Topics in the Theory of Semiconductors.

In part I, we have calculated the structural properties of Si using an iterative method and the pressure dependences of energy gaps of Si, Ge, and GaAs at symmetry points in the Brillouin zone using a variational method within the local-density-functional formalism. The results are in good agreement with experimental values. The negative pressure derivatives of the gaps at the X point of the conduction band relative to the valence-band maxima are due to the d-states. In part II, the electronic structures of the pseudobinary alloy semiconductors Pb(,1-x)Sn(,x)Te are analyzed using the tight-binding model with spin-orbit interaction. The density of states and the band gap at the L point are computed for both the effective medium using the virtual crystal approximation and the realistic medium employing the recursion method, and the results are compared. Both theories exhibit the band broadening and Dimmock's band crossing phenomena. However, the random alloys show disorder effects in the cation-derived s-like states which have the greatest alloying effect. In part III, the Green's function method, with an empirical tight-binding basis, is used to determine the deep levels of the singly ionized and neutral impurities S, Se, and Te in Si. The impurity potentials are determined self-consistently. The resulting theory accounts for the observed charge-state splittings of neutral and singly ionized A(,1) deep levels, obtaining, for S, Se, and Te, 0.33, 0.27, and 0.32 eV (to be compared with experimental values of 0.30, 0.29, and 0.21 eV, and with a self-consistent local-density-theory value for S of 0.20).