DFT calculation on electronic properties of vacancy-ordered double perovskites Cs2(Ti, Zr, Hf)X6 and their alloys: Potential as light absorbers in solar cells

Electronic properties of Cs-2(Ti, Zr, Hf)X-6, where X = I, Br, and Cl in vacancy-ordered double perovskite (VODP) structure were studied by using the density functional theory (DFT) calculation with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and spin-orbit coupling (SOC). The "quasi-direct bandgap" of these semiconductors was found, indicating the significantly small difference between indirect (Gamma-X) and direct (Gamma-Gamma) bandgaps. The bandgaps of VODP are in the range of 1.08-3.51 eV for Cs2TiX6, 2.63-5.21 eV for Cs2ZrX6, and 3.04-5.65 eV for Cs2HfX6, which could be suitable for a wide range of applications such as solar cells, optoelectronics, and photodetectors. Moreover, the electron contributions to the valence band maximum (VBM) and conduction band minimum (CBM) of VODP are dominated from p-orbital of X-site atoms (I, Br, Cl) and d-orbital of B-site atoms (Ti, Zr, Hf), opening up the opportunity to tune the bandgap by mixing X-or B-site atoms. In this study, we also examined two alloy-systems by mixing B-site atoms, which possess lattice mismatches of less than 1%. We found that by mixing Hf and Zr more than 25% (x greater than 0.25) into Cs2TiI6, the bandgaps of Cs2Ti1-xZrxI6 and Cs2Ti1-xHfxI6 change to the direct type. A fraction of Hf and Zr less than 25% could provide the suitable bandgaps for the light-absorber layer of single junction solar cells, while higher fractions of Zr (25-75%) and Hf (25-50%) could achieve the appropriate bandgap for higher-bandgap materials in tandem solar cells. Additionally, when the relationship between bandgaps and mixing concentration (x) was extracted using Vegard's law, we found that this relationship aligned well with the x-dependent bowing parameter, b(x), rather than the constant b. Our investigation proved that Cs-2(Ti, Zr, Hf)X-6 could provide greater benefit than the conventional perovskite (CP) CsBX3 due to their stability, lattice matches, and the wide range of their bandgaps.