Monte Carlo simulation to determine the measurement uncertainty of a metrological scanning probe microscope measurement

A proprietary metrological scanning probe microscope (SPM) with an interferometer, developed by the Institute of Process Measurement and Sensor Technology at the Ilmenau University of Technology (IPMS), is used as a stationary probe system in the nanomeasuring and nanopositioning machine (NPMM). Due to the movements of the NPMM, the total microscope measuring range is 25mm × 25mm × 5mm with a positioning resolution of less than 0.1nm. Examples for specimens are step height standards and one-dimensional gratings. The repeatability has been determined at less than 0.5nm for measurements on calibrated step height standards and less than 0.2nm for the gratings. The measurement results of these samples are always directly related to the corresponding measurement uncertainty, which can be calculated using an uncertainty budget. A new traceable method has been developed using a vectorial modular model. With this approach, it is possible to quickly insert new sub-models and to individually analyze their effects on the total measurement uncertainty. The analysis of these effects with regard to their uncertainties is done by Monte Carlo Simulation (MCS), because some models have partially or fully nonlinear character of which one example is the interferometer model of the metrological SPM. The complete development and analysis of these models is presented for one specific measurement task. The measurement results and the corresponding measurement uncertainty were obtained by Monte Carlo Simulation. Comparisons with the GUM have shown that the proposed procedure is a good alternative to achieve reasonable measurement results with uncertainty estimation.