Computational studies of a 2D tight-binding model of randomly dispersed hydrogenic centers

The impurity band arising from s-orbitals of randomly dispersed hydrogenic dopants in semiconductors in two dimensions is studied via exact diagonalization of a tight-binding model. Ensemble averaged density of states (DOS) and inverse participation ratio (IPR) of eigenstates are obtained as a function of energy at low to intermediate doping densities, where small clusters of sites are most significant. A similar calculation is done for p-orbitals for comparison. A strong peak in the DOS is seen about the impurity level. Increasing the density of sites weakens this peak and produces asymmetry in the DOS and the IPR. A nearest-neighbour pair approximation qualitatively explains several features in the DOS at low densities but does not reproduce the singularity. This motivates a comparison to a hierarchically constructed pair model, as well as random bipartite systems, which is pursued further via a renormalization group approach in a concurrent study.