Defect physics of the kesterite thin-film solar cell absorber Cu$_2$ZnSnS$_4$

Using first-principles calculations, we studied the thermodynamic stability and intrinsic defects of the quaternary Cu$_2$ZnSnS$_4$ (CZTS) semiconductor, which are crucial for further improvement of its solar cell efficiency. We find that (i) The chemical potential region that CZTS can form stoichiometrically is very small. Therefore, it will be very difficult to obtain high quality CZTS samples; (ii) The p-type defects have much lower formation energy than n-type defects, and the dominant acceptor is Cu$_{\mathrm{Zn}}$, however, the associated acceptor level is relatively deep; (iii) The formation of the self-compensated defect pair [Cu$_{\mathrm{Zn}}$+Zn$_{\mathrm{Cu}}$] will not lead to strong carrier separation, and thus will not contribute to the same beneficial effect observed in CuInSe$_2$; (iv) We predict that to avoid the issues in (ii) and (iii), non-equilibrium techniques and Cu-poor/Zn-rich conditions should be used to grow the CZTS sample without ZnS secondary phase, so V$_{\mathrm{Cu}}$ and Zn$_{\mathrm{Cu}}$ become the dominant defects.