Behavior of the electron-hole gas in quantum wells in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures under in-plane magnetic fields

The effect of in-plane magnetic fields B up to 20 T on the electron-hole gas confined in symmetric (SQW’s) and asymmetric (AQW’s) quantum wells in n-type GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures is theoretically investigated by a self-consistent numerical solution of the Poisson and Schrödinger equations. Quantum-well widths $L_w$=75, 150, 225, and 300 Å and two-dimensional electron densities $N_s$=0, 2.5×${10}^{11}$, 5.0×${10}^{11}$ and 7.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$ are considered. The magnetic field produces noticeable changes in the charge distribution inside the QW and drastic changes in the energy dispersion ɛ(k) of both electrons and holes in the in-plane direction perpendicular to B. The dia- magnetic shift in the electron-hole recombination energy is shown to increase with increasing $L_w$ and decreasing $N_s$. For $L_w$≥225 Å and $N_s$≥2.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$ the energy dispersion ${\varepsilon }_1$(k) of the first conduction subband in the SQW presents, at high fields, a double-minimum character so that the gap becomes indirect. For the AQW the symmetry ${\varepsilon }_1$(k)=${\varepsilon }_1$(-k) is broken and the gap is also indirect. Recent photoluminescence measurements are discussed in relation to the present calculations.