Fundamental limits of optical critical dimension metrology: a simulation study

Silver, Richard M.; Germer, Thomas A.; Attota, Ravikiran; Barnes, Brian M.; Bunday, Benjamin; Allgair, John A.; Marx, Egon; Jun, Jay S.

doi:10.1117/12.716604

Cited by 62 publications

(40 citation statements)

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“…5,14 The general strategy of such a model-based identification technology is shown in Figure 1. 15,16 As mentioned before, the noise and the limited information obtained from real measurements lead to uncertainty (dp p) in the reconstructed parameters. To keep this difference smaller than the aspired uncertainties, both an improvement of the physical model used for the simulations and optimized measurement conditions are needed.…”

Section: Solving the Inverse Problem By Model-based Feature Reconstrumentioning

confidence: 97%

Solving the inverse grating problem by white light interference Fourier scatterometry

et al. 2012

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Scatterometry is a well-established, fast and precise optical metrology method used for the characterization of sub-lambda periodic features. The Fourier scatterometry method, by analyzing the Fourier plane, makes it possible to collect the angle-resolved diffraction spectrum without any mechanical scanning. To improve the depth sensitivity of this method, we combine it with white light interferometry. We show the exemplary application of the method on a silicon line grating. To characterize the sub-lambda features of the grating structures, we apply a model-based reconstruction approach by comparing simulated and measured spectra. All simulations are based on the rigorous coupled-wave analysis method.

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Section: Solving the Inverse Problem By Model-based Feature Reconstrumentioning

confidence: 97%

Solving the inverse grating problem by white light interference Fourier scatterometry

et al. 2012

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“…, N. For reasons of simplicity, in the following any systematic error is omitted and only random errors are considered. Following the approach suggested in [12], we assume that the noise of the measured data is normally distributed with standard deviations given just by the measured uncertainties {σ i } [13].…”

Section: Estimated Uncertaintiesmentioning

confidence: 99%

Performance analysis of coherent optical scatterometry

et al. 2011

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Scatterometry is a well established technique currently utilized in research, as well as in industrial applications, to retrieve the properties of a given scatterer (the target) by looking at how the light coming from a certain source is diffracted in the far field. Currently the light source is often a discharge lamp that, after wavelength filtering, can be thought as a quasi-monochromatic, but spatially incoherent, source. In the present work, benefits of using a focused spot from a spatially coherent light source, as that emitted by a laser, are investigated on a theoretical viewpoint. The focused spot is scanned over the object of interest and, for each scan position, a far-field diffraction pattern is recorded. Our results show that spatially coherent light can sensibly increase the accuracy of the technique with respect to the target's geometrical profile.

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“…However, their measurement uncertainties are fundamentally limited by the underlying cross-correlations between the different fit parameters, e.g., line widths and heights. 3 To reduce parametric correlation and improve measurement performance and uncertainties, we have developed a Bayesian statistical approach that integrates a priori information gleaned from other measurements. This allows us to embed information obtained from reference metrology and complimentary ellipsometry of the optical constants, or to constrain the floating parametric range based on physical limits or known manufacturing variability.…”

Section: A New Approach Uses Embedded Data From Reference Metrology Tmentioning

confidence: 99%

“…6 Historically, researchers have used least-squares fitting routines to select a set of parameters with the closest experiment-to-theory agreement. 3 Parametric correlation, measurement noise, and model inaccuracy all lead to measurement uncertainty in the fitting process. Even when a measurement demonstrates good sensitivity, cross-correlation among the parameters can lead to very large uncertainties and is the fundamental limitation to the goodness of fit.…”

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confidence: 99%

“…We used a simulation-based analysis comparing spectroscopic and angleresolved scatterometry. 7 To better understand the effects of parametric correlation, we looked at the sensitivity and covariance matrices from the χ 2 analysis. The upper part of Figure 2 shows reflectivity data calculated for spectroscopic scans, while the middle graphs show angle-resolved scatterometry results.…”

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Bayesian statistics integrates prior information in parametric optical modeling

Silver¹

2009

SPIE Newsroom

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A new approach uses embedded data from reference metrology to reduce parametric correlation and improve measurement performance.Semiconductor manufacturing requires measurements to control the size of nanoscale devices (referred to as the critical dimension: CD) within patterned layers and for monitoring the placement of new levels upon existing layers (known as overlay metrology). As device sizes continue to decrease, new approaches are required to refine these measurements. A significant body of recent research has investigated new optical technologies for CD and overlay metrology on scales of 32nm and smaller. Much of this work has focused on scatterometry and, more recently, scatterfield microscopy, a technique combining well-defined angle-resolved illumination with image-forming optics. 1, 2 These optical methods are of particular interest because of their nondestructive, high-throughput characteristics and their potential for excellent sensitivity and accuracy. However, their measurement uncertainties are fundamentally limited by the underlying cross-correlations between the different fit parameters, e.g., line widths and heights. 3 To reduce parametric correlation and improve measurement performance and uncertainties, we have developed a Bayesian statistical approach that integrates a priori information gleaned from other measurements. This allows us to embed information obtained from reference metrology and complimentary ellipsometry of the optical constants, or to constrain the floating parametric range based on physical limits or known manufacturing variability. We have implemented this approach using scatterfield microscopy, but it applies equally to scatterometry or methods such as scanning-electron microscopy.The scatterfield-microscopy instrument is based on a Köhler illuminated bright-field microscope, such that each point at the conjugate back focal plane maps nominally to a plane wave of illumination at the sample. 4 Access to a large conjugate back Figure 1. Experimental data and library data fits for three die from the overlay-metrology advisory group OMAG-3 wafer. Top and middle critical dimensions (CDs) show good agreement with reference values.focal plane enables engineered illumination. This, in turn, has fueled advances in optical-system performance, characterization, and data analysis. As a result, the microscope-illumination and collection-path errors can be mapped to a functional dependence. They can then be used to normalize the experimental data for accurate comparison with electromagnetic simulations. 5 We acquired both microscope images and backgrounds as a function of angle. We calculated the mean intensity of the angle-resolved images, which we corrected using the background scan that was previously normalized by the known silicon reflectance. This is similar to conventional scatterometry, except that measurements were made with high-magnification image-forming optics.We compared the normalized experimental signatures with electromagnetic scattering simulations using parametric a...

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Fundamental limits of optical critical dimension metrology: a simulation study

Cited by 62 publications

References 0 publications

Solving the inverse grating problem by white light interference Fourier scatterometry

Solving the inverse grating problem by white light interference Fourier scatterometry

Performance analysis of coherent optical scatterometry

Bayesian statistics integrates prior information in parametric optical modeling

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