Dynamical Image Forces near Semiconductor-Vacuum Interfaces and in Vacuum Interlayers between Semiconductors

Abstract

Dynamical image force (polarization) energies WðzÞ induced by charged particles moving perpendicular to the vacuum-semiconductor interface or in the vacuum slab between semiconductors have been calculated on the basis of the perturbation theory developed by the authors earlier. The cases of the uniform and uniformly accelerated motions are treated as an example. The adopted dielectric approach takes into account both spatial and temporal dispersions of the electrode dielectric functions eðk; wÞ. It is shown that the quantum-mechanical character of the k-dependence of eðk; wÞ leads to a smoother WðzÞ dependence than in the semiclassical case. It is also demonstrated that the proper account of the quantum-mechanical screening behavior leads to a drastic reduction of the dynamical corrections to the static image forces. For reasonable values of the relevant parameters of the problem it is sufficient to retain only the first dynamical term of the perturbation series. Thus, the use of the expansion method is justified for multilayer semiconductor structures.

Dynamic image forces near a metal surface and the point-charge motion

“…In an infinite medium, this fact is taken into account by introducing the spatial dispersion of the dielectric function ε(k). In the simplest scenario of the infinite-barrier model and the specular reflection of the intrinsic charge carriers at the vacuum-medium interface, the response of polarized half-space is a functional of ε(k) [4][5][6][7]. Then, the W (z) curve across the vacuum-metal interface has the form shown in figure 1, vanishing at infinity and saturating into the electrode depth.…”

“…This general theory has a vast domain of applicability but the problem of charged particle acceleration near the conducting plane under the influence of image forces falls beyond the scope of the conventional electrostatic approach. The latter fails in the closest neighbourhood of the plane and for fast enough motion of the particle, when the spatial or temporal, respectively, dispersion of the dielectric permittivity ε(k, ω) becomes crucial [4][5][6][7]. Here, k is the wave vector and ω is the circular frequency in the inverse wave-vector-frequency space.…”

“…The non-local dynamic response of a metal or an insulator in the continuum model described in terms of ε(k, ω) leads to a non-divergent W (z) in the whole vacuum half-space (see figure 1), the dynamic corrections usually being small [6,7]. In the bulk of the metal, the electrostatic potential energy matches its image force counterpart and for electrons rapidly tends to the average inner potential value W b if one neglects the periodic ion-lattice structure.…”

“…We intend to demonstrate that both the temporal and spatial dispersions of ε(k, ω) inherent to the grounded metal (insulator) half-space create obstacles for a charged particle to achieve relativistic velocities. For definiteness sake, we shall talk about a metal, although in this context the response of media with free and bound quasi-particles is very similar [7]. Since the temporal dispersion is the most important factor for strongly accelerated particles in the whole range of charge-plane distances, the main attention is paid to this effect, which can alone explain the unattainability of relativistic velocities.…”