Simplex algorithm for band structure calculation of noncubic symmetry semiconductors: application to III-nitride binaries and alloys

Abstract

The simulation of transport and optical properties of semiconductors is based on the availability of an accurate description of the band structures for the materials under investigation. Ab initio techniques are invaluable for predicting the electronic band structure particularly in the absence of reliable experimental information. Nevertheless, the Empirical Pseudopotential Method (EPM) remains the method of choice for transport studies because of its optimum compromise between complexity, accuracy, and computational efficiency. We have developed a set of integrated, interactive software tools which may greatly help in the delicate process of finding the best EPM band structure of a semiconductor compound. At the core of our computational method is an efficient yet general f90 implementation of nonlocal EPM for zinc-blende and wurtzite crystals. A robust simplex algorithm allows the optimization of the EPM adjustable parameters in order to match a set of reference values, i.e. energy gaps in several points of the Brillouin zone, and effective masses along all the principal directions, both for direct and indirect-gap materials. This computational procedure has been integrated with an array of Matlab functions, providing interactive functionalities for defining the local part of the atomic pseudopotentials, checking the convergence of the optimization process, plotting the resulting band structure, and computing detailed information about. e.g. the position and value of minima not located at symmetry points, the nonparabolicity coefficients of secondary valleys, etc.