Quasi-two-dimensional electron system in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterojunction

Under various applied external conditions, we have investigated extensively the electronic energy-sublevel structure in a cap/${\mathit{n}}^{+}$-type ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/spacer/GaAs active layer/buffer/substrate heterojunction. When the buffer is an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As alloy or an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs multiple quantum well, both the electron and the heavy and light holes are found to be confined, and consequently the exciton effect is important. The depletion in the ${\mathit{n}}^{+}$-type ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As is incomplete if the doping concentration in this region is high, or the width of this region is wide, or the applied negative bias (the cap electrically negative, while the substrate grounded) is not very large. The measured energy-level structures of electrons at the interface between the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As spacer and the GaAs active layer have been interpreted with a self-consistent calculation, taking into account the electrons both in the ${\mathit{n}}^{+}$-type ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As region and the GaAs active layer. Based on the present work, previously calculated photoluminescence excitation spectra are reexamined.