Mg2Si and Ca2Si semiconductors for photovoltaic applications: Calculations based on density-functional theory and the Bethe-Salpeter equation

We conduct a comprehensive assessment of the electronic and optical properties, as well as photovoltaic (PV) performance parameters, for low-cost, nontoxic ${\mathrm{Mg}}_{2}\mathrm{Si}$ and ${\mathrm{Ca}}_{2}\mathrm{Si}$ using methods based on density-functional theory and the Bethe-Salpeter equation (BSE). The band gap for ${\mathrm{Mg}}_{2}\mathrm{Si}$ (${\mathrm{Ca}}_{2}\mathrm{Si}$) is found to be in the range of 0.25--0.6 (0.57--0.96) eV when the Perdew-Burke-Ernzerhof (PBE), PBE for solids (PBEsol), and modified Becke-Johnson (mBJ) functionals are used. The effective masses at the last-filled valence and first-empty conduction bands are in the range of 0.14--0.17 (1.17--1.25) ${m}_{e}$ and 0.27--0.29 (0.3--0.41) ${m}_{e}$, respectively. In the independent-particle approximation (IPA), the real and imaginary parts of the dielectric function show maximum values of $\ensuremath{\sim}50$ (16.3) at $\ensuremath{\sim}2.6$ (1.0) eV and $\ensuremath{\sim}61$ (16.2) at $\ensuremath{\sim}3.24$ (3.4) eV, respectively. Within the BSE, these respective values change to $\ensuremath{\sim}59$ (17) at $\ensuremath{\sim}2.5$ (0.86) eV and $\ensuremath{\sim}65$ (16.6) at $\ensuremath{\sim}2.68$ (3.1) eV. The excitonic effect is found to be crucial in understanding the experimental optical spectra of ${\mathrm{Mg}}_{2}\mathrm{Si}$. However, this effect is relatively weaker in ${\mathrm{Ca}}_{2}\mathrm{Si}$. In the active region of the solar spectrum, the highest absorption coefficient and lowest reflectivity change from $\ensuremath{\sim}1.5\phantom{\rule{0.2em}{0ex}}(0.75)\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{\sim}0.39$ (0.3), respectively, in the IPA, to $\ensuremath{\sim}1.6\phantom{\rule{0.2em}{0ex}}(0.88)\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{\sim}0.41$ (0.27) in the BSE. The present study highlights the importance of different levels of theoretical approximations for obtaining optical spectroscopy data of silicides with a high level of accuracy. Finally, we have evaluated the PV efficiency by using a spectroscopic limited maximum efficiency (SLME) calculation. On top of radiative recombination, we have also incorporated nonradiative carrier recombination at a defect trap state via the Shockley-Read-Hall (SRH) mechanism to evaluate the efficiency. Among the studied defects, interstitial $\mathrm{Mg}$ ($\mathrm{Si}$) is identified as the most stable in ${\mathrm{Mg}}_{2}\mathrm{Si}$ (${\mathrm{Ca}}_{2}\mathrm{Si}$), and this provides an SRH lifetime of $\ensuremath{\sim}2\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$ (11.3 ms). The estimated maximum SLME using the BSE absorption spectrum is $\ensuremath{\sim}1.3$% (31.2%), which decreases to $\ensuremath{\sim}1.2$% (28.5%) due to SRH recombination. The present study suggests that ${\mathrm{Ca}}_{2}\mathrm{Si}$ (${\mathrm{Mg}}_{2}\mathrm{Si}$) is a potential candidate for single-junction (bottom cell in multijunction) thin-film PV devices.