Optical spectroscopy of the two-dimensional electron gas in ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$As single quantum wells

We report the results of a detailed photoluminescence investigation on n-type modulation-doped ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$As single quantum wells with intentional Be-acceptor doping in the central region of the well. Strong collective recombinations of electrons with different k states up to the Fermi wave vector in the two-dimensional electronic system and excess photogenerated holes bound to ionized Be acceptors are observed. At higher sample temperatures, the bound holes are thermalized and become free. The optical transitions are then k conserving. A similar effect has been observed when the excess photogenerated holes outnumber the doped acceptors under higher photoexcitation densities. The binding energy of the excess photogenerated holes on Be acceptors is determined to be 12 meV on the basis of temperature-dependent photoluminescence measurements.