Forward-scattered Electrons Research Articles

Calculation of the Absorbed Electron Energy 3D Distribution by the Monte Carlo Method, Presentation of the Proximity Function by Three Parameters α, β, η and Comparison with the Experiment.

The paper presents a program for simulating electron scattering in layered materials ProxyFn. Calculations show that the absorbed energy density is three-dimensional, while the contribution of the forward-scattered electrons is better described by a power function rather than the commonly used Gaussian. It is shown that for the practical correction of the proximity effect, it is possible, nevertheless, to use the classical two-dimensional proximity function containing three parameters: α, β, η. A method for determining the parameters α, β, η from three-dimensional calculations based on MC simulation and development consideration is proposed. A good agreement of the obtained parameters and experimental data for various substrates and electron energies is shown. Thus, a method for calculating the parameters of the classical proximity function for arbitrary layered substrates based on the Monte Carlo simulation has been developed.

Infrared finiteness and forward scattering

Infrared divergences have long been heralded to cancel in sufficiently inclusive cross-sections, according to the famous Kinoshita-Lee-Nauenberg theorem which mandates an initial and final state sum. While well-motivated, this theorem is much weaker than necessary: for finiteness, one need only sum over initial $\textit{or}$ final states. Moreover, the cancellation generically requires the inclusion of the forward scattering process. We provide a number of examples showing the importance of this revised understanding: in $e^+e^- \to Z$ at next-to-leading order, one can sum over certain initial and final states with an arbitrary number of extra photons, or only over final states with a finite number of photons, if forward scattering is included. For Compton scattering, infrared finiteness requires the indistinguishability of hard forward-scattered electrons and photons. This implies that in addition to experimental limits on the energy and angular resolution, there must also be an experimental limit on the momentum at which electric charge can be observed. Similar considerations are required to explain why the rate for $\gamma \gamma$ to scatter into photons alone is infrared divergent but the rate for $\gamma \gamma$ to scatter into photons or charged particles is finite. This new understanding sheds light on the importance of including degenerate initial states in physical predictions, the relevance of disconnected Feynman diagrams, the importance of dressing initial or final-state charged particles, and the quest to properly define the $S$ matrix.

Transmission Kikuchi diffraction versus electron back-scattering diffraction: A case study on an electron transparent cross-section of TWIP steel

The present case study compares transmission Kikuchi diffraction (TKD) with electron back-scattering diffraction (EBSD) on the same area of an electron transparent cross-section of a twinning induced plasticity steel. While TKD expectedly provides better clarity of internal defect substructures in the band contrast map, EBSD returns orientation data that approaches the quality of the TKD map. This was rationalised by Monte Carlo simulations of the electron energy spreads, which showed that due to the geometry-based compromises associated with adapting a conventional EBSD detector (which is off-axis with respect to the incident electron beam) to TKD, a broadening in the electron energy distribution of the forward-scattered electrons collected on the detector phosphor screen, is unavoidable. In this circumstance, the values of the full-widths at half-maximum of the energy distributions for TKD and EBSD are of the same order. It follows that EBSD on electron transparent cross-sections may be a viable alternative to TKD when: (i) conventional EBSD detectors are adapted to TKD and, (ii) sample microstructures comprise features whose sizes do not mandate the application of TKD.

Improved strong-field approximation and quantum-orbit theory: Application to ionization by a bicircular laser field

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

Angularly-selective transmission imaging in a scanning electron microscope

This work presents recent advances in transmission scanning electron microscopy (t-SEM) imaging control capabilities. A modular aperture system and a cantilever-style sample holder that enable comprehensive angular selectivity of forward-scattered electrons are described. When combined with a commercially available solid-state transmission detector having only basic bright-field and dark-field imaging capabilities, the advances described here enable numerous transmission imaging modes. Several examples are provided that demonstrate how contrast arising from diffraction to mass-thickness can be obtained. Unanticipated image contrast at some imaging conditions is also observed and addressed.

B13-P-06Effective surface treatment of non-conductive materials for orientation analysis by transmission EBSD

Electron backscattering diffraction (EBSD) is a very useful technique for crystal orientation analysis by acquiring Kikuchi patterns formed by backscattered electrons [ 1 ]. Non-conductive materials under electron illumination are often suffering from charge-up effects which significantly hamper crystal orientation analysis. Surface coating by a vapour deposition of a conductive solid material is hence very often used to reduce charge-up. However, a special care should be taken to control the deposition thickness because too thick deposition would cause blurred and ambiguous EBSD patterns, whereas too thin deposition could be insufficient to reduce charge-up. A method compensating for charge-up by spraying an ionized gas onto the sample surface [ 2 ] is currently available, though it requires a particular equipment. Transmission EBSD (t-EBSD) is an alternative method to acquire Kikuchi patterns formed by forward-scattered electrons, which transmit through a thin sample like TEM [ 3 ]. In the present study we focus on the two characteristics of t-EBSD: the first one is that t-EBSD can acquire EBSD patterns of the sample even when its surface is contaminated on the side of electron incidence. The second one is that forward-scattered electron has a shorter average traveling path than that of backscattered electrons. Herein, we propose a method for crystal orientation analysis of non-conductive materials, to which t-EBSD is effectively applied with surface coating incorporated. We demonstrate that the surface coating on non-conductive samples exerts not only little influence on the clarity of t-EBSD patterns but also helps better identification of crystal orientation by reducing charge-up.

Scanning transmission low-energy electron microscopy

We discuss an extension to the transmission mode of the cathode-lens-equipped scanning electron microscope, enabling operation down to the lowest energies of electrons. Penetration of electrons through free-standing ultrathin films is examined along the full energy scale, and the contribution of the secondary electrons (SEs), released near the bottom surface of the sample, is shown, enhancing the apparent transmissivity of the sample to more than 100%. Provisional filtering off of the SEs, providing the dark-field signal of forward-scattered electrons, was made using an annular 3-D adjustable detector inserted below the sample. Demonstration experiments were performed on the graphene flakes and on a 3-nm-thick carbon film. Electron penetrability at the lowest energies was measured on the graphene sample.

Pressure effect of growing with electron beam‐induced deposition with tungsten hexafluoride and tetraethylorthosilicate precursor

Electron beam-induced deposition (EBID) provides a simple way to fabricate submicron- or nanometer-scale structures from various elements in a scanning electron microscope (SEM). The growth rate and shape of the deposits are influenced by many factors. We have studied the growth rate and morphology of EBID-deposited nanostructures as a function of the tungsten hexafluoride (WF6) and tetraethylorthosilicate (TEOS) precursor gas pressure and growth time, and we have used Monte Carlo simulations to model the growth of tungsten and silicon oxide to elucidate the mechanisms involved in the EBID growth. The lateral radius of the deposit decreases with increasing pressure because of the enhanced vertical growth rate which limits competing lateral broadening produced by secondary and forward-scattered electrons. The morphology difference between the conical SiO(x) and the cylindrical W nanopillars is related to the difference in interaction volume between the two materials. A key parameter is the residence time of the precursor gas molecules. This is an exponential function of the surface temperature; it changes during nanopillar growth and is a function of the nanopillar material and the beam conditions.

Total electron scattering cross sections of He, Ne and Ar, in the energy range 4eV–2 keV

Total scattering cross sections of the rare gases He, Ne and Ar have been measured,for electrons in the energy range from 4 eV to 2 keV. The measurements wereperformed using a linear transmission device and an electron energy analyser,with an angular resolution better than 1.1 × 10−3 srand with an energy resolution far below the first excitation threshold in the threeatoms. The uncertainties of the experimental results are generally smaller than3%. With a few exceptions, the present results are in good agreement with thedata of other authors. Systematic deviations were found between the presentresults and the data available for the total scattering cross sections of He athigh electron energies. The deviations increase with increasing energyand reach about 13% at 2 keV. It appears that different levels of theseparation of forward-scattered electrons are responsible for these systematicdeviations.

Analysis of High-Acceleration-Voltage Scanning Electron Microscope Images

Scanning electron microscope (SEM) images of holes or trenches obtained at high acceleration voltages, such as 200 kV, are analyzed by computer simulation. Secondary electrons generated by forward-scattered primary electrons (SE1s), and those by backward-scattered primary electrons (SE2s) are calculated separately, although a detector catches both SE1 and SE2 without distinction. The straightforward penetration of the primary electrons accelerated at 200 kV gives large edge effects and slight lateral scattering in the sample. Therefore, the image contrast of the SE1 intensity, which provides information on surface topography, becomes high. Moreover, as the SE2 intensity is almost a uniform background, it becomes easy to extract the SE1 intensity from the detected secondary electrons. For observations of the inside structure of a sample, although the SE2 contrast is low at 200 kV, a small degree of lateral scattering in the sample results in a sharp image.

Measurement of absolute differential cross sections for the excitation of the n = 2 states of helium at and

A novel scheme for the measurement of inelastic differential cross sections (DCS) at is presented. It uses a magnetically collimated electron-impact spectrometer where the backward-scattered electrons are reflected into the forward direction by a potential barrier, and enter the energy analyser located at . Pulsed incident electron beam and time-of-flight detection are used to differentiate the backward- and forward-scattered electrons. The instrument yields the ratio of the forward and backward DCS. This data is then normalized to the absolute DCS at , measured with an instrument using electrostatic hemispherical analysers, to yield absolute DCS at . The combined results from both instruments are absolute DCSs as a function of scattering angle continuously from to plus one more data point at . Absolute DCS is also obtained as a function of incident energy at and at . The technique is applied to measure the DCSs for the excitation of the four n = 2 states of helium as a function of scattering angle at 22, 25, and 29.6 eV, and as a function of energy from threshold to 28 eV at and . The results are compared with recent calculations.

High-energy electron pair production on oxygen

Electron-positron pair production cross sections are calculated for 50-MeV electrons incident on an oxygen nucleus. The symmetric coplanar cross sections are emphasized. Neglecting exchange, the spectra of forward-scattered projectile electrons is numerically calculated. In the extreme relativistic and nonrelativistic limits for the produced pair kinetic energies, calculated cross sections are similar to those of Bhabha.

A quantitative auger electron spectroscopy method (applied to a thin film monolayer overgrowth)

When a thin film grows in a monolayer overgrowth fashion, the AES signal versus film thickness is calculated by a quantitative AES method. The method is applied to the Cases of Ag on Au, Mo on W and Be on Cu. The calculated results agree very well with the experimnetal results. In this method, the following points are considered: (1) the attenuation of a primary beam, (2) the effects of back-scattered and forward-scattered electrons both from thin film and substrate materials, (3) the escape depths of any electrons, and (4) the effect of the three-dimensional movements of secondary electrons and Auger electrons in the solid. Consequently, especially from the above effect (4), the curve of Auger electron signal intensity versus film thickness can be estimated for the various optics (e.g. Cylindrical Mirror Analyzer (CMA), Low Energy Electron Diffraction (LEED) optics,…) used for the usual Auger experiments. Electron mean free paths can be obtained by the interpolation or the extrapolation for the different atomic numbers and the different energies from the published experimental result of Mo and W. The result by this method has a similar tendency as the result obtained by Penn. Also, the number of back-scattered and forward-scattered electrons can be estimated by the coefficient of secondary electrons with energy above the ionization electron energy E C to produce Auger electrons. Then, the values of the secondary electron coefficients are measured and tabulated for the 20 different elements from Be to U as a function of the ionization electron energy.

Analysis of virtualγγcollision processes in the deep-inelastic configuration

In the framework of the helicity method, we propose a simple way of analyzing in first approximation the brute data of a $\ensuremath{\gamma}\ensuremath{\gamma}$ collision experiment in the deep-inelastic configuration in terms of structure functions pertaining to the virtual $\ensuremath{\gamma}\ensuremath{\gamma}$ interaction. The conditions of such an approximation are defined, and its validity is numerically checked for a wide variety of values of the kinematic parameters. One concludes that, in order to make the back-factorization procedure precise enough, tagging angles of the forward-scattered electrons should not exceed a few mrad.

Impact of electron scattering on linewidth control in electron-beam lithography

The importance of electron-scattering on pattern fidelity in electron-beam lithography is examined using computer simulation of the exposure and development of resist images. It is found that electron scattering can be treated in terms of an effective Gaussian half-width which is the quadrature sum of the incident Gaussian half-width and the characteristic width for forward-scattered electrons. Linewidth control is improved by reducing the effective half-width; this is accomplished by using higher beam energies, thinner resists and smaller spot sizes. Developer simulation shows that using 2 pixels per minimum linewidth with a spot size equal to half the pixel size gives better developed images than the more conventional writing strategy which uses four pixels per minimum linewidth and a spot size equal to the pixel size.