Structural, Dynamical and Optical Properties of the Semiconductors Silicon and Germanium and Their Superlattice

Local Density Approximation is used to predict the properties of semiconductors: silicon, germanium and their superlattices, with norm-conserving pseudopotentials for ion-electron interacting, planewave expansion for electron wavefunction and special k-points for Brillouin zone integration. Systematic studies are performed for (1) size of planewave basis and pseudopotentials, (2) density of special k-points, (3) effective of exchange-correlation functions, and (4) self -consistent iterations. The convergence studies show that a 400 planewave basis still leads to a 9% relative error in calculated energy differences, resulting an error of less than.5% in lattice constant and 2% in bulk modulus. The special k-point yields less error,.2% in the energy differences for a 10 point set of diamond structure, hence its contribution to error is less important. The comparison of two exchange -correlation forms, Ceperley-Alder and Wigner, shows that Wigner form gives a larger lattice constant while the Ceperley -Alder form gives a larger bulk modulus; one has to compromise one quantity to get the better agreement with experimental result for the other one. The calculated elastic properties of Ge _1/Si_1 superlattice is discussed and compared to that of bulk Si and Ge, including lattice constant, bulk modulus and other elastic constants. Our calculated results agrees with both the experimental and other calculations for bulk Si and Ge. On linear optical responses, the strain-induced birefringence is calculated with crystalline silicon. Agreement with experiment is very good in the static limit Above 2 eV, the calculation predicts less dispersion than seen by the experiments. Thermal effects and electron-hole interactions are estimated to resolve some of the discrepancies with experiment.