Energy Distribution Of Backscattered Electrons Research Articles

Monte Carlo simulation of electron emission from aluminum after low energy protons impact

A Monte Carlo (MC) simulation approach is developed to describe the proton-induced secondary electron emission in solids. First, we calculate the double differential cross-section (DDCS) of excited electrons for different charge fractions of the projectile resulting from electron screening. The DDCS parameter is used in MC calculations to describe electron transport in the medium. This parameter is calculated for electrons excited in the 1 eV − 100 eV energy range. The theoretical electron transport modeling is based on Mott’s elastic scattering cross-section and Lindhard’s dielectric function for inelastic scattering. The results obtained for aluminum describe the angular and energy distributions of backscattered electrons for incident protons with energy below 25 keV at normal incidence. Additionally, the total electron emission yield is also calculated, showing a good agreement with available measurements. Our predictions for energy and angular distributions could not be compared with experimental results due to a lack of data.

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.

Angular and energy distribution of backscattered electrons simulated by Monte-Carlo—Assessment by experiment I

The angular and energy distributions of backscattered electrons for the primary energies of 0.2, 0.5 and 1 keV and for Cu and Au were calculated by Monte-Carlo method and compared to measurement. The elastic differential cross-sections were calculated by ELSEPA code. For inelastic scattering a modified Tougaard's model of universal cross-section was used. We fit inelastic mean free path (IMFP) obtained from energy loss distribution, given by the modified Tougaard's model, in order they agreed with the value of IMFP from the TPP-2 formula. By this way we obtained an energy-dependent correction of the constants in Tougaard's formula. A very good agreement was found for the calculated and measured values of angular distribution of elastically reflected electrons. For the energy distribution of backscattered electrons some differences between experiment and calculation appeared, which were probably caused mainly by very low energy losses, e.g. losses at exiting of bremsstrahlung radiation.

Monte Carlo simulation of electron-solid interactions in cement-based materials

Knowledge of the size of the electron-solid interaction volume and the sampling volume of various signals within it is important for interpretation of images and analytical results obtained from electron microscopy. In this study we used a Monte Carlo technique to simulate electron trajectories in order to investigate the shape and size of the interaction volume, the spatial and energy distribution of backscattered electrons and characteristic X-rays in cement-based materials. We found that the maximum penetration depth of the electron trajectories ranges from 0.75 to 1.5 μm at 10 keV and from 2.5 to 5.0 μm at 20 keV. For backscattered electrons, the maximum sampling depth is about 30% of the interaction volume depth and its lateral dimension is close to the interaction volume depth. The sampling volume size of characteristic X-rays is a substantial fraction of the interaction volume. For ettringite, the amount of material analysed in X-ray microanalysis is in the order of 1 to 100 μm 3 at conventional SEM accelerating voltages of 10 to 20 keV.

Monte Carlo simulation study of electron interaction with solids and surfaces

AbstractA brief overview is given on several aspects of applications of the Monte Carlo (MC) simulation method to surface‐related electron spectroscopy and microscopy. For the MC modeling of electron interaction with solids, the electron inelastic scattering cross section is calculated by the use of bulk dielectric function with optical constants in a dielectric functional approach. This has enabled the systematic reproductions of the experimental energy distributions of backscattered electrons for a number of elemental materials. An improved calculation of backscattering factor for quantitative AES analysis has been performed on the basis of a new definition and by making use of the up‐to‐date relevant cross sections. The physical reason is given for the backscattering factor that can be less than unity for very low primary energies close to the ionization energy and/or for large incident angles. For the MC modeling of electron interaction with surfaces, the inelastic scattering of electrons moving in a surface region is treated in a self‐energy formalism. The model has enabled the evaluation of the surface excitation effect through the calculation of position‐dependent electron IMFP. A simulation of REELS spectra for Ag is compared with an experiment; a reasonable agreement found on the surface plasmon peak intensity normalized with elastic peak intensity thus verifies this modeling of electron interaction with surfaces. Finally, the MC simulation code has been extended to deal with complex sample geometries. By using basic building blocks to construct a complex geometry and the ray‐tracing technique for correction of electron flight‐step‐length sampling, the structured and/or inhomogeneous sample can be modeled with reasonable flexibility. Copyright © 2006 John Wiley & Sons, Ltd.

Measuring the angular dependent energy distribution of backscattered electrons at variable geometry

An aluminium semisphere system with 120 points of entry and eight detection areas, assembled on a meridian covering 0.0026 steradian each, was put over a solid bulk sample (e.g., aluminium), which was mounted in the eucentric point so that the incident electron beam could be varied by a polar rotation of the sphere in steps of 11.25 degrees. The complete angular distribution of the backscattered electrons became available by a rotation in steps of 11.25 degrees azimuthally. For this particular setup, the signals from the detection areas as well as the signal from the rest of the semisphere were amplified by operational amplifiers (Burr-Brown OPA128LM). However the signal of the semisphere was not available at that time. Specimen current measurements made the total amount of electrons accessible, providing a possibility for normalization of the results and comparison with total backscattering coefficients. By use of counter voltage variable up to 10 kV inside the detection assembly, it was possible to measure an energy resolution of the backscattered electrons for each detection area at the same time. Details of the construction and calibration procedures, possible errors, and sources of systematic deviations as well as first test results are discussed.

Monte-Carlo simulation of low-energy electron scattering in PMMA – using stopping powers from dielectric formalism

The scattering processes of low-energy ( E ⩽ 10 keV) electrons in a bulk PMMA have been simulated using a Monte-Carlo approach. The approach utilized the continuous slowing down approximation, based on the Mott cross-section for elastic scattering of electron. In addition, the stopping powers from Bethe equation modified by Joy and Luo and those from dielectric response theory with exchange were used, respectively, for the energy losses of electrons. Using these two different stopping powers, the differences between the simulated results, such as electron backscattering coefficients, energy distributions of backscattered electrons and energy dissipations in PMMA, have been determined.

Energy spectra of backscattered electrons in Auger electron spectroscopy: comparison of Monte Carlo simulations with experiment

The primary energy dependecne and atomic-number dependence of backscattered electrons in Auger electron spectroscopy in the EN(E) mode have been investigated both theoretically and experimentally. A Monte Carlo simulation method with inclusion of cascade-secondary-electron production has been used to calculate the full energy distribution of backscattered electrons from the elastic peak down to the true-secondary-electron peak. The simulation model is based on the use of a dielectric function for describing inelastic scattering and secondary excitation, and on the use of Mott cross sections for elastic scattering. A systematic comparison between the calculated and experimental spectra measured with a cylindrical mirror analyzer has been made for Au, Ag, and Cu and for primary energies ranging from 0.5 to 5keV. Reasonable agreement was obtained for the backscattering background at primary energies in the keV region. A significant contribution of cascade-secondary electrons to the measured spectra on the low-energy side (less than 200eV ) was found. Experiments performed on elements with a wide range of atomic numbers have shown a quantitative common curve of the backscattering continuum when plotted on a logarithmic intensity scale in the intermediate energy region between 200eV and the low-loss peaks.

MONTE CARLO CALCULATION OF THE ENERGY DISTRIBUTION OF BACKSCATTERED ELECTRONS

The full energy distribution of backscattered electrons from elastic peak down to true secondary electron peak has been calculated by a Monte-Carlo simulation method by including cascade secondary electrons production. The simulation method is based on the use of a dielectric function for describing electron inelastic scattering and secondary excitation, and the use of Mott cross section for electron elastic scattering. This calculation reproduces well the backscattering background observed in the direct mode of AES. The calculated absolute electron yields have been compared with the available experimental data. The simulation has indicated that, due to the effect of the elastic scattering differential cross section and detection solid angles, the shape of the energy distribution measured with a cylindrical mirror analyzer may differ from the overall energy spectrum of emitted electrons.

Measurement & simulation of backscattered electrons from a strip electron beam source

During electron beam processing, a fraction of the incident power gets backscattered from the target surface, which can be as high as 40% of the incident beam power depending on the beam energy and atomic number of the target material. In the case of a strip electron gun, a uniform magnetic field is used for focusing and deflection of electron beam through 270°. With the strip beam (78 mm×5 mm, 36 kW), experimental results of the 2-D distribution of the backscattered electron current from copper target in its plane, parallel and perpendicular to the focal strip are presented. These results are compared with calculated data using reported energy distribution of backscattered electrons (E.H.Darlington, J. Phys. 8 (1975) 85). The integrated heat flux associated with backscattered electron is experimentally measured and compared with calculated values for incident power of 86 kW. With 12.25 kW/cm 2 of incident strip beam power, the back reflected electron peak power density was observed to be 59W/cm 2. This power density will be higher for high incident power densities and for targets of high atomic numbers and can be used in pre-coating treatments of substrate such as outgassing and cleaning, keeping it at elevated temperature during continuous coating process, and also for outgassing, cleaning and sharing heat load required for pre-melting of the feeder material during melting and casting.

CASINO: A new monte carlo code in C language for electron beam interactions—part II: Tabulated values of the mott cross section

AbstractThis paper presents routines to compute the Mott cross section used in the CASINO program (Monte CArlo SImulation of electroN trajectory in sOlid). The routines used tabulated values of the Mott cross section computed in the work of Czyzewski et al. (1990). The cross section is available over the range 0.02 to 30 keV and for the first 94 elements of the Periodic Table. The routines are written in C language and use a binary file to interpolate the cross section. The first routine computes the total Mott cross sections; the second calculates the polar angle of collision. Backscattered coefficients computed using different cross section are compared for C, Al, Ag, and Au. The Rutherford (1911) cross section and the available empirical equations (Browning et al. 1994, Gauvin and Drouin 1993) are compared to tabulated values of Mott. Also, the energy distribution of backscattered electrons is shown for Al and Au at 10 keV. Finally, the relative computation times for the different Mott cross sections are compared. It was found that tabulated Mott cross sections are more accurate and faster than any empirical Mott cross sections. The tabulated Mott cross sections are even faster than simple Rutherford cross sections.

Angular‐dependent energy distributions for backscattered electrons—Calculation of the surface ionization

AbstractAn equation for angular‐dependent energy distributions of backscattered electrons is presented. Extensive Monte Carlo simulations lead to a simple description for the energy distribution. A comparison of the new expression with experimentally derived curves, Monte Carlo results, and an analytical model is performed. The newly derived energy distributions are used for the calculation of the surface ionization ϕ0 for oblique angle of incidence. For normal incidence, a comparison with several published experimental data leads to a mean value for the deviation of < 4%. For tilted specimens the results are compared with findings of other authors.

A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production

AbstractA new Monte Carlo simulation approach has been developed to describe electron scattering and secondary electron generation processes in solids. This approach is based on the uses of Mott's elastic scattering cross section and Penn's dielectric function. A very good agreement has been found on the energy distribution of backscattered electrons between theoretical calculations and accurate experimental measurement recently made by Goto et al. (1994). This fact confirms that the present Monte Carlo model is very useful for more comprehensive understanding of basic phenomena in electron spec‐troscopy and microscopy, particularly in the sub‐keV energy region where cascade secondary electrons play a dominant role. In this paper the details of the Monte Carlo procedure are described and further application to the mechanism of secondary electron generation is presented.

Monte Carlo simulation of background in AES: a comparison with experiment

Monte Carlo simulations of the energy distribution of backscattered electrons including cascade secondary electrons have been carried out. This calculation yields the background observed in direct mode by AES. We found that, based on a dielectric model of electron inelastic scattering and secondary excitation, the simulation describes very well the background of the experimental EN( E) spectra for Si, Cu, Ag and Au measured with a novel cylindrical mirror analyzer which has been developed by Goto for providing standard AES spectra. The results reveal that the Monte Carlo simulation has potentiality for providing an intimate insight into more accurate theoretical background for the quantitative AES study and for establishing the data base of standard spectra.

Monte Carlo Calculation of the X-Ray Depth Distributions in an Aluminum Target

A Monte-Carlo simulation of inelastic scattering process developed by Terrissol has been modified and used to calculate X-Ray depth distributions. The elastic scattering is modelled using the Mott collision cross-section and the Hartree-Fock atomic potential. The validity of this model is discussed in a comparison between the Monte-Carlo results and experimental data describing the energy distribution of backscattered electrons and energy loss data.

Background formation in the low-energy region in Auger electron spectroscopy

Monte Carlo simulations of cascade processes of secondary electron generation in Si, Cu, and Au have been performed to study the energy distribution of backscattered electrons in the low-energy region. Calculation results show that the characteristic hump appearing in the energy distribution above Si-LVV Auger peak in the EN(E) spectrum can be well described by those electrons ejected from the L shell followed by the cascade process. The shape of EN(E) spectra in the low-energy region is dominated by the directly produced secondary electrons and, hence, strongly correlated with the excitation spectrum Im[−1/ε(ω)] for electron generation.

The effect of electron backscattering on the shape of the 63Ni beta -ray spectrum

Backscattering in various backings of the 63Ni beta -sources was simulated by means of the Monte Carlo method under conditions similar to recent experiments. The relative intensity and energy distribution of backscattered electrons were found to depend strongly on the beta -particle energy. These findings should be taken into account in an accurate analysis of low-energy beta -spectra in particular when searching for the 17 keV neutrino.

Accurate description of surface ionization in electron probe microanalysis: An improved formulation

AbstractA new analytical expression of the surface ionization Φ(0) is derived in terms of atomic number and overvoltage. This expression is obtained by means of an analytical description of the energy distribution of backscattered electrons. The Φ(0) data for Pt, W, Sb, InSb, Ni, Co and Mg have been measured using the tracer technique. The Φ(0) values obtained by using the new expression compare more favourably with experimental results, Monte Carlo simulation and backscattering data from the literature than those obtained with the previous analytical models.

Monte Carlo Simulation of Background in electron spectroscopies

Recent progress in getting precise knowledge on inelastic scattering, particularly, on dielectric functions for various types of material has been enabling the electron spectroscopic spectra obtained by Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS) and reflection electron energy loss spectroscopy (REELS) to be reproduced theoretically with considerable success. For this Monte Carlo simulation is probably most powerful tool, leading to more comprehensive understanding of not only the signal generation but also the background formation.In this paper we present a Monte Carlo simulation approach based on the uses of Mott-scattering cross section and appropriate dielectric function for describing elastic scattering and inelastic scatterings, respectively. With respect to the dielectric function one can use, to good approximation in general, the optical dielectric constants from the data base provided by synchrotron radiation facilities.As typical examples of the Monte Carlo simulation the applications to the AES, XPS, and REELS are shown in Figs. 1, 2, and 3, respectively. The N(E)-spectrum in Fig.l demonstrates how the Monte Carlo simulation describes the energy loss spectrum due to plasmon excitation near at primary energy, general shape of energy distributions of backscattered electrons and secondary electrons.

Calculation and comparison of the surface ionization ϕ(0)

AbstractAn analytical expression for the surface ionization ϕ(O) is derived from fundamentals, viz., the ionization cross section and the angular and energy distribution of backscattered electrons. In order to avoid numerical integrations, a simple formula for the energy distribution of backscattered electrons is presented. The values given by the resulting expression for ϕ(O) are compared with those given by already known formulae and with experimental findings. In general, the agreement is quite satisfactory, although the calculated values generally are smaller than those experimentally found, especially at high overvoltages. This can at least partly be explained by secondary fluorescence excited by the continuous radiation, of which the correction has not been taken into account in the experimental determination of the ϕ(O) values.