Abstract
We present and compare three distinct atomistic models—based on first principles and semi-empirical approaches—of the structural and electronic properties of \(\hbox {Ge}_{1-x}\hbox {Sn}_{x}\) alloys. Density functional theory calculations incorporating Heyd–Scuseria–Ernzerhof (HSE), local density approximation (LDA) and modified Becke–Johnson (mBJ) exchange-correlation functionals are used to perform structural relaxation and electronic structure calculations for a series of \(\hbox {Ge}_{1-x}\hbox {Sn}_{x}\) alloy supercells. Based on HSE calculations, a semi-empirical valence force field (VFF) potential and \(sp^{3}s^{*}\) tight-binding (TB) Hamiltonian are parametrised. Comparing the HSE, LDA+mBJ and VFF+TB models, and using the HSE results as a benchmark, we demonstrate that: (1) LDA+mBJ calculations provide an accurate first principles description of the electronic structure at reduced computational cost, (2) the VFF potential is sufficiently accurate to circumvent the requirement to perform first principles structural relaxation, and (3) VFF+TB calculations provide a good quantitative description of the alloy electronic structure in the vicinity of the band edges. Our results also emphasise the importance of Sn-induced band mixing in determining the nature of the conduction band structure of \(\hbox {Ge}_{1-x}\hbox {Sn}_{x}\) alloys. The theoretical models and benchmark calculations we present inform and enable predictive, computationally efficient and scalable atomistic calculations for disordered alloys and nanostructures. This provides a suitable platform to underpin further theoretical investigations of the properties of this emerging semiconductor alloy.
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Acknowledgements
E.J.O’H. and C.A.B. contributed equally to this work. This work was supported by Science Foundation Ireland (SFI; Project Nos. 15/IA/3082, 14/IA/2513 and 13/SIRG/2210), and by the National University of Ireland (NUI; via the Post-Doctoral Fellowship in the Sciences, held by C.A.B.). The authors acknowledge the provision of computing resources by SFI via Tyndall National Institute and the Irish Centre for High-End Computing (ICHEC; additional support for which is provided by the Higher Education Authority, as well as the Departments of Education and Skills, and Business, Enterprise and Innovation of the Government of Ireland). The authors thank Dr. Timothy D. Eales, Dr. Igor P. Marko, and Prof. Stephen J. Sweeney (University of Surrey, U.K.) for useful discussions, and for providing access to the results of their experimental measurements prior to publication.
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O’Halloran, E.J., Broderick, C.A., Tanner, D.S.P. et al. Comparison of first principles and semi-empirical models of the structural and electronic properties of \(\hbox {Ge}_{1-x}\hbox {Sn}_{x}\) alloys. Opt Quant Electron 51, 314 (2019). https://doi.org/10.1007/s11082-019-1992-8
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DOI: https://doi.org/10.1007/s11082-019-1992-8