Density functional study for crystalline structures and electronic properties of Si₁− xSnx binary alloys

We have carried out density functional theory (DFT) calculation for Si 1− x Sn x alloy and investigated the effect of the displacement of Si and Sn atoms with strain relaxation on the lattice constant and E – k dispersion. We calculated the formation probabilities for all atomic configurations of Si 1− x Sn x according to the Boltzmann distribution. The average lattice constant and E – k dispersion were weighted by the formation probability of each configuration of Si 1− x Sn x . We estimated the displacement of Si and Sn atoms from the initial tetrahedral site in the Si 1− x Sn x unit cell considering structural relaxation under hydrostatic pressure, and we found that the breaking of the degenerated electronic levels of the valence band edge could be caused by the breaking of the tetrahedral symmetry. We also calculated the E – k dispersion of the Si 1− x Sn x alloy by the DFT+ U method and found that a Sn content above 50% would be required for the indirect–direct transition.