Method for calculating the electronic structure induced by short-ranged defects in semiconductors

A new method for calculating the electronic structure induced by nonideal point defects characterized by short-range disorder in crystalline semiconductors is introduced. The method exploits the transfer-matrix technique to provide a new way of solving the Dyson equation which requires as input only a few Green's functions of the perfect crystal. These Green's functions are matrices whose size is determined by the number of localized orbitals per atom. The method thus enables determination of deep levels without directly seeking zeros of the commonly employed determinantal condition. Calculations for a model tetrahedral system with an impurity and associated distortions are presented to display the power and calculational ease of the technique. It is then applied to real tetrahedral materials described within the full ${\mathrm{sp}}^3$ hybrid-orbital basis and the empirical tight-binding method, including up to second-nearest-neighbor interactions. Results for oxygen substitutional impurity in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ and for As antisite defect in GaAs are presented. Comparison with experiments reveals remarkably good agreement.