Continuous shrinkage of critical dimension in an integrated circuit impels the development of resolution enhancement techniques for low k 1 lithography. Recently, several pixelated optical proximity correction (OPC) and phase-shifting mask (PSM) approaches were developed under scalar imaging models to account for the process variations. However, the lithography systems with larger-NA (NA > 0.6) are predominant for current technology nodes, rendering the scalar models inadequate to describe the vector nature of the electromagnetic field that propagates through the optical lithography system. In addition, OPC and PSM algorithms based on scalar models can compensate for wavefront aberrations, but are incapable of mitigating polarization aberrations in practical lithography systems, which can only be dealt with under the vector model. To this end, we focus on developing robust pixelated gradient-based OPC and PSM optimization algorithms aimed at canceling defocus, dose variation, wavefront and polarization aberrations under a vector model. First, an integrative and analytic vector imaging model is applied to formulate the optimization problem, where the effects of process variations are explicitly incorporated in the optimization framework. A steepest descent algorithm is then used to iteratively optimize the mask patterns. Simulations show that the proposed algorithms can effectively improve the process windows of the optical lithography systems.

Abstract. Optimization technologies have been widely applied to improve lithography performance, such as optical proximity correction and source mask optimization (SMO). However, most published optimization technologies were performed under fixed process conditions, and only a few parameters were optimized. A method for mask, process, and lithography-tool parameter co-optimization (MPLCO) is developed to extend the process window. A normalized conjugate gradient algorithm is proposed to improve the convergence efficiency of the MPLCO when optimizing different scale parameters. In addition, a parametric mask and source are used in the MPLCO that could obtain exceedingly low mask and source complexity compared with a traditional SMO. © 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.

As the critical dimension of integrated circuits is continuously shrunk, thick mask induced aberration (TMIA) cannot be ignored in the lithography image process. Recently, a set of pupil wavefront optimization (PWO) approaches has been proposed to compensate for TMIA, based on a wavefront manipulator in modern scanners. However, these prior PWO methods have two intrinsic drawbacks. First, the traditional methods fell short in building up the analytical relationship between the pupil wavefront and the cost function, and used time-consuming algorithms to solve for the PWO problem. Second, in traditional methods, only the spherical aberrations were optimized to compensate for the focus exposure matrix tilt and best focus shift induced by TMIA. Thus, the degrees of freedom were limited during the optimization procedure. To overcome these restrictions, we build the analytical relationship between the pupil wavefront and the cost function based on Abbe vector imaging theory. With this analytical model and the Fletcher-Reeves conjugate-gradient algorithm, an inverse PWO method is innovated to balance the TMIA including 37 Zernike terms. Simulation results illustrate that our approach significantly improves image fidelity within a larger process window. This demonstrates that TMIA is effectively compensated by our inverse PWO approach.

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