Directional radiative properties of anisotropic rough silicon and gold surfaces

Abstract

Recent studies have shown that the topography of some chemically etched microrough silicon surfaces is non-Gaussian and may be strongly anisotropic. However, the bidirectional reflectance distribution function (BRDF) of anisotropic surfaces has not been fully understood. The present study uses the Monte Carlo method to investigate the out-of-plane BRDF, multiple scattering, and the change of the polarization state upon reflection. Two ray-tracing algorithms are developed that incorporate the surface topography or slope distribution of the samples obtained by the use of an atomic force microscope. The predicted BRDFs for silicon surfaces with or without a gold coating are in reasonable agreement with the results measured using a laser scatterometer at a wavelength of 635 nm. The employment of surface topographic data is indispensable to the BRDF modeling of anisotropic surfaces. While first-order scattering makes the dominant contribution to reflections from the studied surfaces, it is critical to consider the polarization state change in order to correctly predict the out-of-plane BRDF. The versatile Monte Carlo modeling tools developed through the present study help gain a better understanding of the directional radiative properties of microrough surfaces and, furthermore, will have an impact on thermal metrology in the semiconductor industry.