First-principles calculations of Mg<sub>2</sub>X (X = Si, Ge, Sn) semiconductors with the calcium fluorite structure

Sandong Guo

doi:10.1088/1674-4926/36/5/053002

J. Semicond. > 2015, Volume 36 > Issue 5 > 053002, doi: 10.1088/1674-4926/36/5/053002

SEMICONDUCTOR MATERIALS

First-principles calculations of Mg₂X (X = Si, Ge, Sn) semiconductors with the calcium fluorite structure

Sandong Guo

+ Author Affiliations

Corresponding author: Sandong Guo , Email: guosd@cumt.edu.cn

Abstract: The electronic structures of Mg₂X (X = Si, Ge, Sn) have been calculated by using generalized gradient approximation, various screened hybrid functionals, as well as Tran and Blaha's modified Becke and Johnson exchange potential. It was found that the Tran and Blaha's modified Becke and Johnson exchange potential provides a more realistic description of the electronic structures and the optical properties of Mg₂X (X = Si, Ge, Sn) than else exchange-correlation potential, and the theoretical gaps and dielectric functions of Mg₂X (X = Si, Ge, Sn) are quite compatible with the experimental data. The elastic properties of Mg₂X (X = Si, Ge, Sn) have also been studied in detail with the generalized gradient approximation, including bulk modulus, shear modulus, Young's modulus, Poisson's ratio, sound velocities, and Debye temperature. The phonon dispersions of Mg₂X (X = Si, Ge, Sn) have been calculated within the generalized gradient approximation, suggesting no structural instability, and the measurable phonon heat capacity as a function of the temperature has been also calculated.

Key words: semiconductor, optical properties, elastic properties, phonon

References

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Fig. 1. Calculated energy bands and density of states (DOS, in state/eV per unit cell) of {Mg$_2$Si} within mBJ.

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Fig. 2. The real part $\varepsilon_1$ and imaginary part $\varepsilon_2$ of the dielectric functions of Mg$_2$Si (Top), Mg$_2$Ge (Middle) and Mg$_2$Sn (Bottom) calculated with mBJ (a 0.02 eV broadening for Mg$_2$Si and Mg$_2$Ge; a 0.2~eV broadening for Mg$_2$Sn to match the experimental results.) in comparison with experimental curves^[9].

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Fig. 3. Calculated optical conductivity $\sigma$ and optical absorption $\alpha$ with the mBJ, and a 0.02 eV broadening.

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Fig. 4. Phonon dispersions for Mg$_2$Si (Left), Mg$_2$Ge (Middle) and Mg$_2$Sn (Right) calculated with GGA.

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Fig. 5. Phonon heat capacity for Mg$_2$X (X $=$ Si, Ge, Sn) calculated with GGA.

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Table 1. Calculated energy gaps (using GGA, sX-LDA, PBE0, HSE03, HSE06 and mBJ) of Mg$_2$X (X $=$ Si, Ge, Sn), corresponding experimental results and other calculated values.

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Table 2. Elastic constants $C_{ij}$ (in GPa), bulk modulus $B$ (in GPa) compared to experimental values^{[39, 40]} given in parentheses and anisotropy factor $A$.

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Table 3. The calculated shear modulus $G$ (in GPa), Young's modulus $E$ (in GPa), Poisson's ratio $\nu$, $B/G$.

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Table 4. The calculated sound velocities $v_{\rm l}$, $v_{\rm t}$ and $v_{\rm m}$ (in m/s), $\rho$ (in kg/m$^3$) and Debye temperature $\theta_{\rm D}$ (in K).

DownLoad: CSV

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Received: 03 November 2014 Revised: Online: Published: 01 May 2015

The electronic structures of Mg₂X (X = Si, Ge, Sn) have been calculated by using generalized gradient approximation, various screened hybrid functionals, as well as Tran and Blaha's modified Becke and Johnson exchange potential. It was found that the Tran and Blaha's modified Becke and Johnson exchange potential provides a more realistic description of the electronic structures and the optical properties of Mg₂X (X = Si, Ge, Sn) than else exchange-correlation potential, and the theoretical gaps and dielectric functions of Mg₂X (X = Si, Ge, Sn) are quite compatible with the experimental data. The elastic properties of Mg₂X (X = Si, Ge, Sn) have also been studied in detail with the generalized gradient approximation, including bulk modulus, shear modulus, Young's modulus, Poisson's ratio, sound velocities, and Debye temperature. The phonon dispersions of Mg₂X (X = Si, Ge, Sn) have been calculated within the generalized gradient approximation, suggesting no structural instability, and the measurable phonon heat capacity as a function of the temperature has been also calculated.

First-principles calculations of Mg₂X (X = Si, Ge, Sn) semiconductors with the calcium fluorite structure

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First-principles calculations of Mg₂X (X = Si, Ge, Sn) semiconductors with the calcium fluorite structure

First-principles calculations of Mg₂X (X = Si, Ge, Sn) semiconductors with the calcium fluorite structure