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
26
Journal Issue
2
Pages
378-391
Date Issued
2018
Author(s)
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 traveling 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. ? 2017 IEEE
Subjects
Algorithms; Approximation algorithms; Design; Distortion (waves); Electron beam lithography; Electron beams; Electrons; Fabrication; Heat problems; Heating; Job shop scheduling; Optimization; Photomasks; Scheduling algorithms; Technical writing; Throughput; Traveling salesman problem; Critical dimension; Heating system; Linear-time approximation; Manufacturability; Maximum temperature; performance; Photomask fabrication; Throughput degradation; Scheduling
Type
journal article