TECHNICAL PAPERS: Radiative Heat Transfer

Radiative Properties of Semitransparent Silicon Wafers With Rough Surfaces

[+] Author and Article Information
Y. H. Zhou

Department of Mechanical Engineering, University of Florida, Gainesville, FL 32611

Z. M. Zhang

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Heat Transfer 125(3), 462-470 (May 20, 2003) (9 pages) doi:10.1115/1.1565089 History: Received June 26, 2002; Revised November 20, 2002; Online May 20, 2003
Copyright © 2003 by ASME
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Surface at different scales
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Reflection and refraction at a micro-facet, where n is the unit normal of the micro-facet. Notice that si,sr, and st are the unit directional vectors for the incidence, reflection, and transmission (refraction), respectively.
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Re-striking probability: (a) rays reflected downward, (b) rays reflected upward, and (c) re-striking probability for upward reflected rays.
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Calculated (a) refractive index and (b) absorption coefficient of lightly doped silicon, using equations from Timans 1
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Calculated BRDF of an opaque surface for incidence angle θi=45°
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The in-plane (ϕr=180°) BRDF for different incidence angles at λ=635 nm and for a/σ=8.7: (a) numerical results; and (b) experimental data from Shen and Zhang 9
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Contour plot of the emittance of opaque silicon surfaces versus emission angle and the parameter a/σ
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The spectral radiative properties of 0.625-mm-thick silicon wafer: (a) emittance; (b) reflectance; and (c) transmittance. Case 1. Both surfaces are smooth; Case 2. Only one surface is smooth, the ray is incident on the rough surface; Case 3. Only one surface is smooth, the ray is incident on the smooth surface; Case 4. Both surfaces are rough.
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(a) Radiative properties of a 0.625-mm-thick silicon wafer versus wafer temperature, where the radiation is incident on the rough side and the other side is smooth (Case 2); and (b) The difference between the radiative properties of Case 2 and Case 1 defined in Fig. 8
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The BRDF and BTDF of a semitransparent silicon wafer at λ=1.7 μm and θi=30°, for Tw=500°C and a/σ=5: (a) incident on rough surface, the other side is smooth; (b) incident on smooth surface, the other side is rough; and (c) both surfaces are rough




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