Strain energy and stability of Si-Ge compounds, alloys, and superlattices

First-principles total-energy pseudopotential calculations are carried out for Si, Ge, zinc-blende-structure SiGe, (${\mathrm{Si}}_2$ ${)}_{\mathit{p}}$/(${\mathrm{Ge}}_2$ ${)}_{\mathit{p}}$ superlattices in various layer orientations G and with various choices of substrate lattice parameter ${\mathit{a}}_{\mathit{s}}$, and for the ${\mathrm{Si}}_{0.5}$ ${\mathrm{Ge}}_{0.5}$ random alloy. A subset of the results is used to construct an energy model, incorporating both strain (via an anharmonic valence force field) and chemical interactions (via a rapidly convergent cluster expansion) that closely reproduces the first-principles results, including those not used as input to the model. The model is applied to the study of larger superlattices than are amenable to first-principles treatment, revealing trends in (i) constituent strain energies, (ii) interfacial ‘‘strain-relief’’ relaxation energies, and (iii) interfacial chemical energies. The analysis reveals the major regularities in the dependence of superlattice stability on {p,G,${\mathit{a}}_{\mathit{s}}$}, and permits investigation of the nature of interactions at interfaces, including the substrate-film interface.