Sulfur Vacancy Clustering and Its Impact on Electronic Properties in Pyrite FeS₂

A sulfur vacancy-related defect has been recently experimentally identified as the source of unintentional n-type doping in pyrite FeS2, a potential earth-abundant, nontoxic, ultralow-cost absorber for thin film solar cells. Historically, however, theory has not supported this possibility, as simple S mono-vacancies have high formation energies, as well as donor state energies inconsistent with experiment. Here, we use density functional theory to perform a detailed and systematic study of S vacancies in pyrite, considering not only mono-vacancies but also multiple forms of vacancy clusters. We first confirm that the S mono-vacancy indeed produces a donor state too far from the conduction band minimum to explain recent experiments. Four configurations of S di-vacancies are then investigated, leading to the finding that S-S dimer vacancies induce an elevated donor state near the middle of the gap. Importantly, significant binding energy for defect clustering occurs for both this defect and a trans-S di-vacancy, which features two mono-vacancies across a common Fe coordination center. We then combine these defects to construct a tetra-vacancy complex, calculating a deep donor state 0.41 eV below the conduction band minimum, thus achieving the best agreement to date with the experimental value of 0.23 eV. There is a yet more sizable binding energy associated with this tetra-vacancy, suggesting that further vacancy clustering is likely in pyrite. We then outline how initial vacancy incorporation, as a source for clustering, could occur, via routes governed by either thermal equilibrium or kinetic trapping of surface-created vacancies during pyrite crystal growth. This study thus advances S vacancy clusters as the defects likely responsible for the n-type doping effects observed in pyrite FeS2, advancing the understanding of doping in this promising photovoltaic material.