Multicomponent semiconductor material discovery guided by a generalized correlated function expansion

A correlated function expansion (CFE) is presented to systematically sample an N-dimensional dual composition-processing variable space to efficiently guide the laboratory discovery complex materials with desirable properties. The CFE breaks down the material properties in terms of the independent, pair and higher order cooperative roles of the composition-processing variables. The CFE is expected to rapidly converge in the N-dimensional space of variables to specify (1) minimally sized hierarchical libraries of materials, and (2) how to utilize the observed properties of the library members to rapidly estimate the material properties throughout the entire composition-processing variable space. As an illustration the material properties (i.e., alloy bond length and the direct optical band gap $E_0)$ over the full composition space of the multicomponent semiconductor alloys, ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{P}}_y{\mathrm{As}}_{\text{1−y}},$ ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{As}}_y{\mathrm{Sb}}_{\text{1−y}},$ and ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{P}}_y{\mathrm{Sb}}_z{\mathrm{As}}_{\text{1−y−z}},$ are expressed through the CFE in terms of existing ternary experimental data. Band gap experimental results for ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{P}}_y{\mathrm{As}}_{\text{1−y}}$ lattice matched to InP and for ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{As}}_y{\mathrm{Sb}}_{\text{1−y}}$ lattice matched to GaSb are in good agreement with the CFE estimates from ternary input data alone. The alloy ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}{\mathrm{P}}_y{\mathrm{Sb}}_z{\mathrm{As}}_{\text{1−y−z}}$ is found to provide more diverse opportunities to achieve desired band gaps while still maintaining the lattice matching conditions by controlling the concentration of Sb at the anion site. For even broader classes of materials the CFE is generic tool designed to guide laboratory syntheses to aid in the discovery of new materials with desired properties.