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Cited by 290

The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.

First-principles calculation of temperature-composition phase diagrams of semiconductor alloys

Wei, S.-H., Ferreira, L. G., Zunger, Alex·1990·Physical Review B
DOI 10.1103/physrevb.41.8240
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Abstract

The three-dimensional spin-1/2 Ising model with multiple-site interactions provides a natural framework for describing the temperature-composition phase diagram of substitutional binary alloys. We have carried out a ``first-principles'' approach to this problem in the following way: (i) The total energy of an ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ alloy in any given substitutional arrangement of A and B on a given lattice is expanded in a series of interaction energies {${\mathit{J}}_{\mathit{f}}$(V)} of ``figures'' f. (ii) The ${\mathit{N}}_{\mathit{s}}$ functions {${\mathit{J}}_{\mathit{f}}$(V)} for ``figures'' f are determined as a function of volume V by equating the total energies of a set of ${\mathit{N}}_{\mathit{s}}$ periodic structures, calculated in the local-density formalism, to a series expansion in ${\mathit{J}}_{\mathit{f}}$ with known coefficients. The calculation includes in a natural way atomic relaxation and self-consistent charge transfer, hence providing a link between the electronic structure and the interaction energies which decide phase stability. (iii) The number ${\mathit{N}}_{\mathit{s}}$ and range of the interaction energies needed in such an Ising description is determined by the ability of such cluster expansions to reproduce the independently calculated total energy of other structures.We find that this requires extending the expansion for zinc-blende-based alloys up to the fourth fcc neighbors. (iv) Using such a ``complete'' set of ${\mathit{N}}_{\mathit{s}}$ interaction energies, {${\mathit{J}}_{\mathit{f}}$}, we find approximate solutions to the corresponding Ising Hamiltonian within the cluster-variation method, retaining up to four-body and fourth-neighbor terms. A renormalization procedure, whereby distant-neighbor correlations are folded into a compact set of effective near-neighbor correlations, is used and tested against Monte Carlo solutions. This yields the phase diagram and thermodynamic properties. The set {${\mathit{J}}_{\mathit{f}}$} is also used to perform a ground-state search of all stable structures. This identifies stable and metastable phases. This approach has been applied to five III-V pseudobinary alloys (${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As, ${\mathrm{GaAs}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{P}}_{\mathit{x}}$, ${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$P, ${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As, and ${\mathrm{GaSb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{As}}_{\mathit{x}}$) and three II-VI pseudobinary alloys (${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Hg}}_{\mathit{x}}$Te, ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$Te, and ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$Te). We have calculated (i) excess enthalpies, (ii) phase diagrams, (iii) clustering probabilities, and (iv) equilibrium bond lengths. We discuss in detail the chemical trends in these properties and offer a simple (``\ensuremath{\varepsilon}-G'') model which reveals the underlying physical factors controlling such trends.

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Metadata

Authors
Wei, S.-H., Ferreira, L. G., & Zunger, A.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1990-04-15
Volume
41
Issue
12
Pages
8240-8269
ISSN
  • 0163-1829 (ISSN-L)
  • 1095-3795
DOI
10.1103/physrevb.41.8240
OpenAlex
W2016270720
Cited by
290
References
42
FWCI
59.82
Type
journal article
Language
en
Open access
closed

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