Nonisovalent (${\mathit{A}}^{\mathrm{III}}$${\mathit{B}}^{\mathrm{V}}$${)}_{1\mathrm{-}\mathit{x}}$${\mathit{C}}_{2\mathit{x}}^{\mathrm{IV}}$ semiconductor alloys exhibit a transition as a function of composition between a phase with the zinc-blende symmetry (where the two fcc sublattices of the diamond lattice are unequally occupied by ${\mathit{A}}^{\mathrm{III}}$ and ${\mathit{B}}^{\mathrm{V}}$ atoms) and a phase with the diamond symmetry (where the two sublattices have equal occupations). Previous thermodynamic models of this transition have considered only nearest-neighbor interactions between neutral atoms. This approach ignores the important electrostatic interactions associated with electron transfer between the electron-rich ${\mathit{C}}^{\mathrm{IV}}$-${\mathit{B}}^{\mathrm{V}}$ (‘‘donor’’) bonds and the electron-deficient ${\mathit{A}}^{\mathrm{III}}$-${\mathit{C}}^{\mathrm{IV}}$ (‘‘acceptor’’) bonds. We have reexamined the validity of a three-dimensional bulk thermodynamic model for (GaAs${)}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{2\mathit{x}}$ and (GaP${)}_{1\mathrm{-}\mathit{x}}$${\mathrm{Si}}_{2\mathit{x}}$ using an energy model that includes such electrostatic interactions and pairwise energies extracted from first-principles local-density total-energy calculations.

The associated spin-1 Ising Hamiltonian is solved in the pair approximation of the cluster-variation method. A detailed thermodynamic description is given, including excess enthalpies, phase diagrams, and equilibrium solubilities. Electrostatic interactions stabilize the diamond phase and result in a major increase in the temperature range where both phases are stable. These changes, however, are insufficient to produce a second-order transition at the low (growth) temperatures and intermediate compositions where the transition is observed. While a previous controversy on the validity of thermodynamic models has focused on the question of whether the postulation of ${\mathit{A}}^{\mathrm{III}}$-${\mathit{A}}^{\mathrm{III}}$ and ${\mathit{B}}^{\mathrm{V}}$-${\mathit{B}}^{\mathrm{V}}$ bonds (needed to fit the observed critical compositions in such models) is consistent with independent evidence, we find that, with realistic values for the interaction parameters, the presence or absence of such bonds does not produce any significant change in the phase diagram below melting temperatures. We conclude that bulk thermodynamics is an inappropriate description of the problem. This opens the possibility that surface thermodynamics could be the physical mechanism that determines the final symmetry of the sample.

• Received 19 November 1990

DOI:https://doi.org/10.1103/PhysRevB.43.14055