Integrated circuit (IC) technology lies at the heart of today’s digital world. The immense amount of computational power that came along with the downscaling of circuits allowed us to place faster and smaller chips almost everywhere. However, with today’s requirements, even a one-nanometer error on those chips can drastically change the performance of the chip. Therefore, maintaining product quality is challenging, and more accurate techniques are needed to manufacture future generation chips. Electron beam based techniques are known to provide very high resolution both in production and testing of these chips. However, the ongoing trend is also challenging the established e-beam technologies. Two common problems in both imaging and lithography are addressed in the thesis. One of them is the emerging importance of the 3rd dimension (3D) in imaging and lithography. The other one is the notorious charging effect when the samples involved, such as gate oxides, are not sufficiently electrically conductive. The experimental trial and error approach to understand and solve these problems is too time-consuming and can also be very expensive. Therefore, tools such as Monte Carlo simulations are needed that aid in getting a better fundamental understanding of these issues. The development of a simulator that can help to find solutions for the problems above is one of the primary objectives of this thesis. @en

The sensitivity of simulated scanning electron microscopy (SEM) images to the various physical model ingredients is studied using an accurate, but slow simulator, to identify the most important ingredients to include in a reliable and fast SEM image simulator. The quantum mechanical transmission probability (QT) model and the electron-acoustical phonon scattering model are found to have the most significant effect on simulated 2D and 3D metrology results. The linewidth measurement error caused by not including these models in the simulation is less than 2 nm. Specifically, it was found from a comparison to experimental data that the QT model is essential in accurately predicting particular signal features in linescans such as “shadowing”. The simulator is compared with two other publicly available simulators, JMONSEL and CASINO, where the first one is also based on first-principle physics models and the latter one is using phenomenological models. CASINO is the fastest simulator on CPU, but Nebula on GPU is two orders of magnitude faster compared to a single threaded CPU simulation. Only up to 6% speed increase has been achieved by different model choices.

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Scanning electron microscopy (SEM) is one of the most common inspection methods in the semiconductor industry and in research labs. To extract the height of structures using SEM images, various techniques have been used, such as tilting a sample, or modifying the SEM tool with extra sources and/or detectors. However, none of these techniques focused on extraction of height information directly from top-down images. In this work, using Monte Carlo simulations, we studied the relation between step height and the emission of secondary electrons (SEs) resulting from exposure with primary electrons at different energies. It is found that part of the SE signal, when scanning over a step edge, is determined by the step height rather than the geometry of the step edge. We present a way to quantify this, arriving at a method to determine the height of structures from top-down SEM images. The method is demonstrated on three different samples using two different SEM tools, and atomic force microscopy is used to measure the step height of the samples. The results obtained are in qualitative agreement with the results from the Monte Carlo simulations.

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Background: Charging of insulators is a complex phenomenon to simulate since the accuracy of the simulations is very sensitive to the interaction of electrons with matter and electric fields. Aim: In this study, we report model improvements for a previously developed Monte-Carlo simulator to more accurately simulate samples that charge. Approach: The improvements include both modeling of low energy electron scattering by first-principle approaches and charging of insulators by the redistribution of the charge carriers in the material with an electron beam-induced conductivity and a dielectric breakdown model. Results: The first-principle scattering models provide a more realistic charge distribution cloud in the material and a better match between noncharging simulations and experimental results. The improvements on the charging models, which mainly focus on the redistribution of the charge carriers, lead to a smoother distribution of the charges and better experimental agreement of charging simulations. Conclusions: Combined with a more accurate tracing of low energy electrons in the electric field, we managed to reproduce the dynamically changing charging contrast due to an induced positive surface potential.

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Electron beam lithography (EBL) requires conducting substrates to ensure pattern fidelity. However, there is an increasing interest in performing EBL on less well-conducting surfaces or even insulators, usually resulting in seriously distorted pattern formation. To understand the underlying charging phenomena, the authors use Monte Carlo simulations that include models for substrate charging, electron beam-induced current, and electric breakdown. Simulations of electron beam exposure of glass wafers are presented, exposing regular patterns which become distorted due to charge-induced beam deflection. The resulting displacements within the patterns are mapped and compared to experimental displacement maps obtained from patterns in PMMA resist on glass substrates. Displacements up to several hundreds of nanometers were observed at a primary beam energy of 50 keV. Also, various scan strategies were used to write the patterns, in the simulations as well as the experiments, revealing their strong effect on pattern distortion, in shape and in magnitude. A qualitative, in some cases even quantitative, good agreement was found between the simulations and the experiments, providing enough confidence in Monte Carlo simulations to predict charge-induced pattern displacement and shape distortion and to find smart scan strategies to minimize the effects of charging.

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There is a growing interest for patterning on curved or tilted surfaces using electron beam lithography. Computational proximity correction techniques are well established for flat surfaces and perpendicular exposure, but for curved and tilted surfaces adjustments are needed as the dose distribution is no longer cylindrically symmetric with respect to the surface normal. A graphical processing unit -accelerated 3D Monte Carlo simulation, based on first-principle scattering models, is used to simulate the asymmetric dose distribution. Based on that, an approximate adjustment is made to an existing high-performance proximity effect correction (PEC) algorithm aimed at the correct exposure of a pattern of nanowires on a 17° tilted surface. It was experimentally verified that using the adjusted PEC indeed leads to a more uniform exposure on tilted surfaces.

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Charging of insulators is a complex phenomenon to simulate since the accuracy of the simulations is very sensitive to the interaction of electrons with matter and electric fields. In this study, we report model improvements for a previously developed Monte-Carlo simulator to more accurately simulate samples that charge. The improvements include both modelling of low energy electron scattering and charging of insulators. The new first-principle scattering models provide a more realistic charge distribution cloud in the material, and a better match between non-charging simulations and experimental results. Improvements on charging models mainly focus on redistribution of the charge carriers in the material with an induced conductivity (EBIC) and a breakdown model, leading to a smoother distribution of the charges. Combined with a more accurate tracing of low energy electrons in the electric field, we managed to reproduce the dynamically changing charging contrast due to an induced positive surface potential.

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In this paper key challenges posed on metrology by feature dimensions of 20nm and below are discussed. In detail, the need for software-based tools for SEM image acquisition and image analysis in environments where CD-SEMs are not available and/or not flexible enough to cover all inspection tasks is outlined. These environments include research at universities as well as industrial R and D environments focused on non-IC applications. The benefits of combining automated image acquisition and analysis with computational techniques to simulate image generation in a conventional analytical SEM with respect to the overall reliability, precision and speed of inspection will be demonstrated using real-life inspection tasks as demonstrators.

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The electric field distribution and charging effects in Scanning Electron Microscopy (SEM) were studied by extending a Monte-Carlo based SEM simulator by a fast and accurate multigrid (MG) based 3D electric field solver. The main focus is on enabling short simulation times with maintaining sufficient accuracy, so that SEM simulation can be used in practical applications. The implementation demonstrates a gain in computation speed, when compared to a Gauss-Seidel based reference solver is roughly factor of 40, with negligible differences in the result (~10−6 푉). In addition, the simulations were compared with experimental SEM measurements using also complex 3D sample, showing that i) the modelling of e-fields improves the simulation accuracy, and ii) multigrid method provide a significant benefit in terms of simulation time.@en