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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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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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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The phenomenon of scattering is ubiquitous. The human eye sees it as a ``blue" sky in a summer morning or a diffuse glow during the night, the color of a laser or fog in the air. Alternatively, scattering recorded with a state-of-the-art instrument manifests itself in collisions between atoms, electrons, and photons, such as processes in nuclear reactors or inside an accelerator, and high-energy electrons precipitation in the atmosphere. Scientists across the world are interested in studying the scattering effects that take part in the interaction between the light and matter in order to determine the physical properties of materials. The dimensions of an arbitrary structure and its quality is adequately studied with optical metrology, which is the science of measurements with light. Staring from the height and width determination of a distant object by triangulation over many decades, optical metrology has developed to the vibrant area of technological advancements. Numerous optical techniques and instruments, such as microscopes, wavefront sensors, optical comparators, and interferometers are available now where subnanometer precision is achieved. By studying the properties of the electromagnetic field that is generated from the interaction between the probe and the unknown target, it is nowadays possible to retrieve intricate parameters of the object such as its shape and roughness. Commonly, the measurement in the far-field regime is adopted since it is noninvasive. In the far-field, for successful information retrieval of features smaller than the Rayleigh limit, the inverse problem of scatterometry (optical metrology with scattered light) requires a priori information. In many cases, we assume that the target under the study is guaranteed to exist, and it is partially known. For example, one can deposit particles of certified material on top of a surface, measure the intensity of the scattered field, and by combining this information with electromagnetic models, one can deduce parameters such as size and position of the scatterer. However, when the target becomes extremely small, as for example, a fraction of the wavelength, the question arises: given the measuring instrument, would we still detect this target? The answer is yes, if the sensitivity of the instrument is high enough. Many areas of optics and physics rely on the detection and localization of tiny objects on top of a surface. The main examples include contamination and nanofabricated features and defects in the semiconductor industry, the studies of viruses and bacteria for biological and medical sciences, air and water pollution with toxic particles in environmental science. In this thesis, we will concentrate on the application of scatterometry for isolated nanoparticle detection aimed at quality control in the semiconductor industry. @en

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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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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We demonstrate the far field detection of low-contrast nanoparticles on surfaces using a technique that is based on evanescent-wave amplification due to a thin dielectric layer that is deposited on the substrate. This research builds upon earlier results where scattering enhancement of 200 nm polystyrene (PSL) particles on top of a glass substrate covered with a ≈ 20 nm InSb layer has been observed by Roy et al. [Phys. Rev. A 96, 013814 (2017)]. In this paper, the enhancement effect is analyzed using other dielectric materials with lower absorption than the previous one, resulting in a higher signal-to-noise ratio (SNR) for particle detection. We also consider several polarizations of the incoming field, such as linear, circular, azimuthal, and radial. In our experiments, we observe that the optimum enhancement occurs when linear polarization is used. With this new scheme, PSL nanoparticles of 40 nm in diameter have been detected at a wavelength of 405 nm.

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The analysis of 2D scattering maps generated in scatterometry experiments for detection and classification of nanoparticles on surfaces is a cumbersome and slow process. Recently, deep learning techniques have been adopted to avoid manual feature extraction and classification in many research and application areas, including optics. In the present work, we collected experimental datasets of nanoparticles deposited on wafers for four different classes of polystyrene particles (with diameters of 40, 50, 60, and 80 nm) plus a background (no particles) class. We trained a convolutional neural network, including its architecture optimization, and achieved 95% accurate results. We compared the performance of this network to an existing method based on line-by-line search and thresholding, demonstrating up to a twofold enhanced performance in particle classification. The network is extended by a supervisor layer that can reject up to 80% of the fooling images at the cost of rejecting only 10% of original data. The developed Python and PyTorch codes, as well as dataset, are available online.

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We present an efficient machine learning framework for detection and classification of nanoparticles on surfaces that are detected in the far-field with coherent Fourier scatterometry (CFS). We study silicon wafers contaminated with spherical polystyrene (PSL) nanoparticles (with diameters down to λ/8). Starting from the raw data, the proposed framework does the pre-processing and particle search. Further, the unsupervised clustering algorithms, such as K-means and DBSCAN, are customized to be used to define the groups of signals that are attributed to a single scatterer. Finally, the particle count versus particle size histogram is generated. The challenging cases of the high density of scatterers, noise and drift in the dataset are treated. We take advantage of the prior information on the size of the scatterers to minimize the false-detections and as a consequence, provide higher discrimination ability and more accurate particle counting. Numerical and real experiments are conducted to demonstrate the performance of the proposed search and cluster-assessment techniques. Our results illustrate that the proposed algorithm can detect surface contaminants correctly and effectively.@en

We report a novel method of focus determination with high sensitivity and submicrometre accuracy. The technique relies on the asymmetry in the scattered far field from a nanosphere located at the surface of interest. The out-of-focus displacement of the probing beam manifests itself in imbalance of the signal of the differential detector located at the far field. Up-down scanning of the focussed field renders an error S-curve with a linear region that is slightly bigger than the corresponding vectorial Rayleigh range. We experimentally show that the focus can be determined not only for a surface with high optical contrast, such as a silicon wafer, but also for a weakly reflecting surface, such as fused silica glass. Further, for the probing wavelength of 405 nm, three sizes of polystyrene latex spheres, namely 200, 100, and 50 nm in diameter, are tested. Higher sensitivity was obtained as the sphere diameter became smaller. However, due to the fact that the scattering cross-section decreases as the sixth power of the nanosphere diameter, we envision that further size reduction of the studied sphere would not contribute to a drastic improvement in sensitivity. We believe that the proposed method can find applications in bio/nano detection, micromachining, and optical disk applications.

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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.

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