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Application of the Measured Slope Distribution to the Prediction of the Bidirectional Reflectance for Rough Surfaces

[+] Author Affiliations
Q. Z. Zhu, Z. M. Zhang

Georgia Institute of Technology, Atlanta, GA

Paper No. IMECE2003-41815, pp. 357-364; 8 pages
  • ASME 2003 International Mechanical Engineering Congress and Exposition
  • Heat Transfer, Volume 2
  • Washington, DC, USA, November 15–21, 2003
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 0-7918-3718-1 | eISBN: 0-7918-4663-6, 0-7918-4664-4, 0-7918-4665-2
  • Copyright © 2003 by ASME


Surface topography of the rough side of a silicon wafer is characterized using an atomic force microscope (AFM). The slope distribution calculated from the measured surface profiles deviates significantly from the Gaussian distribution. The experimentally obtained slope distribution is incorporated into a geometric-optics model to predict the bidirectional reflectance distribution function (BRDF) of the rough surface. Comparison has been made between the predicted BRDF and that measured with a recently built bidirectional scatterometer, at 635 nm and 785 nm for different incoming angles. The trends agree well between the predicted and measured BRDFs, especially for the parallel-polarized incidence (p-polarization), although relatively large discrepancies exist near the specular peak and at large reflection angles. This work offers a plausible explanation of the second non-specular peak in the observed BRDF as associated with the subsidiary maximum in the slope distribution. Anisotropic features have been found both in the calculated slope distributions and the measured BRDFs.

Copyright © 2003 by ASME



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