Exciton binding energy and screening length in two-dimensional semiconductors

We approximately solve the Schr\"odinger equation for two-dimensional Wannier-Mott excitons in the effective-mass approximation and derive an expression for the exciton energy levels, hence the exciton binding energy. The electron-hole interaction is described by the Rytova-Keldysh potential in a logarithmic approximation. From the derived expression, we introduce approximate expressions to experimentally determine the exciton binding energy (along with the quasiparticle band gap), the screening length, and the exciton reduced mass from measured exciton transition energies of the ground state ($1s$), and the first ($2s$) and the second ($3s$) excited states. Our results agree well with experimental data and theoretical calculations.