Electronic Properties of Complex Crystalline and Amorphous Phases of Ge and Si. II. Band Structure and Optical Properties

We present calculations of the band structures and the imaginary part of the dielectric function ${\epsilon }_2$ as a function of energy for Ge and Si in the diamond, wurtzite, Si-III (BC-8) and Ge-III (ST-12) structures using the empirical pseudopotential method. In particular we have obtained the symmetries of wave functions along important symmetry directions and identified the major contributions to the optical structure. A further study is made into the optical properties of amorphous Ge and Si using our short-range-disorder model. We find that, unlike long-range-disorder models, short-range disorder can explain both the amorphous density of states and the amorphous ${\epsilon }_2$. In particular we find that the ${\epsilon }_2$ spectrum has the same form as an averaged matrix element as a function of frequency.