Theory of well-width-dependent periodic variation in photoluminescence from ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs quantum wells

The recently discovered periodic variation in photoluminescence (PL) efficiency is theoretically analyzed. The PL intensity $I_{\mathrm{PL}}$ depends on the excitation intensity $I_{\mathrm{ex}}$, in that it varies as a function of the width of the ${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As/GaAs quantum well (QW), following a power law, i.e., $I_{\mathrm{PL}\mathrm{\propto }{I}_{\mathrm{ex}{}^m}}$. The value m was observed to vary periodically between 1 and 2 depending on width. Analysis makes it possible to correlate the m=1 and 2 cases to off-resonance and resonance, respectively, which occur between the highest QW level and the bottom of the conduction band of the barrier. In an off-resonance electrons are tightly trapped in the QW bottom after rapid relaxation; resonating electrons are free to escape from the well, if they are not recombined. Microscopic calculation of the relaxation of hot electrons reproduces the observed behavior of m quite well.