<title>Global space charge effects in high-throughput electron-beam lithography</title>

Abstract

Recently global space charge effects were found to seriously limit the performance of high throughput projection electron beam lithography systems. A fundamental analytical theory describing the global space charge lens has been developed using the variational principle. A modified paraxial ray equation and a set of aberration integrals is derived. All the space charge effects, including the defocus, the magnification variation, and the third order aberrations, are found to be proportional to the perveance, the weighted integrals of the normalized current density distribution, and a combination of the system parameters, such as: the field size and the convergence angle. A simple scaling law for the space charge aberrations, where the aberrations at the image edge scale linearly with the radial dimension, has been found for the telecentric projection configuration. Both the theoretical calculations and the Monte Carlo simulations have been done for a SCALPEL configuration with 25 (mu) A beam current and two scaled systems, whose radial dimensions are scaled from SCALPEL by twice and 3 times, and current by 4 times and 9 times respectively at 10 kV. From both theoretical and simulation results, the space charge aberrations at the edge show approximately a 63 times increase in the twice-scaled system, and about 95 times increase in the three-time-scaled system. All these aberration scaling factors are very close to those predicted from the simple scaling law. An experiment based on the simple scaling law was designed to verify the theory and evaluate the performance of the high throughput projection system. In the scaled testing column which has a 1.6 mA beam current, 5 kV beam voltage, 40 cm column length, 8 mm field diameter, and 4 mrad convergence angle at the mask, the space-charge-aberration blur to be measured will be as large as 200 micrometer. Then the final image blur of the real high throughput system can be derived by using the scaling law.