Process variation-aware mask optimization with iterative improvement by subgradient method and boundary flipping

As one of Resolution Enhancement Techniques, a mask optimization such as Pixel-based Optical Proximity Correction or Inverse Lithography Technology is well discussed. In this paper, a pixel-based mask optimization using 0-1 Quadratic Programming problem (0-1 QP) is proposed to obtain enough image contour fidelity and tolerance to process variation in a short time. By formulating 0-1 QP to maximize intensity slope around between edges of target patterns, suppression of image contour distortion by the process variation is realized. The defined 0-1 QP is relaxed into Lagrangian relaxation problem and an approximate solution of the defined 0-1 QP is obtained by solving Lagrangian relaxation problem by using Subgradient method and gradient deciding method. Moreover, by applying a correction method which corrects boundary pixel of target patterns precisely into the mask obtained by 0-1 QP, enough shape fidelity toward target patterns can be obtained.