Abstract
In Abbe's formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.
Highlights
In recent years, source optimization (SO) and mask optimization (MO) have attracted great interests among semiconductor foundries and equipment vendors because of its capability for further extending the life of 193-nm optical lithography [1,2,3,4,5,6,7,8,9,10,11,12,13]
The proposal of source mask co-optimization (SMO) further permits the exploration of design spaces for both illuminations and masks [14,15,16,17,18]. Since both SO and MO rely on the complexity of computational lithography algorithms to explore all possible solutions, the design of objective functions has a significant impact on the quality of developed patterns [19], the manufacturability of sources and masks, and the convergence
We propose the innovative line-contour objectives and successfully demonstrate their feasibility
Summary
Source optimization (SO) and mask optimization (MO) have attracted great interests among semiconductor foundries and equipment vendors because of its capability for further extending the life of 193-nm optical lithography [1,2,3,4,5,6,7,8,9,10,11,12,13]. The logarithmic sigmoid function has the advantage of being differentiable and its parameters are adjustable according to the sensitivity of photoresists Such objective with a functional form precludes the formulation of SO into a linear or quadratic problem using Abbe’s formulation, as well as to the implementation of simultaneous SMO using the same cost function. The conventional approach for the resist-image objective is not desirable due to an increased computational time and probability of local minimum traps, as seen in MO. To circumvent such problems, Chan et al have proposed a projection-based active set method to improve the convergence [24]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
