First-Principles Statistical Mechanics of Semiconductor Alloys and Intermetallic Compounds

Abstract

A binary substitutional system can exist in 2N configurations that can be formed by occupying any of the N sites of a lattice by either an A or a B atom. Substitutional configurations include compounds, alloys, superlattices, and substitutional impurities. This article addresses the questions of (i) finding the lowest energy configuration of a given NB substitutional system, (ii) calculating its composition-temperature phase diagram, and (iii) its finite-temperature thermodynamic properties, using the first-principles local density approximation (LDA). Mapping of the LDA energies of 10-20 ApBq compounds onto an Ising-like "cluster expansion" enables use of lattice statistical mechanics techniques that elegantly solve the above problems. This extends the utility of the LDA from simple, perfectly-ordered compounds to truly complex structures. We illustrate the method for semiconductor systems and transition-metal intermetallic systems, emphasizing the role of lattice relaxation.