Coherent Fourier Scatterometry (CFS) is a powerful optical metrology technique for the precise characterisation of nanostructures. Conventional CFS systems rely on piezo-based scanning stages for raster scanning, which limits throughput due to slow scanning speeds. In this work, we present a high-speed CFS system incorporating a galvanometric (galvo) mirror for beam scanning. This approach significantly enhances scanning speed while maintaining measurement accuracy. Although galvo mirrors are widely used in optical systems, their implementation in CFS has unique challenges such as off-axis beam aberrations and angle-dependent beam shifts at the split detector. These issues are analysed and mitigated through optical design, alignment and system calibration. Additionally, we derive the minimum detector bandwidth required to capture high-frequency signals generated by the fast scanning. The effectiveness of the system is demonstrated through the calibration of pits with various diameters that are etched onto a silicon wafer. Results show a substantial improvement in scanning speed as compared with piezo-based systems without compromising measurement precision, making this approach highly suitable for high-throughput metrology applications.

We demonstrate a broadband implementation of coherent Fourier scatterometry (CFS) using a supercontinuum source. Spectral information can be resolved by splitting the incident field into two pulses with a variable delay and interfering them at the detector after interaction with the sample, bearing similarities with Fourier-transform spectroscopy. By varying the time delay between the pulses, a collection of diffraction patterns is captured in the Fourier plane, thereby obtaining an interferogram for every camera pixel. Spectrally resolved diffraction patterns can then be retrieved with a per-pixel Fourier transform as a function of the delay. We show the physical principle that motivates the two-pulse approach, the experimental realization, and results for a silicon line grating. The presented implementation using a supercontinuum source offers a cost-effective way to acquire multi-wavelength CFS data over a wide wavelength range, with the potential to improve reconstruction robustness and sensitivity in applications such as dimensional metrology.

Coherent Fourier scatterometry (CFS) is a powerful scanning technique for inspecting defects on structured surfaces, relying on split detectors to measure asymmetry in the far-field scattered light. The split signal, a differential signal derived by subtracting signals from opposing halves of the detector, effectively detects asymmetries along the scan direction. However, this approach is inherently limited when inspecting patterned structures, as it loses information orthogonal to the scan direction. This results in signals that vary depending on the orientation of the patterns, complicating the characterization of certain defects. To overcome this limitation, we introduce a quad detector-based CFS scheme. By utilizing four independent photodetectors and processing their signals to generate integrated, split, and quad outputs, we capture complete far-field information. A Fourier filtering step removes detector-specific offsets, enabling robust signal analysis. Unlike the split-detector approach, this method provides defect and nanostructure inspection independent of the shape and orientation of the underlying patterns. We present the results of implementing this scheme to inspect defects on patterned surfaces. The quad detector signal reveals the edges of defects and demonstrates the versatility of this approach across different surface features. This advancement enhances the capability of CFS for defect inspection, offering a comprehensive and reliable solution for patterned structures where traditional split-detector methods fall short.

Nanopillars are widely used for various applications and require accurate shape characterization to enhance their performance and optimize fabrication processes. In this paper, we employ coherent Fourier scatterometry (CFS) combined with rigorous three-dimensional finite-difference time-domain simulations to accurately determine the shapes of nanopillars with various geometries, including cylindrical, triangular, square, and rectangular shapes. The nanopillars considered here have lateral dimensions (a) ranging from 100 to 1000 nm. Our methodology utilizes the preferential excitation of the nanostructures by a tightly focused beam and leverages their inherent symmetry to capture far-field signatures that vary periodically with rotation. This approach allows us to distinguish between different nanopillar shapes based on these rotational signatures. Our results demonstrate that the CFS method can reliably characterize nanopillars with lateral dimensions a≥300 nm, surpassing the conventional diffraction limit of 351 nm. However, the method reaches its fundamental limits for a≤200 nm, as also confirmed by simulations, where we approach the dipole approximation regime (a≪λ). This constraint is not observed for rectangular nanopillars, owing to their constant breadth (b=1000 nm), which prevents such a regime. Furthermore, our method successfully differentiates nanopillars transitioning from rectangular to square shapes. We also explored the method's limitations concerning nanostructure height (h), finding that triangular and square nanopillars could be characterized accurately for h≥50 nm and h≥150 nm, respectively. Furthermore, the method remains robust against shape distortions such as edge roundness. The method is primarily effective in determining the lateral (top-down) shape of nanopillars, it does not resolve longitudinal features. The ability to accurately characterize nanostructure shapes has significant implications in fields such as photonics and biosensing, where geometry critically influences device performance.

As advanced packaging evolves with 2.5D/3D integration, the demand grows for the inspection of subsurface nanostructures and defects within silicon (Si), ensuring reliability and yield in modern electronics. In this paper, we demonstrate coherent Fourier scatterometry (CFS) at a near-infrared wavelength (λ=1055 nm) for noninvasive inspection of nanostructures buried within Si. Despite Si's transparency in this spectral range, its high refractive index causes strong Fresnel reflections at the air–Si interface. To eliminate these unwanted signals, we employ two distinct approaches: (i) a split detector to subtract reflections in defect inspection mode, and (ii) a reduced coherence length, below lasing threshold, combined with spatial filtering, for retrieving far-field diffraction patterns in grating inspection mode. We systematically investigate how thickness of overlying Si (without overlying Si wafer, with 300 μm thick Si wafer, and with 500 μm thick Si wafer) affects scattering signals of the buried nanostructures. We demonstrate the detection of low contrast polystyrene nanospheres (down to 400 nm, well below the diffraction limit of λ/(2NA)≈959 nm) buried under 500 μm of Si. Further, we successfully detect nanopillars ≥100 nm and nanopits ≥225 nm. We also analyze the influence of spherical aberrations, which increases linearly with the thickness of the Si layer, resulting in a degradation of the focal spot quality. Beyond isolated defects, we retrieve the diffraction patterns of a 1430 nm period grating under 500 μm of Si, with minimal distortion relative to when no Si layer is present. Overall, these results highlight CFS as a robust, high-sensitivity technique for in-depth inspection in microelectronics and photonic applications, demonstrating potential for failure analysis, process control, and metrology in advanced packaging environments.

Coherent Fourier Scatterometry (CFS) enables low-power, high- resolution, non-destructive metrology for nanoscale structures. Recent advancements have extended its applications to improving the measurement of critical dimensions, such as steep-sidewall angles of fabricated nanostructures and the detection and shape determination of defects for semiconductor and power electronics applications. Innovations like beam scanning, multi-beam setups, and synthetic optical holography enhance its speed and sensitivity, making CFS increasingly viable for industrial in-line inspection.

Coherent Fourier scatterometry (CFS) is a very sensitive optical metrology technique that has been applied for detection and characterisation of nanostructures. It is a scanning-based technique where the samplie is illuminated with a focused light spot. However, in practical CFS systems, residual optical aberrations can distort the focused spot and degrade the signal-to-noise ratio during measurements. Here, we present a systematic study of the influence of low-order aberrations: defocus, spherical, astigmatism, oblique astigmatism, and coma on the differential split-detector CFS signal. Controlled amounts of each aberration, described by Zernike polynomials, were introduced into the Fourier plane via a spatial light modulator. Two-dimensional differential scattering maps were recorded on a reference sample of 425 nm diameter, 150 nm deep pits etched in silicon, and the peak-to-peak differential signal was quantified as a function of peak-valley (PV) wavefront error. We find that defocus has the strongest impact, halving the signal at just 0.27λ PV, followed by spherical (0.32λ) and coma (0.40λ), whereas astigmatism and oblique astigmatism require larger wavefront errors (> 0.6λ) to produce comparable signal loss. These results define quantitative aberration tolerances for CFS systems. The insights gained here can guide the design and optimisation of different CFS implementations for in-line process control and nanostructure metrology.

Coherent Fourier scatterometry (CFS) is a non-invasive optical technique widely used for defect detection on planar surfaces. It utilizes split detectors to measure far-field asymmetries as differential signals, making it highly effective for identifying defects such as particles or burrows. Detecting defects near edges of nanostructures, however, is particularly challenging due to interference between the edge signal and the defect signal, a limitation not only of CFS but also of other standard techniques like bright-field and dark-field microscopy. Accurate detection of such defects is critical in fields like semiconductor manufacturing and nanotechnology, where edge-adjacent defects can compromise device performance. Therefore, understanding the limits of CFS for edge-adjacent defect detection is essential for optimizing its application and interpreting its results. In this work, we first demonstrate experimentally that CFS can detect a 200 nm Pt particle positioned 2 µm from an edge. We then perform 3D FDTD simulations to model particles and burrows positioned at varying distances from an edge. By analyzing the split detector signals for these scenarios, we observe that particle and burrow signals become more prominent as their distance from the edge increases. However, for a system using a numerical aperture of 0.9 and wavelength of 633 nm, for distances from the edge smaller than 350 nm for particles and 650 nm for burrows, the characteristic signals diminish, merging with the edge response. This study highlights the challenges and potential solutions for defect inspection near edges, advancing the applicability of CFS for patterned and complex structures.

We present a rotation-based coherent Fourier scatterometry (CFS) system for high-speed, high-resolution surface metrology. Traditional CFS systems rely on piezoelectric stages for point-by-point raster scanning, which limits scan speed due to constant accelerations and decelerations. In our approach, the fast-axis piezo stage is replaced by a rotation stage moving at constant angular velocity, whereas the slow-axis piezo is used to step radially outward to generate concentric scan paths. We introduce a frequency spread–based technique to compensate for probe centering deviation and demonstrate the capability of measuring axial wobble using depth-sensitive CFS signals. Application of the system is shown through the detection of 0.4μm polystyrene latex particles and the calibration of etched pits with diameters ranging from 225 to 1125 nm at the wavelength of 633 nm. The proposed system offers a scalable and low-complexity solution for fast, noncontact nanometrology.

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.

The significance of precise metrology in various industries, particularly within manufacturing plants, is undeniable, especially as components and devices continue to undergo miniaturization. The emergence of nano-manufacturing further amplifies the necessity for meticulous measurement techniques. Coherent Fourier scatterometry (CFS) is a nonimaging, model-based, bright-field optical metrology and inspection technique used for retrieving complex geometric parameters of nanostructures and for detecting isolated nanoparticles and contamination on surfaces. It uses a focused light spot to illuminate the sample and the scattered light is collected as the sample is scanned in the lateral direction. However, the time it takes to inspect a certain area has been a limiting factor in its wider adoption as a commercial metrology tool. To address this limitation, we propose a novel design of CFS utilizing a galvo mirror for faster scanning of the laser spot on the sample, offering significant improvements in scan speed.

Achieving high degree of tunability in photonic devices has been a focal point in the field of integrated photonics for several decades, enabling a wide range of applications from telecommunication and biochemical sensing to fundamental quantum photonic experiments. We introduce a novel technique to engineer the thermal response of photonic devices resulting in large and deterministic wavelength shifts across various photonic platforms, such as amorphous Silicon Carbide (a-SiC), Silicon Nitride (SiN) and Silicon-On-Insulator (SOI). In this paper, we demonstrate bi-directional thermal tuning of photonic devices fabricated on a single chip. Our method can be used to design high-sensitivity photonic temperature sensors, low-power Mach-Zehnder interferometers and more complex photonics circuits.

In power electronics, compound semiconductors with large bandgaps, like silicon carbide (SiC), are increasingly being used as material instead of silicon. They have a lot of advantages over silicon but are also intolerant of nanoscale material defects, so that a defect inspection with high accuracy is needed. The different defect types on SiC samples are measured with various measurement methods, including optical and tactile methods. The defect types investigated include carrots, particles, polytype inclusions and threading dislocations, and they are analysed with imaging ellipsometry, coherent Fourier scatterometry (CFS), white light interference microscopy (WLIM) and atomic force microscopy (AFM). These different measurement methods are used to investigate which method is most sensitive for which type of defect to be able to use the measurement methods more effectively. It is important to be able to identify the defects to classify them as critical or non-critical for the functionality of the end product. Once these investigations have been completed, the measurement systems can be optimally distributed to the relevant defects in further work to realize a hybrid analysis of the defects. In addition to the identification and classification of defects, such a future hybrid analysis could also include characterizations, e.g. further evaluation of ellipsometric data by using numerical simulations.

Nanostructures with steep side wall angles (swa) play a pivotal role in various technological applications. Accurate characterization of these nanostructures is crucial for optimizing their performance. In this study, we propose a far-field detection method based on coherent Fourier scatterometry (CFS) for accurate quantification of steep swa and heights in cliff-like nanostructures. Our approach introduces a parameter termed ‘visibility’, derived from the unique far-field signatures of cliff-like nanostructures. This parameter serves as a quantitative metric for the calibration of swa and heights. The heightened sensitivity of our method is demonstrated, particularly when the incident polarization is perpendicular to the invariant direction of the nanostructure for swa calibration, while both polarization states exhibit sensitivity to height calibration. Furthermore, a comprehensive sensitivity analysis reveals the stable nature of our method, showcasing that even with fluctuations of ±10 nm in the position of the nanostructure, the resulting swa remains stable within a range of ±0.5◦. The exponential variation of the visibility parameter with edge roundness is observed, with fluctuations in edge roundness within 10 nm resulting in swa variations within 1.7◦ for both polarization states. In experimental validations, our results demonstrate reasonable agreement between CFS-derived and AFM measurements. The AFM data for swa (77.99◦ ±1.37◦) and height (148.35 nm ±2.11 nm) are corroborated with CFS-derived value of swa (77.75◦ ±3.61◦, 78.36◦ ±3.89◦) and height (149.42 nm ±1.66 nm, 150.05 nm ±1.04 nm) obtained from calibration curves for TM and TE incident beams, respectively. Overall, our findings underscore CFS as a potential and reliable tool for nanostructure characterization, offering precise measurements that are pivotal for advancing nanotechnology.

We exploit quantum correlations to enhance quantitative phase retrieval of an object in a non-interferometric setting, only measuring the propagated intensity pattern after interaction with the object.

We show a general method to estimate with optimum precision, i.e., the best precision determined by the light-matter interaction process, a set of parameters that characterize a phase object. The method is derived from ideas presented by Pezze et al. [Phys. Rev. Lett. 119, 130504 (2017)0031-900710.1103/PhysRevLett.119.130504]. Our goal is to illuminate the main characteristics of this method as well as its applications to the physics community probably not familiar with the formal quantum language usually employed in works related to quantum estimation theory. First, we derive precision bounds for the estimation of the set of parameters characterizing the phase object. We compute the Crámer-Rao lower bound for two experimentally relevant types of illumination: a multimode coherent state with mean photon number N and N copies of a multimode single-photon quantum state. We show under which conditions these two models are equivalent. Second, we show that the optimum precision can be achieved by projecting the light reflected or transmitted from the object onto a set of modes with engineered spatial shape. We describe how to construct these modes and demonstrate explicitly that the precision of the estimation using these measurements is optimum. As an example, we apply these results to the estimation of the height and sidewall angle of a cliff-like nanostructure, an object relevant in the semiconductor industry for the evaluation of nanofabrication techniques.

We propose a technique which exploits entanglement to enhance quantitative phase retrieval of an object in a non-interferometric setting only measuring the propagated intensity pattern after interaction with the object.

Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly used in the classical domain, e.g., ptychography and diffractive imaging, a demonstration of quantum advantage is still missing. Here, we fill this gap by exploiting entanglement to enhance imaging of a pure phase object in a non-interferometric setting, only measuring the phase effect on the free-propagating field. This method, based on the so-called “transport of intensity equation", is quantitative since it provides the absolute value of the phase without prior knowledge of the object and operates in wide-field mode, so it does not need time-consuming raster scanning. Moreover, it does not require spatial and temporal coherence of the incident light. Besides a general improvement of the image quality at a fixed number of photons irradiated through the object, resulting in better discrimination of small details, we demonstrate a clear reduction of the uncertainty in the quantitative phase estimation. Although we provide an experimental demonstration of a specific scheme in the visible spectrum, this research also paves the way for applications at different wavelengths, e.g., X-ray imaging, where reducing the photon dose is of utmost importance.

For the development of integrated circuits, the accompanying metrology inside the fabrication process is essential. Non-imaging metrology of nanostructure has to be quick and non-destructive. The multilayers are crucial components of today's microprocessor nanostructures and reflective coatings. Coherent Fourier scatterometry (CFS), which is currently employed as a method for determining certain parameters of nanostructures and isolated particle detection, has not been investigated in the context of multilayer characterization. Retrieving the thickness of many wavelength-thick films using a coherent visible-range source at a full-complex-field measurement is the specific application where CFS might be advantageous. Furthermore, due to polishing in the realistic multilayers, the anticipated optical performance suffers from stochastic changes relating to surface roughness. Few non-imaging metrology methods take into consideration these statistic variances and thus are of interest for this study. Operating in the visible regime, CFS can become a viable candidate to provide cover layer reconstruction in the presence of surface roughness that has a correlation length bigger than the characteristic spot size i.e., in the range of microns. We present forward model results of multilayer structure as measured with visible range CFS modality. The influence of surface roughness is taken into account and the simulation results are discussed. Simulations of micron-sized layers of dielectric on silicon substrate suggest an influence on the far field intensity that motivates a future extended study on experimental multiple wavelength thick cover layer reconstruction in the presence of roughness.

It has been a widely growing interest in using silicon carbide (SiC) in high-power electronic devices. Yet, SiC wafers may contain killer defects that could reduce fabrication yield and make the device fall into unexpected failures. To prevent these failures from happening, it is very important to develop inspection tools that can detect, characterize and locate these defects in a non-invasive way. Current inspection techniques such as Dark Field or Bright field microscopy are effectively able to visualize most such defects; however, there are some scenarios where the inspection becomes problematic or almost impossible, such as when the defects are too small or have low contrast or if the defects lie deep into the substrate. Thus, an alternative method is needed to face these challenges. In this paper, we demonstrate the application of coherent Fourier scatterometry (CFS) as a complementary tool in addition to the conventional techniques to overcome different and problematic scenarios of killer defects inspection on SiC samples. Scanning electron microscopy (SEM) has been used to assess the same defects to validate the findings of CFS. Great consistency has been demonstrated in the comparison between the results obtained with CFS and SEM.