Pushing the boundary of the stability and band gap Pareto front by going towards high-entropy perovskites

Lead-free Cs₂BX₆ (B = Zr⁴⁺, Sn⁴⁺, Te⁴⁺, Hf⁴⁺, Re⁴⁺, Os⁴⁺, Ir⁴⁺, and Pt⁴⁺ and X = Cl^-, Br^-, and I^-) vacancy-ordered double perovskites have gained significant attention due to their high performance in solar cell devices. Besides mitigating toxicity concerns associated with the use of lead, the presence of a formally tetravalent B-site in Cs₂BX₆ has been demonstrated to improve the stability against air and moisture. Recently, experimental studies have shown that high-entropy forms of vacancy-ordered double perovskites can be synthesized and stabilized at room temperature, which opens new opportunities for designing better solar cell absorbers. In this work, we employed high throughput density functional theory (DFT) calculations using the HSE06 hybrid functional to study 546 medium-to-high-entropy vacancy-ordered double perovskites. Our results show that Cs₂{B₁B₂B₃B₄}₁X₆ and Cs₂{B₁B₂B₃B₄}₁{XX'}₆ perovskites can break the existing linear scaling relationships between the bandgap and formation energy observed in the pure Cs₂BX₆ and Cs₂B{XX'}₆ perovskites, which enables materials that simultaneously exhibit an optimal band gap of ∼1.3 eV for single-junction solar cells along with a low formation energy. Electronic structure analysis reveals that this can be attributed to the weak coupling between the BX₆ octahedra in Cs₂{B₁B₂B₃B₄}₁X₆ and Cs₂{B₁B₂B₃B₄}₁{XX'}₆. Based on these findings, we identified the analytical equations that can be used to efficiently predict the band gap and formation energy of high-entropy perovskites from their constituent pure perovskites. Our study offers simple and practical guidelines for the design and synthesis of novel high-entropy perovskites with improved photovoltaic performance.