Intersubband resonant scattering in GaAs-Ga1−xAlxAs heterojunctions

Shubnikov–de Haas oscillations have been investigated in the resistivity of three GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As heterojunctions, each with two subbands occupied, at temperatures below 4.2 K. As shown in previous publications, oscillations from the lower subband do not conform to the standard theory. The envelope of these oscillations is strongly modulated at the frequency of the upper subband oscillations and, under conditions where the ratio of temperature to magnetic field is large, the oscillations are anomalously large. The oscillations from the upper subband do not exhibit any measurable anomalies. The results are reasonably well explained by a model due to Coleridge which takes into account elastic intersubband scattering. We find that the model predicts that intersubband resonant scattering produces a series of resistivity oscillations which are not damped as the temperature rises. The effect is analogous to magnetophonon resonance in its insensitivity to thermal damping. Hot-electron studies have also been performed, which are qualitatively similar to the cold electron experiments, but differ in that the modulation envelope is shifted in phase by π. This feature cannot be interpreted by a model which takes into account only elastic scattering, and we conclude that it is due to additional inelastic, electron-phonon, intersubband scattering.