Theory of topologically disordered systems. I. Random cell model

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Abstract
The Hamiltonian of a topologically disordered system of impurities in a semiconductor matrix is studied in a random cell representation. It is shown that at any doping level most of the non-interacting cells are treated by a cluster expansion, the convergence of which is controlled by the respective statistical weight. It is shown that at any doping level most of the non-interacting cells are occupied by small clusters, while for large clusters the interaction cannot be neglected. The authors approach allows a systematic investigation of the single-particle excitation spectrum. Approximate inclusion of the non-diagonal part of the Hamiltonian leads to a generalised Anderson-type model on a coarse-grained cell structure.