Strain-induced confinement in ${\mathrm{Si}}_{0.75}$${\mathrm{Ge}}_{0.25}$ (Si/${\mathrm{Si}}_{0.5}$${\mathrm{Ge}}_{0.5}$) (001) superlattice systems

We report pseudopotential calculations of the electronic structure of strained-layer superlattices consisting of Si and ${\mathrm{Si}}_{0.5}$ ${\mathrm{Ge}}_{0.5}$, with periods in the range 20–140 Å. In our calculation, both the effect of the microscopic crystal potential and that of the strain peculiar to the choice of ${\mathrm{Si}}_{0.75}$ ${\mathrm{Ge}}_{0.25}$ as a buffer layer are taken into account. The superlattice energy levels and wave functions are obtained in the wave-vector space by expanding the wave function in terms of the eigenfunctions of a bulk crystal Hamiltonian of the buffer layer. In this representation, the superlattice wave function is uniquely determined by a set of bulk wave vectors and the optical matrix elements can be obtained directly from the corresponding expansion coefficients. We assume the strain is uniform in both constituents with the lattice constant parallel to the interfaces being determined by the choice of buffer layer. Two different strain configurations are then investigated: firstly the lattice separation in directions perpendicular to the interfaces being the same as in the unstrained bulk constituents and secondly with this lattice separation as in the minimum-energy configuration. A scheme involving the nearly-free-electron model is used to deal with the absolute energies of the constituents. We find that the electron states are confined in the silicon layers, in agreement with existing experimental results. The effective confining barrier in the conduction and valence bands is strain dependent. We model the evolution of the effect of strain upon the formation of confined states and demonstrate that the position of the conduction- and valence-band levels is a sensitive function of strain and well and/or barrier widths. We calculate the optical matrix element across the fundamental superlattice gap and find that the superlattice potential enhances this optical matrix element in ultrathin layers.