Independent and correlated composition behavior of material properties: Application to energy band gaps for the GaαIn1−αPβAs1−β and GaαIn1−αPβSbγAs1−β−γ alloys

Abstract

A correlated function expansion (CFE) is introduced (a) to identify the role of independent and correlated composition variations upon a desired material property, and (b) to provide an efficient means to compute the property throughout the composition space. As an example the contributions of independent and correlated composition behavior upon the principal energy band gaps for the alloys ${\mathrm{Ga}}_{\mathrm{\alpha }}{\mathrm{In}}_{1\mathrm{-}\mathrm{\alpha }}{\mathrm{P}}_{\mathrm{\beta }}{\mathrm{As}}_{1\mathrm{-}\mathrm{\beta }}$ and ${\mathrm{Ga}}_{\mathrm{\alpha }}{\mathrm{In}}_{1\mathrm{-}\mathrm{\alpha }}{\mathrm{P}}_{\mathrm{\beta }}{\mathrm{Sb}}_{\mathrm{\gamma }}{\mathrm{As}}_{1\mathrm{-}\mathrm{\beta }\mathrm{-}\mathrm{\gamma }}$ are calculated and analyzed by applying the CFE to the universal tight-binding (UTB) Hamiltonian model of the alloys. The convergence properties of the CFE over the entire composition variable space (α,β,γ) are examined upon including independent, pair-, and triple-correlated terms. By retaining only independent component contributions in the CFE it was possible to represent the UTB results to better than 90% accuracy for both the alloys ${\mathrm{Ga}}_{\mathrm{\alpha }}{\mathrm{In}}_{1\mathrm{-}\mathrm{\alpha }}{\mathrm{P}}_{\mathrm{\beta }}{\mathrm{As}}_{1\mathrm{-}\mathrm{\beta }}$ and ${\mathrm{Ga}}_{\mathrm{\alpha }}{\mathrm{In}}_{1\mathrm{-}\mathrm{\alpha }}{\mathrm{P}}_{\mathrm{\beta }}{\mathrm{Sb}}_{\mathrm{\gamma }}{\mathrm{As}}_{1\mathrm{-}\mathrm{\beta }\mathrm{-}\mathrm{\gamma }}.$ Pair composition correlations contributed approximately 5–10 % to the band gaps in both alloys and for ${\mathrm{Ga}}_{\mathrm{\alpha }}{\mathrm{In}}_{1\mathrm{-}\mathrm{\alpha }}{\mathrm{P}}_{\mathrm{\beta }}{\mathrm{Sb}}_{\mathrm{\gamma }}{\mathrm{As}}_{1\mathrm{-}\mathrm{\beta }\mathrm{-}\mathrm{\gamma }}$ the triple correlations were at the level of $\sim 3\%.$ The CFE is a generic tool capable of simplifying efforts at finding desired alloy compositions for material properties.