Semi-Implicit Mask Synthesis with Additive Operator Splitting

In this paper, a semi-implicit mask optimization method is investigated by quantifying the nonlinear diffusion quality of the mask pattern into the inverse optimization framework. The mask synthesis problem is addressed as a constrained time-dependent partial differential equation (PDE) which is further solved by the semi-implicit additive operator splitting (AOS) scheme. Thus the updating of the mask patterns is reduced to consecutive one-dimensional updates with respect to coordinate axes, where unconditional stable implicit difference schemes can be applied with larger time steps by solving a tridiagonal linear equation efficiently using the Thomas algorithm. Experimental results merit the superiority of the proposed semi-implicit AOS method with improved convergence performance.