Transversal optical singularity induced precision measurement of step-nanostructures.

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 eilθ, 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.

Optical singularity assisted method for accurate parameter detection of step-shaped nanostructure in coherent Fourier scatterometry.

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.

Direct detection of polystyrene equivalent nanoparticles with diameter of 21 nm (∼λ/19) using coherent Fourier scatterometry: erratum.

We present an erratum to our article Kolenov, D., et al. "Direct detection of polystyrene equivalent nanoparticles with a diameter of 21 nm ( ∼ λ/19) using coherent Fourier scatterometry." Opt. Express29, 16487 (2021)10.1364/OE.421145.

Direct detection of polystyrene equivalent nanoparticles with a diameter of 21 nm (∼λ/19) using coherent Fourier scatterometry.

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.

Machine learning techniques applied for the detection of nanoparticles on surfaces using coherent Fourier scatterometry.

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.

Superresolution effect due to a thin dielectric slab for imaging with radially polarized light.

Improving the image quality of small particles is a classic problem and especially challenging when the distance between particles are below the optical diffraction limit. We propose a imaging system illuminated with radially polarized light combined with a suitable substrate that contains a thin dielectric layer to demonstrate that the imaging quality can be enhanced. The coupling between the evanescent wave produced in a designed thin dielectric layer, the small particles and the propagating wave forms a mechanism to transfer sub-wavelength information about the particles to the far field. The smallest distinguished distance reaches to 0.634λ, when the imaging system is composed of a high numerical aperture (NA=0.9) lens and the illumination wavelength λ = 632nm, beyond the diffraction limit 0.678λ. The lateral resolution can be further improved by combining the proposed structure with superresolution microscopy techniques.

Convolutional neural network applied for nanoparticle classification using coherent scatterometry data.

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.

Phase retrieval of the full vectorial field applied to coherent Fourier scatterometry.

Coherent Fourier scatterometry is an optical metrology technique that utilizes the measured intensity of the scattered optical field to reconstruct certain parameters of test structures written on a wafer with nano-scale accuracy. The intensity of the scattered field is recorded with a camera and this information is used to retrieve the grating parameters. To improve sensitivity in the parameter reconstruction, the phase of the scattered field can also be acquired. Interferometry can be used for this purpose, but with the cost of cumbersomeness. In this paper, we show that iterative phase retrieval methods can be applied to retrieve the scattered complex fields from only intensity measurement data. We show that the accuracy of the retrieved complex fields using phase retrieval is comparable to that measured directly using interferometry.

Focused fields of given power with maximum longitudinal electric field component inside a substrate.

Closed formulas are presented for the electromagnetic field of given power in the lens pupil, which maximizes the longitudinal electric field when focusing through an interface at arbitrary depth along the optical axis. The optimum pupil field is found to be a continuous, monotonously increasing function of the radial pupil coordinate, which differs considerably from the commonly used annular illumination. Several cases of pupil fields and focused fields are shown for different materials, NA, and focusing depth. Also, the effect of absorbing media is considered.

Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate.

A fast noninvasive method based on scattering from a focused radially polarized light to detect and localize subwavelength nanoparticles on a substrate is presented. The technique relies on polarization matching in the far field between scattered and spurious reflected fields. Results show a localization uncertainty of ≈10^{-4}λ^{2} is possible for a particle of area ≈λ^{2}/16. The effect of simple pupil shaping is also shown.

Coherent Fourier scatterometry for detection of nanometer-sized particles on a planar substrate surface.

Inspection tools for nano-particle contamination on a planar substrate surface is a critical problem in micro-electronics. The present solutions are either expensive and slow or inexpensive and fast but have low sensitivity because of limitations due to diffraction. Most of them are also substrate specific. In this article we report how Coherent Fourier Scatterometry is used for detection of particles smaller than λ/4. Merits of the technique, especially, the procedures to improve SNR, its flexibility and its robustness on rough surfaces are discussed with simulated and experimental results.

Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory.

In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM).

Nanostep height measurement via spatial mode projection.

We demonstrate an optical scheme for measuring the thickness of thin nanolayers with the use of light beam's spatial modes. The novelty in our scheme is the projection of the beam reflected by the sample onto a properly tailored spatial mode. In the experiment described below, we are able to measure a step height smaller than 10 nm, i.e., one-eightieth (1/80) of the wavelength with a standard error in the picometer scale. Since our scheme enhances the signal-to-noise ratio, which effectively increases the sensitivity of detection, the extension of this technique to the detection of subnanometric layer thicknesses is feasible.

Through-focus phase retrieval and its connection to the spatial correlation for propagating fields.

Through-focus phase retrieval methods aim to retrieve the phase of an optical field from its intensity distribution measured at different planes in the focal region. By using the concept of spatial correlation for propagating fields, for both the complex amplitude and the intensity of a field, we can infer which planes are suitable to retrieve the phase and which are not. Our analysis also reveals why all techniques based on measuring the intensity at two Fourier-conjugated planes usually lead to a good reconstruction of the phase. The findings presented in this work are important for aberration characterization of optical systems, adaptive optics and wavefront metrology.

Predictive control of thermally induced wavefront aberrations.

In this paper we experimentally demonstrate the proof of concept for predictive control of thermally induced wavefront aberrations in optical systems. On the basis of the model of thermally induced wavefront aberrations and using only past wavefront measurements, the proposed adaptive optics controller is able to predict and to compensate the future aberrations. Furthermore, the proposed controller is able to correct wavefront aberrations even when some parameters of the prediction model are unknown. The proposed control strategy can be used in high power optical systems, such as optical lithography machines, where the predictive correction of thermally induced wavefront aberrations is a crucial issue.

An innovative and efficient method to control the shape of push-pull membrane deformable mirror.

We carry out performance characterisation of a commercial push and pull deformable mirror with 48 actuators (Adaptica Srl). We present a detailed description of the system as well as a statistical approach on the identification of the mirror influence function. A new efficient control algorithm to induce the desired wavefront shape is also developed and comparison with other control algorithms present in literature has been made to prove the efficiency of the new approach.

Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method.

We apply a phase retrieval algorithm to the intensity pattern of a Hartmann wavefront sensor to measure with enhanced accuracy the phase structure of a Hartmann hole array. It is shown that the rms wavefront error achieved by phase reconstruction is one order of magnitude smaller than the one obtained from a typical centroid algorithm. Experimental results are consistent with a phase measurement performed independently using a Shack-Hartmann wavefront sensor.

Direct measurement of the near-field super resolved focused spot in InSb.

Under appropriate laser exposure, a thin film of InSb exhibits a sub-wavelength thermally modified area that can be used to focus light beyond the diffraction limit. This technique, called Super-Resolution Near-Field Structure, is a potential candidate for ultrahigh density optical data storage and many other high-resolution applications. We combined near field microscopy, confocal microscopy and time resolved pump-probe technique to directly measure the induced sub-diffraction limited spot in the near-field regime. The measured spot size was found to be dependent on the laser power and a decrease of 25% (100 nm) was observed. Experimental evidences that support a threshold-like simulation model to describe the effect are also provided. The experimental data are in excellent agreement with rigorous simulations obtained with a three dimensional Finite Element Method code.

On focused fields with maximum electric field components and images of electric dipoles.

We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.

Lateral position correction in ptychography using the gradient of intensity patterns.

Ptychography, a form of Coherent Diffractive Imaging, is used with short wavelengths (e.g. X-rays, electron beams) to achieve high-resolution image reconstructions. One of the limiting factors for the reconstruction quality is the accurate knowledge of the illumination probe positions. Recently, many advances have been made to relax the requirement for the probe positions accuracy. Here, we analyse and demonstrate a straightforward approach that can be used to correct the probe positions with sub-pixel accuracy. Simulations and experimental results with visible light are presented in this work.