Coulomb interactions in particle-beam systems

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Abstract
The interactions due to the Coulomb force between the constituents of charge particle beam systems have long been explored, with emphasis on the effect of the axial component known as `Boersch effect'. Fewer attempts have been made to quantitatively describe the lateral effects, the bulk space charge effect, which can be compensated by lens adjustment, and the stochastic effect due to the statistical interaction between individual particles. It leads to a non- compensatable, current dependent image blur and is at the root of the failure of direct-write e- beam lithography to become a viable technology for semiconductor manufacturing. It is a key limiting factor of throughput: As throughput goes up with the beam current, so do the interactions and consequently the image blur. Therefore the availability of a theory and/or computer program is essential to predict the interaction effects, before any hardware is built. We give a brief revue of the relevant literature, with emphasis on the treatment of the trajectory displacement effect, the exploration of applicability and limitation of analytical theories, and the application of numerical computer simulation to various system configurations to show the trends and dependencies of particle interactions.

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