Ti Doping in Cs ₂ HfX ₆ (X = Cl, Br, I): A Route to Enhanced Photovoltaic and Thermoelectric Performance

Vacancy-ordered double perovskites Cs 2 HfX 6 (X = Cl, Br, I) have emerged as environmentally friendly alternatives to lead-based perovskites for optoelectronic and thermoelectric applications. In this study, we employ state-of-the-art first-principles calculations to investigate the structural, electronic, optical, mechanical, and thermoelectric properties of these halide double perovskites. The pristine and Ti-doped Cs 2 HfX 6 (X = Cl, Br, I) compounds exhibit negative formation energies, indicating thermodynamic stability. Phonon dispersion analysis reveals that Cs 2 HfI 6 is dynamically stable at 0 K, showing no imaginary frequencies across the Brillouin zone, whereas Cs 2 HfBr 6 and Cs 2 HfCl 6 exhibit small soft modes near the Γ-point. These instabilities suggest a tendency toward structural distortion in the harmonic approximation, which may be suppressed at finite temperatures. Ti doping eliminates imaginary modes in Cs 2 HfCl 6, partially stabilizes Cs 2 HfBr 6, but introduces soft modes in Cs 2 HfI 6 . These results highlight the composition-dependent role of cation substitution in tuning lattice stability. Density of states analysis reveals that Ti 3d states introduce additional conduction pathways, resulting in improved charge transport characteristics. Simulated device performance demonstrates that Cs 2 Hf 0.5 Ti 0.5 I 6 achieves a cell efficiency of 20.29%, outperforming pristine absorbers. Additionally, Ti doping significantly enhances thermoelectric performance by increasing electrical conductivity. Since only the electronic component of the thermal conductivity was calculated, the full ZT values cannot be obtained; however, κ e -based estimates are presented to assess trends. The reported thermoelectric figure of merit values (ZTe ≈ 1.6 at 1000 K for pristine Cs 2 HfCl 6, and surpassing 2.0 for Ti-doped Cs 2 Hf 0.5 Ti 0.5 Cl 6 at 1000 K, with trends also evaluated at 50 K) represent electronic-only upper-limit estimates, since the lattice contribution to the thermal conductivity (κ 1 ) has not been included. These findings demonstrate how cation engineering can be used to adjust multifunctional properties. Overall, the results show that mixed-metal halide double perovskites hold promise as lead-free, tunable materials for high-performance thermoelectric and photovoltaic energy conversion applications.