SAW-STM all required electrical connections to the sample are routinely established by contact springs. A 100 nm thick conducting gold film was deposited in situ at a temperature of 400°C and a rate of 0.1 nm/s.

Vmod

fSAW

V0+Vmod

fSAW+∆f

V0

It lock-in tip

∆f

IDT substrate

Figure 1. Experimental setup of the SAW-STM for the measurement of the SAW motion. The SAW-induced tunneling current modulation at the frequency fSAW is mixed with the modulation of the tunneling voltage fSAW + ∆f ∆f at the non-linear current-distance-characteristic of the tunneling gap. A lock-in amplifier extracts the resulting difference frequency signal ∆f ∆f yielding amplitude and phase of the SAW, which both are recorded in addition to the topography.

The experimental set-up of an SAW-STM is schematically illustrated in Fig. 1. The STM tip is positioned above the conducting film on the piezoelectric sample, which is located in the propagation region of the SAW excited by the IDT on the left. The SAW-

401

induced surface oscillations at the frequency fSAW W give rise to a HF contribution to the tunneling current between tip and conducting layer. The HF component is mixed at the non-linear current distance characteristics of the tunneling gap with a HF voltage Vmodd at the frequency fSAW + ∆f ∆f, which is added to the common DC tunneling voltage V0. The mixing signal at the difference frequency ∆f ∆f is chosen to be in the kHz range, where it can be easily analysed by conventional STM electronics and lock-in technique. Also the mixing signal, which is recorded simultaneously with the topography, comprises the amplitude and phase information of the SAW. Particularly the latter can be used to quantitatively determine the eccentricity of the SAW oscillation ellipse on areas as small as 5 × 5 nm2 [3, 7]. 3. Results and discussion The propagation of a Rayleigh wave on Y-cut LiNbO3 was investigated via a 100 nm thick Au film, which forms the conducting electrode for the SAW-STM experiments. The film exhibits a textured morphology characterized by crystalline islands with mainly hexagonal and occasionally rectangular shapes and dimensions ranging from 10 to 150 nm. The STM topview chosen for Fig. 2a displays several flat (111) terraces that are terminated mainly by steps oriented at angles of 60º and 120º. The steps marked by 1−5, which ascend from bottom left to top right, as well as step 6, which vertically crosses the large terrace in the center of Fig. 2a, exhibit step heights between 0.5−1.5 nm. The height of step 7 is about 0.08 nm. Both amplitude and phase of the tunneling signal at the difference frequency due to the SAW-induced surface oscillation are extracted simultaneously from the tunneling current while scanning the topography. Corresponding greyscale images are displayed in Fig. 2b. Obviously the signals of amplitude and phase are convoluted with topographical information, therefore the overall morphology displayed in Fig. 2a can be easily recognized also in the two HF images. In the interior of the terraces amplitude and phase are uniform, significant changes are observed at steps. At the ascending steps of Fig. 2 the phase is generally larger than on the terraces. Also the amplitude of steps 1−6 is increased compared with the adjacent terraces, only step 7 exhibits a smaller amplitude. Step 6 gives rise to a only very faint contrast in Fig. 2b. Due to the exponential decay length of the tunneling process, SAWs strongly affect the tunneling signal by periodically modulating the distance between the STM tip and sample. In addition, the respective HF componentt in the tunneling current is further modified by the local surface corrugation. As described by the model of Chilla et al. [3, 7], both amplitude A and phase ϕ of the distance modulation signal measured in the SAW-STM experiment depend on the local tilt of the surface and the eccentricity β of the SAW oscillation ellipse. Since the electrons tunnel mainly along the shortest line between tip apex and sample surface, a geometrical projection of the oscillation ellipse is monitored, which depends on the local inclination angles γx and γy along and perpendicular to the propagation direction of the SAW. Accordingly, on top of a flat horizontal terrace the normal component of the oscillation trajectory is measured. When scanning over inclined facets also the in-plane component of the surface oscillation is contributing. Hence, amplitude and phase shiftt depend on the inclination of the

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tangential plane at the tip position. The maximum effect is found at steps accompanied by a sudden change of the sign of the phase. The structural features observed in the high frequency images therefore are the result of the imaging process itself and not induced by the linear SAW phase delay with increasing distance from the IDT; on the small length scale of typical STM images compared with the SAW wavelength of about 3.5 µm the relative phase shift is less than 6°. Quantitative evaluation yields the following equations for amplitude A and phase ϕ [3, 7]:

A = u0

sin 2 β cos 2 β + 1 + g y / g x + 1/ g x 1 + g x + g y

(1)

ϕ = − arctan(tan β tan γ x ) Here g x = (tan γ x )

2

the inclination angles

(2)

2 and g y = (tan γ y ) account for the local tilt that is given by

γ x = ∂z / ∂x

and

γ y = ∂z / ∂y ,

respectively.

eccentricity angle of the oscillation ellipse and is calculated by

β

denotes the

β = arctan(u1 / u3 )

from respective longitudinal and transverse displacement amplitudes u1 and u3 with

u0 = u12 + u3 2 . Note that because of the derivatives occurring in Eqs.1 and 2, the structural features are even more pronounced in amplitude and phase images compared with topography. By comparing the experimental results with amplitude and phase images simulated by Eqs. 1 and 2 it is possible to quantitatively determine the eccentricity β of the SAW oscillation ellipse (for a detailed discussion see Refs. 5 and 8). Figures. 2c−2f show simulated amplitude and phase images calculated for β = 25°, 36°, 40° and 50°, respectively; the experimental topography of Fig. 2a was taken as input parameter. As expected, the simulated amplitude and phase images also reproduce the main structural features of the topography. Similar to the experiment, the contrast is uniform at the terraces and enhanced at the steps; only step 7 appears darker. Best agreement between the experimental and simulated images is achieved for β values between 35° and 40°. Only in that range of β, for instance, both amplitude and phase calculated at the four edges surrounding the large terrace in the center of Fig. 2 assume similar magnitudes along the two different directions (i.e. corresponding to similar levels of brightness in Fig. 2d and e). For higher β particularly the respective amplitude, for lower β the corresponding phase signals become asymmetric. A value of β = 35−40° is in good agreement with β = 35.1° calculated for the Rayleigh wave on Y-cut LiNbO3. Notice that in the SAW-STM experiment described here β was determined by means of a film region of only 80 × 70 nm2, i.e. on a length scale two orders of magnitude smaller than the wave length of 3.5 µm. It is noteworthy, however, that the simulated amplitude and phase images match the experiment only on a qualitative level. Particularly the relative magnitude of the simulated amplitude at steps is markedly smaller compared with the experimental findings. The discrepancy certainly originates in the simplifying model assumptions.

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a

5

6 3

7 2

1 b

ac

ß=25°

da

ß=35°

ae

ß=40°

af

ß=50° Figure 2. a) 80×70 nm m2 topview of a 100 nm thick Au film on Y-cut LiNbO3 as well as b) amplitude (left) and phase (right) images of a Rayleigh wave, all recorded simultaneously with the SAW-STM. c−f) Simulated amplitude (left) and phase images (right) at different angles β of the oscillation ellipse. Good agreement with experiment is achieved for β = 35−40°.

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For instance, in the model of Chilla et al. [3, 7] tunneling proceeds from infinite facets that are oscillating due to the SAW. Of course, the model is applicable also on finite facets as long as their dimensions exceed the typical area from which the (majority of the) tunneling current is collected (ca. 1×1 nm m2). But the assumption is probably no longer valid at steps 1−7 because of the small step height of 0.2 −1.0 nm, and definitely not at the step edges itself. Furthermore, the work function is assumed to be constant irrespective of the local suface geometry. However, it is well known that due to the Smoluchowsky effect the work function at steps may be reduced by 25% compared to the terraces, which leads to an increase of the amplitude. Another reason may be the local elastic properties of the Au film. Since atoms at a step bond less strongly than in a terrace, their oscillation behavior is different.

4. Conclusions We have investigated the propagation of a Rayleigh wave on Y-cut LiNbO3 by UHV SAW-STM. Our study demonstrates that UHV SAW-STM is indeed a powerful nanoscale probe for SAWs. The amplitude and phase depend mainly on the tilt of the surface and eccentricity of the SAW, which is in agreement with the model of Chilla et al. Once the feature size reaches atomic dimensions, e.g. at steps, the modulated tunneling current seems to be influenced also by some other factors such as the local work function, the local elastic properties and probably also by the shape of the STM tip.

Acknowledgements The authors wish to thank E. Chilla and P. U. Voigt for helpful discussions, S. Krauß for technical support and W. Seidel for providing the IDT samples. The work was sponsored by the European Union (EFRE).

References 1. 2. 3.

4. 5. 6. 7. 8.

Royer, D. and Dieulesaint, E. (2000) Elastic Wave in Solid I, Springer-Verlag, Berlin. Monchalin, J.-P. (1986) Optical detection of ultrasound, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC-33, 485-499. Chilla, E., Rohrbeck, W., Fröhlich, H.-J., Koch, R., and Rieder, K.H. (1992) Probing of surface acoustic wave fields by a novel scanning tunneling microscopy technique: Effects of topography, Appl. Phys. Lett. 61, 3107-3709. Hesjedal, T., Chilla, E., and Fröhlich, H.-J. (1996) Direct visualization of the oscillation of Au (111) surface atoms, Appl. Phys. Lett. 69, 354-356. Voigt, P.U. and Koch, R. (2002) Quantitative geometry of the Rayleigh wave oscillaton ellipse by surface acoustic wave scanning tunneling microscopy, J. Appl. Phys. 92, 7160-7167. Voigt, P.U., Krauß, S., Chilla, E., and Koch, R. (2001) Surface Acoustic Wave Investigation by UHV Scanning Tunneling Microscopy, J. Vac. Sci. Technol. A 19, 1817-1821. Chilla, E., Rohrbeck, W., Fröhlich, H.-J., Koch, R., and Rieder, K.H. (1994) Scanning tunneling microscopy of rf oscillating surfaces, Ann. Phys. 3, 21-27. Yang, J., Voigt P.U., and Koch, R. (2003) Nanoscale investigation of longitudinal surface acoustic waves, Appl. Phys. Lett. 82, 1866-1868.

SCANNING CAPACITANCE FORCE MICROSCOPY AND KELVIN PROBE FORCE MICROSCOPY OF NANOSTRUCTURES EMBEDDED IN SiO2

G. TALLARIDA, S. SPIGA, M. FANCIULLI Laboratorio MDM – INFM, Via Olivetti 2, 20041 Agrate Brianza, Milan, Italy.

Abstract Scanning capacitance force microscopy and Kelvin probe force microscopy are used to image Sn nanometer sized structures embedded in silicon oxide thin films. The capacitance variation occurring between probe and sample in presence of a metallic cluster modifies the oscillation amplitude off the AFM probe at twice the frequency of the applied voltage. The extreme localisation of the interaction due to the small geometries involved allows a lateral resolution of few nm. Issues related to the contrast mechanism and the spatial resolution are discussed with the support 2D finite element calculation of the electrostatic field distribution between probe and sample.

1. Introduction The characterisation of physical and chemical properties of nanostructures requires techniques with high sensitivity and appropriate spatial resolution. In this framework scanning probe techniques play a major role. The extremely localised interaction between the sharp probe and the sample allows a spatial resolution of few nanometers. Moreover, using particular configurations, it is possible to overlap to the surface morphology image, a map of either the magnetic, optical, thermal or electrical properties of materials. In this work two techniques, kelvin probe force microscopy (KPFM) and scanning probe force microscopy (SCFM), both based on non-contact AFM, are used to image metallic nanostructures embedded in thin SiO2 films. KPFM was first introduced by Nonnemacher et al. [1]. Its working principle follows from the idea of the conventional Kelvin probe [2], a technique widely used to determine the work function of conductive materials. In KPFM, a variable electric field is induced between a conductive AFM probe and the sample by applying an oscillating voltage. Instead of the displacement current as in conventional Kelvin probe, in KPFM the electrostatic force induced on the probe is recorded through the AFM force detector. An additional feedback loop cancels out the detected electrostatic force by adding to the probe-sample system an appropriate dc voltage, usually referred to as the ‘kelvin’ voltage, Vk. 405 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 405-411. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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SCFM was proposed by Abraham et al [3], who suggested it as an alternative to conventional scanning capacitance microscopy (SCM) for the dopant profiling of silicon. The main difference with SCM is that it is based on a non-contact measurement and the detected signal is the force induced on the conductive AFM probe by capacitance variations occurring in the sample, rather than the capacitance signal itself. This is obtained by detecting the amplitude variation at twice the frequency of an applied ac voltage. To differentiate the two techniques, the latter is referred to as SCFM, as recently proposed in [4]. KPFM and SCFM are implemented on a commercial AFM, and the kelvin voltage and the capacitance force signals can be recorded simultaneously. In the work presented here, the best measurement configuration is obtained when Vk is used to cancel out the contact potential differences between probe and sample, whereas the capacitance force signal is exploited to image the nanoclusters embedded in the oxide film. Obtained results compare well with cross sectional and plan view TEM images of the same sample. Simulation by means of a 2D finite element code of the electrostatic interaction between probe and sample allows us to investigate the mechanism responsible for contrast formation and to evaluate the spatial resolution.

2. Experimental Details 2.1. SAMPLE PREPARATION Nanoclusters studied in this work were formed in SiO2 films by Sn ion implantation and successive rapid thermal annealing [5-7]. SiO2 films, 85 nm thick, were thermally grown on 3" (100) p-type silicon substrates by dry oxidation at 1000 °C. Samples were implanted at room temperature with 80 keV Sn+ ions and with fluence 1x1016 cm-2. The implantation parameters were determined by TRIM simulations and the Sn peak position was chosen to be in the middle of the SiO2 film. After ion implantation,

Figure 1. Plan view (left) and cross sectional (right) TEM images of the oxide containing Sn nanoclusters. The size of the two images is approximately 200 nm.

407

samples were annealed in a rapid thermal processing system in N2 atmosphere at 900°C for 10 minutes. TEM, either in cross-section or plan-view geometry, was used to study the size, the position and the structure of nanoclusters in the oxide layers [5]. 119Sn Conversion Electron Mössbauer Spectroscopy and X-ray Absorption Spectroscopy analyses [6,7] performed in these samples confirmed the formation of β−Sn nanocrystals in agreement with high resolution TEM. Plan view and cross sectional TEM images of the measured sample are shown in Fig.1. Isolated nanocrystals are dispersed in the oxide matrix; their diameter ranges between 5 and 20 nm. Their distribution into the oxide is random and the mutual distance between bigger nanocrystals is up to few tens of nm. 2.2. MEASUREMENT SET-UP When an oscillating voltage is applied between the conductive AFM probe and the sample, the electrostatic force induced on the probe is: F=

1 dC 2 V 2 dz

(1)

where V can be written as: V = V dc + V ac sinωt

(2)

In (2) Vdc accounts for every bias difference, either applied or built-in, between the probe and the sample. Substituting (2) into (1), F can be arranged as the sum of 3 terms: F=F Fdc+Fω+F2ω where: (3a) 1 dC ª 2 1 2 º Vdc + Vac » 2 dz «¬ 2 ¼ dC (3b) Fω = VdcVac sinωt dz 1 dC 2 F2ω = − Vac cos 2ωt (3c) 4 dz Fdc indicates a constant bending of the cantilever, independent from the frequency of the applied voltage. Fω is the quantity usually analysed in the electrostatic force microscopy and, if an additional feedback circuit is used to null this component, the potential contact difference between probe and sample is obtained (KPFM). F2ω depends only on the variation of the total capacitance between the probe and sample C, and it is the component analysed through a lock-in amplifier to produce capacitance variation maps in SCFM. To ensure an effective separation of the topographic contribution from the electrostatic one, ω is set different from the fundamental resonance frequency ω0 used in non-contact AFM mode to produce the morphology image. In our set-up KPFM, SCFM and AFM images are simultaneously recorded. This ensures an exact correspondence between images, as well as no resolution worsening due to probe-sample distance increase, as in lift-mode f techniques. Commercial conical Fdc =

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silicon probes covered with a Pt/Ir conductive layer, with a resonance frequency of about 70 kHz, are used in the measurements. The amplitude of the applied voltage is 2 V and ω is around 40 kHz. Image resolution is 300 points x 300 lines. 3. Results In our measurements the best contrast thatt allowed nanocluster imaging was obtained from the SCFM signal. Although through the FȦ component a variation of the KPFM signal related to the presence of nanocrystals in the oxide was observed, it was not possible to rule out an influence in the Kelvin potential of the dC/dz term, perhaps not totally cancelled out by the feedback circuit [8, 9]. On the other hand, by detecting the SCFM signal, it is exactly the dC/dZ term that is exploited to localise and characterise the nanocrystals, while the simultaneous minimizing of the FȦ term ensures a better control of the probe-sample interaction and a better reproducibility of results.

Figure 2. Morphology (left) and capacitance contrast image (right) of a 200x200 nm2 area. The grays scales correspond to 2 nm and [3.6-4.8 V], respectively.

In Fig. 2 the topography and the capacitive force image simultaneously taken on a 200x200 nm2 area are shown. Several hollows can be observed, which are not present in the surface morphology image, as well as in the capacitance contrast images of plain oxide (not reported here). Their lateral size ranges between 8 and 20 nm, compatible with the larger nanocrystals observed in TEM analyses, whereas their depth ranges from 0.25 to 0.45 V [10]. Also their distribution resembles the nanoclusters’ one, as it results from comparison with plan view TEM images. Our conclusion is that these hollows are the image of nanocrystals inside the oxide layer. In fact, a variation of C is expected to occur when the probe scans over a region where a conductive particle is embedded in the oxide. As depicted in Fig. 3, C can be thought as the series of 3 terms: the capacitance of the air gap Cair, which is the only one depending upon z [3], the capacitance of the depletion region at the semiconductor interface Cs, and the capacitance of the oxide Cox. In the presence of a nanocrystal we can assume Cairr and Cs to remain almost constant, whereas Cox is expected to increase to a value Cǯ. The latter

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term accounts for the capacitive force increase experimentally observed. If the parallel plate approximation was appropriate for this experiment, Cǯ would result equal to Cox/k, where at its maximum k=(dox-2r)/dox, r being the radius of the nanocluster. However, due to the complicated geometry involved, the electrostatic force cannot be calculated by means of analytical expressions. In fact, the probe end is of comparable size of the nanostructure to be imaged, and no simple approximation can be used to describe the force field.

z l Cair C

R

s

r

Figure 3. Representation of the variation of capacitance in presence of a metallic nanocrystal.

x

Figure 4. Schematic of the geometry simulated in the 2D finite element code

To confirm the interpretation of the contrastt formation, and to look further into the experimental results, we solved the Laplace equation of the system probe/nanocluster/dielectric layer using a 2D finite element code [11]. A schematic of the simulated geometry is reported in Fig 4. The probe is modelled as a cone with a semispherical end. The cone angle (20°) and the radius of curvature of the semispherical end, R=20 nm, are the typical values for the commercial probes used in the measurements. The distance between the probe apex and the oxide surface is fixed at 30 nm. In Fig. 5 the z component of the electric field along the probe edge l, calculated in the case of bare oxide (open circles) and in the presence of a nanocluster (r=10 nm) underneath the probe (black squares) is reported. The electric field is virtually constant along the conical edge of the probe, and the field variation induced by the nanostructure only concerns the area around probe apex. The capability of imaging single nanocrystals is then explained by the extreme localisation of the interaction that is restricted to the probe end. By changing the position of the nanocluster along the x-axis, the electric field distribution during the scanning of the probe over the oxide surface can be simulated. Starting from the calculated electric field distribution, the electrostatic force exerted on the probe can be derived by evaluating:

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Fz =

³ S

σ2 dS Sn ⋅ uˆ z 2ε 0

(4)

where σ=ε0Ε is the local charge density just outside the metallic probe surface and n is the unitary vector normal to this surface; the integral is calculated on the probe surface area S [12]. Results are reported in Fig. 6. As expected, the magnitude of the force increases as the probe is scanned over the nanocrystal. However, the diameter of the nanocrystal appears enlarged by the probe radius of curvature R. This indicates that two nanocrystals can be distinguished if a distance of at least 2R separates them. Considerations concerning the size and position of the nanocrystals inside the oxide are reported elsewhere [10] -11

-4,0x10

0,0

-11

total force (N) on the probe

-4,2x10 7

-2,0x10

7

-4,0x10

7

-6,0x10

7

-8,0x10

-11

-4,4x10

-11

-4,6x10

-11

-4,8x10

-11

-5,0x10

-11

-5,2x10

-11

-5,4x10 0,0

-8

1,0x10

2,0x10

-8

3,0x10

-8

-8

4,0x10

l (m)

Figure 5. Calculated z-component of the electric field distribution along the probe edge l for bare oxide (open circles) and in presence of a nanocrystal (black squares); ll=0 is the probe apex

-250 -200 -150 -100 -50

0

50

100 150 200 250

scan distance (nm)

Figure 6. Calculated electrostatic force exerted on the probe while scanning over a portion of the oxide layer containing a metallic nanoclusters.

4. Conclusions The variation of the capacitance between probe and sample due to the presence of isolated metallic particles into the oxide, has been exploited to image Sn nanocluster embedded in a silicon oxide films. The results obtained compare well with TEM images acquired on the same sample. A proper interpretation of the contrast mechanism requires an accurate modelling of the electrostatic problem, which in this work was obtained using 2D finite element analysis. The electrostatic interaction is extremely localised between the probe end and the sample, thus allowing imaging of the single nanocluster. However, the radius of curvature R of the probe end limits the lateral resolution of the technique, so that two nanoclusters can be distinguished only if they are separated by at least 2R.

Acknowledgments The authors would like to thank Giuseppe Pavia of STMicroelectronics (Agrate, Italy) for his help in TEM analyses. The Sn ion implantation was performed at the Institute of Ion Beam Physics and Materials Research of the Research Center Rossendorf, Dresden

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(Germany) in the framework of the Large Scale Facility (LSF) project funded by the European Community. We also thank Dr. Bernd Schmidt for his help in sample preparation and Dr. Arnt Mücklich for TEM analyses.

References 1.

Nonnemacher, M., O’Boyle, M.P., and Wickramasinghe, H.K. (1991) Kelvin probe force microscopy, Appl. Phys. Lett. 58, 2921-2923. 2. Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics, HRW International Editions, Philadephia. 3. Abraham, D.W., Williams, C., Slinkman J., and Wickramasinghe, H.K (1991) Lateral dopant profiling in semiconductors by forcing microscopy using capacitive detection, J. Vac. Sci. Technol. B 9, 703-706. 4. Kobayashi, K., Yamada, H., and Matsushige, K. (2002) Dopant profiling on semiconducting sample by scanning capacitance force microscopy, Appl. Phys Lett. 81, 2629-2631. 5. Spiga, S., Ferrari, S., Fanciulli, M., Schmidt, B., Heinig, K.-H., Grötzschel, R., Mücklich, A., and Pavia, G. (2001) Kinetics of ion beam synthesis of Sn and Sb cluster in SiO2 layers, Mat. Res. Soc. Symp. Proc. 647, O11.23.1-6. 6. Spiga, S., Fanciulli, M., Ferretti, N., Boscherini, F., D’Acapito, F., Ciatto, G., and Schmidt, B. (2003) Formation and structure of Sn and Sb nanoclusters in thin SiO2 films, Nuclear Instr. Meth. B 200, 171177. 7. Spiga, S., Mantovan, R., Fanciulli, M., Ferretti, N., Boscherini, F., D'Acapito, F., Schmidt, B., and Grötzschel, R. (2003) Local structure of Sn implanted in SiO2 films, Phys. Rev. B 68, 205419-1-20. 8. Vatel, O.and Tanimoto, M. (1995), Kelvin probe force microscopy for potential distribution measurement of semiconductor devices, J. Appl. Phys. 77, 2358-2362. 9. Efimov, A., Cohen, S., and Vac, J. (2000) Simulation and correction of geometric distortions in scanning Kelvin probe microscopy, J. Vac. Sci. Technol. A 18, 1051-1055. 10. Tallarida, G., Spiga, S., and Fanciulli, M., (2003) Characterisation of nanocrystals by scanning capacitance force microscopy, Mat. Res. Soc. Symp. Proc.. 738, 171-176. 11. Field Precision – EStat 5.0 12. Hudlet, S., Saint Jean, M., and Guthmann, C., Berger, J. (1998) Evaluation of the capacitive force between an atomic force microscopy tip and a metallic surface, Eur. Phys .J. J B 2, 5-10.

ELECTRICAL CHARACTERISATION OF III-V BURIED HETEROSTRUCTURE LASERS BY SCANNING CAPACITANCE MICROSCOPY

O. DOUHERET(*), K. MAKNYS and S. ANAND Laboratory of Materials and Semiconductor Physics,, Royal Institute of Technology (KTH); Department of Microelectronics & Information Technology Electrum 229 S-164 40 KISTA, SWEDEN (*) Corresponding author: [email protected]

Abstract In this work, cross-sectional scanning capacitance microscopy (SCM) is used to investigate GaAs/AlGaAs buried heterostructure (BH) lasers regrown with semiinsulating GaInP:Fe. The basic principles involved in the SCM methodology are first introduced, including resolution. The conceptt of doping contrast in SCM is experimentally demonstrated using InP doping staircase structure where in the doping in the different layers covers a reasonably wide dynamic range [~1018cm-3 to ~1016cm-3]. The capability of SCM to achieve complete electrical characterization of complex optoelectronic devices is then established using BH GaAs based lasers as an example. It is shown that a complete 2D map of the electrical properties of device structure, including delineation of regrown interfaces and the electrical nature of the regrown GaInP layer can be obtained. Characteristic peaks in the SCM signal (dC/dV) are seen at the interface between the regrown layers and the n-doped regions and attributed to bandbending at the interface. The behavior of the SCM signal with ac-bias is used to verify the semi-insulating nature of the regrown layer at different locations of the sample. The measured SCM signal for the regrown GaInP:Fe layer is uniformly zero indicating very low free carrier densities and confirms semi-insulating properties. This observation strongly suggests, in addition, uniform Fe incorporation in the regrown layers, close to and far away from the mesa. Finally, a nanoscale feature in the SCM contrast appearing as a bright spot in dC/dV mode is observed at the mesa sidewall close to the interface between the regrown GaInP:Fe and the p-barrier layer. The origin of this contrast is discussed in terms of local band-bending effects and supported by 2D Poisson simulations of the device structure. 413 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 413-424. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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1. Introduction The continuing shrinkage of semiconductor devices towards sub-micron features, increased complexity and functionality has prompted a strong need for adequate high resolution characterization tools. Mapping the relevant properties of devices in at least two dimensions with high lateral resolution and sensitivity is essential for successful development of semiconductor device technology1,2. The above needs have resulted in a rapid development of scanning probe based techniques, thus incorporating high lateral resolution1,2. One such method, scanning capacitance microscopy (SCM) has emerged as a promising tool for high resolution mapping of the electrical properties3. The technique combines a highly sensitive capacitance sensor with the lateral (geometric) resolution typical of the probe tips used in atomic force microscopy (AFM). Capabilities of SCM such as sensitivity to doping variations, high resolution p-n junction delineation etc, have been first demonstrated on Si-based devices4,5,6. More recently, the SCM technique has been extended to the study of other material systems/structures such as InP and related materials7, GaInP8, GaN9 and SiC10,11. The utility of the method for characterisation of selective area epitaxy which is a critical issue in the fabrication of advanced III-V optoelectronic devices such as buried heterostructure (BH) lasers is well recognized7. Complex issues such as orientation dependent dopant incorporation during regrowth on patterned substrates12, delineation of regrown interfaces7,13 and Zn-Fe interdiffusion7 have been investigated. Clearly, SCM has emerged as a very promising tool for III-V device and process characterization. However, quantitative doping profiling in III-Vs is rather difficult owing to high density of surface states and requires significant effort in improving surface oxide quality. Nevertheless, by using internal doping reference layers that are often present in most epitaxially grown III-V device structures, it has been possible to make quantitative estimates of doping7. Increasingly other techniques, notably Scanning Spreading Resistance Microscopy (SSRM)14, and Tunneling AFM15, have been used to study InP based devices. Although GaAs and related materials and devices are a very important issue in modern III-V technology, in the SCM context it has received much less attention. In buried heterostructure lasers, selective regrowth around laser mesas with high band-gap semi-insulating single-crystalline material is desirable for improved optical and carrier confinement as well as low capacitance and integration feasibility16,17. In GaAs/AlGaAs based lasers, Fe doped Ga0.51In0.49P which is lattice matched to GaAs appears to be an appropriate candidate for this purpose owing to its higher bandgap (1.9eV), lower refractive index (compared to GaAs and AlxGa1-xAs (x<0.38)) and high resistivity (ȡ»1012 ȍcm)18. Moreover it does not contain Al, thus avoiding problems related to oxidation. However, incorporation of Fe and hence the local electrical properties of the regrown material can be strongly affected by orientation dependent growth typical in fabrication on patterned substrates. Besides, due to the dependence of growth on crystal orientation, growth on non-planar substrates can induce modifications in morphology and dopant incorporation. Quality of the regrown interfaces is an important issue that can drastically affect the device performance. Thus successful device development requires characterization methods capable of mapping the local electrical properties. SCM is therefore an appropriate technique to characterize such structures due to its inherent sensitivity to doping variations and its capability to image p-n junctions and

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interfaces. Furthermore, it can be used to estimate the degree of the current confinement in the mesa by investigation of the electrical properties of the regrown material around the mesa. In this article, first we outline the SCM methodology. We illustrate using InP doping staircase structure the SCM contrast due to doping. This is followed by our SCM investigations of GaAs-based BH lasers. The cross-sections of the devices studied were prepared by cleaving. The native oxide that is formed due to exposure to air serves as a thin insulator between the metal-coated tip and the sample. Contrast mechanisms, doping, and the behaviour of the SCM signal att the p-n junction depletion region and at regrown interfaces are first discussed. Ac bias dependence of the SCM signal (dC/dV) at different regions of the sample is shown to provide information that enables verification of the semi-insulating properties of the regrown layer close to and far away from the mesa. Finally, a special type of contrast at the mesa sidewall close to the interface between the regrown GaInP:Fe and the p-cladding layer is investigated. Its origin is attributed to local band-bending and is supported by 2D Poisson simulations of the device structure obtained using Laser Technology Integrated program (LASTIP).

2. The SCM Methodology Contact mode AFM

TOPOGRAPHY DATA Conductive probe

Optical detection

Capacitance Measurement Electronics

Sample

X-Y stage

Bias sample

CAPACITANCE DATA

Feed-back bias mode •dC held constant and the feed-back ac bias is recorded •In general complementary to dC/dV mode

dC/dV mode •dC recorded for fixed ac-bias •higher signal for lower doping and/or thin oxide

Figure 1. Schematic sketch of the SCM system showing the measurement configuration

In the present work, the SCM measurements were performed using Digital Instrument’s Nanoscope Dim 3000 microscope provided with capacitance measurement electronics. The microscope is operated in contact mode AFM wherein the cantilever movement is detected optically and this information is used to maintain the tip-sample separation constant (shown schematically in Fig. 1). Simultaneously, as the tip raster scans the

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sample surface, the capacitance information is obtained by a resonant capacitance sensor that operates at 915 MHz. Small changes in tip-sample capacitance cause large changes in the amplitude of the resonator. The sample can be biased by separately controlled ac (Vac) and dc (Vdc) biases. The tip-sample capacitance is modulated by y low frequency ac (5-100 kHz) biases and lockin detection is used to measure the differential capacitance (dC/dV). The tips that normally have been used include etched tungsten tips, metal-coated etched Si (as in present work; Ir5Pt coating) or metal coated silicon-nitride tips. The tip and the sample form a MIS-like structure, the insulator usually being an oxide. Choice of the dc bias on the tip (= - Vdc) selects the point on the C-V curve (Vop) about which the differential capacitance is measured (Fig. 2a). The tip-sample ac bias voltage can be varied from about 100 mV up to several volts. Under normal imaging conditions, for most samples, 1V ac bias is sufficient for an acceptable signal to noise ratio.

(a) Capacitance

Depletion

Accumulation

∆C1

1

∆C2

Higher doped region

Vop≈ VFB

2 Lower doped region

Bias (V)

b

1016

back contact

3.1016 1017 2.1017 8.10 017 10188 4.1018

-3

a

-3

1E18

1E19

8000

1E18

6000

4000 1E17 2000

0 0

1000

2000

3000

n (converted SCM), cm

a

10000

n (ECV data), cm

(b) native oxide

dC/dV (averaged 2D exp data), arb. units

Vac

4000

Distance, nm

Figure 2. (a) Schematic illustration of the essential principle involved in obtaining doping contrast in the SCM method. The C-V curves are forr an n-type MIS capacitor for higherr and lower doped regions of the sample, and the bias shown on the axis is the bias on the tip relative to the sample (b) Experimentally obtained SCM contrast for a doping staircase structure in InP (1). Vop is chosen to be close to VFB for the lowest doped region. SCM dC/dV data are subsequently converted to doping (2) using a conversion curve that utilizes two doping levels as reference values which are provided by electro-chemical capacitance voltage (ECV) profiling. The ECV data is shown in the inset.

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In accordance with the high frequency MIS capacitance-voltage relationship for an n-type sample (schematically shown in Fig. 2a), for a given ac-bias amplitude, the measured dC will be larger for lower doping (curve 2) and smaller for higher doping (curve 1). Thus, in the dC/dV image low and high doped regions in the sample will appear as bright and dark, respectively, and the signal magnitude is related to the doping levels. This “doping contrast” is illustrated further in Fig. 2b using experimental data obtained on n-InP staircase structure t as an example. The layers were grown on a highly n-doped InP substrate and decreasingly doped from 1018cm-3 to ~1016 cm-3. The monotonic increase of the dC/dV signal as the probe scans from the substrate a to the surface b is shown in Fig. 2b (curve 1). For lower doping levels (below 1017cm-3), although the steps are visible, the lateral resolution degrades. This is due to increased depletion volume for lower doped regions. The experimental data are shown in arbitrary units and simulations are necessary to extract quantitative doping information. Although simulations of SCM data are rather complicated, it has received considerable attention3. In some cases, if the sample has at least two regions with known doping values, it is possible to generate an empirical fitting formula that can be used (by interpolation) to obtain doping values in between these reference levels. This simple conversion procedure may not be applicable for situations wherein the concentrations change abruptly. Here we follow this approach to fit the SCM data. The two reference values are obtained from Electrochemical Capacitance Voltage (ECV) profiling of the sample (separately). The ECV data is shown in the inset of Fig. 2b. We comment that as opposed to a SIMS measurement, ECV data provides the active dopant concentration and is directly relevant to the SCM measurements. The converted dC/dV curve (curve 2 on Fig. 2b) is consistent with the ECV profile with very good agreement on the doping levels. Typically the measured dC/dV signal varies over two orders of magnitude in this doping range, indicating sufficient sensitivity. It is important to point out that the measured dC/dV signal depends on the experimental conditions such as effective tip diameter, oxide thickness, humidityy and biasing conditions. Therefore, such a conversion curve must be generated for individual measurement runs. A different contrast mechanism can be also be visualized: for the same doping, variations in the oxide thickness on the sample appear as dark (thicker oxide region) and bright (thinner oxide region). As to the lateral resolution, it involves several aspects as described above. Nevertheless, the bestt obtainable resolution is fundamentally limited by the Debye length. Improved lateral resolution can be obtained by performing microscopy on the tip side, that is byy using an appropriatly doped semiconducting tip, significant part of the signal can be restricted to the tip19. However, the analysis and interpretation become very complex20. The method outlined above wherein the differential capacitance is recorded for a given tip-sample ac-modulation bias is usually referred to as the dC/dV mode or simply dC-mode. An alternative mode is the feed-back bias mode or simply dV-mode. In this method, δC is chosen and variable ac-bias is applied to maintain δC constant (constant depletion width) as the tip scans the sample. The image generated is complementary to that in the dC-mode. One advantage with this method is that it directly relates to the doping levels. Since the C-V dependence on bias is opposite for an n and p type semiconductor, in SCM applications involving p-n junction profiling, it is generally desirable to retain the sign information of dC/dV. Here, while scanning across the

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junction, the dC/dV goes through zero which approximately locates the position of the electrical p-n junction. However, in some commercial versions of the instrument, such as the one used in this work, only the absolute value of dC/dV is recorded (which incidentally is the appropriate input in the feed-back bias mode). In this case, a minimum in |dC/dV| is obtained for the junction depletion region. We comment that in some circumstances locating the p-n junction with respect to some reference layer, region or topographical feature can provide additional information. In the case of samples composed of different materials, topographical contrastt can be induced, for instance, by different native oxide thickness. In real situations, interpretation and analysis of SCM data is more complex. One factor that affects the data is the oxide charge (e.g. fixed charges) resulting in flat-band voltage (VFB) shifts in the tip-sample MIS capacitor21. The experimental approach towards this has been to compensate for the shift by suitably DC-biasing the sample. This is done by locating Vdc for which the measured dC/dV is a maximum. This Vdc is closely related to VFB. For similar doping type, say n-type, y this is done for the lowest doped region of the sample as illustrated in Fig. 2a. If this is not performed, the SCM data can be in serious error, sometimes resulting in contrast reversal. Very large values of Vdc can result in other effects, such as charge injection and trapping, causing hysteresis, and in some circumstances additional oxidation due to water content in ambient air6. Significant effort is being devoted to studing the oxide quality in the SCM context and on oxide-formation methods6. However, these issues are also material dependent. As shown here (Fig. 2b), for cleaved n-InP (with only the native oxide) a monotonic behaviour of the SCM data with doping (from 1016 to 1018 cm-3) is obtained for Vdc values very close to zero. On the other hand, for similar biases, the SCM data on air-exposed (native oxide) Si invariably show non-monotonic dependence on doping21, the problem being most severe for doping levels below 1 × 1016cm-3. For as cleaved and air exposed GaAs, our research shows that the SCM contrast is qualitatively consistent with doping for doping level > 1 × 1017cm-3. In devices investigated here doping levels (in GaAs) are larger 1 × 1017cm-3. 3. GaAs/AlGaAs BH Lasers with SI GaInP:Fe Figure 3a shows a schematic cross-sectional view of the investigated samples including the essential layers. Fabrication details concerning the structure are available elsewhere18. The basic laser structure was grown byy metal organic vapor phase epitaxy (MOVPE) and regrowth of GaInP was performed using hydride vapor phase epitaxy (HVPE). Prior to regrowth, mesa stripes along the [110] direction were made by wet chemical etching. The mesas are typically 5 µm high and 5 µm wide. Using siliconnitride as a mask, the etched mesas were selectively regrown first with semi-insulating (SI) GaInP:Fe (4 × 1017cm-3) and finally in some samples with a n-GaInP (1 × 1018cm-3) layer. P-type contacts are provided after removing the silicon-nitride mask. 2D-poisson simulation of the structure at equilibrium was performed using LASTIP and the details are reported elsewhere22. A typical SCM (dC/dV) image of the laser structure is shown on Fig. 3b. P- and ndoped claddings appear bright (~1018 cm-3), while the depleted active region in between

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is dark due to a mixed p- and n-like response (a minimum in dC/dV signal). Since only the absolute value of the SCM signal could be recorded, the p and n type behavior are not distinguished. The lower doped buffer layer below the n-cladding appears brighter. The contrast in SI-GaInP:Fe regions is dark (zero-SCM signal) due to very low free carrier densities (intrinsic levels). Variation of the SCM signal as obtained from line scan approximately along the directions indicated on Fig. 3b is shown on Fig. 3c. The line scan includes the main layers of the mesa namely the low doped buffer, the n- and the p- claddings sandwiching the active region, and the p+ doped layer at the top of the structure. 1D Poisson simulation is also shown on Fig. 3c and confirms spatial location of the depletion region. The simulated doping profile is qualitatively consistent with the dC/dV contrast. (b) (a) p –GaAs

AlGaAs undoped d

GaInP n-doped

p –AlGaAs Cladding

Depleted region

Regrown SI GaInP:Fe

Active layer AlGaAss

n –AlGaAs Cladding n- -AlGaAs

n+ -GaAs substrate

0,8

n

-3

p

1E17 0,6

1

1E16

0,4 1E15 0,2

dC/dV (arb. units)

Carrier Concentration (cm )

Depletion region

(c)

1E18

1E14

2

0,0

1E13 0

1

2

3

4

5

Distance (µm)

Figure 3. (a) Schematic cross-section of the GaAs/AlGaAs laser mesa buried in GaInP:Fe. The active region (barriers and well) and the claddings are made up of AlxGa1-xAs but with different Al composition (x=0.59 in the cladding, x=0.351 in the barriers and x=0.065 in the quantum well). The n- and p-type doping were obtained with Se and Zn, respectively. Also shown is the n-doped GaInP regrown layer (side arms). In some samples this layer was not provided. (b) Cross sectional SCM (dC/dV) image of the GaAs/AlGaAs laser mesa with SI GaInP:Fe (4 × 1017cm-3) regrown layers. The dc and ac biases were respectively 0V and 1V and ac bias frequency was 55kHz. Topographical variations are within a few nm. (c) SCM line scan across the GaAs/AlGaAs mesa structure (approximately) along line from 1 to 2 indicated on (b). Doping profile across the mesa extracted from 1D Poisson simulation. Electron and hole concentrations are shown and the n-type and p-type regions are indicated.

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A SCM (dC/dV) image of the laser structure showing the different interfaces involving the regrown layer and the buffer/substrate, the n- and the p- cladding layers, respectively is presented in Fig. 4a. The n-doped GaInP arm above the GaInP:Fe layer is clearly visible with a characteristic bright contour. The bright line is due to the presence of band-bending at the interface between the n-doped and Fe-doped GaInP layers7. The shape of this contour confirms effective planarization in the structure. In general, mapping such contours serves as a guideline for qualifying planarization properties of regrowth methods13. Poisson simulations confirm the existence of a space charge region (bandbending) at the interfaces between the semi-insulating/n- or p-doped layers. The dC/dV signature at these regions leads to characteristic contrast peaks due to decreasing carrier concentration7. Not only is experimentally observed the predicted contrast peak at the interface, but it is also observed in a comparable width range (300-400nm according to Poisson simulation). Interestingly, the observed contrast is uniformly zero in the regrown layer. This clearly indicates uniform electrical properties i.e. sufficient amount of Fe incorporation in the regrown GaInP:Fe layer. The bright band running out from the bottom of the mesa is too wide (about 800 nm) to be the interfacial signature expected between the n+ substrate and the SI-region which is expected to be typically 200-300 nm. This is expected since the buffer layer has not been completely removed during the mesa-etching step. Variation of the SCM signal as obtained from a line scan approximately along the direction indicated in Fig. 4a is shown in Fig. 4b. The line scan shows the interface involving the regrown layer and the buffer/substrate. t As discussed earlier, the contrast peak in Fig. 1(c) corresponds to the interface region between the SI-GaInP, the remaining buffer layer and the substrate. The behavior of the SCM signal at the interfaces and in the semi-insulating regions was investigated further by varying the ac bias. The dC/dV signal is obtained by using a low frequency ac-modulation of the depletion region of the tip-sample capacitance. Proportional increase of the dC/dV signal is expected with the ac bias6 in the doped regions. On the other hand, in the GaInP:Fe regions with sufficient density of deep acceptors (Fe), the dC/dV signal should be zero, irrespective of the applied ac biases, due to the very low free carrier densities (intrinsic levels). The ac bias was varied in the 0.5V- 2V range in steps of 0.5V and the results are compiled in Fig. 4b. Consistent behavior is seen in the n-, p-doped regions as well as at the interfaces: dC/dV signal increases proportionally with ac bias. In striking contrast, in the SI-GaInP regions (indicated by arrow on Fig. 4b) the dC/dV signal does not vary with ac-bias and remains close to zero. Significantly, this behavior is found in the SI-GaInP regions not only far away from the mesa (>5µm) but also close to it (<1µm). Thus, the SCM measurements confirm semi-insulating properties of the regrown layer, both far away from and close to the mesa. Moreover, the absence of contrast variations in the regrown layer suggests uniform incorporation of Fe, consistent with previously reported photo-luminescence decay measurements on similar samples23. As noted earlier we comment here that although the semi-insulating property of the regrown layer can be verified, it is not possible to “directly” ascertain the active Fe concentration by SCM measurements.

GaInP:Fe

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(b)

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Figure 4. (a) Cross sectional SCM (dC/dV) image of the GaAs/AlGaAs laser mesa with SI GaInP:Fe (4 × 1017cm-3) regrown layers. The experimental parameters are similar to Fig. 3. Bright spot at the top of the image between the mesa and the n-doped GaInP arm is due to topography damage at the cleaved edge. Elsewhere, topography variations are within few nm. (b) ac bias dependence of the SCM signal (approximately) along the (dash) line indicated on the image shown on (a) along 1 to 2. The ac bias was varied from 0.5 V to 2V in steps of 0.5 V; the dc bias and the ac bias frequency were 0V and 55kHz, respectively. The arrow indicates the semi-insulating region.

Below we discuss a special feature in the SCM contrast that is seen at the interface between AlGaAs p-cladding and SI-GaInP regrown layers and close to the pn-junction depletion region (circled in Fig. 3b and 4a). This feature appears as a bright spot in dC/dV mode with a spatial extent of about 200 nm (Fig. 5a). This feature appears on both sides of the mesa and is consistently observed in several samples. It is clear as seen on Fig. 5b that there is no damage or void at that region as shown by the simultaneously acquired topography data. Therefore, this contrast feature can be attributed to local band-bending in the structure. This hypothesis is supported by 2D Poisson simulation of the structure17. The variation of the conduction band edge in the structure along different directions (including relevant interfaces) as obtained from the 2D Poisson simulations is shown on Fig. 5c. In the vicinity of the active region (p-n junction depletion region) the band-bending changes sign. The location where this local band-bending occurs is in the vicinity of the observed spot (Fig. 5a). These observations argue that local band-bending present in the structure and the observed contrastt spot are correlated. We recognize that the presence or absence of this contrast spot and its location may depend on the exact band-offsets at the various hetero-interfaces and the electrical properties of the layers in the mesa and the regrown layer. A complete description of this aspect requires detailed analysis of test structures with different regrown layers and is currently under investigation.

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(a) (b)

SI regrown layer p-cladding

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AlGaAs p-cladding AlGaAs p-side barrier

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Distance (µm) Figure 5. (a) Cross sectional SCM (dC/dV mode) image showing the contrast spot at the interface between the AlGaAs active region and the SI GaInP:Fe (4 × 1017cm-3). The DC bias was respectively 0V. (b) Simultaneously recorded AFM image. Topography variations are less than 2nm in the vicinity of the mesa and shows no special topography feature near the spot. (c) Conduction band profile across the mesa and along relevant regions of the sample. These data were extracted from the 2D Poisson simulation. The Fermi level in the GaInP:Fe is pinned close to the Fe acceptor level (Ec-E= 1.14eV).

4. Conclusion In summary, cross-sectional scanning capacitance microscopy (SCM) was used to investigate GaAs/AlGaAs laser mesas selectively regrown with GaInP:Fe by HVPE. Specifically, the relevance of SCM analysis in the context of these structures was established. The basic principles involved in SCM methodology including resolution were addressed. Aspects pertaining to the behavior of the SCM signal in various device specific contexts were elaborated. From the investigations presented here, it is clear that the SCM technique can be a very powerful tool for III-V materials and devices. It was shown that a complete 2D map of the electrical t properties of device structure including delineation of regrown interfaces and the electrical nature of the regrown GaInP layer

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can be obtained. A characteristic peak in the SCM signal (dC/dV) seen at the interface between the regrown layers and the n-doped regions was attributed to band-bending at the interface. The behavior of the SCM signal with ac-bias was used to confirm the semi-insulating nature of the regrown layer at different locations of the sample. The results strongly suggest uniform Fe incorporation in the regrown layers, close to and far away from the mesa. A special nanoscale feature in the SCM contrast was observed at the mesa sidewall close to the interface between the regrown GaInP:Fe and the pcladding layer. The origin of this contrast was attributed to local band-bending in the structure and supported by 2D Poisson simulations of the device structure. Acknowledgements The authors thank S. Lourdudoss and C. A. Barrios for the laser structures. The work was supported by the Swedish strategic research Foundation and the EU-RTN project HERCULAS.

References 1. 2. 3. 4.

5. 6.

7. 8.

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Dagata, J.A. and Kopanski, J.J. (1995) Scanning probe techniques for the electrical characterization of semiconductor devices, Solid State Technol. 38-7, 91-95. Vandervorst, W., Clarysse, T., De Wolf, P., Trenkler, T., Hantschel, T., and Stephenson R. (1997) Dopant/carrier profiling for ULSI. Future Fab. Int. 1-4, 287. Williams, C. C. (1999) Two-dimensional dopant profiling by scanning capacitance microscopy, Annu. Rev. Mater. Sci. 29, 471-504. Edwards, H., Ukraintsev, V.A., San Martin, R., Johnson, F.S., Menz, P., Walsh, S., Ashburn, S., Wills, K.S., Harvey, K., and Chang, M-C (1999) Pn-junction delineation in Si devices using scanning capacitance spectroscopy, J. Appl. Phys. 87 (3), 1485-1495. Kopanski, J.J., Marchiando J.F., and Lowney J. R. (1995) Scanning capacitance microscopy measurements and modelling: Progress towards dopant profiling, J. Vac. Sci. Technol. B 14 (1), 242-247. Zavyalov, V.V., McMurray, J.S., and Williams C. C. (1999) Advances in experimental technique for quantitative two-dimensional dopant profiling by scanning capacitance microscopy, Rev. Sci. Instrum. 70 (1), 158-164. Anand, S. (2000) Anotherr dimension in device characterization: Scanning capacitance microscopy of InPlasers structures, IEEE Circuits and Devices 16, 12-18. Leong, J-K., Williams, C.C., Olson, J.M., and Froyen S. (1996) Evidence for internal electric fields in two variant ordered GaInP obtained by scanning capacitance microscopy, Appl. Phys. Lett. 69 (26), 40814083. Smith, K.V., Yu, E.T., Redwing, J.M., and Boutros, K.S. (1999) Scanning capacitance microscopy of AlGaN/GaN heterostructure field-effect transistor epitaxial layer structures, Appl. Phys. Lett. 75 (15), 2250-2252. Bowallius, O., Anand, S., Nordell, N., Landgren, G., and Karlsson, S. (2001) Scannning capacitance microsopy investigations of SiC structures, Mat. Sci. in Semic. Proc. 4, 209-211. Giannazzo, F., Calcagno, L., Raineri, V., Ciampolini, L., Ciappa, M., and Napolitani, E. (2001) Quantitative carrier profiling in ion-implanted 6H–SiC, Appl. Phys. Lett. 79 (8), 1211-1213. Hammar, M., Rodríguez Messmer, E., Luzuy, M., Anand, S., Lourdudoss, S., and Landgren, G. (1998) Topography dependent doping distribution in selectively regrown InP studied by scanning capacitance microscopy, Appl. Phys. Lett. 72 (7), 815-817. Bowallius, O., Anand, S., Hammar, M., Nilsson, S., and Landgren, G. (1999) Scanning capacitance microscopy investigations on buried heterostructure laser structures, Appl. Surf. Sci. 144-145, 137-140. De Wolf, P., Geva, M., Reynolds, C.L., Hantschel, T., Vandervorst, W., and Bylsma, R.B. (1999) Twodimensional carrier profiling of InP-based structures r using scanning spreading resistance microscopy, J. Vac. Sci. Technol. A 17 (4), 1285-1288.

424 15. Richter, S., Geva, M., Garno, J.P., and Kleiman, R.N. (2000) Metal–insulator–semiconductor tunneling microscope: two-dimensional dopant profiling of semiconductors with conducting atomic-force microscopy, Appl. Phys. Lett. 77 (3), 456-458. 16. Hong, C-S., Kasemset, D., Kim, M-E., and Milano, R.A. (1983) GaAlAs buried-heterostructure lasers grown by a two-step MOCVD process, Electron. Lett. 19, 759-760. 17. Dutta, N.K., Zilko, J.K., Cella, T., Ackerman, D.A., Shen, T.M., and Napholtz, S.G. (1986) InGaAsP laser with semi-insulating current confining layers, Appl. Phys. Lett. 48 (23), 1572-1573. 18. Angulo Barrios, C., Rodríguez Messmer, E., Holmgren, M., and Lourdudoss, S. (2000) GaAs/AlGaAs buried heterostructure laser by wet etching and semi-insulating GaInP:Fe regrowth, Electrochem. and Solid-State Lett. 3 (9), 439-441. 19. Gotto, K. and Hane, K. (1998) Application of a semiconductor tip to capacitance microscopy, Appl. Phys. Lett. 73 (4), 544-546. 20. O’Malley, M.L., Timp, G.L., Timp, W., Moccio, S.V., Garno, J.P., and Kleiman, R.N. (1999) Electrical simulation of scanning capacitance microscopy imaging of the pn junction with semiconductor probe tips, Appl. Phys. Lett. 74 (24), 3672-3674. 21. Bowallius, O. and Anand, S. (2001) Evaluation of different oxidation methods for silicon for scanning capacitance microscopy, Mat. Sci. Sem. Proc. 4, 81-84. 22. Angulo Barrios, C., Lourdudoss, S., and Martinsson, H. (2002) Analysis of leakage current in GaAs/AlGaAs buried-heterostructure lasers with a semi-insulating GaInP:Fe burying layer, J. Appl. Phys. 92 (5), 2506-2517. 23. Gaarder, A., Marcinkevicius, S., Angulo Barrios, C., and Lourdudoss, S. (2002) Time-resolved microphotoluminescence studies of deep level distribution in selectively regrown GaInP:Fe and GaAs:Fe, Semiconductor Science and Technology 17, 129-134.

PROBING THE DENSITY OF STATES OF HIGH TEMPERATURE SUPERCONDUCTORS WITH POINT CONTACT TUNNELING SPECTROSCOPY

L. OZYUZER1, J.F. ZASADZINSKI2, N. MIYAKAWA3, K.E. GRAY4 Department of Physics, Izmir Institute of Technology, Urla, TR-35430 Izmir, Turkey E-mail: [email protected] 2 Physics Division, Illinois Institute of Technology, Illinois, USA 3 Tokyo University of Science, Suwa, Japan 4 Materials Science Division, Argonne National Laboratory,Illinois, USA

1

Abstract Tunneling spectroscopy measurements are performed on single crystals of single CuO2 layer Tl2Ba2CuO6+į, double CuO2 layer Bi2Sr2CaCu2O8+į (Bi2212) and polycrystal quadruple CuO2 layer CuBa2Ca3Cu4O12+į using the point contactt tunneling technique. IV and dI/dV-V characteristics are obtained att 4.2 K. In spite of different number of layers and Tc values, all three high-Tc superconductors exhibit similar spectral features including dip and hump features reminiscentt of strong-coupling effects in conventional superconductors. The doping dependence of Bi2212 is studied and several effects of the hole concentration on spectral features are found. A novel effect is that the energy gap increases in the underdoped region even as Tc decreases. Combining the doping dependence of the energy gap and the dip energy provides additional information in order to understand the mechanism of high-Tc superconductivity. Point contact tunneling studies of the doping dependence of the energy gap in Bi2212 also helped to understand local variations of the gap magnitude observed by scanning tunneling microscopy, indicating that this type of spectroscopy t is an integral part of the tunneling technique.

1. Introduction The density of states (DOS) of a material contains valuable information related to key electronic and magnetic properties. The energy y gap and band structure can be extracted from analysis of the density of states data and the result gives a qualitative account of the macroscopic properties of materials including electrical and thermal conductivity, specific heat, and paramagnetic susceptibility. Tunneling spectroscopy is a direct and vital technique for studying density of states near the Fermi level of wide range of materials such as conductors, superconductors, semiconductors, magnetic and organic 425 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 425-434. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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materials [1]. Tunneling studies t can be performed on two distinct junction geometries, permanent and temporary. While thin film tunnel junctions are permanent and mechanically stable, they need extensive effort to produce. On the other hand, the point contact, break tunnel junctions and Scanning Tunneling Microscopy/Spectroscopy (STM/STS) are easy to realize with minimum sample preparation. The reliability of the STM/STS is improving and there is more demand to use it as a surface imaging of materials and identifying local spectroscopic properties in the nanometer scale, which can answer fundamental questions about electronic properties of materials [2]. One of the important contributions of the ttunneling studies is the observation of fine phonon resonance structures in tunneling conductance resulted understanding of pairing mechanism in conventional superconductors [1]. Here we will present our results of point contact tunneling (PCT) spectroscopy on Tl2Ba2CuO6+į (Tl2201), Bi2Sr2CaCu2O8+į (Bi2212), and CuBa2Ca3Cu4O12+į (Cu1234) high temperature superconductors (HTS) which are used to reveal information about the mechanism underlying the high critical temperature. We will also discuss implications of PCT on STM/STS experiments.

2. Experiment Tl2201 has a tetragonal crystal structure with a single CuO2 layer per unit cell, which is relatively simple when compared to the bilayer Bi2212 and quadruple layer Cu1234. Samples of single crystal Tl2201 and Bi2212 were synthesized t using a method as described elsewhere [3, 4]. Both kind of crystals were cleaved parallel to the a-b plane, leaving a flat, shiny surface. Polycrystal Cu1234 samples were prepared by the high temperature and high pressure synthesis technique. Since Bi2212 can be easily overdoped and underdoped to a certain level, the doping dependence of tunneling study has performed only on Bi2212 system. Heavy overdoping has been conducted using stainless steel cells sealed with samples m immersed in liquid oxygen. Moderate overdoped and underdoped samples were obtained by annealing in O2 gas flow and annealing in Ar gas flow respectively. The critical temperature of the samples has been determined from a.c. magnetic susceptibility measurements. Tl2201 single crystals have Tc of 86 K, and Cu1234 has Tc of 117 K. The single crystals of Bi2212 have been prepared in the range of Tc=56 K overdoped to optimally doped Tc=95 K to underdoped Tc=74 K. Tunneling measurements were done with the apparatus [5] cooled by He gas flow to liquid He temperature. The Superconductor-Insulator-Normal metal (SIN) junctions are formed as follows. After the sample placed in measurement system and cooled down to 4.2 K, the contact force between the tip and sample is adjusted using a differential micrometer. We used Au as a tip. While the tip is approached through the crystal, the I-V curve is continuously monitored until an acceptable SIN junction characteristic is obtained. Here the insulating barrier is the native surface layer of the crystal. In some cases, we also obtained Superconductor-Insulator-Superconductor (SIS) break junction characteristics from Bi2212 samples due to weak bonds along the c-axis of this material. Presumably, Au tip cleaves the Bi2212 and creates an in-situ SIS junction at low temperature. After obtaining an acceptable SIN or SIS junction, first I-V characteristic is recorded. Since

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dI/dV reflects DOS of material under investigation, we used usual lock-in technique to obtain dynamic conductance (dI/dV) of the junction. SIN and SIS junctions can be distinguished from their tunneling conductance curves. For example, SIS spectra show symmetric tunneling conductance at positive and negative bias and in some cases Josephson current at zero bias. SIN and SIS junctions display conductance peaks at ±¨ and ±2¨ respectively. In point contact tunneling measurements, the junction resistance is usually below 100 k suggesting a gentle touch of tip on sample a surface oxide layer that is as a tunnel barrier. The origin of barrier is the BiO/SrO layer in Bi2212 but in general, this layer is not well understood. In case of superconductors, the tunneling regime can be easily distinguished from the Andreev reflection regime by specific features in the data. In this work, we will present conductances only from tunneling regime. In our experimental apparatus, we usually produce Andreev reflections for junction resistances below 200 . The other widely used tunneling technique, STM, usually has 100 M or higher junction resistance, thus the vacuum is the main barrier of the tunnel junction, and any contribution from the surface barrier of the sample adds complexity to the junction. The main advantage of the PCT is that the tip is less sensitive to the mechanical vibrations, because the tip touches on the surface of the sample. This leads more stable junctions with clean spectroscopy data. Because, the estimated diameter of PCT contact area is larger than 100 nm, which is around 30 unit cells along the a-b plane of Bi2212, the measured electronic property of the material is the average over the PCT area of the junction. On the other hand, the local DOS mapping of a HTS using a STM/STS is also important to understand effect of local disorder.

3. Results and Discussions Figure 1 shows one of the representative I-V and dI/dV-V measurement of overdoped Bi2212 with Tc=82 K at 4.2 K. This data set is one of the best examples of the spectral features that are unique to high-Tc superconductors. These features are well seen in dI/dV-V and are well known quasiparticle peaks, which correspond energy gap, ±¨, dip and hump structures at the occupied part of the DOS. The discussion aboutt origin of dip and hump structures is deferred to a later part of this paper. Here and hereafter negative bias corresponds to occupied part of density of states. The subgap conductance of the data (dots) exhibits a cusp like behavior that is not flat around the Fermi level. Since conventional superconductors have s-wave pairing (an isotropic energy gap), we tried to fit our data in Fig. 1(b) to ordinary s-wave model (dashed lines) using ¨=27 meV and ī=2 meV, where ī is the lifetime smearing or could be assumed as a thermal energy broadening. The result is acceptable in the vicinity of the quasiparticle peaks, but it is totally different around the Fermi level. Our second attempt to fit the data in Fig. 1(b) is the dd-wave model (¨=¨ocos(2ĳ)) with ¨=28 meV, ī=0.6 meV and Į=0.4 seen as a solid line, because the subgap conductance of our data resembles momentum averaged dx2íy í 2 wave (d-wave) d DOS. The dd-wave fit is pretty good around the energy gap suggesting dwave pairing symmetry. To understand better what the dd-wave model and Į do in our simple model, we plot a section of the 2-dimensional Fermi surface of Bi2212 as an inset of Fig. 1(a) which is obtained from m angle resolved photoemission experiments, and

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four flower leafs are for representation of energy gap magnitude (¨) along the kx, ky momentum space. We include a weighting function f( f ĳ) to our tunneling conductance, f ĳ)=1+Įcos(4ĳ), where Į is a directionality strength. This term suggests that tunneling f( is preferential along the lobes. This junction is representative and the novel pairing symmetry exists for Bi2212 at all doping levels.

Figure 1. (a) I-V characteristics of overdoped Bi2212 (Tc=82 K) SIN junction at 4.2 K. The inset shows Fermi surface of Bi2212. (b) dI/dV-V characteristics of same junction (dots) with s-wave (dashed line) and d-wave d (solid line) fit.

Since all high-Tc superconductors contain CuO2 layers, which are believed to be responsible for superconductivity, a universal pairing symmetry and mechanism might exist. Fig. 2 shows tunneling conductance of three SIN junctions (dots) from single layer Tl2201, bilayer Bi2212 and quadruple layer Cu1234 at 4.2 K. The solid lines are the best dd-wave fits with the parameters given in the figure. In spite of different number of layers and Tcs, all three high-Tc superconductors exhibit similar subgap conductances consistent with gapless density of states, in other words dd-wave pairing symmetry. This is the first important result that our PCT study revealed. Furthermore, Fig. 2 shows that the dip and hump structures exist for all three HTS at low temperatures. Our earlier study on temperature dependence of tunneling conductance revealed that these structures diminish above Tc [6]. If these structures are due to underlying mechanism of superconductivity, Fig. 2 suggests an equally strong pairing mechanism for HTS. We

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would like to note that the dip and hump structures are also observed in STM/STS studies of YBa2Cu3O7íx which is the most studied HTS [7].

Figure 2. dI/dV-V characteristics of single CuO2 layer Tl2201, double CuO2 layer Bi2212 and polycrystal quadruple CuO2 layer Cu1234 with corresponding d d-wave fits (solid lines).

Figure 3 (a) and (b) show the doping dependence of Bi2212 SIN and SIS break junction tunneling spectra at 4.2 K. In the Fig. 3 (a) and (b), each spectrum corresponds to a different crystal with different hole concentration, p, from heavily overdoped Tc=56 K, optimally-doped Tc=95 K, to underdoped Tc=70 K. Each spectrum is normalized by a constant, shifted vertically and Josephson current peak at zero bias of SIS junctions deleted for clarity. This systematic study shows that the energy gap increases with decreasing doping, even as Tc drops from the optimally-doped value 95 K down to 70 K underdoped. The similar result is also obtained by Fishers group [8]. Fig. 3 (c) shows how the measured energy gap magnitude, which is extracted from Fig. 3 (a) and (b), varies with hole concentration in Bi2212. The solid curve is the mean-field gap prediction for dd-wave superconductors, 2.14kTc. The dots are average energy gaps

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obtained on many different junctions and the hole concentrations are estimated from Tc/Tc,max=1-82.6(p ( -0.16)2. There is thus a clear indication that ¨ does not follow Tc which is contrast to what BCS theory predicts. The influence of hole concentration on Tc and energy gap have to be satisfied by any theory that intents to explain HTS mechanism. This is the second important result that our PCT study revealed.

Figure 3. (a) and (b) doping dependence of normalized conductance for SIN and SIS junctions of Bi2212 respectively. (c) Energy gap versus hole concentration found from SIN and SIS junctions of Bi2212 (filled circles).

Recently, the local superconducting DOS is studied using an STM/STS on optimally doped Bi2212 at low temperatures [9]. One of the striking results is that the local tunneling spectrum exhibit a spatially varying energy gap between 25 and 65 meV, which resembles our doping dependence study from different crystals. The averaged energy gap, 42 meV, is very similar to what we obtained from PCT measurements of optimally doped Bi2212 which is an average of a region about 100 nm in diameter. Using STM/STS similar observation is reported by Cren et al. [10] in Bi2212. Since we

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know the doping dependence of energy gap from Fig. 3, comparison of STM/STS and PCT helped to understand local variations of energy gap, which might be due to the local variation of oxygen stoichiometry. In our previous study on Dy-doped underdoped Bi2212, such a wide spread of energy gaps have been observed on the same sample and attributed to the local inhomogenities of the sample. The sample which is used by Pan et al. [9] shows spatial variation in both the local DOS and energy gap as small as 1.4 nm length. We have found that in Dy-doped Bi2212 has larger than 100 nm correlation length that is only due to Dy impurities. A question of whether the measured gap is fully due to superconductivity or has a contribution from some other effects such as spin density wave or charge density wave might arise from the discussion in the previous paragraph. Here PCT method can answer the question because of ability to create SIS junctions. In Fig. 4, Josephson tunneling addresses the origin of measured gap, because the multiplication of the Josephson current, Ic, and junction resistance, Rn, is expected to be proportional to the superconducting gap. The relation between IcRn and ¨ has shown that the measured gap is predominantly due to superconductivity [11]. This is one of the important advantage of SIS tunnel junctions that STM/STS can not accomplish due to high junction resistance which does not allow Cooper pairs to tunnel through the vacuum without dephasing. On the other hand, after establishing that measured spectra are due to superconductivity, STM/STS measurements might use this information to understand the local quasiparticle spectra of DOS. If the Josephson current is sacrificed, STM/STS can still be used to obtain SIS junction between two superconductors. Recently, Dipasupil et al. [12] was able to obtain very large range temperature dependence of SIS tunneling conductance of Bi2212 using piezo feedback. In our PCT system, any temperature variation above 50 K does not allow us to keep the same junction because of thermal expansions of the apparatus.

Figure 4. I-V characteristics of underdoped Bi2212 (Tc=83 K) SIS junction at 4.2 K. The inset shows hysteretic behavior of Josephson current.

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The advantage of SIS junctions is not only observation of Josephson current but also enhancement of fine spectral features which are shifted by ¨. To show that, we plot one of the SIS spectrum of optimally doped Bi2212 with dd-wave fit (dashed line) in Fig. 5. This data is one of the best example thatt how far dip goes to negative conductance in SIS junctions. Since SIS spectra is convolution of two SIN spectra, we convoluted two d-wave DOS to generate the fit. It is very convincing that the pairing is dd-wave in d Bi2212. We also see that the simple dd- wave model does not fit our data at the outside of the 2¨ peaks. This requires a microscopic model.

Figure 5. dI/dV-V characteristics of an optimally doped Bi2212 (Tc=95 K) SIS junction at 4.2 K with d d-wave fit (dashed line).

As we discussed previously, the enhancement of spectral features in SIS is an advantage over SIN junctions. Furthermore, any smearing such as thermal or lifetime are less effective on spectra. In order to understand the relative change of dip energy (eVdip), we plot doping dependence of tunneling conductance versus normalized V for SIS junctions of Bi2212 in Fig. 6. In the figure, normalization of the voltage axis has been done by 2¨ peak voltage, Vp. The location of the dip feature is consistent with the previous observations that the dip location follows the neutron resonance mode energy, which scales with Tc and not the gap energy [13]. For the heavily overdoped samples, the mode energy (res=eVdip-2¨) approaches the 2¨ but never exceeds. This behavior is consistent with the idea of the dip being a kind of resonance state inside the superconducting gap.

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Figure 6. Normalized dI/dV versus normalized V characteristics of Bi2212 for various hole concentrations.

In summary, we used a PCT technique to obtain SIN and SIS junctions in various HTS. The tunneling conductances demonstrated consistently dd-wave pairing symmetry. The influence of hole concentration on energy gap and tunneling conductance are investigated for different level of oxygen doped Bi2212 single crystals. It is found that energy gap is increasing with decreasing hole concentration. SIS break junctions exhibited a robust Josephson current which indicated that the large energy gaps on the underdoped side were still of superconducting origin. This observation is similar to local DOS measurements of STM/STS of optimally doped Bi2212 and results from the PCT method allowed a proper interpretation of the STM/STS results. Furthermore, the dip and hump structures are observed for all measured high-Tc superconductors and the

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enhancement of the dip feature in SIS junctions showed that this feature is linked to the resonance mode found in neutron scattering. These studies t show that complementary tunneling methods can be crucial to the understanding of spectroscopic data obtained by STM/STS.

4. Acknowledgments This research is supported by the U.S. Department of Energy, Basic Energy Sciences— Materials Sciences, under contract number W–31–109–ENG-38 and TUBITAK (Scientific and Technical Research Council of Turkey) project number TBAG-2031. L.O. acknowledges support from Turkish Academy of Sciences, in the framework of the Young Scientist Award Program (LO/TUBAGEBIP/ 2002-1-17). N.M. acknowledges support from Grant-in-Aid for Encouragement of Young Scientists from the Ministry of Education, Science and Culture, Japan.

References 1. 2. 3. 4. 5. 6.

7. 8. 9.

10.

11.

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Wolf, E.L. (1985) Principles of Electron Tunneling Spectroscopy. Oxford Univ. Press, New York. Bonnel, D. A. (1993) Scanning Tunneling Microscopy and Spectroscopy. VCH Publishers, New York. Ozyuzer, L., Zasadzinski, J.F., Kendziora, C., and Gray, K.E. (2000) Quasiparticle and Josephson tunneling of overdoped Bi2Sr2CaCu2O8+į single crystals, Phys. Rev. B 61, 3629–3640. Ozyuzer, L., Yusof, Z., Zasadzinski, J.F., Li, T.-W., Hinks, D.G., and Gray, K.E. (1999) Tunneling spectroscopy of Tl2Ba2CuO6+x, Physica C 320, 9–20. Ozyuzer, L., Zasadzinski, J.F., and Gray, K.E. (1998) Point contact tunneling apparatus with temperature and magnetic field control, Cryogenics 38, 911–915. Ozyuzer, L., Zasadzinski, J.F., Gray, K.E., Kendziora, C., and Miyakawa, N. (2002) Absence of pseudogap in heavily overdoped Bi2Sr2CaCu2O8+į from tunneling spectroscopy of break junctions, Europhysics Letters 58, 589–595. Cren, T., Roditchev, D., Sacks,W., and Klein, J. (2000) Constraints on the quasiparticle density of states in high-Tc superconductors, Europhysics Letters 52, 203-209. Renner, Ch., Revaz, B., Genoud, J.-Y., and Fischer, Ø. (1996) Oxygen doping and temperature dependence of the tunneling spectroscopy on Bi2Sr2CaCu2O8+į, J. Low Temp. Phys. 105, 1083-1089. Pan, S.H., O’Neal, J.P., Badzey, R.L., Chamon, C., Ding, H., Engelbrecht, J.R., Wang, Z., Eisaki, H., Uchida, S., Gupta, A.K., Ng, K.W., Hudson, E.W., Lang, K.M., and Davis, J.C. (2001) Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+į, Nature 413, 282–285. Cren, T., Roditchev, D., Sacks, W., Klein, J., Moussy, J.B., Deville-Cavellin, C., and Lagues M. (2000) Influence of disorder on the local density of states in high-Tc superconducting thin films, Phys. Rev. Lett. 84, 147–150. Miyakawa, N., Zasadzinski, J.F., Ozyuzer, L., Guptasarma, P., Hinks, D.G., Kendziora, C., and Gray K.E. (1999) Predominantly superconducting origin of large energy gaps in underdoped Bi2Sr2CaCu2O8+į from tunneling spectroscopy, Phys. Rev. Lett. 83, 1018–1021. Dipasupil, R.M., Oda, M., Momono, N., and Ido, M. (2002) Energy gap evolution in the tunneling spectra of Bi2Sr2CaCu2O8+į, J. Phys. Soc. Jpn. 71, 1535–1540. Zasadzinski, J.F., Ozyuzer, L., Miyakawa, N., Gray, K.E., Hinks, D.G., and Kendziora, C. (2001) Correlation of tunneling spectra in Bi2Sr2CaCu2O8+į with the resonance spin excitation, Phys. Rev. Lett. 87, 067005.1-067005.4.

ANNEALING INFLUENCE ON Co ULTRATHIN FILM MORPHOLOGY IN MBE GROWN Co/Au BILAYERS

A. WAWRO1, L.T. BACZEWSKI1, P. PANKOWSKI1, P. ALESZKIEWICZ1, M. KISIELEWSKI2, I. SVEKLO2, A. MAZIEWSKI2 1 Institute of Physics Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland 2 Laboratory of Magnetism, Institute of Physics, University of Biaáystok, á ul. Lipowa 41, 15-424 Biaáystok, á Poland

Abstract A complex study in order to define optimal growth conditions for epitaxial Au/Co/Au sandwiches with a strong perpendicular magnetic anisotropy has been performed. The thermally induced evolution of the sandwich morphology, which determines its magnetic properties, was studied by means of reflection high energy electron diffraction (RHEED) and Auger electron spectroscopy (AES). The roughness of Au and Co surfaces, affected by the sample annealing, was evaluated from the length-dependent variance of topography acquired by atomic force microscopy (AFM). The vacuum annealing of an Au layer deposited on the Mo buffer improves significantly its morphology - a temperature of 170 ºC is high enough to reduce the roughness more than twice. Gold acts as a surfactant appearing on the top of the Co layer after annealing at 250 ºC.

1. Introduction Studies of magnetic properties of thin films and nanostructures, where surfaces and interfaces are an important part of the sample volume, have been one of the most important topics in modern magnetism. Broken symmetry of the material at the surface (and interface) contributes largely to a change in its magnetic properties. One of the properties arising from the presence of interfaces in such low dimensional structures is perpendicular magnetic anisotropy, being of great interest from the point of view of both basic research and practical applications (e.g. for magnetic storage media) points of view. Namely, a thin Co layer of thickness of the order of several atomic planes exhibits a magnetization perpendicular to the film plane, which similarly to other features, such as coercivity, magnetic domain structure, magnetisation reversal and Curie temperature [1-12], is thickness dependent. Above a certain critical thickness a second order phase transition takes place resulting in the magnetisation reorientation to the in-plane direction. 435 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 435-442. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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The earliest theoretical models of these phenomena were based on the assumption that the interfaces were morphologically smooth. However, the existence of interface roughness in real films affects substantially their magnetic properties. Shape and interface anisotropy is strongly dependent on the film structure and the interface roughness due to the appearance of non-compensated magnetic poles. Imperfections of the interfaces may act as pinning centres for domain walls, modifying mechanisms of magnetisation reversal. Therefore, an understanding of a correlation between the film structure, interface morphology and magnetic properties is of a great importance. In this paper the analysis of the growth conditions of Au and Co layers as a function of the type of substrates is presented. On the basis of reflection high energy electron diffraction (RHEED) and Auger electron spectroscopy (AES) analyses, supported by the topography measurements at various scan size, performed by use of atomic force microscopy (AFM), the thermally induced evolution of Au/Co/Au sandwich structure is described.

2. Experimental details The Au/Co/Au sandwiches were grown in a molecular beam epitaxy (MBE) system with the vacuum level in the range of 10-10 Torr. Glass and monocrystalline sapphire(1120) covered with a Mo buffer layer were used as substrates. Co and Mo were evaporated from electron guns and Au from effusion cell at the rate lower than 0.5 Å/s. All deposition processes were performed at room temperature (RT) except the Mo buffer layer on sapphire which was grown at 1100 oC. The bottom Au layer, 200 Å thick, was deposited either directly on a glass substrate or on Mo buffer (200 Å) covering a sapphire substrate. The shape of Co layer was either flat or wedge-like (obtained with the use of a linear motion of the shutter) depending on a specific magnetic measurement purpose. Its thickness range was between 0 and 25 Å. The top Au layer was kept 80 Å in thickness. The crystalline structure of all grown layers was characterised in-situ by RHEED. The AES analysis was carried out to check the chemical composition of the layers and to estimate diffusion processes due to the sample annealing. Ex-situ AFM measurements (Nanoscope III microscope) in the tapping mode were performed for surface roughness investigations.

3. Results and discussion The growth mode of the bottom Au layer is strongly influenced by the substrate type. Au layers deposited on glass wafers are polycrystalline, whereas the epitaxial growth is obtained with sapphire (11-20) substrates. In the latter case the RHEED pattern exhibits clear streaks for all constituent layers, typical for monocrystalline structures. The Mo buffer deposited on the sapphire substrate has (110) orientation. Such a buffer favours the growth of an Au (111) layer. In spite of a large lattice mismatch, about 14%, Co layer deposited on Au exhibits coherent growth t in (001) orientation. On the basis of applied analysis it is impossible to distinguish whether its structure is fcc or hcp type. The top Au layer grows also in the (111) orientation – the same as the bottom Au layer.

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The following relations between in-plane directions of the constituent layers are found: sapphire (11-20) / Mo(110): [0001] Œ [1-1-1], Mo(110) / Au(111): [001] Œ [1-10], Au(111)/Co(0001): [1-10] Œ [11-20], Co(0001) / Au (111): [11-20] Œ [1-10] assuming hcp Co structure. The RHEED streaks for Mo ([001], [1-10] and [1-11] directions) and Au surfaces ([1-12] and [1-10] directions) are sharp with distances between them as for the bulk. These layers are relaxed and no strains on their surface are present. In contrast, the Co layer behaves in a different way. The RHEED streaks along [11-20] and [1-100] directions are blurred and the lattice constant, determined from the distance between them, varies with the Co layer thickness. Due to a remaining coherence and large lattice mismatch in Co layers grown on Au the existence of expanding strains is observed. Even for 15 Å thick Co layer the lattice constant is 3% higher than for the bulk. The annealing of Co layers at 250 ºC leads to substantial strain relaxation. This phenomenon is discussed further in the paper. Because of the strong influence of the layer morphology determined by the growth conditions on magnetic properties, an unambiguous characterisation of the surface roughness is required. For this purpose the scaling theory for self-affine fractal surfaces was applied [13, 14]. The analytic form of a function for roughness analysis is given as: g(R) = 2σ(R)2 = 2ı2[1 - exp(-(R/ȟ)2H)] (1) where R is a linear dimension of the analysed area, ı – calculated rms surface roughness, ȟ – correlation length and H – Hurst dimension. For R << ȟ the value of the correlation function varies as g(R) ~ R2H. Above the correlation length (R >> ȟ) the value of the function g(R) no longer scales with R and saturates at 2ı2. The value of the parameter ȟ may be attributed to the linear dimension of islands. The roughness dependence on the length scale was investigated on the basis of the AFM topography measurements. The microscopic images, recorded with the resolution 512x512 pixels, were divided consecutively by 4, 16, 64, 256, 1024 and 4096 nonoverlapping square tiles of decreasing linear dimension R, covering the whole scanned area and σ was computed for each tile. The mean of sigma over all tiles with the same dimension R gives a final value for s(R) for a given R. This procedure ensures that the smaller images are rightly slope corrected using the average plane found for the large original image. As mentioned earlier, the growth mode was determined by the type of substrate. Au layers deposited on a glass substrate are polycrystalline. Typical 3D growth occurs and as a consequence the surface is very rough –parameter σ ranging from 4 to 6.5 nm for RT and annealing at 300 oC, respectively and ξ– from 87 to 101 nm for the same temperatures. Consecutive annealing at temperatures t in the range from 170 ºC to 350 ºC shows that the roughness has a tendency to increase, similarly to the trend shown by the correlation length, leading to the wider and higher islands of the deposited material. The quality of Au layer morphology is substantially improved by using the sapphire substrate buffered with Mo. The deposition att RT results in 2D-3D growth (StranskiKrastanov mode), typical of (111) plane with the roughness of 0.46 nm. Atomically flat islands, ca 80 nm in diameter, with six-fold symmetry are observed (see Fig. 1). The fluctuation of the surface height is of the order of double (111) plane spacing. Contrary to Au growth on glass, the vacuum annealing of an Au layer deposited on a Mo buffer improves significantly its morphology. The temperature of 170 ºC is high enough to reduce the roughness more than twice (fluctuation of the surface height is suppressed to

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single monolayer step height, sigma = 0.17 nm) and increase the diameter of atomically flat islands by the same factor from 64 to 125 nm. The annealing at higher temperatures up to 600 ºC does not affect the topography markedly. It is worth to mention that even small miscut of a sapphire wafer might change the growth of Au bottom layer from the island-like to terrace-like mode.

Figure1. The AFM image of Au 200 Å thick layer as deposited on Mo buffer (left) and after annealing at 200 ºC (right). The range of the grey scale is 2 nm.

Figure2. The relation between the correlation function g(R) and the scan size R.. Squares denote the data for Au 200 Å thick layer as-deposited on Mo buffer and triangles represent data for the same Au layer but after 30 minutes annealing at 200oC.

In Fig. 2 the relation between the correlation function g(R) and a scan size R is presented. For both Au samples (as deposited on Mo buffer and after annealing at

439

200oC) g(R) first increases with the R dimension and then saturates for larger R. The initial slope is related to the Hurst dimension H, the position of the slope change gives the correlation length (islands dimension) and the curve saturation defines rms roughness σ = (g(R)/2)1/2. The evaporation of Co layers was performed at RT on the Au buffer layer, previously annealed at 200 ºC. The surface of as-deposited Co layer has the island-like structure, similar to that for annealed Au layer (see Fig. 3). Additionally, a weak structure of the islands surface is visible in the AFM image. The Co surface roughness (sigma = 0.18 nm) is comparable to that of the annealed Au layers, but the correlation length takes different values as Co layer thickness changes.

Figure 3. The AFM image of Co 15 Å thick layer as deposited on Au layer (left) and after annealing at 250 ºC(right). The range of the grey scale is 4 nm.

For 8 Å thick Co film the parameter ȟ oscillates around 90 nm, whereas for a thicker layer (15 Å) it increases up to 170 nm. Annealing at 250 ºC for 45 min causes smearing of the surface island structure. Their contours, although still visible in AFM image, are much less pronounced. The annealing process does not affect markedly the roughness of the thin Co layer whereas for the thicker one results in the surface smoothening as reported in the Ref [4]. The RHEED pattern observation allows to investigate the existence of strains due to the lattice mismatch of both components of the sandwich. The surface lattice parameter of as-deposited 8 Å Co layer is substantially enhanced up to the value of 2.72 Å, in comparison to 2.51 Å for the bulk. In 15 Å thick Co layer the strain relaxation is stronger, revealing the value of 2.59 Å. Annealing of the Co layer performed at 250 ºC evidently affects its crystalline structure. For 8 Å thick Co film the splitting of the RHEED streaks occurs (see Fig. 4), being a proof of the lattice constant relaxation to the values of 2.54 Å and 2.84 Å for Co and Au, respectively. Surprisingly, such splitting is not observed for 15 Å Co layers. For this sample the lattice parameter after annealing, measured by the distance between the RHEED streaks, is equal to 2.83 Å - very close to the Au bulk value (2.88 Å).

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Figure 4. The 12 kV RHEED streaks observed on as deposited (left) and after annealing at 250 ºC (right) 8 Å thick Co layer. Before annealing streaks are blurred, but single and corresponds to the lattice constant 2.72 Å. After annealing they are split revealing the lattice parameter 2.59 Å and 2.83 Å for outer and inner, respectively.

Figure 5. Auger spectra (energy 3 keV) for the sample: sapphire/Mo/Au/Co15 Å in the as-deposited state (top) and after annealing at 250 oC (bottom).

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On the basis of AES spectra comparison of both as deposited and annealed 15 Å Co layer it is evident that Au behaves as a surfactant. As can be clearly seen in Figure 5 the intensity of Auger signal of Au (around 220 eV) after annealing is more pronounced and at the same time a suppression of the respective intensity for Co is observed. This fact suggests that gold atoms are diffusing through the Co layer towards the surface during annealing and some of them are present at the cobalt/vacuum interface.Since Au and Co are mutually insoluble, the reverse diffusion may take place after the annealing. Most probably, due to the diffusion activated by annealing, a non-continuous Au film appears on the surface of thin Co layer, whereas in the case of the thick Co film, it is fully covered with Au. Moreover the coherence between Au and Co layers is lost, giving rise to the relaxation of strains. This is compatible with the evolution of Co surface morphology, monitored changes in the RHEED pattern and the Auger electron spectrum after the annealing of the samples. Thus it is reasonable to expect that the annealing lowers substantially magnetoelastic contribution to the magnetic properties of Co layers.

4. Conclusions The sapphire substrate buffered with Mo is ideal for growth of smooth Au/Co/Au sandwiches. The annealing above 170 ºC improves the flatness of Au surface atomically smooth areas of a few hundred nanometers in diameter occur. In the as deposited Co layers the expanding strains should result in the significant magnetoelastic contribution to magnetic properties. The thermal treatment releases strains and lattice parameter relaxes. The Au acts as a surfactant appearing on the top of Co layer after annealing at 250 ºC.

Acknowledgements This work was supported in part within European Community program ICA1-CT-200070018 (Centre of Excellence CELDIS).

References 1. 2. 3. 4. 5. 6. 7.

Chappert, C., Le Dang, K., Beauvillain, P., Hurdequint, H., and Renard, D. (1986) Ferromagnetic resonance studies of very thin cobalt films on a gold substrate, Phys. Rev. B 34, 3192-3197. Chappert C. and Bruno, P. (1988) Magnetic anisotropy in metallic ultrathin films and related experiments on cobalt films, J. Appl. Phys. 64, 5736-5741. Bruno, P., Bayureuther, G., Beauvillain, P., Chappert, C., Lugert, G., Renard, D., Renard, P., and Seiden, J. (1990) Hysteresis properties of ultrathin ferromagnetic films, J. Appl. Phys. 68, 5759-5766. Speckmann, M., Oepen, H.P., and Ibach, H. (1995) Magnetic Domain Structures in Ultrathin Co/Au(111): On the Influence of Film Morphology, Phys. Rev. Lett. 75, 2035-2038. Henh, M., Padovani, S., Ounadjela, K., and Bucher, P. (1996) Nanoscale magnetic domain structures in epitaxial cobalt films, Phys. Rev. B 54, 3428-3433. Oepen, H.P., Millev, Y., and Kirschner, J., (1997) The reorientation transition in Co/Au(111), J. Appl. Phys. 81, 5044-5046. Rüdiger, U., Yu, J., Thomas, L., Parkin, S.S., and Kent, A.D., (1999) Magnetoresistance, micromagnetism, and domain-wall scattering in epitaxial hcp Co films, Phys. Rev. B 59, 11914-11918.

442 8. 9. 10.

11.

12. 13. 14.

Murayama, A., Hyomi, K., Eickmann, J., and Falco, C.F., (1999) Magnetoresistance, micromagnetism, and domain-wall scattering in epitaxial hcp Co films, Phys. Rev. B 60, 15245-15250. Train, C., Mégy, R., and Chappert, C. (1999) Magnetic anisotropy and magneto-optical Kerr effect of a Pt/Co/Au(111) sandwich at low Pt thickness, J. Magn. Magn. Mat. 202, 321-326. Schneider, C.M., Bressler, P., Schuster, P., Kirschner, J., de Miguel, J.J., and Miranda, R. (1990) Curie temperature of ultrathin films of fcc-cobalt epitaxially grown on atomically flat Cu(100) surfaces, Phys. Rev. Lett. 64, 1059-1062. Huang, F., Kief, M.T., Mankey, G.J., and Willis, R.F. (1994) Magnetism in the few-monolayers limit: A surface magneto-optic Kerr-effect study of the magnetic behavior of ultrathin films of Co, Ni, and Co-Ni alloys on Cu(100) and Cu(111), Phys. Rev. B 49, 3962-3971. Zhang, R.and Willis, R.F. (2001) Thickness-Dependent Curie Temperatures of Ultrathin Magnetic Films: Effect of the Range of Spin-Spin Interactions, Phys. Rev. Lett. 86, 2665-2668. Palasantzas, G. and Krim, J. (1993) Effect of the form of the height-height correlation function on diffuse x-ray scattering from a self-affine surface, Phys. Rev. B 48, 2873-2877. Palasantzas, G. (1993) Roughness spectrum and surface width of self-affine fractal surfaces via the Kcorrelation model, Phys. Rev. B 48, 14472-14478.

CORRELATION BETWEEN THE SURFACE RELIEF AND INTERFACES STRUCTURE OF Fe/Cr SUPERLATTICES AND ELECTROMAGNETIC WAVES PENETRATION

A. RINKEVICH, L. ROMASHEV, V. USTINOV Institute of Metal Physics Ural Division of RAS 18 S.Kovalevskaya St, Ekaterinburg 620219 Russia

1. Introduction Investigation of the physical properties of magnetic metallic multilayers is one of the subject matters in modern nanophysics. Essential attention to this topic is supported by the GMR effect. Very essential information about magnetic and magnetoresistive properties of metallic nanostructures can be extracted using microwaves. Two phenomena that influence the penetration of electromagnetic waves through a multilayer are of especial interest. They are the giant magnetoresistive effect and the ferromagnetic resonance (FMR) [1-3]. Microwaves of millimeter waveband provide a way to observe simultaneously the result of two above phenomena and to estimate the constants of exchange interaction between neighboring ferromagnetic layers. Currently the effect of the structure of interfaces between the layers on the electromagnetic penetration is carefully investigated [4, 5]. Most interest is paid to the damping of the magnetic moment oscillations and to the measuring of the magnetic moments of the interfaces. Direct penetration of electromagnetic waves through the multilayers is used here in comparison to the tunneling microscopy data. The Fe/Cr superlattices, sandwiches and ultrathin Fe films are the objects of the present investigation.

2. Experimental The penetration coefficient of electromagnetic waves from the frequency interval of 25 to 38 GHz was studied experimentally. The scheme of measurements is shown in Fig.1. The sample is positioned into the cross section of a rectangular waveguide and the module of transmission coefficient is measured. The objects of investigation were the Fe/Cr superlattices with different thickness of layers, sandwiches and Fe films covered by thin chromium layer. All the samples were grown by the molecular beam epitaxy method on the MgO and Al2O3 substrates. The superlattices had the thickness of Fe layers of 2 to 28 Å and Cr layers of 9 to 18 Å. The number of bilayers varied from 6 to 50. The external magnetic field up to 16 kOe was applied in the plane of the sample always perpendicularly to the k wavevector. Two variants of the external field direction 443 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 443-448. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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were employed. The first one is shown in Fig.1. Direction of the dc magnetic field H vector is perpendicular to the microwave electric E~ vector. So, the H vector lies in the plane of microwave magnetic field H~. In the second variant the orientation H// H /E~ is realized.

Figure1. Position of a sample in the waveguide

3. Results and discussion The peculiarities in electromagnetic penetration were compared to the surface relief of multilayers and superlattices. The surface relief was obtained with the STM microscope SMM2000. The scans of thin Fe films and Fe/Cr superlattices were measured at the scanning fields from 15 x 15µm to 320 x 320 nm. The minimal Rq values (that is the square-root roughness) of the Fe/Cr superlattices are about 5 ǖ. The roughness of the hybrid-cluster nanostructures is barely higher than in superlattice samples. The typical tunnel scan is presented in Fig.2. The scan is relevant to the sandwich Al2O3/[Fe (30ǖ)/Cr (100ǖ) sample. The scanning field is 1.133 x 1.133 µm and the peak-to-peak difference in heights is 83 ǖ. In order to characterize the surface relief quantitatively the Hurst parameter is introduced [6, 7]. The square-root roughness Rq is measured at the profiles of different length L. The peak-to-peak difference in heights Rmax is measured in addition and Rmax / Rq ratio is calculated. The results are plotted in double logarithmic scale. For the several classes of surfaces the graph is a straight line. The Hurst parameter H is calculated from the slope of this line. The value of the Hurst parameter H = -0.5 corresponds to a

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random process with the spectrum of white noise. It is generally agreed that the Hurst parameter is a measure of steadiness of the process. This parameter is used in our paper in order to characterize the surface relief of nanostructures. The Hurst plot for the socalled hybrid-cluster Al2O3/Cr(70A)/[Fe(2A)/ɋr(10Ⱥ)]50 structure is shown in Fig.3 for two tunnel scans.

Figure 2. Tunnel scan for the Al2O3/[Fe (30ǖ)/Cr (100ǖ) sample

0,8

lo g (R max / R q )

0,7

0,6

0,5

0,4

0,3 1,0

1,5

2,0

2,5

3,0

3,5

4,0

log L (n m ) Figure 3. The Hurst plot for the Al2O3/Cr(70A)/[Fe(2A)/ɋr(10Ⱥ)]50 sample

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Microwave measurements gave the following results. It was shown that the microwave GMR is very similar to that measured on dc. The relative variations of penetration coefficient rm=[D(H)-D(0)]/D(0) versus magnetic field are usually plotted, where D(H) is the penetration coefficientt module in the field H. The magnetic field dependence of the rm was measured at several frequencies of millimeter-waveband for the [Cr(19Å)/Fe(23Å)]12/Cr(80Å)/MgO superlattice, see Fig.4. Two origins of microwave variations are evident. The first origin is due to the microwave GMR effect. Variations caused by this mechanism are negative, monotonic and non-resonant [1, 3]. The absolute values of the microwave variation due to this mechanism are almost equal to the dc GMR. So, the structure of Fe-Cr interfaces acts on the microwave penetration just in the same manner as on the dc magnetoresistance. Resonant-type variations of the penetration t coefficient are caused by the ferromagnetic resonance. They are observed only if the dc external magnetic field is parallel to the E~ vector, that is perpendicular to the plane of H~ vectors. So, the acoustic or uniform resonance mode manifests itself in the penetration coefficient. The structure of interfaces influences essentially the damping of the magnetic moments rotation.

2 ,5

rm , %

f, GHz 32 34 36

0 ,0 -2 ,5 -5 ,0 -7 ,5

- 10 ,0 - 12 ,5 - 15 ,0 - 17 ,5

0

2

4

6

8

10

12

14

Magnetic field H, kOe Figure 4. Magnetic field dependence of the relative variations of penetration coefficient

The frequency dependence of the FMR line width is shown in Fig.5 for the Fe/Cr superlattice [Cr(19Å)/Fe(23Å)]12/Cr(80Å)/MgO, the thin iron film

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Cr(10Å)/Fe(573Å)/Al2O3, and the hybrid-cluster structure [Cr(11Å)/Fe(9Å)]40/Cr(85Å)/MgO. The definite correlation is observed between the width of the FMR line and the surface relief characteristics. In the hybrid-cluster nanostructures with very thin discontinuous Fe layers the FMR width is relatively large up to 0.7 kOe. It is safe to assume that the large width is connected with inhomogeneous demagnetizing field near the discontinuities of Fe layers. The Gilbert constant G of magnetic damping was calculated in different multilayers. In the [Cr(19Å)/Fe(23Å)]12/Cr(80Å)/MgO superlattice G = (1,1 ÷ 1,2)⋅108 s-1 and in the Cr(10Å)/Fe(573Å)/Al2O3 iron film G = (1,5 ÷ 1,7)⋅108 s-1.

0,7 [Cr(19A)/Fe(23A)]12 film Fe (573A) hybride-cluster structure [Cr(11A)/Fe(9A)]40

∆ H , kOe

0,6

0,5

0,4

0,3 26

28

30

32

34

36

38

Frequency f, GHz Figure 5. Frequency dependence of the FMR line width in multilayers

4. Conclusion The relative variation of the transmission coefficient through the Fe/Cr superlattices and thin Fe films has been studied. For the frequencies higher then 30 GHz a clear narrow line of the ferromagnetic resonance (FMR) is seen besides the non-resonant variations caused by the GMR effect. The roughness of the surface relief in the best superlattice samples and in the films is as low as 5 Å. The roughness of the hybrid-cluster structures with very thin Fe layers is a bit higher. The roughness of the interfaces influences the

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monotonic part of microwave variation in the same manner as the dc magnetoresistance. A distinct correlation is observed between the width of the FMR line observed in the penetration coefficient and the thickness of Fe layers. In the hybride-cluster structures the Fe layers are discontinuous. So, the FMR line width is much larger because of inhomogeneous demagnetizing fields. The non-resonantt variation of the transmission coefficient is practically absent in the thin Fe film. The FMR line, however, in this sample is narrower and has larger amplitude then in superlattices. The work was partially supported by the RFBR and INTAS grants.

References 1.

2. 3. 4. 5. 6. 7.

Krebs, J.J., Lubitz, P., Chaiken, A., and Prinz, G.A. (1991) Magnetoresistance origin for nonresonant microwave absorption in antiferromagnetically coupled epitaxial Fe/Cr/Fe(001) sandwiches, J. Appl. Phys. 69, Pt. II, 4795-4797. Kuanr, B.K., Kuanr, A.V., Grunberg, P., and Nimtz, G. (1996) Swept-Frequency FMR on Fe/Cr Trilayer Ultrathin Films – Microwave Giant Magnetoresistance, Physics Letters, A 221, 245-252. Rinkevich, A.B., Romashev, L.N., and Ustinov, V.V. (2000) Radiofrequency Magnetoresistance of Fe/Cr Superlattices, JETP, 90, 834-841. Urban, R., Woltersdorf, G., and Heinrich, B. (2001) Gilbert Damping in Single and Multilayer Ultrathin Films: Role of Interfaces in Nonlocal Spin Dynamics, Phys. Rev. Letters, 87, 217204-1-4. Celinski, Z., Urquhart, K.B., Heinrich, B. (1997) Using ferromagnetic resonance to measure the magnetic moments of ultrathin films, JMMM, M 166, 6-26. Hurst, H.E., Black, R.P., and Simaika, Y.M. (1965) Long Term Storage: An Experimental Study. L.: Constable. Schroeder, M. (1991) Fractals, Chaos, Power Laws. Miniatures from an Infinite Paradise. NY: W.H.Freeman & Company.

MAGNETORESISTANCE AND MICROSTRUCTURE OF MAGNETIC THIN FILM MULTILAYERS

J. NEAMTU∗, M. VOLMER∗∗ ∗Advanced Research &Development Institute for Electrical Engineering, SplaiulUnirii 313, Bucharest 030138,Romania [email protected] ∗∗∗Transilvania University Brasov, B-dul Eroilor 29, Brasov Romania

Abstract The magnetic properties and the magnetoresistance in correlation with microstructural properties of [NiFe(t)/Cu(s)/NiFe(t)]n and [NiFe(t)/Mo(s)/NiFe(t)] multilayers have been investigated. The thickness (t) of permalloy (Ni 80%Fe 20%) layers was ranged from 4 to 12 nm, while the copper and molybdenum layers (s) was ranged from 3 to 8 nm. The multilayers exhibit magnetoresistive properties correlated with microstructure and roughness at the interface of permalloy film and cooper or molybdenum layer. By decreasing of the NiFe layer thickness and by increasing of the non-magnetic interlayer thickness, the influence of interfacial intermixing effects on magnetic properties become more important. Although the thickness of layers has the leading part for magnitude of Giant Magnetoresistance effect, the microstructural properties of interfaces and the grain boundaries scattering must not be neglected. 1. Introduction The magneto-transport properties of ferromagnetic/nonmagnetic/ferromagnetic multilayers are dependent of the thickness of thin films, the roughness and the nature of thin film. Giant Magnetoresistance (GMR) effect results from two factors: (1) spin dependence of the electronic band structure of a defect-free system, and (2) spin dependence of scattering potential [1]. The aim of this paper is to investigate the influence of nature and microstructure of spacer-layer and influence of interface roughness on the magnetoresistance properties of the multilayers [NiFe(t)/Cu(s)/NiFe(t)]n and [NiFe(t)/Mo(s)/NiFe(t)]. 2

2. Experimental Four types of samples are considered in this paper: 1) Si/SiO2/ (Permalloy Ni 80%Fe20%) monolayer films 2) Si/SiO2/Py (10 nm)/Cu (4 nm)/Py(10 nm) in which Py is Ni80Fe20. 3) Si/SiO /Py(10 nm)/Mo(6 nm)/Py(10 nm) 449 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 449-456. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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4) Si/SiO2/[Py(10 nm)/Cu (4 nm)]9/Py(10 nm) Permalloy Ni80%Fe20% monolayer films were deposited, with thickness in range 4100 nm, using high vacuum evaporation with a base pressure of 10-7Torr, on Si/SiO2 substrates. During deposition the magnetic field of 15 kA/m was applied in the plane of the substrates in order to induce an easy magnetization axis in the films. The multilayers were prepared by R.F. sputtering at a base pressure of 10-7 Torr and an argon pressure of 1.5 mTorr (target to substrate distance is 100 mm). As substrates we used Si (100) single-crystal wafers, cut to a size of 5x10 mm2, with a thickness of 0.5 mm. Prior to insertion into the sputtering machine, the substrates were chemically etched using a 2% HF solution to have a flat surface and then oxidized. The permalloy layer thickness (t) was changed from 4 to 12 nm, while the copper and molybdenum layers thickness (s) was changed from 3 to 8 nm. The number of layers n for multilayer [Ni80Fe20 (10nm)/Cu (4nm)/Ni80Fe20 (10nm)]n was up to 10. 3. Results The magnetization measurements were performed att room temperature using a vibrating sample magnetometer (VSM). The magnetoresistance effect measurements were performed at room temperature in four-point contactt geometry with the contacts in line, using a DC current of 10 mA. The magnetoresistance measurements of permalloy (Ni80Fe20) films were made for two configurations: a) magnetic field applied parallel to the current direction and b) magnetic field perpendicular to the current direction. The magnetoresistance (MR) is defined as the variation ∆R=(R0-RH) of the resistance due to magnetic field normalized by the resistance R0 at zero magnetic field: MR=∆R/R0. The magnetic properties of Si/SiO2/Py(10 nm)/Cu (4 nm)/Py (10 nm) trilayer has presented in figure 1.The magnetic field is applied in the film plane, directed along the easy axis. 0.008

Py (10 nm)/Cu (4 nm)/Py (10 nm)

0.006

Moment (e.m.u.)

0.004 HC=250 Oe M r=0.0022 u.e.m.

0.002 0.000 -0.002 -0.004 -0.006

H in plan

-0.008 -4000

-2000

0

2000

4000

H (Oe) Figure 1. Magnetization curve measured at room temperature for NiFe (10 nm)/Cu (4 nm)/ NiFe (10 nm) trilayer with magnetic field applied in the film plane directed along the easy axis.

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S /Py (10 nm)/Mo (6 nm)/Py (10 nm) 2 0.015 Si/SiO

Moment (e.m.u.)

0.010

HC=200 Oe Mr=0.003 u.e.m.

0.005 0.000 -0.005

0 .0 1 5 0 .0 1 0 0 .0 0 5

-0.010

0 .0 0 0 -0 .0 0 5 -0 .0 1 0

-0.015

-0 .0 1 5 - 1 5 0 0 0- 1 0 0 0 0- 5 0 0 0

-4000

-2000

0 H (Oe)

0

5 0 00 1 0 00 01 5 00 0

2000

4000

Figure 2. Magnetization curves of NiFe(10 nm)/Mo(6 nm)/NiFe(10 nm) trilayer, at medium and high magnetic fields.

Figure 2 shows the magnetization curve for Py (10 nm)/Mo (6 nm)/Py (10 nm) multilayer with the magnetic field directed along the easy axis. The insert figure shows the behavior of Py (10 nm)/Mo (6 nm)/Py (10 nm) multilayer at high magnetic fields. One can see descending slope of the saturation magnetization for high magnetic fields, due to the diamagnetic contribution of Si/SiO2 substrate. 0.06

Si/SiO2/[Py(10 nm)/Cu(4 nm)]*9 - Py (10 nm)

Moment (e.m.u.)

0.04 0.02

Mr=0.021 u.e.m. HC=202 Oe

0.00 -0.02 -0.04 -0.06 -3000

-2000

-1000

0

1000

2000

3000

H (Oe)

Figure 3 Magnetization curve of [NiFe(10 nm)/Cu(4 nm)]9/NiFe(10 nm) multilayer, measured at room temperature.

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Figure 3 shows magnetization curve of [Py (10 nm)/Cu (4 nm)]9/Py (10 nm) multilayer, with magnetic field directed along the easy axis. We observe the increase of saturation magnetization, comparison with Py(10 nm)/Cu (4 nm)/ Py (10 nm) trilayer.

Flux density(T) Figure 4. Longitudinal and transversal resistance, (RB-R0)/R0, versus flux density, for NiFe film of 100 nm.

Figure 4 shows the longitudinal and transversal magnetoresistance for Ni80Fe20 monolayer of 100 nm thickness. Transversal magnetoresistance has relative high value for small field (B<0.05T).

Figure 5. Longitudinal and transversal MR effect performed on Py(10 nm)/Mo(6 nm)/Py (10nm) with magnetic field in the film plane.

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Figure 6. Longitudinal and transversal MReffect for system [Py(10 nm)/Cu(4nm)]9/Py(10 nm)

Figure 5 shows the magnetoresistance effect, MR, for Py (10 nm)/Mo (6 nm)/Py (10 nm) multilayer, with the magnetic field in the film plane. The effect is small because of very small coupling between the magnetic layers with molybdenum spacer. However, one can be observed the effect of spin-dependentt scattering of the electrons. In both cases (longitudinal and transversal), the MR effect has the same sign and depends on the relative orientations between the magnetization of the Py layers. The difference between longitudinal and transversal effect is due to anisotropic magnetoresistance effect (AMR). Figure 6 shows the magnetoresistance (MR) measurements for the system [Py(10 nm)/Cu(4 nm)]9/Py(10 nm) multilayer. The magnetoresistive (MR) effect is bigger than the MR effect for the system with Mo spacer, showing the good magnetic coupling of permalloy layers through copper layer. The pemalloy films, [NiFe/Cu] multilayers and [NiFe/Mo] multilayers were characterized using atomic force microscopy (AFM) for surface texture, grain size and roughness. Figure 7 shows the 3D AFM image of Ni80Fe20(10nm)/Cu(4nm)/ Ni80Fe20(10nm) film. The average roughness is low: 6.4265 nm. Figure 8 shows the 3D AFM image of Ni80Fe20(10nm)/Mo(6nm)/ Ni80Fe20(10nm) film. The average roughness is 8.5384 nm.

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Figure 7. 3D AFM image of [NiFe(10nm)/Cu(4nm)]9/ NiFe(10nm) multilayer. The average roughness is 6.4265 nm

Figure 8. 3D AFM image of NiFe(10nm)/Mo(6nm)/ NiFe(10nm) trilayer. The average roughness is 8.5384 nm.

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4. Discussion and Conclusion We used a state-dependent reversible magnetization model [2], to fit the magnetization data of the form:

M (H) = M 0 + A 1 (

(

1

))

2

(

(

2

))

(1)

where M0, A1, A2, t1, 2 are constants and H is the applied magnetic field. From figure 1, saturation magnetic moment has mS= 0.007 e.m.u. and from figure 2, mS=0.015 e.m.u. We consider that difference is mainly due to the quality of the interfaces Permalloy/Cu and Permalloy/Mo. The degree of interfacial roughness and intermixing is mainly determined by the kinetic energy of the atoms at the momentt of impact on the substrate. At low Ar pressure (smaller than 3 mTorr), the bombardment of the high-energetic particles causes collision mixing, resulting in the formation of inter-mixed regions at the interfaces. This causes a decrease of the effective thickness of the magnetic layer and of total magnetic moment. This effect is very important in the case of Py/Cu/Py multilayers[3], because of the high surface mobility of the Cu-atoms. Since Ni and Cu can form alloys, the interface of Permalloy/Cu multilayers cannot be expected to have a sharp magnetic boundary. The coercive force (fig 1), of about 250 Oe, can be attributed to crystallite shape anisotropy and the extrinsic properties such as grain size. On the other hand the Py/Mo multilayers have a strong resistance due to the atomic interdiffusion between layers. This observation can explain the difference observed between the saturation magnetization of the two films, presented in figure1 and figure 2. The layers, for Permalloy/Cu systems, become better defined after few periods [4]. We observe an increase of the magnetic moment per ferromagnetic layerr from about 0.0035 e.m.u, for Py/Cu/Py system, to about 0.006 e.m.u. for (Py/Cu)9/Py multilayer (figure 3). This result suggests that the layers be better defined in this last case, in good agreement with Reiss et al.[4]. The magnetoresistance effect, MR, (figure 5) of Py(10 nm)/Mo (6 nm)/Py(10 nm) multilayer is small because of small coupling between the magnetic layers with molybdenum spacer. However one can be observed the effect of spin-dependent scattering of the electrons. The MR (longitudinal and transversal) effect has the same sign and depends on the relative orientations between the magnetization of the permalloy layers. The difference between longitudinal and transversal effect is due to anisotropic magnetoresistance effect (AMR). In order to explain the giant magnetoresistive effect it is necessary to consider the scattering processes due to upward spin and to downward spin, the electron scattering at the film boundary and the grain boundary scattering. Mayadas et al. [5] proposed a model for transport properties in multilayers based on diffusive electron scattering at the film m boundary, expressed in terms of mean free path parameters. The grain boundary scattering was also taken into account by a mean free path parameter λgrr assumed to be spin independent, related to the total mean free path parameter λ using the following formula: 1/λ(t)=1/λi+1/λgr(t)

(2)

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where λi is the spin dependent mean free path parameter for intrinsic scattering, while t is the NiFe layer thickness. For our NiFe thin films, with thickness ranging from 10 to 50 nm, λgrr was found to be of the order of 8-15 nm, and MR effect become higher. One can see that the microstructure (figure 7) and magnetoresistance effect (figure 6) for multilayers [NiFe(10 nm)/Cu(4 nm)]9/NiFe(10 nm) are in good agreement with this result concerning the spin independent grain boundary term of the electron scattering. The above experimental results for [NiFe(10 nm)/Cu(4 nm)]9/NiFe(10 nm) multilayers show that GMR performance is associated with a low roughness and a sufficiently small average grain size, directly influencing the amount of grain boundary scattering. References: 1. Miyazaki, T. (1993) Magnetoresistance of Alloy Films and Multilayers, IEEE Trans. J. on Magnetism in Japan 8(5) 351-360. 2. Vajda, F., Della Torre, E. (1997) Reversible Magnetization Models for Magnetic Recording Media, Physica B 233, 330-336 3. Neamtu Jenica, Volmer M., Coraci, A. (1999) Magnetoresistive Properties and Microstructure of NiFe Thin Films and NiFe(t)/Cu(s)/NiFe(t) Multilayer Films, Thin Solid Films 343-344, 218-221 4. Reiss G., Van Loyen, Lucinski T., Elefant D., Ernst W, (1998)Presence and absence of antiferomagnetic coupling and giant magnetoresistance in sputtered and evapored permalloy cooper multilayers, J .M. M.M. 184,281-288 5. Mayadas A.F. , Shatzkes, M. (1970) Electrical-Resistivity Model for Polycrystalline Films: the Case of Arbitrary Reflection at External Surfaces, Phys. Rev. B 1, 1382-1389

SPM INVESTIGATION OF THIOLATED GOLD NANOPARTICLE PATTERNS DEPOSITED ON DIFFERENT SELF-ASSEMBLED SUBSTRATES

F. SBRANA, M.T. PARODI, D. RICCI, E. DI ZITTI Department of Biophysicall and Electronic Engineering, University of Genoa Via Opera Pia 11a, 16145 – Genoa – Italy

Abstract We present the results of a Scanning Probe Microscopy (SPM) investigation of ordered nanosized metallo-organic structures. Our aim is to investigate the organization and stability of thiolated gold nanoparticles in a compact pattern when deposited onto gold substrates functionalized with self-assembled monolayers made from two molecules that differ essentially in their terminating group: 1,4-benzenedimethanethiol and 4methylbenzylthiol. The dodecanethiol capped gold-nanoparticles were synthesized in a two-phase liquid-liquid system. Cluster size-selection byy chromatographic technique was performed in order to obtain a narrow core diameter distribution peaked around 2 nm. A Langmuir film of size-selected nanoparticles was formed at the air-water interface using the multi-step creep method and was transferred onto the functionalized substrates. Overall quality assessment was performed by Transmission Electron Microscopy image analysis. Room temperature scanning tunneling microscopy images of nanoparticles arranged in compact patterns deposited on these functionalized substrates are shown. A high degree of 2-D local organization is found and the role of 1,4benezenedimethanethiol as grafting element between the gold nanoparticle pattern and the substrate is investigated.

1. Introduction Recently novel strategies for non-conventional nanoelectronic devices, capable of working at room temperature and in air, have been developed. A bottom-up approach based on the fabrication of nanoarchitectures assembled from building blocks such as nanometer size metallic particles, organic molecules or atomic systems is an innovative and possible strategy [1]. The basic structure consists on an electrically coupled planar array of nanometer sized metallic islands, self-assembled onto an appropriate substrate whose current-voltage characteristic has a non-monotonic nonlinearity. Self assembling and Langmuir Blodgett (LB) techniques have been found to be highly suitable in the fabrication of such an architecture. 457 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 457-466. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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In this study we have directed our efforts at building up a prototype system based on this model. In particular we have been concerned with the fabrication, by combining self-assembly and LB techniques, of a planar array of gold nanoclusters, each separated by a tunneling gap from its neighbors and ohmically linked to a conductive substrate. The tunneling gap between clusters is assured by the dodecanethiol coating of the gold nanoparticles, while the ohmical link to a conductive substrate is guaranteed by a functionalized self assembled monolayer on the gold substrate. In the literature, essentially two methods have been used to make such metallic nanoparticles: gas-phase gold cluster synthesis followed by solution-phase encapsulation [2] and liquid phase gold growth using alkyl thiol as surfactants [3]. We have focused our attention on the latter choosing to synthesize dodecanethiol monolayer coated gold nanoclusters and tuning the synthesis parameters in order to obtain a solution of clusters with an average core radius of about 1 nm. In order to be suitable for Langmuir film making and deposition the as-prepared nanoparticles need a size selective treatment such as vapor transfer or liquid phase chromatography. These techniques are the most commonly used for obtaining a monodisperse nanoparticle distribution [3, 4]. Our efforts have been directed initially on vapor transfer, successively on the liquid phase chromatography method. Deposition of these nanoparticles and studies of their aggregation and ordering properties have been extensively carried out [5-9]. Long range ordered planar arrangement of gold nanoclusters capped by different long-chain molecules have been obtained by X.Chen et al. [10] applying the multi-step creep method to the Langmuir- Blodgett technique. Encouraged by these good results we have applied the same method to the dodecanethiol capped gold nanoclusters. The ordered film was then transferred onto gold substrates functionalized with self-assembled monolayers made from two molecules that differ essentially in their terminating group: 1, 4-benzenedimethanethiol and 4-methylbenzylthiol. STM investigations, in air and room temperature, have been carried out on these samples.

2. Material and Methods 2.1 SYNTHESIS AND NANOCLUSTER SIZE DISTRIBUTION DETERMINATION Thiolated gold nanoparticles were prepared following the modified version of the Brust method [3] as described in [11]. In order to obtain an average particle core radius of 1 nm, we have chosen the following preparation conditions: 1:1 dodecanethiol:AuCl-4 mole ratio, fast delivery of the NaBH4 reducing agent (10 s) and a reaction time of 3 hours after reducing agent addition, all performed at room temperature. In order to obtain a mono-disperse nanoparticle distribution initially we have employed the vapour transfer method following the procedure described by Whetten et al. [4]. Acetone was used as solvent and slowly added to the nearly saturated toluene solution (20 mg/mL) of the as-prepared nanoparticles until the solution volume was increased by 85%. The precipitate obtained after a prolonged equilibration time was separated from the soluble fraction by centrifugation. f The latter, as well as the recovered precipitate, was then treated with a series of purification steps, until the cluster amount

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was not less than 20 mg, applying the following procedure: the precipitated clusters were dissolved in toluene (20 mg/mL) and then a new controlled vapor transfer was preformed so that the amount of acetone added was slightly smaller than in the previous step. The smaller clusters, still in the solution, were once again by vapor transfer so that a further addition of acetone induced the precipitation of a new particle fraction. In order to compare results a trial liquid phase chromatography method was applied. This technique is one of the most practical methods to separate molecules or particles on the basis of their size. The chromatographic column was filled and packed with a porous inert matrix, as stationary phase. The as-prepared nanoparticles, dissolved in chloroform, were loaded in the column, followed by further gradual addition of the solvent as eluent. Aliquots of the separated particles were collected from the column effluent. This procedure was repeated on successive collected aliquots, depending on the amount of material available. Each fraction obtained from both size selective techniques was examined for cluster core size distribution determination via Transmission Electron Microscopy (TEM). 2.2 FILM MAKING Langmuir films of thiolated gold nanoparticles were made at the air-water interface using a standard LB trough (KVS LB5000). The films were prepared spreading 1mg/mL hexane solution of particles on a Millipore grade water subphase kept at 12 °C. Two batches of 200 µL of solution were deposited at 15 minutes intervals. The subphase temperature was then brought up to 24 °C and the multi-step creep method was applied to form the monolayer as described in [10]. Two series of compression and expansion were carried out starting from a totally expanded film: the first was performed reaching the surface pressure of 5 mN/m five times, the second bringing the surface pressure up to 10 mN/m twice. The barrier speed used to compress the gold nanoparticles was 15.6 mm/min. The film thus formed was transferred onto a functionalized Self Assembled Monolayer (SAM) substrate at a surface pressure of 10 mN/m by the horizontal lifting technique [12]. 2.3 SUBSTRATE PREPARATION Gold <111> was prepared by high vacuum m evaporation (Univex 300, Leybold-Heraeus) of pure gold (99.999%) onto freshly cleaved mica sheets (Agar Scientific). Mica was heated in the vacuum chamber, kept at 6 x 10-6 Torr, for 2 h at 400 °C, in order to allow the removal of adsorbed molecules from the surface. A 100 nm thick gold layer was then evaporated at an evaporation rate of 0.5 nm/s. The sample was subsequently annealed keeping the same temperature and pressure in the vacuum chamber for 2h. This procedure yielded gold surfaces <111> oriented with atomically flat terraces having lateral dimensions of approximately 100 nm. The gold quality and terrace dimensions were assessed by STM imaging. Self-assembled monolayers of 1,4-benzenedimethanethiol (Aldrich) and of 4methylbenzylthiol were prepared by immersion of the gold substrates in a 1 mM solution in ethanol for 24 h. After incubation the treated samples were removed from the

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solution, rinsed copiously with pure ethanol to remove excess molecules and dried under a nitrogen stream. 2.4 TEM Phase contrast images of particles were obtained with a JEOL JEM 2010 microscope operating at 200 KeV. Samples for TEM analysis were prepared by the drop cast method. One drop of 1mg/ml cluster solution in toluene was deposited onto carboncoated grids (400mesh). The samples were dried in air for at least 45 min. Size distribution of the Au cores was measured using computer automated particle detection software (SPIP, Image Metrology) applied to TEM images containing several hundreds of particles each. 2.5 STM STM measurements were carried out with a Pico-SPM (Molecular Imaging) in air at room temperature, using a 1 µm scanner and tips cut from Pt/Ir (80/20) wire (Goodfellow). All images were obtained in the constant-current mode with a bias voltage set between 0.5 and 1 V and a tunneling t current ranging from 10 to 100 pA.

3. Results and discussion In this study we first focused our attention on the two phase liquid-liquid system to synthesize dodecanethiol monolayer coated gold nanoclusters. We tuned the synthesis parameters in order to obtain a solution of clusters with an average core radius of about 1 nm. The as-prepared nanoparticles showed a rather broad particle size distribution, and necessitated further treatment in order to be suitable for Langmuir film making and deposition. Initially vapor transfer and successively liquid phase chromatography were employed to narrow down size distribution of the nanoparticles. We collected successive aliquots of the separated particles and detected the cluster core-size distribution for each fraction via software elaboration of TEM images, by drop casting of the nanoparticles solution in toluene onto carbon-coated grids. In Figure 1 we show, as an example, a comparison between the size distribution histograms of the raw solution and one that has undergone nine steps of size-selective vapor transfer treatment. The raw solution particle core average radius is found to be 1.18 nm with a standard deviation of 0.45 nm, while the size-selected fraction has a mean particle radius value of 0.78 nm with a standard deviation of 0.23 nm. A notable shift of the peak towards smaller diameters and a cut-off of large cluster occurrence can be observed. These encouraging and perceptible results point out the effectiveness of the size-selection procedure. In Figure 2 we show the size distribution histogram of an intermediate solution fraction obtained after applying only twice the liquid phase chromatography treatment. The size-selected fraction has a mean particle radius value of 0.98 nm with a standard deviation of 0.23 nm. These good results point out the performance of this size-selection technique.

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Figure 1. Comparison between the particle core size distribution histograms of the raw solution before (hollow bars) treatment and after nine vapor transfer size-selective step (solid gray bars).

Figure 2. Nanoparticle core size distribution histogram of the intermediate solution obtained applying twice the liquid phase chromatography treatment.

In Figure 3 we show TEM images taken from the sets of TEM data used for the calculation of the size distribution t histograms, corresponding to the raw solution and to the solution of the nanoparticles size separated by liquid phase chromatography method respectively. In the top image of Figure 3 a tendency of the particles to separate and aggregate on the basis of their dimension may be observed. This is typically a size dependent phase separation behaviour, as well described and reported by Leff et al. [8]. The direct observation of the TEM image att the bottom of Figure 3, confirms the performance of the liquid phase chromatography technique. It can also be observed that the nanoparticles exhibit a tendency to aggregate in a homogeneous “phase”.

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Figure 3. TEM images taken from the data sets used for the calculation of the size distribution histograms shown in Figure1. The top image corresponds to the raw solution, while the bottom one to the intermediate solution obtained by the liquid phase chromatography treatment: the effectiveness of the size-selection procedure is readily perceivable.

In Figure 4 a high resolution image of a single 2.4 nm diameter cluster from the raw solution is shown, where the crystalline nature of the particle is reflected in the electron diffraction pattern. The successive step in the building-up of the model nanostructure has been the assembling of the size separate nanoparticles into 2D ordered arrays onto an appropriate functionalised substrate. In order to form an ordered array of tunnelling junctions between neighbouring particles we exploited the properties of Langmuir film making, applying the multi-step creep method. Langmuir film making allows us to control the interparticle distance and enables the nanoparticles to arrange in a homogeneous and ordered planar array. The multi-step creep method applied to Langmuir film enhances its ability to produce long range highly ordered arrangements of clusters. This occurs especially in the case of clusters with capping molecules that have longer chain lengths,

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as well described by Chen et al. [10]. We have chosen to use thiols with C12 chain lengths (dodecanethiols) to coat the gold nanoparticles, because they form a stable, compact and defect free SAM on the gold cluster surface, and so they are the most suitable for the Langmuir film making.

Figure 4. TEM high resolution of a single 2.4 nm diameter cluster from the raw solution

The monolayer obtained at the air-water interface was transferred first of all onto the 1,4-benzenedimethanethiol and then on 4-methylbenzylthiol SAMs on gold <111> substrates by horizontal lifting. The two self-assembled monolayers differ essentially in their terminating group: the first is functionalized at both ends with an –SH group, while the second only at one end. In Figure 5 we report room temperature STM images of a cluster film deposited on 1,4-benzenedimethanethiol t SAM on gold substrate. One can notice a homogeneous 2D long range organization with a dense packing of the nanoclusters. Reproducible results were achieved on several samples obtained starting from different Langmuir films prepared in the same way, in good accord with what found in our previous work. Imaging was very stable with an extremely low presence of artifacts confirming that the nanoparticles are tightly packed and well ordered within the film.

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Figure 5. Room temperature air STM image of a nanoparticle Langmuir film obtained by the multi-step creep method and deposited onto a 1,4-benzenedimethanethiol SAM on gold <111>. Image size is 300 nm x 300 nm, It =20 pA, Vt = 1 V, scan rate 2 lines/s.

In Figure 6 we report room temperature STM images of a film deposited on 4methylbenzylthiol SAMs on gold <111> substrates. One can notice a folding (a local multilayer formation) of the nanoparticle layer on the non-functionalized SAM surface. The parameters used for the Langmuir film making were the same in the case of as the monolayer transferred on 1,4-benzenedimethanethiol SAM. These different film organizations on the two SAM substrates confirm that a strong link is established between the clusters and the functionalized (1,4-benzenedimethanethiol) surface, in accord with what reported in [13]. We may assume that an exchange between a dodecanethiol chain adsorbed on the cluster surface with a dithiol chain of the SAM substrate surface occurs, so that the free –SH group of the dithiol adsorbed on the substrate surface bonds to the gold surface of the cluster. It is noteworthy that tight assembly of the clusters in the planar array is due to the interpenetration of the thiol chains absorbed on the cluster surface with those of the near neighbor cores. The same type of hydrophobic interaction is established between the nanoclusters and the 4methylbenzylthiol SAM substrate, where the molecular chain differ from alkyl thiol chain for a benzene ring. In the case of the functionalized SAM substrate the interaction between the clusters and the substrate surface is stronger than the one between clusters within the array, so that a homogeneous 2D long range organization with a densely packing of the nanoclusters is formed. In the case of the non-functionalized SAM substrate the interaction between clusters and the substrate surface is weaker than the one between clusters. A folding of the cluster film during transfer on the SAM surface occurs, creating deep trenches on the array surface, as shown in Figure 6.

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Figure 6. Room temperature air STM image of a nanoparticle Langmuir film obtained by the multi-step creep method and deposited onto a 4-methylbenzylthiol SAM on gold <111>. Image size is 150 nm x 150 nm, It =50 pA, Vt = 0.5 V, scan rate 3.4 lines/s.

4. Conclusions An ordered 2D system of thiolated gold nanoparticles as a bottom-up approach to nonconventional nanoelectronic devices have been fabricated and investigated. Vapor transfer and liquid phase chromatography have been employed as size selection techniques with the purpose of excluding large particles from the solution and hence allow forming close-packed monolayers. The good performance of both techniques has been assessed, with a preference for the liquid phase chromatography as it is the most practical to be employed. Room temperature STM investigations have shown the role of 1,4benzenedimethanethiol as grafting element. A high degree of 2D local organization of the nanoclusters is found when the film is transfer on SAMs of 1,4benzenedimethanethiol on gold >111> substrate, while a folding of the film is found on SAMs of 4-methylbenzylthiol on gold substrate.

5. Acknowledgments We thank Prof. Flavio Gatti of the Physics Department of University of Genoa, for support in substrate preparation and Prof. Sergio Thea, Dr. Chiara Natale of the Chemistry Department of University of Genoa, for the synthesis of gold particles.

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Work supported by the Italian Ministry t of University and Scientific and Technological Research (National Research Program m Physical properties and interfacing of single-electron devices for quantum computing”) and by the national Research Council (Grant “Nanoarchitetture organiche per l’elettronica e paradigmi computazionali”).

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Ingram, R.S., Hostetler, M.J., Murray, R.W., Schaaff, T.G., Khoury, J.T., Whetten, R.L., Bigioni, T.P., Guthrie, D.K., and First, P.N., (1997) 28kDa alkanethiolate-protected Au clusters give analogous solution electrochemistry and STM Coulomb staircases, J. Am. Chem. Soc. 119, 9279-9280.

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Ohara, P.C., Leff, D.V., Heath, J.R. and Gelbart, W.M. (1995) Crystallization of opals from polydisperse nanoparticles, Phys. Rev. Lett. 75, 3466-3469.

9.

Burghard, M., Philipp, G., Roth, S., Von Klitzing, K., Pugin, R., and Schmid, G. (1998) Multilayered Langmuir –Blodgett films of thiol substituted ultrasmall gold clusters, Adv. Mater. 10, 842-845.

10. Chen, X.Y., Li, J.R., and Jiang, L. (2000) Two-dimensional arrangement of octadecylaminefunctionalized gold nanoparticles using the LB technique, Nanotechnology 11, 108-111. 11. Hostetler, M.J., Wingate, J.E., Zhong, C-J., Harris, J.E., Vachet, R.W., Clark, M.R., Londono, J.D., Green, S J., Stokes, J.J., Wignall, G.D., Glish, G.L., Porter, M.D., Evans, N.D., and Murray, R.W. (1998) Alkanethiolate gold clusters molecukles with core diameters from m 1.5 to 5.2nm: core and monolayer properties as a function of core size, Langmuir 14, 17-30. 12. Langmuir, I. and Schaefer V.J. (1938) J. Am. Chem. Soc. 60, 1351. 13. Harrell, L.E., Bigioni, T.P., Cullen, W.G., Whetten, R.L., First, P.N. (1999) Scanning tunneling microscopy of passivated Au nanocrystals immobilized on Au(111) surfaces, J. Vac. Sci. Technol B 17, 2411-2416.

AFM OF GUANINE ADSORBED ON HOPG UNDER ELECTROCHEMICAL CONTROL A.-M. CHIORCEA, A.M. OLIVEIRA BRETT l de Ciências e Tecnologia, Departamento de Química, Faculdade Universidade de Coimbra, 3004-535 Coimbra, Portugal

Abstract The characterisation of the adsorption mechanism of guanine on a highly oriented pyrolytic graphite (HOPG) electrode surface was carried out using in situ MAC Mode Atomic Force Microscopy (MAC Mode AFM) and the electrochemical t behaviour of the guanine layer was investigated with Electrochemical AFM. Guanine adsorbs spontaneously on the HOPG substrate as a stable molecular layer, covering the surface uniformly and almost completely. The adsorption of DNA at the HOPG surface was controlled by adjusting the potential of the HOPG electrode and electrochemical adsorption provides better attachment of the guanine at the electrode surface compared to natural adsorption. The characteristics of the adsorbed guanine films were dependent on the deposition time and on the electrochemical adsorption procedure. The film was dissolved by carrying out cyclic voltammetry between 0 and + 1.3 V, after which guanine started to readsorb freely on the clean HOPG surface. The guanine molecules were held together on the substrate mainly by non-covalent interactions such as hydrogen bonding, van der Waals and hydrophobic interactions.

1. Introduction Guanine is one of the constituent purine bases of nucleic acids. Together with the other purine, adenine, and the pyrimidine bases, thymine and cytosine, it forms the units of the DNA which transport genetic information. The structure of guanine, Fig. 1, assembled at solid surfaces has been examined using a variety of approaches [1-3]. Electrochemical studies showed that guanine oxidises irreversibly at the C8-H position by a two-step mechanism involving the loss of 4H+ and 4e- and leading to 8-oxoguanine, one of the oxidation products, which is also electroactive [4]. Guanine is more easily oxidised than the other DNA bases adenine, thymine and cytosine, as it has a lower oxidation potential for the same experimental conditions [5]. Electrochemical studies with guanine at concentrations near saturation led to the formation of dimers and trimers within the oxidation products, but the oligomers are difficult to detect due to the low solubility of guanine [6, 7]. Guanine adsorbates on solid surfaces have been studied at the molecular level using AFM and STM [8-10], but problems were encountered due to guanine’s weak interaction with the substrate. However, Magnetic AC mode AFM (MAC Mode AFM) is a technique that permits the visualisation of the molecules that are weakly bonded to the substrate material [11]. 467 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 467-473. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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O HN 1

6

7

4

9

N 8

2 3

H2N

5

N

N H

Figure 1. The chemical structure of guanine

MAC mode uses a solenoid placed under the sample to make a magnetically coated AFM cantilever oscillate near its resonant frequency. As it scans the sample, the AFM tip oscillates and touches the sample surface only at the bottom of this oscillation. Because there is no need to drive the cantilever holder, cantilever chip and solution as in tapping mode, control of cantilever movement increases considerably, which enables operation at smaller oscillation amplitudes, the lateral forces being better eliminated. This paper presents results from in situ MAC Mode AFM imaging, under electrochemically controlled conditions, of adsorbed guanine molecules at the highly oriented pyrolytic graphite (HOPG) electrode.

2. Experimental Materials. Guanine was purchased from Sigma Chemical Co. and was used without further purification. The supporting electrolyte used was pH 4.5 0.2 M acetate buffer solution and was prepared using analytical grade reagents and purified water from a Millipore Milli-Q system (conductivity < 0.1 µS cm-1). Guanine was dissolved directly in buffer solution, and a concentration of 10-3 M in the supernatant was obtained in saturated solutions [12]. Highly oriented pyrolytic graphite (HOPG), grade ZYH, of rectangular shape with 15 x 15 x 2 mm dimensions, from Advanced Ceramics Co., UK, was used as substrate. The HOPG was freshly cleaved with adhesive tape prior to each experiment and was imaged by Contact Mode AFM in order to establish its cleanliness. Apparatus. AFM was performed with a Pico SPM controlled by a MAC Mode module and interfaced with a PicoScan controller from Molecular Imaging Co., USA. All the experiments were performed with a CS AFM S scanner with the scan range 6 µm in x-y and 2 µm in z directions. Electrochemical control was carried out with a potentiostat/galvanostat PicoStatTM. Silicon type II MAClevers 225 µm length, 2.8 N m-1 spring constant and 27-30 kHz resonant frequencies in liquid (Molecular Imaging Co.) were used. All images (256 samples/line x 256 lines) were taken at room temperature, at a scan rate of 1.95 lines s-1. The images were processed by flattening in order to remove the background slope and the contrast and brightness were adjusted. Both Atomic Force Microscopy and voltammetric experiments were carried out in a one-compartment Teflon cell of approximately 12.5 mm internal diameter holding the HOPG sample – the working electrode – on the base. A Pt wire counter electrode and a Ag wire as quasi-reference electrode were placed in the cell, dipping approximately 5 mm into the solution. All images were visualised three-dimensionally using the Scanning Probe Image Processor SPIP, version 2.3011, Image Metrology ApS. Origin (version 6.0) from Microcal Software was used for the presentation of the experimental voltammogram reported in this work.

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Sample preparation. For the guanine samples prepared by free adsorption 500 µl solution of guanine were placed in the AFM cell and the guanine was left to adsorb at the HOPG surface over periods from 5 min to 1h. For the guanine samples prepared under electrochemically controlled conditions the following procedure was carried out. The freshly cleaved HOPG was first examined by cyclic voltammetry in pH 4.5 0.2 M acetate buffer solution, with potential window from 0 to + 1.3 V (vs. Ag wire), in order to establish its cleanness. Then 5 successive cyclic voltammograms were registered in saturated guanine solution between 0 and + 1.3 V (vs. Ag wire), scan rate 0.1 V s-1, followed by the application of a positive potential of +0.75 V (vs. Ag wire) to the HOPG electrode during 5 min. The HOPG with guanine adsorbed by both immobilisation procedures was immediately imaged by in situ MAC Mode AFM.

3. Results and Discussion 3.1 FREE ADSORPTION OF GUANINE WITH THE ELECTROCHEMICAL CELL AT OPEN CIRCUIT The HOPG electrode was modified by a ffilm of guanine obtained by free adsorption from a saturated guanine solution at different adsorption times using the method described in the experimental section. The results, in 10-3 M saturated guanine in pH 4.5 0.2 M acetate buffer solution, indicate that the guanine molecules adsorb spontaneously on the HOPG surface and the AFM images obtained in situ reveal a good surface coverage. The adsorption of guanine molecules on the HOPG surface occurs very fast. After introducing the guanine solution into the electrochemical cell, the molecules immediately start to condense in small nuclei that appear as bright spots in the images, without forming a well packed structure. Afterr 5 min of free adsorption the molecules appeared condensed in small nuclei of 2–3 nm height and 20 to 40 nm diameter, covering the HOPG surface uniformly, Fig. 2A. Considering the dimensions of a guanine molecule these aggregates correspond to several hundred guanine molecules lying flat on the surface [9]. The effect of altering the time of exposure of the HOPG surface to guanine solution was investigated using periods from 5 min to 1 h and the guanine layer appears to reorganise over time. After an exposure of 1 h the MAC Mode AFM shows that the electrode surface is completely covered by a very thick film of guanine, Fig. 2B. The topography of the film shows nuclei of different sizes from 3 to 6 nm height and 20 to 40 nm diameter that are organised in clusters of approximately 100 nm diameter. The molecules are stabilised on the HOPG surface by hydrophobic interactions between the hydrophobic aromatic rings of the guanine molecules and the hydrophobic carbon surface. Performing one cyclic voltammogram from 0 to + 1.3 V (vs. Ag wire), scan rate 0.05 V s-1, the guanine layer starts to dissolve byy forming small pits inside the guanine layer with dimensions of approximately 30 nm diameter and 1−3 nm deep, Fig. 2C. After 5 min of successive cyclic voltammograms the film dissolves completely, Fig. 2D, showing an almost clean HOPG surface.

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Figure 2. In situ MAC Mode AFM topographical images of the guanine layer, in a solution of 10-3 M saturated guanine in pH 4.5 0.2 M acetate buffer, prepared by free adsorption onto HOPG. (A) 5 min free adsorption and (B) 1 h free adsorption. (C) After one cyclic voltammogram from 0 to + 1.3 V (vs. Ag wire), scan rate 0.05 V s-1, the guanine layer starts to dissolve. (D) The film is completely removed after 5 min of successive cyclic voltammograms.

3.2 ELECTROCHEMICAL DEPOSITION - THE INFLUENCE OF THE HOPG POTENTIAL IN THE PROCESS OF GUANINE ADSORPTION The electrochemical potential applied to the HOPG substrate influences the processes of nucleation and growth of the guanine adsorbates on the HOPG surface. The surface characteristics of the electrode modified by guanine according to the electrochemical procedure described in the experimental section was investigated. Guanine adsorbs freely on the surface at the moment of injection of the solution in the AFM cell. In order to induce desorption of the adsorbed guanine and clean the surface electrochemically, 5 cyclic voltammograms were performed in the saturated guanine solution between 0 and + 1.3 V (vs. Ag wire), scan rate 0.1 V s-1. Subsequently, the HOPG was held for 5 min at the positive potential of +0.75 V (vs. Ag wire), which corresponds to the oxidation potential of guanine. The guanine molecules condensed into larger nuclei of 90–150 nm diameter and 10–30 nm height, Fig. 3. The nuclei appear grouped together in intercalated polymer-like chains of many different lengths, some longer than 1 µm, uniformly distributed over the HOPG surface, Fig. 4A.

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Figure 3. In situ MAC Mode AFM topographical images of the guanine layer, in the solution of 10-3 M saturated guanine in pH 4.5 0.2 M acetate buffer, on HOPG.

Figure 4. Sequence of 3 consecutive MAC Mode AFM topographical images obtained in situ in 10-3 M saturated guanine in pH 4.50 0.2 M buffer acetate solution and showing the dissolution of the guanine film. The images were taken (A) before, (B) during and (F) after performing one cyclic voltammogram that induced desorption of the guanine layer. The cyclic voltammogram from 0 to + 1.3 V (vs. Ag wire), scan rate 0.1 V s-1, was performed inside the AFM cell during scanning (B).

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Guanine oxidation can induce the formation of dimers and trimers at the HOPG electrode [6, 7]. The guanine molecules are stacked at the surface together with guanine oligomers, forming a complex polymer chain. All the components interact between themselves and with the HOPG surface by hydrogen bonding, van der Waals forces, and hydrophobic interactions. The stability of the guanine film obtained during controlled oxidation was very much enhanced when compared with spontaneous condensation, due to the electrostatic interaction of guanine rings with the positively charged HOPG surface. The cyclic voltammogram in the saturated guanine solution, Fig. 4B, shows a peak at + 0.76 V (vs. Ag wire) which corresponds to the oxidation reaction of guanine. During the cyclic voltammetric scan it was observed that the guanine layer was stable between 0 and + 0.75 V (vs. Ag wire). Increasing the potential led to abrupt changes in the guanine film. The products of oxidation of guanine are 8-oxoguanine and guaninedimers [6]. The 8-oxoguanine is oxidised at lower potentials and the oxidation products are hydrolysed and go to the solution. At approximately + 0.9 V all polymer-like chains completely disappeared, only the strongly adsorbed guanine-dimers remaining adsorbed at the electrode surface, Fig. 4C. After the film was dissolved by carrying out cyclic voltammetry the guanine layer began to grow immediately again by spontaneously adsorption, the undissolved guanine-dimers serving as nucleation centres. After approximately 30 min the guanine layer was completely reformed, Fig. 5.

Figure 5. In situ MAC Mode AFM topographical images obtained in the solution of 10-3 M saturated guanine in pH 4.50 0.2 M acetate buffer showing reconstruction of the guanine layer after approximately 30 min free adsorption.

4. Conclusion The process of adsorption of guanine at the HOPG surface can be controlled by the applied potential and the electrochemical deposition method provides better attachment of the molecules at the HOPG surface compared to passive adsorption. The characteristics of the guanine layer and the apparent height of the film depend on the applied potential. The guanine is adsorbed onto the HOPG surface only by non-covalent interactions such as hydrogen bonding, electrostatic, van der Waals and hydrophobic interactions. MAC Mode AFM in an electrochemically controlled environment is capable of showing in situ the surface morphological structure of guanine adsorbates and may

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contribute to the understanding of the mechanism of adsorption and the nature of the guanine-electrode surface interaction.

Acknowledgements Financial support from Fundação para a Ciência e Tecnologia (FCT), Ph.D. grant PRAXIS XXI/ BD/ 19728/99 (A.-M. C.), POCTI (co-financed by the European Community Fund FEDER) ICEMS (Research Unit 103) and European Projects ERBICT15-CT960804 and QLK3-2000-01311 are gratefully acknowledged.

References 1.

Sowerby, S.J., Edelwirth, M. and Heckl, W.M. (1998) Self-assembly at the prebiotic solid-liquid interface: Structures of self-assembled monolayers of adenine and guanine bases formed on inorganic surfaces, J. Phys. Chem. B 102, 5914-5922. 2. Tao, N.J., Shi, Z. (1994) Monolayerr guanine and adenine on graphite in NaCl solution: A comparative STM and AFM study, J. Phys. Chem. 98, 1464-1471. 3. Oliveira-Brett, A.M., Brett, C.M., Silva, L.A. (2002) An impedance study of the adsorption of nucleic acid bases at glassy carbon electrodes, Bioelectrochemistry 56 (1-2), 33-35. 4. Brett, C.M.A., Oliveira Brett, A.M., Serrano, S.H.P. (1994) On the adsorption and electrochemical oxidation of DNA at glassy carbon electrodes, J. Electroanal. Chem. 366, 225-231. 5. Oliveira Brett, A.M., Serrano, S.H.P., Piedade, J.A.P. (1999) Electrochemistry of DNA, in: R.G. Compton, G. Hancock (eds.), Comprehensive Chemical Kinetics, vol. 37, Elsevier, Amsterdam, cap. 3, pp. 91-199. 6. Oliveira-Brett, A.M., Diculescu, V., Piedade, J.A. (2002) Electrochemical oxidation mechanism of guanine and adenine using a glassy carbon microelectrode, Bioelectrochemistry 55 (1-2), 61-62. 7. Subramanian, P., Dryhurst, G. (1987) Electrochemical oxidation of guanosine - formation of some novel guanine oligonucleosides, J. Electroanal. Chem. 224, 137-162. 8. Heckl, W.M., Smith, D.P.E., Binning, G., Klagges, H., Hansch, T.W. and Maddocks, J. (1991) Twodimensional ordering of the DNA base guanine observed by scanning tunneling microscopy, Proc. Natl. Acad. Sci. USA 88, 8003-8005. 9. Tao, N.J., DeRose, J.A., Lindsay, S.M. (1993) Self-assembly of molecular superstructures studied by in situ scanning tunneling microscopy: DNA bases on Au (111), J. Phys. Chem. 97, 910– 919. 10. Tao, N.J., Shi, Z. (1994) Potential induced changes in the electronic states of monolayer guanine on graphite in NaCl solution, Surf. Sci. Lett. 301, 217-223. 11. Han, W., Lindsay, S.M., Jing, T.W., (1996) A magnetically driven oscillating probe microscope for operation in liquids, Appl. Phys. Lett. 69, 4111-4113. 12. Oliveira Brett, A.M., Matysik, F.-M. (1997) Sonoelectrochemical studies of guanine and guanosine, Bioelectrochemistry and Bioenergetics 42, 111-116.

DYNAMICS IN MODEL MEMBRANES AND DNA-MEMBRANE COMPLEXES USING TEMPERATURE CONTROLLED ATOMIC FORCE MICROSCOPY

Z.V. LEONENKO, D.T. CRAMB Department of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada [email protected]

Abstract In this paper we review our recent work studying biomolecular self-assembly using temperature controlled atomic force microscopy. In particular, we examined supported planar bilayers (SPBs), DNA-SPBs complexes, and their transitions during heating the system above the melting transition temperature. 1. Introduction The invention of atomic force microscopy has proven to be invaluable to the study of so-called “soft” biological samples1. Single macromolecules, like DNA and proteins as well self – assembled structures, like lipid membrane can be directly visualized by AFM. Based on Van der Waal’s interactions between the sample and scanning probe, AFM has overcome the restrictions of STM for studying nonconductive samples, allowing the study biomolecules in their native liquid environment. In particular, the imaging of such “soft” samples has benefited from Tapping Mode or oscillating mode 24 , where the probe oscillates, driven acoustically or magnetically. The oscillating probe makes only intermittent contact with the sample, m and minimizes shear forces, which in contact mode AFM can cause sample damage or displacement. In this mode, changes in amplitude and phase shift of the oscillating probe can be measured. Monitoring of the changes in oscillation amplitude produces topographic information. The differences in phase between the input and output oscillations upon interaction with the sample surface can give information about differences in chemical (hydrophobic or electrostatic) and mechanical (elastic) properties of the sample surface at the nanometer scale.

2. Materials and Methods We investigated several different kinds of phospholipids: 1,2-Dioleoyl-sn-Glycero-3Phosphocholine (DOPC), 1,2-Dipalmitoyl-sn-Glycero-3-Phosphocholine (DPPC), 1,2Dioleoyl-sn-Glycero-3-Phosphoethanolamine (DOPE), 1,2-Dipalmitoyl-sn-Glycero-3475 P.M. Vilarinho et al. (eds. ), Scanning probe Microscopy: Characterization, Nanofabrication, and Device Application of Functional Materials, 475-483. © 2005 Kluwer Academic Publishers. Printed in the Netherlands.

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Phosphoethanolamine (DPPE), 1,2Dioleoyl-3-Trimethylammonium-Propane (DOTAP), 1,2- Dipalmitoyl-3-Trimethylammonium-Propane (DPTAP). DOTAP and DPTAP are positively charged lipids, DOPE, DPPE, DOPC are neutral zwitterionic lipids. Phospholipids DOPC, DPPC (lyophilized or in chloroform solution), DOPE, DPPE, DOTAP (chloroform solution), and DPTAP were purchased from Avanti Polar Lipids Inc., Alabaster, AL and were used without further purification. Tris-EDTA (TE), phosphate buffer and distilled, Nanopure water were used in the preparation of all vesicles and DNA solutions. Freshly cleaved ASTMV-2 quality, scratch-free ruby mica (Asheville-Schoonmaker Mica Co., Newport News, VA) was used as the solid support. The 14 base pair oligonucleotide (ODN) (ATATAAATTTATAT) was obtained, desalted, from UCDNA services (University off Calgary, AB). The longer 1000 base pair DNA was calf thymus (Sigma), type II, fragmented by ultra-sonication. In our work, we employed MAC (magnetic A/C) mode, where the magnetically coated probe oscillates near its resonant frequency driven by an alternating magnetic field. All images were taken using a Pico SPM microscope with an AFMS-165 scanner (Molecular Imaging Inc., Phoenix, Az.). Au-Cr coated Maclevers® (Molecular Imaging Inc., Phoenix, Az.) were used for MAC mode imaging. Their specifications are: length 85 µm, force constant 0.5 N/m and resonant frequency 38-40 kHz in water. The standard MAC mode fluid cell (Molecular Imaging) was used throughout. The scanning speed was 2-3 lines per second. The height scale was calibrated using colloidal gold spheres of well-defined size5. For elevated temperature experiments the AFM Temperature Controller and Hot Mac Mode Stage from Molecular Imaging Inc., were used. Temperature was varied from 22 to 70 °C, with a 1 °C per minute ramp. For our AFM experiments we formed supported planar bilayers on mica by method of vesicle fusion. When sonicated, lipid bilayers spontaneously form closed spherical structures, called vesicles or liposomes. We apply vesicle solution to the mica support and when vesicles adsorb to the mica they fuse and form a planar supported bilayer. In some cases mica was modified with APTES (2-aminopropyltriethoxysilane) and PLL (poly-L-lysine). We also used Mg2+ ions as binding bridges between DNA and regular mica. Supported planar bilayers were prepared for AFM imaging by method of vesicle fusion6-7. Aliquots of liposome solution were deposited on modified or unmodified freshly cleaved mica. After a controlled period of time the mica was gently rinsed with ultrapure water. Solutions of DNA (100-200 µL, 2 – 1000 µg/mL) were pipetted onto the wet phospholipid bilayer surface and were left to incubate at 4oC for 1- 24 hours. The excess DNA was gently rinsed away and the surface was imaged under water in the liquid cell, at room temperature t and at various higher temperatures.

3. Results and Discussions Supported planar phospholipid bilayers are widely used as a model for studying biological membranes. Supported planar bilayers (SPBs) are composed of phospholipids adsorbed to a planar hydrophilic solid support. In water environment most phospholipids spontaneously form bilayer structures t hiding hydrophobic tails inside and pointing hydrophilic heads outside the bilayer - water interface. Understanding the physical and chemical properties of SPBs is critical to our understanding of membrane structure-function relationships. Model membranes are also good candidates for

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nanotechnology applications in nanosensor development. They can serve as a template for the incorporation of proteins and receptors and reduce non-specific interactions. In the following sections, we present our results on supported phospholipid bilayers (SPB) and structural changes in SPB and SPB-DNA complexes during transition above melting transition temperature (Tm)8-10. 3.1. SUPPORTED PLANAR BILAYER AND VESICLES ON MICA. Using MAC-mode AFM, we examined the process of supported planar bilayer preparation on mica via vesicle fusion7, Figure 1 a) shows disk-like surface features associated with single DOPC vesicle deposition. In the Figure 1 b) a complete bilayer was formed. Interestingly, this bilayer developed defects that were found to be quite dynamic in nature and allowed us to measure the bilayer thickness.

a

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Figure 1. A three-dimensional rendering of the AFM topography image of pure DOPC vesicles on APTES modified mica surface in aqueous solution, a), DOPC supported planar bilayer, b).

3.2. INTRODUCTION TO DNA-CATIONIC LIPID INTERACTIONS. Positively charged or Cationic Lipids (CL) are promising as gene delivery vehicles. They can deliver gene material to the cell and can be targeted to a specific tissue. There are several advantages to using liposomes over other drug delivery systems, the major being nontoxicity11. The process of gene delivery includes lipoplex formation between DNA and cationic lipids. The mechanism by which genetic material is delivered to the nucleus is not entirely clear. Moreover, despite their promise as gene transfer reagents, the phase dependence of DNA-cationic lipid interactions has not been extensively studied at the single molecule level. The formation and stability of the lipoplexes depend on many factors; examples of which are the type of helper lipids12, and the solvent environment. Several recent studies have investigated phospholipid - DNA interactions in solution13-19. However, AFM can be a powerful tool to study DNA interaction and complex formation at the surface of a supported phospholipid bilayer. There have been only a few studies using AFM to examine DNA on supported cationic

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bilayers, using gel phase bilayers20-21. Using fluid phase bilayers, we hope to elucidate stages in the process of complexation at the single DNA level in a real time. Clearly, there is a considerable challenge in using AFM to study DNA on supported planar bilayers in the liquid phase because of fluidity of bilayer. Such bilayer systems are challenging for current AFM technology, since they are soft and dynamic. However, because of their ease of deformation, fluid bilayers must be very sensitive to the presence of DNA and may easily respond to perturbations caused by adsorbed DNA and serve as a good model system to study DNA-CL lipoplex formation. 3.3. DNA ADSORPTION ON MICA. Since DNA in TE buffer solution does not bind to regular mica (negative surface charge), the surface was modified with APTES or PLL (positive surface charge). We also used Mg2+ ions as binding bridges between DNA and regular mica22,23. A height of 2.0 ± 0.2 nm was measured for 14 base pair ODN on mica. Small DNA appear as flat ovoids, due to the convolution of the tip radius (~10–40 nm) onto the surface feature. This results in the width of the DNA being overestimated. The height measurements, however, are not limited by the tip radius and give a better representation of the true DNA diameter on a solid surface. Our data for large DNA adsorbed on solid mica surface give a height of 2.0 ± 0.1 nm. Without surface modification or use of Mg2+, no DNA was observed to bind. Figure 2 shows topography images of DNA adsorbed on mica surface imaged by MAC mode AFM in a liquid cell.

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Figure 2. 14 basepair oligodeoxynucleotides (double stranded) on APTES-modified mica, a). 3000 base pair 2+ linearized plasmid DNA bridged onto mica by Mg , b).

3.4. DNA ADSORPTION ON SUPPORTED PLANAR BILAYER. The same DNA were applied to the bilayer surface8 – Figure 3. Figure 3. (a) Solution of (2 mg/ml) 14 base pair DNA was exposed to a DOTAP/DOPE SPB for 30 minutes and then gently rinsed, the oligodeoxynucleotide was found to associate with the surface. The height of 14 base pair DNA on the supported planar bilayer is 1.3 ± 0.2 nm.

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Figure 3. 14 basepair oligodeoxynuleotides adsorbed onto a DOTAP/DOPE supported bilayer, a). 1000 base pair linearized plasmid DNA adsorbed on a DOTAP/DOPE supported bilayer, b). 1000 base pair linearized plasmid DNA adsorbed onto a DOTAP/DOPC supported bilayer, c). Image scale 1500 nm.

Adsorption of 14 base pair DNA does not appear to disturb the bilayer. Only a few defects were observed after removal of the excess of DNA from the cell. This effect is comparable to rinsing the sample cell with buffer solution containing no DNA. (b) 1000 base pair DNA adsorption onto DOTAP/DOPE changed the bilayer dramatically. Large DNA strips bilayer from the surface changing the structure of bilayer, we observed aggregate formation, which were a double bilayer thick. When negatively charged DNA adsorbs to the bilayer it interacts preferentially with positively charged DOTAP lipids, possibly causing demixing of lipids in a fluid DOTAP/DOPE bilayer. As a result of this demixing process regions of pure DOTAP and DOPE are formed. Pure DOPE readily transforms to a hexagonal phase and causes wrapping of a bilayer around DNA forming big aggregates, which can be easily detached from the surface. In a control experiment, when DNA-free (TE) buffer solution was applied to supported bilayer, no bilayer removal was observed. (c) In order to assess the role off the helper lipid, DOPE on the above-mentioned behaviour, we examined the effectt of DNA adsorption to a binary system with a different zwitterionic helper lipid, DOPC. The addition of DNA to the supported DOTAP/DOPC bilayer shows adsorption of DNA at the bilayer surface and partially removes a bilayer from mica, but not as severely as it does for DOTAP/DOPE. No changes of bilayer thickness were observed. Statistical analysis of our data on the height of DNA adsorbed on a fluid phase SPB gives 0.8 - 1.5 nm8. Resolution and the height of DNA were also low, likely due to the partial penetration of DNA into the fluid phase bilayer. To elucidate the reason for low contrast and height of DNA we formed the complex of DNA on a gel phase mixed DPTAP/DPPE bilayer9. Upon heating the SPB above Tm, it will become analogous to DOTAP (or DOTAP/DOPE). In this case DNA can be clearly seen and the height of DNA is similar to that observed on solid support, Figure 4 (a).

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Figure 4. Heating supported mixed DPTAP/DPPE bilayer with adsorbed DNA: a) room temperature, 22°C; b) heating to 50°C; c) cooling back to room temperature, 23°C. Image scale 850 nm.

Heating the complex of DNA on the DPTAP/DPPE bilayer shows that the contrast and resolution of DNA adsorbed on the bilayer were lost at elevated temperature (data not shown). After slow cooling, the contrast t and resolution of DNA were restored. In the fluid phase bilayer DNA can easily penetrate into the head group area of bilayer, which leads to low resolution and height. In a mixed DPTAP/DPPE bilayer, additional to the changes in height and resolution of DNA we observed structural changes in the bilayer9, Figure 4. DNA, initially adsorbed on the higher domains after bilayer melting DNA was found on the lower domains, while higher domains did not contain DNA. We assume that during bilayer melting the demixing of lipids occurs and DNA appear at the lower (DPTAP enriched domains), and (DPPE enriched) higher domains do not contain DNA. 3.5. PHASE TRANSITIONS IN SPB AND DNA-SPB COMPLEXES. An understanding of structure-function relations of biomembranes ultimately relies on knowledge of the properties of lipid bilayers. The complex structural dynamics of membranes is related to specific membrane functions. Such structural parameters as average interfacial area per lipid, bilayer thickness and disorder of hydrophobic tails are very important for understanding intermolecular interactions in membranes. All these membrane parameters change during phase transition. The phase behaviour is dominated by the main L - L (gel-fluid) phase transition. In gel phase, hydrophobic tails are more ordered and the mobility of lipids is reduced. In fluid phase hydrophobic tails are very flexible and disordered, which decreases the bilayer thickness. A gel phase bilayer can be easily transformed to the fluid phase by melting a bilayer above melting transition temperature. Below the main transition, a basic equilibrium structure is the gel - subgel (crystalline) Lc phase24. A large number of intermediate stable, metastable, and transient lamellar gel structures are adopted by different lipids24 – with perpendicular or tilted chains, with interdigitated or partially interdigitated chains. We observed several phase transitions in the DPPC gel phase bilayer upon heating and cooling back to room temperature, Figure 5. During heating of the DPPC bilayer, a broad main transition was observed at 42-50°C. Dynamic coexistence of 2 domains was observed during this temperature interval. Further increase in temperature leads to formation of lower domains with this additional transition complete at 60°C. The second transition is likely attributed to the formation of fluid disordered phase formation, possibly with

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interdigitated lipid chains. Slow cooling the system back restores bilayer reversibly to the initial thickness - Figure 5.

a

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f

Figure 5. The AFM topography images showing phase transition in DPPC bilayer in liquid cell upon heating and cooling back. A heating DPPC bilayer: a) room temperature, 22°C; b) heating to 50°C; c) heating to 52°C, d) heating to 54°C, e) heating to 60°C, f) cooling back to 54°C. Image scale 1500 nm.

Phase transitions in a mixed DPTAP/DPPE bilayers are interesting in that we observed irreversible changes9. The supported bilayers formed from water solutions were planar, contained defects and elevated regions (domains) – Figure 6. The difference in the thickness of the two domains was 1.7 nm. The difference here is likely due to domains rich in DPPE versus domains rich in DPTAP. DPPE is known to have a thickness of 6 nm. Whereas an annealed DPTAP supported bilayer has been observed to have a thickness between 4 and 5 nm. The two lowest domains in Fig 6 could be domains in the enriched DPTAP bilayer similar to those observed by Longo and coworkers with difference between two domains being 1.4 nm10. We observe the difference in two lower domains being 1.2-1.4 nm and assume that they could appear during non-equilibrium bilayer formation by vesicle fusion, because the vesicle solution was preheated during sonication. After heating bilayer to 70°C we observe that domains and defects disappear and the surface was covered with a flat bilayer with only few small defects.

482

a

b

c

Figure 6. Heating supported mixed DPTAP/DPPE bilayer, formed from water vesicle solution: a) room temperature, 22°C, b) heating to 70°C, c) cooling back to room temperature, 23°C. Image scale 800 nm.

After cooling the system back to room temperature, we observed a redistribution of the domains. We observed the formation of only two domains (5.5 nm and 4.0 nm) in addition to defect formation. This is suggestive again of the formation of DPPE rich and DPTAP rich bilayer areas, respectively. Various experimental and theoretical studies have suggested the existence of domains in both biological and model membranes25. Nonequilibrium domain formation, which offers local geometrical environment for membrane processes, may be of considerable importance for the functionality of biological membranes.

4. Conclusions Here we demonstrated that atomic force microscopy is a powerful method to investigate phase transitions in phospholipid bilayers and structural transformations in macromolecular membrane complexes. During dynamic processes, temperature control AFM can provide additional information and insight into membrane behaviour. For example, we believe that melting a complex of gel phase bilayer with DNA provides a reproducible way to form and image by AFM complex of DNA adsorbed on a fluid phase bilayer, which is very challenging for current AFM techniques. By choosing appropriate phospholipids, which may interact with DNA in the fluid phase, it can be possible to observe and control the process of complexation.

Acknowledgement This research has been financially supported by NSERC, ACB and the University of Calgary. We thank the staff at Molecular Imaging for their continued support.

References 1. Morris, V.J., Kirby A.R., and Gunning A.P. (2001) Atomic force microscopy for Biologists, Imperial College Press, London. 2. Han, W., Lindsay, S.M., and Jing, T.A (1996) Magnetically driven oscillating probe microscope for operation in liquids, Appl. Phys. Lett. 69, 1-3.

483 3. Han, W. and Lindsay, S.M. (1998) Probing molecular ordering at a liquid-solid interface with a magnetically oscillated atomic force microscope, Appl. Phys. Lett. 72, 1656-1658. 4. Fasolka, M.J., Mayes, A.M. and Magonov, S.N. (2001) Thermal enhancement of AFM phase contrast for imaging diblock copolymer thin film morphology, Ultramicroscopy 90, 21-31. 5. Vesenka, J., Manne, S., Giberson, R., Marsh, T., and Henderson, E. (1993) Colloid gold particles as an incompressible atomic force microscope imaging standard for assessing the compressibility of biomolecules, Biophys. J. 65, 992-997. 6. Brian, A.A. and McConnell, H.M. (1984) Allogenic stimulation of cytoxic T cells by supported planar membranes, Proc. Natl. Acad. Sci. U.S.A. 81, 6159-6163. 7. Leonenko, Z.V., Carnini, A., and Cramb, D.T. (2000) Supported planar bilayer formation by vesicle fusion: the interaction of phospholipid vesicles with surfaces and the effect of gramicidin on bilayer properties using atomic force microscopy, Biochim. Biophys. Acta. 1509, 134-147. 8. Leonenko, Z., Merkle, D., Lees-Miller, S.P. and Cramb, D. (2002) Lipid Phase Dependence of DNA Cationic Phospholipid Bilayer Interactions examined using Atomic Force Microscopy, Langmuir, 18, 48734884. 9. Leonenko, Z. and Cramb, D. (2002) Effect of DNA adsorption on the phase cycling of a supported phospholipid bilayer, Nanoletters, 2, 305-309. 10. Leonenko, Z.V., Ma, H., Dahms, T.E.S., and Cramb, m D.T., (2004) Investigation Of Temperature Induced Phase Transitions In DOPC And DPPC Phospholipid Bilayers Using Temperature-Controlled Scanning Force Microscopy, Biophys. J. (in press). 11. Sorgi F.L. and Huang, L. (1997) Drug delivery applications, In Lipid polymorphism and membrane properties. Current Topics in Membranes. 44, 449-475. 12. May, S., Harris, D., and Ben-Shaul, A. (2000) The Phase Behavior of Cationic Lipid-DNA Complexes, Biophys. J. 78, 1681-1697. 13. Koltover, I., Salditt, T., Rädler, J.O., and Safinya, C.R. (1998) An inverted hexagonal phase of cationicDNA complexes related to DNA release and delivery”, Science. 281, 78-81. 14. Rädler, J.O., Koltover, I., Jamieson, A., Salditt, T., and Safinya, C.R. (1998) Structure and interfacial aspects of self-assembled cationic lipid-DNA gene carrier complexes, Langmuir. 14, 4272-4283. 15. Wong, F.M.P., Reimer, D.L., and Bally, M.B. (1996) Cationic lipid binding to DNA: characterization of complex formation, Biochem. 35, 5756-5763. 16. May, S. and Ben-Shaul, A. (1997) DNA-lipid complexes: stability of honeycomb-like and spaghetti-like structures, Biophys. J. 73, 2427-2440. 17. Dan, N. (1998) The structure of DNA complexes with cationic liposomes-cylindrical or lamellar?, Biochim. Biophys. Acta. 1369, 34-38. 18. Wagner, K., Harries, D., May, S., Kahl, V., Radler, J. O., and Ben-Shaul, A. ( 2000 ) Counterion release upon cationic lipid-DNA complexation, Langmuir.16, 303-306. 19. Dan, N. (1997) Multilamellar structures of DNA complexes with cationic, liposomes Biophys. J. 73, 1842-1846. 20. Mou, J., Czajkowsky, D.M., Zhang, Y., and Shao, Z. (1995) High Resolution Atomic Force Microscopy of DNA: the pitch of the double helix, FEBS Lett. 371, 279-282. 21. Fang, Y. and Yang, J. (1997) Effect of Cationic Strength and Species on 2-D Condensation of DNA, J. Phys. Chem. B 101, 3453-3456. 22. Hansma H. G. and Laney, D. E. (1996) DNA binding to mica correlates with cationic radius: assay by atomic force microscopy, Biophys. J. 70, 1933-1939. 23. Han, W., Dlakic, M., Zhu, Y.J., Lindsay, S.M., and Harrington, R.E. (1997) Strained DNA is kinked by 2+ low concentrations of Zn , Proc. Natl. Acad. Sci. U.S.A. 94, 10565-10570. 24. Tenchov, B., Koynova, R., and G.Rapp, (2001) New ordered metastable phases between the gel and subgel phases in hydrated phospholipids, Biophys. J. 80, 1873-1890. 25. Kinnunen, P.K.J. and Mouritsen, O.G., (1994) Special Issue of Functional Dynamics of Lipids in Biomembranes, Chem. Phys. Lipids, 73, 1-2.

INDEX OF KEYWORDS

Part I – Fundamentals of Functional Materials FUNCTIONAL MATERIALS, P. VILARINHO Keywords: Dielectrics, piezoelectrics, pyroelectrics, ferroelectrics, ferroelectrics, relaxor ferroelectrics, preparation, properties, applications.

incipient

SCALING OF SILICON-BASED DEVICES TO SUBMICRON DIMENSIONS, A.I. KINGON Keywords: Scaling, silicon-based microelectronics, nanoelectronics, functional electronics, new materials. UNSOLVED PROBLEMS IN FERROELECTRICS FOR SCANNING PROBE MICRSOCOPY, J.F. SCOTT Keywords: Ferroelectric thin films, lead zirconate titanate (PZT), hafnia, zirconia, strontium bismuth tantalite, strontium titanate/barium titanate superlattices, Fe-RAM, DRAM Part II – Fundamentals of Scanning Probe Techniques PRINCIPLES OF BASIC AND ADVANCED SCANNING PROBE MICROSCOPY, D.A. BONNELL, R. SHAO Keywords: Scanning probe microscopy, multiple modulation, spatial resolution, complex materials, molecular wires, ferroelectric domains. NANOSCALE PROBING OF PHYSICAL AND CHEMICAL FUNCTIONALITY WITH NEAR-FIELD OPTICAL MICROSCOPY, L.M. ENG Keywords: Near-field optical microscopy, organic and inorganic materials, microscopical and sensoric applications NANOSCALE ELECTRONIC MEASUREMENTS OF SEMICONDUCTORS USING KELVIN PROBE FORCE MICROSCOPY, Y. ROSENWAKS AND R. SHIKLER Keywords: Kelvin probe force microscopy, semiconductor GaP, minority-carrier diffusion length, potential distribution EXPANDING THE CAPABILITIES OF THE SCANNING TUNNELING MICROSCOPE, K.F. KELLY, Z.J. DONHAUSER, B.A. MANTOOTH, AND P.S. WEISS Keywords: Scanning tunneling microscopy, semiconductors, dopant profiling, advanced image processing techniques

485

486

FUNCTIONS OF NC – AFM ON ATOMIC SCALE, S. MORITA, N. OYABU, T. NISHIMOTO, R. NISHI, O. CUSTANCE, I. YI, Y. SUGAWARA Keywords: Noncontact atomic force microscope, atomic force mechanisms, threedimensional mapping tool, atom manipulation tool

Part III – Application of Scanning Tecnhiques to Functional Materials SCANNING PROBE MICROSCOPY OF PIEZOELECTRIC AND TRANSPORT PHENOMENA IN ELECTROCERAMIC MATERIALS, S.V. KALININ AND D.A. BONNELL Keywords: Scanning Probe Microscopy, electronic ceramic materials, ZnO, Nb-doped SrTiO3, BaTiO3, BiFeO3, transport properties, electric phenomena, ferroelectric domain structure SFM-BASED METHODS FOR FERROELECTRIC STUDIES, A. GRUVERMAN Keywords: Scanning force microscopy, piezoresponse force microscopy, ferroelectrics, films, domain imaging, polarization mechanism SCANNING TUNNELING SPECTROSCOPY. Local density of states and spin distribution of interacting electron systems, M. MORGENSTERN Keywords: Scanning tunneling spectroscopy, electron t systems in InAs, domains in ferro-magnetic particles. NANOINSPECTION OF DIELECTRIC AND POLARIZATION PROPERTIES AT INNER AND OUTER INTERFACES IN FUNCTIONAL FERROELECTRIC PZT THIN FILMS, L.M. ENG Keywords: piezoresponse force microscopy, Kelvin probe force microscopy, pull-off force spectroscopy, PZT thin films, polarization profile, local dielectric properties MICROSCALE CONTACT CHARGING ON A SILICON OXIDE, S. MORITA, T. UCHIHASHI, K. OKAMOTO, M. ABE, Y. SUGAWARA Keywords: Electrostatic force microscopy, noncontactt atomic force microscopy, Kelvin probe force microscopy, silicon oxide, GaAs, contact charging, charge distribution CONSTRUCTIVE NANOLITHOGRAPHY, S.R. COHEN, R. MAOZ, AND J. SAGIV Keywords: Scanning Probe Microscopy, constructing nanolithography, self-assembled monolayers (SAMs), silane-based SAMs NANOMETER-SCALE ELECTRONICS AND STORAGE, K.F. KELLY, Z.J. DONHAUSER, P.A. LEWIS, R.K. SMITH, AND P.S. WEISS Keywords: Scanning tunneling microscopy (STM), self-assembly techniques, alkanethiolate SAMs, nanoscale electronic devices

487

Part IV – Contributed papers STM TIPS FABRICATION FOR CRITICAL DIMENSION MEASUREMENT, A.PASQUINI, G.B.PICOTTO, M. PISANI Keywords: Fabrication, STM tips, Tungsten (W), electrochemical reaction SCANNING PROBE MICROSCOPY CHARACTERIZATION OF FERROELECTRICS DOMAINS AND DOMAINS WALLS IN KTiOPO4, C. CANALIAS, R. CLEMENS, J. HELLSTRÖM, F. LAURELL, J. WITTBORN, H. KARLSSON Keywords: Scanning probe microscopy, inverse piezoelectric effect, KTiOPO4, ferroelectric domains, domain imaging, single crystals and waveguides. IMAGING LOCAL DIELECTRIC AND MECHANICAL RESPONSES WITH DYNAMIC HETERODYNED ELECTROSTATIC FORCE MICROSCOPY, D. R. OLIVER, K.M. CHENG, A. PU, D.J. THOMSON AND G.E. BRIDGES Keywords: scanning probe microscopy, electrostatic force microscopy, polarization dynamics, nanotechnology, micro-electro-mechanical systems. AFM PATTERNING OF SrTiO3-δ THIN FILMS AND DEVICE APPLICATIONS, L. PELLEGRINO. Keywords: Atomic Force Microscope, conducting SrTiO3-δ thin films, functional electronics conducting element. NANOSCALE INVESTIGATION OF A RAYLEIGH WAVE ON LiNbO3, J. YANG AND R. KOCH Keywords: Surface acoustic waves, elastic properties of solid, scanning tunneling microscopy. SCANNING CAPACITANCE FORCE MICROSCOPY AND KELVIN PROBE FORCE MICROSCOPY OF NANOSTRUCTURES EMBEDDED IN SiO2, G. TALLARIDA, S. SPIGA, M. FANCIULLI Keywords: Scanning capacitance force microscopy, Kelvin probe force microscopy, Sn nanostructures, silicon oxide thin films ELECTRICAL CHARACTERISATION OF III-V BURIED HETEROSTRUCTURE LASERS BY SCANNING CAPACITANCE MICROSCOPY, O. DOUHÉRET, K. MAKNYS AND S. ANAND Keywords: Scanning capacitance microscopy, GaAs/AlGaAs heterostructures, GaInP:Fe, optoelectronic devices PROBING THE DENSITY OF STATES OF HIGH TEMPERATURE SUPERCONDUCTORS WITH POINT CONTACT TUNNELING SPECTROSCOPY, L. OZYUZER, J.F. ZASADZINSKI, N. MIYAKAWA, K.E. GRAY Keywords: Point contact tunneling spectroscopy, I-V and dI/dV-V characteristics, double CuO2 layer Bi2Sr2CaCu2O8+į, high-Tc superconductivity

488

ANNEALING INFLUENCE ON CO ULTRATHIN FILM MORPHOLOGY IN MBE GROWN Co/Au BILAYERS, A. WAWRO, L.T. BACZEWSKI, P. PANKOWSKI, P. ALESZKIEWICZ, M. KISIELEWSKI, I. SVEKLO, A. MAZIEWSKI Keywords: Atomic force microscopy, Auger electron spectroscopy, reflection high energy electron diffraction, Au/Co/Au, magnetic applications. CORRELATION BETWEEN THE SURFACE RELIEF AND INTERFACES STRUCTURE OF FE/CR SUPERLATTICES AND ELECTROMAGNETIC WAVES PENETRATION, A.RINKEVICH, L.ROMASHEV, V.USTINOV Keywords: Penetration of electromagnetic waves, tunneling microscopy, ferromagnetic resonance, Fe/Cr superlattices, thin films, magnetic properties. MAGNETORESISTANCE AND MICROSTRUCTURE OF MAGNETIC THIN FILM MULTILAYERS, JENICA NEAMTU AND M. VOLMER Keywords: magnetoresistance, nickel iron permalloy, multilayers, thickness, microstructure SPM INVESTIGATION OF THIOLATED GOLD NANOPARTICLE PATTERNS DEPOSITED ON DIFFERENT SELF-ASSEMBLED SUBSTRATES, F. SBRANA, M. T. PARODI, D. RICCI, E. DI ZITTI Keywords: Scanning Probe Microscopy, Transmission Electron Microscopy, thiolated gold nanoparticles, self-assembled monolayers. AFM OF GUANINE ADSORBED ON HOPG UNDER ELECTROCHEMICAL CONTROL, A.-M. CHIORCEA AND A.M. OLIVEIRA BRETT Keywords: Atomic Force Microscopy, Magnetic AC Mode, electrochemical deposition, guanine, adsorption mechanism. DYNAMICS IN MODEL MEMBRANES AND DNA-MEMBRANE COMPLEXES USING TEMPERATURE CONTROLLED ATOMIC FORCE MICROSCOPY, Z.V. LEONENKO AND D.T. CRAMB Keywords: Atomic force microscopy, phospholipid bilayers, macromolecular membrane complexes, phase transition.

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