Warm-electron power loss in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As multiple quantum wells: Well-width dependence

We report the observation of the well-width dependence of the two-dimensional (2D) warm-electron power loss in GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells. Electron-energy-loss rates via the emission of acoustic phonons are determined from the measurements of the amplitudes of Shubnikov–de Haas oscillations as a function of both lattice temperature and the applied electric field. The samples studied have quantum well widths ranging between L=50 and 145 Å. However, the 2D electron density in all the samples studied is kept constant to within 10%. Experimental results are compared with the existing theoretical models including a recent numerical model developed by one of us. All the models include piezoelectric and deformation-potential scattering. It is shown that the theoretical models predict a dependence of power loss on electron temperature and well width which is similar to that observed experimentally. However, all the models considered fail to estimate the magnitude of the power loss correctly, especially in narrower quantum wells. This suggests that with decreasing confinement length, acoustic phonons become less efficient in cooling electrons than those predicted by the theoretical models. It is argued that this discrepancy may be associated with the overestimated piezoelectric component and with the simplifying assumptions made in the theoretical calculations regarding both the 2D nature of phonons and the ideal quantum-well approximation in the extreme quantum limit.