INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761 -4700 800/521-0600 Order Number 0211246 Structural, dynamical and optical properties of the semiconductors Si and Ge and their superlattice Wei, Siqing, Ph.D. The Ohio State University, 1991 Copyright ©1991 by Wei, Siqing. All rights reserved. 300 N. Zeeb Rd. Ann Arbor, MI 48106 STRUCTURAL, DYNAMICAL AND OPTICAL PROPERTIES OF THE SEMICONDUCTORS Si AND Ge AND THEIR SUPERLATTICE DISSERTATION Presented in Partial Fulfillment of the Requirment for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University by Siqing Wei, B.S., M.S. The Ohio State University 1991 Dissertation Committee: Approved by John W. Wilkins ^ ^ , r \ n Ken G. Wilson R. Sooryakumar Adviser Department of Physics © Copyright by Siqing Wei 1991 To My Parents ii ACKNOWLEDGMENTS To Professor John Wilkins, my thesis advisor, I wish to express my deepest gratitude and appreciation. His everlasting encouragement and his healthy skepti­ cism combines with his fairness has motivated me to do the best that I can. My special thanks to him for his understanding and kindness towards me who come from a totally different culture background. It is my great fortune to have him as my advisor. I would like to express heartfelt thanks for Professors John Perdew and Mel Levy who started me into serious research in physics, and helped me settled in a foreign environment in New Orleans. Many thanks go to Professor Peter Nordlander with whom I have spent many long working nights when we were at Vanderbilt. It was his suggestion that I finish my graduate research at Ohio State. I would also like to thank Professors R. Sooryakumar and Ken Wilson for serving on my graduate committee. During the years at Ohio State University, Dr. Zachary Levine helped me to get deeper understanding of the fields. I owe him many thanks for helpful discussion, advises and suggestions. My gratitude to Dr. Douglas Allan and Mike Teter at Corning for making their code available to me. The tough life of a graduate student was eased somewhat by my officemates over the years. They were: Nick Bonesteel, Krishna Balasubramaniana, Ben Hu, Chris Lin, Jim Reynolds, Dan Sullivan, Mingqiu Sun, Ned Wingreen and Hua Zhong at Ohio State, and all the others at Vanderbilt and Tulane, with name list so long that I am unable to finish here, with apologies for omissions. I have fonded the memory of many interactions with the cheerful faculty, vis­ itors and postdocs at The Ohio State University. These include: Franco Buda, Eivend Hauge, Myung-Ho Kang, Mark Kvale, Zachary Levine, Pavel Lipavsky, Ross McKenzie, John Mintmire, Frank Pelzer, Michael Reizer, and Jon Andreas Stoevneng. Brett Lowry and Marijan Adam have each lent me able technical assistance with the computers and made computing ‘fun’, Linda Antolik and Karen Costantino have made my life easier in the difficult paper work ‘shuffling’ and provided me a guide to the campus life at Ohio State. Their helps will be remembered. I would like to express my thanks to my fellow Chinese friends here at Ohio State who shorten the distance between me and my home in Shanghai. My special thanks to Jingmin Leng with whom I spent undergraduate life together back home, Zhiqiang Wang with whom I learned a lot, and Shulai Zhao, my long suffering roommate in Columbus. I would like also to express my gratitude to my friends, H. F. C., X. L., Chie Soong, Chenjie Wang, and Yuchen Yan. for their friendship supports me through my life at various stages. My research was supported by grants from the Department of Energy — Basic Energy Sciences, Division of Materials Research. The computational facilities are provided by National Super-Computer Center at Cornell and Ohio Super-Computer Center. Finally, my deepest gratitude to my parents who have given me neverending support and encouragement through the years while I am thousands of miles away from home. My deepest admiration for their honesty and fairness. No words can express my thanks to my parents for raising me in a very difficult situation. I owe them everything I have been today. Vitae August 29, 1963 .........................Born - Shanghai, Shanghai, PR of China 1984 ..............................................B. S., Fudan University, Shanghai, PR of China 1986-1987 ..................................... Research Assistant, Department of Physics, Tulane University, New Orleans, LA 1987-1988 ..................................... Research Assistant, Department of Physics, Vanderbilt University, Nashville, TN 1988 ..............................................M. S., Department of Physics, Vanderbilt University, Nashville, TN 1988-Presen t .................................Research Assistant, Department of Physics, The Ohio State University PUBLICATIONS Mel Levy, Rajeev K. Pathak, John P. Perdew and Siqing Wei, “Indirect-Path Meth­ ods for Atomic and Molecular Energies, and New Koopmans Theorems,” Phys. Rev. A. 36, 2491 (1987). John P. Perdew, Mel Levy, G. S. Painter, Siqing Wei and Jolanta B. Lagowski, “Chemical Bond as a Test of Density-Gradient Expansion for Kinetic and Exchange Energies,” Phys. Rev. B. 37, 838 (1988). Y. Wang, P. Nordlander, Siqing Wei and M. Ronay, “Surface and Diffusion Barriers to Oxygen Penetration on Simple Metals and Their Oxides,” Diffusion and Defect Data 61A, 1 (1988). FIELD OF STUDY Major Field: Physics vi TABLE OF CONTENTS D ED ICA TIO N ....................................................................................................................ii ACKNOWLEDGEMENTS..........................................................................................iii VITA ................................................................................................................................... vi LIST OF TABLES .......................................................................................................... ix LIST OF FIGURES ...................................................................................................... xi Page Chapter I Introduction: A Review of Dynamical and Structural Properties of Crystals . 1 1.1. Overview of the T h e s is ....................................................................................... 1 1.2. Basic Concepts of Harmonic Crystals: A Classical Description .... 3 1.3. Emperical Models for Force Constant and Dynamical Matrix .... 10 1.4. Microscopic Study of Force Constant: Dielectric Matrix Method . 16 1.5. Direct (Supercell) Approach of Calculating Frozen Phonon Frequency 26 1.6. Elastic Constants: Direct Calculation of Stress ....................................... 30 1.7. Green’s Function Approach of Linear Response Calculation ..............36 1.8. Some Systematic Studies of Local Density Approximation .......................40 1.9. Summary of Thesis R e s u lts ............................................................................ 47 References for Chapter I .................................................................................50 Chapter II Elastic Constants of Si/Ge Superlattice and Bulk Si and G e ...............................53 2.1. Introduction ..................................................................................................... 54 2.2. The Molecular Dynamical Scheme and Calculation M ethod ...................56 2.3. The Systematic Studies .................................................................................59 2.4. The Calculated Results For Si, Ge and S i/G e ............................................73 vii 2.5. Conclusions .....................................................................................................79 References for Chapter I I ................................................................................. 81 Chapter III Strained Silicon: A Dielectric Response Calculation ................................................83 3.1. Introduction ......................................................................................................84 3.2. Symmetry Considerations ............................................................................. 8 6 3.3. R e s