Bethe Lattices Incorporating Short-Range Disorder: Application to Hydrogenated Amorphous Silicon

A new class of Bethe lattices formed by two or more chemical elements of fixed but usually different coordinations is presented. The atoms are randomly bonded. The Green's function of the system is governed by a probabilistic equation, which can be solved by an iterative numerical procedure. Hydrogenated $a$-Si is modeled by a random Bethe lattice in which Si has coordination four and H has coordination one. Comparison with experiment shows that this model incorporates the main attributes of the real material.