Calculation of Coulomb Interaction among Electrons in a High-Current Electron-Beam Exposure System

In the present study, we propose a new calculation method for the Coulomb interaction among electrons in an electron beam running at a given optical system. In the simulation, the interaction is expressed by separating the global and the stochastic mechanisms, and then, they are combined in a Monte Carlo electron trajectory simulation. In the case of the global Coulomb effect, the potential distribution is obtained in the beam, and the electron trajectory deflection due to the distribution is calculated. In the case of the stochastic Coulomb effect, it is assumed that electrons interact with only their nearest neighbor electrons in the beam. All electron trajectories in the entire optical system are traced three-dimensionally. Since the Coulomb interaction is calculated for only one pair of electrons instead of all pairs of other electrons around the electron in the present model, the computation time is markedly reduced. It is found that the results obtained by the present simulation show a fair agreement with that obtained by considering all existent electrons in the beam, as in the conventional Monte Carlo simulation of the Coulomb interaction.