Dynamical image charge theory

Ray, Rashmi; Mahan, G. D.

doi:10.1016/0375-9601(72)90431-8

Cited by 126 publications

(33 citation statements)

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“…The simplest case here is that of the constant velocity vY for incident or emitted particles. Although it is rather academic, because the feedback acceleration effect of the image forces on the charge movement requires self-consistent treatment, the respective modifications occurred to be not crucial [4,5,7,8]. Therefore, this set-up still serves as a useful testground for more sophisticated models [9 to 13].…”

Section: Introductionmentioning

confidence: 99%

“…However, a new feature arises here, namely, oscillating terms in Wz due to the excitation of the real plasmons. In the semiclassical limit [1,3,5,6] oscillations change the profile of the image force energy drastically, having amplitudes comparable with the background classical term W cl z, especially for emitted particles. This behaviour is conserved in the quantum-mechanical theory when the recoil effect is small (the``above-thresholdº situation) [9 to 12].…”

Section: Introductionmentioning

confidence: 99%

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Importance of the Plasmon Damping for the Dynamical Image Forces

Gabovich

Розенбаум

Войтенко

1999

phys. stat. sol. (b)

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Importance of the Plasmon Damping for the Dynamical Image Forces

Gabovich

Розенбаум

Войтенко

1999

phys. stat. sol. (b)

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“…the electron tunnels more slowly close to the top of the barrier. 3 The calculation of τ BL is done by considering t has being the complex transmission amplitude for the right outgoing elastic channel calculated from the matrix method with the coupling to the SP modes. The derivative with respect to V is done by modulating the height V 0 of the static square barrier.…”

Section: Resultsmentioning

confidence: 99%

“…For example, the dynamical image potential has been treated (i) classically [3,4], (ii) within the selfenergy approach by non self-consistent [5,6], semiclassical self-consistent [7] or fully self-consistent [8] calculations and (iii) by using a path integral technique [9][10][11][12].…”

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confidence: 99%

Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Ness

Fisher

1998

Applied Physics A: Materials Science & Processing

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The dynamical effective potential felt by an electron tunneling in a one-dimensional model STM junction is considered. The electron is coupled inside the barrier to surface plasmons. The corresponding many body Schrödinger equation is solved exactly by means of a matrix method. Results for the electron effective potential and for tunneling times are presented. They are compared to calculations for the same model barrier described within the path integral formalism. As is well known, significant differences from the corresponding static image potential are obtained when tunneling times are shorter than the inverse surface plasmon frequency. However, our results show that path integral calculations underestimate the tunneling traversal time, leading to a larger effective electron potential relative to that obtained by the matrix method.The actual conductance of an STM junction, with a given geometry and tip-sample separation, depends crucially on the potential felt by a tunneling electron [1,2]. A substantial contribution to this potential depends on the extent to which the tunnel junction is polarized by the electron's field. As well known, if tunneling is sufficiently slow (in comparison to the inverse surface plasmon frequency), the electron will feel the "image force" potential. If the tunneling is very rapid, however, the redistribution of the charge around the junction cannot occur sufficiently rapidly to build up the image charge.The dynamical aspects of the image potential have been studied by several authors within different approaches and approximations. For example, the dynamical image potential has been treated (i) classically [3, 4], (ii) within the selfenergy approach by non self-consistent [5, 6], semiclassical self-consistent [7] or fully self-consistent [8] calculations and (iii) by using a path integral technique [9][10][11][12].In this paper, we present a general matrix approach to treat the electron-plasmon coupling inside a tunneling junction. The corresponding many body Schrödinger equation is solved on a real-space mesh. We apply the method to a onedimensional model case and compare the results with those obtained within the path integral formalism for the same model. The modelsWe consider a model case where an electron tunnels through a static barrier V(r) between two planar metallic surfaces. Describing the metallic electrodes by a local scalar dielectric function, the electron is coupled, within the barrier, only to the surface plasmon (SP) modes. Each mode, of frequency ω ν and coupling matrix elements Γ ν (r), is characterized by a composite index ν = (q, α) where q is a vector parallel to the electrode surfaces and α = (±) represents the even and odd SP modes (i.e. in phase and out of phase oscillation of the charge on the two electrode surfaces).Due to the translation invariance parallel to the electrode surfaces, it is possible to recast the problem into a onedimensional system (only the motion of the electron perpendicular to the electrode surfaces is considered). The corresponding H...

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“…A convenient starting point for a microscopic description of the polarization-induced interaction between an electron and a boundary is the single electron Hamiltonian [41,42],…”

Section: A Microscopic Model For the Image Potentialmentioning

confidence: 99%

Physisorption kinetics of electrons at plasma boundaries

2009

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Abstract. Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions leading to the formation of a quasi-stationary electron film at the boundaries. We propose to interpret the build-up of surface charges at inert plasma boundaries, where other surface modifications, for instance, implantation of particles and reconstruction or destruction of the surface due to impact of high energy particles can be neglected, as a physisorption process in front of the wall. The electron sticking coefficient se and the electron desorption time τe, which play an important role in determining the quasi-stationary surface charge, and about which little is empirically and theoretically known, can then be calculated from microscopic models for the electron-wall interaction. Irrespective of the sophistication of the models, the static part of the electron-wall interaction determines the binding energy of the electron, whereas inelastic processes at the wall determine se and τe. As an illustration, we calculate se and τe for a metal, using the simplest model in which the static part of the electron-metal interaction is approximated by the classical image potential. Assuming electrons from the plasma to loose (gain) energy at the surface by creating (annihilating) electron-hole pairs in the metal, which is treated as a jellium half-space with an infinitely high workfunction, we obtain se ≈ 10 −4 and τe ≈ 10 −2 s. The product seτe ≈ 10 −6 s has the order of magnitude expected from our earlier results for the charge of dust particles in a plasma but individually se is unexpectedly small and τe is somewhat large. The former is a consequence of the small matrix elements occurring in the simple model while the latter is due to the large binding energy of the electron. More sophisticated theoretical investigations, but also experimental support, are clearly needed because if se is indeed as small as our exploratory calculation suggests, it would have severe consequences for the understanding of the formation of surface charges at plasma boundaries. To identify what we believe are key issues of the electronic microphysics at inert plasma boundaries and to inspire other groups to join us on our journey is the purpose of this colloquial presentation.PACS. 52.27.Lw Dusty or complex plasmas -52.40.Hf Plasma-material interaction, boundary layer effects -68.43.-h Chemi-/Physisorption: adsorbates on surfaces -73.20.-r Electron states at surfaces and interfaces

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Dynamical image charge theory

Cited by 126 publications

References 9 publications

Importance of the Plasmon Damping for the Dynamical Image Forces

Importance of the Plasmon Damping for the Dynamical Image Forces

Dynamical effective potential for tunneling: an exact matrix method and a path-integral technique

Physisorption kinetics of electrons at plasma boundaries

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