Image blurring as a result of stochastic particle–particle interactions has been investigated for projection electron- and ion-beam lithography systems. A comparative analysis of the currently available analytical theories is presented. The results from these theories are also compared with Monte Carlo simulation results and experimental data. Large variations in results and serious disagreements between the different theoretical approaches are found. We have formulated a new theory on the basis of a simple, analytical approach that overcomes most of the difficulties experienced by earlier theories with two key concepts: consideration of nearest-neighbor interactions only, and a randomization length, over which the interactions are correlated. Our model displays satisfactory functional and numerical agreement with Monte Carlo simulation results over a large range of beam currents, as well as with the only available experimental data. The physical basis of our model also enables us to understand the origins of the discrepancies arising from earlier theories.
Image blurring as a result of stochastic particle interactions has been investigated for projection electron- and ion-beam lithography systems. The investigation was made on the basis of a simple, nearest-neighbor, analytical model, proposed and developed here, for stochastic particle–particle interactions. The results obtained using this model are in close agreement with those given by Jansen [Coulomb Interactions in Particle Beams (Academic, Boston, 1990)] for an extended parallel beam segment in the Holtsmark regime; at the same time they are extendable over a wide range of conditions, unlike Jansen’s results. The results obtained for a parallel beam are applied to more realistic systems by dividing the beam into nearly cylindrical, uncorrelated slices. This method is used to determine the dependence of the image blur on beam parameters for a doublet. Our results correlate well with those obtained by Monte Carlo calculations.
We investigate space-charge by analytic methods and Monte Carlo simulations as a possible source of blur in high-resolution TEM images. In doing so we believe to have identified a novel type of space charge effect, namely quantum space charge(QSC) effect. We predict the blur for typical HRTEM images and for electron holograms. Inclusion of this hitherto unrecognized effect in image simulations (and experimental design for HRTEM and related techniques, such as holography) should permit further progress in the critical field of quantitative HRTEM image matching as a means for atomic structure determination.
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