Optical Alignment Optimizations for Reducing Wafer-Induced Shift

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We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and non-minimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then proceeding to BRST quantize this system. Our analysis includes the introduction of constant ghosts and associated auxiliary fields needed to gauge fix symmetries associated with zero modes. All fields introduced in the process of quantization can be integrated out explicitly, resulting in the prescriptions for computing scattering amplitudes that have appeared previously in the literature. The zero mode insertions in the path integral follow from the integration over the constant auxiliary fields.

Section: Introductionmentioning

confidence: 78%

“…We have proposed a new system that classifies measurement errors into position shifts induced by amplitude error and phase error. 5) Figure 3 shows the outline of the new classification.…”

Section: Classification System For Measurement Errorsmentioning

confidence: 99%

Tool-Induced Shift and Pupil Transmittance Distribution in Measurement Optics

Sugaya

Nagayama

Masada

2005

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“…Recent exposure apparatus includes a two-dimensional digital imaging sensor utilizing wideband white light, which has little sensitivity to variations in the resist thickness. [25][26][27][28][29][30] The experimental and theoretical confirmation of the FWM metrology concept in the latest ArF exposure apparatus are topics for future research.…”

Section: Embedment To Feedback System Of Exposure Apparatusmentioning

confidence: 99%

Accuracy of focus wedge mark measurement using fitting function for partially coherent illumination

Yashiki¹,

Suwa²,

Takeuchi³

2015

The theory of best focus determination in focus wedge mark (FWM) metrology is extended from coherent illumination to partially coherent illumination. Through a theoretical analysis, we propose a focus curve fitting function suitable for the FWM, which is expressed by the sinc function. The experimental results for best focus estimations using two types of fitting functions, which are a conventional quadratic polynomial and the proposed sinc function, are reported for various defocus regions to be fitted. When the first inflection points of the sinc function are included in the fitting defocus region, we can achieve stable best focus estimation within 3 nm in our i-line exposure experiments.

“…The measurement is usually performed with an exposure apparatus equipped with a laser spot sensor employing a monochromatic wavelength, 14) but recently we have employed a two-dimensional digital imaging sensor utilizing wideband white light, which has little sensitivity to variations in the resist thickness. [25][26][27][28][29][30] Both of these sensors detect the tip of the FWM on the resist and determine the length using several algorithms. The thinnest point of the resist is at the tip, and this three-dimensional structure can sometimes lead to an undesirable optical interference phenomenon in the laser spot measurement and increase the uncertainty in the FWM length measurement.…”

Section: Measurement Accuracymentioning

confidence: 99%

Theoretical analysis of focus wedge mark for best-focus determination in photolithography

Suwa¹,

Yashiki²,

Hirukawa³

2014

The focus wedge mark (FWM), a periodic array of wedge shaped marks, is a tool used to determine the best-focus position in photolithography. Here, we develop a one-dimensional physical model for the FWM and analyze the focus dependence of the wedge length under coherent imaging conditions. The amplification factor of the FWM, which describes the superiority of the FWM compared to measurements based on line and space marks, is determined by the geometrical magnification of the wedge. We show that around the exposure dose energy typically used in lithography the amplification factor is much higher than the geometrical magnification. Numerical lithography simulations confirm that the focus sensitivity of the FWM is much higher than that of a line and space pattern.