Electron-phonon scattering in the presence of a magnetic field in quasi-two-dimensional quantum-well structures

We have obtained the expressions for the relaxation times due to electron-phonon scattering in the presence of a magnetic field in quasi-two-dimensional semiconductor quantum-well structures. For the electron-acoustic phonon scattering we find that the relaxation rate at low temperature is (i) directly proportional to the density of states in a magnetic field (magnetic field in the $z$ direction) in the $x-y$ plane, and (ii) inversely proportional to the thickness of the well in the $z$ direction. For the nonpolar optical phonons similar behavior of the relaxation rate is obtained. In the case of the polar optical-phonon scattering the relaxation rate diverges due to complete quantization of the electronic states in a magnetic field in contrast to finite results in the absence of a magnetic field. Furthermore, in the limiting case of $B\to 0$, our results reduce to those in the absence of a magnetic field. Explicit calculations are presented for the variations of the relaxation times as a function of temperature and magnetic field for the acoustic and nonpolar optical-phonon scattering.