We present a formalism for calculating the temperature-composition phase diagrams of isostructural solid alloys from a microscopic theory of electronic interactions. First, the internal energy of the alloy is expanded in a series of volume-dependent multiatom interaction energies. These are determined from self-consistent total-energy calculations on periodic compounds described within the local-density formalism. Second, distant-neighbor interactions are renormalized into composition- and volume-dependent effective near-neighbor multisite interactions. Finally, approximate solutions to the general Ising model (using the tetrahedron cluster variation method) underlying these effective interactions provide the excess enthalpy \ensuremath{\Delta}H, entropy \ensuremath{\Delta}S, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (${\mathrm{GaAs}}_{\mathrm{x}}$${\mathrm{Sb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$) and one with a small size mismatch (${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As), producing excellent agreement with the measured miscibility temperature and excess enthalpies. For lattice-mismatched systems, we find 0${H}^{O}$${H}^{D}$, where O denotes some ordered Landau-Lifshitz (LL) structures, and D denotes the disordered phase. We hence predict that such alloys will disproportionate at low-temperature equilibrium into the binary constituents, but if disproportionation is kinetically inhibited, some special ordered phases (i.e., chalcopyrite) will be thermodynamically stabler below a critical temperature than the disordered phase of the same composition. For the lattice-matched systems, we find 0${H}^{D}$${H}^{O}$ for all LL structures, so that only a phase-separating behavior is predicted. However, in these systems, longer-period ordered superlattices are found to be stabler, at low temperatures, than the disordered alloy.

First-principles calculation of alloy phase diagrams: The renormalized-interaction approach

We propose a classification scheme for phase equilibria in elemental metal‐gallium‐arsenic systems. Using available data we assign as many metals as possible to seven generic types of ternary phase diagrams. We describe how the phase diagrams can provide a framework for interpreting previous studies of metal reactions with GaAs substrates and for identifying stable materials for GaAs metallizations.

Phase equilibria in metal‐gallium‐arsenic systems: Thermodynamic considerations for metallization materials

https://iopscience.iop.org/article/10.1143/JJAP.21.797/pdf

Calculation of Miscibility Gap in Quaternary InGaPAs with Strictly Regular Solution Approximation

This paper presents a comprehensive review of the method of liquid phase epitaxy (LPE) of semiconductors. In Sect. 1 the physical principles including diffusion-limited growth and solid-liquid phase diagrams are treated in detail. In Sect. 2 technological aspects and various kind of growth systems including industrial versions are described. Section 3 summarizes the relevant properties of LPE grown layers. Section 4 contains the application of LPE to the material system InP/InGaAs/InGaAsP as a model system. In Sect. 5 the advantages and weaknesses of LPE with respect to device applications in comparison with competing methods are discussed, and finally we attempt to predict the future direction of LPE.

Liquid phase epitaxy

The behavior of unstable regions in the composition plane for III–V quaternary solid solutions made from among Al, Ga, In, P, As and Sb is analyzed, based on the strictly regular solution approximation for solid solutions. Temperature dependences of spinodal isotherms at 400–1000°C show that unstable regions cover a wide range of compositions. It is suggested that composition ranges exist where the spinodal temperature exceeds the melting point, so that such solid solutions can never be grown by near-equilibrium growth methods. Positions of quaternary critical points in the composition plane are also shown.

M.B. Panish

Papers

Phase equilibria in ternary III–V systems