Energy losses of charged particles moving parallel to the surface of an overlayer system

Kwei, C. M.; Hwang, Sheue‐Ling; Li, Y. C.; Tung, C. J.

doi:10.1063/1.1569974

Cited by 12 publications

(9 citation statements)

References 25 publications

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“…In their work, however, conservations of energy and momentum were not completely satisfied due to the treatment of momentum transfer in cylindrical coordinates that carried no restriction on the normal component. In order to satisfy conservations of energy and momentum, spherical coordinates [13] should be adopted. The newly developed model by the present authors applied spherical coordinates in the derivation of position-dependent inelastic cross-section for an electron with arbitrary crossing angle [14].…”

Section: Introductionmentioning

confidence: 99%

Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface

Kwei

Tung

2006

Surface Science

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Section: Introductionmentioning

confidence: 99%

Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface

Kwei

Tung

2006

Surface Science

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“…In this work, the SEP is calculated by an integration of the surface excitation part of the DIIMFP both inside and outside the solid, including the Begrenzungs effect inside the solid. The SEPs, P s , for escaping electrons (from solid to vacuum: S → V ) and incoming electrons (from vacuum to solid: V → S ) can be expressed by, respectively,

\begin{matrix} left \\ {P_{s}}^{s \to v} = \frac{8 cos α}{π^{2}} \int_{0}^{E} d ω true \int_{q_{-}}^{q_{+}} d q \int_{0}^{π / 2} d italicθ \\ \times {([], normalIm ({}, \frac{- 1}{ε (Q, ω) + 1}) ((), {sin}^{2} italicθ - \frac{1}{2}) - \frac{1}{2} normalIm ({}, \frac{- 1}{ε (Q, ω)})) \frac{sin θ sin φ sin α}{B Q^{2} {v_{⊥}}^{2} {cos}^{2} α} \\ + normalIm ({}, \frac{- 1}{ε (Q, ω) + 1}) \frac{tan α}{q^{2} v^{2} sin θ} ([], \frac{sin φ tan α}{B} - \frac{1}{B^{3}} ((), \frac{ω}{Q v_{∥}} cos 3 φ + cot α sin 3 φ)) true} \end{matrix}

and

\begin{matrix} left \\ {P_{s}}^{v \to s} = \frac{8 cos α}{π^{2}} \int_{0}^{E} d ω true \int_{q_{-}}^{q_{+}} d q \int_{0}^{π / 2} d italicθ \\ \times {([], normalIm ({}, \frac{- 1}{ε (Q)})) \end{matrix}

…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…Tung considered the surface excitation effect in an oversimplified model in which the surface excitations occur just at the surface boundary without extending to both sides of the surface boundary. Chen and Kwei used a semi‐classical expression of the position‐dependent differential inverse IMFP (DIIMFP) to evaluate the surface excitation effect, which decays exponentially on both the vacuum and solid sides. The SEPs were calculated by an integration of the inverse IMFP over the electron path length in vacuum only.…”

Section: Introductionmentioning

confidence: 99%

Systematic calculation of the surface excitation parameters for 22 materials

Da¹,

Sun²,

Mao³

et al. 2012

Surface & Interface Analysis

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Quantitative surface analysis requires knowledge of surface excitations by electrons. These excitations are characterized by the surface excitation parameter (SEP) which represents the surface excitation probability while an electron moves across a solid surface. In this work, a systematic calculation of a SEP database has been performed for 22 materials, including metals, oxides and semiconductors, for electron energies between 100 eV and 5000 eV, and for angles a of incidence/emission between 0.5 o and 89.5 o with respect to the surface normal. Surface excitations are considered for both sides of a solid-vacuum interface when an electron is incident on or emitted from a surface. These SEPs represent not only the appearance of surface excitations but also the inhibition of bulk excitations. Four common SEP formulas are evaluated, and we present best-fit parameters for the most satisfactory formula. SEP can then be readily determined for about 22 materials and various energies and electron incidence or emission angles.

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“…Taking E 0 D E, Eqn (2) reduces to the formula without the memory effect. 4 Note that all quantities in this work are expressed in atomic units (a.u.) unless otherwise specified.…”

Section: Theorymentioning

confidence: 99%

“…This function was previously employed to characterize the response of semi-infinite solids 7,8 and overlayer systems. 4,9,10 The formulae with the memory effect for electron DIIMFP and IMFP are applicable to all materials with known dielectric functions. Calculations of electron DIIMFP and IMFP are made here using these formulae for the Cu surface.…”

Section: Introductionmentioning

confidence: 99%

Memory effect on the inelastic interaction of electrons moving parallel to a solid surface

Kwei

Hsu

et al. 2006

Surf. Interface Anal.

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It is generally assumed that two successive inelastic interactions between an electron and a solid are independent of each other. In other words, the electron has no memory of its previous interaction. However, the previous interaction of the electron generates a potential that should influence its succeeding inelastic interaction. The aim of this work is to establish a model to account for the memory effect of an electron between two successive inelastic interactions. On the basis of the dielectric response theory, formulae for differential inverse inelastic mean free paths (DIIMFPs) and inelastic mean free paths (IMFPs) considering the memory effect were derived for electrons moving parallel to a solid surface by solving the Poisson equation and applying suitable boundary conditions. These mean free paths were then calculated with the extended Drude dielectric function for a Cu surface. It was found that the DIIMFP and the IMFP with the memory effect for electron energy E lay between the corresponding values without the memory effect for electron energy E and previous energy E 0 . The memory effect increased with increasing electron energy loss, E 0 − E, in the previous inelastic interaction.

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Energy losses of charged particles moving parallel to the surface of an overlayer system

Cited by 12 publications

References 25 publications

Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface

Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface

Systematic calculation of the surface excitation parameters for 22 materials

Memory effect on the inelastic interaction of electrons moving parallel to a solid surface

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