Acousto-electric interaction in magnetised piezoelectric semiconductor quantum plasma

Amplification of an acoustic wave is considered in magnetised piezoelectric n-type semiconductor plasma under quantum hydrodynamic regime. The important ingredients of this study are the inclusion of quantum diffraction effect via the Bohm potential, statistical degeneracy pressure, and externally applied magnetostatic field in the momentum balance equation of the charged carriers. A modified dispersion relation is derived for evolution of acoustic wave by employing the linearization technique. Detailed analysis of quantum modified dispersion relation of acoustic wave is presented. For a typical parameter range, relevant to n-InSb at 77 K, it is found that the non-dimensional quantum parameter H reduces the gain while magnetic field enhances the gain of acoustic wave. The crossover from attenuation to amplification occurs at (ϑ₀/ϑₛ)=1 and this crossover point is found to be unaffected by quantum correction and magnetic field. It is also found that the maximum gain point shifts towards lower drift velocity regime due to the presence of magnetic field while quantum parameter H shifts this point towards higher drift velocity. Numerical results on the acoustic gain per radian and acoustic gain per unit length are also illustrated. Our results could be useful in understanding acoustic wave propagation in magnetised piezoelectric semiconductor in quantum regime.