Exploring the Interrelation between Urbach Energy and Dielectric Constant in Hf-Substituted BaTiO₃

The variation of dielectric constant (ε_r) in the low-frequency region (∼10⁶ Hz) in Hf-substituted BaTiO₃ has been modelled considering the electronic disorder in the form of Urbach energy (E _U) with the help of a Bohr-like model. Optical absorption spectroscopy has been employed in order to estimate E _U and also the band gap (E _g), which are found to scale systematically with Hf incorporation, whereas dielectric measurements reveal a decrease in the value of ε_r observed in the frequency range up to 10⁶ Hz with Hf substitution in these prepared samples. The model predicts E _U ∝ 1/ε_r ² and E _g ∝ 1/ε_r ², which agrees with the variation of the corresponding experimental values. Thus, the present work contributes to understanding the interconnection between the optical and dielectric properties of such materials and successfully demonstrates the decrease in dielectric constant with increasing disorder.