Momentum transfer dependence of reflection electron energy loss spectra: theory and experiment

Calliari, L.; Dapor, Maurizio; Garberoglio, Giovanni; Fanchenko, S. D.

doi:10.1002/sia.5495

Cited by 15 publications

(19 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They are due to the interaction of the travelling electron with the surface charge induced by the electron in the earlier part of the trajectory . While the oscillating surface contribution is superimposed to the bulk IIMFP in the solid, it is not in the vacuum, leading to negative IIMFP values, interpreted as energy gained by the exiting electron …”

Section: Resultsmentioning

confidence: 99%

“…An estimate of the thickness of the surface scattering zone is thus also given by the decay length

t_{Q} = \frac{1}{Q}

. We take

Q = \frac{m v}{ℏ} \sqrt{{(θ_{E} \sin α - θ \cos α \cos φ)}^{2} + {(θ \sin φ)}^{2}}

, where

θ_{E} = \frac{normalℏ ω}{2 E}

, while θ and φ are the polar and azimuthal angles of scattering. For α = 0,

Q = \frac{m v}{ℏ} θ_{E}

.…”

Section: Resultsmentioning

confidence: 99%

“…Details to calculate the space‐dependent DIIMFP Chen‐Kwei are given elsewhere . Here, we note that DIIMFP Chen‐Kwei is the sum of several contributions related to the electron trajectory (ingoing and outgoing electrons), to the electron position (in the vacuum and in the solid), to the type of excitation (surface and bulk plasmons).…”

Section: Calculationsmentioning

confidence: 99%

“…For β , we take the random phase approximation value,

β_{R P A} = \frac{6}{5} E_{F}

, where E F = 12.2eV is the Si Fermi energy. Parameters ℏ ω p = 15.8eV, ℏ ω g = 4.9eV and ℏ γ = 3.5eV are defined by comparison with a measured reflection electron energy loss spectrum excited from Si by 2keV electrons and taking into account that the static dielectric function of Si is

ε ((),, 00) = 1 + \frac{ω_{p}^{2}}{ω_{g}^{2}} \approx 11 - 12

…”

Section: Calculationsmentioning

confidence: 99%

“…In previous papers, we have used the Chen–Kwei theory to focus on effects of momentum transfer in inelastic scattering . Recently, we considered the surface‐related part of the differential inverse inelastic mean free path ( DIIMFP Chen‐Kwei ), to calculate the differential surface excitation parameter (DSEP) by integration over the electron trajectory .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The spatial extent of surface effects on electron inelastic scattering

Calliari

Fanchenko

2015

Surface & Interface Analysis

View full text Add to dashboard Cite

We calculate the thickness of the surface scattering layer, defined as the region where electron inelastic scattering is affected by the surface, using the semi-classical treatment of electron energy loss provided by the Chen-Kwei theory. To this end, we consider the depth-dependent, surface-related contributions to the inverse inelastic mean free path, namely, the excitation of surface plasmons and the reduction in bulk plasmon excitation (Begrenzung effect). We find that surface effects extend further after electrons cross the surface than before they cross it. The 'pre-surface thickness' is given by the ratio of the electron velocity to the plasma frequency, the characteristic decay length for surface effects. All thickness estimates increase linearly with the electron velocity and decrease as (cosα)x with the angle α between the electron trajectory and the surface normal.

show abstract

Section: Resultsmentioning

confidence: 99%

“…An estimate of the thickness of the surface scattering zone is thus also given by the decay length

t_{Q} = \frac{1}{Q}

. We take

Q = \frac{m v}{ℏ} \sqrt{{(θ_{E} \sin α - θ \cos α \cos φ)}^{2} + {(θ \sin φ)}^{2}}

, where

θ_{E} = \frac{normalℏ ω}{2 E}

, while θ and φ are the polar and azimuthal angles of scattering. For α = 0,

Q = \frac{m v}{ℏ} θ_{E}

.…”

Section: Resultsmentioning

confidence: 99%

Section: Calculationsmentioning

confidence: 99%

“…For β , we take the random phase approximation value,

β_{R P A} = \frac{6}{5} E_{F}

ε ((),, 00) = 1 + \frac{ω_{p}^{2}}{ω_{g}^{2}} \approx 11 - 12

…”

Section: Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The spatial extent of surface effects on electron inelastic scattering

Calliari

Fanchenko

2015

Surface & Interface Analysis

View full text Add to dashboard Cite

show abstract

Momentum transfer effects in near surface electron energy loss

Calliari

Fanchenko

2015

Surface & Interface Analysis

View full text Add to dashboard Cite

We examine two formulations for the differential surface excitation parameter (DSEP): one provided by Tung et al. and the other given by the Chen–Kwei position‐dependent differential inverse inelastic mean free path integrated over the electron trajectory. We demonstrate that the latter converges to the former provided that the dielectric function of the solid does not depend on the momentum transfer or it depends on just the momentum transfer component parallel to the surface. Tung's DSEP represents therefore an approximation to the Chen–Kwei DSEP calculated for a dielectric function with no restrictions on the momentum dependence. The approximation is shown to work in the limit of small momentum transfer and to imply an error of 4%–5% for electrons traveling through the solid with energy E = 1 keV. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

Monte Carlo Strategies

Dapor¹

2020

Transport of Energetic Electrons in Solids

View full text Add to dashboard Cite

Momentum transfer dependence of reflection electron energy loss spectra: theory and experiment

Cited by 15 publications

References 44 publications

The spatial extent of surface effects on electron inelastic scattering

The spatial extent of surface effects on electron inelastic scattering

Momentum transfer effects in near surface electron energy loss

Monte Carlo Strategies

Contact Info

Product

Resources

About