Electron Backscattering Coefficient Research Articles

Electron inelastic mean free path measured by elastic peak electron spectroscopy for 24 solids between 50 and 3400 eV

Elastic electron backscattering coefficients have been measured for 24 elemental solids (Ag, Al, Au, Be, Bi, C, Co, Cu, Fe, Ge, Mg, Mn, Mo, Ni, Ta, Te, Ti, Pb, Pd, Pt, Si, V, W, Zn) for energies between 50 and 3400 eV. Values for the electron inelastic mean free path (IMFP) were derived from the experimental intensities on the basis of a simple physical model for elastic backscattering that accounts for bulk elastic and inelastic scattering only. For energies ⩾200 eV the IMFP values were found to be well described by the Bethe equation for inelastic scattering, as found earlier by analysis of optical scattering data with the aid of linear response theory (Surf. Interf. Anal. 21 (1994) 165). The parameters β and γ appearing in the Bethe equation are compared with corresponding results derived from optical data. Both, the parameter β, that is related to the total dipole matrix element for inelastic scattering, as well as the parameter γ, that describes the energy dependence of the IMFP, were found to coincide with the results based on optical data within the experimental accuracy of our analysis. Since the present analysis of electron scattering data is entirely free of linear response theory, the present results may be regarded as an independent test of the previous analysis based on optical scattering data.

Coating Effects On BSE Imaging

Abstract Poorly conducting specimens can be examined without coating by using a variable pressure SEM. However, many labs may only have a high vacuum SEM, or for other reasons, choose a high vacuum mode. In order to examine insulating specimens in a high vacuum SEM (using operating conditions conducive to BSE and X-ray analysis) specimens must be coated with a conductive thin film. The perspective of this article is from a materials point of view, but the principles remain the same for biological examinations requiring similar information. Back Scattered Electron (BSE) image contrast is primarily a function of the average atomic number of an imaged area. This is particularly true for polished specimens where there is no topography to contribute to contrast. The BSE coefficient is the ratio of back scattered electrons to incident (beam) electrons.

Optimum energy for high resolution low voltage electron beam lithography — Monte Carlo simulations and experiments

The electron backscattering coefficients of thin tri-level-process layer systems in the energy range from 2.5 to 40.0 keV have been calculated by Monte Carlo simulations. The results show a significant variation of the backscattering with the primary electron energy and the atomic number of the materials used in the layer systems. A local backscattering minimum in the region of 4–5 keV has been found for the investigated multilayer systems. Its stability to variations of the layers' parameters has been investigated. First high resolution experiments at 5.0 keV primary electron energy were carried out to determine the minimal achievable grating period with line-to-space ratio of 1:1. Using ZEP-7000 and hexaacetate p-methylcalix[6]arene resist gratings with 60 and 50 nm minimum period, respectively, were manufactured.

EELS peak intensity dependence on primary electron energy for the Si(111)7×7 and Si(111)-Cr surface structures

The intensity of elastic and bulk plasma loss peaks and also the energy position of the bulk plasma loss peak in the electron energy loss spectra of the Si(111)7×7, Si(111)1×1-Cr and ( 3 × 3 )R30-Cr surface structures were studied as a function of the primary electron energy, E o, in the 200–3000 eV range. It was found that the intensity of elastic and bulk plasma loss peaks had oscillations with periods of 120–140 and 750–900 eV. These oscillations can be caused by the effects of electron diffraction from lattice planes and variation of the electron backscattering coefficient with depth, respectively. During formation of the Si(111)1×1-Cr and α( 3 × 3 )R30-Cr structures the oscillations with periods 120–140 eV were partly retained, showing the existence of an Si(111) lattice framework in subsurface region of the substrate. However, under formation of the Cr-rich phase with β( 3 × 3 )R30-Cr structure they disappeared, showing reconstruction of the Si(111) lattice in the subsurface region. The evolution with E o of the intensity of elastic and bulk loss peaks is correlated with the change in composition and thickness of the different structures of the Si(111)-Cr surface layer. It has been estimated that the thickness of the Cr-rich phase with β( 3 × 3 )R30-Cr structure is between 8 and 15 Å.

Theoretical Investigation of Total Secondary Electron Yield for Teflon

The simplest physical model of the ≈1 eV–2.5 keV electron scattering in insulating polymers is proposed. The simulation of electron trajectories was performed using Monte Carlo technique. The integral characteristics of electron scattering such as total secondary electron yield and backscattering coefficients for Teflon were investigated for 50 eV–2.5 keV electron beams. The difference between theoretical and experimental data was within 50%.

Monte Carlo calculation method on low energy electron scattering in polybasic medium

A novel Monte Carlo method of simulating low energy electron (LEE) scattering in polybasic medium is presented. The Mott cross section is adopted to describe the elastic scattering of LEE, and a mean cross section idea is proposed instead of usual determination of the scattering center. The Joy’s modified Bethe equation is used to calculate energy loss of LEE. The scattering processes of LEE in bulk PMMA have been simulated. And the electron backscattering coefficients, the electron interaction range and energy dissipation distribution of LEE in bulk PMMA have been calculated and compared with those calculated by the method of determining scattering center.

Mean atomic number and backscattered electron coefficient calculations for some materials with low mean atomic number

AbstractIn modelling electron backscattering from solids using Monte Carlo simulations, knowledge of mean atomic number, mean atomic weight, and density of the bulk material are required. We studied four different ways in common useforthe calculation of mean atomic number. An alternative and improved approach is to calculate the mean backscattered electron (BSE) coefficient, η, from a knowledge of the elemental composition and values of η for the elements. Again, we studied a number of formulae suggested for this averaging process. As it is not possible to measure η directly for a number of elements, the method used to interpolate between elements with known η was also examined. In addition, we obtained experimental backscattering relationships for topography‐free samples of poly (methylmethacrylate) (PMMA), carbon, aluminium, and a series of novel halogenated resins, all solids with relatively low mean atomic numbers, and calcified tissues. None of the methods for determining mean atomic number placed the materials of interest in the correct sequence of their experimentally determined BSE peaks: the data differed widely between the individual methods. The averaged BSE coefficient calculated by the Castaing formula gave the best agreement with the experimentally derived data.

Monte Carlo simulation of electron backscattering from compounds with low mean atomic number.

This paper reports a Monte Carlo simulation where a single atom scattering model is adopted. The element taking part in each electron-atom interaction is selected on the basis of its contribution either to the total elastic cross section or to the electron's mean free path. Both Rutherford and Mott scattering are considered, with the continuous slowing down process of Bethe used to calculate the energy loss to the system. The backscattered electron coefficients show good agreement with experimental results from a large group of low atomic number materials when using a model which selects the scattering atom by its contribution to the whole compound calculated from its atomic fraction of the total elastic cross-section.

Theoretical explanation of the relationship between backscattered electron and x-ray linear attenuation coefficients in calcified tissues.

X-ray absorption and backscattered electron (BSE) microscopies are two commonly used techniques for estimating mineral contents in calcified tissues. The resolution in BSE images is usually higher than in x-ray images, but due to the previous lack of good standards to quantify the grey levels in BSE images of bones and teeth, x-ray microtomography (XMT) images of the same specimens have been used for calibration. However, the physics of these two techniques is different: for a specimen with a given composition, the x-ray linear attenuation coefficient is proportional to density, but there is no such relation with the BSE coefficient. To understand the reason that this calibration appears to be valid, the behaviour of simulated bone samples was investigated. In this, the bone samples were modelled as having three phases: hydroxyapatite (Ca10(PO4)6(OH)2), protein, and void (either empty or completely filled with polymethylmethacrylate (PMMA), a resin which is usually used for embedding bones and teeth in microscopic studies). The x-ray linear attenuation coefficients (calculated using published data) and the BSE coefficients (calculated using Monte Carlo simulation) were compared for samples of various phase proportions. It was found that the BSE coefficient correlated only with the x-ray attenuation coefficient for samples with PMMA infiltration. This was attributed to the properties of PMMA (density and mean atomic number) being very similar to those of the protein; therefore, the sample behaves like a two-phase system which allows the establishment of a monotonic relation between density and BSE coefficient. With the newly developed standards (brominated and iodinated dimethacrylate esters) for BSE microscopy of bone, grey levels can be converted to absolute BSE coefficients by linear interpolation, from which equivalent densities can be determined.

Anomalous backscattered electron behavior of MoB and Mo5SiB2(T2) phases in an as-cast Mo-B-Si alloy

It is well established that backscattered electron (BSE) image contrast in SEM is primarily associated with differences in mean atomic number (Z) of the phases. The BSE coefficient increases with higher Z with slight dependence on beam energy (Eo), except for some materials at < 5 keV.We report here the anomalous BSE behavior of MoB and T2(Mo5SiB2) phases observed imaging a 60Mo-30B-10Si (at%) alloy with a CAMECA SX-50. Specifics of the material and EMPA are reported in a companion communication. Mo-ss and Mo3Si are also present. The drastic differences in BSE behavior are shown in Figures 1 (7 keV), 2(15 keV) and 3 (25 keV). The material has not been coated; addition of 100 Å carbon does not change the observed behavior.At 25 keV (Fig 3), MoB dendrites are the darkest phases present, the expected behavior based on their mean Z (Table 1). The T2matrix is gray, whereas smaller regions containing Mo+Mo3Si have the greatest brightness.

Topographically induced bone formation in vitro: implications for bone implants and bone grafts.

We have investigated the influence of substrate topography on the timing and location of bone formation by rat osteoblasts. 250 mu m thick slabs of dental tissues were used intact or had a rectangular grid of grooves (350 mu m wide and of variable depth) cut with a diamond wheel. They were then seeded with rat calvarial osteoblasts and cultured in MEM with 10% FCS at 37 degrees C in 5% CO(2). Ascorbic acid 50 mu g/mL and beta-glycero-phosphate 2 mmol/L were added at confluence. Cultures were observed daily from 2 to 4 weeks, until fixation (and storage) in 70% ethanol. Most were stained with alizarin red S to visualize the newly formed bone. The presence of gap junctions in the bone nodules was determined using connexin-43 immunolabeling and confocal microscopy. Two specimens were embedded in polymethylmethacrylate (PMMA): micromilled blockfaces were coated with carbon and examined by digital backscattered electron (BSE) microscopy. Bone formation began in the second week, preferentially wherever cellular condensation was favored: these locations were (a) within the grooves; (b) at the junction between the slab and the bottom of the culture dish; (c) at the periphery of the dish; and (d) in cracks where dissimilar tissues had separated. In the grooves, a grid of aligned bone developed, the deeper trenches showing bone formation earlier than shallower ones, with bone formation tapering off as a groove became shallower. BSE images showed that the bone formed was well mineralized and contained a high volume proportion of osteocytes. Mean and median values for the mean BSE coefficients were: in vitro bone in grooves 0.138528, 0.141484; in vivo aged bone (2 year old rat mandible) 0.143431, 0.144206; and in vivo young bone (neonate rat cranium) 0.129011, 0.132696. Connexin-43 gap junctions were immunolocalized on osteocytes fully enclosed within bone and on osteoblasts overlying it. We conclude first that local topography is an important factor in the location and timing of bone formation in vitro, and that it is likely to be equally important in vivo in normal bone turnover, fracture repair and the incorporation of bone grafts. Second, the mineral density of the bone formed in vitro is consistent with its being true bone.

Determination of thickness maps of thin coatings by EDS EPMA

AbstractA new experimental procedure for the measurement of the thickness fo thin coatings on substrates is presented. Based on the experimental determination of the electron backscattering coefficient η (via the measurement of the electric current of the correctly polarized specimen holder), the number of reference specimens to be used for the calibration during measurements can be reduced. Thickness maps free of artifacts associated with local changes in the substrate composition illustrate the proposed methods.

Determining the energy response of a silicon surface-barrier detector to incident 3- to 25-keV electrons

An energy-sensitive silicon surface-barrier detector is employed to measure the number of secondary electrons emitted during a collision between an energetic macromolecular ion and a surface. Each extracted secondary electron impacts the detector with energy U, but due to backscattering and other effects, only energy ηU is deposited in the detector. The electron energy deposition function, η = η( U) ≤ 1, is not well known for the 3- to 25-keV energies employed in our setup. In this paper, η( U) is measured with a specially developed compact electron-pulse source placed at variable potential relative to the detector. For a particular detector, it was found that η(U) = k(1− 1.59 √U ) , where U is in units of keV. Although the proportionality constant k is not directly determined in this experiment, an estimate of k ≈ 1.35 was calculated by combining literature values of the electron transmission probability of the detector gold window and the electron backscattering coefficient for silicon for 20 keV electrons.

Influence of Surface Roughness on Secondary Electron Emission and Electron Backscattering from Metal Surface

Because of its acute importance in the understanding of low-energy ( ≤1 keV) electron-material interactions in thermonuclear fusion devices, the effect of surface roughness on the secondary electron yield and backscattering coefficient, as well as on the energy and angular distributions of emitted electrons, is investigated using a Monte Carlo simulation combined with a model of ripple structure for the roughness. Two different effects of surface roughness are demonstrated. One is that low-energy and obliquely oriented electrons, which cannot escape from a flat surface, can escape from an inclined plane of the rough surface. The other is that electrons emitted near the bottom of the rough area re-enter into the surface. The former effect, which is dominant for small roughness, causes an increase in the secondary electron yield and an increase of the low-energy component in the energy distribution. The latter effect, which is dominant for large roughness, causes a decrease in the secondary electron yield and backscattering coefficient, as well as angular distributions of the over-cosine type.

Secondary Electron Emission and Backscattering from a Metal Surface under Low-Energy Positron and Electron Bombardment

A Monte Carlo simulation is performed to study the secondary electron emission and backscattering from Al bombarded by positrons and electrons. In the simulation, the elastic scattering cross section is calculated by taking into account the polarization of Al atoms by the projectiles and the indistinguishability of electrons, whereas excitation of conduction electrons is described using Lindhard's dielectric scattering formalism. The calculated secondary electron yield and backscattering coefficient for positrons are smaller than those for electrons.

Secondary Electron Emission from Hydrogen-Implanted Graphite with Real Depth Profile of Hydrogen

An experimental hydrogen depth profile is applied to a Monte Carlo simulation of secondary electron emission from hydrogen-implanted graphite. Due to hydrogen implantation, the secondary electron yield increases but the electron backscattering coefficient does not clearly change. Through thermal annealing of the specimen at a temperature higher than 600°C, the secondary electron yield returns to that of a clean graphite without implantation.

Review of φ(ρz) curves in electron probe microanalysis

AbstractSeveral workers have proposed different models for the ionization distribution function ϕ(ρz), involving features related to the interaction of electrons with matter, e.g. ionization cross‐section, stopping power, electron back‐scattering and mass absorption coefficients (MACs). A number of expressions have been developed for these parameters, on which the accuracy of the correction procedures depends. This paper presents a comparison among three of the more successful models for ϕ(ρz): Packwood and Brown's Gaussian model, the quadrilateral model proposed by Sewell et al. and Pouchou and Pichoir's model.In order to test these models, a set of 1547 measurements in binary samples of known composition has been complied. Several models for the ionization cross‐section have been tested, along with different expressions for the mean ionization potential J, in which the shell effect can be taken into account. In addition, two possibilities for both the MACs and the electron backscattering coefficient are available. In general, all the tested models showed similar performances. Finally, the advantages of the models related to basic principles over the mathematically optimized ones, in the shape of ϕ(ρz) or in the parameters, are considered.

Simulation of electron transport in plasmas and solids

A cascade model for 1–10 5 eV electron transport in plasmas and solids is proposed. The model is based on the Monte Carlo technique and quantum mechanical description of electron-ion elastic scattering, ionization of ion shells with electron binding energy less than 100 eV, plasmon and electron-hole generation and classical description of inner shell ionization. The main advantage of this model is the detailed description of secondary electron generation without any semiempirical cross sections. The calculated electron backscattering coefficients from Al and Ti are in good agreement with experiments.

Characterisation of surface flatness by the backscattered electron coefficient

In scanning electron microscopy the backscattered electron yield has been shown to depend integrally on the specimen surface roughness. This means that if the surface contains many small inhomogeneities with a typical size of a few nanometres or less, then although the signal line remains smooth (without local perturbations), its level increases compared with that of an ideally flat surface. The authors study this effect by using a model of signal formation developed previously and a Monte Carlo simulation. The results obtained are compared with experimental data and are used for surface flatness mapping.

An expression for the Auger backscattering factor and the ϕ(0) function at oblique incidences

Based on simple physical arguments, the proposed analytical expression: describes the evolution as a function of the incident angle a, of the Auger backscattering factor r (= 1 + R) and of the ionization function of EPMA at the surface, ~(0). This expression leads to a new procedure of quantification in AES and EPMA by the measurement of the electron backscattering coefficient ~ via the measurement of electric current of the correctly polarized specimen holder, which allows the local determination of r and ~(0) without the knowledge of the substrate composition. Its field of application concerns point analysis and images acquisition in Auger electron spectroscopy and X-ray emission spectroscopy with a special attention for the in-depth profiling by AES and the non destructive profilometry of coatings by EDS-EPMA. The results deduced from the proposed expres- sion are in excellent agreement (at least for Uo ~ 3) with the numerical values deduced from Monte Carlo simulations and from the solutions of the transport equation as proposed by other authors. Some aspects related to the influence of the roughness of the surface on the measurements are also indicated.