Skip to main content
Log in

Regularized level-set-based inverse lithography algorithm for IC mask synthesis

  • Published:
Journal of Zhejiang University SCIENCE C Aims and scope Submit manuscript

Abstract

Inverse lithography technology (ILT) is one of the promising resolution enhancement techniques, as the advanced IC technology nodes still use the 193 nm light source. In ILT, optical proximity correction (OPC) is treated as an inverse imaging problem to find the optimal solution using a set of mathematical approaches. Among all the algorithms for ILT, the level-set-based ILT (LSB-ILT) is a feasible choice with good production in practice. However, the manufacturability of the optimized mask is one of the critical issues in ILT; that is, the topology of its result is usually too complicated to manufacture. We put forward a new algorithm with high pattern fidelity called regularized LSB-ILT implemented in partially coherent illumination (PCI), which has the advantage of reducing mask complexity by suppressing the isolated irregular holes and protrusions in the edges generated in the optimization process. A new regularization term named the Laplacian term is also proposed in the regularized LSB-ILT optimization process to further reduce mask complexity in contrast with the total variation (TV) term. Experimental results show that the new algorithm with the Laplacian term can reduce the complexity of mask by over 40% compared with the ordinary LSB-ILT.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Reference

  • Cobb, N.B., Zakhor, A., 1995. Fast sparse aerial image calculation for OPC. SPIE, 2621:534–545. [doi:10.1117/12.228208]

    Article  Google Scholar 

  • Cobb, N.B., Zakhor, A., Miloslavsky, E.A., 1996. Mathematical and CAD framework for proximity correction. SPIE, 2726:208–222. [doi:10.1117/12.240907]

    Article  Google Scholar 

  • Granik, Y., 2004. Solving inverse problems of optical micro-lithography. SPIE, 5754:506. [doi:10.1117/12.600141]

    Article  Google Scholar 

  • Granik, Y., 2006. Fast pixel-based mask optimization for inverse lithography. J. Micro/Nanolith. MEMS MOEMS, 5(4):043002. [doi:10.1117/1.2399537]

    Article  Google Scholar 

  • Hopkins, H.H., 1953. On the diffraction theory of optical images. Proc. R. Soc. A, 217(1130):408–432. [doi:10.1098/rspa.1953.0071]

    Article  MathSciNet  MATH  Google Scholar 

  • Jia, N.N., Lam, E.Y., 2010. Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis. J. Opt., 12(4):045601. [doi:10.1088/2040-8978/12/4/045601]

    Article  Google Scholar 

  • Jia, N.N., Wong, A.K., Lam, E.Y., 2009. Regularization of inverse photomask synthesis to enhance manufacturability. SPIE, 7520:75200E. [doi:10.1117/12.837512]

    Article  Google Scholar 

  • Li, Y.H., Shi, Z., Geng, Z., Yang, Y.W., Yan, X.L., 2012. A new algorithm of inverse lithography technology for mask complexity reduction. J. Semicond., 33(4):045009. [doi:10.1088/1674-4926/33/4/045009]

    Article  Google Scholar 

  • Lin, B., Yan, X.L., Shi, Z., Yang, Y.W., 2011. A sparse matrix model-based optical proximity correction algorithm with model-based mapping between segments and control sites. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 12(5): 436–442. [doi:10.1631/jzus.C1000219]

    Article  Google Scholar 

  • Ma, X., Arce, G.R., 2008. Binary mask optimization for inverse lithography with partially coherent illumination. J. Opt. Soc. Am. A, 25(12):2960–2970. [doi:10.1364/JOSAA. 25.002960]

    Article  Google Scholar 

  • Ma, X., Arce, G.R., 2010. Computational Lithography. Wiley Series in Pure and Applied Optics. Wiley & Sons, Hoboken, New Jersey, p.11. [doi:10.1002/9780470618 943]

    Book  Google Scholar 

  • Ma, X., Arce, G.R., 2011. Pixel-based OPC optimization based on conjugate gradient. Opt. Expr., 19(3):2165–2180. [doi:10.1364/OE.19.002165]

    Article  Google Scholar 

  • Ma, X., Li, Y.Q., 2011. Resolution enhancement optimization methods in optical lithography with improved manufacturability. J. Micro/Nanolith. MEMS MOEMS, 10(2): 023009. [doi:10.1117/1.3590252]

    Article  Google Scholar 

  • Ma, X., Li, Y.Q., Dong, L.S., 2012a. Mask optimization approaches in optical lithography based on a vector imaging model. J. Opt. Soc. Am. A, 29(7):1300–1312. [doi:10.1364/JOSAA.29.001300]

    Article  Google Scholar 

  • Ma, X., Li, Y.Q., Guo, X.J., Dong, L.S., Arce, G.R., 2012b. Vectorial mask optimization methods for robust optical lithography. J. Micro/Nanolith. MEMS MOEMS, 11(4): 043008. [doi:10.1117/1.JMM.11.4.043008]

    Article  Google Scholar 

  • Marquina, A., Osher, S., 2000. Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM J. Sci. Comput., 22(2):387–405. [doi:10.1137/S1064827599351751]

    Article  MathSciNet  MATH  Google Scholar 

  • Osher, S., Sethian, J.A., 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys., 79(1):12–49. [doi:10.1016/0021-9991(88)90002-2]

    Article  MathSciNet  MATH  Google Scholar 

  • Pang, L.Y., Dai, G., Cecil, T., Dam, T., Cui, Y., Hu, P., Chen, D., Baik, K., Peng, D., 2008. Validation of inverse lithography technology (ILT) and its adaptive SRAF at advanced technology nodes. SPIE, 6924:69240T. [doi:10.1117/12.775084]

    Article  Google Scholar 

  • Poonawala, A., Milanfar, P., 2007a. Mask design for optical microlithography—an inverse imaging problem. IEEE Trans. Image Process., 16(3):774–788. [doi:10.1109/TIP.2006.891332]

    Article  MathSciNet  Google Scholar 

  • Poonawala, A., Milanfar, P., 2007b. A pixel-based regularization approach to inverse lithography. Microelectron. Eng., 84(12):2837–2852. [doi:10.1016/j.mee.2007.02.005]

    Article  Google Scholar 

  • Santosa, F., 1996. A level-set approach for inverse problems involving obstacles. ESAIM Control Optim. Calcul. Var., 1:17–33. [doi:10.1051/cocv:1996101]

    Article  MathSciNet  MATH  Google Scholar 

  • Schellenberg, F.M., 2004. Resolution enhancement technology: the past, the present, and extensions for the future. SPIE, 5377. [doi:10.1117/12.548923]

  • Shen, S.H., Yu, P., Pan, D.Z., 2008. Enhanced DCT2-based inverse mask synthesis with initial SRAF insertion. SPIE, 7122:712241. [doi:10.1117/12.801409]

    Article  Google Scholar 

  • Shen, Y.J., Wong, N., Lam, E.Y., 2009. Level-set-based inverse lithography for photomask synthesis. Opt. Expr., 17(26): 23690–23701. [doi:10.1364/OE.17.023690]

    Article  Google Scholar 

  • Shen, Y.J., Wong, N., Lam, E.Y., 2010. Aberration-aware robust mask design with level-set-based inverse lithography. SPIE, 7748:77481U. [doi:10.1117/12.863973]

    Article  Google Scholar 

  • Wong, A.K.K., 2001. Resolution Enhancement Techniques in Optical Lithography. SPIE Press, Bellingham, Washington, USA, p.28. [doi:10.1117/3.401208]

    Book  Google Scholar 

  • Wong, B.P., Zach, F., Moroz, V., Mittal, A., Starr, G.W., Kahng, A., 2009. Nano-CMOS Design for Manufacturability Robust Circuit and Physical Design for Sub-65nm Technology Nodes. John Wiley & Sons, Inc., Hoboken, New Jersey, p.27.

  • Yu, J.C., Yu, P.C., 2010. Impacts of cost functions on inverse lithography patterning. Opt. Expr., 18(22):23331–23342. [doi:10.1364/OE.18.023331]

    Article  Google Scholar 

  • Yu, P., Pan, D.Z., 2007. TIP-OPC: a New Topological Invariant Paradigm for Pixel Based Optical Proximity Correction. Proc. IEEE/ACM Int. Conf. on Computer-Aided Design, p.847–853. [doi:10.1109/ICCAD.2007.4397370]

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhen Geng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Geng, Z., Shi, Z., Yan, Xl. et al. Regularized level-set-based inverse lithography algorithm for IC mask synthesis. J. Zhejiang Univ. - Sci. C 14, 799–807 (2013). https://doi.org/10.1631/jzus.C1300050

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.C1300050

Key words

CLC number

Navigation