In the present paper, an analytical study has been presented to examine the acousto–electric interactions in piezoelectric inhomogeneous semiconductor quantum plasma. The analysis is made by deriving the quantum-modified dispersion relation and subsequently deducing the expression of gain coefficient of acoustic wave using quantum hydrodynamic (QHD) model for inhomogeneous semiconductor plasma. The linearly and quadratically varying plasma density profiles have been chosen to investigate the effects of inhomogeneity through density gradient. We address the role of quantum parameter-H, scale length of density variation L and propagation distance z on gain profiles of acoustic wave. It has been found that the presence of these parameters can significantly modify the crossover and resonance characteristics of acoustic wave. Results reveal that the crossover point for wave amplification is found to be greater than unity in inhomogeneous quantum plasma media while the resonance condition is effectively influenced by these parameters in all the considered cases. We found that more acoustic gain would be possible if the acoustic mode propagates from low to high plasma density region in the medium. It is also found that as the medium tends to have high inhomogeneity, more pronounced modifications on resonance characteristics of acoustic wave are expected.
Phonon-Electron Interactions in Piezoelectric Semiconductor Bulk Acoustic Wave Resonators
