Influence of confined optical phonons and laser radiation on the hall effect in a compositional superlattice

The effect of confined optical phonons and laser radiation are taken into account to study the Hall effect in a compositional semiconductor superlattice (CSSL). The new theoretical expressions of the Hall conductivity, the Hall coefficient and the magnetoresistance are obtained as functions of the external fields (the magnetic field B , the laser frequency Ω and amplitude E ), the CSSL parameters (the well length d I , the barrier length d II and height U ) and the quantum number m characterizing the phonon confinement effect. The magneto-confined phonon resonance condition in a CSSL is also carried out to explain the numerical evaluation results for the GaAs / Al x Ga 1 − x As CSSL. When optical phonons are confined, the Hall conductivity has more resonance peaks in comparison with that for bulk phonons. In addition, these sub-peaks are more separate from the main peaks as the CSSL layers thickness decreases. The tighter CSSL period is, the more forcefully the phonon confinement makes. When the CSSL period d is smaller than 30 nm , the contribution of confined optical phonons is significant and could not be neglected. The magnetophonon resonance for bulk semiconductor could be achieved in the limit the CSSL period goes to infinity. Furthermore, the Hall conductivity increases and the Hall coefficient, the magnetoresistance decrease due to the laser radiation and the effect of confined optical phonons. Especially, the near-linear dependence of the magnetoresistance on temperature is in good agreement with the experimental result.