Modeling and Measurements of the Bidirectional Reflectance of Microrough Silicon Surfaces

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Zhu, Qunzhi
Zhang, Zhuomin
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Bidirectional reflectance is a fundamental radiative property of rough surfaces. Knowledge of the bidirectional reflectance is crucial to the emissivity modeling and heat transfer analysis. This thesis concentrates 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, respectively. The slope distribution calculated from the surface topographic data deviates from the Gaussian distribution. Both nearly isotropic and strongly anisotropic features are observed in the two-dimensional (2-D) slope distributions and in the measured BRDF for more than one sample. The 2-D slope distribution is used in a geometric-optics based model to predict the BRDF, which agrees reasonably well with the measured values. 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. The correlation between the 2-D slope distribution and the BRDF has been developed. A boundary integral method is applied to simulate the bidirectional reflectance of thin-film coatings on rough substrates. The roughness of the substrate is one dimensional for simplification. The result is compared to that from a hybrid method which uses the geometric optics approximation to model the roughness effect and the thin-film optics to consider the interference due to the coating. The effects of the film thickness and the substrate roughness on the validity of the hybrid method have been investigated. The validity regime of the hybrid method 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 to other anisotropic or non-Gaussian rough surfaces. The measured BRDF may be used to model the apparent emissivity of silicon wafers to improve the temperature measurement accuracy in semiconductor manufacturing processes. The developed validity regime for the hybrid method can be beneficial to future research related to the modeling for thin-film coated rough surfaces.
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