Bidirectional Reflectance Distribution Function of Rough Silicon Wafers
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The trend towards miniaturization of patterning features in integrated circuits (IC) has made traditional batch furnaces inadequate for many processes. Rapid thermal processing (RTP) of silicon wafers has become more popular in recent years for IC manufacturing. Light-pipe radiation thermometry is the method of choice for real-time temperature monitoring in RTP. However, the radiation environment can greatly affect the signal reaching the radiometer. The bidirectional reflectance distribution function (BRDF) of rough silicon wafers is needed for the prediction of the reflected radiation that reaches the radiometer and for reflective RTP furnace design. This paper presents the BRDF measurement results for several processing wafers in the wavelength range from 400 to 1100 nm with the spectral tri-function automated reference reflectometer (STARR) at the National Institute of Standards and Technology (NIST). The rms roughness of these samples ranges from 1 nm to 1 μm, as measured with an optical interferometric microscope. Correlations between the BRDF and surface parameters are obtained using different models by comparing theoretical predictions with experiments.
- R. G. Hering and T. F. Smith, Intl. J. Heat Mass Transfer 13:725 (1970).
- B. Hapke, Icarus 59:41 (1984); B. Hapke, Theory of Reflectance and Emittance Spectroscopy (Cambridge University Press, Cambridge, UK, 1993), Chap. 12.
- D. P. Greenberg, K. E. Torrance, P. Shirley, J. Arvo, J. A. Ferwerda, S. Pattanaik, E. Lafortune, B. Walter, S.-C. Foo, and B. Trumbore, in SIGGRAPH 97 (Association for Computing Machinery, Annual Conference Series, 1997), pp. 477-494.
- J. C. Stover, M. L. Bernt, E. L. Church, and P. Z. Takacs, Proc. SPIE 2260:182 (1994).
- M. Bjuggren, L. Krummenacher, and L. Mattsson, Opt. Eng. 36:874 (1997).
- E. L. Church and P. Z. Takacs, in Handbook of Optics, Volume I, 2nd ed., M. Bass, ed. in chief (McGraw-Hill, New York, 1995), Chap. 7.
- J. C. Stover, Optical Scattering-Measurement and Analysis, 2nd ed. (SPIE Optical Engineering Press, Bellingham, Washington, 1995), Chap. 4.
- F. Rosa, Y. H. Zhou, Z. M. Zhang, D. P. DeWitt, and B. K. Tsai, in Advanced in Rapid Thermal Processing, F. Roozeboom, J. C. Gelpey, M. C. Öztürk, and J. Nakos, eds. (The Electrochemical Society, Pennington, New Jersey, 1999), Proc. Vol. 99-10, pp. 419-426.
- Z. M. Zhang, Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, New York, 2000), Vol. 11, Chap. 6.
- P. J. Timans, Mat. Sci. Semicon. Processing 1:169 (1998).
- Y. H. Zhou, Y. J. Shen, Z. M. Zhang, B. K. Tsai, and D. P. DeWitt, in Proc. 8th Int. Conf. on Advanced Thermal Processing of Semiconductors (RTP'2000), Gaithersburg, Maryland (2000), pp. 94-103.
- F. E. Nicodemus, Appl. Opt. 9:1474 (1970).
- P. Y. Barnes, E. A. Early, and A. C. Parr, Spectral Reflectance, NIST Special Publication 250-48 (US Government Printing Office, Washington, DC, 1998); J. E. Proctor and P. Y. Barnes, J. Res. Natl. Inst. Stand. Technol. 101:619 (1996).
- M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993), Chap. 2.
- WYKO Corp., Tucson, AZ. The identification within this paper of particular commercial equipment does not imply recommendation or endorsement by NIST, nor does it imply that the identified products are the best available for the purpose.
- D. J. Whitehouse, Meas. Sci. Technol. 8:955 (1997).
- E. I. Chaikina, R. Hernández-Walls, and E. R. Méndez, Proc. SPIE 3141:164 (1997); E. I. Chaikina, P. Negrete-Regagnon, G. Martínez-Niconoff, and E. R. Méndez, Proc. SPIE 3426:153 (1998).
- J. Q. Lu and A. A. Maradudin, Proc. SPIE 3141:186 (1997).
- D. F. Edwards, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, Orlando, Florida, 1985), pp. 547-569.
- P. J. Timans, in Advances in Rapid Thermal and Integrated Processing, F. Roozeboom, ed. (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996), Chap. 2.
- J. A. Ogilvy, Rep. Prog. Phys. 50:1553 (1987).
- R. A. Dimenna and R. O. Buckius, J. Thermophys. Heat Transfer 8:393 (1994).
- K. Tang, R. A. Dimenna, and R. O. Buckius, Int. J. Heat Mass Transfer 40:49 (1997).
- D. W. Cohn, K. Tang, and R. O. Buckius, Int. J. Heat Mass Transfer 40:3223 (1997).
- H. Davies, Proc. IEE 101:209 (1954); L.M. Spetner and H. Davies, Proc. IEE 102C:148 (1955).
- P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 3.
- A. F. Houchens and R. G. Hering, Prog. Astron. Aeron. 20:65 (1967).
- K. E. Torrance and E. M. Sparrow, J. Opt. Soc. Am. 57:1105 (1967).
- J. G. Burnell, J. V. Nicholas, and D. R. White, Opt. Eng. 34:1749 (1995).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd Ed. (Cambridge University Press, New York, 1992), Chap. 15.
- Bidirectional Reflectance Distribution Function of Rough Silicon Wafers
International Journal of Thermophysics
Volume 22, Issue 4 , pp 1311-1326
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- bidirectional reflectance distribution function (BRDF)
- radiometric temperature measurement
- rapid thermal processing (RTP)
- silicon wafers
- surface roughness
- Industry Sectors
- Author Affiliations
- 1. Department of Mechanical Engineering, University of Florida, Gainesville, Florida, 32611, U.S.A
- 2. Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899, U.S.A