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Unformatted text preview: Solid State Theory Spring Semester 2011 Manfred Sigrist Institut f¨ur Theoretische Physik HIT K23.8 Tel.: 044-633-2584 Email: [email protected] Website: http://www.itp.phys.ethz.ch/research/condmat/strong/ Lecture Website: http://www.itp.phys.ethz.ch/education/lectures fs11/solid Literature: • N.W. Ashcroft and N.D. Mermin: Solid State Physics , HRW International Editions, 1976. • C. Kittel: Einf¨uhrung in die Festk¨orperphysik , R. Oldenburg Verlag, 1983. • C. Kittel: Quantentheorie der Festk¨orper , R. Oldenburg, 1970. • O. Madelung: Introduction to solid-state theory , Springer 1981; auch in Deutsch in drei B¨ anden: Festk¨operphysik I-III , Springer. • J.M. Ziman: Prinzipien der Festk¨orpertheorie , Verlag Harri Deutsch, 1975. • M.P. Marder: Condensed Matter Physics , John Wiley & Sons, 2000. • G. Grosso & G.P. Parravicini: Solid State Physics , Academic Press, 2000. • G. Czychol: Theoretische Festk¨orperphysik , Springer 2004. • P.L. Taylor & O. Heinonen, A Quantum Approach to Condensed Matter Physics , Cam- bridge Press 2002. • numerous specialized books. 1 Contents Introduction 5 1 Electrons in the periodic crystal 8 1.1 Bloch states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Crystal symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Bloch’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Nearly free electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Symmetry properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 k · p- expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5 Approximate band calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.1 Pseudo-potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 Augmented plane wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6 Tightly bound electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.7 Semi-classical description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.7.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.7.2 Current densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.8 Metals and semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2 Semiconductors 29 2.1 The band structure in group IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 Crystal and band structure . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 k · p- expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Elementary excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2.1 Electron-hole excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2.2 Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Excitons ....
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This note was uploaded on 10/04/2011 for the course PHYS fs11 taught by Professor Sigrist during the Spring '11 term at Swiss Federal Institute of Technology Zurich.

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notes - Solid State Theory Spring Semester 2011 Manfred...

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