Geometric analysis of measurement errors in a surface metrology class with closed-loop probes

•Metrological evaluation of microstructure surfaces is vital to their performances.•Dynamic mode SPMs are more suitable for surfaces with large height distribution.•Error source sensitivity guides the design and setup of metrological equipment.•Surface geometry has a great influence on the final measurement error distribution.•Compensation scheme based on geometric error model promise better accuracy. This paper presents a novel measurement error model for closed-loop surface metrology. In these surface metrology systems, the motion of the probe tip is strictly constrained on a parallel surface that is separated from the measured sample surface of constant displacement by closed-loop controllers. Examples of such metrology systems include constant signal mode scanning probe microscopes and coordinate measuring machines. The combined effect of volumetric errors and surface tracking controllers on the final measurement error was analyzed using an error model developed based on multi-body system theory and surface geometry. A comprehensive overview of the errors of a typical large-scale scanning tunneling microscopy system is provided as an example. Simulations were performed to illustrate the influence of the systematic errors on the final accuracy. Experiments were also conducted on the measurement of a typical micro-structured surface to both verify the proposed error model and establish a possible compensation scheme.