Extended Mermin Method for Calculating the Electron Inelastic Mean Free Path

Da, Bo; Shinotsuka, Hiroshi; Yoshikawa, Hideki; Ding, Zejun; Tanuma, Shigeo

doi:10.1103/physrevlett.113.063201

Cited by 62 publications

(61 citation statements)

References 38 publications

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“…) by considering Levine–Louie dielectric function instead of the Lindhard dielectric function. Da et al have proposed an extended Mermin method, which seems to be more reasonable for low energy electrons for correction of non‐Born effect. However, all these models have ignored phonon excitation.…”

Section: Resultsmentioning

confidence: 99%

A comparative study on Monte Carlo simulations of electron emission from liquid water

et al. 2019

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Purpose Liquid water being the major constituent of the human body, is of fundamental importance in radiobiological research. Hence, the knowledge of electron‐water interaction physics and particularly the secondary electron yield is essential. However, to date, only very little is known experimentally on the low energy electron interaction with liquid water because of certain practical limitations. The purpose of this study was to gain some useful information about electron emission from water using a Monte Carlo (MC) simulation technique that can numerically model electron transport trajectories in water. Methods In this study, we have performed MC simulations of electron emission from liquid water in the primary energy range of 50 eV–30 keV by using two different codes, i.e., a classical trajectory MC (CMC) code developed in our laboratory and the Geant4‐DNA (G4DNA) code. The calculated secondary electron yield and electron backscattering coefficient are compared with experimental results wherever applicable to verify the validity of physical models for the electron‐water interaction. Results The secondary electron yield vs. primary energy curves calculated using the two codes present the same generic curve shape as that of metals but in rather different absolute values. G4DNA underestimates the secondary electron yield due to the application of one step thermalization model by setting a cutoff energy at 10 eV so that the low energy losses due to phonon excitations are omitted. Our CMC code, using a full energy loss spectrum to model electron inelastic scattering, allows the simulation of individual phonon scattering events for very low energy losses down to 10 meV, which then enables the calculated secondary electron yields much closer to the experimental data and also gives quite reasonable energy distribution curve of secondary electrons. Conclusions It is concluded that full dielectric function data at low energy loss values below 10 eV are recommended for modeling of low energy electrons in liquid water.

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Section: Resultsmentioning

confidence: 99%

A comparative study on Monte Carlo simulations of electron emission from liquid water

et al. 2019

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“…Da et al . proposed an extended Mermin model for the dielectric function . In their algorithm, the ELF of a material in the optical limit ( q = 0) is obtained by a fit to the experimental ELF with a summation of Mermin‐type ELFs,

normalI normalm ({}, \frac{- 1}{ε (q = 0, ω)}) = true {true\sum}_{i = 1}^{N} a_{i} normalI normalm ({}, \frac{- 1}{ε_{normalM} (q = 0, ω; ω_{p i}, γ_{i})}) ≡ true {true\sum}_{i = 1}^{N} \frac{a_{i} γ_{i} ω ω_{normalp i}^{2}}{{(ω^{2} - ω_{p i}^{2})}^{2} + γ_{i}^{2} ω^{2}},

where ε M ( q = 0, ω ; ω p i , γ i ) is the Mermin dielectric function .…”

Section: Inelastic Mean Free Path Calculationsmentioning

confidence: 99%

“…We also performed IMFP calculations for water by using the SPA and the SSPA (and the same optical ELF as for our FPA calculations) to determine the effects of algorithm choice on the resulting IMFPs. We determined ELFs for q > 0 from the optical ELF (where q = 0) with the extended Mermin model proposed by Da et al . to determine differences between the resulting IMFPs and those obtained with the FPA.…”

Section: Introductionmentioning

confidence: 99%

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

Shinotsuka

Tanuma

et al. 2016

Surf. Interface Anal.

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We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy-loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm (FPA) that has been used for previous IMFP and electron stopping-power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single-pole approximation (SPA), the relativistic simplified SPA, and the relativistic extended Mermin method. These calculations were made using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP-2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the FPA. The resulting values were in good agreement with results from first-principles calculations and with inelastic X-ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length (EAL). There were large variations in the measured IMFPs and EALs (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs.

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“…The thicknesses t of the Ta 2 O 5 films were 25 (1), 36 (1), 45 (1), 58 (1), 75 (1), 95 (2), 110 (3), and 173 (3) nm. The roughness was 0.5 nm for films with t ≤ 95 nm, and the average mass density was 8.22 (0.06) g/cm 3 , where the uncertainty was given by the standard deviation of the density values in the fits. For films with t = 110 and 173 nm, in which the use of the reflectivity technique is not appropriate, their thicknesses were estimated by comparing the widths of the Ta structure in the Rutherford backscattering (RBS) spectra with the respective ones obtained for thinner films.…”

Section: Experimental Determination Of the Energy Loss Of H And Hementioning

confidence: 99%

Energy Loss Function of Solids Assessed by Ion Beam Energy-Loss Measurements: Practical Application to Ta₂O₅

et al. 2015

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We present a study where the energy loss function of Ta 2 O 5 , initially derived in the optical limit for a limited region of excitation energies from reflection electron energy loss spectroscopy (REELS) measurements, was improved and extended to the whole momentum and energy excitation region through a suitable theoretical analysis using the Mermin dielectric function and requiring the fulfillment of physically motivated restrictions, such as the f-and KK-sum rules. The material stopping cross section (SCS) and energy-loss straggling measured for 300−2000 keV proton and 200− 6000 keV helium ion beams by means of Rutherford backscattering spectrometry (RBS) were compared to the same quantities calculated in the dielectric framework, showing an excellent agreement, which is used to judge the reliability of the Ta 2 O 5 energy loss function. Based on this assessment, we have also predicted the inelastic mean free path and the SCS of energetic electrons in Ta 2 O 5 .

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Extended Mermin Method for Calculating the Electron Inelastic Mean Free Path

Cited by 62 publications

References 38 publications

A comparative study on Monte Carlo simulations of electron emission from liquid water

A comparative study on Monte Carlo simulations of electron emission from liquid water

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

Energy Loss Function of Solids Assessed by Ion Beam Energy-Loss Measurements: Practical Application to Ta₂O₅

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Extended Mermin Method for Calculating the Electron Inelastic Mean Free Path

Cited by 62 publications

References 38 publications

A comparative study on Monte Carlo simulations of electron emission from liquid water

A comparative study on Monte Carlo simulations of electron emission from liquid water

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

Energy Loss Function of Solids Assessed by Ion Beam Energy-Loss Measurements: Practical Application to Ta2O5

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Energy Loss Function of Solids Assessed by Ion Beam Energy-Loss Measurements: Practical Application to Ta₂O₅