Structure, stability, and defect analysis of potential solar absorber Cu$_3$PSe$_4$

The semiconductor Cu$_3$PSe$_4$ has recently been established to have a direct band gap of 1.4 eV and exhibit p-type conductivity [Applied Physics Letters, 99, 181903 (2011)]. Here we present density functional theory (DFT) and post-DFT results regarding the structure, stability, and dopability of Cu$_3$PSe$_4$. We a find a strong coupling between the electronic band gap and the atomic structure, clearly caused by the strong P-Se antibonding character of the conduction band. Using the Heyd-Scuseria-Enzerhof hybrid functional and $GW$ approximation methods, we find that structural relaxation using standard DFT is not sufficiently accurate to be used as input to static, post-DFT electronic structure calculations. We use the generalized gradient approximation (GGA) and the GGA+$U$ method to show a thermodynamically stable low temperature region. We calculate the formation enthalpies of intrinsic and extrinsic defects in order to understand the observed p-type behavior and to examine n-type doping mechanisms.