THE INVERSE DIELECTRIC FUNCTION OF A QUASI-2-DIMENSIONAL ELECTRON-GASIN A QUANTUM-WELL - PLASMONS IN A THIN METAL LAYER

A formal expression for the energy-loss function of a fast electron in teracting with an inhomogeneous quasi-2D electron gas in a quantum wel l is given in the quasiclassical approximation. It uses the non-local inverse dielectric function derived in a previous paper. As an illustr ative example, the plasmon dispersion relations of a thin metal film e mbedded in dielectric caps are calculated, taking into consideration t he influence of the empty part of the electronic spectrum, the dielect ric discontinuity of the system and the influence of various occupied subbands. By following the peaks of the loss function, rather than see king zeros of the secular determinant, one can easily obtain the plasm on branches even when these enter the domains of Landau damping. For s everal occupied subbands the number of acoustic plasmon branches is th e same as the number of occupied subbands, and the intersubband plasmo n branches at q = 0 appear at energies close to each one of the transi tions allowed in the system, which we call the leading transition of t he plasmon branch. The depolarization effect is shown to be strongly d ependent on the population of the system and on the type of the leadin g transition involved, i.e. a leading transition between occupied subb ands or between one occupied and one empty subband. Some regularities for this effect are observed, correlating the depolarization energy wi th the order of the states involved as the leading transition of the p lasmon mode.