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

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

Inspection of surface and nanostructure imperfections play an important role in high-throughput manufacturing across various industries. This paper introduces a novel, parallelised version of the metrology and inspection technique: Coherent Fourier scatterometry (CFS). The proposed strategy employs parallelisation with multiple probes, facilitated by a diffraction grating generating multiple optical beams and detection using an array of split detectors. The article details the optical setup, design considerations, and presents results, including independent detection verification, calibration curves for different beams, and a data stitching process for composite scans. The study concludes with discussions on the system's limitations and potential avenues for future development, emphasizing the significance of enhancing scanning speed for the widespread adoption of CFS as a commercial metrology tool.@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.

@en

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.

@en

A new method for fast, high resolution interrogation of an array of photonic sensors is proposed. The technique is based on the integrated Fourier transform (FT) interrogator previously introduced by the authors. Compared to other interferometric interrogators, the FT-interrogator is very compact and has an unprecedented tolerance to variations in the nominal values of the sensors’ resonance wavelength. In this paper, the output voltages of the interrogator are written as a polynomial function of complex variables whose modulus is unitary and whose argument encodes the resonance wavelength modulation of the photonic sensors. Two different methods are proposed to solve the system of polynomial equations. In both cases, the Gröbner basis of the polynomial ideal is computed using lexicographical monomial ordering, resulting in a system of polynomials whose complex variable contributions can be decoupled. Using an NVidia graphics processing card, the processing time for 1 026 000 systems of algebraic equations takes around 9 ms, which is more than two orders of magnitude faster than the interrogation method previously introduced by the authors. Such a performance allows for real time interrogation of high-speed sensors. Multiple solutions satisfy the algebraic system of equations, but, in general, only one of the solutions gives the actual resonance wavelength modulation of the sensors. Other solutions have been used for optimization, leading to a reduction in the cross-talk among the sensors. The dynamic strain resolution is 1.66 nε/√Hz.

@en

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.

@en

Coherent Fourier scatterometry (CFS) has been introduced to fulfil the need for noninvasive and sensitive inspection of subwavelength nanoparticles in the far field. The technique is based on detecting the scattering of coherent light when it is focused on isolated nanoparticles. In the present work, we describe the results of an experimental study aimed at establishing the actual detection limits of the technique, namely the smallest particle that could be detected with our system. The assessment for particles with a diameter smaller than 40 nm is carried out using calibrated nano-pillars of photoresist on silicon wafers that have been fabricated with e-beam lithography. We demonstrate the detection of polystyrene equivalent nanoparticles of diameter of 21 nm with a signal-to-noise ratio of 4 dB using the illuminating wavelength of 405 nm.

@en

We report a highly sensitive ultrasound sensor based on an integrated photonics silicon Mach-Zehnder interferometer (MZI). One arm of the MZI is located on a thin membrane, acting as the sensing part of the device. Ultrasound waves excite the membrane's vibrational mode, thus inducing modulation of the MZI transmission. The measured sensor transfer function is centered at 0.47 MHz and has a -6 dB bandwidth of 21.2%. For 1.0 mW optical input power, we obtain a high sensitivity of 0.62 mV/Pa, a low detection limit of 0.38 mPa/Hz^1/2 at the resonance frequency and a large dynamic range of 59 dB. In preliminary ultrasound imaging experiments using this sensor, an image of a wire phantom is obtained. The properties of this sensor and the generated image show that this sensor is very promising for ultrasound imaging applications.

@en

A highly sensitive ultrasound sensor based on an integrated photonics Mach–Zehnder interferometer (MZI) fabricated in silicon-on-insulator technology is reported. The sensing spiral is located on a membrane of size 121 μm × 121 μm. Ultrasound waves excite the membrane’s vibrational mode, which translates to modulation of the MZI transmission. The measured sensor transfer function is centered at 0.47 MHz and has a −6 dB bandwidth of 21.2%. The sensor sensitivity is linear in the optical input power and reaches a maximum 0.62 mV/Pa, which is limited by the interrogation method. At 0.47 MHz and for an optical power of 1.0 mW the detection limit is 0.38 mPa∕Hz ¹ ∕ ² and the dynamic range is 59 dB. The MZI’s gradual transmission function allows a wide range of wavelength operation points. This strongly facilitates sensor use and is promising for applications.

@en

We present a compact integrated photonics interrogator for a ring-resonator (RR) ultrasound sensor, the so-called MediGator. The MediGator consists of a special light source and an InP Mach-Zehnder interferometer (MZI) with a 3 × 3 multi-mode interferometer. Miniaturization of the MZI to chip size enables high temperature stability and negligible signal drift. The light source has a −3 dB bandwidth of 1.5 nm, a power density of 9 dBm/nm and a tuning range of 5.7 nm, providing sufficient signal level and robust alignment for the RR sensor. The mathematical procedure of interrogation is presented, leading to the optimum MZI design. We measure the frequency response of the sensor using the MediGator, giving a resonance frequency of 0.995 MHz. Further, high interrogation performance is demonstrated at the RR resonance frequency for an ultrasound pressure range of 1.47 − 442.4 Pa, which yields very good linearity between the pressure and the resulting modulation amplitude of the RR resonance wavelength. The measured signal time traces match well with calculated results. Linear fitting of the pressure data gives a sensor sensitivity of 77.2 fm/Pa. The MediGator provides a low detection limit, temperature robustness and a large measurement range for interrogating the RR ultrasound sensor.

@en

Coherent Fourier Scatterometry (CFS) is a scanning optical technique that is particularly suitable for nanoparticle detection. Inspection of wafer surfaces is one of the critical bottle-necks for high yield in the production of semiconductor chips. Ideally, inspection systems are required to work fast, be sensitive, and should not thermally damage the samples with an excess of illuminating light power. The sensitivity of detection of nanoparticles, attributed to the smallest size of the scatterer that can be detected, is severely limited by noise. The optical readout of the scatterometer consists of a bi-cell (a split photodetector) that collects the scatterred light from the surface to be inspected while the latter is scanned in the lateral direction (2D scan). The difference voltage signal resulting from integrating and subtracting the two halves of the bi-cell is recorded as a function of the lateral scanning position of the sample surface. The bi-cell has two functions: first, it allows us to acquire signals in a fast manner, and second, it eliminates effects due to substrate spurious reflections, which is usually a big issue in dark field based particle detection systems. In this paper, we present an extension of the original CFS detection system by incorporating a heterodyne technique to the detection system. We show the implementation of the new detector system as well as a comparative signal-to-noise ratio (SNR) gain studies that are used to determine the suitable frequencies and waveforms for both modulation and reference signals. We demonstrate the detection of polystyrene nanoparticles with a diameter of 80 nm, which were deposited on top of a silicon wafer, with high SNR at low illuminating light power. The experiments were performed with a diode laser at the wavelength of 405 nm. In this particular particle size, we have observed an improvement of the SNR of about 45 dB as compared to the original detection system of the CFS. Although the proposed heterodyne CFS technique already shows excellent performance for detection of polystyrene nanoparticles on silicon wafer, there is still room for improving the sensitivity towards even smaller particles, as discussed in the outlook and conclusions section.

@en

In this paper, the design and the characterization of a novel interrogator based on integrated Fourier transform (FT) spectroscopy is presented. To the best of our knowledge, this is the first integrated FT spectrometer used for the interrogation of photonic sensors. It consists of a planar spatial heterodyne spectrometer, which is implemented using an array of Mach-Zehnder interferometers (MZIs) with different optical path differences. Each MZI employs a 3_3 multi-mode interferometer, allowing the retrieval of the complex Fourier coefficients. We derive a system of non-linear equations whose solution, which is obtained numerically from Newton's method, gives the modulation of the sensor's resonances as a function of time. By taking one of the sensors as a reference, to which no external excitation is applied and its temperature is kept constant, about 92% of the thermal induced phase drift of the integrated MZIs has been compensated. The minimum modulation amplitude that is obtained experimentally is 400 fm, which is more than two orders of magnitude smaller than the FT spectrometer resolution.

@en

We experimentally demonstrate an interrogation procedure of a ring-resonator ultrasound sensor using a fiber Mach-Zehnder interferometer (MZI). The sensor comprises a silicon ring resonator (RR) located on a silicon-oxide membrane, designed to have its lowest vibrational mode in the MHz range, which is the range of intravascular ultrasound (IVUS) imaging. Ultrasound incident on the membrane excites its vibrational mode and as a result induces a modulation of the resonance wavelength of the RR, which is a measure of the amplitude of the ultrasound waves. The interrogation procedure developed is based on the mathematical description of the interrogator operation presented in Appendix A, where we identify the amplitude of the angular deflection Φ0 on the circle arc periodically traced in the plane of the two orthogonal interrogator voltages, as the principal sensor signal. Interrogation is demonstrated for two sensors with membrane vibrational modes at 1.3 and 0.77 MHz, by applying continuous wave ultrasound in a wide pressure range. Ultrasound is detected at a pressure as low as 1.2 Pa. Two optical path differences (OPDs) of the MZI are used. Thus, different interference conditions of the optical signals are defined, leading to a higher apparent sensitivity for the larger OPD, which is accompanied by a weaker signal, however. Independent measurements using the modulation method yield a resonance modulation per unit of pressure of 21.4 fm/Pa (sensor #1) and 103.8 fm/Pa (sensor #2).@en