Effects of defocus and algorithm on optical step height calibration

Abstract

Defocus effects on step height measurements by interferometric microscopy are estimated using different algorithms to calculate the step height. The interferometric microscope here is a Mirau-type with a 20x objective and a numerical aperture (NA) of 0.4. Although the focus is adjusted within the range of the depth of focus, a defocus corresponding to 4 fringes (∼1.3 μm) distorts the measured profile into a curve with a radius of curvature of about 24 m. The effect of this distortion on step height determination by a basic ISO step height algorithm is estimated to be 0.11 nm/fringe. An algorithm developed by NIST and a second-order fitted ISO step-height algorithm show good robustness against defocus errors. Because of sample imperfection, a discrepancy of about 1 % exists among step-height values determined by the different algorithms at the optimum fringe contrast position. It has been pointed out theoretically that the NA correction factor varies with the difference of optical path length between the sample and the reference surface. However, in our case, the changes of optical path length do not change the NA correction factor by more than 0.3 %.