Dynamics of Electrons in Graded Semiconductors

TL;DR

This paper develops a theoretical framework for understanding electron behavior in graded semiconductors with varying composition, linking optical properties to band structures and deriving new sum rules for electronic oscillator strengths.

Contribution

It introduces a novel theory connecting electron dynamics in graded semiconductors to band structures, including new sum rules and a general expression for absorption peak width.

Findings

Derived new sum rules for electronic oscillator strengths.

Established a relation between low-frequency dynamics and semiclassical motion.

Provided a general expression for intraband absorption peak width.

Abstract

I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge of the band structures and momentum matrix elements of homogeneous semiconductor alloys. New sum rules for the electronic oscillator strengths, which apply within a given energy band or between any two bands, are derived, and a general expression for the width of the intraband absorption peak is given. Finally, the low-frequency dynamics is discussed, and a correspondence with the semiclassical motion is established.