Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles

Naqvi, S. Sohail H.; Krukar, Richard H.; McNeil, J. R.; Franke, James E.; Niemczyk, Thomas M.; Haaland, David M.; Gottscho, Richard A.; Kornblit, A.

doi:10.1364/josaa.11.002485

Cited by 39 publications

(17 citation statements)

References 23 publications

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“…To solve the inverse problem, the grating shape is parametrized, 8 and a parameter space is defined by allowing each grating shape parameter to vary over a chosen range. A rigorous diffraction model 9 based on a modal method ͑MMFE-modal method by Fourier expansion, 10 or rigorous coupled-wave analysis ͑RCWA͒ is used to calculate the diffracted light fingerprint from each grating in the parameter space.…”

Section: Introductionmentioning

confidence: 99%

Measurement of residual thickness using scatterometry

Fuard¹,

Perret²,

Farys³

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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Nanoimprint lithography (NIL) processes have the characteristic that a residual resist layer is always present between the nanoimprinted features. This residual resist layer must be removed to obtain usable resist masks for pattern transfer. As this resist layer is removed using oxygen-based plasma processes, the residual thickness nonuniformity translates into feature width dispersion. Thus, the uniformity of this residual thickness after imprint remains an important issue for nanoimprint lithography and a reliable metrology procedure is required for. At present, the standard measurement method is based on scanning electron microscopy (SEM) cross section, which is destructive, time consuming, and may sometimes provide only moderate accuracy. The work presented here will assess and show the interest of scatterometry, which is a nondestructive optical method of metrology that can be easily applied to NIL. This measurement procedure exhibits very good accuracy on the two-dimensional-feature geometry determination, especially for residual thickness. Scatterometry also eases time-consuming studies like residual thickness measurement at the local scale or at the wafer scale. Moreover, this article shows that the imprint uniformity studies provide very interesting information on the mold deformation

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Section: Introductionmentioning

confidence: 99%

Measurement of residual thickness using scatterometry

Fuard¹,

Perret²,

Farys³

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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show abstract

“…eT.e = (y -I.C)T.(y Xc) (5) Minimization of eTe, solving for c and executing these operations for all column vectors y of Y results in the well-known formula for the regression matrix C: C = (1T1) -1 .1Ty (6) After performing this regression step, the properties of an unknown sample in terms of the row vector yT easily obtained from the measured diffraction intensities expressed by the row vector T by multiplying it by the C-matrix: Y:11=C•X: (7) with yT (y1y2y.y) and yT Of course, the mean centering and other data pretreatment procedures have to be considered during prediction. But there is another critical shortcoming in the ThS-calculation of C. For XX to be invertible it must be full rank.…”

Section: Basic Principle and Linear Methodsmentioning

confidence: 99%

<title>Photoresist metrology based on light scattering</title>

Bischoff

Baumgart

Truckenbrodt

et al. 1996

Metrology, Inspection, and Process Control for Microlithography X

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Angle resolved light scatteromeiry along with advanced data analysis is a promising new metrology technique to meet the challenges oftoday's and tomorrow's submicron technology. The measurement accuracy strongly depends on the performance capabilities of the algorithms utilized for data exploration and analysis. Presently, multivariate regression methods such as inverse least squares and principal component approaches are prefened. Substantial accuracy gains may be achieved by applying quasi-nonlinear methods, i.e. nonlinear data pretreatment followed by the usual linear regression. In this way, not only were the linewidth prediction errors in measuring developed resist lines pushed to below 20 nm, but likewise more complicated tasks as silylation profile evaluation and latent image measurement could be addressed satisfactorily. . INTRODUCTIONRecently, a new method was introduced in micrometrology, which consists in a combination of angle resolved scattered light measurement (ARS) and sophisticated data analysis '. A high measurement throughput, sufficient accuracy in the submicron range, nondesiructive probing and on-line capability are the crucial benefits ofthis metrology. The basic principle ofthe light measurement is straightforward: A focused laser beam is impinging on the surface under investigation. Caused by the diffraction and the microroughness ofthe sample, the light is scattered into the full hemisphere above the specimen. Considering only onedimensional surfaces (e.g. line space patterns) and adjusting the incident beam perpendicular to the lines, the light distribution will essentially be confmed to the plane of incidence. The resulting light distribution strongly depends on the topographic and optical properties ofthe sample. Thus, it may be regarded as a kind of "optical fingerprint". Particularly, ifa periodic line/space pattern is illuminated with a laser spot covering more than a few pitches, sharp diffraction orders stand out from the noisy background. Now, the difficulty remains of identifying the profile ofthe scatterer from this "fingerprint". Due to the ambiguity between scattering surface and measured light intensity distribution, an analytical solution ofthe problem may not be gained in general. However, if certain a-priori information about the surface profile and the refraction indices is given, a quantitative assignment between light intensities and profile parameters such as linewidth, height, slope angle and others may be obtained by establishing multivariate regression models. Until now, several applications such as DRAM trench depth characterization 2, latent image and post exposure bake monitoring , PSM meirology and submicron linewidth resist metrology based on scatterometry were published. Predominantly, linear regression models including the inverse least squares method (ILS), the principal component regression (PCR) and the partial least squares method (PLS) known from chemometrics 6 are applied. Owing to the linearization inherent in these models, the resulting accuracy is ...

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“…In the GS method, a Fourier transform loop is set up between the di raction and grating domains; it is known that di raction from a periodic structure is sensitive to small changes in the shape of the structure pro le [23]. Figure 1 shows a schematic diagram of the GS phase retrieval routine (see [1][2][3], especially reference [3], for theory of the GS Fourier transform iterative method, the algorithm with applications, and algorithm convergence).…”

Section: Theory and Algorithms: Gerchberg-saxton Algorithm Rigorous mentioning

confidence: 99%

Characterization of 1D diffractive optical elements by phase inversion

Yuan¹,

Burge²,

Tam³

et al. 2001

Journal of Modern Optics

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We consider the feature dimensions of selected 1D di ractive optical elements (DOE) such that the Fourier transform based GerchbergSaxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction.We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ¹ 5 ¶ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10 ¶ periodicity, its sampled binary equivalent with minimum feature sizes of 0:1 ¶ and for continuous linear blazed gratings with period varied from ¹ 16 ¶ to ¹ 2 ¶. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more in uenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods >¹ 5 ¶.

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Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles

Cited by 39 publications

References 23 publications

Measurement of residual thickness using scatterometry

Measurement of residual thickness using scatterometry

<title>Photoresist metrology based on light scattering</title>

Characterization of 1D diffractive optical elements by phase inversion

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