Dynamics of electrons in graded semiconductors

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 hands, 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.