Electron Backscattering Coefficient Research Articles

Prediction of electron-solid interaction parameters using machine learning.

Electron backscattering coefficient and electron-stopping power are essential concepts in many disciplines, from radiation to materials science, semiconductor manufacturing, and space exploration. They enable precise calculations, measurements, and simulations of electron interactions with matter, which contribute to advancing science, technology, and safety in a variety of applications. The availability of these data is fundamental to scientific research to validate hypotheses, conduct experiments, and explore new theories. A relatively novel machine learning approach has demonstrated notable success in enhancing data quality and completeness, significantly contributing to the facilitation of data discovery. Using fundamental material property data, the stacking ensemble machine learning (EML) technique was established in this study to generate electron-solid interaction parameters for any target material over a wide range of energies. The final stacking EML was built using the base and meta learners bagging regressor (BR), K-nearest neighbors (k-NN), random forest (RF), support vector regression (SVR), and eXtreme Gradient Boosting (XGB). In this study, two publicly available databases with a total of 4030 data points were used. Training datasets have 785 and 525 data points for electron backscattering coefficient and stopping power, respectively, whereas testing datasets contain 262 and 175 data points. Fivefeatures were used as input variables to train different individual algorithms and their combinations. On both the training and test datasets, the model was evaluated using different error metrics, including R-squared (R2), mean-absolute-error (MAE), root-mean-squared-error (RMSE), and mean-absolute-percentage-error (MAPE). Our model evaluation tests revealed that combining RF and XGB with a k-NN meta-learner outperformed other algorithms. The analysis of error metrics demonstrated a very close fit to all samples in each training dataset. Furthermore, predictions made by the model on unseen test data indicated accurate estimations of new backscattering and stopping power data. The developed model achieved high prediction accuracy for various target materials across the broad electron energy spectrum. The outcomes demonstrate the effectiveness of machine learning methodology and the chosen models' suitability for addressing substantial physics challenges.

Electron backscattering coefficients for Cr, Co, and Pd solids: A Monte Carlo simulation study

We have calculated electron backscattering coefficients, η(Ep), at primary electron energies Ep of 0.1–100 keV for three elemental and intermediate atomic number solids, Cr, Co and Pd, with an up-to-date Monte Carlo simulation model. A relativistic dielectric functional approach is adopted for the calculation of the electron inelastic cross section, where several different datasets of optical energy loss function (ELF) are adopted. The calculated backscattering coefficient is found to be substantially affected by the ELF, where the influence can be seen to follow the f- and ps-sum rules and the resultant energy dependence of electron inelastic mean free path. To understand the uncertainties involved in a comparison with experimental data both the theoretical uncertainty due to the elastic cross-section model and the experimental systematic error for the contaminated surfaces are investigated. A total of 192 different scattering potentials are employed for the calculation of Mott's electron elastic cross section and this theoretical uncertainty is confirmed to be small. On the other hand, the simulation of contaminated Co and Pd surfaces with several carbonaceous atomic layers can well explain the experimental data. The present results indicate that accurate backscattering coefficient data should be either measured from fully cleaned surfaces or obtained from modern Monte Carlo theoretical calculations involving reliable optical constants data. With the recent progress in the accurate measurement of optical constants by reflection electron energy loss spectroscopy technique, constructing a reliable theoretical database of electron backscattering coefficients for clean surfaces of elemental solids is highly hopeful.

A comprehensive open-access database of electron backscattering coefficients for energies ranging from 0.1KeV to 15MeV.

The characterization of electron backscattering is essential in medical physics for accurately assessing dose deposited around inhomogeneities where backscattering alters the spatial energy distribution pattern and for determining Monte-Carlo code's ability to effectively describe electron scattering and does calculation in a target volume. Recent machine learning advances have provided physicists with powerful tools for effectively extracting information and trends from extensive experiment observations if sufficiently sizeable datasets are available for data mining. We report on the development of a publicly accessible database on electron backscattering coefficients for solid targets. The first database on electron-solid interactions was assembled in 1995. Data for bulk materials, limited to normal incidence and energies up to 100keV, were primarily focusing on electron microscopy. To accommodate broad high-energy applications and include the most recent publications we have created a comprehensive database of electron backscattering coefficients, listed as a function of target atomic number and thickness, electron energy, and incidence angle. These additions resulted in a database of 3566 data points, compared to the previous database of 1430. The data collection includes only published experimental observations (no calculations or results fitting) with no attempt to judge their accuracy or quality. A limited number of data points were compared to recently published Monte-Carlo results. The presented database provides values of electron backscattering coefficients for 50 elements and 19 compounds at electron energies ranging from 0.1keV to 15MeV, presented in ASCII files. Each file contains the electron energy and backscattering coefficient with target thickness or electron incidence angle included where available, and the reference number shown in the last column. Additionally, the presented data were shown in the graphs for better visualization. The online database can be accessed from the website https://doi.org/10.5281/zenodo.7810951. The database provides the most up-to-date source of experimentally obtained electron backscattering coefficients that can be used in theoretical and MC calculations and modeling validations. The data availability is still very limited for many solids and almost non-existent for compounds. Novel machine learning methods should be well adapted to predict these unknown values for various targets, thicknesses, energies, and incident angles utilizing the presented cleaned dataset.

An extensive theoretical quantification of secondary electron emission from silicon

Though intensive experimental studies have been carried out on electron emission properties in past decades, the reliable data from accurate experimental measurements for clean and smooth surfaces are still quite limited. In this work, we have performed a comprehensive Monte Carlo simulation of electron emission yields, the secondary electron yield (SEY, δ), backscattered electron coefficient (BSC, η) and total electron yield (TEY, σ=δ+η), from silicon and the uncertainty quantification of the theoretical calculation results for the first time. The simulations were made on total 17280 scattering models. The considered uncertainty factors in the physical modelling that can influence the calculated yields include work function data, optical energy loss function data, dielectric function models for electron inelastic scattering and the scattering potentials for electron elastic scattering. The calculation results show that δ is significantly influenced by the work function while the dielectric function model has a slight effect. Elastic scattering potential (or elastic scattering cross section) and energy loss function affects to a certain extent both δ and η. Our simulated η data agree with most of the experimental measurements while the simulated mean δ data are well below most of the experimental data. At a 75% level of confidence, the experimental σ data measured by Goto et al. lie within the uncertainty range of our simulation results. This work has provided sufficient ground for the necessity of building a theoretical database of electron emission yield considering the fact that most of the previous experimental data are not reliable due to the presence of surface contamination during the measurements.

The Role of Molecular Structure in Monte Carlo Simulations of the Secondary Electron Yield and Backscattering Coefficient from Methacrylic Acid.

In this paper, we show the influence of the chemical structure of four different conformers on the secondary electron emission and backscattering of an electron beam from a gel of methacrylic acid. The conformers have different permanent dipole moments, which determines the cross sections for elastic collisions with electrons. The cross sections are used in Monte Carlo simulations of an electron beam, which enters the gel of methacrylic acid. The secondary electron yield and the backscattering coefficient are computed as a function of the beam energy.

Influence of energy loss function to the Monte Carlo simulated electron backscattering coefficient

We report an improved calculation of the electron backscattering coefficients (BSCs) for beryllium, molybdenum and tungsten at electron energies of 0.1–100 keV based on an up-to-date Monte Carlo simulation method with different input of energy loss function (ELF) data. The electron inelastic cross-section is derived from the relativistic dielectric functional formalism, where the full Penn’s algorithm is applied for the extension of the ELF from the optical limit of q to 0 into the left( {q,omega } right)-plane. We have found that the accuracy of energy loss function may affect largely the calculated BSC. We also show that this has close relationship with the f- and ps-sum rules.

An empirical model for the Backscattering coefficient of 1-30 keV electrons from thin film targets

In this paper, the electron backscattering coefficient for normally incident beams with energy up to 30 keV impinging on thin film targets is stochastically modeled using a Monte Carlo simulation.Accordingly, a generalized model describing the realisticbackscattering behaviortaking into account both the atomic number and the thickness for energy up to 30keV is proposed. The obtained results are compared to the experimental and theoretical data, where an excellent agreement is achieved. Moreover, the usefulness of the proposed model as a probe for investigating the electrons backscattered behavior of several materials is thoroughly discussed. It is revealed that the developedmodel allowsidentifying the critical thickness of thin film exhibiting the same electron backscattering behavior as that of a semi-infinite solid, which contributes to an accurate assessment of surface properties of various thin-films.The use of our empirical model enables reducing the simulation time as compared to that of complicated Monte Carlo time consuming simulation.Therefore, the presented model can be implemented to accurately determinatethe electron backscattering coefficient of various thin-film materials with dissimilar thicknesses, making it appropriate for surface analysis applications.

Electron and positron backscattering from condensed targets

The backscattering process for electron and positron impinging on condensed targets is studied here. The calculation is performed for Li, Na, Al and Cu atoms in the 500–3000 eV energy range. The well known Vicanek and Urbassek theory is used to determine the backscattering coefficient for present solid atoms. To analyze the elastic scattering cross section, spherical complex optical potential formalism is used. Apart from the backscattering coefficient, momentum transfer cross section, range of penetration, and mean number of wide-angle collisions are also tabulated and compared to the available data. No previous work was found reporting the range of penetration for the atoms. Hence, we also report the electron backscattering coefficient and range of penetration for liquid water for which experimental and theoretical data are available for the range of penetration. The electron backscattering coefficient for liquid water is reported for the first time here.

Electron backscattering coefficients of molybdenum and tungsten based on the Monte Carlo simulations

Monte Carlo simulation is employed for the calculation of electron backscattering coefficients of molybdenum (Mo) and tungsten (W) at normal incidence angle and at energies between 100 eV to 100 keV. For the modelling of the electron elastic scattering we have applied the partial-wave expansion method using the Mott's cross-section, where the scattering potential includes the electron electrostatic potential, exchange potential and correlation-polarization potential. A relativistic dielectric functional approach with full Penn's algorithm is adopted for the calculation of the electron inelastic cross-section. The effect of phonon excitation, the interband transition of the loosely bound valance electrons, and the inner-shells electrons excitations are considered in the energy loss functions of the materials via the optical constants. We found that our present simulated data agree well with the experimental data at energies above 20 keV for both elements while they are well above the experimental data at lower incident energies. The disagreement can be explained by the possible surface contamination of carbonaceous atomic layers exist in the measurements by additional simulation for the contaminated surfaces. Moreover, for the better and detailed understanding of the energy dependence of the backscattering coefficients, we also present the backscattered electron energy spectra, angular distributions, and depth distributions for both samples.

Determination of electron backscattering coefficient of beryllium by a high-precision Monte Carlo simulation

We present an up-to-date Monte Carlo simulation of electron backscattering coefficient of beryllium, which is an important material in fusion reactor, at an impact energy range of electrons between 100 eV and 100 keV. The Mott’s cross section calculated with more accurate scattering potential and a relativistic dielectric functional formalism with full Penn algorithm and experimental optical data are used in the modelling of electron elastic and inelastic scatterings, respectively. This Monte Carlo simulation modelling enabled us to derive comprehensive theoretical values of backscattering coefficient, which are found significantly smaller than the previous published experimental data particularly at energies below 10 keV. Simulation of electron backscattering spectra was then carried out with and without Auger electron emission, which confirmed that Auger electrons have negligible contribution to backscattering coefficient. To validate our simulation results, we have also performed calculation for amorphous boron and carbon, while the comparison with the available experimental data shows reasonable agreement. Further simulation for carbon and water covered Be sample has revealed that the surface contamination in low vacuum conditions with several atomic/molecular layers can drastically alter the measurement values for beryllium at low energies. The low backscattering coefficient values of beryllium are partly attributed to the extremely strong forward elastic scattering for low atomic number element. Therefore, we recommend to use the here reported backscattering coefficient data of beryllium for applications.

Two-Stream Model of Monoenergetic Electron-Beam Backscattering: Application to Problems of the Diagnostics of Thin-Film Structures

The energy spectra of electrons reflected from individual layers located inside a multilayer thin-film target are calculated as applied to problems of the backscattered electron spectroscopy method (BESM). The structure of analytical expressions describing the distribution of the electron-backscattering coefficient over the sample depth is refined. A formula for the two-dimensional polar-angle distribution of backscattered electrons after their exit from a thin-film target with a given thickness is obtained. An algorithm for calculations required to construct the energy distributions of backscattered electrons is developed for a given angular position of the input diaphragm of an analyzer spectrometer. This makes it possible to bring our calculations closer to the actual conditions for recording backscattered electrons. The results of comprehensive verification of the obtained relations based on comparing our model calculations of the energy distributions of backscattered electrons with the experimental spectra of free films, bulk samples, and a multilayer thin-film sample on a massive substrate are given.

Monte Carlo simulation study of electron yields from compound semiconductor materials

A systematic study has been performed based on a Monte Carlo simulation for the investigation of secondary electron yields, backscattering coefficients, and total electron yields for eight compound semiconductor materials, i.e., AlN, TiN, VN, VC, GaAs, InAs, InSb, and PbS, at different incident electron energies in the range 0.1–10 keV. Our Monte Carlo simulation model is based on the Mott cross section for electron elastic scattering as calculated by a partial wave method and a dielectric functional approach to electron inelastic scattering with the full Penn algorithm. We used Palik's optical data for lower photon energies below 100 eVs and Henke's data for higher photon energies. The cascade production of secondary electrons in electron inelastic scattering and low energy is included in the simulation. The simulated results of electron backscattering coefficients are compared with the experimental data available in the literature. Considering the fact that the experimental data for these compound materials are not available, we have compared them with experimental data for elements having the nearest mean atomic numbers. The simulation predicted much larger backscattering coefficient values than the empirical Staub formula.

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

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. In this study, we have performed MC simulations of electron emission from liquid water in the primary energy range of 50eV-30keV 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. 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 10eV 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. It is concluded that full dielectric function data at low energy loss values below 10eV are recommended for modeling of low energy electrons in liquid water.

О возможности применения бета-альбедно-абсорбционного метода для создания приборов неразрушающего контроля размерных параметров наноматериалов (толщины, поверхностной плотности и покрытий) при их производстве

The explanation is given of the feasibility of using of a relatively unknown beta-albedo-absorption (BAA) technique, which was the research topic of the PHD thesis of the author, for the creation of a modern, unparalleled anywhere in the world, non-destructive testing (NDT) system to be used for the production of nanomaterials with main dimension parameters (thickness, surface density, and coating) in the nanorange, i.e., practically from zero to several hundreds of nanometers. The importance of the problem is determined by the present time intense development both in Russia and all over the world of the production of nanomaterials of different types in the practical absence of the development and production of NDT devices. Analytical expressions are given for the calculation of the main quantitative characteristics of BAA measurement geometry, namely, the radial density distribution and the integral electron backscattering coefficient at the variables of the parameters of the reflecting gas or air medium. The principle of developing the optimum measurement geometry, little dependent on changing parameters of the reflecting medium and minimizing measurement errors for BAA method, is described. The design of the developed detectors is shown. The following recommendations are given on additional experimental studies of the BAA method aiming to provide a possibility of parameter measurement in the nanorange: using the industrial beta sources with a lower value of the maximum beta spectrum energy; increasing the activity of beta sources or measurement time; using special filters for degradation of the beta source emission spectrum; and using beta radiation detectors with the largest possible measurement area.

Composition dependence of penetration range and backscattering coefficient of electrons impinging on SixGe1−x and GaAsxN1−x semiconducting alloys

The alloy composition dependence of penetration range and backscattering coefficient of electrons normally impinging on SixGe1−x and GaAsxN1−x semiconductor alloys targets for beam energies in the range 0.5–3.5 keV has been investigated. The electron penetration range is calculated using the Ashley's model. The electron backscattering coefficient is determined using both the Vicanek and Urbassek theory where the transport cross-sections are obtained more accurately via an improved approximation and Monte Carlo method in which the inelastic scattering processes are treated via Ashley's optical model. Our results regarding the electron backscattering coefficient for Si and Ge targets are found to be much higher than those of experiment when using the Vicanek and Urbassek theory. However, the use of Ashley's model via Monte Carlo method gives results that are in reasonably good accord with the experimental data reported in the literature in the low energy regime being considered here.

Transmission probability and energy distribution of electrons impinging on indium thin film targets

Based on a home‐made Monte Carlo simulation, the electron backscattering coefficient, mean penetration depth, transmission probability, and transmission energy distribution of 1–5 keV electron normally incident penetrating in indium thin film targets have been computed. The trend of all features of interest as a function of the indium film thickness at both nanometric scale region and bulk material region has been examined and discussed. The present predictions may be seen as the first investigation regarding 1–5 keV electrons impinging on indium thin film targets. Copyright © 2016 John Wiley & Sons, Ltd.

Electron backscattering from solid targets: Elastic scattering calculations

Analytical expression of the target atomic number dependence of the numerical coefficient in the Nigam atomic screening factor is proposed here to approximate the Rutherford elastic scattering cross sections for slow electron beams impinging on selected solid targets (from Be to Au) in the primary energy range 1–4keV. Applications are then proposed in terms of Monte Carlo calculation of backscattering coefficient. In this respect, tabulations of backscattering coefficients are here reported for slow electrons in solid targets of interest pointing out a reasonable agreement with the data available in the literature. Analytical expressions of the target atomic number dependence of the electron backscattering coefficient is also suggested for selected electron primary energies ranging from 1 to 4keV allowing thus an accurate determination of backscattering coefficients for low-energy electrons in solid targets without any resort in Monte Carlo type calculations.

Electron back-scattering coefficient below 5 keV: Analytical expressions and surface-barrier effects

Simple analytical expressions for the electron backscattering coefficient, η, are established from published data obtained in the ∼0.4-5 keV range for 21 elements ranging from Be to Au. They take into account the decline in η with a decrease in energy E° for high-Z elements and the reverse behavior for low-Z elements. The proposed expressions for η (E°) lead to crossing energies situated in the 0.4-1 keV range and they may be reasonably extended to any of the other elements—via an interpolation procedure—to metallic alloys and probably to compounds. The influence of the surface barrier on the escape probability of the back-scattered electrons is next evaluated. This evaluation provides a theoretical basis to explain the observed deviation between various published data as a consequence of surface contamination or oxidation. Various practical applications and strategies are deduced for the η-measurements in dedicated instruments as well for the image interpretation in low voltage scanning electron microscopy based on the backscattered electron detection. In this microscopy, the present investigation allows to generalize the scarce contrast changes and contrast reversals previously observed on multi elemental samples and it suggests the possibility of a new type of contrast: the work function contrast.

Penetration range and backscattering ratio of low-energy electrons in metals

The accuracy of the Ashley's optical-data model [J.C. Ashley, J. Electron Spectrosc. Relat. Phenom. 50 (1990) 323] for describing the energy loss rate and inelastic mean free path of low-energy electrons in Al and Cu has been examined through the use of Ashley's model for calculating the electron penetration range. The latter has also been calculated using the empirical expressions reported by Iskef et al. [Phys. Med. Biol. 28 (1983) 535] and Gryzinski excitation function. The resulting range of penetration is used for determining the electron backscattering coefficients via the use of Vicanek and Urbassek theory [Phys. Rev. B 44 (1991) 7234] where the transport cross-sections are obtained from Rouabah et al. [Appl. Surf. Sci. 255 (2009) 6217] approximation. Besides the electron backscattering coefficients have been calculated from Monte Carlo simulation in which the inelastic scattering processes are handled using Ashley dielectric approach. It is found that the use of Ashley's optical model via Monte-Carlo method gives backscattering coefficients more accurate than those obtained via Vicanek and Urbassek theory. This confirms the accuracy of Ashley's optical model and shows that the Monte-Carlo method is much more accurate and precise than the Vicanek and Urbassek semi-empirical approach.

Backscattered electrons from gold surface films deposited on silicon substrates: a joint experimental and computational investigation to add new potentiality to electron microscopy

This paper addresses the problem of the thickness determination of thin gold overlayers deposited on silicon bulk substrates by looking at the electron backscattering coefficient involved in scanning electron microscopy (SEM). A Monte Carlo code, used to calculate the backscattering coefficient, together with a simple experimental setup, which uses a conventional SEM, allow to determine thin film thickness (in the range 25–200 nm) with an estimated accuracy of 20%. This adds obviously new potentiality to SEM. Copyright © 2012 John Wiley & Sons, Ltd.