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.
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.
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)10.1103/PhysRevA.96.013814]. 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.
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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