Electron-hole plasma effect on excitons in ${\mathrm{G}\mathrm{a}\mathrm{N}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ quantum wells

The self-consistent procedure of solving both the Schrödinger and Poisson equations for electron and hole wave functions has been combined with the variational calculation of exciton states in strained ${\mathrm{G}\mathrm{a}\mathrm{N}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ quantum wells. The procedure accounted properly for the free-carrier effects on the excitonic wave function, namely, the exciton bleaching and the quantum exclusion effects. It also allowed us to quantify the dependence of the exciton energy and of the oscillator strength on the optical pumping density. The calculation revealed an interesting interplay between the screening of the polarization fields, which leads to the increase of the electron-hole overlap, and the screening of the electron-hole interaction, which affects the exciton Bohr radius. The peculiar nonmonotonic behavior of the exciton binding energy as a function of the density of the electron-hole plasma results from these combined effects.