High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmos...High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmost zone-width is shrinking down to 50 nm or even below,patterning the zone plates with high aspect ratio by electron beam lithography still remains a challenge because of the proximity effect.The uneven charge distribution in the exposed resist is still frequently observed even after standard proximity effect correction(PEC),because of the large variety in the line width.This work develops a new strategy,nicknamed as local proximity effect correction(LPEC),efficiently modifying the deposited energy over the whole zone plate on the top of proximity effect correction.By this way,50 nm zone plates with the aspect ratio from 4:1 up to 15:1 and the duty cycle close to 0.5 have been fabricated.Their imaging capability in soft(1.3 keV)and hard(9 keV)x-ray,respectively,has been demonstrated in Shanghai Synchrotron Radiation Facility(SSRF)with the resolution of 50 nm.The local proximity effect correction developed in this work should also be generally significant for the generation of zone plates with high resolutions beyond 50 nm.展开更多
The shrinking of the size of the advanced technological nodes brings up new challenges to the semiconductor manufacturing community.The optical proximity correction(OPC)is invented to reduce the errors of the lithogra...The shrinking of the size of the advanced technological nodes brings up new challenges to the semiconductor manufacturing community.The optical proximity correction(OPC)is invented to reduce the errors of the lithographic process.The conventional OPC techniques rely on the empirical models and optimization methods of iterative type.Both the accuracy and computing speed of the existing OPC techniques need to be improved to fulfill the stringent requirement of the research and design for latest technological nodes.The emergence of machine learning technologies inspires novel OPC algorithms.More accurate forward simulation of the lithographic process and single turn optimization methods are enabled by the machine learning based OPC techniques.We discuss the latest progress made by the OPC community in the process simulation and optimization based on machine learning techniques.展开更多
In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The p...In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.展开更多
Optical proximity correction (OPC) is a key step in modern integrated circuit (IC) manufacturing.The quality of model-based OPC (MB-OPC) is directly determined by segment offsets after OPC processing.However,in conven...Optical proximity correction (OPC) is a key step in modern integrated circuit (IC) manufacturing.The quality of model-based OPC (MB-OPC) is directly determined by segment offsets after OPC processing.However,in conventional MB-OPC,the intensity of a control site is adjusted only by the movement of its corresponding segment;this scheme is no longer accurate enough as the lithography process advances.On the other hand,matrix MB-OPC is too time-consuming to become practical.In this paper,we propose a new sparse matrix MB-OPC algorithm with model-based mapping between segments and control sites.We put forward the concept of 'sensitive area'.When the Jacobian matrix used in the matrix MB-OPC is evaluated,only the elements that correspond to the segments in the sensitive area of every control site need to be calculated,while the others can be set to 0.The new algorithm can effectively improve the sparsity of the Jacobian matrix,and hence reduce the computations.Both theoretical analysis and experiments show that the sparse matrix MB-OPC with model-based mapping is more accurate than conventional MB-OPC,and much faster than matrix MB-OPC while maintaining high accuracy.展开更多
Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximat...Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as predic- tion-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm I; in the same way, Algorithm II is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm II usually outperforms Algorithm I. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm II to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some nu- merical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.U1732104)China Postdoctoral Science Foundation(Grant No.2017M611443)Shanghai STCSM2019-11-20 Grant,China(Grant No.19142202700)。
文摘High resolution Fresnel zone plates for nanoscale three-dimensional imaging of materials by both soft and hard x-rays are increasingly needed by the broad applications in nanoscience and nanotechnology.When the outmost zone-width is shrinking down to 50 nm or even below,patterning the zone plates with high aspect ratio by electron beam lithography still remains a challenge because of the proximity effect.The uneven charge distribution in the exposed resist is still frequently observed even after standard proximity effect correction(PEC),because of the large variety in the line width.This work develops a new strategy,nicknamed as local proximity effect correction(LPEC),efficiently modifying the deposited energy over the whole zone plate on the top of proximity effect correction.By this way,50 nm zone plates with the aspect ratio from 4:1 up to 15:1 and the duty cycle close to 0.5 have been fabricated.Their imaging capability in soft(1.3 keV)and hard(9 keV)x-ray,respectively,has been demonstrated in Shanghai Synchrotron Radiation Facility(SSRF)with the resolution of 50 nm.The local proximity effect correction developed in this work should also be generally significant for the generation of zone plates with high resolutions beyond 50 nm.
基金by National Science and Technology Major Project of China(2017ZX02315001-003,2017ZX02101004-003)National Natural Science Foundation of China(61874002,61804174),Beijing Natural Fund(4182021).
文摘The shrinking of the size of the advanced technological nodes brings up new challenges to the semiconductor manufacturing community.The optical proximity correction(OPC)is invented to reduce the errors of the lithographic process.The conventional OPC techniques rely on the empirical models and optimization methods of iterative type.Both the accuracy and computing speed of the existing OPC techniques need to be improved to fulfill the stringent requirement of the research and design for latest technological nodes.The emergence of machine learning technologies inspires novel OPC algorithms.More accurate forward simulation of the lithographic process and single turn optimization methods are enabled by the machine learning based OPC techniques.We discuss the latest progress made by the OPC community in the process simulation and optimization based on machine learning techniques.
基金The author was supported by NSFC Grant 10271054MOEC grant 20020284027 and Jiangsur NSF grant BK20002075.
文摘In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.
文摘Optical proximity correction (OPC) is a key step in modern integrated circuit (IC) manufacturing.The quality of model-based OPC (MB-OPC) is directly determined by segment offsets after OPC processing.However,in conventional MB-OPC,the intensity of a control site is adjusted only by the movement of its corresponding segment;this scheme is no longer accurate enough as the lithography process advances.On the other hand,matrix MB-OPC is too time-consuming to become practical.In this paper,we propose a new sparse matrix MB-OPC algorithm with model-based mapping between segments and control sites.We put forward the concept of 'sensitive area'.When the Jacobian matrix used in the matrix MB-OPC is evaluated,only the elements that correspond to the segments in the sensitive area of every control site need to be calculated,while the others can be set to 0.The new algorithm can effectively improve the sparsity of the Jacobian matrix,and hence reduce the computations.Both theoretical analysis and experiments show that the sparse matrix MB-OPC with model-based mapping is more accurate than conventional MB-OPC,and much faster than matrix MB-OPC while maintaining high accuracy.
基金Project (No. 1027054) supported by the National Natural Science Foundation of China
文摘Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as predic- tion-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm I; in the same way, Algorithm II is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm II usually outperforms Algorithm I. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm II to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some nu- merical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.
