Calculations of the acoustoelectric current in a quantum well by using a quantum kinetic equation

An analytic expression for the acoustoelectric current (AC) jac induced by electron-external acoustic wave interactions and electron-internal acoustic wave (internal phonons) scattering in a quantum well (QW) is calculated by using the quantum kinetic equation for electrons. The physical problem is investigated in the region ql >> 1 (where q is the acoustic wave number and l is the electrons mean free path). The dependence of the AC jac on the external acoustic wave frequency ωq, the width of the QW L and the temperature T for a specific QW of AlGaAs/GaAs/AlGaAs is achieved by using a numerical method. The computational results show that the dependence of the AC jac on the temperature T, the external acoustic wave frequency ωq, the width of the QW L is non-monotonic and that the peaks can be attributed to transitions between mini-bands n → n'. The dependence of the AC jac on the temperature T and the Fermi energy εF is obtained, and a maximum of the AC jac for εF = 0.038 eV and ωq = 3 x 1011 s-1 seen at T = 50 K, which agrees with the experimental results for AlGaAs/GaAs/AlGaAs QWs. All these results are compared with those for normal bulk semiconductors and superlattices to show the differences. Finally, the quantum theory of the acoustoelectric effect in a quantum well is newly developed.