Monte Carlo simulation of secondary electron images for real sample structures in scanning electron microscopy

Monte Carlo simulation methods for the study of electron beam interaction with solids have been mostly concerned with specimens of simple geometry. In this article, we propose a simulation algorithm for treating arbitrary complex structures in a real sample. The method is based on a finite element triangular mesh modeling of sample geometry and a space subdivision for accelerating simulation. Simulation of secondary electron image in scanning electron microscopy has been performed for gold particles on a carbon substrate. Comparison of the simulation result with an experiment image confirms that this method is effective to model complex morphology of a real sample.     

Surface roughness of preparations for backscattered electron-scanning electron microscopy: the image differences and their Monte Carlo simulation

Patterns and levels of mineralisation in the biological hard tissues have been studied using the backscattered electron (BSE) mode in the scanning electron microscope (SEM). To prevent gross topographic detail overwhelming changes in signal from composition, samples are embedded in polymethylmethacrylate (PMMA) and a flat block surface produced by polishing or micromilling. This study was undertaken to establish the degree of residual topography achieved in these finishing processes. A sample of human rib was embedded in PMMA and prepared, as for examination in the SEM, by polishing on graded abrasives and pre- and, finally, ultramilling. After each preparation step, the block face was imaged using a confocal reflection microscope surface mapping facility. The recorded topographies were used in a Monte Carlo simulation to model the surface interface and thus, for each of the sample preparation techniques, to calculate predicted variations in BSE signal. The latter were compared with experimental data derived under standard operating conditions in the SEM. Micromilling produced block faces with typical peak-trough relief of 80 nm, while hand polishing left occasional scratches 1.5 microns deep with a general undulation of 150-250 nm. Monte Carlo simulations of a rough surface of bone using these data predicted that additional contrast levels of 5% could be expected from micromilled surfaces and > 10% for hand polished samples of bone. Thus, micromilling is the best preparation method for bone, since this tissue develops a collagen orientation-related relief on polishing, which may be largely responsible for the (incorrect) supposition that lamellation in bone is related to changes in net degree of mineralisation.     

Monte Carlo simulation of scanning electron microscope signals for lithographic metrology

Two computer codes for simulating the backscattered, transmitted, and secondary-electron signals from targets in a scanning electron microscope are described. The first code, MONSEL-II, has a model target consisting of three parallel lines on a three-layer substrate, while the second, MONSEL-III, has a model target consisting of a two-by-two array of finite lines on a three-layer substrate. Elastic electron scattering is determined by published fits to the Mott cross section. Both plasmon-generated electrons and ionized valence electrons are included in the secondary production. An adjustable quantity, called the residual energy loss rate, is added to the formula of Joy and Luo to obtain the measured secondary yield. The codes show the effects of signal enhancement due to edge transmission, known as blooming, as well as signal reduction due to neighboring lines, known as the “black-hole” effect.     

Assessment and correction of geometric distortions in low-magnification scanning electron microscopy images

A method is introduced to assess and correct the geometric distortions which frequently occur in low-magnification scanning electron microscopy (SEM) images. Such images typically exhibit a complex pattern of varying deviations from orthogonality which cannot be adequately corrected by simple geometric transformations such as shifting, scaling, rotation, or shearing. A suitable approach to rectify low-magnification SEM images is polynomial warping, a correction procedure which also accomplishes rubber sheet transformation. To demonstrate the approach, a reference grid for low magnifications has been scanned at 40- and 55-fold magnifications by means of a microanalyzer. Calculated geometric distortions range from 1.5 to 3.5% of the image dimensions; applying polynomial warping, distortions could be reduced to approximately 0.1% of the image dimensions. Because of its easy application and the widespread availability in image processing packages, polynomial warping can be recommended as a routine procedure for rectifying low-magnification SEM images.     

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.     

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 eitherto 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.     

Comparison in spatial spreads of secondary electron information between scanning ion and scanning electron microscopy

Monte Carlo simulations have been carried out to compare the spatial spreads of secondary electron (SE) information in scanning ion microscopy (SIM) with scanning electron microscopy (SEM). Under Ga ion impacts, the SEs are excited by three kinds of collision-partners, that is, projectile ion, recoiled target atom, and target electron. The latter two partners dominantly contribute to the total SE yield gamma for the materials of low atomic number Z2. For the materials of high Z2, on the other hand, the projectile ions dominantly contribute to gamma. These Z2 dependencies generally cause the gamma yield to decrease with an increasing Z2, in contrast with the SE yield delta under electron impacts. Most of the SEs are produced in the surface layer of about 5lambda in depth (lambda: the mean free path of SEs), as they are independent of the incident probe. Under 30 keV Ga ion impacts, the spatial spread of SE information is roughly as small as 10 nm, decreasing with an increasing Z2. Under 10 keV electron impacts, the SEI excited by the primary electrons has a small spatial spread of about 5lambda, but the SEII excited by the backscattered electrons has a large one of several 10 to several 100 nanometers, decreasing with an increasing Z2. The main cause of a small spread of SE information at ion impact is the short ranges of the projectile ions returning to the surface to escape as backscattered ions, the recoiled target atoms, and the target electrons in collision cascade. The 30 keV Ga-SIM imaging is better than the 10 keV SEM imaging in spatial resolution for the structure/material measurements. Here, zero-size probes are assumed.     

Use of backscattered electron detector arrays for forming backscattered electron images in the scanning electron microscope

The backscattered electron (BSE) signal in the scanning electron microscope (SEM) can be used in two different ways. The first is to give a BSE image from an area that is defined by the scanning of the electron beam (EB) over the surface of the specimen. The second is to use an array of small BSE detectors to give an electron backscattering pattern (EBSP) with crystallographic information from a single point. It is also possible to utilize the EBSP detector and computer-control system to give an image from an area on the specimen--for example, to show the orientations of the grains in a polycrystalline sample ("grain orientation imaging"). Some further possibilities based on some other ways for analyzing the output from an EBSP detector array, are described.     

Registration of confocal scanning laser microscopy and quantitative backscattered electron images for the temporospatial quantification of mineralization density in 18-month old thoroughbred racehorse articular calcified cartilage

Combined backscattered electron scanning electron microscopy (BSE SEM) and confocal scanning laser microscopy (CSLM) have been used to put tissue mineralization data into the context of soft tissue histology and fluorescent label information. Mineralization density (Dm) and linear accretion rate (LAR) are quantifiable parameters associated with mineralizing fronts within calcified tissues. Quantitative BSE (qBSE) may be used to determine Dm, while CSLM may be used to detect label fluorescence from which LAR is calculated. Eighteen-month old Thoroughbred horses received single calcein injections 19 and 8 days prior to euthanasia, labeling sites of active mineralization with fluorescent bands. Confocal scanning laser microscopy images of articular calcified cartilage (ACC) from distal third metacarpal condyles were registered to qBSE images of the same sites using an in-house program. ImageJ and Sync Windows enabled the simultaneous collection of LAR and Dm data. The repeatability of the registration and measurement protocols was determined. Dm profiles between calcein labels were explored for an association with time. Dm was 119.7 +/- 24.5 (mean +/- standard deviation) gray levels (where 0 = backscattering from monobrominated and 255 from monoiodinated dimethacrylate standards, respectively), while modal and maximum LAR were 0.45 and 3.45 microm/day, respectively. Coefficients of variation (CV) for Dm were 0.70 and 0.77% with and without repeat registration, respectively; CVs for LAR were 1.90 and 2.26% with and without repeat registration, respectively. No relationship was identified between Dm and time in the 11-day interlabel interval. Registration of CSLM to qBSE images is sufficiently repeatable for quantitative studies of equine ACC.     

The effect of subsurface topography on secondary electron images from chromate pretreated aluminium surfaces

In secondary and scanning transmission electron microscopes, secondary electron images of surface films can be dominated by an image derived from electrons back-scattered from the interface between the film and the substrate. The extent of the domination has been established by studying the variation in image obtained using primary beams of different energy and by platinum coating to enhance surface secondary electron emission. Studies of thicker films also established that chemical or structural difference within a film also lead to imaging effects. In general, 5 keV electrons are the most effective in producing subsurface and structural or chemical imaging effects.     

Use of Monte Carlo modeling for interpreting scanning electron microscope linewidth measurements

A scanning electron microscope (SEM) can be used to measure the dimensions of the microlithographic features of integrated circuits. However, without a good model of the electron-beam/specimen interaction, accurate edge location cannot be obtained. A Monte Carlo code has been developed to model the interaction of an electron beam with one or two lines lithographically produced on a multilayer substrate. The purpose of the code is to enable one to extract the edge position of a line from SEM measurements. It is based on prior codes developed at the National Institute of Standards and Technology, but with a new formulation for the atomic scattering cross sections and the inclusion of a method to simulate edge roughness or rounding. The code is currently able to model the transmitted and backscattered electrons, and the results from the code have been applied to the analysis of electron transmission through gold lines on a thin silicon substrate, such as is used in an x-ray lithographic mask. Significant reductions in backscattering occur because of the proximity of a neighboring line.     

Monte Carlo analysis of the detection of clay occlusion of respirable quartz particles using multiple voltage scanning electron microscopy

The electron incident-energy dependence of the relative intensities of Al and Si x-rays produced in a respirable-sized quartz particle by scanning electron microscopy is sensitive to the inhomogeneity of the distribution of Al and Si in the particle. Realistic Monte Carlo calculations of this energy dependence validate the proposal to use this effect for the detection of particles in which an aluminosilicate coating occludes the surface of a silica core.     

Resolution in low voltage scanning electron microscopy

As the energy of an electron beam is reduced, the range falls and the secondary electron yield rises. A low voltage scanning electron microscope can therefore, in principle, examine without damage or charging samples such as insulators, dielectrics or beam sensitive materials. This paper investigates the way in which the choice of beam energy affects the spatial resolution of a secondary electron image. It is shown that for samples which are thin compared to the electron range, the edge resolution and contrast in the image improve with increasing beam energy. In samples that are thicker than the electron range, the resolution can be optimized at either high or low energies, but low energy operation will produce images of higher contrast. At an energy of 2 keV or less beam interaction limited resolutions of the order of 3 nm should be possible.     

A simple backscattered electrons and specimen current detection device for the scanning electron microscope

A simple, low-investment device has been developed that allows the collection of backscattered electrons (BSEs) and specimen current (SC) signals for imaging purposes and current measurement. Originally, this system was designed for detection, measurement, and display of specimen current, with a video signal output whose level was modulated by this current. Eventually, a BSE detector was developed, using a graphite disk (about 8 cm in diameter) to collect the BSEs. The disk was mounted on a Philips SEM 5O5, attached and concentrically to the final lens aperture. This configuration gives a large solid angle of collection. The collected charge is further processed by the same electronics used in the aforementioned SC detection system. Electron channeling, topographic contrast with BSE, and material contrast with BSE and SC images can be obtained with reasonably good edge definition.     

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.     

New system for secondary electron detection in variable-pressure scanning electron microscopy

A novel secondary electron detection system combining a two‐stage detector head and a differential pumping system is presented. The detector head consisted of a scintillation Everhart‐Thornley detector and a microsphere plate, separating it from the lower vacuum in the intermediate chamber (below 0.1 mbar). The system was arranged asymmetrically, which should contribute to a lower gas leakage through the plate and a longer life span of the plate. The system offered all the advantages of the scintillator detector in a wide range of gas pressures, from high vacuum to those of the order of 10 mbar, typical of high‐pressure scanning electron microscopy.     

Line profile reconstruction from simultaneously recorded secondary and backscattered electron signals

We propose a reconstruction method of surface morphology using a combination of secondary and back-scattered electron signals from the scanning electron microscope (SEM). Compared with multiple-detector methods, the proposed system requires only conventional secondary and backscattered electron detectors for a line profile reconstruction in one direction. This method is an application of genetic algorithms to the measurement of surface morphology in SEM. We use the chi-square distribution of the reconstruction error as the objective function within a scheme to minimize the number of vertices in the reconstructed surface profile. (The reconstruction error is the relative difference between the calculated and experimental data.) To evaluate the efficacy of our method, a surface profile is successfully reconstructed from a pair of line scans across the center of a latex particle.     

Correlative light and backscattered electron microscopy of bone--Part I: Specimen preparation methods

A method for preparing nondecalcified bone and tooth specimens for imaging by both light microscopy (LM) and backscattered electron microscopy in the scanning electron microscope (BSE-SEM) is presented. Bone blocks are embedded in a polymethylmethacrylate (PMMA) mixture and mounted on glass slides using components of a light-cured dental adhesive system. This method of slide preparation allows correlative studies to be carried out between different microscopy modes, using the same histologic section. It also represents a large time savings relative to other mounting methods whose media require long cure times.     

Mc3D: A three-dimensional Monte Carlo system simulating image contrast in surface analytical scanning electron microscopy I—Object-oriented software design and tests

The main features of a three-dimensional (3-D) Monte Carlo software system (Mc3D), designed for the simulation of electron scattering and image contrast in a scanning electron microscope, are reported. Before simulating electron trajectories in the sample, impingement of the incident electron beam is described by introducing the idea of a virtual scan path in 3-D space. A general and concise algorithm is given for simulating the intersection of electron trajectories leaving the sample onto multidetector entrance apertures distributed in 3-D space. By optimising the object-oriented design in conjunction with the use of a process-oriented and data-oriented code structure, Mc3D is capable of simulating microscopic analysis of a sample with a 3-D geometry or structure that can be expressed with formulae. Three examples of the use of Mc3D are given. The first is for linescans across a block of SiO₂ on top of a Si substrate; the second is for a stripe of SiO₂ embedded in a Si substrate. Finally, the simulation of Auger linescans across an Au overlay on Si is compared with experimental results. The relationships between experimental linescans and the true beam impact positions on the sample are revealed through the virtual scan path. An edge effect, parallel-edge enhancement, is predicted when the incident electron beam size, the distance of impact position to the terrace edge, and the inelastic mean free path of the Auger electron from a given element are comparable, and the linescan is parallel to the terrace edge. All three examples demonstrate the sensitivity of image contrast to the disposition of the sample with respect to the electron column and the detector position.     

Dynamic secondary electron contrast effects in liquid systems studied by environmental scanning electron microscopy

We report an investigation into a dynamic contrast phenomenon in water-oil emulsions imaged in the environmental scanning electron microscope. Secondary electron contrast between oil and water phases is shown to change with scan rate, even inverting in extreme cases. This effect is attributed to the fact that charge carriers in liquids have intermediate mobilities compared with those in metallic conductors and solid insulators. Thus, increasing the electron energy flux density (via slower scan rates) results in the temporary accumulation of excess charge, which in turn gives rise to increased secondary electron emission. Excess charge dissipates between frames, however, such that classical charging of the specimen is not observed. The oils used here have conductivities lower than that of water, making them more susceptible to the effect. However, the material within the primary electron interaction volume is a conductive medium. We demonstrate that charging effects are not seen in regions of the oil where the interaction volume is in contact with the more conductive continuous water phase. Secondary electron emission from these regions therefore approximates to the intrinsic yield.