Provably Good Max-Min-m-Neighbor-TSP-Based Subfield Scheduling for Electron-Beam Photomask Fabrication
Journal
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Journal Volume
7372596
Pages
324-337
Date Issued
2018
Author(s)
Zhi-Wen Lin
Shao-Yun Fang
Yao-Wen Chang
Fellow
IEEE
Wei-Cheng Rao
Chieh-Hsiung Kuan
CHIEH-HSIUNG KUAN
Abstract
Electron beam lithography (EBL) has been used for high-resolution photomask fabrication; its successive heating process in a certain region, however, may cause critical dimension (CD) distortion. As a result, subfield scheduling which reorders a sequence of subfields in the writing process is desirable to avoid the heating problem and thus CD distortion. To consider longer-range heat dissipation, this paper models a subfield scheduling problem with blocked region consideration as a constrained max-min m-neighbor travelling salesman problem (called constrained m-nTSP). To solve the constrained m-nTSP which is NP-complete in general, we decompose a constrained m-nTSP into subproblems conforming to a special case with points on two parallel lines, solve each of them with a provably good linear-time approximation algorithm, and merge them into a complete scheduling solution. In particular, our algorithm can also minimize the distances between successive subfields to alleviate the throughput degradation of EBL writing due to moving a writing head, while minimizing the heating problem. Average reductions of 10% in the maximum temperature and 14% in the distances between successive subfields over the state-of-the-art work can be achieved.
Type
journal article