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

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.@en

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.

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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.@en

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.

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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.@en

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.

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Detecting defects on diffraction gratings is crucial for ensuring their performance and reliability. Practical detection of these defects poses challenges due to their subtle nature.We performnumerical investigations and demonstrate experimentally the capability of coherent Fourier scatterometry (CFS) to detect particles as small as 100 nm and also other irregularities that are encountered usually on diffraction gratings.Our findings indicate that CFS is a viable tool for inspection of diffraction gratings.

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Integrated photonic platforms have proliferated in recent years, each demonstrating its unique strengths and shortcomings. Given the processing incompatibilities of different platforms, a formidable challenge in the field of integrated photonics still remains for combining the strengths of different optical materials in one hybrid integrated platform. Silicon carbide is a material of great interest because of its high refractive index, strong second- and third-order nonlinearities, and broad transparency window in the visible and near-infrared range. However, integrating silicon carbide (SiC) has been difficult, and current approaches rely on transfer bonding techniques that are time-consuming, expensive, and lacking precision in layer thickness. Here, we demonstrate high-index amorphous silicon carbide (a-SiC) films deposited at 150 °C and verify the high performance of the platform by fabricating standard photonic waveguides and ring resonators. The intrinsic quality factors of single-mode ring resonators were in the range of Q_int = (4.7-5.7) × 10⁵ corresponding to optical losses between 0.78 and 1.06 dB/cm. We then demonstrate the potential of this platform for future heterogeneous integration with ultralow-loss thin SiN and LiNbO₃ platforms.

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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.

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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.

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Optical singularities indicate zero-intensity points in space where parameters, such as phase, polarization, are undetermined. Vortex beams such as the Laguerre–Gaussian modes are characterized by a phase factor e^ilθ, and contain a phase singularity in the middle of its beam. In the case of a transversal optical singularity (TOS), it occurs perpendicular to the propagation, and its phase integral is 2π in nature. Since it emerges within a nano-size range, one expects that TOSs could be sensitive in the light-matter interaction process and could provide a great possibility for accurate determination of certain parameters of nanostructure. Here, we propose to use TOSs generated by a three-wave interference to illuminate a step nanostructure. After interaction with the nanostructure, the TOS is scattered into the far field. The scattering direction can have a relation with the physical parameters of the nanostructure. We show that by monitoring the spatial coordinates of the scattered TOS, its propagation direction can be determined, and as consequence, certain physical parameters of the step nanostructure can be retrieved with high precision.

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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.

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We demonstrate that the sensitivity of nanoparticle detection on surfaces can be substantially improved by implementing synthetic optical holography (SOH) in coherent Fourier scatterometry (CFS), resulting in a phase-sensitive confocal differential detection technique that operates at very low power level (P=0.016 mW). The improvement in sensitivity is due to two reasons: first, the boost in the signal at the detector due to the added reference beam; and second, the reduction of background noise caused by the electronics. With this new system, we are able to detect a 60-nm polystyrene latex (PSL) particle at a wavelength of 633 nm (∼λl/10) on a silicon wafer with an improvement in the signalto- noise ratio (SNR) of approximately 4 dB. c 2022 Optica Publishing Group

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Accurate determination of the physical parameters of nanostructures from optical far-field scattering is an important and challenging topic in the semiconductor industry. Here, we propose a novel metrology method to determine simultaneously the height and side-wall angle of a step-shaped silicon nanostructure. By employing an optical singular beam into a typical coherent Fourier scatterometry system, both parameters can be retrieved through analyzing the intensity profile of the far-field scattering pattern. The use of singular beam is shown to be sensitive to slight changes of the parameters of the step. By changing the relative direction between the singularity and structure, the height and side-wall angle can both be retrieved with high precision. This new method is robust, simple, and can provide valuable means for micro-and-nano- metrologies.

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Shortly after their inception, superconducting nanowire single-photon detectors (SNSPDs) became the leading quantum light detection technology. With the capability of detecting single-photons with near-unity efficiency, high time resolution, low dark count rate, and fast recovery time, SNSPDs outperform conventional single-photon detection techniques. However, detecting lower energy single photons (<0.8 eV) with high efficiency and low timing jitter has remained a challenge. To achieve unity internal efficiency at mid-infrared wavelengths, previous works used amorphous superconducting materials with low energy gaps at the expense of reduced time resolution (close to a nanosecond), and by operating them in complex milliKelvin (mK) dilution refrigerators. In this work, we provide an alternative approach with SNSPDs fabricated from 5 to 9.5 nm thick NbTiN superconducting films and devices operated in conventional Gifford-McMahon cryocoolers. By optimizing the superconducting film deposition process, film thickness, and nanowire design, our fiber-coupled devices achieved >70% system detection efficiency (SDE) at 2 μm and sub-15 ps timing jitter. Furthermore, detectors from the same batch demonstrated unity internal detection efficiency at 3 μm and 80% internal efficiency at 4 μm, paving the road for an efficient mid-infrared single-photon detection technology with unparalleled time resolution and without mK cooling requirements. We also systematically studied the dark count rates (DCRs) of our detectors coupled to different types of mid-infrared optical fibers and blackbody radiation filters. This offers insight into the trade-off between bandwidth and DCRs for mid-infrared SNSPDs. To conclude, this paper significantly extends the working wavelength range for SNSPDs made from polycrystalline NbTiN to 1.5-4 μm, and we expect quantum optics experiments and applications in the mid-infrared range to benefit from this far-reaching technology.

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In recent years, a lot of works have been published that use parameter retrieval using orbital angular momentum (OAM) beams. Most make use of the OAM of different Laguerre-Gauss modes. However, those specific optical beams are paraxial beams and this limits the regime in which they can be used. In this paper, we report on the first results on retrieving the geometric parameters of a diffraction grating by analysing the corresponding complex-valued (i.e. amplitude and phase) Helmholtz Natural Modes (HNM) spectra containing both the azimuthal (i.e. n) and radial (i.e. m) indices. HNMs are a set of orthogonal, non-paraxial beams with finite energy carrying OAM. We use the coherent Fourier scatterometry (CFS) setup to calculate the field scattered from the diffraction grating. The amplitude and phase contributions of each HNM are then obtained by numerically calculating the overlap integral of the scattered field with the different modes. We show results on the sensitivity of the HNMs to several grating parameters.

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Single photon detectors are indispensable tools in optics, from fundamental measurements to quantum information processing. The ability of superconducting nanowire single photon detectors (SNSPDs) to detect single photons with unprecedented efficiency, short dead time, and high time resolution over a large frequency range enabled major advances in quantum optics. However, combining near-unity system detection efficiency (SDE) with high timing performance remains an outstanding challenge. In this work, we fabricated novel SNSPDs on membranes with 99.5-2.07+0.5% SDE at 1350 nm with 32 ps timing jitter (using a room-temperature amplifier), and other detectors in the same batch showed 94%-98% SDE at 1260-1625 nm with 15-26 ps timing jitter (using cryogenic amplifiers). The SiO2/Au membrane enables broadband absorption in small SNSPDs, offering high detection efficiency in combination with high timing performance. With low-noise cryogenic amplifiers operated in the same cryostat, our efficient detectors reach a timing jitter in the range of 15-26 ps. We discuss the prime challenges in optical design, device fabrication, and accurate and reliable detection efficiency measurements to achieve high performance single photon detection. As a result, the fast developing fields of quantum information science, quantum metrology, infrared imaging, and quantum networks will greatly benefit from this far-reaching quantum detection technology.

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The sidewall angle (SWA) of a nanostructure exerts influence on the performance of the nanostructure and plays an important role in processing nano-structural chips. It is still a great challenge to determine steep SWAs from far field measurements especially when the SWAs are close to 90°. Here, we propose a far-field detection system to determine steep SWA of a cliff-shape step structure on a silicon substrate by combining a split detector with a scanning method. The far-field radiation field is asymmetric due to the scattering of the step structure, and further numerical analysis demonstrates the reliability of this far-field measurement method. In the simulations, two key variables, i.e. the polarization state and the focus position of the incident laser beam, are considered to explore their impacts. By scanning over the structure laterally and longitudinally with both TE and TM polarizations, polarization effects on the far-field occur. These effects show higher sensitivity to steep SWA variation for TM polarization as compared to TE. Furthermore, with a comprehensive longitudinal scanning analysis for the TM polarization case, a feasible focus interval can be optimized to retrieve the steep SWA. As the proposed method is fast, highly sensitive and easy to implement, it provides a powerful approach to investigate the scattering behavior of nanostructures.

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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.

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