Resonant Raman scattering in $p$-type $\mathrm{GaAs}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}-\mathrm{AlAs}$ quantum wells

We show that measuring the resonance cross section of Raman signals in deliberately asymmetric $p$-type quantum-well structures yields a series of sharp peaks corresponding to the transitions from the uppermost hole subband to the conduction subbands. Thus we could determine the conduction-band well states up to the state $n=11\mathrm{}$. The deliberate asymmetry of the wells has not only proven to produce excellent mobility, but also causes a breakdown of the usual selection rules which are only valid in symmetric quantum wells. Therefore all electron subbands can be observed. We observe no conduction subbands above $n=11\mathrm{}$. This yields experimental bounds of 264-312 meV for the conduction-band offset. We identify the Raman scattering processes. We show that the shape of the electron and hole wave functions participating in the Raman process is crucial for the details of the resonance curve.