Fast nonlinear compressive sensing lithographic source and mask optimization method using Newton-IHTs algorithm.

Source and mask optimization (SMO) is an important method to improve lithography imaging fidelity. However, constrained by the computational inefficiency, the current SMO method can be used only in clip level applications. In this paper, to our best knowledge, the fast nonlinear compressive sensing (CS) theory is for the first time applied to solve the nonlinear inverse reconstruction problem in SMO. The proposed method simultaneously downsamples the layout pattern in the SMO procedure, which can effectively reduce the computation complexity. The space basis and two-dimensional (2D) discrete cosine transform (DCT) basis are selected to sparsely represent the source pattern and mask pattern, respectively. Based on the sparsity assumption of source and mask pattern, the SMO can be formulated as a nonlinear CS reconstruction problem. A Newton-iteration hard thresholding (Newton-IHTs) algorithm, by taking into account the second derivative of the cost function to accelerate convergence, is innovated to realize nonlinear CS-SMO with high imaging fidelity. Simulation results show the proposed method can significantly accelerate the SMO procedure over a traditional gradient-based method and IHTs-based method by a factor of 9.31 and 7.39, respectively.