Intrinsic Point Defects and Frenkel Pair Formation in Photovoltaic Absorber Zn$_3$P$_2$: Regulating $p$-type Conductivity through Growth and Annealing Conditions

Abstract

This study investigates the ground-state energetics and thermodynamics of intrinsic point defects in zinc phosphide Zn$_3$P$_2$ using \emph{ab initio} density functional theory combined with an extensive potential energy landscape search. Our analysis reveals that the defect chemistry is dominated by zinc vacancies $V_\mathrm{Zn}$ and zinc interstitials Zn$_i$, with equilibrium concentrations significantly surpassing those of other intrinsic species. Notably, we find that phosphorus interstitials P$_i$, previously suggested to be significant, possess high formation energies and likely exist only in negligible quantities. The characteristic $p$-type conductivity of undoped Zn$_3$P$_2$ is shown to be a direct consequence of zinc vacancies, which act as shallow acceptors and pull the Fermi level toward the valence band. Furthermore, we identify a positive binding energy between $V_\mathrm{Zn}$ and Zn$_i$, leading to the formation of electrically benign Frenkel pairs that partially compensate the intrinsic p-type conductivity. Our results suggest that achieving $n$-type conductivity is fundamentally limited by these thermodynamic constraints. We conclude that hole densities can be optimized through phosphorus-rich growth conditions and high-temperature annealing, and suggest that future photovoltaic strategies should prioritize interface engineering over bulk $n$-type doping.