Model-driven convolution neural network for inverse lithography.

Optical lithography is a fundamental process to fabricate integrated circuits, which are the basic fabric of the information age. Due to image distortions inherent in optical lithography, inverse lithography techniques (ILT) are extensively used by the semiconductor industry to improve lithography image resolution and fidelity in semiconductor fabrication. As the density of integrated circuits increases, computational complexity has become a central challenge in ILT methods. This paper develops a new and powerful framework of a model-driven convolution neural network (MCNN) to obtain the approximate guess of the ILT solutions, which can be used as the input of the following ILT optimization with much fewer iterations as compared with conventional ILT algorithms. The combined approach to use the proposed MCNN together with the gradient-based method can improve the speed of ILT optimization algorithms up to an order of magnitude and further improve the imaging performance of coherent optical lithography systems. This paper, to the best of our knowledge, is the first to exploit a state-of-the-art MCNN to solve the ILT problem and provide considerable performance advantages. The imaging model of optical lithography is utilized to establish a neural network architecture and an unsupervised training strategy. The neural network architecture and the initial network parameters are derived by unfolding and truncating the model-based iterative ILT optimization procedure. Then, a model-based decoder is proposed to enable the unsupervised training of the neural network, which averts the time-consuming labelling process in training data. This work opens a new window for MCNN techniques to effectively improve the computational efficiency and imaging performance of conventional ILT algorithms. Some impressive good simulation results are provided to verify the superiority of the proposed MCNN approach.

[1]  Xu Ma,et al.  Pixel-based OPC optimization based on conjugate gradients. , 2011, Optics express.

[2]  Peyman Milanfar,et al.  OPC and PSM design using inverse lithography: a nonlinear optimization approach , 2006, SPIE Advanced Lithography.

[3]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[4]  Y. Liu,et al.  Manufacturability study of masks created by inverse lithography technology (ILT) , 2005, SPIE Photomask Technology.

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

[6]  Edmund Y. Lam,et al.  Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis , 2010 .

[7]  Edmund Y Lam,et al.  Robust and efficient inverse mask synthesis with basis function representation. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[9]  Rui Luo,et al.  Optical proximity correction using a multilayer perceptron neural network , 2013 .

[10]  Gonzalo R. Arce,et al.  Binary mask optimization for inverse lithography with partially coherent illumination , 2008 .

[11]  H. Hopkins.  On the diffraction theory of optical images , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  Yanqiu Li,et al.  Mask optimization approaches in optical lithography based on a vector imaging model. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  Gerald Penn,et al.  Convolutional Neural Networks for Speech Recognition , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[14]  H. H. Hopkins,et al.  The concept of partial coherence in optics , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[15]  Amyn Poonawala,et al.  Model-based assist feature placement for 32nm and 22nm technology nodes using inverse mask technology , 2009, Photomask Technology.

[16]  Ngai Wong,et al.  Robust level-set-based inverse lithography. , 2011, Optics express.

[17]  Yanqiu Li,et al.  Block-based mask optimization for optical lithography. , 2013, Applied optics.

[18]  Yanqiu Li,et al.  Optimal 3D phase-shifting masks in partially coherent illumination. , 2011, Applied optics.

[19]  E. Lam,et al.  Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step , 2013 .

[20]  Yanqiu Li,et al.  A fast and manufacture-friendly optical proximity correction based on machine learning , 2017 .

[21]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[22]  Yanqiu Li,et al.  Fast pixel-based optical proximity correction based on nonparametric kernel regression , 2014 .

[23]  Jue-Chin Yu,et al.  Impacts of cost functions on inverse lithography patterning. , 2010, Optics express.

[24]  Guillermo Sapiro,et al.  Learning Efficient Sparse and Low Rank Models , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Ah Chung Tsoi,et al.  Face recognition: a convolutional neural-network approach , 1997, IEEE Trans. Neural Networks.

[26]  Yuri Granik,et al.  Dense OPC for 65nm and below , 2005, SPIE Photomask Technology.

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

[28]  Xiaolang Yan,et al.  SVM based layout retargeting for fast and regularized inverse lithography , 2014, Journal of Zhejiang University SCIENCE C.

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