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

Abstract

Recent work on quaternary semiconductors Cu 2 BaSn(S,Se) 4 and Ag 2 BaSnSe 4 for photovoltaic and thermoelectric applications, respectively, has shown the promise of exploring the broader family of defect-resistant I 2 -II-IV-X 4 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 I 2 -II-IV-X 4 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 wellstudied 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 I 2 -II-IV-X 4 compounds, Ag 2 BaSiS 4 , Ag 2 PbSiS 4 , Cu 2 PbGeS 4 , and Cu 2 SrSiS 4 , can be synthesized in correctly predicted phases. One of these compounds, Ag 2 PbSiS 4 , shows potentially promising optoelectronic properties for photovoltaic applications.

Synthesis, crystal structure, and electronic structure of Li2PbSiS4: a quaternary thiosilicate with a compressed chalcopyrite-like structure

“…Likewise, comparisons of the calculated bandgaps for Li 2 PbGeS 4 (Aitken et al 2001) and Ag 2 PbGeS 4 (Nhalil et al, 2018;Vu et al 2018), as well as Li 2 BaGeS 4 and Ag 2 BaGeS 4 (Wu et al, 2017), further exemplify this trend (Table 5). As expected, the calculated bandgap of 2.22 eV determined for the title compound, Li 2 PbSiS 4 , is notably larger than the bandgaps of 2.13 and 0.91 eV that were calculated for the silver and copper analogs Ag 2 PbSiS 4 and Cu 2 PbSiS 4 , respectively (Sun et al, 2020;Nhalil et al, 2018) (Table 5).…”

“…the distortion of the polyhedra causes a lowering of the symmetry from tetragonal (stannite) to orthorhombic (Teske & Vetter, 1976;Assoud et al, 2005). Additionally, there are several other related structures that can be stabilized, as explained recently by Sun and co-workers (Sun et al, 2020). For example, a number of compounds can be found in the Cu 2 SrSnS 4 structure type, crystallizing in the space group P3 1 (Teske, 1976), as well as the two different structure types with Ama2 symmetry, i.e.…”

“…Recently, a strategy towards improved, next-generation multinary metal chalcogenides has been proposed, where the difference among the constituent elements can be exploited to avoid anti-site defects that can sometimes be detrimental to the optimization of semiconductor properties, due to issues such as band tailing (Sun et al, 2020). This strategy can be implemented by choosing cations with disparate crystal radii, and therefore coordination environments, resulting in what have been termed 'defect-resistant' semiconductors.…”

“…Just as there are multiple crystal structures for quaternary diamond-like chalcogenides (Brunetta et al, 2013), there exist numerous structures for the compressed versions (Sun et al, 2020). The closest relatives to the compressed chalcopyrites with the space group I42m are those crystallizing in the space group I222, for example, Ag 2 BaSnS 4 and Ag 2 BaSnSe 4 , where Cross-substitution diagram demonstrating the hierarchy of tetrahedral structures.…”

Mechanistic insight of KBiQ2 (Q = S, Se) using panoramic synthesis towards synthesis-by-design

“…This work is one of the pioneer studies in proposing a tolerance factor for a chalcogenide system. [52][53][54] We have also performed density functional theory (DFT) calculations to show that the cation-ordered β-KBiQ 2 polymorphs are thermodynamically stable and demonstrated that DFT can be used as a complimentary tool in the panoramic studies to determine the phase stabilities.…”