Showing papers by "Alex Zunger published in 1989"

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

Abstract: 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.

Band gaps and spin-orbit splitting of ordered and disordered AlxGa1-xAs and GaAsxSb1-x alloys.

Abstract: Spontaneous long-range ordering of the otherwise disordered isovalent semiconductor alloys A/sub x/B/sub 1-x/C has been recently observed in numerous III-V alloy systems exhibiting the CuAu-I, CuPt, and chalcopyrite structures. We present a theory for the ordering-induced changes in the Brillouin-zone-center electronic properties, with application to the Al/sub x/Ga/sub 1-//sub x/As and GaAs/sub x/Sb/sub 1-//sub x/ alloys. The dominant effect for these systems is shown to be level repulsion between different-symmetry states of the binary constituents which fold into equal-symmetry states in the ordered ternary structures. Strong variations in the band gaps, spin-orbit splittings, and charge densities among the three basic ordered structures reflect the different magnitudes of the symmetry-enforced coupling between the folded states. An extension of the model to the disordered alloys yields good agreement with the observed optical bowing parameters for the fundamental gaps; however, the positive (downward concave) bowing of the spin-orbit splitting observed in some common-cation semiconductor alloy remains an unexplained puzzle.

Epitaxial effects on coherent phase diagrams of alloys.

Abstract: We present a cluster-based description of coherent binary or pseudobinary alloys and predict and contrast bulk and epitaxial composition-temperature phase diagrams and excess thermodynamic functions. This formalism addresses in a unified way phenomena characteristic of coherent epitaxial solids, including the following: for phase-separating alloys (whose constituents are insoluble in bulk below a miscibility-gap temperature), (i) epitaxial ordered phases not present in the bulk phase diagram and (ii) a stabilization of the disordered phase to far lower temperatures; and for all alloys, (iii) epitaxial changes of order-disorder transition temperatures and (iv) the pinning (``lattice latching'') of the composition near where an epitaxial alloy is lattice matched to a given substrate. We illustrate these effects for ${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Au}}_{\mathrm{x}}$, a typical ``ordering'' alloy (with stable ordered compounds in bulk) and for ${\mathrm{GaAs}}_{\mathrm{x}}$${\mathrm{Sb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$, a typical ``phase-separating'' alloy. Using a simple thermodynamic description of the reactions describing molecular-beam epitaxy growth of a coherent epitaxial isovalent semiconductor alloy, we demonstrate that composition pinning persists even in this growth method, and compare with available experiments.

Negative spin-orbit bowing in semiconductor alloys

Abstract: Early measurements on many bulk III-V alloys showed that the spin-orbit splitting ${\ensuremath{\Delta}}_{0}$ at the valence-band maximum (VBM) was universally reduced relative to the average value of the end-point constituents. This led to the assumption, guiding much of the subsequent data analysis, that such alloys universally mix some conduction-band s character into the VBM (``interband coupling''), suppressing ${\ensuremath{\Delta}}_{0}$. Our self-consistent electronic-structure calculations for Ga(As,Sb) show very little s mixing in the VBM and an enhancement of ${\ensuremath{\Delta}}_{0}$. Intraband p-p coupling is shown to dominate the changes in ${\ensuremath{\Delta}}_{0}$.

Electronic structure of [110] Si-Ge thin-layer superlattices

Abstract: First‐principles electronic structure calculations for SinGen superlattices ( for n=4, 6, and 8) grown epitaxially on a (110) Si substrate reveal a nearly direct band gap (to within ≊0.04 eV for n=4) despite the pronounced indirectness of its constituents. This is unlike superlattices grown in the [001] direction which are indirect when grown on Si and quasi‐direct only on substrates with larger lattice constants, e.g., Ge. Transition dipole matrix elements for the lowest energy direct transition vanish for all repeat periods n but are finite for several other new low‐energy transitions.

Bonding charge density in GaAs.

Abstract: A Comment on the Letter by J. M. Zuo, J. C. H. Spence, and M. O'Keeffe, Phys. Rev. Lett. 61, 353 (1988).

First-principles calculation of the formation energies of ordered and disordered phases of AlAs-GaAs

Abstract: The total energy of ordered and disordered phases of AlAs-GaAs systems is expanded in a series of multiatom interaction energies determined from first-principles linear muffin-tin orbital and linear augmented-plane-wave calculations of simple superstructures. These interaction energies are used to discuss the stability of different superlattices and that of the random alloy.