Effect of interaction among the three time scales on the propagation characteristics of coupled waves in a piezoelectric semiconductor rod

Based on small fluctuation of carrier concentration, a linearly-algebra equation on velocities of coupled waves in a piezoelectric semiconductor rod is established and two wave velocities together with the attenuation effects are obtained hard on the heels. Two kinds of coupling waves were distinguished by polarization-vector analysis (modal identification): One is the generalized acoustic wave with coupling between electromechanical fields and charge carriers, and the other is an electric-field/carriers interaction wave without coupling to mechanical quantities. There exist three time-scales in the system, respectively, corresponding to the vibration frequency of a coupled wave and the conductivity frequency of carrier drift and the frequency related to carrier diffusion. Effect of interaction among these three time scales on the propagation characteristics of two coupling waves are studied in detail. Analysis on the attenuation effects caused by wave-particle drag shows that these two coupling waves can propagate well only in the micro-scale or nano-scale, but decay to a very weak extent after a relatively-large size. An energy conversion rate is put forward to define an optimal operating frequency range for a coupling wave to have strong interaction between mechanical fields/piezoelectric-potential and carrier motions. The results obtained will provide some guidance for the further theoretical analysis of wave propagating in piezoelectric semiconductors and practical application and design of piezotronics devices.