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, (Si2)p/(Ge2)p superlattices in various layer orientations G and with various choices of substrate lattice parameter alpha-s and for the Si0.5Ge0.5 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,alpha-s}, and permits investigation of the nature of interactions at interfaces, including the substrate-film interface.