Coherent Fourier Scatterometry Research Articles

Multi-beam coherent Fourier scatterometry

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.

Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure

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.

Coherent Fourier scatterometry: a holistic tool forinspection of isolated particles or defects ongratings.

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 perform numerical investigations and demonstrate experimentally the capability of coherent Fourier scatterometry (CFS) to detect particles as small as 100nm 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.

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

Geometrical dimensions in nanostructures can be determined through indirect optical measurements carried out by a scatterometer. This includes solving a non-linear regression task in which a physical model is fitted to the observed optical diffraction pattern. We developed a virtual experiment which produces simulated diffraction patterns in coherent Fourier scatterometry measurements including perturbations due to various error sources. We utilize this virtual experiment to assess the suitability of data analysis and uncertainty quantification methods employed in scatterometry. In addition to investigating relevant physical parameters we explore the impact of deviations between the regression model utilized for the analysis and the scatterometry model used to produce the virtual diffraction pattern. We choose coverage probabilities of interval estimates of the geometrical dimensions as the main metric for the assessment. One of our findings is that the discretization level, expressed as the number of retained Fourier orders, can be relaxed up to order 9 in our case study, which is relevant as calculation times strongly depend on this parameter. Another result is that the least-squares approach considered here for solving the regression task in combination with the propagation of variances yields uncertainties which have somewhat lower coverage probabilities than the envisaged 95%. It turned out that it was critically important to model the oxide layer in order to get proper estimates of the width, or ‘critical dimension’, of the sample, while the uncertainty of the side wall angle had the largest impact on the uncertainty of the measurands. Our findings can help establishing traceability of Fourier scatterometry and underline the usefulness of high-quality virtual experiments in connection with complex measurement principles. At the same time the presented case study can be seen as a generic approach that could be followed for assessing uncertainty quantifications in other applications as well.

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.

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.

Coherent Fourier scatterometry nanoparticle detection enhanced by synthetic optical holography.

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 (∼λ/10) on a silicon wafer with an improvement in the signal-to-noise ratio (SNR) of approximately 4 dB.

Diffraction grating parameter retrieval using non-paraxial structured beams in coherent Fourier scatterometry

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.

Coherent Fourier Scatterometry for defect detection on SiC samples

Coherent Fourier Scatterometry (CFS) is a scatterometry technique that has been applied for grating and nanoparticle detection. Here, it has been challenged to verify the detectability of the so-called killer defects on SiC samples for power electronic applications. It has been shown that CFS is able to precisely recognize these defects regardless of their shape or size. CFS could be considered as a possible alternative for this purpose.

Coherent Fourier scatterometry for particle detection on structured surfaces

We demonstrate the detection of particles/contamination present on a structured surface using Coherent Fourier scatterometry (CFS) by applying Fourier filtering to the scanned maps, which eliminates background effects due to the electronic noise as well the structure itself. We show that by using filters in the Fourier space we can significantly improve the detection capabilities of the particles present on the structure.

Particle detection enhancement by combining coherent Fourier scatterometry with synthetic optical holography

By combining coherent Fourier scatterometry (CFS) with synthetic optical holography (SOH) we show that the sensitivity of detection of isolated nanoparticles on surfaces can be substantially increased. This improvement is a result of the boost in the signal at the detector due to the added reference beam, and the reduction of background noise caused by the electronics. We demonstrate an improvement of sensitivity of about 4 dB for the case of detection of a 60 nm polystyrene latex (PSL) particle on a silicon wafer at the wavelength of 633 nm (∼ λ/10).

Scatterometry Measurements With Scattered Light Imaging Enable New Insights Into the Nerve Fiber Architecture of the Brain

The correct reconstruction of individual (crossing) nerve fibers is a prerequisite when constructing a detailed network model of the brain. The recently developed technique Scattered Light Imaging (SLI) allows the reconstruction of crossing nerve fiber pathways in whole brain tissue samples with micrometer resolution: the individual fiber orientations are determined by illuminating unstained histological brain sections from different directions, measuring the transmitted scattered light under normal incidence, and studying the light intensity profiles of each pixel in the resulting image series. So far, SLI measurements were performed with a fixed polar angle of illumination and a small number of illumination directions, providing only an estimate of the nerve fiber directions and limited information about the underlying tissue structure. Here, we use a display with individually controllable light-emitting diodes to measure the full distribution of scattered light behind the sample (scattering pattern) for each image pixel at once, enabling scatterometry measurements of whole brain tissue samples. We compare our results to coherent Fourier scatterometry (raster-scanning the sample with a non-focused laser beam) and previous SLI measurements with fixed polar angle of illumination, using sections from a vervet monkey brain and human optic tracts. Finally, we present SLI scatterometry measurements of a human brain section with 3 μm in-plane resolution, demonstrating that the technique is a powerful approach to gain new insights into the nerve fiber architecture of the human brain.

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.

Coherent Fourier scatterometry using orbital angular momentum beams for defect detection.

Defect inspection on lithographic substrates, masks, reticles, and wafers is an important quality assurance process in semiconductor manufacturing. Coherent Fourier scatterometry (CFS) using laser beams with a Gaussian spatial profile is the standard workhorse routinely used as an in-line inspection tool to achieve high throughput. As the semiconductor industry advances toward shrinking critical dimensions in high volume manufacturing using extreme ultraviolet lithography, new techniques that enable high-sensitivity, high-throughput, and in-line inspection are critically needed. Here we introduce a set of novel defect inspection techniques based on bright-field CFS using coherent beams that carry orbital angular momentum (OAM). One of these techniques, the differential OAM CFS, is particularly unique because it does not rely on referencing to a pre-established database in the case of regularly patterned structures with reflection symmetry. The differential OAM CFS exploits OAM beams with opposite wavefront or phase helicity to provide contrast in the presence of detects. We numerically investigated the performance of these techniques on both amplitude and phase defects and demonstrated their superior advantages-up to an order of magnitude higher in signal-to-noise ratio-over the conventional Gaussian beam CFS. These new techniques will enable increased sensitivity and robustness for in-line nanoscale defect inspection and the concept could also benefit x-ray scattering and scatterometry in general.

Optical metrology beyond Abbe and Rayleigh

For many years, it was believed that optical microscopy and metrology was limited in resolution related to the light wavelength as suggested by Ernst Abbe and Lord Rayleigh. In recent past, several approaches have been developed to overcome these limitations such as Nobel price honored STED or optical CD as widely used in semiconductor metrology. Unfortunately, both techniques need special samples. While STED relies on fluorescence, OCD requires grating samples. In our contribution, we present two model based (mb) approaches to overcome some of these restrictions. One is mb Laser Focus Scanning (mLFS). Here, we show how to improve the accuracy of edge detection from several hundred nm to about 10 - 20 nm by exploiting rigorous modeling. The second one is Scanning Coherent Fourier Scatterometry (SCFS) where the diffracted Fourier spectrum is detected and the attempt is undertaken to retireve the sample profile. It is shown that this technique is very sensitive, particularly when the phase is recorded by means of a wave-front sensor. Measurements and simulations for periodic as well as for aperiodic sub-resolution features are show already good agreement. Moreover, we strongly believe that the observed high sensitivity of the Fourier spectra opens the path to quantitatively measurements below the resolution limits of light.

Coherent Fourier scatterometry reveals nerve fiber crossings in the brain.

Previous simulation studies by Menzel et al. [Phys. Rev. X 10, 021002 (2020)] have shown that scattering patterns of light transmitted through artificial nerve fiber constellations contain valuable information about the tissue substructure such as the individual fiber orientations in regions with crossing nerve fibers. Here, we present a method that measures these scattering patterns in monkey and human brain tissue using coherent Fourier scatterometry with normally incident light. By transmitting a non-focused laser beam (λ = 633 nm) through unstained histological brain sections, we measure the scattering patterns for small tissue regions (with diameters of 0.1–1 mm), and show that they are in accordance with the simulated scattering patterns. We reveal the individual fiber orientations for up to three crossing nerve fiber bundles, with crossing angles down to 25°.

Far-field sectioning for the retrieval of subwavelength grating parameters using coherent Fourier scatterometry

Optical inspection of periodic nanostructures is a major challenge in the semiconductor industry due to constantly decreasing critical dimensions. In this paper we combine coherent Fourier scatterometry (CFS) with a sectioning mask for subwavelength grating parameter determination. By selecting only the most sensitive regions of the scattered light in the Fourier plane, one can retrieve grating parameters faster and with higher sensitivity than previous approaches. Moreover, the full process of CFS using focused light is explained and implemented in a subwavelength grating regime. The results of using transverse magnetic polarized input fields together with the proposed sectioning mask are presented and compared to the non-mask case.

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.

A highly sensitive laser focus positioning method with sub-micrometre accuracy using coherent Fourier scatterometry

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.

Phase retrieval applied to coherent Fourier scatterometry using the extended ptychographic iterative engine

We have demonstrated that the extended ptychographic iterative engine (ePIE) algorithm can be applied to retrieve the phase information of the vectorial scattered field of a subwavelength object with the amplitude of the scattered field as input. We applied this technique combined with coherent Fourier scatterometry to determine the phase of the scattered field of a subwavelength grating, illuminated by a focused laser beam.