Monte Carlo study for correcting the broadened line-scan profile in scanning electron microscopy

Line-scan profile is always broadened due to the probe shape of the primary electron (PE) beam in scanning electron microscopy (SEM), which leads to an inaccurate dimension metrology. Currently, the effective electron beam shape (EEBS) is suggested as the broadening function to overcome this issue for theoretical analysis, rather than the widely used Gaussian profile. However, EEBS is almost impossible to be acquired due to it strongly depends on both the sample topography and the electron beam focusing condition, which makes it is impossible to be applied in practical analysis. Taking the case of gate linewidth measurement, an approach is proposed to find a best-fit traditional Gaussian profile, which can optimally replace the EEBS in the case of the same sample structure and experimental condition for construction of a database of the parameter in traditional Gaussian profile. This approach is based on the use of the ideal and broadened line-scan profiles which are both obtained from Monte Carlo (MC) simulation, but respectively by an ideal and a focusing incident electron beam model. The expected value of parameter can be obtained through deconvoluting (here using a maximum-entropy algorithm) the broadened line-scan profile then fitting it to the ideal profile. Experimenters can benefit from this database to obtain true line-scan profiles for accurate gate linewidth measurement. This work should prove useful for samples of other structures and be an extension of the database in the future.     

SMART – a program to measure SEM resolution and imaging performance

It is important to be able to measure the parameters, such as spatial resolution, astigmastism, signal‐to‐noise ratio, and drift and instability, that characterize the performance of a scanning electron microscope. These quantities can be determined most reliably by a Fourier analysis of digital micrographs from the instrument, recorded under conditions of interest. A program designed to implement all of the necessary steps in an automated manner has been developed as a ‘macro’ for the popular, and freely available, NIH Image and SCION Image programs.     

The spatial distribution and resolution of coaxial backscattered electrons in SEM, calculated by Monte Carlo simulations

We simulate, within a sample, the trajectories of the backscattered electrons detected in a scanning electron microscopy with a particular detection geometry. Thus we obtain the depth and lateral distributions, according to the adjustable parameter values, of the detected electrons. Finally, the scanline profile across a chemical edge is drawn. The conditions corresponding to the best lateral resolution are established; we obtain an ultimate resolution of the same order as the beam diameter.     

High resolution SE-I SEM study of enamel crystal morphology

Until recently high resolution TEM was the only imaging mode capable of probing the atomic lattice structure of crystals composing tooth enamel. Studies designed to determine the polyhedral shape of normal enamel crystals and initiation of carious lesions in enamel crystals were hampered and limited by interpretation of two-dimensional TEM images from thin section and freeze fracture replica specimens lacking depth of field. The newly developed SE-I signal mode for SEM (SE-I/SE-II ratio) can produce images of enamel crystals approaching beam diameter dimensions (0.7–2.0 nm), rivaling the resolution of the TEM technique and generating topographic contrasts for three dimensional imaging at very high magnification (≈?1,000,000 X). Ultrathin chromium (Cr) films generate enriched high resolution SE-I contrasts of enamel crystal surfaces and when imaged using an immersion lens field emission SEM operated at high voltage (20–30 KeV) produce unsurpassed topographic contrasts. Since the grain size of Cr is below the resolution of any SEM and is ultrathin (≈?1 nm), then SE-I images can provide a more accurate representation of enamel crystal structure than TEM methodologies. Our SE-I SEM observations of normal human enamel crystals reveal fractured spicules which contain angled flat surfaces delineated by a prominent 2 nm wide SE-I edge brightness contrast. Although microscopic observations often show crystals which are hexagonal in cross-section, in both SEM and TEM many other growth habits, including rectangular or irregular crystals (30–40 nm in width) which contain “notches,” are also observed. More detailed morphological studies are therefore required to determine the most likely habit planes and their relevance to the function of the enamel crystals. The granular appearing fine structural contrast imposed onto <100> lattice planes of sectioned enamel in TEM micrographs is also resolved with topographic contrasts in SE-I micrographs. These granules probably represent one or both of the enamel protein classes.     

Monte Carlo modeling of secondary x-ray fluorescence across phase boundaries in electron probe microanalysis

Secondary fluorescence induced by photoelectric absorption of x-rays generated by an electron beam can occur when the characteristic x-ray energy of material “A” exceeds the critical excitation energy of material “B.” An expression is developed to calculate secondary fluorescence across a planar boundary from a discrete source placed at any (X, Y, Z) coordinates relative to the boundary. The expression can be incorporated into a Monte Carlo electron trajectory simulation which calculates the discrete distribution of primary x-ray generation.     

Beam interactions,contrast and resolution in the SEM

Backscattered and secondary electrons are both used in the SEM for imaging purposes. The backscattered signal is the result of high angle elastic scattering events, while the secondary signal is the result of knock-on inelastic collisions. The characteristic differences between images in the two modes arise from the details of the relevant interactions in the two cases. In order to examine this in a quantitative manner Monte Carlo electron trajectory simulation techniques have been used. Calculations of the ultimate resolution and depth of information of the secondary and backscattered images are presented, together with simulations of the edge brightness effect in high resolution secondary images and an analysis of the microanalytical application of atom number contrast in the backscattered mode.     

A monte carlo study of the position of phase boundaries in backscattered electron images

A Monte Carlo simulation of the contrast variation across phase boundaries in backscattered electron images of multiple phase composition systems has been used to develop a model for prediction of the position of the interface based solely on a knowledge of the signal intensity levels on either side of the interface. A wide range of average atomic numbers of the phases on either side of the boundary have been investigated at incident beam energies of 5, 10, 15, and 25 kV and a least-squares minimisation procedure used to optimise the parameters of a generalised model.     

扫描电子显微镜探头新进展

介绍了扫描电子显微镜（SEM）信号探头研究的最新成果。针对常见扫描电子显微镜缺陷而开发的新型探头不仅改善了仪器成像质量,也极大地扩展了仪器的使用范围,简化了样品的准备工艺过程。     

Studies of supported metal catalysts using high resolution secondary electron imaging in a STEM

An additional technique for use in the characterization of catalysts by electron microscopy is presented. High resolution secondary electron images obtained in a VG HB501 scanning transmission electron microscope have been used to study the surface topography of catalysts consisting of small metal particles on high surface area carbon supports. Surface features down to nanometre dimensions can be seen, allowing the examination of micropores in the support as well as larger pore structures. The results are compared with pore size distributions determined by gas adsorption methods, and are shown to yield valuable additional information. In addition, the method in principle allows examination of the locations of small metal catalyst particles on the support.     

Determination of paper filler Z-distribution by low-vacuum SEM and EDX

Paper, mainly constituted of cellulose fibres, often contains mineral fillers. These fillers increase some of the properties of the paper (whiteness, printability, etc.) and are cheaper than the cellulose fibres. Nevertheless, the fillers reduce the mechanical properties of the sheet. Paper presents an anisotropy corresponding to three main directions. This anisotropy characterises the sheet mechanical properties, structure and filler distribution. Analyses of the cross section of the paper sheet with a low‐vacuum scanning electron microscope with an energy dispersive spectrometer analysis module can show this distribution. The procedure developed consists in analysing discrete profiles to build the mean profile known as filler Z‐distribution for each of the fillers. To develop this method, problems such as determination of the surface points, the number of points to analyse to define a cross section profile and the time required for the test, have been solved. Paper is sensitive to electron irradiation. In order to avoid deterioration of the material and to obtain satisfactory results, the time span for analyses is restricted to 40 s with a 12 kV electron beam accelerating voltage. Monte Carlo simulations are used to determine the diffusion cloud size and thus to determine the number of points that constitute a profile. The samples are gold sputtered and, with the aid of backscattered imaging, the coated surface allows determination of the sample surface points.     

Monte Carlo modeling of cathodoluminescence generation using electron energy loss curves

This work demonstrates the validity of approximating cathodoluminescence generation throughout the electron interaction volume by the total electron energy loss profile. The energy loss profiles in multilayer specimens were accurately calculated using the Monte Carlo simulation CASINO. Resolution of cathodoluminescence images can be estimated from the electron beam spot diameter, the electron penetration range, and the minority carrier diffusion length.     

An improved model for gaseous amplification in the environmental SEM

We present a new model for the gas amplification effect used in many environmental scanning electron microscopes, wherein molecular complexity is shown to be the critical factor. Monte Carlo simulations, based on experimental electron scattering cross-sections, are used to deduce a predictive model for the amplification process that is superior to the Townsend gas capacitor model. These predictions are compared with experimentally obtained amplification curves. Significantly, it is shown that the ionization efficiency of the electrons changes dramatically over the gap distance, and a constant value cannot be assumed. Atomic and molecular excitations affect the amplification process in two ways: first, they serve to lower the average kinetic energy of the imaging electrons, thereby keeping a greater fraction near the ionization threshold energy. Second, molecular normal modes determine the effectiveness of positive gas ions in producing additional secondaries upon surface impact. Practical implications such as signal gain and fraction of useful signal as a function of operating conditions are discussed in the light of the new model. Finally, we speculate on potential new contrast mechanisms brought about by the presence of an imaging gas.     

Electron-specimen interactions in low-voltage scanning electron microscopy

Measurements of the electron range R, and the backscattering coefficient η and the secondary electron yield δ at normal and tilted incidence for different elements show characteristic differences for electron energies in the range of 0.5 to 5 keV, compared with energies larger than 5 keV. The backscattering coefficient does not increase monotonically with increasing atomic number; for example, the secondary electron yield shows a lesser increase with increasing tilt angle. This can be confirmed in back-scattered electron (BSE) and secondary electron (SE) micrographs of test specimens. The results are in rather good agreement with Monte Carlo simulations using elastic Mott cross-sections and a continuous-slowing-down model with a Rao Sahib-Wittry approach for the stopping power at low electron energies. Therefore, this method can be used to calculate quantities of BSE and SE emission, which need a larger experimental effort. Calculations of the angular distribution of BSEs show an increasing intensity with increasing atomic number at high takeoff angles than expected from a cosine law that describes the angular characteristics at high electron energies. When simulating the energy distribution of BSEs, the continuous-slowing-down model should be substituted by using an electron energy-loss spectrum (EELS) that considers plasmon losses and inner-shell ionizations individually (single-scattering-function model). The EELS can be approached via the theory for aluminium or from EELS spectra recorded in a transmission electron microscope for other elements. Measurements of electron range Rα Eⁿ of 1 to 10 keV electrons are obtained from transmission experiments with thin films of known mass thickness. In agreement with other authors the exponent n is lower than at higher electron energies.     

Choosing the optimum accelerating voltage (EO) to visualize submicron precipitates with a field emission scanning electron microscope

With the advent of field emission scanning electron microscopes (FESEM), the observation of small phases in the 5 to 50 nm range seems to be possible at low accelerating voltage using backscattered electron imaging mode. In this context, it is important to understand the contrast of multiphased materials at such low energy. A Monte Carlo program to simulate electron trajectories of multiphased materials (CASINO) was used to compute electron backscattering images. Simulations of images for various compositions of spherical precipitates embedded in a homogeneous matrix as a function of precipitate size and accelerating voltage are presented. These simulations show the concept of an optimum accelerating voltage to maximize the contrast of electron backscattering images. The results presented in this paper show that the contrast of backscattering images of multiphased images in the scanning electron microscope is not only a function of the atomic number difference, but that it is also strongly related to the geometry and the size of the phases.     

New scintillation detector of backscattered electrons for the low voltage SEM

The new scintillation detector of backscattered electrons that is capable of working at primary beam energy as low as 0.5 keV is introduced. Low energy backscattered electrons are accelerated in order to generate a sufficient number of photons. Secondary electrons are deflected back by the energy filter so that the true compositional contrast of the specimen is obtained. The theoretical models of the detector function are described and first demonstration images are presented.     

Software acceleration techniques for the simulation of scanning electron microscope images

A scanning electron microscope (SEM) simulator was developed based on the models used in the MONSEL software. This simulator extends earlier work by introducing an object-oriented framework and adding optimization methods based on precomputation of electron trajectories. Several optimizations enable speedup by factors of 5-100 on a single processor over unoptimized simulations without introducing additional approximations. The speedup for a particular surface depends on the self-similarity of the surface at the scale of the electron penetration depth. We further accelerate by parallelizing the calculations for a total speedup of about 100-2000 on 30 processors. The goal of this work was to create a system capable of simulating a quantitatively accurate SEM image of a relatively unconstrained surface. Results of this work include simulation software, optimization algorithms, performance measurements with various optimizations, and examples of simulated images.     

Resolution limit for electron beam-induced deposition on thick substrates

Recently, the fabrication resolution in electron beam-induced deposition (EBID) has improved significantly. Dots with an average diameter of 1 nm have been made. These results were all obtained in transmission electron microscopes on thin samples. As one may think that such resolution can be achieved on thin samples only, it is the objective of this paper to show that this should also be possible on thick samples. For that purpose we use Monte Carlo simulations of the electron-sample interaction and determine the surface area where secondary electrons are emitted. Assuming that these electrons cause the deposition in EBID, a comparison can be made between deposition on a thin and a thick sample. The Monte Carlo code we developed will be described and applied to the deposition induced by a 200 keV primary electron beam on an ultra-thin (10 nm) and a bulk-like (1,000 nm) Cu sample. Near the point of incidence of the primary beam, the deposit size is independent of the substrate thickness, such that a 1-nm resolution should be possible to achieve on a thick substrate as well. Thicker substrates only affect the tails of the deposit distribution which contain more mass than thin substrate deposit tails.     

Reconstructing the microstructure of polyimide–silicalite mixed‐matrix membranes and their particle connectivity using FIB‐SEM tomography

Properties of a composite material made of a continuous matrix and particles often depend on microscopic details, such as contacts between particles. Focusing on processing raw focused‐ion beam scanning electron microscope (FIB‐SEM) tomography data, we reconstructed three mixed‐matrix membrane samples made of 6FDA‐ODA polyimide and silicalite‐1 particles. In the first step of image processing, backscattered electron (BSE) and secondary electron (SE) signals were mixed in a ratio that was expected to obtain a segmented 3D image with a realistic volume fraction of silicalite‐1. Second, after spatial alignment of the stacked FIB‐SEM data, the 3D image was smoothed using adaptive median and anisotropic nonlinear diffusion filters. Third, the image was segmented using the power watershed method coupled with a seeding algorithm based on geodesic reconstruction from the markers. If the resulting volume fraction did not match the target value quantified by chemical analysis of the sample, the BSE and SE signals were mixed in another ratio and the procedure was repeated until the target volume fraction was achieved. Otherwise, the segmented 3D image (replica) was accepted and its microstructure was thoroughly characterized with special attention paid to connectivity of the silicalite phase. In terms of the phase connectivity, Monte Carlo simulations based on the pure‐phase permeability values enabled us to calculate the effective permeability tensor, the main diagonal elements of which were compared with the experimental permeability. In line with the hypothesis proposed in our recent paper (?apek, P. et al. (2014) Comput. Mater. Sci. 89 , 142–156), the results confirmed that the existence of particle clusters was a key microstructural feature determining effective permeability.     

Monte Carlo simulation of charging effects on linewidth metrology

Charging effects of scanning electron microscopes on the linewidth metrology of polymethylmethacrylate (PMMA) insulatorpatterns are investigated using Monte Carlo simulation. It is first revealed in detail how the nonunity yield of electron generation in the PMMA target leads to local charge accumulation and affects the image profile of secondary electrons as charging develops. Then the measurement offset due to charging effects is identified for various target patterns of isolated and array types. Finally, it is concluded that the measurement uncertainty caused by the measurement offset exceeds the error budget limit that will be allowed in the linewidth metrology of the next generation of semiconductors.