International Journal of Advanced Research in Physical Science (IJARPS) Volume 1, Issue 8, December 2014, PP 19-27 ISSN 2349-7874 (Print) & ISSN 2349-7882 (Online) www.arcjournals.org ©ARC Page | 19 Effect of Density Gradient on Longitudinal Phonon-Plasmon Interactions in Colloids Laden Semiconductor Quantum Plasmas Aartee Sharma, Nilesh Nimje School of Studies in Physics, Vikram University, Ujjain (M.P.) India aartee.sharma08@gmail.com N. Yadav, S. Ghosh School of Studies in Physics, Vikram University, Ujjain (M.P.) India somyadav@gmail.com Abstract: Quantum hydrodynamic model of plasmas including Bohm potential and Fermi degenerate pressure has been employed to derive the linear dispersion relation for longitudinal phonon-plasmon interaction in inhomogeneous colloid laden semiconductor plasma, for two different cases in which colloidal grains are either stationary ) 0 ( 0 d or streaming ) 0 ( 0 d . It is found that in the velocity regime d s e 0 0 , one may get sound amplification even if the electron drift velocity is less than the sound velocity. It is hoped that the analysis may become useful in designing semiconductor devices using density gradient as controlling parameter for acoustic gain. Keywords: Electron density gradient, Bohm potential, Acousto electric effect. 1. INTRODUCTION Motivated by the intense interest in the field of semiconductor quantum plasma [1-9], in the present paper using quantum hydrodynamic model of plasmas we have reported the results of the analytical investigations of the effect of density gradient on acoustic wave amplification characteristics in colloids laden semiconductor quantum plasmas and discussed the possibilities of using density gradient as controlling parameter to control growth of the unstable acoustic mode in the crystal. The interaction between mobile carriers and acoustic vibrations is one of the imperatives in physics pedagogy and research. This interaction gives useful informations regarding the physical properties of the host medium. The amplification of sound waves by the application of electric field has been commercially exploited for the fabrications of several solid state devices. It is well established that for the amplification of sound wave to occur, the carrier drift velocity induced due to applied dc electric field should exceed the possible sound velocity in the crystal lattice. The presence of required large dc electric field if applied to a colloids laden semiconductor then the resultant streaming electron beams will stick on the neutral colloid particulates to make them negatively charged colloidal ions. The semiconductor plasma medium so created will behave like dusty plasma [10] with electrons, vibrating lattice ions and dust like colloid ions and therefore becomes an interesting host to study the acoustic wave amplification characteristics. A number of interesting phenomena have been observed in these colloid laden semiconductor plasmas. Ghosh and his coworkers reported the number of new modes [11, 12] and effective modifications [13-16] in the characteristic of the existing mode in these media. Interesting to note that if the system has gradients of different parameters such as density, temperature, pressure, magnetic field etc. an additional carrier drift exist which enhances the carrier drift magnitude induced due to presence of dc electric field. In media where wave functions of the neighbouring particles overlapped, the consideration of quantum correction becomes imperable while studying the characteristic of the wave propagating through these media. These wave function overlapping becomes possible only when the