Real space formulation for the electronic structure of randomly disordered quaternary semiconductor alloys applied on two dimensional (C₂)_x(BN)_1-x

Though the experimental work on random semiconductor alloys is prolific, theoretical investigations are limited. This is because of mainly two reasons, firstly, the orthodox density functional approximations often underestimate the band gaps of semiconductors, and secondly, a randomly alloyed structure with some concentration ratio of constituents may produce a lot of different configurations in reality and the necessary configuration averaging is always challenging for theorists. The advanced localized basis set of full potential N-th order muffin tin orbital (FP-NMTO) together with the improved exchange proposed by vanLeeuwen-Baerends (vLB) can predict the electronic properties of various semiconductors almost exactly. We extract the tight-binding parameters from the vLB-FP-NMTO first. Then, real-space Green functional method within augmented space formalism [J. Phys. C 6 1340 (1973)] which can perform configurational averaging on all possible arrangements by a tricky and fast mathematical formulation is utilized to propose an elegant method of calculating the electronic properties of semiconductor alloys, especially, the quaternary alloys with a preference towards the formation of particular bonds. We further exemplify this method on two-dimensional random (C₂)_x(BN)_1-x alloy.