Line Edge Roughness Measurement Research Articles

Effect of white noise on roughness measurements of self-affine fractals

This study formulated and clarified the presentation of the noise-related error terms in the power spectral density (PSD) and height–height correlation function (HHCF) through a roughness analysis of self-affine fractals. Assuming the noise as white noise, this study simulated the PSD and HHCF of the noisy roughness profile in a typical situation: line-edge roughness measurements involved in semiconductor lithography technology. It was found that conventional noise-correction techniques can bias the PSD/HHCF from those of the true roughness profiles because they do not account for the residual noise-induced error. The findings obtained from the roughness analysis and simulation techniques are expected to benefit various applications, such as clarifying the quantitative residual error in specific situations, selecting the optimum analysis method (PSD or HHCF), estimating the required number of averaged profiles (measurements) that yields sufficiently small noise errors, and considering strategies for noise reduction.

Enhancing the precision of 3D sidewall measurements of photoresist using atomic force microscopy with a tip-tilting technique

A key issue associated with advanced lithography techniques for semiconductor-device manufacturing is the reduction in the sidewall roughness of photoresist line patterns, known as line-edge roughness (LER). We have developed a technique for measuring the sidewall of the resist pattern using atomic force microscopy (AFM) that enables three-dimensional (3D), high-resolution, low-noise, and nondestructive measurements. Conventional LER measurement technology using scanning electron microscopy (SEM) causes shrinkage of the resist pattern due to electron-beam (EB) exposure, whereas our new AFM technique can in principle avoid EB-induced shrinkage. This AFM technology is capable of 3D measurements because it employs a tip-tilting mechanism that enables the sharp AFM tip to scan the vertical sidewalls, which is difficult for a conventional AFM technique. In addition, laser interferometers are equipped for the measurement of the AFM tip displacement, which yields high-resolution, high-accuracy, and low-noise results. This technology overcomes issues such as low resolution, noise, and destructive measurements that afflict conventional SEM measurements. In addition, it enables observations and quantitative analyses of the 3D sidewall roughness. For example, in the present experiment, we observed that grain shapes (several tens of nm in size) were formed randomly on the resist sidewall and that there were almost no footing shapes. By analyzing the sidewall profiles with a height resolution of 1 nm, we obtain the roughness (self-affine fractal) parameters at each height. This AFM-based resist sidewall measurement technique can, thus, provide important insights into resist patterning and related process technologies for next-generation semiconductor-device manufacturing.

Canny Algorithm Enabling Precise Offline Line Edge Roughness Acquisition in High-Resolution Lithography.

The line edge roughness (LER) is one of the most critical indicators of photoresist imaging performance, and its measurement using a reliable method is of great significance for lithography. However, most studies only investigate photoresist resolution and sensitivity because LER measurements require an expensive and not widely available critical dimension scanning electron microscopy (SEM) technology; thus, the imaging performance of photoresist has not been adequately evaluated. Here, we report an image processing software developed for offline calculation of LER that can analyze lithographic patterns with resolutions up to ∼15 nm. This software can effectively process all graphic files obtained from commonly used SEM machines by utilizing the adjustable double threshold. To realize the effective detection of high-resolution patterns in advanced lithography, we used SEM images generated from extreme ultraviolet and electron beam lithography to develop and validate the software's graphic recognition algorithm. This image processing software can process typical SEM images and produce reliable LER in an efficient and user-friendly manner, constituting a powerful tool for promoting the development of high-performance photoresist materials.

Unbiased line edge roughness measurement using profile-averaging method for precise roughness parameters measurement

Background: Scanning electron microscopy (SEM)-based line edge roughness (LER) measurement suffers from an error due to noise in SEM image. Noise correction methods have been developed to obtain unbiased roughness results, however, there are still concerns in the viewpoint of measurement precision. Aim: To develop an unbiased roughness analysis for highly precise LER measurement. Approach: Combining the conventional unbiased roughness analysis with a profile-averaging method, where a line pattern is repeatedly measured and then the obtained profiles are aligned and averaged. The experimental result measured by SEM was verified using atomic force microscopy (AFM)-based LER metrology, which has higher reliability than SEM. Results: The experimental evaluation showed that the proposed method can obtain roughness parameters more precisely than the conventional method. Conclusions: When the noise in the line edge profile by SEM is too large, it is necessary to reduce the noise beforehand and then perform roughness analysis in order to obtain precise roughness results. The proposed method enables to measure LER with the highest precision using SEM. Additionally, the AFM-based LER metrology was demonstrated as a feasible technique to evaluate the performance of SEM-based LER metrology.

Measuring line edge roughness with pixel sizes larger than its value: a mathematical and computational approach

In this work, we present a sound mathematical result that may correct the pixelization bias in the calculation of the line edge roughness (LER) even when the pixel size of SEM images is much larger than its rms value. This result can be useful in the LER metrology of current and future lithographic patterns where the desired rms value of LER is in the deep sub-nm range and smaller than the used pixel sizes. We computationally justify the predictions of the mathematical result and then demonstrate its application in synthesized SEM images where we can separate the impact of noise and focus on the pixelization effects in LER measurements. Furthermore, this result emphasizes the power of mathematical and computational methods to enhance the metrological output of SEM images in deep nanometer scale.

Direct comparison of line edge roughness measurements by SEM and a metrological tilting-atomic force microscopy for reference metrology

Background: Conventional scanning electron microscopy (SEM) that is used for 2D top-view metrology, a classical line edge roughness (LER) measurement technique, is incapable of measuring 3D structures of a nanoscale line pattern. For LER measurements, SEM measurement generates a single line-edge profile for the 3D sidewall roughness, although the line-edge profile differs at each height in the 3D sidewall. Aim: To develop an evaluation method of SEM-based LER measurement techniques and to verify how the 3D sidewall shape is reflected in the SEM’s 2D result. Approach: Direct comparison by measuring an identical location of a line pattern by SEM and an atomic force microscopy (AFM) with the tip-tilting technique that is capable of measuring the 3D sidewall. The line pattern has vertical stripes on the sidewall due to its fabrication process. Measured line edge profiles were analyzed using power spectral density, height-height correlation function, and autocorrelation function. Results: Line edge profiles measured by SEM and AFM were well matched except for noise level. Frequency and scaling analyses showed that SEM profile contained high noise and had lost a property of self-affine fractals in contrast to AFM. Conclusions: In the case of the line pattern with vertical stripes on the sidewall, SEM profile is generally consistent with 3D sidewall shape. The AFM-based LER measurement technique is useful as LER reference metrology to evaluate other LER measurement techniques.

Line edge roughness measurement on vertical sidewall for reference metrology using a metrological tilting atomic force microscope

Line edge roughness (LER) measurement is one of the metrology challenges for three-dimensional device structures, and LER reference metrology is important for reliable LER measurements. For the purpose of LER reference metrology, we developed an LER measurement technique that can analyze LER distribution along the height of a line pattern, with high resolution and repeatability. A high-resolution atomic force microscopy (AFM) image of a vertical sidewall of a line pattern was obtained using a metrological tilting-AFM, which offers SI-traceable dimensional measurements. The tilting-tip was controlled with an inclined servo axis, and it scans the vertical sidewall along a line pattern with a high sampling density to enable an analysis of the LER height distribution at the sidewall. A horizontal cross-section of the sidewall shows sidewall roughness with sub-nm resolution. Power spectral density (PSD) analysis of the sidewall profile showed that the PSD noise in the high-frequency region was several orders of magnitude lower than the noise of typical scanning electron microscopy methods. AFM measurements were sequentially repeated three times to evaluate the repeatability of the LER measurement; results indicated a high repeatability of 0.07 nm evaluated as a standard deviation of LER at each height.

Deep learning denoising of SEM images towards noise-reduced LER measurements

As chip sizes decrease and node dimensions break the sub-10 nm barrier, Line Edge Roughness (LER) metrology becomes a critical issue for the semiconductor research and industry. Scanning Electron Microscopy (SEM) imaging being the widely used tool for LER metrology suffers from the presence of noise that degrades measurement accuracy. To solve this issue without damaging the measured pattern, the applicability of deep Convolutional Neural Networks (CNNs) is explored, tackling the problem at the image level. The SEM image Denoising model (SEMD) is trained on synthesized image data to detect the variations of noise and provides as an output a denoised image of the pattern. The results are presented and compared with the state-of-art predictions, showing the effectiveness and enhanced performance of the SEMD method.

Line edge roughness metrology: recent challenges and advances toward more complete and accurate measurements

Two fundamental challenges of line edge roughness (LER) metrology are to provide complete and accurate measurement of LER. We focus on recent advances concerning both challenges inspired by mathematical and computational methods. Regarding the challenge of completeness: (a) we elaborate on the multifractal analysis of LER, which decomposes the scaling behavior of edge undulations into a spectrum of fractal dimensions similarly to what a power spectral density (PSD) does in the frequency domain. Emphasis is given on the physical meaning of the multifractal spectrum and its sensitivity to pattern transfer and etching; (b) we present metrics and methods for the quantification of cross-line (interfeature) correlations between the roughness of edges belonging to the same and nearby lines. We will apply these metrics to quantify the correlations in a self-aligned quadruple patterning lithography. Regarding the challenge of accuracy, we present a PSD-based method for a noise-reduced (sometimes called unbiased) LER metrology and validate it through the analysis of synthesized SEM images. Furthermore, the method is extended to the use of the height–height correlation functions to deliver noise-reduced estimation of the correlation length and the roughness exponent of LER.

Measurement of pattern roughness and local size variation using CD-SEM

Measurement of line edge roughness (LER) is discussed from four aspects: edge detection, power spectrum densities (PSD) prediction, sampling strategy, and noise mitigation. General guidelines and practical solutions for LER measurement today are introduced. Advanced edge detection algorithms such as the wave-matching method are shown to be effective for robustly detecting edges from low SNR images, whereas a conventional algorithm with weak filtering is still effective in suppressing SEM noise and aliasing. An advanced PSD prediction method such as the multitaper method is effective in suppressing sampling noise within a line edge to analyze, whereas a number of lines are still required for suppressing line-to-line variation. Two types of SEM noise mitigation methods, such as the “apparent noise floor” subtraction method and LER-noise decomposition using regression analysis, are verified to successfully mitigate SEM noise from PSD curves. These results are extended to local critical-dimension uniformity (LCDU) measurement to clarify the impact of SEM noise and sampling noise on LCDU.

PMMA–ZnO Hybrid Arrays Using in Situ Polymerization and Imprint Lithography

Imprint lithography has been explored as a method to transfer arrays of patterned features onto pure polymers and polymer/metallic nanoparticle composites. However, it has never been achieved on the submicrometer scale with polymer–oxide particle hybrids. This study uses in situ polymerization and imprint lithography to form ZnO–PMMA hybrid patterns. The polymerization temperature is varied to study its effects on feature fidelity, film flexibility, and pattern photoluminescence (PL) response. For a given polymerization temperature, the feature fidelity decreases with increasing ZnO content according to line-edge roughness (LER), inverse circularity (IC), and surface roughness (SR) measurements. This decrease in feature fidelity indicates an increase in particle agglomeration as the ZnO content increases. The elongation at failure for the hybrids decreases with the polymerization temperature and the ZnO content while the bending radius increases. Even at the lowest feature fidelity, the LER is <10% of the...

Uncertainty in roughness measurements: putting error bars on line-edge roughness

Measurement of line-edge or linewidth roughness involves uncertainty, like all measurements, and an estimate of that uncertainty should be reported whenever a roughness measurement is reported. However, roughness measurement uncertainty estimates are complicated by the correlations along the length of the rough feature. As a result, roughness measurements are often not accompanied by uncertainty estimates or error bars on graphs. Here, both theoretical considerations and simulations of random rough features will be used to derive a simple formula to estimate the uncertainty of a roughness measurement using the standard parameters describing that roughness: standard deviation, correlation length, and roughness exponent. Additionally, a more accurate formula to estimate the systematic bias in roughness standard deviation is provided.

Noise filtering for accurate measurement of line edge roughness and critical dimension from SEM images

Measurements of the line edge roughness (LER) and critical dimension (CD) from scanning electron microscope (SEM) images are often required for analyzing circuit patterns transferred onto substrate systems. A common approach is to employ image processing techniques to detect feature boundaries from which the LER and CD are computed. SEM images usually contain a significant level of noise which affects the accuracy of measured LER and CD. This requires reducing the noise level by a certain type of low-pass filter before detecting feature boundaries. However, a low-pass filter also tends to destroy the boundary detail. Therefore, a careful selection of low-pass filter is necessary in order to achieve the high accuracy of LER and CD measurements. In this paper, a practical method to design a Gaussian filter for reducing the noise level in SEM images is proposed. The method utilizes the information extracted from a given SEM image in adaptively determining the sharpness and size of a Gaussian filter. The results from analyzing the effectiveness of the Gaussian filter designed by the proposed method are provided.

Biases and uncertainties in the use of autocovariance and height–height covariance functions to characterize roughness

Measuring the frequency response of roughness is necessary in many applications, leading to the common use of the power spectral density (PSD) of the roughness. But biases and random uncertainties in the PSD have led some to explore the use of the autocovariance function (ACF) and the height–height covariance function (HHCF) instead. These functions also entail systematic biases and random uncertainties when applied to measured roughness, requiring detailed characterization. A combination of analytical derivations and simulations of rough edges have led to a thorough characterization of these biases and uncertainties for the measurement of line-edge and linewidth roughness of lithographically produced features. The results show that ACF estimation is problematic, but that HHCF estimation is a reasonable alternative to PSD analysis under conditions typical of linewidth roughness measurement in the semiconductor industry.

Sensitivity analysis and line edge roughness determination of 28-nm pitch silicon fins using Mueller matrix spectroscopic ellipsometry-based optical critical dimension metrology

Measurement and control of line edge roughness (LER) is one of the most challenging issues facing patterning technology. As the critical dimensions (CDs) of patterned structures decrease, an LER of only a few nanometers negatively impacts device performance. Here, Mueller matrix (MM) spectroscopic ellipsometry-based scatterometry is used to characterize LER in periodic line-space structures in 28-nm pitch Si fin samples fabricated by directed self-assembly patterning. The optical response of the MM elements is influenced by structural parameters like pitch, CDs, height, and side-wall angle, as well as the optical properties of the materials. Evaluation and decoupling MM element response to LER from other structural parameters requires sensitivity analysis using scatterometry models that include LER. Here, an approach is developed that can be used to characterize LER in Si fins by comparing the optical responses generated by systematically varying the grating shape and measurement conditions. Finally, the validity of this approach is established by comparing the results obtained from power spectral density analysis of top down scanning electron microscope images and cross-sectional transmission electron microscope image of the 28-nm pitch Si fins.

More systematic errors in the measurement of power spectral density

Power spectral density (PSD) analysis is an important part of understanding line-edge and linewidth roughness in lithography. But uncertainty in the measured PSD, both random and systematic, complicates inter- pretation. It is essential to understand and quantify the sources of the measured PSD's uncertainty and to develop mitigation strategies. Both analytical derivations and simulations of rough features are used to evaluate data window functions for reducing spectral leakage and to understand the impact of data detrending on biases in PSD, autocovariance function (ACF), and height-to-height covariance function measurement. A generalized Welch window was found to be best among the windows tested. Linear detrending for line-edge roughness measurement results in underestimation of the low-frequency PSD and errors in the ACF and height-to-height covariance function. Measuring multiple edges per scanning electron microscope image reduces this detrending

Atomic force microscopy study of photoresist sidewall smoothing and line edge roughness transfer during gate patterning

With the constant decrease of semiconductor device dimensions, gate line edge roughness (LER) becomes an important source of device variability. Gate LER originates from photoresist (PR) LER that is partially transferred into the gate during plasma etching. A plasma treatment is typically used to reduce the PR LER before the transfer. LER control at the nanometer scale also requires accurate measurements. We have recently developed a technique for LER measurement based upon atomic force microscopy (AFM). In this technique, the sample is tilted at about 45 deg and feature sidewalls are scanned along their length with the AFM tip to obtain three-dimensional images. The AFM technique is applied to the study of a pattern transfer into a gate stack starting from untreated PR, PR treated by conventional HBr plasma, and PR treated by HBr/O 2 plasma followed by a bake at 150°C. It is found that the plasma etching reduces the LER at each etching step. The reduction is more important when starting from untreated PR which has the highest initial LER. However, the final LER in the Si layer remains significantly smaller when starting with cured PR, especially with PR cured by an HBr/O 2 plasma treatment followed by a bake at 150°C.

An atomic force microscopy-based method for line edge roughness measurement

With the constant decrease of semiconductor device dimensions, line edge roughness (LER) becomes one of the most important sources of device variability and needs to be controlled below 2 nm for the future technological nodes of the semiconductor roadmap. LER control at the nanometer scale requires accurate measurements. We introduce a technique for LER measurement based upon the atomic force microscope (AFM). In this technique, the sample is tilted at about 45° and feature sidewalls are scanned along their length with the AFM tip to obtain three-dimensional images. The small radius of curvature of the tip together with the low noise level of a laboratory AFM result in high resolution images. Half profiles and LER values on all the height of the sidewalls are extracted from the 3D images using a procedure that we developed. The influence of sample angle variations on the measurements is shown to be small. The technique is applied to the study of a full pattern transfer into a simplified gate stack. The images obtained are qualitatively consistent with cross-section scanning electron microscopy images and the average LER values agree with that obtained by critical dimension scanning electron microscopy. In addition to its high resolution, this technique presents several advantages such as the ability to image the foot of photoresist lines, complex multi-layer stacks regardless of the materials, and deep re-entrant profiles.

Effect of tip shape on line edge roughness measurement based on atomic force microscopy

Atomic force microscopy (AFM) is an important tool in line edge roughness (LER) measurements, where accuracy for line edge identification is influenced by the shape of the tip. In this article, the effect of tip shape on LER measurement based on AFM is studied theoretically. The formulas for calculating the distance between the measured and actual line edge of the sample are presented. The effects of the three kinds of tips with different shapes are experimentally compared for validation. Suggestions on how to reduce measuring error caused by tip shape are also given.

Grazing incidence broad ion beams for reducing line-edge roughness

As semiconductor feature sizes continue to decrease, the phenomena of line-edge roughness (LER) becomes more disruptive in chip manufacturing. While many efforts are underway to decrease LER from the photoresist, post-developed smoothing techniques may be required to continue shrinking chip features economically. This paper reports on one such method employing the use of a broad ion beam at grazing incidence along the features. This method smooths relatively long spatial-length LER, a potential advantage over other smoothing techniques that focus on just molecular-scale LER. LER reduction numbers using Ne and Ar beams are reported at both short and long spatial wavelengths. Variables include beam energy, length of time and angular dependence. LER measurements are taken using the Hitachi image-analysis software on top–down analytical scanning electron microscope (SEM) measurements. Line-profile data are taken from cross-sectional SEM photographs. Tests have achieved a reduction in LER from 9.8 ± 0.67 nm to 5.5 ± 0.86 nm for 45 nm critical dimensions using an Ar beam at 500 eV for 6 s at an 85° angle of incidence. A reduction from 10.1 ± 1.07 nm to 6 ± 1.02 nm was shown using an Ar beam at 1000 eV for 4 s at a 60° angle of incidence.