X-ray reflectometry (XRR) is a highly used tool for the measurement of semiconductor and other high-performance surfaces. This work presents novel models and methods for the evaluation of surfaces having geometries that have not been addressed previously.
A model and experimental procedure are developed to determine the effect that mid-spatial frequency errors have on the x-ray reflectivity of optics. This model is used to simultaneously determine the surface roughness and waviness of surfaces; greatly extending the breadth of XRR. To evaluate this model, borosilicate glass optics were magnetorheologically polished to have waviness features of 100 nm peak-valley and spatial wavelength 4 mm/cycle. XRR measurements of these samples predicted the high-frequency surface roughness and the mid-spatial frequency waviness as measured by atomic force microscopy (AFM) and Fizeau interferometry with sub-nanometer accuracy.
Additionally, a comprehensive model for the evaluation of surface roughness of curved surfaces using XRR is developed. This work extends XRR as a technique for evaluating the surface roughness of external and internal surfaces of cylinders and spherical shells. Experimental measurements using thin polished silicon wafers that were bent using a specialized flexure-based fixture to various radii and the predicted RMS roughness from XRR is compared with AFM measurements.