Lone-pair effect on carrier capture in Cu$_2$ZnSnS$_4$ solar cells

The performance of kesterite thin-film solar cells is limited by a low open-circuit voltage due to defect-mediated electron-hole recombination. We calculate the non-radiative carrier-capture cross sections and Shockley-Read-Hall recombination coefficients of deep-level point defects in Cu$_2$ZnSnS$_4$ (CZTS) from first-principles. While the oxidation state of Sn is +4 in stoichiometric CZTS, inert lone pair (5$s^2$) formation lowers the oxidation state to +2. The stability of the lone pair suppresses the ionization of certain point defects, inducing charge transition levels deep in the band gap. We find large lattice distortions associated with the lone-pair defect centers due to the difference in ionic radii between Sn(II) and Sn(IV). The combination of a deep trap level and large lattice distortion facilitates efficient non-radiative carrier capture, with capture cross-sections exceeding $10^{-12}$ cm$^2$. The results highlight a connection between redox active cations and `killer' defect centres that form giant carrier traps. This lone pair effect will be relevant to other emerging photovoltaic materials containing n$s^2$ cations.