Abstract. We propose a new regularization framework for inverse lithography that regularizes masks directly by applying a mask filtering technique to improve computational efficiency and to enhance mask manufacturability. This technique is different from the conventional regularization method that regularizes a mask by incorporating various penalty functions to the cost function. We design a specific mask filter for this purpose. Moreover, we introduce a metric called edge distance error (EDE) to guide mask synthesis and establish the correlation between pattern error and edge placement error (EPE) via EDE. We prove that EDE has the same dimension as EPE and has a continuous expression as pattern error. Simulation results demonstrating the validity and efficiency of the proposed method are presented. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Inverse mask synthesis is achieved by minimizing a cost function on the difference between the output and desired patterns. Such a minimization problem can be solved by a level-set method where the boundary of the pattern is iteratively evolved. However, this evolution is timeconsuming in practice and usually converges to a local minimum. The velocity of the boundary evolution and the size of the evolution step, also known as the descent direction and the step size in optimization theory, have a dramatic influence on the convergence properties. This paper focuses on developing a more efficient algorithm with faster convergence and improved performance such as smaller pattern error, lower mean edge placement error, wider defocus band, and higher normalized image log slope. These improvements are accomplished by employing the conjugate gradient of the cost function as the evolution velocity, and by introducing an optimal time step for each iteration of the boundary evolution. The latter is obtained from an extended Euler time range by using a line search method. The authors present simulations demonstrating the efficacy of these two improvements.

Mask optimization is essential in the resolution scaling of optical lithography due to its strong ability to overcome the optical proximity effect. However, it often demands extensive computation in solving the nonlinear optimization problem with a large number of variables. In this paper, we use a set of basis functions to represent the mask patterns, and incorporate this representation into the mask optimization at both the nominal plane and various defocus conditions. The representation coefficients are updated according to the gradient to the coefficients, which can be easily obtained from the gradient to the pixel variables. To ease the computation of the gradient, we use an adaptive method that divides the optimization into two steps, in which a small number of kernels is used as the first step, and more kernels are used for fine optimization. Simulations performed on two test patterns demonstrate that this method can improve the optimization efficiency by several times, and the optimized patterns have better manufacturability compared with regular pixel-based representation.

We propose a general method called convolution-variation separation (CVS) to enable efficient optical imaging calculations without sacrificing accuracy when simulating images for a wide range of process variations. The CVS method is derived from first principles using a series expansion, which consists of a set of predetermined basis functions weighted by a set of predetermined expansion coefficients. The basis functions are independent of the process variations and thus may be computed and stored in advance, while the expansion coefficients depend only on the process variations. Optical image simulations for defocus and aberration variations with applications in robust inverse lithography technology and lens aberration metrology have demonstrated the main concept of the CVS method.