Microscopic atomic structure and stability of Si-Ge solid solutions

Within the spirit of the recently proposed model for the atomic microscopic structure of ternary semiconducting alloys, a corresponding model for binary alloys which can be applied also to quaternary alloys is introduced. With use of the density-functional theory and norm-conserving pseudopotentials, nine different ordered structures of ${\mathrm{Si}}_{\mathrm{x}}$ ${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ are studied. It has been found that none of them is thermodynamically stable. Good agreement between the x variation of the bond lengths of Ge-Ge and Ge-Si pairs and the available experimental and theoretical results has been found, and the variation of that of Si-Si is predicted. The ionicity of the Si-Ge bond is found to be very small and unaffected by changes in concentration and chemical environment, which explains the instability of any ordered Si-Ge structure and the fact that the chemical term of the interaction parameter of the energy of mixing is x independent, respectively. However, around 20% of the interaction parameter is found to be x dependent.