Experimental and model-based study of the robustness of line-edge roughness metric extraction in the presence of noise

Naulleau, Patrick; Cain, Jason P.

doi:10.1116/1.2778697

Cited by 29 publications

(16 citation statements)

References 9 publications

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“…Integration times were adjusted to produce images with signal-to-noise ratio ͑SNR͒ ranging from 10 to 15. 35 A Hitachi S4800 analytical SEM was employed for some EUV resist, NIL, and directed self-assembly ͑DSA͒ image acquisition. A 1.2 m horizontal field of view was used, with corresponding pixel edge length of 0.94 nm.…”

Section: B Sem Image Acquisition and Postprocessing Of Datamentioning

confidence: 99%

“…The methodology used to optimize image acquisition and analysis will be described briefly and follows guidelines previously described by others. [34][35][36][37] Following acquisition, images were processed through the SUMMIT software package for line edge extraction. 38 Numerous systematic distortions are typical in CD-SEM images.…”

Section: B Sem Image Acquisition and Postprocessing Of Datamentioning

confidence: 99%

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Robust estimation of line width roughness parameters

Patel¹,

Lahiri

Spanos

2010

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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Estimation of line width roughness (LWR) parameters is necessary for semiconductor process optimization, comparison of next-generation lithography processes as well as device performance simulation. According to previous studies [V. Constantoudis et al., J. Vac. Sci. Technol. B 21, 1019 (2003); J. Vac. Sci. Technol. B 22, 1974 (2004)], a complete description of LWR can be provided by three parameters: root-mean square roughness (σ), correlation length (ξ), and roughness exponent (α). However, the primary challenge in the estimation of the aforementioned LWR parameters is the limited availability of data in the scanning electron micrograph (SEM) image. A typical SEM image consists of 8–20 lines of 300–1500 nm length. It has been recognized that for a given line, in the presence of correlation between line widths at a given separation, the estimate of σ for a finite length of line can be significantly biased. Furthermore, for next-generation lithography (NGL) technologies such as double patterning, the number of lines available to estimate each lithography step is cut in half since alternate lines are produced from different processes. Thus, there is a need for an estimation procedure that performs robustly for arbitrarily shorter and fewer numbers of lines. Using a vectorized block or block of blocks bootstrap technique for dependent data and a weighted least-squares (WLS) fitting procedure, the authors fit a specific form of a variogram model. Block of blocks bootstrap is used to estimate the variance of a variogram, which in turn provides the WLS weights. Additionally, the bootstrap approach also allows us to estimate the error in the estimated LWR parameters, a vital requirement that has not been addressed by any of the previously reported procedures on this subject. The authors’ procedure works even in the presence of some unknown local critical dimension (CD) variation or if there is a systematic difference in CD (by design or otherwise) between the lines. The authors validate their procedure with simulated roughness profiles with deterministic LWR parameters. Lastly, as an application of their procedure, they evaluate actual profiles from a variety of different mainstream NGL processes such as litho-freeze-litho-etch double patterning lithography, self-aligned double patterning, and extreme ultraviolet, as well as alternatives such as directed self-assembly and nanoimprint lithography. It was shown that σ can be overestimated by over two times if local variation is not treated properly.

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Section: B Sem Image Acquisition and Postprocessing Of Datamentioning

confidence: 99%

Section: B Sem Image Acquisition and Postprocessing Of Datamentioning

confidence: 99%

Robust estimation of line width roughness parameters

Patel¹,

Lahiri

Spanos

2010

Journal of Vacuum Science &Amp; Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phen

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“…Modeling photon shot noise in a direct EUV mask-imaging configuration with ideal line intensity profiles enables us to predict the minimum photon flux requirements of EUV mask inspection tools and to understand the dependencies on magnification, ILS, and linewidth. This modeling is similar to studies of shot noise in photoresist [8], but here is applied to direct EUV imaging with a charge-coupled device (CCD) camera. We compare the flux requirements predicted by modeling to the imaging parameters of the AIT.…”

Section: Linewidth Roughnessmentioning

confidence: 98%

Photon flux requirements for EUV reticle imaging microscopy in the 22- and 16nm nodes

Wintz

Goldberg²,

Mochi

et al. 2010

SPIE Proceedings

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EUV -wavelength actinic microscopy yields detailed information about EUV mask patterns, architectures. defects, and the performance of defect repair strategies. without the complications of photoresist imaging. The measured aerial image intensity profiles provide valuable feedback to improve mask and lithography system modeling methods.In order to understand the photon-flux-dependent pattern measurement limits of EUV mask-imaging microscopy, we have investigated the effects of shot noise on aerial image linewidth measurements for lines in the 22 and 16-nm generations. Using a simple model of image formation near the resolution limit, we probe the influence of photon shot noise on the measured. apparent line roughness. With this methodology, vve arrive at general flux density requirements independent of the specific EUV microscope configurations.Analytical and statistical analysis of aerial image simulations in the 22 and 16-nm generations re\"Cal the trade-offs between photon energy density (controllable with exposure time), effective pixel dimension on the CCO (controlled by the microscope's magnification ratio), and image log slope (lLS). We find that shot-noise-induced linewidth roughness (LWR) varies imersely with the square root of the photon energy density, and is proportional to the imaging magnification ratio. While high magnification is necessary for adequate spatial resolution, for a gil'en flux density, higher magnification ratios have diminishing benefits. With practical imaging parameters, we find that in order to achieve an L WR (30) value of 5% of linewidth for dense, 88-nm mask features with 80% aerial image contrast and 13.5-nm effective pixel width (JOOOx magnification ratio). a peak photon flux of approximately 1400 photons per pixel per exposure is required.

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“…In sub-100-nm lithography, however, stochastic variations give rise to roughness at the edges of the printed features with RMS edge deviations of several nanometers [3][4][5][6]. Further, frequency analysis of this roughness shows correlation lengths that can be tens of nanometers [4,5].…”

Section: ( )mentioning

confidence: 99%

Stochastic modeling in lithography: autocorrelation behavior of catalytic reaction-diffusion systems

Mack¹

2009

Advances in Resist Materials and Processing Technology XXVI

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Reaction-diffusion chemical systems where the catalyst of the reaction is the only diffusing species are investigated. Here, the correlation length and Hurst roughness exponent are derived in one-, two-and three-dimensional firstorder catalytic reaction-diffusion problems. These results are relevant to many chemical systems, and in particular to chemically amplified photoresists used in semiconductor lithography, where the correlation length and Hurst exponent affect the line-edge roughness of sub-100-nm printed features.The stochastic behavior of reaction-diffusion chemical systems, where chemical species are simultaneously reacting and diffusion, has been extensively studied [1]. Unfortunately, analytic solutions to the stochastic differential equations governing these systems are rarely available, and so numerical simulations are frequently employed [2]. Still, there is a need for simple analytical descriptions of key phenomenon, to provide insight and to validate and guide model development.An important class of reaction-diffusion problems is that of a diffusing catalyst with all other reactants immobile. As an example, consider chemically amplified photoresists used in semiconductor lithography. Exposure of the polymer-based resist to light causes the generation of acid. A subsequent bake step allows the acid to diffuse and cause chemical reactions at specific sites on the surrounding polymer molecules that change their solubility in developer. Since the acid is not consumed in the reaction, it acts as a catalyst. This acid−polymer reaction is first order in acid concentration (H) and first order in concentration of reactive polymer sites (M), so that the governing kinetic rate equations arewhere k is the reaction rate constant and D is the acid (catalyst) diffusivity. Of course, these reaction-diffusion rate equations apply to many other catalytic systems as well.Mean-field solutions to the reaction-diffusion system of equation (1) are useful in higherdimensional problems (for example, Euclidian dimension d = 3) when the size of the domain of interest is large enough to ignore stochastic variations. In sub-100-nm lithography, however,

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Experimental and model-based study of the robustness of line-edge roughness metric extraction in the presence of noise

Cited by 29 publications

References 9 publications

Robust estimation of line width roughness parameters

Robust estimation of line width roughness parameters

Photon flux requirements for EUV reticle imaging microscopy in the 22- and 16nm nodes

Stochastic modeling in lithography: autocorrelation behavior of catalytic reaction-diffusion systems

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