Effect of Valence Subband Dispersion on Near-Band-gap Transitions Ingaas∕alxga1−xas…

The reflection (R) and photoluminescence (PL) spectra of several $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ modulation-doped quantum wells (MDQWs) were studied at $T=2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The $n$ doping was either on one side of the quantun well (width of $25\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$) or symmetrically on both sides (width of $20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$), and the resulting two-dimensional electron gas (2DEG) density was in the range of ${n}_{e}=(0.7--2.0)\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The reflection spectra of the two-side MDQW's show sharp but weak lines $(\ensuremath{\Delta}R<0.02)$, which are attributed to e1-hh1 and e1-lh1 interband transitions at in-plane wave vectors ${k}_{\ensuremath{\parallel}}={k}_{F}$. These spectra were analyzed by calculating the dispersion of the lowest conduction and top valence subbands and the contribution of the 2DEG interband transitions to the MDQW optical susceptibility. The reflection spectral shape was then calculated as a function of ${n}_{e}$ and of the layer widths. This model explains the observed differences between the intensity and line shape of the one-side and two-side MDQW's. The PL spectral shape of all the MDQW's shows a marked dependence on laser excitation intensity. It was calculated by using the e1 and hh1 dispersion curves and assuming that the interband transitions are ${k}_{\ensuremath{\parallel}}$ conserving. The observed PL spectral dependence on laser excitation intensity was analyzed by assuming that the effective temperature of the photoexcited holes increases with excitation intensity in the range of ${T}_{h}=4--15\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while the 2DEG temperature remains unchanged and equal to that of the lattice.