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The Physics of Low-dimensional Semiconductors by John H. Davies

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APPENDIX

6

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KRAMERS–KRONIGRELATIONS ANDRESPONSE FUNCTIONS

In this appendix we shall derive the Kramers–Kronig relations. This requires an excursion into the complex frequency plane and Cauchy’s integral theorem; readers unfamiliar with complex analysis can skip Section A6.1 without loss of continuity. We shall then derive two common models for the optical response of semiconductors.

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A6.1   Derivation of the Kramers–Kronig Relations

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The complex conductivity ...

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