Stitch-aware routing for multiple e-beam lithography

Abstract

Multiple e-beam lithography (MEBL) is one of the most promising next generation lithography (NGL) technologies for high volume manufacturing, which improves the most critical issue of conventional single e-beam lithography, throughput, by simultaneously using thousands or millions of e-beams. For parallel writing in MEBL, a layout is split into stripes and patterns are cut by stripe boundaries, which are defined as stitching lines. Critical patterns cut by stitching lines could suffer from severe pattern distortion or even yield loss. Therefore, considering the positions of stitching lines and avoiding stitching line-induced bad patterns are required during layout design. In this paper, we propose the first work of stitch-aware routing framework for MEBL based on a two-pass bottom-up multilevel router. We first identify three types of stitching line-induced bad patterns which should not exist in an MEBL-friendly routing solution. Then, stitch-aware routing algorithms are respectively developed for global routing, layer/track assignment and detailed routing. Experimental results show that our stitch-aware routing framework can effectively reduce stitching line-induced bad patterns and thus may not only improve the manufacturability but also facilitate the development of MEBL.

Stitch aware detailed placement for multiple e-beam lithography

“…1(b) we can see that the vertical wires are malformed in the stitch regions. Similar observations were also reported by Fang et al [7] that the vertical wires are more susceptible to stitch errors than the horizontal wires. There are several methods to minimize the impacts of stitch errors from lithography perspective, e.g., avoiding dividing a critical pattern into adjacent sub-fields [8], using different field sizes [9], or reducing the field size [10].…”

“…There are several methods to minimize the impacts of stitch errors from lithography perspective, e.g., avoiding dividing a critical pattern into adjacent sub-fields [8], using different field sizes [9], or reducing the field size [10]. Recently, Fang et al [7] considered the stitch error during detailed routing stage. However, detailed routing is a very late stage in physical design flow, thus there may exist some stitch errors difficult to be removed.…”

EUV and e-beam manufacturability

“…Liu et al proposed the first work of stitch-aware routing for MEBL [12,22]. Considering the impacts of the three stitch- ing line-induced bad patterns on manufacturability, the router strictly forbids wires and vias to route and land on stitching lines.…”

“…A short polygon occurs due to dithering with error diffusion in the EBL data processing flow[12,22].…”

Stitch-Aware Routing for Multiple E-Beam Lithography

“…Constraint (7) is used to guarantee that the number of paths flowing into a node equals that draining from the node. Constraint (8) guarantees that a track in a tile is occupied by at most one segment. Finally, (9) prevents segments from crossing with each other.…”