PHYSICAL REVIEWER 8 VOLUME 37, NUMBER 6 15 FEBRUARY 1988-II Stability of bulk and yseudomoryhic epitaxial semiconductors and their alloys A. A. Mbaye, ' D. M. Wood, and Alex Zunger Solar Energy Research Institute, Golden, Colorado 80401 (Received 21 May 1987) The Landau-Lifshitz theory of structural phase transitions permits identi6cation of distinct classes of ordered ternary structures A„84 „C4 {n =0-4) whose structural units are the A„84 „C clusters spanning all possible nearest-neighbor environments in A„B, „C pseudobinary semicon- ductor alloys. A detailed description of how disordered bulk or epitaxial alloys may be described as a superposition of such clusters is given. Using Landau-Lifshitz structures as examples, the very diferent energetics of bulk-versus-epitaxial (ordered or disordered) ternary phases are de- scribed and investigated quantitatively via a simple valence-force-Seld model and harmonic elasti- city theory. Under epitaxial conditions on a substrate of lattice constant a„a tetragonal degree of freedom for a ternary ordered compound controls the curvature about the minimum of the energy E(a, ), while ce11-internal structural parameters control the minimum of E and hence stability. Stable bulk compounds when grown under epitaxial conditions may change in relative stability, permitting artificial stabilization of desired ordered phases. Exotic ordered ternary compounds un- stable in bulk form (and hence not found in the bulk phase diagram) may become stable when epitaxy-induced strain is accommodated more successfuBy in the ternary than in the binary con- stituents; the occurrence of miscibibty gaps and spinodal decomposition for disordered alloys may be similarly suppressed under epitaxial conditions. Relaxation of cell-internal structural parame- ters is found crucial to a quantitative theoretical description of the eathalpies of mixing of bulk- or epitaxially-grown disordered alloys. I. INTRODUCTION Our current understanding of chemical trends in the structure and stability of crystals' has been largely directed to the vast database of bulk materials, such as that compiled recently by Villars and Calvert. ~ Ad- vances in epitaxia1 growth methods have pointed, how- ever, to the possibility of equilibrium structural forms of semiconductors which do not appear in the equilibrium bulk phase diagrams of the same compounds. Such are, for example, rhombohedral3" SiGe and '' GalnAsi, the famatinite forms of InGa&As~ and In3GaAs&, chalcopy- ritelike and CuAu-I-like forms of Ga2AsSb, CuAu- I-like (tetragonal6i"} GaAlAs2 and@ ' InGaAsz (none of which are observed in the bulk phase diagram of Si„Gei „, In„Ga, „As, GaAs„Sb, „, and Ga„Ali „As, respectively}, cubic epitaxial phases of CdS and" SiC (observed at temperatures where the bulk phase diagrams show only hexagonal phases) and the a phase of Sn (not the normal P phase) observed to grow on InSb(110). It has similarly been noted' that epitaxial lattice matching to a substrate can signi6cantly perturb the solid composition from that mandated by the bulk equilibrium phase diagram, even permitting epitaxial growth of an alloy inside the bulk miscibility gap region (e. g. , " GaAs, „Sb„). Similar epitaxy-induced phase sta- bilization effects were recently observed in metallurgy, e.g. , ferromagnetic fcc (not bcc) Fe grown' on Cu(111), bcc (not fcc} Ni grown' on Fe(001), ferromagnetic fcc (not hexagonal) Co grown' "' on Cu(001) or bcc Co grown' ' ' on GaAs, and bcc (not fcc) Ag grown on'+" InSb. Such epitaxy-induced structural stabilization has been previously analyzed in terms of phenomenological elastic continuum models of substrate strain, ' ' but only recently' has a microscopic (atomistic) model been advanced for the epitaxial SiGe system. In this paper we illustrate the general physical principles of epitaxial stabilization of tetrahedral adamantine semiconductor crystals using a simple valence-force-field method' and the ternary Ga„In4 „P4 system as a prototypical exam- ple. A brief description of some of this work has already appeared. '8 II. ORDERED LANDAU-LIFSHITX ADAMANTINE STRUCTURES The systems we will consider consist of two isovalent zinc-blende semiconductors AC and BC (specifically GaP and InP) and their mixtures. These mixtures can form, among others, a single-phase disordered alloy A„B, „C, a two-phase (AC-rich and BC-rich) mixture, or ternary ordered compounds A„84 „C4 with n =0, 1, 2, 3, and 4. These ordered structures can be stable low- temperature phases of the aHoy according to the general principles outlined by Landau and Lifshitz. ' ' The conditions for selecting such possible ground-state or- dered phases of a face centered cubic (fcc) parent lattice with A-B, A-C, and B-C interactions are' ' (i) the space group of the ordered structure must be a subgroup of that of the disordered alloy, and (ii) the possible or- dered structure must be associated with an ordering vec- tor located at a special k point of the parent space group. ' These necessary conditions permit not only selection of the ordered structures but also their classi5cation in families associated with the same star of 37 3008 1988 The American Physical Society