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arXiv · 2012.11311

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

Conor O'Donnell·Alfonso Sanchez-Soares·Christopher A. Broderick·James C. Greer
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Abstract

We calculate the electronic structure of germanium-tin (Ge$_{1-x}$Sn$_{x}$) binary alloys for $0 \leq x \leq 1$ 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 $Γ$. On the other hand, compressive strain has comparatively less impact on the alloy band gap at $Γ$. 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'') $Γ_{7}^{-}$-$Γ_{8}^{+}$ 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.

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Conor O'Donnell, Alfonso Sanchez-Soares, Christopher A. Broderick, James C. Greer. 2020-12-21. Impact of stoichiometry and strain on Ge$_{1-x}$Sn$_{x}$ alloys from first principles calculations. https://doi.org/10.1088/1361-6463%2Fabed6f

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