Global electronic structure of semiconductor alloys through direct large-scale computations for III-V alloys GaxIn1−xP

Abstract

We critically examine two nominally equivalent approaches for treating a random alloy: (1) by using one very large supercell as a direct simulation of the alloy and (2) by performing configuration averaging over many smaller supercells; and the common practice using a virtual crystal as the reference for analyzing the alloy band structure and discussing the electronic transport in the alloy. Specifically, (1) we show that, in practice, the size of the ``very large'' supercell depends on the particular property of interest, and the ideal of configuration averaging is only useful for certain properties. (2) We also examine the assumed equivalency by comparing the results of the two approaches in band-gap energy, energy fluctuation, and intervalley and intravalley scattering, and conclude that the two approaches often lead to nonequivalent physics. (3) We use a generalized moment method that is capable of computing the global electronic structure of a sufficiently large supercell (e.g., \ensuremath{\sim}260 000 atoms) to obtain the intrinsic broadening of a \ensuremath{\Gamma}-like electron state caused by the ``inelastic'' intravalley scattering in a direct-band-gap semiconductor alloy. (4) We demonstrate an efficient way to construct the effective dispersion curves of the alloy with high accuracy for calculating effective masses and examining anisotropy and nonparabolicity of the dispersion curve. (5) Finally, we discuss the limitation of using the virtual-crystal approximation as the reference for evaluating alloy scattering and studying transport properties.