Strong enhancement of Ge direct transition by biaxial-tensile strain was observed. The reduction in band gap difference between the direct and indirect valleys by biaxial tensile strain increases the electron population in the direct valley, and enhances the direct transition. The band gap reduction in the direct and indirect valleys can be extracted from the photoluminescence spectra and is consistent with the calculations using k • p and deformation potential methods for conduction bands and valence bands, respectively.

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Electronic structures of Ge1−xSnx alloys (0 ≤ x ≤ 1) are theoretically studied by nonlocal empirical pseudopotential method. For relaxed Ge1−xSnx, a topological semimetal is found for x > 41% with gapless and band inversion at Γ point, while there is an indirect-direct bandgap transition at x = 8.5%. For strained Ge1−xSnx on a Ge substrate, semimetals with a negative indirect bandgap appear for x > 43%, and the strained Ge1−xSnx on Ge is always an indirect bandgap semiconductor for x < 43%. With appropriate biaxial compressive strains, a topological Dirac semimetal is found with band inversion at Γ and one pair of Dirac cones along the [001] direction.

The enhanced photoluminescence of direct transition is observed on (100), (110), and (111) Ge under biaxial tensile strain. The enhancement is caused by the increase in electron population in the Γ valley. The shrinkage of energy difference between the lowest L valleys and the Γ valley is responsible to the population increase on (100) and (110) Ge. For (111) Ge, the energy difference increases under biaxial tensile strain but the strain decreases energy difference between the electron quasi-Fermi level and the Γ valley due to the small density of state of the lowest L valleys, and thus enhances direct recombination.

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