Fast Pixelated Lithographic Source and Mask Joint Optimization Based on Compressive Sensing

Pixelated source-mask joint optimization (SMO) plays a crucial role in improving the resolution and image fidelity of optical lithography process. However, the ever growing integration density of semiconductor devices incurs the explosion of data throughput, and poses a considerable challenge on the computational efficiency of pixelated SMO algorithms. This paper proposes to use compressive sensing (CS) to effectively reduce the computational complexity of the SMO algorithm. The proposed SMO algorithm is sequential, where the lithographic source and mask patterns are optimized alternatively. Based on the lithography imaging model, source optimization is transformed to a linear CS reconstruction problem with a nonnegative constraint on the illumination intensity. On the other hand, the problem of mask optimization is solved by a nonlinear CS method aided by sparsity and low-rank regularizations. The dimensionality of the objective function is reduced by downsampling the layout pattern to be printed. The improvement in computational efficiency is verified, and a set of simulations are presented to assess the proposed SMO algorithms. Speedup by several-fold is attained over traditional gradient-based SMO method. Improvement in lithography image fidelity and mask manufacturability is obtained compared to the traditional SMO method and state-of-the-art CS-based SMO method.