Lin Z.-WFang S.-YChang Y.-WRao W.-CCHIEH-HSIUNG KUANChang, Y.-W.Y.-W.Chang2021-09-022021-09-02201810638210https://www.scopus.com/inward/record.uri?eid=2-s2.0-85032823733&doi=10.1109%2fTVLSI.2017.2761850&partnerID=40&md5=1de4a1af3151db28d4838d442628b6cfhttps://scholars.lib.ntu.edu.tw/handle/123456789/580668— 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 IEEEAlgorithms; 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[SDGs]SDG4journal article10.1109/TVLSI.2017.27618502-s2.0-85032823733