Gaussian random field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics

Latypov, Azat; Khaira, Gurdaman; Fenger, Germain; Wang, Shuling; Chew, Marko; Shang, Shumay

doi:10.1117/12.2583792

Cited by 9 publications

(29 citation statements)

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“…EUV stochastic model based on Gaussian Random Field deprotection 4,5 are reviewed, and the idea of Importance Sampling methods is presented. The approaches and challenges of applications of Importance Sampling methods to experimental measurements are discussed.…”

Section: Conclusion and Acknowledgementsmentioning

confidence: 99%

“…Quantification of variability of EUVL-patterned vias caused by EUV exposure and resist stochastic phenomena has been the subject of a significant interest among EUV lithographers in the past decades [1][2][3][4][5][6][7][8] . The obvious motivation for such an interest is the need to reduce this variability by properly tuning the EUVL process or using the optimization techniques of OPC and SMO.…”

Section: Introductionmentioning

confidence: 99%

“…Computational estimation of failure probability or other stochastic metrics in more generic cases may require the use of Monte Carlo trials. The introduction of the Gaussian Random Field (GRF) deprotection stochastic EUVL model 4,5 allows to reduce the set of pixels or voxels involved in such Monte Carlo trials only to pixels/voxels participating in the definition of the assessed failure or the stochastic metrics, resulting in Fast Methods 4 based on factorization of the covariance matrix of the GRF deprotection.…”

Section: Introductionmentioning

confidence: 99%

“…The absorption of these photons results in the generation of a certain deprotection, modeling 4,5 the photo-chemical processes triggered by the absorption of these photons:…”

Section: Introductionmentioning

confidence: 99%

“…If the mean number of absorbed photons, h N  , is sufficiently large, the deprotection random field, () n x , is well approximated 4 by Gaussian Random Field (GRF) with the mean and covariance functions given by ( 4)- (5), by virtue of the Central Limit Theorem. Typical EUV doses result in a sufficiently high number of absorbed photons to ensure a good accuracy of estimates for failure probability or other stochastic metrics obtained from the GRF deprotection model 4,5 .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Importance sampling in Gaussian random field EUV stochastic model for quantification of stochastic variability of EUV vias

Pan

Latypov

Wei

et al. 2023

Optical and EUV Nanolithography XXXVI

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Importance Sampling methods allow to substantially reduce the number of trials in estimation of the rare failure probability or other stochastic metrics. These methods can be viewed as a rigorous generalization of quantitative "torture" or "stress" methods where the process is artificially modified to increase the probability of failure, and the failure probability estimations obtained for such modified process are extrapolated to the original process with rare failures. Applications of Importance Sampling methods are presented and demonstrated on computationally efficient estimations of via failure probability and via LCDU. The accuracy of the Importance Sampling LCDU estimates is verified by comparison with experimental results. Applications of Importance Sampling methods to experimental measurements are discussed.

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Section: Conclusion and Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The absorption of these photons results in the generation of a certain deprotection, modeling 4,5 the photo-chemical processes triggered by the absorption of these photons:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Importance sampling in Gaussian random field EUV stochastic model for quantification of stochastic variability of EUV vias

Pan

Latypov

Wei

et al. 2023

Optical and EUV Nanolithography XXXVI

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Stochastic hotspots in extreme ultraviolet exposed nano-patterns as correlated molecular sub-cluster formation probabilities

Fukuda

2023

Journal of Applied Physics

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Stochastic pattern anomalies limit the shrinking of the size of nano-patterns in extreme-ultraviolet lithography at around 10 nm due to the discrete/probabilistic nature of photon–electron-reaction systems. We express the patterns and their anomalies as probability distributions and predict stochastic hotspots where the anomaly generation probabilities rise unexpectedly in arbitrary pattern features. Three-dimensional chemo-physical event distributions in pattern-exposed resist films are calculated by the fully coupled first-principles Monte Carlo simulation combined with the discrete development/etching models. The aggregates of molecular level solubility flipping (sub-cluster) well express spatial correlations in the observed anomalies. Spatial correlation in sub-cluster generation is not scaled and their impact increases with shrinking patterns. The correlation is squeezed near the pattern edge, inducing edge placement error, and it spreads in the areas between edges causing stochastic pattern defects. For materials with sub-cluster size not negligible compared to image size, the stochastic hotspots appear when the correlated area spreads in areas far from the edges adjacent to the higher probability region. Deep neural networks successfully predict the probability distributions of sub-clusters and anomaly generation in arbitrary pattern features without the Monte Carlo method.

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Applications of large field of view e-beam metrology to contour-based optical proximity correction modeling

Wei,

Kang,

Das

et al. 2023

J. Micro/Nanopattern. Mats. Metro.

Self Cite

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.BackgroundFor complex two-dimensional (2D) patterns, optical proximity correction (OPC) model calibration flows cannot always satisfy accuracy requirements with the standard cutline-based input data. Utilizing after-development inspection e-beam metrology image contours, better model predictions of 2D shapes and wafer hotspots can be realized.AimWe compare model accuracy performance of conventional cutline-based and contour-based OPC models on the regular and hotspots patterns.ApproachBy utilizing image contours that are directly extracted from large field of view (LFoV) e-beam metrology, OPC models were calibrated and verified with both cutline-based and contour-based modeling flows. We also used a wafer sampling plan that contained bridging hotspots. Using that sampling plan, a hotspot-aware three-dimentional resist (R3D) compact model was created.ResultsFirst, a contour-based OPC model was generated with <1 nm root mean square error of contour sites. Compared with cutline-based models, it shows better predictions on 2D feature corners. Second, when combined with a hotspot sampling plan, a hotspot-aware compact model could be generated. The accuracy of hotspot predictions on false positives and false negatives was reduced to around 1% with this approach.ConclusionsOPC model calibration and verification with LFoV image contours provide improved predictions on corner rounding shapes and great potential to increase design space coverage. We also observed improved accuracy of hotspot predictions when using an update hotspot aware model when comparing with that of the OPC model. Furthermore, the combination of R3D and stochastic compact models also demonstrated great potential on predictions of rare wafer failure events.

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Gaussian random field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics

Cited by 9 publications

References 0 publications

Importance sampling in Gaussian random field EUV stochastic model for quantification of stochastic variability of EUV vias

Importance sampling in Gaussian random field EUV stochastic model for quantification of stochastic variability of EUV vias

Stochastic hotspots in extreme ultraviolet exposed nano-patterns as correlated molecular sub-cluster formation probabilities

Applications of large field of view e-beam metrology to contour-based optical proximity correction modeling

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