With the continuously growing transistor density in the semiconductor industry, where smaller features and tighter tolerances in the nanometer scale are the norm, there is a growing demand for more advanced metrology tools during manufacturing. While optical metrology in the visible range is the main workhorse, such as scatterometry, its performance is limited by the wavelength. Moving beyond the visible spectrum to extreme ultraviolet (EUV) and soft X-ray (SXR) wavelengths promises higher resolutions, but not without challenges. In this wavelength regime traditional microscopy struggles due to the non-availability of high numerical aperture optics for EUV and SXR at reasonable costs, failing to fully make use of the potential benefits of the shorter wavelength.

This thesis covers an alternative route to traditional microscopy through advanced lensless imaging or coherent diffractive imaging (CDI) techniques, particularly focusing on ptychography within the EUV and soft X-ray ranges demonstrated on a designed EUV beamline. Before we go into details about the setup we start with the basics of diffraction, coherent imaging, and ptychography in chapter 2. In chapter 3 we cover the generation of coherent EUV and SXR light from various sources, ranging from large scale facilities like synchrotrons to table-top High Harmonic Generation (HHG) setups.

From this point we cover the design and construction of a table-top EUV lensless imaging beamline in chapter 4, which has been designed and built from scratch at the Optics Research Group at the Delft University of Technology as part of this thesis. This section covers the design, optimization, and assembly of the beamline tailored for lensless imaging of industry relevant samples in a reflection configuration using EUV and soft X-rays from HHG sources. The beamline is split into several subsystems, a high intensity femtosecond fiber laser, the HHG EUV source, optical components for spectral filtering and illumination, and optomechanical systems required for ptychography which are individually covered in the chapter.

In chapter 5 we demonstrate one of the first ptychography reconstructions obtained on the EUV beamline, as presented in chapter 4, by illuminating an object with EUV light at 17.3 nm and 17.9 nm in a grazing reflection orientation of 20 degrees. The object, a silicon substrate which has been patterned with a 20 nanometer thick gold layer with feature sizes from a few microns down to 15 nanometers, has been reconstructed. This reconstruction has been generated with an in-house developed ptychography algorithm, based on automatic differentiation, for the ptychography reconstruction process. The experimental results demonstrate the feasibility of achieving high resolution reconstructions.

Line features down to 50 nanometers were retrieved with this method, close to the diffraction limit given an imaging NA of 0.17 at 18 nm wavelength. A reconstructed structure height of 23.6 ± 0.62 nm agrees well with the 20 nm nominal design value and the height retrieved from an atomic force microscope (AFM) measurement of 22.8 ± 1.45 nm.

The results in chapter 5 are quite promising, though there are certain challenges which need to be solved to further improve the reconstruction quality. One of these challenges are intensity stability issues which are typically associated with EUV sources based on high harmonic generation. Chapter 6 proposes a simple computational method to mitigate intensity fluctuations during ptychography scans by introducing a scanning position dependent multiplication factor. The algorithm effectively corrects for power fluctuations, enabling object reconstruction even in the presence of significant intensity variations up to 50 percent during the overall scan.

Chapter 7 presents a compact schlieren (from the German word ’streak’) imaging system integrated within the HHG EUV source, enabling quantitative density retrieval of the gas jet used to drive the high harmonic generation process. Schlieren imaging provides a straightforward alternative to vibration sensitive techniques like interferometry and can be used as a standardized tool for HHG sources, allowing for a better comparison among different HHG setups and for the optimization of HHG light sources.

In summary, this thesis does not only cover the field of lensless EUV microscopy but also covers the design process of such a beamline and the challenges associated with HHG EUV sources. This work presents a starting point for experimental EUV metrology within the Optics Research Group at the Delft University of Technology and enables future academic research relevant for the semiconductor industry.
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Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.@en

Ptychography as a means of lensless imaging is used in wafer metrology applications using Extreme Ultraviolet (EUV) light, where use of high quality optics is out-of-scope. To obtain sufficient diffraction intensity, reflection geometries with shallow (ca. 20 degrees) grazing incidence angles are used, which require re-sampling the diffraction data in a process called tilted plane correction (TPC). The tilt angle used for TPC is conventionally obtained through either experimentally tricky calibration, manual estimation based on diffraction pattern symmetry, although computational approaches are emerging. In this work we offer an improved numerical optimization approach as an alternative to TPC, where we use the flexibility offered by our Automatic Differentiation (AD)-based ptychography approach to include the data resampling into the forward model to learn the tilt angle. We demonstrate convergence of the approach across a range of incidence angles on simulated and experimental data obtained on an EUV beamline with either a high-harmonic generation (HHG)-based or a visible light source.@en

Next-generation metrology solutions in various technology areas require to image sample areas at the nanoscale. Coherent diffractive imaging based on ptychography is the route towards EUV imaging of nanostructures without lenses. A key component in a table-top EUV beamline is a high-brightness high-harmonic generation (HHG) source. Since our research is mainly directed towards wafer metrology for lithography in the semiconductor industry, we adhere to a reflection setup: the EUV light is scattered by the nanostructures at the surface of the sample, and is reflected towards a CCD camera, where a far-field diffraction pattern is recorded. A data-set comprising a multitude of these diffraction patterns is generated for partially overlapping positions of the focused probe on the sample. This provides the necessary redundancy for phase retrieval of the complex-valued field of the sample. Recent advancements in both hardware and software for computation enable the development of advanced algorithms. In particular, the benefits of automatic differentiation are exploited in order to cope with a drastic growth in model complexity. Our computational imaging algorithms realize wavelengthmultiplexed reconstruction and a modal approach for the spatial coherence of the source.@en

Ptychography in a reflection geometry shows great promise for non-destructive imaging of 3-dimensional nanostructures at the surface of a thick substrate. A major challenge to obtain high quality reflection-ptychographic images under near-grazing conditions has been to calibrate the incidence angle used to straighten the measured curved diffraction patterns in a process referred to as ‘tilted plane correction’ (TPC). In this work, we leverage the flexibility of automatic differentiation (AD)-based modeling to realize an alternative approach, where the tilted propagation is included in the forward model. Use of AD allows us to jointly optimize the tilt angles with the typical probe and object, eliminating the need for accurate calibration or random search optimization. The approach was validated using datasets generated with an extreme ultraviolet (EUV) beamline based on both a tabletop high harmonic generation (HHG) source and a visible laser. We demonstrate that the proposed approach can converge to a precision of ±0.05◦ for probe beams at 70◦ angle of incidence, possibly precise enough for use as a calibration approach. Furthermore, we demonstrate that optimizing for the tilt angles reduces artifacts and increases reconstruction fidelity. Use of AD not only streamlines the current ptychographic reconstruction process, but should also enable optimization of more complex models in other domains, which will likely be useful for future advancements in computational imaging.@en

We demonstrate our beamline using a table-top HHG EUV source for lensless imaging application in reflection m ode. T he s ample r eflection fu nction is reconstructed using an auto-differentiation based ptychographic algorithm built on TensorFlow platform.

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We present a highly stable, easy-to-use HHG source delivering a record photon flux of >10¹¹ photons/s at 69eV-75eV, being tunable to approx. 100eV which will be used for future photon-hungry applications.

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High-harmonic generation (HHG) driven by ultrashort laser pulses is an established process for the generation of coherent extreme ultraviolet (XUV) to soft X-ray radiation, which has found widespread use in various applications [1]. In recent years photon-hungry applications such as coherent diffractive imaging [2] , [3] and applications based on statistical analysis [3] have required more powerful HHG sources, in particular, at high repetition rates. This need can be addressed by using high average power fiber lasers as the HHG drivers [4]. Here, we present a HHG-based XUV source, capable of providing a large photon flux across a wide range between 66 eV and 150 eV. It is driven by a commercial XUV beamline from Active Fiber Systems GmbH consisting of 100-W average power fiber-laser system, delivering up to 300J at <300-fs pulse duration. For HHG this system is operated at 100 W, 600 kHz. A post-compression unit is part of the device to shorten the pulses to ~35 fs, the average power remains at 63W. The turnkey source can provide unprecedented photon fluxes of >10 11 photons/s in each harmonic between 69 eV and 75 eV (HH57-HH63). All fluxes are given at the generation point, i.e. directly after the source.

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