Theoretical consideration on Urbach energy for doped III–V semiconductors

Abstract

This work develops an analytical model for quantitatively estimating the Urbach energy (Formula presented) (Formula presented) 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 the 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 phonon–carrier interactions. The total (Formula presented) (Formula presented) is expressed separately for n-type and 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. © 2026 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved. This article is available under the terms of the IOP-Standard License.