Theoretical consideration on Urbach energy for doped III-V Semiconductors

This work develops an analytical model for quantitatively estimating the Urbach energy 〖(E〗_U) as a function of doping concentration in semiconductors with non-isovalent doping, accounting contributions from structural disorder, carrier-impurity interactions, and carrier-phonon interactions. In the first part of the paper the contribution from carrier-impurity interaction is formulated as per Halperin-Lax and Edwards model, the correction term due to structural disorder is included and the carrier-phonon interaction contribution is formulated by analytically solving the correlation function for longitudinal-optical (LO) phonon-carrier interactions. The total E_U is expressed separately n-type or p-type impurities and the calculated values agree very well with the experimental data available in the literature for Group III-V semiconductors at 300 K. We further quantify the relative scaling of individual contributions with doping concentration at 300 K.