Hybrid-Functional and Quasi-Particle Calculations of Band Structures of Mg2Si, Mg2Ge, and Mg2Sn

Abstract

We perform hybrid functional and quasi-particle band structure calculations with spin-orbit interaction to investigate the band structures of Mg2Si, Mg2Ge, and Mg2Sn. For all Mg2X materials, where X = Si, Ge, and Sn, the characteristics of band edge states, i.e., band and valley degeneracies, and orbital characters, are found to be conserved, independent of the computational schemes such as density functional generalized gradient approximation, hybrid functionals, or quasi-particle calculations. However, the magnitude of the calculated band gap varies significantly with the computational schemes. Within density-functional calculations, the one-particle band gaps of Mg2Si, Mg2Ge, and Mg2Sn are 0.191, 0.090, and -0.346 eV, respectively, and thus severely underestimated compared to the experimental gaps, due to the band gap error in the density functional theory and the significant relativistic effect on the low-energy band structures. By employing hybrid-functional calculations with a 35% fraction of the exact Hartree-Fock exchange energy (HSE-35%), we overcame the negative band gap issue in Mg2Sn. Finally, in quasi-particle calculations on top of the HSE-35% Hamiltonians, we obtained band gaps of 0.835, 0.759, and 0.244 eV for Mg2Si, Mg2Ge, and Mg2Sn, respectively, consistent with the experimental band gaps of 0.77, 0.74, and 0.36 eV, respectively. _____________________________ a) Corresponding author: byungkiryu@keri.re.kr.

Overcoming Asymmetric Contact Resistances in Al-Contacted Mg2(Si,Sn) Thermoelectric Legs

“…where E tot [D q ] and E 0 are total energies with and without defects, subscript i indicates the atomic element, µ i is the atomic chemical potential, δn i is the change of number of i-th element in the defective supercell with respect to the pristine one, and E F is the Fermi level of the system. Detailed information can be found in our previous work [39][40][41].…”

Native point defects and low p-doping efficiency in Mg2(Si,Sn) solid solutions: A hybrid-density functional study

“…As their charge states are fixed when EFermi changes in the range inside the band gap, they are shallow donors and acceptors, respectively. Compared to conventional DFT, the VBM positions are lowered in the hybrid-DFT calculations [20]. While the DFT calculations gives the defect formation energy of IMg 2+ at the VBM to be about 0.5 eV [18], our 2020-03-20 (v4.00) 6 / 28 hybrid calculations show the formation energy of IMg 2+ at the VBM to be about 0 eV.…”

“…Experimental lattice parameters were used for Mg2Si (6.35 Å) and Mg2Sn (6.75 Å) 2020-03-20 (v4.00) 5 / 28 [8]. In conventional DFT the band gap problem is severe: for Mg2Sn the DFT Eg is negative (-0.341 eV) whereas the experimental gap is about 0.36 eV [8,20]. As the charge state of the defects are sensitive to the Fermi level (EFermi), the positions of band edge states are critical for the defect stability.…”

“…However, while the Eg underestimation in density functional theory (DFT) is challenging in defect physics [19], many of these recent defect computations in thermoelectric materials are merely based on this scheme using conventional local-density approximation or generalized-gradient approximation (GGA). For example, as the Mg2Sn is negative in DFT calculations [20], the detailed quantitative role of intrinsic defects in Mg2Sn and Mg2(Si,Sn) 2020-03-20 (v4.00…”

Understanding the dopability of p-type Mg2(Si,Sn) by relating hybrid-density functional calculation results to experimental data

“…Therefore we used hybrid-DFT calculations to obtain the band gaps of Mg 2 Si and Mg 2 Sn. Note that non-hybrid DFT calculations severely underestimate the corresponding band gaps [40].…”