Structural Tolerance Factor Approach to Defect-Resistant I₂-II-IV-X₄ Semiconductor Design

Recent work on quaternary semiconductors Cu2BaSn(S,Se)4 and Ag2BaSnSe4 for photovoltaic and thermoelectric applications, respectively, has shown the promise of exploring the broader family of defect-resistant I2-II-IV-X4 materials (where I, II, and IV refer to the formal oxidation state of the metal cations and X is a chalcogen anion) with tetrahedrally coordinated I/IV cations and larger II cations (i.e., Sr, Ba, Pb, and Eu) for optoelectronic and energy-related applications. Chemical dissimilarity among the II and I/IV atoms represents an important design motivation because it presents a barrier to antisite formation, which otherwise may act as electronically harmful defects. We herein show how all 31 experimentally reported I2-II-IV-X4 examples (with large II cations and tetrahedrally coordinated smaller I/IV cations), which form within five crystal structure types, are structurally linked. Based on these structural similarities, we derive a set of tolerance factors that serve as descriptors for phase stability within this family. Despite common usage in the well-studied perovskite system, Shannon ionic radii are found to be insufficient for predicting metal–chalcogen bond lengths, pointing to the need for experimentally derived correction factors as part of an empirically driven learning approach to structure prediction. We use the tolerance factors as a predictive tool and demonstrate that four new I2-II-IV-X4 compounds, Ag2BaSiS4, Ag2PbSiS4, Cu2PbGeS4, and Cu2SrSiS4, can be synthesized in correctly predicted phases. One of these compounds, Ag2PbSiS4, shows potentially promising optoelectronic properties for photovoltaic applications.