Abstract
To determine step heights between a few nanometers and several micrometers, we present a statistical evaluation procedure which overcomes the limitations of the unambiguity range of conventional multi-wavelength interferometry. The experimental setup consists of a shear interferometer with two different wavelengths to measure the phase difference between light reflected from an object with regions of two different heights. The statistical averaging over a large area of both regions of the object for both wavelengths generates a pair of phase difference values. A diagram of the space of phase values converts the pair of phase difference values into a step height. This statistical method enables the determination of step heights greater than the synthetic wavelength with an accuracy of a few nanometers even with small tilts of the object.
Zusammenfassung
Zur Bestimmung von Stufenhöhen zwischen wenigen Nanometern und mehreren Mikrometern präsentieren wir ein neues statistisches Verfahren, um die Limitierung des Eindeutigkeitsbereiches durch die synthetische Wellenlänge bei der Mehrwellenlängen-Interferometrie zu überwinden. Der experimentelle Aufbau besteht aus einem Scher-Interferometer mit zwei verschiedenen Wellenlängen, mit dem wir die Phasendifferenz des reflektierten Lichts eines Objekts mit zwei unterschiedlichen Höhenbereichen gemessen haben. Durch statistische Mittelung der gemessenen Phasenwerte über größere Flächen für beide Wellenlängen wird ein Phasendifferenz-Wertepaar gebildet. Ein Phasenwert-Diagramm erlaubt es, das Phasendifferenz-Wertepaar in eine Stufenhöhe umzuwandeln. Diese Methode ermöglicht die Bestimmung von größeren Stufenhöhen als die synthetische Wellenlänge auch unter leichter Verkippung auf wenige Nanometer genau.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 430572965
Funding statement: The authors thank the Deutsche Forschungsgemeinschaft (DFG) for funding this research within the frame of project HyperCOMet (grant number 430572965).
About the authors
Corinna Krause did her Master’s degree in the research group of experimental astrophysics at the Faculty of Physics of the University Duisburg-Essen. Since 2020 she works as a research associate in the group “Coherent Optics and Nano-Photonics” at BIAS – Bremen Institute of Applied Beam Technology. Her research interest is optical metrology like multi-wavelength interferometry and digital holography.
Prof. Dr. Ralf B. Bergmann studied physics in Heidelberg and Freiburg, received his doctorate with his work at the Max Plank Institute for Solid State Research (MPI-FKF) from the University of Stuttgart, worked as a postdoc at of the University of New South Wales and habilitated at the University of Freiburg. After leading a research group at the University of Stuttgart he headed the department of applied physics at the central research and advance engineering facility of the Robert Bosch GmbH and later in the Automotive Electronics division. Since 2008 he is a professor at the University of Bremen and head of the Bremen Institute for Applied Beam Technology (BIAS) with the field “Optical Metrology and Optoelectronic Systems”.
Dr. Claas Falldorf studied physics at the University of Bremen, where he received his doctorate at the Faculty of Physics and Electrical Engineering in 2009. Since then he heads the group “Coherent Optics and Nano-Photonics” at BIAS – Bremen Institute of Applied Beam Technology. His research focusses on optical metrology, coherence theory, signal processing and optimization theory.
Acknowledgment
The authors thank R. Klattenhoff for technical support.
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