Bi-Directional Reflectivity of Surfaces with Anisotropic Roughness on the Wafer Backside

Abstract

Light scattering from rough surfaces is an area of research that has received a great deal of interest from several engineering disciplines. Analytical models for reflectivity have been useful in the study of medical imaging, atomic physics, remote sensing and rapid thermal processing (RTP) of silicon semiconductor wafers. This paper presents a new variation of the surface generation method (SGM) approach to geometric optics (GO) modeling of reflectivity. The presented approach employs a triangular facet (TF) surface treatment instead of the conventional rectangular facets. This new method is used to calculate bidirectional reflectivity distribution function (BRDF) results for one-dimensional and two-dimensional surfaces with varying microscale roughness characteristics. The results agree well with published analytical and experimental findings, indicating that the TF method is a reliable means of estimating surface reflectivity when the geometric optics regime is valid. At large angles of incidence and the BRDF results exhibit an interesting off-specular reflectivity peak that appears to correspond well with existing experimental findings. This behavior is caused by the effects of Fresnel reflectivity at large incident light angles and the geometrical relationship between the incident beam and the number of facets covered by the beam width. A comparison with the rigorous finite-difference time-domain solution of the light scattering from the one-dimensional random roughness surfaces allows the validity regime map of the GO to be drawn. The map will facilitate the use of the GO solution that is computationally efficient than many other methods.