Bound States in Optical Absorption of Semiconductor Quantum Wells Containing a Two-Dimensional Electron Gas

The dependence of the optical absorption spectrum of a semiconductor quantum well on two-dimensional electron concentration $n_e$ is studied using CdTe samples. The trion peak $\left(X^{-}\right)$ seen at low $n_e$ evolves smoothly into the Fermi edge singularity at high $n_e$. The exciton peak $\left(X\right)$ moves off to high energy, weakens, and disappears. The ${X,X}^{-}$ splitting is linear in $n_e$ and closely equal to the Fermi energy plus the trion binding energy. For ${\mathrm{Cd}}_{0.998}{\mathrm{Mn}}_{0.002}\mathrm{Te}$ quantum wells in a magnetic field, the ${X,X}^{-}$ splitting reflects unequal Fermi energies for $M=\pm 1/2$ electrons. The data are explained by Hawrylak's theory of the many-body optical response including spin effects.