The electronic properties of strained Si_1−xGe_x alloys epitaxially grown on (001) Si_1−yGe_y relaxed substrates for any x and y Ge concentrations are presented here. Our calculations are based on an sp³d⁵s^* nearest-neighbour 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 Si_1−xGe_x and Si_1−yGe_y, as well as the fundamental energy gap for Si_1−xGe_x 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 -space and direct in -space. With this aim we adopt the decimation–renormalization method 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 - and in -space) semiconducting heterostructures based on silicon and germanium can be realized. As an example, the case of pure Ge sandwiched between Si_0.25Ge_0.75 alloys, grown on a Si_0.2Ge_0.8 substrate, is fully discussed.

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