Mathematical Modeling of Urbach Tail States in Semiconductors With Iso‐valent Impurity Concentration

The electronic disorder in a semiconductor, commonly quantified in terms of Urbach energy (), is known to be influenced by both temperature and impurity concentration (). The temperature dependence of has been extensively investigated in various research articles, whereas a quantitative understanding of as a function of remains limited. In this work, we present an analytical theory of in iso‐valent‐doped semiconductors within the Edwards and Halperin–Lax theoretical framework, explicitly incorporating the screening Length () to derive a scaling relation . This theoretical formalism is experimentally verified through Hf‐doped BaTiO 3 and Cr‐doped PrFeO 3 samples. Additionally, the developed theoretical model enables estimation of the carrier effective mass (𝑚∗) as a function of , yielding good agreement with experimental results. The obtained results are consistent with prior research, supporting the validity of this approach. Overall, this study provides a quantitative framework for understanding electronic disorders and their implications for semiconductor performance.