Electronic Structure and Optical Properties of Semiconductors

We began planning and writing this book in the late 1970s at the suggestion of Manuel Cardona and Helmut Lotsch. We also received considerable en- couragement and stimulation from colleagues. Some said there was a need for instructional material in this area while others emphasized the utility of a research text. We tried to strike a compromise. The figures, tables, and references are included to enable researchers to obtain quickly essential information in this area of semiconductor research. For instructors and stu- dents, we attempt to cover some basic ideas about electronic structure and semiconductor physics with applications to real, rather than model, solids. We wish to thank our colleagues and collaborators whose research re- sults and ideas are presented here. Special thanks are due to Jim Phillips who influenced us both during our formative years and afterwards. We are grateful to Sari Yamagishi for her patience and skill with the typing and production of the manuscript. Finally, we acknowledge the great patience of Helmut Lotsch and Manuel Cardona. Berkeley, CA M.L. Cohen Minneapolis, MN, J.R. Chelikowsky March 1988 VII Contents 1. Introduction............................................... 1 2. Theoretical Concepts and Methods ..................... 4 2.1 The One-Electron Model and Band Structure............ 7 2.2 Properties of En(k) ...................................... 11 3. Pseudopotentials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . 3.1 The Empirical Pseudopotential Method.................. 20 3.2 Self-Consistent and Ab Initio Pseudopotentials ........... 25 4. Response Functions and Density of States .............. 30 4.1 Charge Density and Bonding ................... . . . . . . . . . 38 .