Magnetoacoustic Amplification by Conduction Electrons

A theory, based on Chambers' method to the classical Boltzmann equation, is developed for an acoustic amplification in both degenerate and nondegenerate piezoelectric semiconductors subjected to the Hall geometrically configured electric and magnetic fields. It is found that an amplification constant for qR>1 holds not only for a magnetic field ω(c)τ>1 but for ω(c)τ<1 under ql>1 while the amplification constant for qR<1 does for ql≦1 under　ω(c)τ>1; q is the wave number vector of sound, R the cyclotron radius, ω(c) the cyclotron frequency, 1 the mean free path and τ the relaxation time. A generalized attenuation (amplification) constant is presented through an energy conservation law, being applicable to the sounds propagating at any angle with respect to the particle drift so the off-axis as well as on-axis amplifications are surely involved. An application of the present theory to n-InSb reveals a threshold dependence for the acoustic amplification, which is semi-quantitative agreement with the experimental result of Arizumi et al.. The amplification constant by that nondegenerate particles is found to be almost equal to that by the degenerate ones, provided that the former carrier density should be replaced by its three times as much.