Polynomial time optimal algorithm for stencil row planning in e-beam lithography

Electron beam lithography (EBL) is a very promising candidate for integrated circuit (IC) fabrication beyond the 10 nm technology node. To address its throughput issue, the Character Projection (CP) technique has been proposed, and its stencil planning can be optimized with aware of overlapping characters. However, the top level 2D stencil planning problem has been proved to be an NP-hard problem. As its most essential step, the 1D row ordering is believed hard as well, and no polynomial time optimal solution has been provided so far. In this paper, we propose a polynomial time optimal algorithm to solve the row ordering problem, which serves as the major subroutine for the entire stencil planning problem. Proof and experimental results are also provided to verify the correctness and efficiency of our algorithm.