Type-I alignment and direct fundamental gap in SiGe based heterostructures

The electronic properties of strained Si1-xGex alloys epitaxially grown on (001) Si1-yGey relaxed substrates for any x and y Ge concentrations are presented here. Our calculations are based on an sp3d5s* nearestneighbour tight-binding Hamiltonian and exploit appropriate scaling laws of the Hamiltonian interactions to account for strain effects. Spin-orbit interaction is also included in the Hamiltonian. We first provide the valence and conduction band offsets at the heterointerfaces between Si1-xGex and Si1-yGey, as well as the fundamental energy gap for Si1-xGex strained alloys. We are thus able to distinguish the region in the (x, y) plane where robust type- I alignment is achieved. Then this information on band alignment is exploited to propose a heterostructure which is both type I in r -space and direct in kspace. With this aim we adopt the decimation-renormalizationmethod for the determination of the electronic properties of the multilayer structure; from the Green's function the energy spectrum and the partial and the total densities of states projected on each layer of the system are obtained. Our conclusion is that by suitable control of alloying, stress, band offsets and folding, truly direct (both in r- and in k-space) semiconducting heterostructures based on silicon and germanium can be realized. As an example, the case of pure Ge sandwiched between Si0.25Ge0.75 alloys, grown on a Si0.2Ge0.8 substrate, is fully discussed.