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Ordering thermodynamics of surface and subsurface layers in the Ga 1 − x <mml:mi mathvariant="normal…

1992; American Physical Society; Volume: 45; Issue: 19 Linguagem: Inglês

10.1103/physrevb.45.11173

1095-3795

Roberto R. Osorio, James E. Bernard, Sverre Froyen, Alex Zunger,

Chalcogenide Semiconductor Thin Films

Although bulk III-V alloys exhibit phase separation, vapor-phase epitaxial growth of ${\mathrm{Ga}}_{0.5}$${\mathrm{In}}_{0.5}$P/GaAs (001) at \ensuremath{\approxeq}900--1000 K shows spontaneous ordering into the 〈111〉-oriented monolayer (GaP${)}_{2}$(InP${)}_{1}$ superlattice (the ``CuPt'' structure). Only two superlattice directions ([11\ifmmode\bar\else\textasciimacron\fi{}1] and [1\ifmmode\bar\else\textasciimacron\fi{}11], which define the ${\mathrm{CuPt}}_{\mathit{B}}$ variant) out of four possible are seen. Both [11\ifmmode\bar\else\textasciimacron\fi{}1] and [1\ifmmode\bar\else\textasciimacron\fi{}11] subvariants are observed on flat surfaces or when surface steps are perpendicular to the cation dimers. Ordering was seen also in nonstoichiometric (e.g., ${\mathrm{Ga}}_{0.7}$${\mathrm{In}}_{0.3}$P) alloys. Previous total-energy calculations at T=0 show that (i) phase separation is eliminated by the constraint that the alloy and its constituents are coherently matched to a substrate; (ii) the epitaxially stable chalcopyrite order is eliminated by surface reconstruction; (iii) surface reconstruction stabilizes the ${\mathrm{CuPt}}_{\mathit{B}}$ variant over the other structures.A relaxed but unreconstructed surface does not lead to any significant preference for ordering. Here we develop thermodynamic (T\ensuremath{\ne}0) calculations based on cluster-variation solutions to a configurational Hamiltonian whose interaction energies are fit to T=0 total-energy calculations. This shows that (iv) significant ${\mathrm{CuPt}}_{\mathit{B}}$ ordering persists to \ensuremath{\sim}1500 K not only for the equimolar ${\mathrm{Ga}}_{0.5}$${\mathrm{In}}_{0.5}$P alloy, but also at other compositions, e.g., ${\mathrm{Ga}}_{0.7}$${\mathrm{In}}_{0.3}$P; (v) the cation-terminated surface couples to the fourth layer in such a way as to select the correct three-dimensional ${\mathrm{CuPt}}_{\mathit{B}}$ structure; (vi) once formed, the two-dimensional ${\mathrm{CuPt}}_{\mathit{B}}$ layers near the surface are remarkably stable towards atomic swaps; (vii) a flat surface leads to a sufficiently small coupling between cation layers so that either of the two ${\mathrm{CuPt}}_{\mathit{B}}$ variants can form. We conclude that the main features of the observed ordering can be explained as a thermodynamically stable phase at growth temperatures of either the surface or the first few subsurface layers, depending on how deeply into the alloy atomic mobilities remain sufficiently large.