Johannes Degenhardt

The precise calibration of indenter geometries is a critical factor in ensuring reliable instrumented indentation experiments, particularly at the microscale and nanoscale. This study presents the comprehensive and highly accurate calibration of a modified Berkovich indenter using a metrological large-range atomic force microscope, reaching a relative standard uncertainty of less than 1% for the projected area function (PAF) for indentation depths of 200 nm and more. In contrast to previous works, this study specifically focuses on the influence of data evaluation methods on the determination of indenter geometry and the estimation of the measurement uncertainty. A refined uncertainty estimation approach is implemented, overcoming the limitations of both the classical “Guide to the Expression of Uncertainty in Measurement” and the Monte Carlo method, which either require restrictive idealization assumptions on the indenter geometry or entail high computational costs. By leveraging a systematic simulationbased uncertainty assessment, this work provides a robust evaluation of the PAF uncertainty and its dominant contributing factors.

As nanostructures in the semiconductor industry become smaller and more complex, non-destructive characterization methods capable of measuring buried domains become crucial. Grazing emission x-ray fluorescence (GEXRF) spectroscopy is a measurement technique capable of resolving nanometer-sized features of buried nanostructures while providing information about the sample’s elemental distribution. In this work, a study was conducted to realistically assess the uncertainties of this method, considering correlations between geometric parameters. Furthermore, we showed strategies to effectively reduce the measurement time in GEXRF experiments by applying state-of-the-art single photon evaluation and machine learning denoising techniques for two-dimensional detectors. The study was performed on two different sample positions on a HfO₂/TiO₂ nanograting, where the GEXRF method was able to resolve geometric differences between them. Based on a finite element method model of the nanograting, the expected fluorescence intensities can be simulated, from which the nanostructure’s geometry can be reconstructed. The reconstructed geometric shapes show good agreement with atomic force microscope and transmission electron microscope measurements, highlighting the method’s capability for investigating samples within the nanometer regime.

This paper addresses the problem of uncertainty estimation for measurements made with computationally expensive numerical models, which are increasingly applied today. Typically, the Monte Carlo method (MCM) is used for uncertainty propagation in these cases. However, due to its stochastic nature, the MCM is inefficient, requiring a large number of model evaluations and thus resulting in long computation times. In this paper, an efficient alternative to the MCM is introduced. By using systematic samples of the influence quantities which are individually propagated through the measurement model, the overall number of required model evaluations can by drastically reduced. Additionally, the new method offers the possibility to simplify the measurement model for further reduced computational effort. The distributions of the propagated samples are reconstructed using a method specifically designed for systematic samples and combined to the uncertainty distribution of the measurand using convolution. The new method does not only offer increased computational efficiency but also a high information yield, as it estimates the uncertainty distribution of the measurand and the uncertainty contribution of individual influence quantities.

This paper introduces a paradigm shift in atomic force microscope (AFM) scan control, leveraging an artificial intelligence (AI)-based controller. In contrast to conventional control methods, which either show a limited performance, such as proportional integral differential (PID) control, or which purely focus on mathematical optimality as classical optimal control approaches, our proposed AI approach redefines the objective of control for achieving practical optimality. This presented AI controller minimizes the root-mean-square control deviations in routine scans by a factor of about 4 compared to PID control in the presented setup and also showcases a distinctive asymmetric response in complex situations, prioritizing the safety of the AFM tip and sample instead of the lowest possible control deviations. The development and testing of the AI control concept are performed on simulated AFM scans, demonstrating its huge potential.

Article Systematische Simulationsmethode zur effizienten Abschätzung von Unsicherheiten komplexer Messungen – ein Zwischenweg von klassischem GUM und der Monte-Carlo Methode was published on September 1, 2023 in the journal tm - Technisches Messen (volume 90, issue s1).

We present a new method for traceable calibration of size and form error of microspheres, which was realised by stitching a series of atomic force microscopic (AFM) images measured at different orientations of microspheres using the metrological large range AFM of the PTB. The stitching algorithm is achieved using an iterative closest point point-to-plane algorithm. As the AFM tip geometry is one of the most significant error sources for the developed method, it was traceably calibrated to a line width standard (type IVPS100-PTB), whose feature geometry was calibrated with a traceable route to the lattice constant of crystal silicon. Measurement setup, scan strategy, and data evaluation processes have been detailed in the paper. Measurement results show high stability and robustness of the developed method. For instance, the standard deviation of four repeated measurements reaches 5 nm, indicating promising performance.

A method to correct non-linear drift distortions in all three coordinate axes of atomic force microscope (AFM) images is presented. The method uses two measurements of the sample with two fast scan axes orthogonal to each other. Both AFM images are divided into segments and the shifts of the surface features of the segments of both images are determined. From these shifts subsequently the drift of both measurements is calculated. Depending on the segments used, significant non-linearities of the drift can be corrected. The two required measurements for this method do not have to be carried out in direct succession. With this method it is therefore possible to correct drift in an existing AFM image by measuring the sample again later. Although the method has been developed for AFM, it can also be used for other scanning probe microscopes.

A novel approach for accurate and traceable calibration of stylus tip geometry is introduced in the paper. The approach consists of several steps. Firstly, the geometry of an AFM tip is calibrated to a kind of line width standard whose geometry is traceably calibrated to the lattice constant of crystal silicon. Then, the stylus tip to be calibrated is measured by the calibrated AFM tip in an AFM, thus its tip geometry can be accurately determined after the contribution of the AFM tip geometry being corrected from the measured AFM image. After being calibrated, the stylus tip can be applied in measurements of vast microstructures and surfaces, where the measurement results can be in turn corrected using the characterized stylus tip geometry. In such a way, the stylus tip geometry and its measurement results can be finally traceable to the lattice constant of silicon, using this bottom-up approach. Detailed experimental examples are illustrated. For a stylus type RFTHB-50 studied in this paper, its tip radius is measured as 1.727 μm with a standard deviation of 0.007 μm. It is significantly smaller than its nominal value of 2 μm, indicating the need of the calibration. The application of calibrated stylus tip in measurements of microspheres is demonstrated. Compared to conventional tip characterization methods based on tip characterizers the proposed method has advantages of (i) no risk of damaging sharp edges of tip characterizers, (ii) capable of directly characterizing the 3D geometry of stylus tip, (iii) high accuracy.