Generalized Scaling Law for Exciton Binding Energy in Two-Dimensional Materials

Binding energy calculation in two-dimensional (2D) materials is crucial in determining their electronic and optical properties pertaining to enhanced Coulomb interactions between charge carriers due to quantum confinement and reduced dielectric screening. Based on full solutions of the Schrodinger equation in a screened hydrogen model with a modified Coulomb potential (1/r(beta-2)), we present a generalized and analytical scaling law for the exciton binding energy, E-beta = E-0 (alpha beta(b) + c) (mu/epsilon(2)), where beta is a fractional-dimension parameter that accounts for the reduced dielectric screening. The model is able to provide accurate binding energies, benchmarked using the reported Bethe-Salpeter equation and experimental data, for 58 monolayer 2D and eight bulk materials, respectively, through beta. For a given material, beta is varied from beta = 3 for bulk three-dimensional materials to a value lying in the range 2.55-2.7 for 2D monolayer materials. With beta(mean) = 2.625, our model improves the average relative mean square error by a factor of 3 in comparison to existing models. The results can be used for Coulomb engineering of exciton binding energies in the optimal design of 2D materials.