Spectral analysis of line edge and line-width roughness with long-range correlation

Hiraiwa, Atsushi; Nishida, Akio

doi:10.1063/1.3466777

Cited by 20 publications

(11 citation statements)

References 34 publications

(59 reference statements)

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“…To extract the noise level of the CD-SEM, we have recently developed a method, 13 based on the PSD fitting method proposed by Hiraiwa et al 10,11,14,15 It consists of acquiring a large set of CD-SEM images (N Ã ) of a line in order to calculate a PSD (PSD) of the line LWR. The final PSD is the average of the N Ã calculated PSD.…”

Section: Lwr Characterizationmentioning

confidence: 99%

Plasma treatments to improve line-width roughness during gate patterning

Azarnouche

Pargon²,

Menguelti³

et al. 2013

J. Micro/Nanolith. MEMS MOEMS

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The major issue related to line width roughness (LWR) is the significant LWR of the photoresist patterns printed by 193-nm lithography that is partially transferred into the gate stack during the subsequent plasma etching steps. The strategy used today to overcome this issue is to apply postlithography treatments to reduce photoresist pattern LWR before transfer. In this article, we investigate the impact of various plasma treatments (HBr, H 2 , He, Ar) on the minimization of the LWR of dense and isolated photoresist patterns and its transfer during gate patterning. To do so, we use critical dimension scanning electron microscopy measurements combined with power spectrum density fitting method to extract unbiased LWR values and provide a spectral analysis of the LWR. We show that plasma treatments that lead to carbon redeposition from the gas phase on the resist pattern sidewalls are less efficient to reduce LWR than plasma treatments where the redeposition is limited. Among all plasma chemistries, H 2 plasmas seem very promising to decrease resist LWR in the whole spectral range, while maintaining square resist profiles. In addition, we show that all frequency roughness components are not equally transferred during gate patterning, and more particularly that the high frequency roughness components are lost.

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Section: Lwr Characterizationmentioning

confidence: 99%

Plasma treatments to improve line-width roughness during gate patterning

Azarnouche

Pargon²,

Menguelti³

et al. 2013

J. Micro/Nanolith. MEMS MOEMS

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show abstract

“…[12][13][14][15] In this study we investigated the latter, because the former is not suitable for analyzing multi-component LWR 16) such as that observed in our samples. 17) In the analyses using the PSD, we usually fit theoretical PSDs to an experimental one and estimate LWR statistics as the values used in the best fitting. The problem with previous PSD methods was that the theoretical PSDs were calculated using a formula that was derived by assuming widths obtained continuously with infinitely long lines.…”

Section: Introductionmentioning

confidence: 99%

“…The formula has been further revised to permit a long correlation length, well beyond the conventional analysis limit. 17) Although our methods accurately analyze the LER/LWR of photoresist lines, they cannot be applied to actual patterns, which are formed through processing steps, such as plasma etching, that introduce a smoothing effect. [18][19][20][21] The purpose of this work is to provide a method for analyzing the smoothed LWRs on the basis of the aforementioned discrete PSD method.…”

Section: Introductionmentioning

confidence: 99%

Power Spectrum of Smoothed Line-Edge and Line-Width Roughness

Hiraiwa

Nishida

2011

Jpn. J. Appl. Phys.

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Line-edge and line-width roughness (LER and LWR) is a challenge for device variability control, especially in future devices. Actual device patterns have LER/LWR that is smoothed from the original photoresist patterns used as etching masks. In this study, the LER/LWR of these actual patterns was assumed to have a modified exponential autocorrelation function, which was smoothed by another exponential function. An analytical formula of the discrete power spectral density (PSD) of this LER/LWR was derived on the basis of the previous formula for non-smoothed LER/LWR, for use in a PSD fitting method. The PSDs calculated using this formula excellently fit the experimental PSDs of both types of polycrystalline-silicon lines without and with sidewall spacers. Through these fittings, it was found that the actual LER/LWR is accurately characterized using the variance and correlation length of the original non-smoothed LER/LWR simply by introducing a third parameter that characterizes the smoothing effect.

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“…Note that the actual PSD is achieved when N approaches infinity and the expected value can be obtained accurately. In real world cases, the number of real measurement samples is finite hence averaging PSD over many trials is necessary to more accurately estimate the underlying physical process: 29 , 30 PSD(f)=limN→inf (Δd)2(2N+1)Δd|∑n=−NNxne−i2πfnΔd|2.…”

Section: Results and Analysismentioning

confidence: 99%

“…(14) 31 – 33 σintrinsic refers to the stochasticity of LER profiles caused by process variation, σmetrology is the measurement uncertainty introduced by metrology algorithm and in our case influenced by IQ, σextrinsic refers to extrinsic noise contributions from factors such as SEM shot noise, SEM tool stage movement, and beam profile. Unbiasing could be used to remove high frequency extrinsic noise and the results are shown in Fig.…”

Section: Results and Analysismentioning

confidence: 99%

Unsupervised neural network-based image restoration framework for pattern fidelity improvement and robust metrology

Du,

Pu,

Wei

et al. 2023

J. Micro/Nanopattern. Mats. Metro.

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Background: Scanning electron microscope (SEM) images acquired by E-beam tools for inspection and metrology applications are usually degraded by blurring and additive noises. Blurring sources include the intrinsic point spread function of optics, lens aberration, and potential motion blur caused by the wafer stage movements during the image acquisition process. Noise sources include shot noise, quantization noise, and electronic read-out noise. Image degradation caused by blurring and noise usually leads to noisy, inaccurate metrology results. For low-dosage metrology applications, metrology algorithms often fail to obtain successful measurements due to elevated levels of blurring and noise. Image restoration and enhancement are necessary as preprocessing steps to obtain meaningful metrology results. Initial success was obtained by applying neural network-based framework to drastically improve image quality and metrology precision as is demonstrated in the previous work.Aim: We aim to provide more details on the neural network model architecture, model regularization, and training dynamics to better understand the model's behavior. We also analyze the effect of image restoration on key metrology performances such as line edge roughness and mean critical dimension of the patterns.Approach: Non-machine learning-based image quality enhancement methods fail to restore low-quality SEM images to a satisfactory degree. More recent convolutional neural networks and vision transformer-based, supervised deep learning models have achieved superior performance in various low-level image processing and computer vision tasks. Nevertheless, they require a huge amount of training data that contain high-quality ground truth images. Unfortunately, high-quality ground truth images for low-dosage SEM images do not exist. Instead, we use self-supervised U-Net combined with a fully connected network (FCN) to recover low-dosage images without the need for ground truth training images. The methodology can be applied to various one-and two-dimensional patterns with different scales, shapes, spatial density, and image intensity statistics. We use image quality metrics and loss function to guide model architecture optimization and study how regularization strength affects the restoration process. These studies provide a better understanding of how the model learns to restore images and how parameters and hyperparameters affect results.Results: It is demonstrated that image quality metrics could be successfully used to evaluate self-supervised image restoration process and determine stopping criteria. The restored images show significantly improved image quality and metrology performance. Together, these pave the road to a systematic and automatic implementation of this methodology in real metrology applications.Conclusions: A self-supervised U-Net-based model combined with FCN proved itself as a powerful tool to restore highly blurry and noisy low-dosage SEM images. It can be used to improve image quality, suppress metrology noise, and pro...

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Spectral analysis of line edge and line-width roughness with long-range correlation

Cited by 20 publications

References 34 publications

Plasma treatments to improve line-width roughness during gate patterning

Plasma treatments to improve line-width roughness during gate patterning

Power Spectrum of Smoothed Line-Edge and Line-Width Roughness

Unsupervised neural network-based image restoration framework for pattern fidelity improvement and robust metrology

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