Modeling the systematic behavior at the micro and nano length scales

Abstract

The assessment of the systematic behavior based on frequentist statistics was analyzed in the context of micro/nano metrology. The proposed method is in agreement with the well-known GUM recommendations. The investigation assessed three different case studies with definition of model equations and establishment of the traceability. The systematic behavior was modeled in Sq roughness parameters and step height measurements obtained from different types of optical microscopes, and in comparison with a calibrated contact instrument. The sequence of case studies demonstrated the applicability of the method to micrographs when their elements are averaged. Moreover, a number of influence factors, which are typical causes of inaccuracy at the micro and nano length scales, were analyzed in relation to the correction of the systematic behavior, viz. the amount of repeated measurements, the time sequence of the acquired micrographs and the instrument-operator chain. The possibility of applying the method individually to the elements of the micrographs was instead proven not convenient and too onerous for the industry. Eventually, the method was also examined against the framework of the metrological characteristics defined in ISO 25 178-600 with hints on possible future developments.