Research Journal of Physical Sciences _____________________________________________________________ Vol. 1(1), 11-16, February (2013) Res. J. Physical Sci. International Science Congress Association 11 Dispersion of longitudinal electro-kinetic waves in Ion-Implanted Quantum Semiconductor Plasmas Chaudhary S., Yadav Nishchhal and Ghosh S. School of Studies in Physics, Vikram University, Ujjain-456010, MP, INDIA Available online at: www.isca.in Received 15 th December 2012, revised 9 th January 2013, accepted 20 th January 2013 Abstract Dispersion properties of longitudinal electro-kinetic wave in multi-component (electron, ion and dust (e-i-d)) quantum plasmas are studied. The variation of dispersion characteristics of longitudinal electro-kinetic wave, with and without quantum effect in ion-implanted semiconductor plasma is also explored. It is found that the quantum Bohm potential term modifies the dispersion characteristics of fast and slow electro-kinetic waves in multi-component (e-i-d) plasmas. Keywords: Bohm potential, electro-kinetic wave, ion-implantation, semiconductor plasma. Introduction During the past few years quantum plasma have generated tremendous interest owing to their wide ranging applications in dusty plasmas 1,2 , in dense astrophysical environment 3 , (such as white dwarfs and neutron stars), in micro-electronic devices 4 , in intense laser beam produced plasmas 5 , in nonlinear quantum optics 6,7 , etc. Plasmas, in general, are characterized by high temperature and low density regimes where quantum effects are negligible. However, there are examples in nature where both plasma and quantum effects can coexist. The quantum effects become important in plasmas, when the de-Broglie wavelength associated with particles is comparable to dimension of the system. In such situation plasmas behave like Fermi gas and quantum mechanical effect are expected to play a significant role in the behavior of charged particles 8-12 . The quantum hydrodynamic model (QHD) for plasmas was enunciated by Manfredi and Hass 13 . Later, the same methodology has been applied to a multitude of problems involving the ion acoustic wave excitations in plasmas using two species quantum plasma and was reported by Haas et al. 14 . The stimulated Brillouin scattering of a laser radiation in an unmagnetized piezoelectric semiconductor using QHD model was reported by Uzma et al. 15 . The parametric amplification characteristics in piezoelectric semiconductor were reported by Ghosh et al. 16 . This status reflects tremendous scope of work in the field of quantum semiconductor plasmas. The quantum hydrodynamic model (QHD) is an extension of classical fluid model used for plasma media. In QHD model, there are two different quantum effects exist – (1) quantum diffraction, and (2) quantum statistics. Quantum diffraction will be taken into account by the terms proportional to 2  in equations of motion and continuity in the quantum hydrodynamic model. These contributions may be interpreted alternative as quantum pressure terms or as quantum Bohm potential. The quantum statistics will be included in the model via the equation of state, which takes into account the fermionic character of electrons. The equation of state for electrons shall be found assuming a local zero temperature Fermi distribution, a choice dictated by the spin ½ statistics for these particles. The Bohm potential, on the other hand, will exist even for a pure quantum mechanical state and has nothing to do with the statistical properties of the system. In a broad sense, we will refer to these particularities arising from the wave like nature of the charge carriers as quantum diffraction effects. The Bohm potential term appropriately describes the negative differential resistance in resonance tunneling diodes. Negative resistance is based on resonant tunneling which is a quantum phenomenon and it does not occur in classical transport model. In quantum dusty plasmas, the dispersion caused by the strong density correlations due to quantum fluctuations play an important role in the investigation of collective effects. It is known that cold quantum plasmas can support new dust modes 1,8 and the observations suggest that the frequency spectra of these modes should be useful in the study of charged dust impurities in micro-electro-mechanical systems 10 . Shukla and Ali 1 studied the propagation of dust acoustic wave in quantum plasma and found that the dispersion characteristics of the wave get significantly modified due to the quantum corrections. The study of linear and nonlinear quantum ion acoustic waves have been investigated in unmagnetized electron-ion plasmas by Hass et al. 14 using the well known QHD model. In classical frame work, Ghosh and Thakur 17 , have studied longitudinal electro-kinetic wave, in ion-implanted semiconductor plasma and reported that the effects of charged colloids on the properties of the host semiconducting medium modify existing modes and also introduce new modes. The studies of electro-kinetic wave have been a subject of many investigations 18-22 . However; these important study has not been worked out in a multi-component quantum plasma case according to the authors’ best information.