Anisotropic Slope Distribution and Bidirectional Reflectance of a Rough Silicon Surface

Both one-dimensional (1D) and two-dimensional (2D) slope distributions were obtained from the surface topographic data, measured using an atomic force microscope for a rough silicon surface. The resulted slope distributions deviate significantly from the Gaussian distribution, with noticeable side peaks. The bidirectional reflectance distribution function (BRDF) of the same surface, measured with a laser scatterometer at 635 nm and 785 nm, exhibits subsidiary peaks. The measured slope distributions are implanted into a geometric optics model to predict the in-plane BRDF for different azimuthal angles. The 1D slope distribution has some success in predicting the BRDF at limited azimuthal angles, but is not applicable to other cases. On the other hand, the BRDF predicted using the 2D slope distribution matches well with the experimental results for any azimuthal angles. The method developed here may also help predict the BRDF for other rough surfaces with microstructures.