Abstract
In the semiconductor industry, there is an increasing demand for thermal stability to optimize the performance of lithography machines. This results in a need for computational tools that are able to accurately model radiation heat transfer, with the ability to include specular and angle-dependent reflection and take the influence of the polarization into account. An analytical approximation model of a square passage is formulated, that includes angle-dependent reflecting surfaces and the influence of polarization. These problems can be used as benchmarks to verify radiation modeling tools, e.g., comsol. The tool is validated by modeling an experiment and comparing the numerical results with the experimental data. The impact of angle dependency and polarization on the heat flux through passages is discussed.
References
1.
Jasper
,
H. C.
, and
van Schoot
,
J.
, 2018
, “
Fundamentals of EUVL Scanners
,” EUV Lithography
, 2nd ed., Chap. 9, Fundamentals of EUVL Scanners.2.
Edwards
,
D. K.
, and
Tobin
,
R. D.
, 1967
, “
Effect of Polarization on Radiant Heat Transfer Through Long Passages
,” ASME J. Heat Transfer-Trans. ASME
,
89
(2
), pp. 132
–138
.10.1115/1.36143353.
Miranda
,
P. C.
, 1996
, “
A Calculation and Experimental Verification of the Infrared Transmission Coefficient of Straight Cylindrical Metal Tubes
,” ASME J. Heat Transfer-Trans. ASME
,
118
(2
), pp. 495
–497
.10.1115/1.28258764.
Edwards
,
D. K.
, and
Bevans
,
J. T.
, 1965
, “
Effect of Polarization on Spacecraft Radiation Heat Transfer
,” AIAA J.
,
3
(7
), pp. 1323
–1329
.10.2514/3.31315.
Oppenheim
,
U. P.
, and
Feiner
,
Y.
, 1995
, “
Polarization of the Reflectivity of Paints and Other Rough Surfaces in the Infrared
,” Appl. Opt.
,
34
(10
), pp. 1664
–1671
.10.1364/AO.34.0016646.
Howell
,
J. R.
,
Mengüç
,
M. P.
, and
Siegel
,
R.
, 2016
, Thermal Radiation Heat Transfer
, 6th ed.,
CRC Press
, Boca Raton, FL.7.
Modest
,
M. F.
, 2013
, Radiative Heat Transfer
, 3rd ed.,
Elsevier
, Amsterdam, The Netherlands.8.
Qu
,
Y.
,
Howell
,
J. R.
, and
Ezekoye
,
O. A.
, 2007
, “
Monte Carlo Modeling of a Light-Pipe Radiation Thermometer
,” IEEE Trans. Semicond. Manuf.
,
20
(1
), pp. 39
–49
.10.1109/TSM.2007.8907739.
Sparrow
,
E. M.
,
Eckert
,
E. R. G.
, and
Jonsson
,
V. K.
, 1962
, “
An Enclosure Theory for Radiative Exchange Between Specularly and Diffusely Reflecting Surfaces
,” ASME J. Heat Transfer-Trans. ASME
,
84
(4
), pp. 294
–299
.10.1115/1.368437510.
COMSOL
, 2018, COMSOL Multiphysics Reference Manual, Version 5.4,
COMSOL
, accessed Sept., www.comsol.com11.
Wallace
,
A. M.
,
Liang
,
B.
,
Trucco
,
E.
, and
Clark
,
J.
, 1999
, “
Improving Depth Image Acquisition Using Polarized Light
,” Int. J. Comput. Vision
,
32
(2
), pp. 87
–109
.10.1023/A:100815441534912.
Ho
,
C. Y.
, and
Chu
,
T. K.
, 1977
, “
Electrical Resistivity and Thermal Conductivity of Nine Selected AISI Stainless Steels
,” Defense Technical Information Center, Fort Belvoir, VA, Report No. CINDAS 45.13.
Fouaidy
,
M.
, and
Hammoudi
,
N.
, 2006
, “
RRR of Copper Coating and Low Temperature Electrical Resistivity of Material for TTF Couplers
,” Phys. C Superconduct.
,
441
, pp. 137–144.14.
Birkebak
,
R. C.
, and
Eckert
,
E. R. G.
, 1965
, “
Effects of Roughness of Metal Surfaces on Angular Distribution of Monochromatic Reflected Radiation
,” ASME J. Heat Transfer-Trans. ASME
,
87
(1
), pp. 85
–93
.10.1115/1.368906115.
Leen
,
L.
,
Severins
,
I.
,
Peeters
,
J.
, and
Steenackers
,
G.
, 2018
, “
Diffuse Versus Specular Reflection: The Influence of Hot Spots on Reflected Apparent Temperature
,” QIRT Proceedings
, Berlin, June 25–29, pp. 412
–417
.16.
Sparrow
,
E. M.
, 1960
, “
Application of Variational Methods to Radiation Heat-Transfer Calculations
,” ASME J. Heat Transfer-Trans. ASME
,
82
(4
), pp. 375
–380
.10.1115/1.367995717.
Sparrow
,
E. M.
,
Gregg
,
J. L.
,
Szel
,
J. V.
, and
Manos
,
P.
, 1961
, “
Analysis, Results, and Interpretation for Radiation Between Some Simply-Arranged Gray Surfaces
,” ASME J. Heat Transfer-Trans. ASME
,
83
(2
), pp. 207
–214
.10.1115/1.368052318.
Eckert
,
E. R. G.
, and
Sparrow
,
E. M.
, 1961
, “
Radiative Heat Exchange Between Surfaces With Specular Reflection
,” Int. J. Heat Mass Transfer
,
3
(1
), pp. 42
–54
.10.1016/0017-9310(61)90004-719.
Hering
,
R. G.
, 1966
, “
Radiative Heat Exchange Between Conducting Plates With Specular Reflection
,” ASME J. Heat Transfer-Trans. ASME
,
88
(1
), pp. 29
–36
.10.1115/1.3691466Copyright © 2021 by ASME
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