Several writing methods were previously introduced for massively parallel electron-beam systems, e.g., single-row writing and multirow writing. A straightforward application of these methods for realizing nonuniform dose distributions often required for the proximity effect correction (PEC) including line/space patterns would turn off certain beams, sometimes all, selectively in several cycles. Consequently, the utilization of beams is reduced considerably. In this study, two different approaches to increasing the beam utilization and thereby reducing the exposing (writing) time are investigated, i.e., lowering the dose difference among the regions of a feature while implementing the PEC and utilizing the cycles with all the beams turned off. It has been shown that with these methods, the exposing time can be reduced significantly.

The massively-parallel e-beam system (MPES) provides a large number of programmable beams of which the optimal use is critical to maximizing the efficiency of the system. In our previous study of proximity effect correction (PEC) under the constraints of the MPES, the critical dimension error and the line edge roughness were minimized by reducing the feature area to be exposed and varying the dose spatially. In another study, a method to reduce the exposing time while still ensuring a near-optimal PEC result was developed. In this method, the maximum dose difference between two regions of a feature was carefully decreased after first obtaining the optimal linewidth reduction and the spatial dose distribution for the PEC. However, this method designed with an emphasis on the PEC and simplicity may miss the optimal result due to the fixed order of performance metrics considered and was developed for a single feature. To address these limitations, an adaptive optimization method that can handle any combination of performance metrics in a cost function is proposed. It allows for more flexible optimization and can achieve better results than the old method. Additionally, the optimization method is extended for large-scale patterns with uniform features, such as line-space patterns. Also, an effective way to handle the recursive effect among critical locations in a large-scale pattern is described. The simulation results show that the proposed optimization method outperforms the old method in terms of the cost function and linewidth uniformity among the features.