Theory of fluctuations and localized states in amorphous tetrahedrally bounded solids

We present a general solution of a Bethe lattice with arbitrary coordination for a Hamiltonian with an arbitrary number of degrees of freedom per site and an arbitrary number of interaction integrals. This solution is used in conjunction with a realistic tight-binding Hamiltonian to study the effects of rings and bond-angle fluctuations on the $p$-like region and gap region of the electronic density of states of amorphous tetrahedrally bonded solids. It is shown that even for completely connected networks with no dangling bonds, bond-angle fluctuations create well-defined localized states which lie predominantly at the top of the valence band. These fluctuations also account for the steepening of the valence-band edge with disorder as observed experimentally in photoemission measurements. It is shown that rings do not play a direct role in this effect.