Ph. D. Dissertation Defense by Qunzhi Zhu
Friday, July 2, 2004

(Dr. Zhuomin Zhang, Chair)

"Modeling and Measurements of the Bidirectional Reflectance of Microrough Silicon Surfaces"


The study of the bidirectional reflectance of silicon surfaces is very important to the temperature measurement and control in rapid thermal processing of semiconductors. This thesis focuses on the modeling and measurements of the bidirectional reflectance for microrough silicon surfaces and on the validity of a hybrid method in the modeling of the bidirectional reflectance for thin-film coated rough surfaces.

The surface topography and the bidirectional reflectance distribution function (BRDF) of the rough side of several silicon wafers have been extensively characterized using an atomic force microscope and a laser scatterometer. Both nearly isotropic and strongly anisotropic features are observed in the two-dimensional (2-D) slope distributions and in the measured BRDF. The BRDF is predicted from the 2-D slope distribution using a unified geometric-optics model and the predicted BRDF trends agree well with those measured with the laser scatterometer. The side peaks in the slope distribution and the subsidiary peaks in the BRDF for two anisotropic samples are attributed to the formation of {311} planes during chemical etching.

A rigorous electromagnetic wave approach is performed to simulate the bidirectional reflectance of silicon wafers with thin-film coatings on the rough side. The roughness of the substrate is one dimensional for simplification. The result is compared to that obtained from a hybrid method, which incorporates the geometric optics approximation and thin-film optics. The effects of film thickness and substrate roughness on the validity of the hybrid method have been investigated. The regime of validity is established for silicon dioxide films on silicon substrates in the visible wavelength range.

The proposed method to characterize the microfacet orientation and to predict the BRDF may be applied for other anisotropic or non-Gaussian rough surfaces. The measured BRDF may be used to model the effective emissivity of silicon wafers to improve the temperature measurement accuracy. The developed validity regimes for the hybrid method can be beneficial to future research related to the modeling for thin-film coated rough surfaces.