Onset of exciton absorption in modulation-doped GaAs quantum wells

We study the evolution of the absorption spectrum of a modulation-doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ semiconductor quantum well with decreasing the carrier density. We find that at some critical electron density there is a sharp change in the line shape and the transitions energies of the exciton peaks. We show that this critical density marks an abrupt transition from a simple excitonic behavior to a Fermi edge singularity.