Hot electron energy relaxation via acoustic-phonon emission in GaAs/Ga_1 xAl_xAs multiple quantum wells: well-width dependence

Abstract

The well-width dependence of the two-dimensional (2D) electron energy relaxation associated with acoustic-phonon emission in GaAs/Ga 1−x Al x As multiple quantum wells (MQWs) has been investigated using Shubnikov-de Haas (SdH) effect measurements in the temperature range of 3.3-15 K and at applied electric fields up to 300 V m −1. The modulation-doped MQW samples studied have quantum-well widths (L z) in the range between 40 and 145Å; only the lowest subband in each sample is populated with a 2D carrier density in the range from 1.04 × 10 16 m −2 to 1.38 × 10 16 m −2. The power loss-electron temperature characteristics of the samples have been obtained from the lattice temperature and electric field dependences of the amplitude of the SdH oscillations. It is found that the power loss decreases markedly when L z increases from 40Å to about 120Å and it increases for L z > 120Å. The experimental results are compared with the current 2D and three-dimensional (3D) theoretical models for power loss, which include both piezoelectric and deformation-potential scattering. The electron-temperature dependence of power loss determined experimentally fits well to both the 2D and 3D theoretical models in the intermediatetemperature regime but with different values for the acoustic deformation potential. It is shown that for samples with L z in the range of 40-120Å, the 2D model predicts a dependence of power loss on the well width, which is similar to that observed experimentally. The 3D model, however, predicts a power loss which increases with increasing well width and describes well the well-width dependence of the experimental power loss for wide wells (L z 120Å). The results provide useful information about the relative magnitude of the deformation-potential and piezoelectric contributions to power loss.

Electron Energy Relaxation via Acoustic Phonon Emission in GaAs/Ga1?xAlxAs Multiple Quantum Wells: Effects of Base Lattice Temperature

“…This indicates that the magnetic field used in the experiments does not affect significantly the energy relaxation process. This observation is also supported by the experimental finding that, for each sample studied in this work, the quantum lifetime of 2D electrons remains constant to within in 2% in the whole lattice temperature, magnetic field and applied electric field ranges of the measurements [2,27,30]. It is evident from Fig.…”

“…This indicates that the experiments were carried out in the low-temperature regime and that the energy relaxation is due to acoustic phonon emission via mixed unscreened piezoelectric and deformation potential interactions [1,9]. On the other hand, the values found for g (Table 2), from the P(T e ) data measured at T L0 ffi 3.5 and 5.9 K, are typical for an intermediate regime between the low-temperature and hightemperature limits (see also [1,6,14,27]). It should be noted that the g values determined from the measurements at T L0 ffi 1.7 K are much higher (by a factor of about 2) than those at T L0 ffi 3.5 K and 5.9 K. We have, therefore, fitted the experimental P(T e ) data, obtained from the measurements at liquid-helium temperatures with T L0 ffi 1.7 K, to the analytical expressions for power loss in the low-temperature regime for both the 2D (Eq.…”

“…1 that the magnitude of power loss depends on the base lattice temperature T L0 and varies somewhat from one sample to another. The well-width dependence of the energy-loss rates of 2D electrons in GaAs/Ga 1--x Al x As MQWs has been discussed by us elsewhere [2,27]. In this paper, we concentrate on the effects of the base lattice temperature on the P(T e ) characteristics of the MQW samples studied.…”

“…The electron temperature has been determined as a function of the applied electric field by comparing the relative amplitudes of the SdH oscillations measured as functions of T L and F. For further details of data analysis refer to [2,18,27].…”

“…An approximation, often used [1,2,11,18,27] for the electron energy-loss rates in a temperature regime, which is intermediate between the low-temperature and high-temperature limits, is represented by…”