Electron states in glassy semiconductors

Trial wavefunctions for the valence band in an amorphous semiconductor are constructed out of linear combinations of bond orbitals. In the absence of long range order, these functions are assumed to be statistically homogeneous and isotropic over extended regions of the material, yet satisfying the same strong local conditions for the bond coefficients as in the perfect crystal. The importance of topological restraints on the assignment of these coefficients is emphasized. In particular, it is shown that three mutually orthogonal extended states can always be found near the top of the band, analogous to the triple degeneracy at Gamma 25' in the crystal. Some observable characteristics of the electronic structure of these materials are conjectured.