Simulation analysis of a miniaturized electron optics of the massively parallel electron-beam direct-write (MPEBDW) for multi-column system

In this study, a simulation analysis of a miniaturized electron optics for the Multi-Column Massively Parallel Electron Beam Writing system is demonstrated. Analytical evaluation of space charge effect with prototype Massively Parallel Electron Beam Writing (MPEBW) system showed 2.86 nm blur in radius occurs on each beam with a convergence half angle of 3 mrad. The angle of each beam was increased to 10 mrad to reduce the space charge effect, the coulomb blur amount can be kept to less than 1 nm in radius. However, there was limitation to increasing the angle due to a spherical aberration. Since the beam current density from the electron emitter array in the prototype MPEBW system was 100 μA/cm²and the total beam current was 1μA with 100×100 array of 10μm square emitter, the influence of coulomb blur was small. By contrast, considerably increasing the number of beams and the beam current are planned in near future in MPEBW. The coulomb blur and other aberrations will not be controlled by merely adjusting the beam convergence angle. In order to increase total beam current, miniaturized electron optics have been designed for Multi-beam+Multi-column system. Reduction lens in the designed miniaturized electron optics with crossover free to reduce the influence of coulomb repulsion with narrow convergence half angle. Unlike conventional methods, the electron beams as principal rays do not intersect at one point, so even if the beam becomes extremely narrow, the coulomb repulsion effect does not increase at the crossover area. The reduction of the entire size of parallel beams in the designed electron optics was confirmed by simulation software. The simulation results showed that least confusion disk of 6.5 nm size was obtained at the beam convergence half angles of 3 mrad corresponding to the incident beam of ±0.1 mrad divergence angle. It showed that the miniaturized electron optics was suitable for 10 nm order EB writing. The crossover free electron optics of the miniaturized electron optics is possible due to dispersing the intersection points of the principal rays by a combination of a concentric electron optics and a tapered lens electrode of the reduction lens.