Impact of stoichiometry and strain on Ge${}_{1-x}$Sn${}_x$ alloys from first principles calculations

Abstract

We calculate the electronic structure of germanium-tin (Ge${}_{1-x}$Sn${}_x$) binary alloys for $0\le x\le 1$ using density functional theory (DFT). Relaxed alloys with semiconducting or semimetallic behaviour as a function of Sn composition $x$ are identified, and the impact of epitaxial strain is included by constraining supercell lattice constants perpendicular to the [001] growth direction to the lattice constants of Ge, zinc telluride (ZnTe), or cadmium telluride (CdTe) substrates. It is found that application of 1% tensile strain reduces the Sn composition required to bring the (positive) direct band gap to zero by approximately 5% compared to a relaxed Ge${}_{1-x}$Sn${}_x$ alloy having the same gap at $\Gamma$. On the other hand, compressive strain has comparatively less impact on the alloy band gap at $\Gamma$. Using DFT calculated alloy lattice and elastic constants, the critical thickness for Ge${}_{1-x}$Sn${}_x$ thin films as a function of $x$ and substrate lattice constant is estimated, and validated against supercell DFT calculations. The analysis correctly predicts the Sn composition range at which it becomes energetically favourable for Ge${}_{1-x}$Sn${}_x$/Ge to become amorphous. The influence of stoichiometry and strain is examined in relation to reducing the magnitude of the inverted (``negative'') ${\Gamma }_7^{-}$-${\Gamma }_8^{+}$ band gap, which is characteristic of semimetallic alloy electronic structure. Based on our findings, strategies for engineering the semimetal-to-semiconductor transition via strain and quantum confinement in Ge${}_{1-x}$Sn${}_x$ nanostructures are proposed.

16 pages, 9 figures

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Cited by in corpus (1)

• Electronic and optical properties of Si${}_x$Ge${}_{1-x-y}$Sn${}_y$ alloys lattice-matched to Ge