This thesis addresses particular topics in the field of the length metrology for nanometrology. Nanometrology deals with dimensional measurements of micro- and nanostructures with a high spatial resolution. It typically combines a microscope imaging with a precise coordinate measurement, usually capable of nanometre resolution using the state-of-art laser interferometry techniques. The development in this field is driven, among others, by emerging advanced nanotechnologies that demand to push further the capabilities and limits of the interferometric techniques to make the nanometre-level dimensional measurement of nanostructures possible. The principal limitations of current systems are the environmental conditions and especially the fluctuations in the refractive index of air. The theoretical part of this thesis aim at analysis of individual parts of laser interferometer. I oriented myself on the study of their advantages/disadvantages and further also the possibilities of their industrial applications. The second part of the thesis presents my work that focused on the influence of the refractive index of air (RIA) on the measurement uncertainty. I experimentally demonstrated an interferometric system with a self-cancellation RIA fluctuations: a transparent photodetector is used for the measurement of the standing wave along the axis of a passive resonator, where the resonator also serves as a reference for the laser wavelength stabilisation. Another optical arrangement, based on a setup of several Michelson interferometers, represents a combination of an interferometer and a refractometer into a single system. This setup was used to study the behaviour of the ambient airflow with respect to the optical path difference and physical separation of the interferometer’s and refractometer’s path. Based on the experimental results I proposed new arrangements for shape measuring interferometers, which combine length interferometry and a tracking refractometer for the direct compensation of RIA fluctuations with geometrically adjacent optical beams. The results indicate an improvement in RIA fluctuation induced uncertainty by a factor of 100. Third part describes the design and implementation of interferometric systems for specific applications. For the industrial environment I developed a compact interferometric displacement gauge which is designed to allow nanometre level measurement using a simplified interferometer construction. For coordinate measurement of the position of the sample up to six degrees of freedom, I realised a compact modular interferometric system, which represents a unique setup together with a stabilised laser source. To measure the position of the sample in an electron beam writer chamber, I designed and implemented a differential interferometer that works in the near infrared domain and uses a new detection method developed for this system. In the fourth part I describe the realisation of a high-speed interferometer with a differential arrangement, which allows evaluation of high-cycle fatigue in material engineering. This method of studying high-cycle fatigue should be beneficial for both the basic research and the engineering practice.

Hintergrund: Die Entwicklung von Nanotechnologien und insbesondere integrierten Schaltkreisen beruht auf dem Verständnis von Struktur und Funktion auf der Nanoskala, wofür exakte Messungen erforderlich sind. Kleinwinkel-Röntgenstreuung unter streifendem Einfall (GISAXS) ist eine Methode zur schnellen, berührungs- und zerstörungsfreien dimensionellen Messung von nanostrukturierten Oberflächen. Ziele: Es soll die Möglichkeit untersucht werden, die zunehmend komplexeren Proben aus Wissenschaft und Industrie mit Hilfe von GISAXS präzise zu vermessen. Ein weiteres Ziel ist es, Messtargets aus der Halbleiter-Qualitätskontrolle mit einer Größe von ca. 40x40 µm² zu messen, deren Signal typischerweise nicht zugänglich ist, weil ein Bereich von ca. 1x20 mm² auf einmal beleuchtet wird. Methoden: Synchrotron-basierte GISAXS-Messungen verschiedener Proben werden mit Hilfe einer Fourier-Konstruktion, der "distorted wave Born approximation" und einem Maxwell-Gleichungs-Löser basierend auf finiten Elementen analysiert. Ergebnisse: Aus GISAXS-Messungen kann die Linienform von Gittern mit einer Periode von 32 nm rekonstruiert werden und sie weicht weniger als 2 nm von Referenzmessungen ab. Eine sorgfältige Bayes'sche Unsicherheitsanalyse zeigt jedoch, dass wichtige dimensionelle Parameter innerhalb der Unsicherheiten nicht übereinstimmen. Für die Messung von kleinen Gittertargets entwerfe ich ein neuartiges Probendesign, bei dem das Target in Bezug auf die umgebenden Strukturen gedreht wird, und stelle fest, dass dadurch parasitäre Streuung effizient unterdrückt wird. Fazit: GISAXS-Messungen von komplexen Nanostrukturen und kleinen Targets sind möglich, jedoch würde GISAXS enorm von effizienteren Simulationsmethoden profitieren, die alle relevanten Effekte wie Rauhigkeit und Randeffekte einbeziehen. Hier gibt es vielversprechende theoretische Ansätze, so dass GISAXS eine zusätzliche Methode für die Halbleiter-Qualitätskontrolle werden könnte. / Background. The development of nanotechnology such as integrated circuits relies on an understanding of structure and function at the nanoscale, for which reliable and exact measurements are needed. Grazing-incidence small angle X-ray scattering (GISAXS) is a versatile method for the fast, contactless and destruction-free measurement of sizes and shapes of nanostructures on surfaces. Aims. A goal of this work is to investigate the possibility of precisely measuring the increasingly complex samples produced in science and industry using GISAXS. A second objective is to measure targets used in semiconductor quality control with a size of approx. 40x40 µm², whose signal is typically not accessible because an area of approx. 1x20 mm² is illuminated at once. Methods. I take synchrotron-based GISAXS measurements and analyze them using reciprocal space construction, the distorted wave born approximation, and a solver for Maxwell's equations based on finite elements. Results. I find that the line shape of gratings with a period of 32 nm can be reconstructed from GISAXS measurements and the results deviate less than 2 nm from reference measurements; however, a careful Bayesian uncertainty analysis shows that key dimensional parameters do not agree within the uncertainties. For the measurement of small grating targets, I create a novel sample design where the target is rotated with respect to the surrounding structures and find that this efficiently suppresses parasitic scattering. Conclusions. I show that GISAXS measurements of complex nanostructures and small targets are possible, and I highlight that further development of GISAXS would benefit tremendously from efficient simulation methods which describe all relevant effects such as roughness and edge effects. Promising theoretical approaches exist, so that GISAXS has the potential to become an additional method in the toolkit of semiconductor quality control.

The presented doctoral thesis deals with measurements of extremely small sizes in nanometrology using a touch probe, which constitutes a part of a three-coordinate measuring system. It addresses a newly developed method of exact measurements in nanometrology by touch probes. The aim of this work was to expand the measurement options of this device and design a methodology proposal for the measurement of small parts, including the determination of accuracy of measurement of this device when used in nanometrology. The work includes the new methodology for the calculation of uncertainty of measurement, which constitutes a keystone in determining the accuracy of measurement of a accuracy three coordinate measuring system (hereinafter only nano-CMM). The first part of the doctoral thesis analyzes the present situation in the area of evaluation of accuracy of measurement in very accurate length measurements. It defines and describes individual methods implemented in the determination of accuracy of measurement on the instrument nano-CMM. A great emphasis is placed on the methodology of the measurement uncertainty, which draws from the author’s experience as a metrologist working in the laboratories of the Department of Primary nanometrology and technical length, Czech Metrology Institute Brno (hereinafter only CMI Brno). The second part of the doctoral thesis focuses on the determination of accuracy of length measurement in nanometrology, using a large set of measurements that were carried out under the reproducibility and repeatability conditions. There is also described and tested a model procedure utilizing the Monte Carlo method to simulate the measuring system nano-CMM in order to extent the newly created methodology of the measurement of uncertainty using a touch probe on the instrument nano-CMM. A substantial part of this doctoral thesis provides a detailed evaluation of results obtained from experiments that were executed under the repeatability and reproducibility conditions, especially for the purposes of the determination of the uncertainty of measurement. In this doctoral thesis, the uncertainty of measurement is chosen to quantify the accuracy of measurement of the instrument nano-CMM. The final part of this thesis summarizes the knowledge obtained during the scientific research and provides its evaluation. For the methodology used to determine the accuracy of measurement in nanometrology, it also outlines the future development in the area of scientific research, including the practical use in metrological traceability and extremely accurate measurements for customers. Furthermore, it deals with the possible use of other scanning systems compatible with the instrument nano-CMM.

The diploma thesis deals with the design of three length standards, which will serve to ensure metrological traceability between Rigaku nano3DX, SIOS NMM-1, Zeiss UPMC Carat 850 and other devices located at ÚVSSR BUT and CEITEC Brno. The first part of the thesis focuses on the theoretical acquaintance with concepts closely related to the issue of ensuring metrological traceability. In addition, this section deals with computed tomography and the description of individual devices. The second part of the thesis is devoted to design, production process and testing of individual standards. The last part describes the ensuring the calibration of the smallest standard, the so-called Nano standard and the calculation of the uncertainty of measuring its calibrated length. At the end of the thesis, the outputs of these activities are evaluated.