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Abstract

Directed self-Assembly (DSA) lithography poses challenges in line edge roughness (LER)/line width roughness metrology due to its self-organized and pitch-based nature. To cope with these challenges, a characterization approach with metrics and/or updates of the older ones is required. To this end, we focus on two specific challenges of DSA line patterns: (a) the large correlations between the left and right edges of a line (line wiggling) and (b) the cross-line correlations, i.e., the resemblance of wiggling fluctuations of nearby lines. The first is quantified by the line center roughness whose low-frequency part is related to the local placement errors of device structures. For the second, we introduce the c-factor correlation function, which quantifies the strength of the correlations between lines versus their horizontal distance in pitches. The proposed characterization approach is first illustrated and explained in synthesized scanning electron microscope images with full control of their dimensional and roughness parameters; it is then applied to the analysis of line/space patterns obtained with the Liu-Nealey flow (post-Polymethyl methacrylate removal and pattern transfer), revealing the effects of pattern transfer on roughness and uniformity. Finally, we calculate the c-factor function of various next-generation lithography techniques and show their distinct footprint on the extent of cross-line correlations. © 2017 Society of Photo-Optical Instrumentation Engineers (SPIE).

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... In order to characterize the propagation of correlation across edges and lines, the function of c-factor correlation function between the line center roughness of nearby lines has been proposed and articulated in excess of the simple c-factor defining the similarity of the LER between left and right edges. 8,9 In this paper, we present this function and apply it to the quantification of cross-line correlation, in the process steps of an SAQP lithography (see Sec. 4). The challenge of accuracy is very critical, mainly in the SEM-based metrology of LER, since the SEM image formation suffers from the inevitable presence of noise effects, which deteriorate the accuracy of the detection of line edges. ...
... A systematic methodology for the quantification of these features and an extended LER metrology has been published some years ago from our group and applied in DSA patterns. 8 Here, we focus on the measurement of edge and cross-line correlations, which are quantified by the c-factor (c) and the c-factor-function, respectively where e R;L are the x-coordinates of the right and left edges, respectively, and lc i stands for the x-coordinate of line centers. ...
... In the third row, the pattern has edge roughness [rmsðLERÞ > 0], left/right edge correlations (c-factor > 0), and also the line centers fluctuate in a correlated manner [c-factor-function ðr > 1Þ > 0]. The extend at which crossline correlations exist, i.e., the number of lines with correlated fluctuations, is measured with the c-factor correlation length computed by the c-factor function as explained in Ref. 8. Fig. 12 The difference δf quantifying the inhomogeneity of scaling behavior (multifractality) versus process steps. ...
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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).
... Furthermore, it was recently realized that LER characteristics are sensitive to the applied lithographic technique [33]. The main point of differentiation comes from the degree of correlations between the fabricated edges and lines. ...
... Here, c is the c-factor quantifying the cross-correlations between the left and right edges of lines. For totally uncorrelated edges, c = 0, whereas for fully correlated (anti-correlated), c = 1 (−1) [26,33]. By combining (2), (3), and (4) we read: ...
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We investigate the effects of Line Edge Roughness (LER) of electrode lines on the uniformity of Resistive Random Access Memory (ReRAM) device areas in cross-point architectures. To this end, a modeling approach is implemented based on the generation of 2D cross-point patterns with predefined and controlled LER and pattern parameters. The aim is to evaluate the significance of LER in the variability of device areas and their performances and to pinpoint the most critical parameters and conditions. It is found that conventional LER parameters may induce >10% area variability depending on pattern dimensions and cross edge/line correlations. Increased edge correlations in lines such as those that appeared in Double Patterning and Directed Self-assembly Lithography techniques lead to reduced area variability. Finally, a theoretical formula is derived to explain the numerical dependencies of the modeling method.
... 56 This methodology follows a procedure employed by Constantoudis et al. to describe cross-line correlations in DSA-templated patterns. 26 Similar definitions may be used to compare cylinder widths and placements. This approach allows us to measure the extent of lateral correlation across a trench based on PCC values ranging from −1 (negative correlation) to 1 (positive correlation). ...
... This range exceeds correlation lengths measured of DSA patterns on chemically templated substrates, in which correlations are limited by the three-fold periodicity of the underlying guide pattern. 26 While edge correlations are consistently positive, the intensity of correlations between adjacent cylinders is observed to modulate between alternating edges: Edges that span PMMA domains (e i,L → e i,R ) show a stronger correlation than those across PS domains (e i,R → e i+1,L ). The effect is most apparent when examining the adjacent off-diagonal terms in Figure 6a at 150°C. ...
... (3) Roughness (LCR) has been introduced tracking the fluctuations of the center of lines coupled with the c-factor correlation function and length to characterize the degree of correlations between the LCR of pattern lines. The whole picture of the generalized LER characterization methodology is shown in Fig. 3 and explained thoroughly in [3] while a similar approach is reported in [4]. Despite the fact that LER is considered an important contribution of stochastics to EPE, there has not been a systematic and quantitative investigation of their relationship. ...
... In the case of diblock copolymer directed self-assembly, even measurement of line-edge roughness presents a new challenge. 19 A more difficult question is whether or not the self-assembly process can be controlled sufficiently well to avoid defects. [20][21][22][23][24][25][26] As a first step, it is important to be able to see defects in what are predominantly soft-material systems. ...
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Control of Line Width Roughness (LWR) is one of the biggest challenges of next generation lithographies. However, control necessitates accurate definition and characterization schemes. In this paper, a new definition of LWR is proposed with the benefit of being independent on the resist line length used in the measurement. The definition corresponds to the sigma value of LWR for infinite resist-line-length, but it can be measured using any finite line length. It is based on an appropriate combination of LWR and CD metrology. As the line length (gate width) decreases the LWR is being partitioned between the sigma of LWR for finite lengths and the CD variation. This partitioning is controlled by the correlation length and the roughness exponent. A protocol for LWR characterization is described using these three parameters. Furthermore, LWR modeling using methods for generating lines similar to the experimental ones is investigated. The aim is to control LWR deliberately for better input to device simulators and solving characterization problems. An algorithm based on the convolution method is shown to reproduce reliably the roughness characteristics of real lines. This algorithm needs as input a triplet of parameters similar to those defined above for LWR characterization.
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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 ITRS roadmap. The Advanced Metrology Advisory Group (AMAG, a council composed of the chief CD-metrologists from the International SEMATECH 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 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. Measurements on different CD-SEMs of major suppliers will be used to comparatively demonstrate the current state of LER measurement. These measurements are 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 will be explored, as well as how CD-SEM parameters can effect the measurements.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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The role of the gate width in the effects of Line Width Roughness (LWR) on transistor performance is investigated. Two mathematical results regarding the statistical nature of LWR are presented and discussed. The implications of these results on the effects of LWR on transistor performance are investigated through a 2D modeling approach. It is found that, for fixed LWR induced by manufacturing processes, transistors designed with large gate widths seem to mitigate the degradation effects of LWR on transistor performance. © 2010