Theoretical study of the linear dispersion relation and the stationary energy-transport velocity of a coupled polar LO phonon-plasmon system

Abstract

A semiclassical investigation of the linear dispersion relation and the stationary energy-transport velocity associated with coupled LO phonon-plasmon waves in polar semiconductors is made. The influence of a free-carrier drift velocity on the frequency dispersion of the modes is considered. The complex wave vector of the coupled mode is obtained from the roots of an effective dielectric function which has been calculated on the basis of the appropriate linearized Boltzmann transport equation, the Maxwell equations, the long-wavelength equation of motion of the polar-optical lattice vibrations, and the Born and Huang expression for the lattice polarization. The minor contribution arising from the collision-drag effect associated with impurity scattering is included in the general framework of the theory. With main emphasis on small or even vanishing electronic drift velocities, inverse dispersion relations valid for low-density Maxwellian plasmas are obtained and discussed. The limiting cases, outside the quantum region, where local or extremely nonlocal approaches can be adopted, are examined. By means of a simple nonlinear Boltzmann equation the energy-balance equation associated with the LO phonon-plasmon mode is derived. A general expression for the stationary energy-transport velocity associated with damped (or amplified) coupled modes is established. Finally, the basic concepts of velocity of energy propagation are applied to classical plasmas.