The magic angle: a solved mystery

We resolve the long-standing mysterious discrepancy between the experimental magic angle in EELS--approximately 2theta(E)--and the quantum mechanical prediction of approximately 4theta(E). A relativistic approach surpassing the usually applied kinematic correction yields a magic angle close to the experimental value. The reason is that the relativistic correction of the inelastic scattering cross section in anisotropic systems is significantly higher than in isotropic ones.     

Analysis of Kikuchi band contrast reversal in electron backscatter diffraction patterns of silicon

We analyze the contrast reversal of Kikuchi bands that can be seen in electron backscatter diffraction (EBSD) patterns under specific experimental conditions. The observed effect can be reproduced using dynamical electron diffraction calculations. Two crucial contributions are identified to be at work: First, the incident beam creates a depth distribution of incoherently backscattered electrons which depends on the incidence angle of the beam. Second, the localized inelastic scattering in the outgoing path leads to pronounced anomalous absorption effects for electrons at grazing emission angles, as these electrons have to go through the largest amount of material. We use simple model depth distributions to account for the incident beam effect, and we assume an exit angle dependent effective crystal thickness in the dynamical electron diffraction calculations. Very good agreement is obtained with experimental observations for silicon at 20 keV primary beam energy.     

Some effects of electron channeling on electron energy loss spectroscopy

As an electron beam (of order 100 keV) travels through a crystalline solid it can be channeled down a zone axis of the crystal to form a channeling peak centered on the atomic columns. The channeling peak can be similar in size to the outer atomic orbitals. Electron energy loss spectroscopy (EELS) measures the losses that the electron experiences as it passes through the solid yielding information about the unoccupied density of states in the solid. The interaction matrix element for this process typically produces dipole selection rules for small angle scattering. In this paper, a theoretical calculation of the EELS cross section in the presence of strong channeling is performed for the silicon L23 edge. The presence of channeling is found to alter both the intensity and selection rules for this EELS signal as a function of depth in the solid. At some depths in the specimen small but significant non-dipole transition components can be produced, which may influence measurements of the density of states in solids.     

Validity of the dipole approximation in TEM‐EELS studies

Nondipole effects in electron energy‐loss spectroscopy are evaluated in terms of deviation of the inelastic scattering from a Lorentzian angular distribution, which is assumed in established procedures for plural‐scattering deconvolution, thickness measurement, and Kramers‐Kronig analysis. The deviation appears to be small and may be outweighed by the effect of plural (elastic + inelastic) scattering, which is not removed by conventional deconvolution methods. In the core‐loss region of the spectrum, non‐Lorentzian behaviour stems from a reduction of the generalized oscillator strength from its optical value and (for energies far above an ionization threshold) formation of a Bethe‐ridge angular distribution. At incident energies above 200 keV, retardation effects further distort the angular dependence, even for core losses just above threshold. With an on‐axis collection aperture, non‐dipole effects are masked by the rapid falloff of intensity with scattering angle, but they may become important for off‐axis measurements. Near‐edge fine structure is sensitive to nondipole effects but these can be minimized by use of an angle‐limiting collection aperture. Microsc. Res. Tech. 77:773–778, 2014. © 2014 Wiley Periodicals, Inc.     

An accurate approximation for the highly efficient sampling of polar scattering angle of electron elastic single-scattering events

In single-event Monte Carlo electron transport simulations, elastic scattering events dominate the changes in electron trajectories due to collisions. Classically, the polar scattering angle due to an elastic collision can be sampled efficiently from the screened Rutherford cross section. However, the screened Rutherford cross section fails for both high Z materials and when the incident electron energy becomes too low. Alternatively, improved simulation accuracy for electrons in all energy ranges and through all materials may be obtained by sampling directly from differential data derived from partial-wave-expansion method (PWEM) calculations based on theoretical atomic potential models. While sampling directly from wave calculations will yield simulation results to the best known physical accuracy, it comes at the cost of simulation time. This is due to a sampling process that is typically more involved when compared with using the screened Rutherford cross section. In this work we present a relationship capable of reproducing the moments of the differential cross section derived from PWEM calculations, resulting in good preservation of forward and backscattering peaks. The relationship is directly invertible and is as easily sampled as the Rutherford cross section. Most important, the data presented in this paper in combination with this relationship produce Monte Carlo simulation results which are comparable with those using the exact differential cross section from PWEM calculations for elements Z = 1 to 96 and for incident electron energies from 300,000 down to 50 eV.     

Validity of the dipole-selection rule for the Al-L2,3 edge of alpha-Al2O3 under channeling conditions.

The validity of the dipole-selection rule for the Al-L2,3 electron energy-loss edge of alpha-Al2O3 is investigated. Dipole forbidden transitions can be observed in a transmission electron microscope operated with large collection apertures. In addition, it is shown that channeling along a highly symmetrical zone axis in alpha-Al2O3 can lead to the detection of dipole forbidden transitions even with small collection apertures. For an incident electron direction parallel to the <0001> orientation it is observed experimentally that the fine structure of the Al-L2,3 edge shows additional features compared to measurements with the electron beam parallel to <1100>. This effect is due to the occurrence of channeling conditions, indicated by the dependence of the additional dipole forbidden features on the sample thickness. These additional features disappear when tilting the crystal by 1.8 degrees (0.84 A(-1)) or even into the less-symmetrical <1100> zone axis. It is suggested that these observations are explained by differences in local symmetry at the excited center with respect to the incident beam directions.     

Absolute energy calibration for relativistic electron beams with pointing instability from a laser-plasma accelerator

The pointing instability of energetic electron beams generated from a laser-driven accelerator can cause a serious error in measuring the electron spectrum with a magnetic spectrometer. In order to determine a correct electron spectrum, the pointing angle of an electron beam incident on the spectrometer should be exactly defined. Here, we present a method for absolutely calibrating the electron spectrum by monitoring the pointing angle using a scintillating screen installed in front of a permanent dipole magnet. The ambiguous electron energy due to the pointing instability is corrected by the numerical and analytical calculations based on the relativistic equation of electron motion. It is also possible to estimate the energy spread of the electron beam and determine the energy resolution of the spectrometer using the beam divergence angle that is simultaneously measured on the screen. The calibration method with direct measurement of the spatial profile of an incident electron beam has a simple experimental layout and presents the full range of spatial and spectral information of the electron beams with energies of multi-hundred MeV level, despite the limited energy resolution of the simple electron spectrometer.     

Depth sectioning in scanning transmission electron microscopy based on core-loss spectroscopy

Recent and ongoing improvements in aberration correction have opened up the possibility of depth sectioning samples using the scanning transmission electron microscope in a fashion similar to the confocal scanning optical microscope. We explore questions of principle relating to image interpretability in the depth sectioning of samples using electron energy loss spectroscopy. We show that provided electron microscope probes are sufficiently fine and detector collection semi-angles are sufficiently large we can expect to locate dopant atoms inside a crystal. Furthermore, unlike high angle annular dark field imaging, electron energy loss spectroscopy can resolve dopants of smaller atomic mass than the supporting crystalline matrix.     

Scattering angle dependence of signal/background ratio of inner-shell electron excitation loss in eels

Scattering angle dependence of the signal/background ratio of Si K-shell and A1 K-shell electron excitation losses has been measured for single crystals and evaporated films. The ratio changed periodically with the scattering angle, and maxima were found to be located between Bragg reflections including the center beam. Thus the ratio is improved between the Bragg reflections and just outside the incident beam, which is very important as a practical technique for elemental analysis in the higher energy loss region in EELS.     

Angle-resolving time-of-flight electron spectrometer for near-threshold precision measurements of differential cross sections of electron-impact excitation of atoms and molecules

This article presents a new type of low-energy crossed-beam electron spectrometer for measuring angular differential cross sections of electron-impact excitation of atomic and molecular targets. Designed for investigations at energies close to excitation thresholds, the spectrometer combines a pulsed electron beam with the time-of-flight technique to distinguish between scattering channels. A large-area, position-sensitive detector is used to offset the low average scattering rate resulting from the pulsing duty cycle, without sacrificing angular resolution. A total energy resolution better than 150 meV (full width at half maximum) at scattered energies of 0.5-3 eV is achieved by monochromating the electron beam prior to pulsing it. The results of a precision measurement of the differential cross section for electron-impact excitation of helium, at an energy of 22 eV, are used to assess the sensitivity and resolution of the spectrometer.     

Measurement of total gas scattering cross‐section

Experimental measurements are presented of the total scattering cross‐section of four gases: He, Air, CH₄, and Argon as a function of electron beam energy. The method used was that of Gauvin. A comparison of theoretical estimates of the total scattering cross‐section with the experimental data indicates that the model used gives generally reliable results. The data confirm that the gases tend to be molecular rather than atomic in nature in this pressure range (1–300 Pascal). The factors affecting the accuracy of these results are examined.     

Influence of the angular distribution of backscattered electrons on signals at different take-off angles in low-voltage scanning electron microscopy (LVSEM)

It is well known that the differential Mott cross section for large-angle elastic scattering shows maxima and minima at angles depending on material and electron energy. For electron energies of 10–30 keV, the averaging by frequent elastic scattering processes results in approximate Lambert angular distributions of backscattered electrons (BSE). However, the present Monte Carlo calculations for electron energies E = 1–5 keV and different angles of incidence show strong deviations from a Lambert distribution which increases with decreasing energy. The signals of the BSE detector with five annular segments for different take-off directions show good agreement with the calculations for normal electron incidence.     

一种新型单元的频率选择表面

本文通过对传统的十字单元进行改进,设计了一种新型单元的频率选择表面（FSS）。利用模式匹配法,对传统十字单元FSS和这种新型单元FSS从理论上进行了对比分析,对TE波入射时角度变化和大角度入射时极化方式变化对中心频率的影响两个方面进行了研究,并采用镀膜和光刻技术制备了新型单元FSS的实验样件,在微波暗室中进行测试,得到的实验曲线与理论仿真曲线基本一致。结果表明：传统十字单元FSS不能实现中心频率的角度稳定性,TE波0°到45°时中心频率漂移300MHz,并且45°入射时中心频率的极化稳定性很差,漂移量为800MHz,而新型单元FSS具有中心频率的角度稳定性,TE波０°到45°入射中心频率漂移量仅为100MHz,同时对于大的入射角度,具有中心频率的极化稳定性。     

Monte Carlo Simulation of CD‐SEM Images for Linewidth and Critical Dimension Metrology

In semiconductor industry, strict critical dimension control by using a critical dimension scanning electron microscope (CD‐SEM) is an extremely urgent task in near‐term years. A Monte Carlo simulation model for study of CD‐SEM image has been established, which is based on using Mott's cross section for electron elastic scattering and the full Penn dielectric function formalism for electron inelastic scattering and the associated secondary electron (SE) production. In this work, a systematic calculation of CD‐SEM line‐scan profiles and 2D images of trapezoidal Si lines has been performed by taking into account different experimental factors including electron beam condition (primary energy, probe size), line geometry (width, height, foot/corner rounding, sidewall angle, and roughness), material properties, and SE signal detection. The influences of these factors to the critical dimension metrology are investigated, leading to build a future comprehensive model‐based library. SCANNING 35: 127‐139, 2013. © 2012 Wiley Periodicals, Inc.     

Analyzer system capable of determining energy and direction of charged particles in ultrahigh vacuum

We have constructed and tested a system capable of measuring the energy of charged particles emitted from a sample at any angle relative to the sample or the incident beam of exciting particles. The energy analysis is accomplished by a 180 degrees spherical deflecting-type analyzer, operated at constant pass energy with a series of electrostatic lenses. The analyzer system is properly apertured to accept incoming particles from a spot of 1.5 mm diameter at the sample and within a cone of 2.5 degrees half-angle. The lens system used has constant transmission independent of the incident energy. The energy analyzer is independently rotatable about two orthogonal axes, giving it complete freedom of access to any angle of collection relative to the sample orientation. The sample can rotate about two orthogonal axes so that any angle of incidence can be used. Specific examples are given of the performance of the system when used for the measurement of the angular distribution of photoelectrons excited by synchrotron radiation.     

微粗糙光学表面与多个镶嵌粒子差值散射场特性

本文基于时域有限差分算法,研究了微粗糙光学表面与多个镶嵌粒子的差值场光散射问题。将光学基片视为微粗糙光学表面,利用蒙特卡洛方法解决了光学表面存在粗糙度的问题,并将差值场散射理论加入到计算模型中,更好地分析了缺陷粒子的散射特性,将计算区域划分成上下两个半空间,建立了微粗糙光学表面与镶嵌多体粒子复合散射模型,并与矩量法计算结果比较验证了理论的有效性。运用此模型分析了入射角、镶嵌粒子尺寸、粒子间距、粒子个数等物性特征对微粗糙光学表面与镶嵌多体粒子差值散射场的影响。实验结果表明:在一定激光入射角下,以相同回波探测角度间距20°对光学表面进行测量能够有效地检测出缺陷粒子。本文结果为光学无损检测、光学薄膜、微纳米结构的光学性能设计等提供了理论依据和技术支持。     

Effect of electron beam-induced deposition and etching under bias

Electron-beam-induced deposition (EBID) and etching (EBIE) provides a simple way to fabricate or etch submicron or nanoscale structures of various materials in a direct-write (i.e.nonlithographic) fashion. The growth rate or the etch rate are influenced by many factors such as beam energy, beam current, temperature of the substrate material, pressure of the chamber, and geometry of the gas injector etc. The mechanism of EBID and EBIE involves the interaction of the incident electron beam or emitted electron from the target material. The role of these electrons is still not completely understood although the contribution of low energy secondary electrons (SE) has been assumed to be the dominant contributor of EBID and EBIE based on its overlap with the dissociation cross section. We have studied the growth and etching phenomenon under various biasing conditions to investigate how low voltage biasing of the substrate affects secondary electron trajectories and subsequently modifies electron-beam-induced deposition and etching.     

Effects of the introduction of the discrete energy loss process into Monte Carlo simulation of electron scattering

First, the single scattering model is briefly described. Next, the hybrid model is explained, which takes into consideration a part of the discrete energy loss processes. The Vriens or the Gryzinski cross section is used for core electron ionizations, and the Moller cross section for free electron excitations. The model is applied to the calculations of the energy distribution of transmitted electrons through a thin film and the depth distribution of generated x-rays. From comparisons among the calculated results with and without energy straggling and experimental data, it is found that the Gryzinski cross section shows the best result.     

Diffraction effects and inelastic electron transport in angle‐resolved microscopic imaging applications

We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle‐resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in‐depth theoretical modelling of the energy‐ and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations.     

Short note on parallel illumination in the TEM

Parallel illumination conditions are required for several experiments in the transmission electron microscope (TEM). The image rotation induced by the helical trajectory of electrons passing through the magnetic field of the TEM lenses inevitably induces an inclination of the beam relative to the optical axis in the object plane--even for an electron which travels parallel to the optical axis in the far field. This angle (shear angle) is vectorially added to the convergence angle; it depends both on the distance to the optical axis and the magnetic field. By using a beam tilt compensation method, the minimum shear angle is found to be of the order of 1 mrad for a field of view of 2 microm in a 200 kV TEM. In practice, "parallel illumination" can only be obtained for fields of view 1 microm.