A Semi-empirical tight-binding theory of the electronic structure of semiconductors2

A nearest-neighbor semi-empirical tight-binding theory of energy bands in zincblende and diamond structure materials is developed and applied to the following sp³-bonded semiconductors: C, Si, Ge, Sn, SiC, GaP, GaAs, GaSb, InP, InAs, InSb, AlP, AlAs, AlSb, ZnSe, and ZnTe. For each of these materials the theory uses only thirteen parameters to reproduce the major features of conduction and valence bands. The matrix elements exhibit chemical trends: the differences in diagonal matrix elements are proportional to differences in free-atom orbital energies and the off-diagonal matrix elements obey the d^?2 rule of Harrison et al. The lowest energy conduction bands are well described as a result of the introduction of an excited s state, s¹. on each atom. Examination of the chemical trends in this sp³s¹ model yields a crude but “universal” sp³s¹ model whose parameters do not depend explicitly on band gaps, but rather are functions of atomic energies and bond lengths alone. The “universal” model, although cruder than the sp³s¹ model for any single semiconductor, can be employed to study relationships between the band structures of different semiconductors; we use it to predict band edge discontinuities of heterojunctions.