Nonlinear compressive inverse lithography aided by low-rank regularization

Photolithography is at the core of the semiconductor industry that is used to fabricate microscale and nanoscale integrated circuits. Inverse lithography is a technique extensively used to compensate for lithography patterning distortions. It refers to methods that pre-distort the photomask patterns such that their projection, through the photolithography system, results in a pattern that is as close as possible to the intended original. However, most inverse lithography technique (ILT) methods suffer from large computational complexity. This paper develops a nonlinear compressive sensing framework for ILT that effectively improves the computational efficiency and image fidelity, while at the same time controlling the mask complexity. Based on a nonlinear lithography imaging model, the compressive ILT is formulated as an inverse optimization problem aimed at reducing the patterning error, and enforcing the sparsity and low rank properties of the mask pattern. A downsampling strategy is adopted to reduce the dimensionality of the cost function, thus alleviating the computational burden. Sparsity and low-rank regularizations are then used to constrain the solution space and reduce the mask complexity. The split Bregman algorithm is used to solve for the inverse optimization problem. The superiority of the proposed method is verified by a set of simulations and comparison to traditional ILT algorithms.