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.     

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.     

Ionic liquid‐based observation technique for nonconductive materials in the scanning electron microscope: Application to the characterization of a rare earth ore

A new approach for preparing geological materials is proposed to reduce charging during their characterization in a scanning electron microscope. This technique was applied to a sample of the Nechalacho rare earth deposit, which contains a significant amount of the minerals fergusonite and zircon. Instead of covering the specimen surface with a conductive coating, the sample was immersed in a dilute solution of ionic liquid and then air dried prior to SEM analysis. Imaging at a wide range of accelerating voltages was then possible without evidence of charging when using the in‐chamber secondary and backscattered electrons detectors, even at 1 kV. High resolution x‐ray and electron backscatter diffraction mapping were successfully obtained at 20 and 5 kV with negligible image drifting and permitted the characterization of the microstructure of the zircon/fergusonite‐Y aggregates encased in the matrix minerals. Because of the absence of a conductive layer at the surface of the specimen, the Kikuchi band contrast was improved and the backscatter electron signal increased at both 5 and 20 kV as confirmed by Monte Carlo modeling. These major developments led to an improvement of the spatial resolution and efficiency of the above characterization techniques applied to the rare earth ore and it is expected that they can be applied to other types of ores and minerals. Microsc. Res. Tech. 77:225–235, 2014. © 2014 Wiley Periodicals, Inc.     

Scanning electron microscope charging effect model for chromium/quartz photolithography masks

We propose a new method for fitting a model of specimen charging to scanning electron microscope (SEM) images. Charging effects cause errors when one attempts to infer the size or shape of a specimen from an image. The goal of our method is to enable image analysis algorithms for measurement, segmentation, and three-dimensional (3-D) reconstruction that would otherwise fail on images containing charging effects. Our model is applied to images of chromium/quartz photolithography masks and may also work in the more general case of isolated metal islands on a flat insulating substrate. Unlike methods based on Monte Carlo simulation, our simulation method does not handle more general topographies or specimens composed entirely of an insulator; it is a crude approximation to the physical charging process described in more detail in Cazaux (1986) and Melchinger and Hofmann (1985), but can be fit with quantitative accuracy to real SEM images. We only consider changes in intensity and do not model charging-induced distortion of image coordinates. Our approach has the advantage over existing methods of enabling fast prediction of charging effects so it may be more practical for image analysis applications.     

Fractal behavior of electron trajectories and spatial distributions of secondary electron birth sites in solids

The fractal behavior of electron scattering in solids, simulated by the Monte Carlo method, has been studied. The trajectories of electrons of 1–10 keV primary energies in Si, Cu, Ag, and Au have been simulated. The Hausdorff dimensions of trajectories of primary electrons, trajectories of primary electrons plus secondary electrons, and spatial distributions of secondary electron birth sites have been determined by the box-counting method. The fractal geometry can be used to describe quantitatively the complexity of the electron scattering process in solids.     

An empirical energy loss equation of electrons

A modified Love-Cox-Scott (1978) equation of electron energy loss has been suggested. The stopping powers predicted by the modified Love-Cox-Scott equation are compared with those by the Tung et al. (1979) model, the Joy and Luo (1989) equation, and the experimental data given in database of Joy at: http://web.ukt. edu/-scrutk. In the energy range of E0< or = 5 keV, the Monte Carlo simulations of the electron scattering in Al, Ag, and Au have been performed, applying the Mott cross section for elastic scattering and the modified Love-Cox-Scott equation (1978) and the equations by Love et al. (1978) and Joy and Luo (1989), respectively, for the inelastic scattering. The calculated results on the backscattering coefficients, the energy distributions of the backscattered electrons, and the energy dissipation of the electron based on the three equations are compared.     

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.     

Theoretical study of the ultimate resolution of SEM

This work aims to clarify the problem of why the ultimate resolution assessed experimentally from the observation of 0.8 nm separation of Au-Pd fine particles is beyond the theoretical resolution limit of scanning electron microscopy (SEM). The correlation between the spatial distribution of secondary electrons on a sample surface and the resolution estimated by edge-to-edge separation in SEM was studied by a Monte Carlo simulation with secondary electron generation included. The result clearly indicates that the edge-to-edge separation can extend beyond the theoretical ultimate resolution, particularly by image processing for contrast expansion and by improving the signal to noise ratio (S/N).     

Calculation of Bohmian quantum trajectories for STEM

We present in this work the calculation of Bohmian quantum trajectories representing the wave function propagation in a crystal for a focused electron probe in a scanning transmission electron microscope (STEM). The wave function and quantum trajectories are obtained from the calculation of time‐dependent Schrödinger equation by fast Fourier transformation multislice algorithm. In our work, the Bohmian quantum trajectories of a scanning probe penetrating a Cu crystal are studied as an example of this calculation scheme. The results help us to better understand the electron diffraction process in a microscopic imaging from a trajectory‐based point of view. This Bohmian quantum trajectory method can be used to extend the application of classical Monte Carlo method from the study of electron interaction with amorphous solid to crystalline structure.     

Monte Carlo simulation of secondary electron and backscattered electron images in scanning electron microscopy for specimen with complex geometric structure

A new Monte Carlo technique for the simulation of secondary electron (SE) and backscattered electron (BSE) of scanning electron microscopy (SEM) images for an inhomogeneous specimen with a complex geometric structure has been developed. The simulation is based on structure construction modeling with simple geometric structures, as well as on the ray-tracing technique for correction of electron flight-step-length sampling when an electron trajectory crosses the interface of the inhomogeneous structures. This correction is important for the simulation of nanoscale structures of a size comparable with or even less than the electron scattering mean free paths. The physical model for electron transport in solids combines the use of the Mott cross section for electron elastic scattering and a dielectric function approach for electron inelastic scattering, and the cascade SE production is also included.     

Application of channel electron multipliers in an electron detector for low‐voltage scanning electron microscopy

An electron detector containing channel electron multipliers was built and tested in the range of low‐voltage scanning electron microscopy as a detector of topographic contrast. The detector can detect backscattered electrons or the sum of backscattered electrons and secondary electrons, with different amount of secondary electrons. As a backscattered electron detector it collects backscattered electrons emitted in a specific range of take‐off angles and in a large range of azimuth angles enabling to obtain large solid collection angle and high collection efficiency. Two arrangements with different channel electron multipliers were studied theoretically with the use of the Monte Carlo method and one of them was built and tested experimentally. To shorten breaks in operation, a vacuum box preventing channel electron multipliers from an exposure to air during specimen exchanges was built and placed in the microscope chamber. The box is opened during microscope observations and is moved to the side of the scanning electron microscope chamber and closed during air admission and evacuation cycles enabling storing channel electron multipliers under vacuum for the whole time. Experimental tests of the detector included assessment of the type of detected electrons (secondary or backscattered), checking the tilt contrast, imaging the spatial collection efficiency, measuring the noise coefficient and recording images of different specimens.     

A systematic investigation of the charging effect in scanning electron microscopy for metal nanostructures on insulating substrates

Scanning electron microscopy is perhaps the most important method for investigating and characterizing nanostructures. A well‐known challenge in scanning electron microscopy is the investigation of insulating materials. As insulating materials do not provide a path to ground they accumulate charge, evident as image drift and image distortions. In previous work, we have seen that sample charging in arrays of metal nanoparticles on glass substrates leads to a shrinkage effect, resulting in a measurement error in the nanoparticle dimension of up to 15% at 10 kV and a probe current of 80 ± 10 pA. In order to investigate this effect in detail, we have fabricated metal nanostructures on insulating borosilicate glass using electron beam lithography. Electron beam lithography allows us to tailor the design of our metal nanostructures and the area coverage. The measurements are carried out using two commonly available secondary electron detectors in scanning electron microscopes, namely, an InLens‐ and an Everhart–Thornley detector. We identify and discriminate several contributions to the effect by varying microscope settings, including the size of the aperture, the beam current, the working distance and the acceleration voltage. We image metal nanostructures of various sizes and geometries, investigating the influence of scan‐direction of the electron beam and secondary electron detector used for imaging. The relative measurement error, which we measure as high as 20% for some settings, is found to depend on the acceleration voltage and the type of secondary electron detector used for imaging. In particular, the Everhart–Thornley detectors lower sensitivity to SE₁ electrons increase the magnitude of the shrinkage of up to 10% relative to the InLens measurements. Finally, a method for estimating charge balance in insulating samples is presented.     

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.     

A three‐dimensional statistical model for imaged microstructures of porous polymer films

A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of nonstationarities in the material and facilitates computationally efficient methods for simulation and model fitting. A Markov Chain Monte Carlo algorithm is developed and used to fit the model to three‐dimensional confocal laser scanning microscopy images. The methods are applied to study a porous ethylcellulose/hydroxypropylcellulose polymer blend that is used as a coating to control drug release from pharmaceutical tablets. The aim is to investigate how mass transport through the material depends on the microstructure. We derive a number of goodness‐of‐fit measures based on numerically calculated diffusion through the material. These are used in combination with measures that characterize the geometry of the pore structure to assess model fit. The model is found to fit stationary parts of the material well.     

Monte Carlo electron-trajectory simulations in bright-field and dark-field STEM: Implications for tomography of thick biological sections

A Monte Carlo electron-trajectory calculation has been implemented to assess the optimal detector configuration for scanning transmission electron microscopy (STEM) tomography of thick biological sections. By modeling specimens containing 2 and 3 at% osmium in a carbon matrix, it was found that for 1-μm-thick samples the bright-field (BF) and annular dark-field (ADF) signals give similar contrast and signal-to-noise ratio provided the ADF inner angle and BF outer angle are chosen optimally. Spatial resolution in STEM imaging of thick sections is compromised by multiple elastic scattering which results in a spread of scattering angles and thus a spread in lateral distances of the electrons leaving the bottom surface. However, the simulations reveal that a large fraction of these multiply scattered electrons are excluded from the BF detector, which results in higher spatial resolution in BF than in high-angle ADF images for objects situated towards the bottom of the sample. The calculations imply that STEM electron tomography of thick sections should be performed using a BF rather than an ADF detector. This advantage was verified by recording simultaneous BF and high-angle ADF STEM tomographic tilt series from a stained 600-nm-thick section of C. elegans. It was found that loss of spatial resolution occurred markedly at the bottom surface of the specimen in the ADF STEM but significantly less in the BF STEM tomographic reconstruction. Our results indicate that it might be feasible to use BF STEM tomography to determine the 3D structure of whole eukaryotic microorganisms prepared by freeze-substitution, embedding, and sectioning.     

Reducing scanning electron microscope charging by using exponential contrast stretching technique on post‐processing images

An exponential contrast stretching (ECS) technique is developed to reduce the charging effects on scanning electron microscope images. Compared to some of the conventional histogram equalization methods, such as bi‐histogram equalization and recursive mean‐separate histogram equalization, the proposed ECS method yields better image compensation. Diode sample chips with insulating and conductive surfaces are used as test samples to evaluate the efficiency of the developed algorithm. The algorithm is implemented in software with a frame grabber card, forming the front‐end video capture element.     

Specimen‐thickness effects on transmission Kikuchi patterns in the scanning electron microscope

We report the effects of varying specimen thickness on the generation of transmission Kikuchi patterns in the scanning electron microscope. Diffraction patterns sufficient for automated indexing were observed from films spanning nearly three orders of magnitude in thickness in several materials, from 5 nm of hafnium dioxide to 3 μm of aluminum, corresponding to a mass‐thickness range of ～5 to 810 μg cm^–2. The scattering events that are most likely to be detected in transmission are shown to be very near the exit surface of the films. The energies, spatial distribution and trajectories of the electrons that are transmitted through the film and are collected by the detector are predicted using Monte Carlo simulations.