### Abstract

Six models, including a single-scattering model, four hybrid models, and one dielectric function model, were evaluated using Monte Carlo simulations for aluminum and copper at incident beam energies ranging from 0.5 keV to 10 keV. The inelastic mean free path, mean energy loss per unit path length, and backscattering coefficients obtained by these models are compared and discussed to understand the merits of the various models. ANOVA (analysis of variance) statistical models were used to quantify the effects of inelastic cross section and energy loss models on the basis of the simulated results deviation from the experimental data for the inelastic mean free path, the mean energy loss per unit path length, and the backscattering coefficient, as well as their correlations. This work in this study is believed to be the first application of ANOVA models towards evaluating inelastic electron beam scattering models. This approach is an improvement over the traditional approach which involves only visual estimation of the difference between the experimental data and simulated results. The data suggests that the optimization of the effective electron number per atom, binding energy, and cut-off energy of an inelastic model for different materials at different beam energies is more important than the selection of inelastic models for Monte Carlo electron scattering simulation. During the simulations, parameters in the equations should be tuned according to different materials for different beam energies rather than merely employing default parameters for an arbitrary material. Energy loss models and cross-section formulas are not the main factors influencing energy loss. Comparison of the deviation of the simulated results from the experimental data shows a significant correlation (p < 0.05) between the backscattering coefficient and energy loss per unit path length. The inclusion of backscattering electrons generated by both primary and secondary electrons for backscattering coefficient simulation is recommended for elements with high atomic numbers. In hybrid models, introducing the inner shell ionization model improves the accuracy of simulated results.

Original language | English |
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Pages (from-to) | 103-112 |

Number of pages | 10 |

Journal | Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms |

Volume | 394 |

DOIs | |

Publication status | Published - 2017 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Instrumentation

### Cite this

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**A comparative study of inelastic scattering models at energy levels ranging from 0.5 keV to 10 keV.** / Hu, Chia Yu; Lin, Chun Hung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A comparative study of inelastic scattering models at energy levels ranging from 0.5 keV to 10 keV

AU - Hu, Chia Yu

AU - Lin, Chun Hung

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Six models, including a single-scattering model, four hybrid models, and one dielectric function model, were evaluated using Monte Carlo simulations for aluminum and copper at incident beam energies ranging from 0.5 keV to 10 keV. The inelastic mean free path, mean energy loss per unit path length, and backscattering coefficients obtained by these models are compared and discussed to understand the merits of the various models. ANOVA (analysis of variance) statistical models were used to quantify the effects of inelastic cross section and energy loss models on the basis of the simulated results deviation from the experimental data for the inelastic mean free path, the mean energy loss per unit path length, and the backscattering coefficient, as well as their correlations. This work in this study is believed to be the first application of ANOVA models towards evaluating inelastic electron beam scattering models. This approach is an improvement over the traditional approach which involves only visual estimation of the difference between the experimental data and simulated results. The data suggests that the optimization of the effective electron number per atom, binding energy, and cut-off energy of an inelastic model for different materials at different beam energies is more important than the selection of inelastic models for Monte Carlo electron scattering simulation. During the simulations, parameters in the equations should be tuned according to different materials for different beam energies rather than merely employing default parameters for an arbitrary material. Energy loss models and cross-section formulas are not the main factors influencing energy loss. Comparison of the deviation of the simulated results from the experimental data shows a significant correlation (p < 0.05) between the backscattering coefficient and energy loss per unit path length. The inclusion of backscattering electrons generated by both primary and secondary electrons for backscattering coefficient simulation is recommended for elements with high atomic numbers. In hybrid models, introducing the inner shell ionization model improves the accuracy of simulated results.

AB - Six models, including a single-scattering model, four hybrid models, and one dielectric function model, were evaluated using Monte Carlo simulations for aluminum and copper at incident beam energies ranging from 0.5 keV to 10 keV. The inelastic mean free path, mean energy loss per unit path length, and backscattering coefficients obtained by these models are compared and discussed to understand the merits of the various models. ANOVA (analysis of variance) statistical models were used to quantify the effects of inelastic cross section and energy loss models on the basis of the simulated results deviation from the experimental data for the inelastic mean free path, the mean energy loss per unit path length, and the backscattering coefficient, as well as their correlations. This work in this study is believed to be the first application of ANOVA models towards evaluating inelastic electron beam scattering models. This approach is an improvement over the traditional approach which involves only visual estimation of the difference between the experimental data and simulated results. The data suggests that the optimization of the effective electron number per atom, binding energy, and cut-off energy of an inelastic model for different materials at different beam energies is more important than the selection of inelastic models for Monte Carlo electron scattering simulation. During the simulations, parameters in the equations should be tuned according to different materials for different beam energies rather than merely employing default parameters for an arbitrary material. Energy loss models and cross-section formulas are not the main factors influencing energy loss. Comparison of the deviation of the simulated results from the experimental data shows a significant correlation (p < 0.05) between the backscattering coefficient and energy loss per unit path length. The inclusion of backscattering electrons generated by both primary and secondary electrons for backscattering coefficient simulation is recommended for elements with high atomic numbers. In hybrid models, introducing the inner shell ionization model improves the accuracy of simulated results.

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U2 - 10.1016/j.nimb.2016.12.035

DO - 10.1016/j.nimb.2016.12.035

M3 - Article

AN - SCOPUS:85008693346

VL - 394

SP - 103

EP - 112

JO - Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms

JF - Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms

SN - 0168-583X

ER -