EBL Overlapping Aware Stencil Planning for MCC System

Abstract

Electron beam lithography (EBL) is a promising, maskless solution for the technology beyond 14nm logic nodes. To overcome its throughput limitation, industry has proposed character projection (CP) technique, where some complex shapes (characters) can be printed in one shot. Recently, the traditional EBL system was extended into a multi-column cell (MCC) system to further improve the throughput. In an MCC system, several independent CPs are used to further speed-up the writing process. Because of the area constraint of stencil, the MCC system needs to be packed/planned carefully to take advantage of the characters. In this article, we prove that the overlapping aware stencil planning (OSP) problem is NP-hard. Then we propose E-BLOW, a tool to solve the MCC system OSP problem. E-BLOW involves several novel speedup techniques, such as successive relaxation and dynamic programming. Experimental results show that, compared with previous works, E-BLOW demonstrates better performance for both the conventional EBL system and the MCC system.

A highly-efficient row-structure stencil planning approach for e-beam lithography with overlapped characters

“…Yuan et al [12] proposed the first systematic study on this topic, but the greedy and heuristic methods that were used are time consuming and lack of global view. E-BLOW [10] was then developed for OSP in the MCC system. The problem was formulated as an LP and solved iteratively by successive relaxation.…”

“…Furthermore, it failed to recognize the difference between conventional EBL and the MCC system. So, although the approach in [10] already performs much better than that in [12], the quality and efficiency can be further optimized for both types of EBL.…”

“…Notice that in this paper we assume that CP shot and VSB shot have equal cost, as in the previous works [12,10], but our approach can be easily extended to process CP shot that requires longer time. After putting the characters in C ′ , the total shot number will be:…”

“…All characters have the same size and uniform top and bottom blank areas. Vertical overlapping can thus be optimized easily and only horizontal overlapping need to be considered [12,10]. In this case, the stencil can be viewed as a set of rows, and the selected characters need to be packed into the rows.…”

“…As shown in Figure 2, two characters i and j are placed in one row, overlapping with each other. Note that the uniform top and bottom blank areas are omitted w.l.o.g as in the previous work [10].…”