In situ, back-focal-plane-based determination of the numerical apertures in optical microscopes.

In this contribution, we present a technique for in situ determination of the numerical apertures (NAs) of optical microscopes using calibrated diffraction gratings. Many commonly practiced procedures use an external setup to determine the objective and condenser NAs. However, these values may become modified in the used microscope systems, e.g., by system intrinsic apertures. Therefore, in our improved technique, determination of the imaging NA is conducted in situ within the corresponding microscope at hand. Furthermore, the method has been extended to yield the microscope's illumination NA as well. In total, we tested this procedure for determination of the imaging NA for four different microscope objectives with nominal values of 0.55 and 0.9, together with the illumination NAs for four different circular aperture diaphragms with diameters between 10 µm and 500 µm using several gratings of different pitches. All determined NA values agree essentially with their nominal values within their experimental uncertainties, but the uncertainties have been reduced by typically an order of magnitude as compared with the manufacturer's specifications.

Quasi-bound states in the continuum for deep subwavelength structural information retrieval for DUV nano-optical polarizers.

We demonstrate the retrieval of deep subwavelength structural information in nano-optical polarizers by scatterometry of quasi-bound states in the continuum (quasi-BICs). To this end, we investigate titanium dioxide wire grid polarizers for application wavelengths in the deep ultraviolet (DUV) spectral range fabricated with a self-aligned double-patterning process. In contrast to the time-consuming and elaborate measurement techniques like scanning electron microscopy, asymmetry induced quasi-BICs occurring in the near ultraviolet and visible spectral range provide an easily accessible and efficient probe mechanism. Thereby, dimensional parameters are retrieved with uncertainties in the sub-nanometer range. Our results show that BICs are a promising tool for process control in optics and semiconductor technology.

Some aspects on the uncertainty calculation in Mueller ellipsometry.

In this paper, we focus on the metrological aspects of spectroscopic Mueller ellipsometry-i.e. on the uncertainty estimation of the measurement results. With the help of simulated Mueller matrices, we demonstrate that the commonly used merit functions do not return the correct uncertainty for the measurand under consideration (here shown for the relatively simple case of the geometrical parameter layer thickness for the example system of a SiO2 layer on a Si substrate). We identify the non-optimal treatment of measured and sample- induced depolarization as a reason of this discrepancy. Since depolarization results from sample properties in combination with experimental parameters, it must not be minimized during the parameter fit. Therefore, we propose a new merit function treating this issue differently: It implicitly uses the measured depolarization as a weighting parameter. It is very simple and computationally cheap. It compares for each wavelength the measured Jones matrix elements to Cloude's covariance matrix: ∼∑λ jsim,λ†Hmeas,λ + j sim,λ . Moreover, an extension will be presented which allows us to include the measurement noise into this merit function. With this, reliable statistical uncertainties can be calculated. Except for some pre-processing of the raw data, there is no additional computational cost.

Using DNA origami nanorulers as traceable distance measurement standards and nanoscopic benchmark structures.

In recent years, DNA origami nanorulers for superresolution (SR) fluorescence microscopy have been developed from fundamental proof-of-principle experiments to commercially available test structures. The self-assembled nanostructures allow placing a defined number of fluorescent dye molecules in defined geometries in the nanometer range. Besides the unprecedented control over matter on the nanoscale, robust DNA origami nanorulers are reproducibly obtained in high yields. The distances between their fluorescent marks can be easily analysed yielding intermark distance histograms from many identical structures. Thus, DNA origami nanorulers have become excellent reference and training structures for superresolution microscopy. In this work, we go one step further and develop a calibration process for the measured distances between the fluorescent marks on DNA origami nanorulers. The superresolution technique DNA-PAINT is used to achieve nanometrological traceability of nanoruler distances following the guide to the expression of uncertainty in measurement (GUM). We further show two examples how these nanorulers are used to evaluate the performance of TIRF microscopes that are capable of single-molecule localization microscopy (SMLM).

Metrology of nanoscale grating structures by UV scatterometry.

In this contribution we demonstrate goniometric scatterometry measurements of gratings with linewidths down to 25 nm on silicon wafers with an inspection wavelength of 266 nm. For each sample, measurements have been performed in four different configurations and the obtained data have been evaluated in parallel. As results we present the reconstruction of the complete cross-section profile. We introduce a novel geometry parameterization which overcomes some limitations of the default parameterization. A co-variance analysis of the parameters is offered to indicate the soundness of the results. A qualitative comparison with cross-section scanning electron microscope (SEM) images shows excellent agreement.

A new flexible scatterometer for critical dimension metrology.

At Physikalisch-Technische Bundesanstalt, the National Metrology Institute of Germany, a new type of deep ultraviolet scatterometer has been developed and set up. The concept of the system is very variable and versatile, so that many different types of measurements, e.g., classical scatterometry, ellipsometric scatterometry, polarization-dependent reflectometry, and ellipsometry can be performed. The main application is the characterization of linewidth/critical dimension (CD), grating period (pitch), and edge profile of periodically nanostructured surfaces mainly, but not only, on photomasks. Different operation wavelength between 840 and 193 nm can be used, giving also access to a variety of different at-wavelength metrology connected with state-of-the-art photolithography. It allows to adapt and to vary the measurand and measurement geometry to optimize the sensitivity and the unambiguity for the measurement problem. In this paper the concept, design, and performance of the system is described in detail. First measurement examples are shown and current and future applications are discussed.