Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

[1]  P. Jedrasik.  Neural networks application for OPC (optical proximity correction) in mask making , 1996 .

[2]  Edmund Y. Lam,et al.  Inverse image problem of designing phase shifting masks in optical lithography , 2008, 2008 15th IEEE International Conference on Image Processing.

[3]  Linyong Pang,et al.  Inverse lithography technology principles in practice: unintuitive patterns , 2005, SPIE Photomask Technology.

[4]  Yuri Granik,et al.  Solving inverse problems of optical microlithography , 2005, SPIE Advanced Lithography.

[5]  A. Zakhor,et al.  Optical Proximity Correction With Linear Regression , 2008, IEEE Transactions on Semiconductor Manufacturing.

[6]  Stanley H. Chan,et al.  Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography. , 2008, Optics express.

[7]  Yuri Granik,et al.  OPC methods to improve image slope and process window , 2003, SPIE Advanced Lithography.

[8]  George D. Magoulas,et al.  Learning Rate Adaptation in Stochastic Gradient Descent , 2001 .

[9]  Ethem Alpaydin,et al.  Introduction to machine learning , 2004, Adaptive computation and machine learning.

[10]  Zhiping Yu,et al.  A highly efficient optimization algorithm for pixel manipulation in inverse lithography technique , 2008, ICCAD 2008.

[11]  Thomas Kailath,et al.  Phase-shifting masks for microlithography: automated design and mask requirements , 1994 .

[12]  Linyong Pang,et al.  Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45-nm and 32-nm , 2007, Photomask Japan.

[13]  Edmund Y. Lam,et al.  Computation lithography: virtual reality and virtual virtuality. , 2009, Optics express.

[14]  Avideh Zakhor,et al.  Binary and phase shifting mask design for optical lithography , 1992 .

[15]  Alfred Kwok-Kit Wong,et al.  Resolution enhancement techniques in optical lithography , 2001 .

[16]  Akira Kawai,et al.  Durability of self-standing resist sheet composed with micro holes , 2009, Lithography Asia.

[17]  Peyman Milanfar,et al.  Double-exposure mask synthesis using inverse lithography , 2007 .

[18]  Bahaa E. A. Saleh,et al.  Binary image synthesis using mixed linear integer programming , 1995, IEEE Trans. Image Process..

[19]  Edmund Y. Lam,et al.  Regularization of inverse photomask synthesis to enhance manufacturability , 2009, Lithography Asia.

[20]  Andreas Erdmann,et al.  Toward automatic mask and source optimization for optical lithography , 2004, SPIE Advanced Lithography.

[21]  Avideh Zakhor,et al.  Optimal binary image design for optical lithography , 1990, Advanced Lithography.

[22]  L. Bottou.  Stochastic Gradient Learning in Neural Networks , 1991 .

[23]  David Z. Pan,et al.  Machine learning based lithographic hotspot detection with critical-feature extraction and classification , 2009, 2009 IEEE International Conference on IC Design and Technology.

[24]  Gonzalo R. Arce,et al.  Generalized inverse lithography methods for phase-shifting mask design , 2007 .

[25]  Ngai Wong,et al.  Level-set-based inverse lithography for photomask synthesis. , 2009, Optics express.

[26]  Y. Granik,et al.  Considerations for the use of defocus models for OPC , 2005, SPIE Advanced Lithography.

[27]  David Z. Pan,et al.  True process variation aware optical proximity correction with variational lithography modeling and model calibration , 2007 .

[28]  Frank Liu,et al.  Predicting variability in nanoscale lithography processes , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[29]  Edward A. Rietman,et al.  Neural network proximity effect corrections for electron beam lithography , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[30]  Qi-De Qian,et al.  Focus latitude optimization for model-based OPC , 2003, SPIE Photomask Technology.

[31]  Kevin Lucas,et al.  Process variation aware OPC modeling for leading edge technology nodes , 2009, Advanced Lithography.

[32]  Amyn Poonawala,et al.  Mask Design for Optical Microlithography—An Inverse Imaging Problem , 2007, IEEE Transactions on Image Processing.

[33]  James C. Spall,et al.  Introduction to Stochastic Search and Optimization. Estimation, Simulation, and Control (Spall, J.C. , 2007 .