Stability of bulk and pseudomorphic epitaxial semiconductors and their alloys

The Landau-Lifshitz theory of structural phase transitions permits identification of distinct classes of ordered ternary structures $A_n$ $B_{4\mathrm{-}n}$ $C_4$ (n=0–4) whose structural units are the $A_n$ $B_{4\mathrm{-}n}$C clusters spanning all possible nearest-neighbor environments in $A_x$ $B_{1\mathrm{-}x}$C pseudobinary semiconductor 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 different energetics of bulk-versus-epitaxial (ordered or disordered) ternary phases are described and investigated quantitatively via a simple valence-force-field model and harmonic elasticity theory. Under epitaxial conditions on a substrate of lattice constant $a_s$, a tetragonal degree of freedom for a ternary ordered compound controls the curvature about the minimum of the energy E($a_s$), while cell-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 unstable in bulk form (and hence not found in the bulk phase diagram) may become stable when epitaxy-induced strain is accommodated more successfully in the ternary than in the binary constituents; the occurrence of miscibility gaps and spinodal decomposition for disordered alloys may be similarly suppressed under epitaxial conditions. Relaxation of cell-internal structural parameters is found crucial to a quantitative theoretical description of the enthalpies of mixing of bulk- or epitaxially-grown disordered alloys.