Immersion lithography systems with hyper-numerical aperture (hyper-NA) (NA>1) have become indispensable in nanolithography for technology nodes of 45 nm and beyond. Source and mask optimization (SMO) has emerged as a key technique used to further improve the imaging performance of immersion lithography. Recently, a set of pixelated gradient-based SMO approaches were proposed under the scalar imaging models, which are inaccurate for hyper-NA settings. This paper focuses on developing pixelated gradient-based SMO algorithms based on a vector imaging model that is accurate for current immersion lithography. To achieve this goal, an integrative and analytic vector imaging model is first used to formulate the simultaneous SMO (SISMO) and sequential SMO (SESMO) frameworks. A gradient-based algorithm is then exploited to jointly optimize the source and mask. Subsequently, this paper studies and compares the performance of individual source optimization (SO), individual mask optimization (MO), SISMO, and SESMO. Finally, a hybrid SMO (HSMO) approach is proposed to take full advantage of SO, SISMO, and MO, consequently achieving superior performance.

To keep pace with the shrinkage of critical dimension, source and mask optimization (SMO) has emerged as a promising resolution enhancement technique to push the resolution of 193 nm argon fluoride immersion lithography systems. However, most current pixelated SMO approaches relied on scalar imaging models that are no longer accurate for immersion lithography systems with hyper-NA (NA>1). This paper develops a robust hybrid SMO (HSMO) algorithm based on a vector imaging model capable of effectively improving the robustness of immersion lithography systems to defocus and dose variations. The proposed HSMO algorithm includes two steps. First, the individual source optimization approach is carried out to rapidly reduce the cost function. Subsequently, the simultaneous SMO approach is applied to further improve the process robustness by exploiting the synergy in the joint optimization of source and mask patterns. The conjugate gradient method is used to update the source and mask pixels. In addition, a source regularization approach and source postprocessing are both used to improve the manufacturability of the optimized source patterns. Compared to the mask optimization method, the HSMO algorithm achieves larger process windows, i.e., extends the depth of focus and exposure latitude, thus more effectively improving the process robustness of 45 nm immersion lithography systems.

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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.

As a promising resolution enhancement technique, a set of pixelated source and mask optimization (SMO) methods has been introduced to further improve the lithography at 45 nm node and beyond. Recently, some papers studied the impact of the scanner errors on SMO, and the results revealed that the source blur and flare seriously impact on the lithography performance of the optimal source and mask resulting from SMO. However, current SMO methods did not propose an effective method to compensate for the impact of these nonideal factors of the actual scanners. To overcome this drawback, this paper focuses on developing a robust hybrid SMO (HSMO) method where the sensitivities of the aerial image to source blur and flare are introduced into the cost function. Simulation results are compared with traditional SMO to demonstrate the benefit of the proposed source blur-flare-aware HSMO method in pattern fidelity and process window.

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