Electron-phonon interaction in a very low mobility GaAs/Ga1-xAlxAs δ-doped gated quantum well

The energy relaxation rate for hot electrons in a gated GaAs/Ga1-xAlxAs delta-doped quantum well has been measured over the temperature range 0.3-3 K. At higher temperatures the loss rate varies as T-5 and the magnitude agrees well with that predicted by the standard theory for piezoelectric electron-phonon scattering. At low temperatures the observed dependence changes to T-4, the crossover occuring near ql similar to 0.35, where q is the average magnitude of the phonon wave vector and I the electron mean free path. This is in agreement with recent theoretical predictions for piezoelectric scattering in the dirty limit. The theory also predicts that the magnitude of the energy-loss rate should depend inversely on the conductivity of the sample. Good agreement is found at higher conductivities, but the measured values show saturation when the conductivity becomes very low.