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Bidirectional Reflectance Distribution Function of Rough Silicon Wafers

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Abstract

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.

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REFERENCES

  1. R. G. Hering and T. F. Smith, Intl. J. Heat Mass Transfer 13:725 (1970).

    Google Scholar 

  2. B. Hapke, Icarus 59:41 (1984); B. Hapke, Theory of Reflectance and Emittance Spectroscopy (Cambridge University Press, Cambridge, UK, 1993), Chap. 12.

    Google Scholar 

  3. 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.

  4. J. C. Stover, M. L. Bernt, E. L. Church, and P. Z. Takacs, Proc. SPIE 2260:182 (1994).

    Google Scholar 

  5. M. Bjuggren, L. Krummenacher, and L. Mattsson, Opt. Eng. 36:874 (1997).

    Google Scholar 

  6. 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.

    Google Scholar 

  7. J. C. Stover, Optical Scattering-Measurement and Analysis, 2nd ed. (SPIE Optical Engineering Press, Bellingham, Washington, 1995), Chap. 4.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. Z. M. Zhang, Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, New York, 2000), Vol. 11, Chap. 6.

    Google Scholar 

  10. P. J. Timans, Mat. Sci. Semicon. Processing 1:169 (1998).

    Google Scholar 

  11. 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.

  12. F. E. Nicodemus, Appl. Opt. 9:1474 (1970).

    Google Scholar 

  13. 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).

    Google Scholar 

  14. M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993), Chap. 2.

    Google Scholar 

  15. 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.

  16. D. J. Whitehouse, Meas. Sci. Technol. 8:955 (1997).

    Google Scholar 

  17. 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).

    Google Scholar 

  18. J. Q. Lu and A. A. Maradudin, Proc. SPIE 3141:186 (1997).

    Google Scholar 

  19. D. F. Edwards, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic Press, Orlando, Florida, 1985), pp. 547-569.

    Google Scholar 

  20. P. J. Timans, in Advances in Rapid Thermal and Integrated Processing, F. Roozeboom, ed. (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996), Chap. 2.

    Google Scholar 

  21. J. A. Ogilvy, Rep. Prog. Phys. 50:1553 (1987).

    Google Scholar 

  22. R. A. Dimenna and R. O. Buckius, J. Thermophys. Heat Transfer 8:393 (1994).

    Google Scholar 

  23. K. Tang, R. A. Dimenna, and R. O. Buckius, Int. J. Heat Mass Transfer 40:49 (1997).

    Google Scholar 

  24. D. W. Cohn, K. Tang, and R. O. Buckius, Int. J. Heat Mass Transfer 40:3223 (1997).

    Google Scholar 

  25. H. Davies, Proc. IEE 101:209 (1954); L.M. Spetner and H. Davies, Proc. IEE 102C:148 (1955).

    Google Scholar 

  26. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chap. 3.

    Google Scholar 

  27. A. F. Houchens and R. G. Hering, Prog. Astron. Aeron. 20:65 (1967).

    Google Scholar 

  28. K. E. Torrance and E. M. Sparrow, J. Opt. Soc. Am. 57:1105 (1967).

    Google Scholar 

  29. J. G. Burnell, J. V. Nicholas, and D. R. White, Opt. Eng. 34:1749 (1995).

    Google Scholar 

  30. 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.

    Google Scholar 

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Shen, Y.J., Zhang, Z.M., Tsai, B.K. et al. Bidirectional Reflectance Distribution Function of Rough Silicon Wafers. International Journal of Thermophysics 22, 1311–1326 (2001). https://doi.org/10.1023/A:1010636914347

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