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Abstract
This dissertation presents a body of work developing novel models and methods for surface evaluation with X-ray reflectometry (XRR). At the time of this work, XRR is a highly used tool for the measurement of flat wafers and laminated semiconductors and surfaces having additional geometric features have not been addressed. Surfaces having mid-spatial frequency features at the scale of several millimeters per cycle and surfaces having constant curvature are measured with XRR and models are developed to predict the effect of surface roughness on the measurements of these surfaces.First, a model is developed to investigate the effect that mid-spatial frequency errors have on the X-ray reflectivity of a surface. The model predicts the effect of RMS surface roughness, RMS surface waviness, and the cutoff spatial frequency between the feature bandwidths. Measurements on BK7 glass samples are used to verify the ability to simultaneously measure RMS surface roughness at spatial wavelengths less than 16 μm within 0.5 nm of AFM measurements and within 1.1 nm of surface profilometry measurements and the RMS surface waviness at spatial wavelengths greater than 16 μm and less than 4 mm within 7.0 nm of Fizeau interferometry and surface profilometry measurements. The result of this development is to extend the use case of X-ray reflectometry to include the measurement of longer-range surface waviness. Additionally, a comprehensive model for the evaluation of surface roughness of curved surfaces is presented. This work explores X-ray reflectometry as a technique for measuring the surface roughness of cylinders and spheres as well as the surface roughness of the inner surface of hollow cylinders and spherical shells. Measurements are presented on polished Silicon wafers having different surface roughness as measured by AFM that are bent to various radii to verify the ability of this model to predict the surface roughness of the curved surface. XRR RMS surface roughness measurement results from Silicon wafers bent between 1.5 and 2.5 m deviate less than 1.1 nm from AFM measurements