Computational imaging technologies for optical lithography extension

Abstract

With the development and production of integrated circuits at the 22nm node, optical lithography faces increasing challenges to keep up with the specifications on its performance along various metrics, such as pattern fidelity and process window. The past few years saw the emergence of source mask optimization (SMO) as an important technique in computational lithography, which allows lithographers to rise to the challenges by exploiting a larger design space on both mask and illumination configuration, and integrates with methods such as inverse imaging. Yet, many methods that are used to tackle SMO problem arising in the inverse imaging involve heavy computation and slow convergence, making the technique unappealing for full-chip simulations or large circuits. Therefore, the purpose of this research is to take advantage of computational imaging technologies to solve source and mask design problems, extending the lifetime of optical lithography.

The computational burden results in part from identical optimization over the whole mask pattern, consequently, we propose a weighted SMO scheme which applies different degrees of correction in the corresponding regions so that the optimal solutions are reached with fewer iterations. Additionally, undesirably long time is also attributed to the algorithm adopted to solve SMO problem. A fast algorithm based on augmented Lagrangian methods is therefore developed, which use the quasi-Newton method to accelerate convergence, thereby shortening the overall execution time. However, as semiconductor lithography is pushed to even smaller dimensions, mask topography effects have to be taken into account for a more accurate solution of SMO. At this stage, intensive computation is spent mainly in rigorous 3D mask modeling and simulations. To address this issue, we devise an optimization framework incorporating pupil aberrations into SMO procedure, which is performed based on the thin mask model so as to ensure a faster speed.

We apply the above approaches to various mask geometries with different critical dimensions. Compared to conventional SMO, simulation results show that the proposed methods lead to better pattern fidelity and larger process window, especially in rigorous calculations. This demonstrates that the source and mask design generated through our algorithms are more practical. More importantly, the improved performance is not at the cost of speed. Instead, our methods take the least time to achieve it. This allows the advantages of computational imaging technologies to be worth exploring for further applications in optical lithography.