Trions, excitons, and scattering states in multiple quantum wells with a variable-concentration electron gas

$\mathrm{CdTe}/{\mathrm{Cd}}_{1-x}{\mathrm{Zn}}_x\mathrm{Te}$ multiple quantum wells were modulation doped with indium donors compensated by nitrogen acceptors so that the two-dimensional electron concentration in the wells ${(n}_e)$ could be varied from near 0 up to $\approx {10}^{11}{\mathrm{cm}}^{-2}$ by optical pumping. In zero field at $T=2\mathrm{}\mathrm{K},$ the optical absorption spectra show trion ${(X}^{-})$ and exciton (X) resonance peaks at low $n_e,$ with an electron-exciton scattering wing extending to high energy from the exciton resonance. At the highest $n_e,$ the spectrum evolves towards the single asymmetric peak traditionally associated with the many-body “Fermi edge singularity” but its total integrated intensity remains almost constant, in agreement with recent few-body theories of the optical response at $n_e\ll {1/a}_B^2.$ Under magnetic field $B=8\mathrm{}\mathrm{T}$ at $T=2\mathrm{}\mathrm{K},$ sharp $X^{-}$ and X resonance peaks are seen as well as a broad band Z situated about $ħ{\omega }_{\mathrm{ce}}$ (the electron cyclotron energy) higher in energy. Band Z is attributed to a known exciton-electron scattering process [Yakovlev et al., Phys. Rev. Lett. $79,$ 3974 (1997)] where the electrons are magnetically quantized. In ${\sigma }^{+}$ circular polarization, the X resonance attenuates rapidly with $n_e$ but the $X^{-}$ resonance grows almost as rapidly (“intensity sharing”) so that their intensity sum falls only slowly. In ${\sigma }^{-}$ the X resonance also attenuates rapidly with $n_e$ and the Z band grows to compensate, with the intensity sum again falling only slowly. It is concluded that the spectrum evolution as $n_e$ varies from 0 to ${10}^{11}{\mathrm{cm}}^{-2}$ in CdTe is due to intensity sharing between the X and $X^{-}$ resonances and between these resonances and scattering processes. This is a low $n_e$ (and low $B)$ model of the excitonic properties, where screening and phase-space filling contribute only to the $<10\%$ decrease of the oscillator strength sums. As regards the samples’ luminescence properties, two series of phonon peaks seen in emission spectra are attributed to recombination of two-dimensional electrons with nitrogen acceptors that have migrated close to and into the wells.