Wafer-based aberration metrology for lithographic systems using overlay measurements on targets imaged from phase-shift gratings

Haver, Sven van; Coene, W.; D’havé, Koen; Geypen, Niels; Adrichem, Paul van; Winter, Laurens de; Janssen, Ajem Guido; Cheng, Stone

doi:10.1364/ao.53.002562

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…Using equation (134), we can compute the PSF of an optical system with an exit pupil defined by a set of βcoefficients (equation ( 131)). The extended Nijboer-Zernike theory has been used in several applications, such as aberration retrieval in high-NA optical lithography systems [121][122][123] and acoustic diffraction problems [124,125].…”

Section: Psf Computation Using the Extended Nijboer-zernikementioning

confidence: 99%

Zernike polynomials and their applications

Niu

Tian

2022

J. Opt.

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The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However, due to the lack of a unified definition, many confusing indices have been used in the past decades and mathematical properties are scattered in the literature. This review provides a comprehensive account of Zernike circle polynomials and their noncircular derivatives, including history, definitions, mathematical properties, roles in wavefront fitting, relationships with optical aberrations, and connections with other polynomials. We also survey state-of-the-art applications of Zernike polynomials in a range of fields, including the diffraction theory of aberrations, optical design, optical testing, ophthalmic optics, adaptive optics, and image analysis. Owing to their elegant and rigorous mathematical properties, the range of scientific and industrial applications of Zernike polynomials is likely to expand. This review is expected to clear up the confusion of different indices, provide a self-contained reference guide for beginners as well as specialists, and facilitate further developments and applications of the Zernike polynomials.

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Section: Psf Computation Using the Extended Nijboer-zernikementioning

confidence: 99%

Zernike polynomials and their applications

Niu

Tian

2022

J. Opt.

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Artificial Neural Network for Diffraction Based Overlay Measurement

Kuo

Faricha

2016

IEEE Access

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Spatially varying aberration calibration using a pair of matched periodic pinhole array masks

Shao

Loktev²,

Tang

et al. 2019

Opt. Express

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For advanced imaging systems, e.g., projection systems for optical lithography, spatially varying aberration calibration is of utmost importance to achieve uniform imaging performance over the entire field-of-view (FOV). Here we present an efficient, accurate, and robust spatially varying aberration calibration method using a pair of 2-dimensional periodic pinhole array masks: the first mask in the object plane and the second mask in the image plane. Our method divides the entire FOV of the imaging system into partially overlapping subregions by using a measurement system consisting of an additional imaging system and a camera sensor. Each subregion, which covers several mask periods, is imaged onto a distinct camera pixel by the measurement system. Our method measures "Airy disc"-like patterns simultaneously in all subregions by scanning the second mask relative to the first mask over one mask p eriod. The number of subregions is equal to the number of camera pixels, and the sampling number of the measured patterns is equal to the scanning step number. The aberrations can be retrieved from the patterns measured in through-focus planes using an iterative optimization algorithm. In this paper, we performed experimental validation on a realistic lithography machine and demonstrate that our method is capable of retrieving the coefficients of 37 aberration terms, expressed as Zernike polynomials, with a sensitivity at nanometer scale.

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Wafer-based aberration metrology for lithographic systems using overlay measurements on targets imaged from phase-shift gratings

Cited by 3 publications

References 6 publications

Zernike polynomials and their applications

Zernike polynomials and their applications

Artificial Neural Network for Diffraction Based Overlay Measurement

Spatially varying aberration calibration using a pair of matched periodic pinhole array masks

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