Influence of Cu and Na incorporation on the thermodynamic stability and electronic properties of $β-In_2 S_3$

The aim of this study is to understand the effect of Na and Cu incorporation in $In_2S_3$, which is representing a Cd-free buffer system for chalcopyrite-type thin film solar cells based on $Cu(In,Ga)Se_2$ (CIGS). The formation energies and charge states of sodium and copper dopants in $In_2S_3$ are investigated by means of calculations based on electronic hybrid density functional theory using supercells of 320-atoms. Our results reveal a negative formation enthalpy of sodium in both In-rich and S-rich samples, which indicates the occurrence of side reactions and explains the existence of a chemically modified buffer layer in the presence of a Na-reservoir. Copper, in contrast, can be incorporated in large concentrations in In-rich $In_2S_3$ under n-type conditions, acting as an acceptor and thus limiting the n-type conductivity. For lower Fermi energies, however, reactions between Cu and the buffer material lead to the formation of Cu-containing secondary phases in the buffer side which is in qualitative agreement with experimental observations of Bär et al. [Bär et al., Appl. Mater. Interfaces, 2016, 8, 2120]. Sulfur rich samples are found to be more heavily doped under n-type conditions and we expect to have Na- and Cu-containing secondary phases formed under metal-poor growth conditions