Lithographic stochastics: beyond 3σ

Bristol, Robert; Krysak, Marie

doi:10.1117/1.jmm.16.2.023505

Cited by 23 publications

(8 citation statements)

References 6 publications

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“…It was reported that CD histograms often deviate from the normal distribution and show exponential or multiple Gaussian distributions in their tails, 3,5,7 and its relation to image profiles has also been pointed out. 11 This is observed also in our results [ Fig. 3(a)].…”

Section: Resultssupporting

confidence: 91%

Estimating extremely low probability of stochastic defect in extreme ultraviolet lithography from critical dimension distribution measurement

Fukuda

Momonoi

Sakai

2019

J. Micro/Nanolith. MEMS MOEMS

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Projection lithography using extreme ultraviolet (EUV) light at 13.5-nm wavelength will be applied to the production of integrated circuits below 7-nm design rules. In pursuit of further miniaturization, however, stochastic pattern defect problems have arisen, and monitoring such defect generation probabilities in extremely low range (<10 −10) is indispensable. We discuss a method for predicting stochastic defect probabilities from a histogram of feature sizes for patterns several orders of magnitude fewer than the number of features to inspect. Based on our previously introduced probabilistic model of stochastic pattern defect, the defect probability is expressed as the product sum of the probability for edge position and the probability that film defect covers the area between edges, and we describe the latter as a function of edge position. The defect probabilities in the order between 10 −7 and 10 −5 were predicted from 10 5 measurement data for real EUV-exposed wafers, suggesting the effectiveness of the model and its potential for defect inspection.

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Section: Resultssupporting

confidence: 91%

Estimating extremely low probability of stochastic defect in extreme ultraviolet lithography from critical dimension distribution measurement

Fukuda

Momonoi

Sakai

2019

J. Micro/Nanolith. MEMS MOEMS

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“…Bristol and Krysak 6 have evaluated the issues associated with counting statistics and EUV lithography in some detail. They observe that, with integrated circuits of leading edge design containing populations of up to one trillion features, we can expect to find multiple occurrences where the photon, PAG, or quencher count in a feature deviates from its median value by seven standard deviations (7σ).…”

Section: Counting Statisticsmentioning

confidence: 99%

Contribution of EUV resist counting statistics to stochastic printing failures

Hinsberg

Wallraff

Sanchez

et al. 2021

J. Micro/Nanopattern. Mats. Metro.

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Background: Stochastic printing failures, manifested as random defects in a patterned photoresist image, result from statistical fluctuations in photon flux and resist components and are a key issue confronting extreme ultraviolet (EUV) lithography. Empirical data indicate that photoresist composition and processing influence stochastic printing failure rates. Aim: To devise a simple and flexible model framework for assessing how changes in photoresist composition and imaging chemistry can be expected to impact the frequency of stochastic printing failures Approach: A simple physicochemical description based solely on resist component and photon statistics is combined with combinatorial calculations of resist imaging chemistry and Monte Carlo analysis to estimate rates of random printing failures. Results: This model yields results consistent with experimental observations. The method is applied to predict impacts of resist formulation, composition, and process changes on the rates of stochastic printing failures. Conclusions: This approach provides rapid assessment of the relative impact of resist materials and process modifications and is useful as a tool to advance EUV photoresist design.

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“…Today, shot noise is widely recognized as a serious problem when printing near the resolution limit of extreme ultraviolet (EUV) lithography. 21,22 But the concept of shot noise as a limiter to lithographic performance is not new to EUV. In the 1970s, x-ray lithography was considered a potential successor to optical lithography.…”

Section: Shot Noise In Lithographymentioning

confidence: 99%

“…More recently, the reduction in exposure latitude for undersized contacts has been added to O'Brien and Mason's model, predicting a much higher probability of contact hole failure. 21 These models, while calibrated with experimental data, must still be extrapolated very far along the tail of a probability distribution. 22 Even if the critical dimension distribution of a million contacts was measured, it is still very hard to accurately predict the expected number of failures for 100 billion contacts.…”

Section: Shot Noise In Lithographymentioning

confidence: 99%

Shot noise: a 100-year history, with applications to lithography

Mack¹

2018

J. Micro/Nanolith. MEMS MOEMS

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The term "shot effect" (schroteffekt) was coined in 1918 when Walter Schottky studied electrical noise in vacuum tubes. Earlier still, the foundations of shot noise theory go back to Einstein, who in 1905 explained the photoelectric effect as caused by discrete "particles" of light and Brownian motion as caused by discrete particles of matter. When the numbers of particles that affect observable outcomes are large, shot noise effects (variability in number as a fraction of the mean number) become small, and the continuum approximation (energy and matter are continuous) becomes accurate. For most of the history of semiconductor lithography, the continuum approximation has served well. But at small dimensional scales, where the number of discrete particles or events is small, the counting statistics of shot noise can dominate. The 100-year history of shot noise in science and engineering is today playing a role in our understanding of shot noise in lithography.

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Lithographic stochastics: beyond 3σ

Cited by 23 publications

References 6 publications

Estimating extremely low probability of stochastic defect in extreme ultraviolet lithography from critical dimension distribution measurement

Estimating extremely low probability of stochastic defect in extreme ultraviolet lithography from critical dimension distribution measurement

Contribution of EUV resist counting statistics to stochastic printing failures

Shot noise: a 100-year history, with applications to lithography

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