Band gaps in some group-IV materials: A theoretical analysis

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Abstract
We have studied the effects of expansion of the lattice on band-edge levels in Si, Ge, Sn, and SiSn. The variation in the gap in the Si→Ge→Sn series can be explained as moving along a universal curve of the variation of band-edge levels with the combined effect of volume and potential. For all of the materials studied, the gap at low volumes is from Γ to X. There is a small range of volumes where the gap is from Γ to L, and at high voulmes the gap is direct until it closes. Thus, in addition to the usual process of applying positive pressure to close the gap, applying negative pressure also causes band overlap and metal- lization.