Weighted average effective band structure of disordered solids

Abstract

In this paper, a straightforward first-principles based method is proposed to determine the average effective electron band structure of disordered solids using supercell approach and plane-wave basis. Calculations have been done by determining the expectation values of the supercell Hamiltonian in a primitive-cell-periodic basis. The formulation and implementation details are presented and discussed. Also, it is shown that, in the cases with small differences in bonding characteristics at atomic-scale resolution, the weighted average bands are almost continuous. Therefore, it is possible to calculate the average effective band gap and average effective mass of electron/hole in different valleys. Analysis of the results for a number of disordered compounds shows that the proposed technique has the potential to explain and predict the experimental observations. This method is a promising tool for the study of the role of order/disorder in the electronic properties of random alloys and 2D and 3D imperfect materials.