Energy band structure and linear optical properties of Si and Ge strained along the [111] and [110] directions

The electronic and optical properties of Si and Ge coherently grown on (111) and (110) surfaces of ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ alloy substrates are calculated with the use of a realistic empirical tight-binding model. The dependence of band-edge energies on strain and direction of growth is presented and the results are compared to those of the linear deformation potential theory. Nonlinear effects in the deformation potential theory are also considered for the conduction-band minima of Si along the Δ direction. The calculations show that these strained materials remain indirect gap semiconductors for all substrates and for both directions of growth. Their linear optical properties are analyzed in detail. Distortion along the [111] and [110] directions transforms the materials into uniaxial and biaxial crystals, respectively. The imaginary part of the dielectric function, ${\mathrm{\varepsilon }}_2$(ω), along the principal axes are also calculated. The resulted anisotropy, as well as the structures in the ${\mathrm{\varepsilon }}_2$ spectra, are analyzed in terms of the band structure and transition probabilities.