Mg${}_2$Si and Ca${}_2$Si 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 Mg${}_2$Si and Ca${}_2$Si using density-functional theory and Bethe-Salpeter equation (BSE) based methods. The band-gap for Mg${}_2$Si (Ca${}_2$Si) is found to be in the range of 0.25-0.6 (0.57-0.96) eV when PBE, PBEsol and mBJ functionals are used. In the independent-particle approximation (IPA), the real and imaginary parts of dielectric function show maximum values of 50 (16.3) at 2.6 (1.0) eV and 61 (16.2) at $\sim$3.24 (3.4) eV, respectively. Within BSE, these respective values change to 59 (17) at 2.5 (0.86) eV and 65 (16.6) at 2.68 (3.1) eV. The excitonic effect is found to be crucial in understanding the experimental optical spectra of Mg${}_2$Si. However, this effect is relatively weaker in Ca${}_2$Si. Present study highlights the importance of different levels of theoretical approximations for obtaining the optical spectroscopy data of silicides with a high level of accuracy. Finally, we have evaluated PV efficiency by using spectroscopic limited maximum efficiency (SLME) calculation. On the top of radiative recombination, we have also incorporated non-radiative carrier recombination at a defect trap state via Shockley-Read-Hall (SRH) mechanism to evaluate the efficiency. Among the studied defects, the interstitial Mg (Si) is identified as the most stable in Mg${}_2$Si (Ca${}_2$Si) and this provides SRH lifetime of 2 $\mu s$ (11.3 $ms$). The estimated maximum SLME using BSE absorption spectrum is 1.3 (31.2)%, which decreases to 1.2 (28.5)% due to SRH recombination. The present study suggests that Ca${}_2$Si (Mg${}_2$Si) is a potential candidate for single-junction (bottom cell in multi-junction) thin-film PV devices.