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... Figs. 5 and 6). 30 Instead of the fully periodic edges, in MFA LER is projected to scaling domain and is decomposed in different fractal dimensions that co-operate in the formation of LER. The two approaches (PSD and MFA) are apparently complementary offering different angles of views in LER characterization. ...
Article
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. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).
Article
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Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within a space, they are not necessarily equivalent on a more rigorous level. This review article aims at unifying the multifractal methodology by presenting the multifractal theoretical framework and principal practical methods, namely the moment method, the histogram method, multifractal detrended fluctuation analysis (MDFA) and modulus maxima wavelet transform (MMWT), with a comparative and interpretative eye.
Article
Full-text available
Photoresist line-edge roughness (LER) is precisely what its name implies: The sidewalls or edges of resist features are rough, not smooth. At feature sizes <∼100nm, this roughness makes a nontrivial contribution to CD variation and transistor leakage.
Article
Full-text available
Line edge (or width) roughness (LER or LWR) of photoresists lines constitutes a serious issue in shrinking the critical dimensions (CD) of the gates to dimensions of a few tens of nanometers. In this article, we address the problem of the reliable LER characterization as well as the association of LWR with the CD variations. The complete LER characterization requires more parameters than the rms value σ since the latter neglects the spatial aspects of LER and does not predict the dependence on the length of the measured line. The further spatial LER descriptors may be the correlation length ξ and the roughness exponent α, which can be estimated through various methods. One aim of the present work is to perform a systematic comparative study of these methods using model edges generated by a roughness algorithm, in order to show their advantages and disadvantages for a reliable and accurate determination of the spatial LER parameters. In particular, we compare the results from (a) the study of the height–height correlation function (HHCF), (b) the Fourier [or power spectrum (PS)] analysis, and (c) the variation of rms value σ with measured line edge L[σ(L) curve]. It is found that the HHCF can be considered approximately a rescaled version of σ(L) and that the value of σ becomes almost independent of the measured edge length for lengths larger than ten times the correlation length. As regards the PS, it is shown that the finite length of the edge may harmfully affect the reliable estimation of α and ξ. Finally, we confirm theoretically and generalize an experimental observation [Leunissen etal, Microelectron. Eng. (to be published)] regarding the relationship between LWR and the σ of the CD variations within a die of a wafer. It is shown that they behave in a complimentary way as line length increases so that the sum of their squares remains constant and equal to the square of the LWR σ of the infinite line. © 2004 American Vacuum Society.
Article
Most scanning electron microscope (SEM) measurements of pattern roughness today produce biased results, combining the true feature roughness with noise from the SEM. Further, the bias caused by SEM noise changes with measurement conditions and with the features being measured. The goal of unbiased roughness measurement is to both provide a better estimate of the true feature roughness and to provide measurements that are independent of measurement conditions. Using an inverse linescan model for edge detection, the noise in SEM edge and width measurements can be measured and removed statistically from roughness measurements. This approach was tested using different pixel sizes, magnifications, and frames of averaging on several different post-lithography and post-etch patterns. Over a useful range of metrology conditions, the unbiased roughness measurements were effectively independent of these metrology parameters.
Article
During the last years, several methods from the statistical physics of complex systems have been applied to the study of natural language written texts. They have mostly been focused on the detection of long-range correlations, multifractal analysis and the statistics of the content word positions. In the present paper, we show that these statistical aspects of language series are not independent but may exhibit strong interrelations. This is done by means of a two-step investigation. First, we calculate the multifractal spectra using the word-length representation of huge parallel corpora from ten European languages and compare with the shuffled data to assess the contribution of long-range correlations to multifractality. In the second step, the detected multifractal correlations are shown to be related to the scale-dependent clustering of the long, highly informative content words. Furthermore, exploiting the language sensitivity of the used word-length representation, we demonstrate the consistent impact of the classification of languages into families on the multifractal correlations and long-word clustering patterns.
Conference Paper
The line edge roughness (LER) and line width roughness (LWR) transfer in a self-aligned quadruple patterning (SAQP) process is shown for the first time. Three LER characterization methods, including conventional standard deviation method, power spectral density (PSD) method and frequency domain 3-sigma method, are used in the analysis. The wiggling is also quantitatively characterized for each SAQP step with a wiggling factor. This work will benefit both process optimization and process monitoring.
Conference Paper
Self-Aligned Quadruple Patterning (SAQP) is targeted to support the sub 10nm technology nodes. It is consisted of several process steps starting with lithography and Etch to define the pattern backbone. Followed by additional set of processes based on thin-films deposition and etch that quadruple the number of patterns, shrinking pattern and pitch sizes. Pattern roughness is derived from the physical and chemical characteristics of these process steps. It is changing with each of the SAQP process steps, based on material stack and the etch process characteristics. Relative to a sub 10 nm pattern sizes pattern, edge roughness can significantly impact pattern physical dimensions. Unless controlled it can increase the variability of device electrical performance, and reduce yield. In this paper we present the SAQP process steps and roughness characterization, performed with Power Spectral Density (PSD) methodology. Experimental results demonstrates the ability of PSD analysis to sensitively reflect detailed characterization of process roughness, guiding process development improvements, and enabling roughness monitoring for production.
Article
Roughness of lithographic patterns is typically expressed as the absolute 3σ variation of resist lines by means of edge variation. However, full characterization of the roughness requires both its amplitude and frequency distribution. This necessity arises from the requirement to reduce different roughness frequencies for different lithographic levels. The International Technology Roadmap of Semiconductors (ITRS) has established a dedicated specification for low frequency roughness. To obtain full knowledge of the roughness behavior in the frequency domain, a power spectral density analysis technique is used. It is found that power spectral density has a unique profile for each process. Moreover, the major contribution to the roughness came from the low frequencies range. Besides this, an on-line metrological study on scanning electron microscopy resist roughness repeatability is executed to optimize the capturing image parameters and estimate eventual short- (daily) and long-term (yearly) contributions. In the end, 0.2-nm 3σ line width roughness stability value is found. To verify the validity of analysis and metrology, 32-nm extreme ultraviolet lithography exposures at different flare levels, 45-nm ArF immersion lithography through dose, and a rinse postlithography smoothing process are characterized with the aim to highlight the importance of low frequency roughness detection.
Book
The function of a component part can be profoundly affected by its surface topography. There are many examples in nature of surfaces that have a well-controlled topography to affect their function. Examples include the hydrophobic effect of the lotus leaf, the reduction of fluid drag due to the riblet structure of shark skin, the directional adhesion of the gecko foot and the angular sensitivity of the multi-faceted fly eye. Surface structuring is also being used extensively in modern manufacturing. In this way many properties can be altered, for example optical, tribological, biological and fluidic. Previously, single line (profile) measurements were adequate to control manufacture of surfaces, but as the need to control the functionality of surfaces increases, there is a growing need for three-dimensional (areal) measurement and characterisation techniques. For this reason there has been considerable research, development and standardisation of areal techniques. This book will present the areal framework that is being adopted by the international community. Whereas previous books have concentrated on the measurement aspects, this book concentrates on the characterisation techniques, i.e. how to interpret the measurement data to give the appropriate (functional) information for a given task. The first part of the book presents the characterisation methods and the second part case studies that highlight the use of areal methods in a broad range of subject areas - from automobile manufacture to archaeology. © 2013 Springer-Verlag Berlin Heidelberg. All rights are reserved.
Article
We formerly developed the "assembly method" for analyzing the line-edge and line-width roughness (LER/LWR) that has a long-range correlation beyond the conventional analysis limit. In the method, we repeatedly assembled virtual long lines by gathering line segments, which were arbitrarily disposed on actual long lines and by randomly changing their combination and order, permitting the assembled lines to share the same line segments. Then, we obtained the PSD of the LER/LWR of the assembled lines considering the lines as seamless. We also derived an analytic formula of the assembled-line PSDs. This formula excellently agreed with experimental PSDs. In this report, we propose guidelines for suppressing the statistical-noise effect on the assembly method for the purpose of accurately analyzing the long-range- correlated LER/LWR. The guidelines will greatly help shed light on the long-range correlation, which causes the variability even in large devices but has long been veiled due to the lack of metrology.
Article
The measurement of line-edge roughness (LER) has recently become a major topic of concern in the litho-metrology community and the semiconductor industry as a whole, as addressed in the 2001 International Technology Roadmap for Semiconductors (ITRS) roadmap. The Advanced Metrology Advisory Group (AMAG, a council composed of the chief metrologists from the International SEMATECH (ISMT) consortium"s Member Companies and from the National Institute of Standards and Technology (NIST) has begun a project to investigate this issue and to direct the critical dimension scanning electron microscope (CD-SEM) supplier community towards a semiconductor industry-backed solution for implementation. The AMAG group has designed and built a 193 nm reticle that includes structures implementing a number of schemes to intentionally cause line edge roughness of various spatial frequencies and amplitudes. The lithography of these structures is in itself of interest to the litho-metrology community and will be discussed here. These structures, along with several other photolithography process variables, have been used to fabricate a set of features of varying roughness value and structure which span the LER process space of interest. These references are, in turn, useful for evaluation of LER measurement capability. Measurements on different CD-SEMs of major suppliers were used to demonstrate the current state of LER measurement. These measurements were compared to roughness determined off-line by analysis of top-down images from these tools. While no official standard measurement algorithm or definition of LER measurement exists, definitions used in this work are presented and compared in use. Repeatability of the measurements and factors affecting their accuracy were explored, as well as how CD-SEM parameters can affect the measurements.
Article
A search for the best and most complete description of line-edge roughness (LER) is presented. The root mean square (rms) value of the edge (sigma value) does not provide a complete characterization of LER since it cannot give information about its spatial complexity. In order to get this missing information, we analyze the detected line edges as found from scanning electron microscope (SEM) image analysis [see Paper I: G. P. Patsis etal, J. Vac. Sci. Technol. B 21, 1008 (2003)] using scaling and fractal concepts. It is shown that the majority of analyzed experimental edges exhibit a self-affine character and thus the suggested parameters for the description of their roughness should be: (1) the sigma value, (2) the correlation length ξ, and (3) the roughness exponent α. The dependencies of ξ and α on various image recording and analysis parameters (magnification, resolution, threshold value, etc.) are thoroughly examined as well as their implications on the calculation of sigma when it is carried out by averaging over the sigmas of a number of segments of the edge. In particular, ξ is shown to be connected to the minimum segment size for which the average sigma becomes independent of the segment size, whereas α seems to be related to the relative contribution of high frequency fluctuations to LER. © 2003 American Vacuum Society.
Article
The effects of Line Width Roughness (LWR) on transistor performance are one of the hottest issues in semiconductor industry. However, in most related studies, LWR is considered as the fluctuations of gate lengths and not of resist lines. In this paper, we examine the direct effects of one of the spatial resist LWR parameters, the fractal dimension, on transistor off current deviations for various correlation lengths and gate widths. The aim is to exploit the fractality of LWR in order to link the gap between the LWR of long resist lines and the gate length roughness that affects transistor performance. The used methodology is based on the simulation of both resist lines and transistor operation. The results of the two step methodology are presented for both narrow and wide gates. For the first, it is found that for all correlation lengths, higher fractal dimension (smaller roughness exponent) of the resist line leads to off state currents closer to the nominal value. For wide gates, an interesting differentiation is found at the dependence of the standard deviation from the fractal dimension as correlation length decreases. For sufficiently low correlation length, the behavior is reversed and the low fractal dimension are more beneficial that the higher ones. An explanation of that reverse is provided by means of the dependence of the CD variation on gate width for various fractal dimensions. Finally, the implications of these findings on the dependencies of the yield of transistors on fractal dimension and correlation length are also discussed.
Article
Various approaches can be used to quantify line width roughness (LWR). One of the most commonly used estimators of LWR is the standard deviation. However, this approach is incomplete and ignores a substantial amount of information. We propose here a full spectral analysis to investigate and monitor LWR. A variety of estimators, such as standard deviation, peak-to-valley, average, correlation length and Fourier analysis have been implemented on-line on CDSEM. The algorithms were successfully tested against e-beam written LWR patterns, both deterministic and random. This approach allows a fully automated investigation of LWR. This methodology was used to monitor LWR over a long period of time, benchmark new resists and to investigate the effect of LWR on device performance and yield.
Article
Line edge roughness becomes an important factor in linewidth control as lithographic dimensions approach the 0.1 μm region. In order to understand different contributions to roughness, we explored the relationship between roughness and deprotection in the case of a positive chemically amplified resist. Experiments show that the roughness of the remaining resist depends on process history and it is not a simple function of the degree of deprotection. Scaling analysis of atomic force microscopy images shows that an equal degree of deprotection yields a self-affine rough surface with constant fractal dimensions which imply a similar surface morphology, but with a different standard deviation. The correlation between sidewall and top surface roughness is also discussed. © 1998 American Vacuum Society.
Chapter
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Article
The multifractal formalism for describing distributions of measures on sets which may be fractal is reviewed, with particular attention to random resistor networks, diffusion limited aggregates and mass fractals. The formalism has been very successful in describing crossover phenomena, but its use is somewhat dangerous due to problems with negative moments, with averaging procedures and with finite size effects.
Article
Over the last years, fractal and multifractal geometries were applied extensively in many medical signal (1D, 2D or 3D) analysis applications like pattern recognition, texture analysis and segmentation. Application of this geometry relies heavily on the estimation of the fractal features. Various methods were proposed to estimate the fractal dimension or multifractal spectral of a signal. This article presents an overview of these algorithms, the way they work, their benefits and their limits. The aim of this review is to explain and to categorize the various algorithms into groups and their application in the field of medical signal analysis.
Surfaces and their Measurement
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