Impact of confined LO-phonons on the Hall effect in doped semiconductor superlattices

Based on the quantum kinetic equation method, the Hall effect in doped semiconductor superlattices (DSSL) has been theoretically studied under the influence of confined LO-phonons and the laser radiation. The analytical expression of the Hall conductivity tensor, the magnetoresistance and the Hall coefficient of a GaAs:Si/GaAs:Be DSSL is obtained in terms of the external fields, lattice period and doping concentration. The quantum numbers N, n, m were varied in order to characterize the effect of electron and LO-phonon confinement. Numerical evaluations showed that LO-phonon confinement enhanced the probability of electron scattering, thus increasing the number of resonance peaks in the Hall conductivity tensor and decreasing the magnitude of the magnetoresistance as well as the Hall coefficient when compared to the case of bulk phonons. The nearly linear increase of the magnetoresistance with temperature was found to be in good agreement with experiment.