Enhancement of the in-plane effective mass of electrons in modulation-doped ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells due to confinement effects

We present investigations on the in-plane effective mass of conduction electrons in pseudomorphic, strained GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As quantum wells. The samples are modulation doped by silicon leading to electron sheet densities in the range of ${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ in the ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As layers. In photoluminescence experiments at low temperature we observe that all electrons of the two-dimensional electron gas up to the Fermi energy contribute to the luminescence. This leads to an asymmetric broadening of the luminescence line shape and indicates a breakdown of the k-conservation rule. This offers the possibility of determining the Fermi energy from the low-temperature spectra. From contactless microwave Shubnikov–de Haas measurements we determine a quantity correlated to the sheet carrier density. By combining both methods we deduce the in-plane effective electronic mass and investigate its dependence on confinement. We observe a slight increase of the mass due to the built-in strain of the pseudomorphic layers and a strong increase due to confinement effects by up to 40% for 2-nm wells. Self-consistent calculations of the electronic-energy levels, the wave functions, and the perpendicular effective mass show that the observed dependence of the effective mass on the confinement is supported from a theoretical point of view. We compare the in-plane effective mass with the perpendicular one.