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

Abstract

$\mathrm{CdTe}/{\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}\mathrm{Te}$ 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 $\ensuremath{\approx}{10}^{11}{\mathrm{cm}}^{\ensuremath{-}2}$ by optical pumping. In zero field at $T=2\mathrm{K},$ the optical absorption spectra show trion ${(X}^{\ensuremath{-}})$ 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 ${n}_{e}\ensuremath{\ll}{1/a}_{B}^{2}.$ Under magnetic field $B=8\mathrm{T}$ at $T=2\mathrm{K},$ sharp ${X}^{\ensuremath{-}}$ and X resonance peaks are seen as well as a broad band Z situated about $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathrm{ce}}$ (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 ${\ensuremath{\sigma}}^{+}$ circular polarization, the X resonance attenuates rapidly with ${n}_{e}$ but the ${X}^{\ensuremath{-}}$ resonance grows almost as rapidly (``intensity sharing'') so that their intensity sum falls only slowly. In ${\ensuremath{\sigma}}^{\ensuremath{-}}$ 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 ${10}^{11}{\mathrm{cm}}^{\ensuremath{-}2}$ in CdTe is due to intensity sharing between the X and ${X}^{\ensuremath{-}}$ 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.