Determination of subband structure, depolarization shift, and depletion charge in an ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As-GaAs heterostructure

Resonant subband-Landau-level coupling (RSLC) spectroscopy is applied to study intersubband-resonance excitations in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As-GaAs heterostructures. The carrier density $N_s$ in our device can be tuned via a front gate voltage $V_g$ in a controlled and reproducible way. The detailed analysis of the $N_s$ dependence of the intersubband resonance and the comparison with a self-consistent calculation demonstrate that the anti-level-crossing in the RSLC experiment occurs at an energy E${̃}_{10}$ which is shifted by the collective depolarization effect with respect to the subband separation $E_{10}$. From the same analysis we can also determine the depletion charge $N_{\mathrm{depl}}$ with an accuracy of 5%. This gives us the possibility to distinguish between a persistent photoeffect upon illumination arising first from carriers out of the GaAs buffer layer and later on from the doped ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As region.