Using hydrodynamic model of inhomogeneous plasma, an analytical investigation of excitation of acousto-electric mode was made in n-type piezoelectric ion-implanted semiconductor plasma. By employing the multi-fluid balance equations along with the elastic and Maxwell equations, a compact dispersion relation for the cases in which colloidal grains are either stationary (ϑ_{0d}=0) or streaming (ϑ_{0d}≢0$) is derived. We find that the choice of homogeneous medium is favorable in achieving higher acoustic gain per radian and the results of the investigation should be useful in understanding the characteristics of longitudinal acousto-electric wave in ion-implanted piezoelectric semiconductor whose main constituents are electrons and negatively charged colloidal particles.
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