Abundant defects and defect clusters in kesterite Cu$_2$ZnSnS$_4$ and Cu$_2$ZnSnSe$_4$*

Cu$_2$ZnSnS$_4$ and Cu$_2$ZnSnSe$_4$ are drawing intensive attention as the light-absorber materials in thin-film solar cells. A large variety of intrinsic defects can be formed in these quaternary semiconductors, which have important influence on their optical and electrical properties, and hence their photovoltaic performance. We will present our first-principles calculation study on a series of intrinsic defects and defect clusters in Cu$_2$ZnSnS$_4$ and Cu$_2$ZnSnSe$_4$, and discuss: (i) strong phase-competition between the kesterites and the coexisting secondary compounds; (ii) the dominant Cu$_{\mathrm{Zn}}$ antisites and Cu vacancies which determine the intrinsic p-type conductivity, and their dependence on the elemental ratios; (iii) the high population of charge-compensated defect clusters (like V$_{\mathrm{Cu}}+$Zn$_{\mathrm{Cu}}$ and 2Cu$_{\mathrm{Zn}}+$Sn$_{\mathrm{Zn}})$ and their contribution to non-stoichiometry ; (iv) the deep-level defects which act as recombination centers. Based on the calculation, we will explain the experimental observation that Cu poor and Zn rich conditions give the highest solar cell efficiency, as well as suggesting an efficiency limitation in Cu$_2$ZnSn(S,Se)$_4$ cells with high S composition.