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Type-I, type-II, reverse type-I, and reverse type-II band alignments are found theoretically in strained Ge1−x Sn x (0 ≤ x ≤ 0.3) grown on relaxed Ge1−y Sn y substrates (0 ≤ y ≤ 0.3) using the model-solid theory. The prerequisite bandgaps, and energy difference between the top valence band edge and the average valence band position of GeSn are obtained by the nonlocal empirical pseudopotential method. For the indirect-gap (L valleys) Ge1−x Sn x on relaxed Ge1−y Sn y , the band alignments are type-I and reverse type-I under biaxial compressive strain (x > y) and biaxial tensile strain (x < y), respectively. For the direct-gap (Γ valley) Ge1−x Sn x on relaxed Ge1−y Sn y , the biaxial compressive strain yields type-I and type-II alignment, while the biaxial tensile strain yields reverse type-I and reverse type-II alignments.

The band structure of Ge in the lonsdaleite phase is calculated using first principles. Lonsdaleite Ge has a direct band gap at the Γ point. For the conduction band, the Γ valley is anisotropic with the low transverse effective mass on the hexagonal plane and the large longitudinal effective mass along the c axis. For the valence band, both heavy-hole and light-hole effective masses are anisotropic at the Γ point. The in-plane electron effective mass also becomes anisotropic under uniaxial tensile strain. The strain response of the heavy-hole mass is opposite to the light hole.