Effects of mathematical models and algorithms on quantitative characterization of areal step height with optical and stylus profilometers

Abstract Step height characterization is essential for the quality control of various functional components, such as graphene and the step features of semiconductor devices. Two methods are proposed to characterize the areal step heights. The first method extends the two-dimensional characterization in the ISO specification into a three-dimensional one by extracting multiple parallel profiles. The second method calculates the step heights by projecting from the measurement points to the normal vector at the surface centroid. Mathematical models and algorithms of the two methods are introduced and validated by synthetic data. Experiments are conducted by comparing the assessment results of the two methods and of a method proposed in a previous research. The calibrated values of the standards are utilized for validation. The characterization results may differ notably or slightly, depending on the properties of the data and the algorithm.