Research Papers

Lumped-Parameter Modeling of an Immersion Flow Field for Analyzing Meniscus Dynamic Behavior

[+] Author and Article Information
Ying Chen

State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University,
Hangzhou, 310027, China;
Georgia W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: yingchen@zju.edu.cn

Kok-Meng Lee

Georgia W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405;
State Key Laboratory of Digital Manufacturing
Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: kokmeng.lee@me.gatech.edu

Chun-Yeon Lin

Georgia W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: cylin219@gatech.edu

Xin Fu

State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University,
Hangzhou, 310027, China
e-mail: xfu@zju.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received September 11, 2012; final manuscript received June 14, 2013; published online August 30, 2013. Assoc. Editor: Prashant Mehta.

J. Dyn. Sys., Meas., Control 136(1), 011001 (Aug 30, 2013) (8 pages) Paper No: DS-12-1298; doi: 10.1115/1.4024889 History: Received September 11, 2012; Revised June 14, 2013

Motivated by the interest to increase production throughputs of immersion lithography machines, wafers are scanned at increasingly high velocities and accelerations, which may result in liquid loss at the receding contact line. The dynamic characteristics of the immersion fluid with free boundary play an important role for fluid management system, and are concerned in various potential immersion unit designs. To offer intuitive insights into the dynamic effects of the immersion fluid due to scan speeds, a lumped-parameter model based on two-dimensional (2D) image data has been developed to characterize the 3D hydrodynamics of the immersion flow process. To validate the model, meniscus behavior information under dynamic conditions is extracted experimentally and analyzed using image processing techniques. The reduced model agrees qualitatively well with the experimental data.

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Grahic Jump Location
Fig. 1

Illustration of immersion lithography

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Fig. 2

Liquid deformation and symbols

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Fig. 3

Lumped-parameter meniscus model

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Fig. 4

x-stage velocity and displacement

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Fig. 5

Edge finding process

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Fig. 6

Curve fits of edge data

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Fig. 7

Dynamic contact angles versus meniscus displacement

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Fig. 8

Meniscus transient responses (60 mm/s)

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Fig. 9

Meniscus transient responses (65 mm/s)

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Fig. 10

Dynamic contact angles (60 mm/s)

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Fig. 11

Dynamic contact angles (65 mm/s)



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