Probability prediction of EUV process failure due to resist-exposure stochastic: applications of Gaussian random fields excursions and Rice's formula

Latypov, Azat; Khaira, Gurdaman; Fenger, Germain; Sturtevant, John L.; Wei, Chih-I; Bisschop, Peter De

doi:10.1117/12.2551965

Cited by 9 publications

(40 citation statements)

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“…The probabilistic feature formation in our work is somewhat closely related to former works in [4,5]. However, our work elaborates discussions in those works with the detailed quantum mechanical acid generation and rather refined statistical analysis.…”

Section: Introductionsupporting

confidence: 60%

“…The probabilistic nature of the deprotection density reveals the relation between the expectation of the deprotection and the resist image intensity of the convolution imaging. Also, the explicit form of the deprotection density allows us the asymptotic analysis at the large absorption condition, which refines the works in [4,5]. In a typical lithography process, the large absorption condition can be achieved by enlarging the exposed area of interest, the asymptotic analysis can be thus taken to construct a simulation model for the quantum fluctuation in the patterning process.…”

Section: Discussionmentioning

confidence: 56%

“…By using probabilistic acid generation, we have constructed the probabilistic description of the deprotection density in the photoresist, which has been noticed by [4,5]. The probabilistic nature of the deprotection density reveals the relation between the expectation of the deprotection and the resist image intensity of the convolution imaging.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, by approximating the deprotection blur κ = E d 4 xη × E d 4 yρ 2 D (y) to be constant, we may write the asymptotic formula as ρ D,total x, t f ∼ N i resist x, t f , κi aerial x, t f so that κ is fit by the measurement under the given resist image intensity and aerial intensity computed by a conventional simulation model. This simulation model is conceptually somewhat similar to the work in [5], but has a relatively simple formula in its construction.…”

Section: Discussionmentioning

confidence: 99%

“…In the patterning process, a pixel for a feature on a photoresist is formed if the density of deprotected polymer exceeds a certain threshold τ at the development process [4,5]. Thus, the probability for the generation of a pixel at a given position x is given by…”

Section: Probabilistic Feature Formationmentioning

confidence: 99%

See 4 more Smart Citations

Quantum electrodynamical formulation of photochemical acid generation and its implications on optical lithography

Lee

2021

Preprint

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The photochemical acid generation is refined from the very first principles of elementary particle physics. We first briefly review the formulation of the quantum theory of light based on the quantum electrodynamics framework to establish the probability for acid generation at a given spacetime point. The quantum mechanical acid generation is then combined with the deprotection mechanism to obtain the probabilistic description of the deprotection density, directly related to the feature formation in a photoresist. A statistical analysis of the random deprotection density is presented to reveal the leading characteristics of stochastic feature formation.

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Section: Introductionsupporting

confidence: 60%

Section: Discussionmentioning

confidence: 56%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Probabilistic Feature Formationmentioning

confidence: 99%

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Quantum electrodynamical formulation of photochemical acid generation and its implications on optical lithography

Lee

2021

Preprint

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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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Compact modeling of stochastics and application in OPC

Gillijns

Lee

Kim

et al. 2023

Optical and EUV Nanolithography XXXVI

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To maintain good critical dimension control, optical proximity correction (OPC) has relied on fast compact models to capture the underlying lithography process in advanced nodes. Compact models have always been deterministic in the sense that they predict the average dimensions or contours on wafer. With the introduction of extreme ultraviolet (EUV) lithography, this approach breaks down due to large variabilities in EUV lithography processes. Recently, empirical correlations were found between this variability and imaging metrics, allowing the development of compact models. Such stochastic models have been used successfully to predict hotspots. In this paper an attempt is made to apply such stochastic models during OPC to reduce the number of stochastic failures. Different OPC strategies are applied on an advanced random logic and SRAM design, focusing on a via layer with a calibrated stochastic model. Through simulations, we show that the failure rate can be reduced by using a stochastic model during OPC, at the expense of edge placement error. However, when reducing the stochastic band width to match the process variation band width, no meaningful differences were observed between process-window OPC and stochastic OPC due to uniformity of pattern dimensions in sample layout.

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Probability prediction of EUV process failure due to resist-exposure stochastic: applications of Gaussian random fields excursions and Rice's formula

Cited by 9 publications

References 0 publications

Quantum electrodynamical formulation of photochemical acid generation and its implications on optical lithography

Quantum electrodynamical formulation of photochemical acid generation and its implications on optical lithography

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

Compact modeling of stochastics and application in OPC

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