Carrier cooling in undoped and modulation-doped ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As multiple quantum wells

Carrier cooling, as observed by time-resolved photoluminescence, is completely different for undoped and $n$-type modulation-doped ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As/${\mathrm{Al}}_{0.48}$${\mathrm{In}}_{0.52}$As multiple-quantum-well structures. Fast cooling by carrier-LO-phonon scattering is observed for the undoped quantum wells at low excitation and is well described using the theoretical three-dimensional carrier-LO-phonon scattering time. Cooling in the $n$-type modulation-doped sample, however, is reduced by a factor of 35 for the same excitation densities. Our comparative study shows that the reduced energy-loss rate is not caused by the reduced dimensionality of the carrier system, but is an effect of the high electron density.