Character Design and Stamp Algorithms for Character Projection Electron-Beam Lithography P. Du, W. Zhao, S.H. Weng, C.K. Cheng, and R. Graham UC San Diego 1

Outline Introduction Problem Formulation Character Design for Wire Layouts Character Design and Stencil Compaction for Via Layouts Experimental Results Conclusion 2

Introduction Electron Beam Lithography (EBL): maskless fabrication Variable Shaped Beam (VSB): variant rectangles for the layout Character Projection (CP): improves VSB throughput 3 Wire LayoutVia Layout

Previous Works of CP Previous Character Designs Rows of wire segments with various separation Arrays of vias Usage Apply Characters to stamp most wires and vias Use VSB to patch up the rest wires and vias 4

Problem Formulation Character and Stencil designs: – Prescribe a set of characters and assemble in a stencil. Stamp algorithm: – Match the characters to the most of layout One stencil for wires and the other for vias 5

Wire Layout Layout is cut into blocks of size c x x c y. Wire layout on grid with unit size u x and u y. 6

Stamp Process 7 Assumption of character projection Arbitrary shifting Arbitrary rectangular masking Projected regions can overlap

Normalization of Wire Layouts Segment: a column of wire grid in the block Normalization: expand the wires in each segment into four types. 8

Segments Categorization Type 1: A segment split into two wires Type 2: A wire with a gap on the top. Type 3: A wire with no gaps. Type 4: A segment split into 3 or more wires. 9

Character Design for Wire Layouts A character starts with Type 1 segment followed by c x -1 segments of Type 2 and 3. The number of Type 2 segments is no more than a constant B g. 10

Stamp Algorithm for Wire Layouts 11 Cut layout into rows of height c y. Cut each row into groups at Types 1 and 4 segments. Match the characters greedily from left to right.

Experimental Results 12

Experimental Results The row heights are chosen dynamically to balance the overhead of dummy fill against the improvement of CP. 13

Experimental Results 14 Improvement vs. overhead of dummy fill.

Via Layout Assumption: Vias are of the same size and on the grids. Observation: Vias are sparse comparing to wires. 15

Character Design for Via Layouts Characters: k vias linked in a path of length w. The paths are oriented in top-right direction. Three characters are shown in the figures (k=3) 16

Stencils: Character Compaction 17 A single via v at center and two vias at I and III quadrants. Vias at quadrants are aligned for each length w. Example: Three windows in the figure correspond to three characters.

Stamp Algorithm for Via Layouts Construct a directed acyclic graph G(V,E). – The vertex set V contains all vias. – An edge (u,v) belongs to E if and only if v is in the first quadrant of u with distance less than w. Use the minimum vertex-disjoint path cover algorithm to match characters with the layout. 18

Experimental Results Improvement: average number of vias per shot Path length: upper bound of Improvement Improvement increases with Character Size and Path Length. 19

Conclusion A framework includes character design, stencil compaction and layout matching algorithms. For wires, we normalize the wires with dummy fills and expansion. For vias, we devise k-via sets and compact the sets into a stencil. A path covering algorithm maps the set. The approach improves the throughput of manufacturing over VSB. 20

Thank you for your attention! 21