Origins of varying carrier concentration in Cu$_2$SnS$_3$ photovoltaic absorbers

Within the Cu-Sn-S family of earth abundant photovoltaic absorbers, the Cu$_2$SnS$_3$ phase is predicted to be the most promising absorber material [P. Zawadzki, et al.]. To date there has been limited synthetic work on the Cu$_2$SnS$_3$ phase, particularly the carrier concentration. In this study, we develop an understanding of the effects of RF sputtering growth conditions on the hole concentrations of Cu$_2$SnS$_3$ absorber films, and use these results to identify the underlying causes of the observed variations in carrier concentration. Two effects are identified that control the carrier concentration in Cu$_2$SnS$_3$ films. The first effect, which occurs during Cu-rich growth, is isostructural alloying with a metallic Cu$_3$SnS$_4$ phase, which gives rise to hole concentrations above 10$^{19}$ cm$^{-3}$. The second effect is that, when the Cu$_2$SnS$_3$ films are grown under Sn-rich conditions, varying the S chemical potential during film deposition gives 10$^{18}$-10$^{19}$ cm$^{-3}$ holes. This variation in carrier concentration with S chemical potential can be explained by a Cu vacancy defect model. Understanding the origins of the varying doping density in Cu$_2$SnS$_3$ films allows for targeted growth to achieve desired carrier concentrations for device integration.