Interpolation of the properties of compound semiconductor alloys from those of their constituents

Several expressions have been proposed for estimating the value of material properties of quaternary III-V alloys from those of their binary and ternary components. These expressions all agree when bowing terms are neglected. They differ in how the bowing terms of the multiple ternary constituents should be combined. Little has been published on how to estimate parameters for alloys with more than four elements. Compound semiconductors can be thought of as the combination of a mixture of group-III elements on the group-III sublattice with a mixture of group-V elements on the group-V sublattice. Each mixture can be described using a simplex space. The geometry of the compound semiconductor alloy’s interpolation space is then the direct sum of the group-III and group-V subspaces. Parameters of alloys with arbitrary numbers of elements can be expressed using a joint polynomial expansion in each group’s elemental concentrations. An interpolation expression for parameters of a quinary alloy is provided using this approach. Finally, a bowing term for the quaternary alloy GaInAsSb is proposed that improves agreement with experiment for alloys lattice matched to InP, InAs, and GaSb.