Interpolation of compound semiconductor alloy parameters from those of their constituents

• Published in: Journal of applied physics 2024-12, Vol.136 (21)
• Main Author: Olesberg, Jonathon T.
• Format: Article
• Language: English
• Subjects: Algorithms; Alloying elements; Alloys; Binary alloys; Bowing; Composition; Interpolation; Lattice matching; Metallurgical constituents; Mixtures; Parameters; Physical properties; Polynomials; Quaternary alloys; Semiconductor materials
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/5.0217016

Several methods have been proposed for interpolation of the value of physical parameters of quaternary alloys from those of their constituent ternary and binary sub-alloys. These expressions agree when non-linear bowing terms are not required; they differ in how the bowing terms of the bounding ternaries should be utilized. Common interpolation expressions for quaternaries can be generalized into two groups: (1) those that use a linear interpolation of the nearest ternary parameter values and (2) those that interpolate over binary values with a bowing term derived from the bounding ternaries. The second group of methods is equivalent to a polynomial expansion over the alloy’s interpolation space. For compound semiconductor alloys, the geometry of the composition space is the direct sum of the group-III and group-V mixture sub-spaces. The mixture sub-spaces are best described using barycentric coordinates on a regular simplex. A general polynomial expansion of the value of an alloy parameter using barycentric coordinates for the group-III and group-V simplex spaces is described along with an algorithm to generate interpolation expressions for alloys with arbitrary numbers of elements, including quinary and senary alloys. It is shown that a polynomial expansion produces values in closer agreement with the direct gap of quaternaries lattice-matched to common substrates than do approaches using an interpolation of the ternary values, despite a prominent recommendation to the contrary. Finally, a quaternary correction term is described that improves the predicted direct bandgap energies of GaInAsSb for compositions near those lattice matched to InP, InAs, and GaSb.