Design Rules for Optimizing Quaternary Mixed-Metal Chalcohalides

TL;DR

The study presents a data-driven design framework for quaternary mixed-metal chalcohalides (MMCHs) by integrating density functional theory with random forest regression and SHAP analysis across 54 compounds and three crystal phases. It reveals that electron-acceptor sites on the Ch and X atoms predominantly govern thermodynamic stability and band-edge positions, while electron-donor metal sites enable property fine-tuning; phase choices shift band gaps and carrier masses, with $P2_1/c$ generally more indirect and heavier than $Cmcm$ and $Cmc2_1$. The work establishes concrete design rules linking site identity and elemental substitutions to formation energies, band gaps, and effective masses, and highlights promising Pb- and Sn-based MMCH candidates (e.g., Pb$_2$SbSe$_2$Cl$_3$, Sn$_2$BiS$_2$I$_3$) for experimental exploration. These insights advance materials-by-design for stable, efficient, lead-containing or lead-free photovoltaic absorbers in the MMCH family. Overall, the combination of DFT, RF, and SHAP provides a robust path to tailor composition and structure for targeted optoelectronic performance in complex quaternary semiconductors.

Abstract

Quaternary mixed-metal M(II)2M(III)Ch2X3 chalcohalides are an emerging material class for photovoltaic absorbers that combines the beneficial optoelectronic properties of lead-based halide perovskites with the stability of metal chalcogenides. Inspired by the recent discovery of lead-free mixed-metal chalcohalides materials, we utilized a combination of density functional theory and machine learning to determine compositional trends and chemical design rules in the lead-free and lead-based materials spaces. We explored a total of 54 M(II)2M(III)Ch2X3 materials with M(II) = Sn, Pb, M(III) = In, Sb, Bi, Ch = S, Se, Te, and X = Cl, Br, I per phase (Cmcm, Cmc21 , and P21/c). The P21/c phase is the equilibrium phase at low temperatures, followed by Cmc21 and Cmcm. The fundamental band gaps in Cmcm and Cmc21 are smaller than those in P21/c, but direct band gaps are more common in Cmcm and Cmc21. The effective electron masses in P21/c are significantly larger compared to Cmcm and Cmc21, while the effective hole masses are nearly the same across all three phases. Using random forest regression, we found that the two electron acceptor sites (Ch and X) are crucial in shaping the properties of mixed-metal chalcohalide compounds. Furthermore, the electron donor sites (M(II) and M(III)) can be used to finetune the material properties to desired applications. These design rules enable precise tailoring of mixed-metal chalcohalide compounds for a variety of applications.

Figures (7)

• Figure 1: Illustration of different phases; a) $Cmcm$, b) $Cmc2_1$, and c) $P2_1/c$ in MMCH structures. The respective M(II) coordination polyhedrons are depicted in cyan and the M(III) coordination polyhedrons in green. The coordinates of each phase were taken from the Materials Projectmaterialsproject2013 and were visualized with VESTA.momma2008
• Figure 2: Summary of the feature importance of the formation energy in the RF model for the $Cmcm$ phase: a) Normalized atom site importance for the predicted formation energy in percent; b) impact of elements on the M(II)-, M(III)-, Ch-, and X-sites measured in terms of their mean SHAP values on the predicted base formation energy value in . The error bars denote the standard deviation for each mean SHAP value. Since the formation energy is negative, negative mean SHAP values indicate a stabilization of the material and positive SHAP values a destabilization.
• Figure 3: Summary of the feature importance of the fundamental band gap in the RF model for the $Cmcm$ phase: a) Normalized atom site importance for the predicted fundamental band gap in percent; b) impact of elements on the M(II)-, M(III)-, Ch- and X-sites quantified in terms of their mean SHAP values for the predicted base fundamental band gap in . The error bars denote the standard deviation for each mean SHAP value.
• Figure 4: Summary of the feature importance of the effective electron mass in the RF model for the $Cmcm$ phase: a) Normalized atom site importance for the predicted electron mass in percent; b) impact of elements on the M(II)-, M(III)-, Ch-, and X-sites quantified in terms of their mean SHAP values for the predicted base effective hole mass value per $m_0$ (free electron mass). The error bars denote the standard deviation for each mean SHAP value.
• Figure 5: Summary of the feature importance of the effective hole mass in the RF model for the $Cmcm$ phase: a) Normalized atom site importance for the predicted effective hole mass in percent; b) impact of elements on the M(II)-, M(III)-, Ch-, and X-sites quantified in terms of their mean SHAP values for the predicted base effective hole mass value per $m_0$. The error bars denote the standard deviation for each mean SHAP value.