Directional radiative properties of anisotropic rough silicon and gold surfaces

International Journal of Heat and Mass Transfer

Volumn 49, Issue 23-24, 2006, Pages 4482-4495

  Lee, H J ^a   Chen, Y B ^a   Zhang, Z M ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bidirectional reflectance; Monte Carlo method; Radiative properties; Surface roughness

Indexed keywords

ANISOTROPY; GOLD; MONTE CARLO METHODS; SILICON; SURFACE ROUGHNESS; SURFACE TOPOGRAPHY;

BIDIRECTIONAL REFLECTANCE; BIDIRECTIONAL REFLECTANCE DISTRIBUTION FUNCTION (BRDF); RADIATIVE PROPERTIES;

HEAT RADIATION;

ANISOTROPY; GOLD; HEAT RADIATION; MONTE CARLO METHODS; SILICON; SURFACE ROUGHNESS; SURFACE TOPOGRAPHY;

EID: 33746899059     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2006.05.022     Document Type: Article

References (44)

1. Timans P.J. The thermal radiative properties of semiconductors. In: Roozeboom F. (Ed). Advances in Rapid Thermal and Integrated Processing (1996), Academic Publishers, Dordrecht, Netherlands 35-102
2. Schietinger C. Wafer temperature measurement in RTP. In: Roozeboom F. (Ed). Advances in Rapid Thermal and Integrated Processing (1996), Academic Publishers, Dordrecht, Netherlands 103-123
3. Zhang Z.M. Surface temperature measurement using optical techniques. In: Tien C.L. (Ed). Annual Review of Heat Transfer vol. 11 (2000), Begell House, New York 351-411
4. Vandenabeele P., and Maex K. Influence of temperature and backside roughness on the emissivity of Si wafers during rapid thermal processing. J. Appl. Phys. 72 12 (1992) 5867-5875
5. Zhou Y.H., Shen Y.J., Zhang Z.M., Tsai B.K., and DeWitt D.P. A Monte Carlo model for predicting the effective emissivity of the silicon wafer in rapid thermal processing furnaces. Int. J. Heat Mass Transfer 45 9 (2002) 1945-1949
6. Modest M.F. Radiative Heat Transfer (1993), McGraw-Hill, New York (Chapter 3)
7. Masuda K., Takashima T., and Takayama Y. Emissivity of pure and sea waters for the model sea-surface in the infrared window regions. Remote Sens. Environ. 24 2 (1988) 313-329
8. H.J. Lee, Q.Z. Zhu, Z.M. Zhang, Radiative properties of anisotropic microrough silicon surfaces, in: Proceedings of 38th AIAA Thermophysics Conference, 2005, AIAA-2005-5209.
9. Burnell J.G., Nicholas J.V., and White D.R. Scattering model for rough oxidized metal surfaces applicable to radiation thermometry of reformer furnaces. Opt. Eng. 34 6 (1995) 1749-1755
10. B. Adams, A. Hunter, M. Yam, B. Peuse, Determining the uncertainty of wafer temperature measurements induced by variations in the optical properties of common semiconductor materials, in: Proceedings of the 197th ECS Meeting, 2000 pp. 363-374.
11. Maradudin A.A., Michel T., McGurn A.R., and Mendez E.R. Enhanced backscattering of light from a random grating. Ann. Phys. 203 2 (1990) 255-307
12. Sanchez-Gil J.A., and Nieto-Vesperinas M. Light scattering from random rough dielectric surfaces. J. Opt. Soc. Am. A 8 8 (1991) 1270-1286
13. Beckmann P., and Spizzichino A. The Scattering of Electromagnetic Waves from Rough Surfaces (1987), Artech House, Norwood, Massachusetts (Chapter 5)
14. Ogilvy J.A. Theory of Wave Scattering from Random Rough Surfaces (1991), Adam Hilger, Bristol, England (Chapter 4)
15. Tsang L., and Kong J.A. Scattering of Electromagnetic Waves: Advanced Topics (2001), Wiley, New York (Chapter 2)
16. Torrance K.E., and Sparrow E.M. Theory for off-specular reflection from roughened surfaces. J. Opt. Soc. Am. 57 9 (1967) 1105-1114
17. Tang K., and Buckius R.O. A statistical model of wave scattering from random rough surfaces. Int. J. Heat Mass Transfer 44 21 (2001) 4059-4073
18. Tsang L., and Kong J.A. Energy conservation for reflectivity and transmissivity at a very rough surface. J. Appl. Phys. 51 1 (1980) 673-680
19. Caron J., Lafait J., and Andraud C. Catastrophe theory interpretation of multiple peaks produced by light scattering from very rough dielectric surfaces. Physica B 325 1-4 (2003) 76-85
20. Macaskill C. Geometric optics and enhanced backscatter from very rough surfaces. J. Opt. Soc. Am. A 8 1 (1991) 88-96
21. Tang K., and Buckius R.O. The geometric optics approximation for reflection from two-dimensional random rough surfaces. Int. J. Heat Mass Transfer 41 13 (1998) 2037-2047
22. Zhou Y.H., and Zhang Z.M. Radiative properties of semitransparent silicon wafers with rough surfaces. J. Heat Transfer 125 3 (2003) 462-470
23. Lee H.J., Lee B.J., and Zhang Z.M. Modeling the radiative properties of semitransparent wafers with rough surfaces and thin-film coatings. J. Quant. Spectrosc. Radiat. Transfer 93 (2005) 185-194
24. Yoshimori K., Itoh K., and Ichioka Y. Optical characteristics of a wind-roughened water surface: a two-dimensional theory. Appl. Opt. 34 27 (1995) 6236-6247
25. Lyons A.P., Fox W.L.J., Hasiotis T., and Pouliquen E. Characterization of the two-dimensional roughness of wave-rippled sea floors using digital photogrammetry. IEEE J. Oceanic Eng. 27 3 (2002) 515-524
26. Karabacak T., Zhao Y.-P., Liew T., Wang G.-C., and Lu T.-M. Anisotropic scaling of hard disk surface structures. J. Appl. Phys. 88 6 (2000) 3361-3366
27. Zhu Q.Z., and Zhang Z.M. Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface. J. Heat Transfer 126 6 (2004) 985-993
28. Zhu Q.Z., and Zhang Z.M. Correlation of angle-resolved light scattering with the microfacet orientation of rough silicon surfaces. Opt. Eng. 44 7 (2005) 073601
29. Shen Y.J., Zhu Q.Z., and Zhang Z.M. A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces. Rev. Sci. Instrum. 74 11 (2003) 4885-4892
30. Zhu Q.Z., Lee H.J., and Zhang Z.M. The validity of using thin-film optics in modeling the bidirectional reflectance of coated rough surfaces. J. Thermophys. Heat Transfer 19 4 (2005) 548-557
31. Wu S.C., Chen M.F., and Fung A.K. Non-Gaussian surface generation. IEEE Trans. Geosci. Remote Sens. 26 6 (1988) 885-888
32. Thorsos E.I. The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum. J. Acoust. Soc. Am. 83 1 (1988) 78-92
33. Zhao Y.-P., Wang G.-C., and Lu T.-M. Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications (2001), Academic Press, San Diego, California (Chapter 2)
34. Knotts M.E., Michel T.R., and O'Donnell K.A. Comparisons of theory and experiment in light scattering from a randomly rough surface. J. Opt. Soc. Am. A 10 5 (1993) 928-941
35. Press W.H. Numerical Recipes in C: The Art of Scientific Computing. second ed. (1992), Cambridge University Press, Cambridge, New York (Chapter 7)
36. Smith B.G. Geometrical shadowing of a random rough surface. IEEE Trans. Antennas Propagation 15 5 (1967) 668-671
37. Tsai B.K., Dewitt D.P., and Shaffer G.H. Macroscopic spread function analysis for subsurface scattering of semitransparent materials. J. Thermophys. Heat Transfer 8 2 (1994) 202-207
38. Zaworski J., Welty J.R., Palmer B.J., and Drost M.K. Comparison of experiment with Monte Carlo simulations on a reflective gap using a detailed surface properties model. J. Heat Transfer 118 2 (1996) 388-393
39. Howell J.R. The Monte Carlo method in radiative heat transfer. J. Heat Transfer 120 3 (1998) 547-560
40. Bruce N.C. Calculations of the Mueller matrix for scattering of light from two-dimensional surfaces. Waves Random Media 8 1 (1998) 15-28
41. E.L. Church, P.Z. Takacs, Effects of non-vanishing tip size in mechanical profile measurements, in: C.P. Grover (Ed.), Proceedings of the Society of Photo-Optical Instrumentation Engineers, vol. 1332, 1991, pp. 504-514.
42. O'Donnell K.A. Effects of finite stylus width in surface-contact profilometry. Appl. Opt. 32 25 (1993) 4922-4928
43. Palik E.D. Handbook of Optical Constants of Solids (1985), Academic Press, Orlando, Florida
44. O'Donnell K.A., and Mendez E.R. Experimental study of scattering from characterized random surfaces. J. Opt. Soc. Am. A 4 7 (1987) 1194-1205