Nonlinear structure-composition relationships in the Ge _1-ySn_y/Si(100) (y<0.15) system

The compositional dependence of the cubic lattice parameter in Ge _1-ySn_y alloys has been revisited. Large 1000-atom supercell ab initio simulations confirm earlier theoretical predictions that indicate a positive quadratic deviation from Vegard's law, albeit with a somewhat smaller bowing coefficient, θ = 0.047, than found from 64-atom cell simulations (θ = 0.063). On the other hand, measurements from an extensive set of alloy samples with compositions y < 0.15 reveal a negative deviation from Vegard's law. The discrepancy with earlier experimental data, which supported the theoretical results, is traced back to an unexpected compositional dependence of the residual strain after growth on Si substrates. The experimental bowing parameter for the relaxed lattice constant of the alloys is found to be θ = -0.066. Possible reasons for the disagreement between theory and experiment are discussed in detail.