The characterization of optical anisotropy in thin van der Waals (vdW) materials is crucial for both fundamental studies and nanophotonic applications. However, conventional techniques such as spectroscopic ellipsometry face significant limitations in measuring out-of-plane anisotropy and require large-area, uniform films. In this work, we present a novel framework based on coherent Fourier scatterometry (CFS) combined with deep learning for the rapid, label-free characterization of in-plane and out-of-plane refractive indices of anisotropic thin films. We designed a specialized deep neural network, AnisoVision, and trained it on simulated far-field angular spectra from multilayer stacks using the 4 × 4 Berreman matrix formalism. To efficiently capture the directional dependence of anisotropy, we utilize radially polarized light and extract only three far-field azimuthal cross sections (0, 45, 90°), enabling robust retrieval while minimizing data requirements. Our method demonstrates accurate index retrieval for both isotropic and anisotropic materials, including uniaxial h-BN and biaxial α-MoO3 flakes of varying thickness. We further validate the model’s stability by testing multiple flakes of the same material across a range of thicknesses, yielding consistent optical constants. Our approach is single-shot, nondestructive, and applicable to localized sample regions, making it suitable for heterogeneous or exfoliated samples. Additionally, the technique can be readily extended to broadband operation for spectroscopic analysis. Our work establishes CFS coupled with deep learning as a powerful platform for high-throughput optical metrology of low-dimensional materials.

Coherent Fourier scatterometry (CFS) is a powerful scanning technique for inspecting defects on structured surfaces, relying on split detectors to measure asymmetry in the far-field scattered light. The split signal, a differential signal derived by subtracting signals from opposing halves of the detector, effectively detects asymmetries along the scan direction. However, this approach is inherently limited when inspecting patterned structures, as it loses information orthogonal to the scan direction. This results in signals that vary depending on the orientation of the patterns, complicating the characterization of certain defects. To overcome this limitation, we introduce a quad detector-based CFS scheme. By utilizing four independent photodetectors and processing their signals to generate integrated, split, and quad outputs, we capture complete far-field information. A Fourier filtering step removes detector-specific offsets, enabling robust signal analysis. Unlike the split-detector approach, this method provides defect and nanostructure inspection independent of the shape and orientation of the underlying patterns. We present the results of implementing this scheme to inspect defects on patterned surfaces. The quad detector signal reveals the edges of defects and demonstrates the versatility of this approach across different surface features. This advancement enhances the capability of CFS for defect inspection, offering a comprehensive and reliable solution for patterned structures where traditional split-detector methods fall short.

Coherent Fourier Scatterometry (CFS) enables low-power, high- resolution, non-destructive metrology for nanoscale structures. Recent advancements have extended its applications to improving the measurement of critical dimensions, such as steep-sidewall angles of fabricated nanostructures and the detection and shape determination of defects for semiconductor and power electronics applications. Innovations like beam scanning, multi-beam setups, and synthetic optical holography enhance its speed and sensitivity, making CFS increasingly viable for industrial in-line inspection.

Coherent Fourier scatterometry (CFS) is a non-invasive optical technique widely used for defect detection on planar surfaces. It utilizes split detectors to measure far-field asymmetries as differential signals, making it highly effective for identifying defects such as particles or burrows. Detecting defects near edges of nanostructures, however, is particularly challenging due to interference between the edge signal and the defect signal, a limitation not only of CFS but also of other standard techniques like bright-field and dark-field microscopy. Accurate detection of such defects is critical in fields like semiconductor manufacturing and nanotechnology, where edge-adjacent defects can compromise device performance. Therefore, understanding the limits of CFS for edge-adjacent defect detection is essential for optimizing its application and interpreting its results. In this work, we first demonstrate experimentally that CFS can detect a 200 nm Pt particle positioned 2 µm from an edge. We then perform 3D FDTD simulations to model particles and burrows positioned at varying distances from an edge. By analyzing the split detector signals for these scenarios, we observe that particle and burrow signals become more prominent as their distance from the edge increases. However, for a system using a numerical aperture of 0.9 and wavelength of 633 nm, for distances from the edge smaller than 350 nm for particles and 650 nm for burrows, the characteristic signals diminish, merging with the edge response. This study highlights the challenges and potential solutions for defect inspection near edges, advancing the applicability of CFS for patterned and complex structures.

As advanced packaging evolves with 2.5D/3D integration, the demand grows for the inspection of subsurface nanostructures and defects within silicon (Si), ensuring reliability and yield in modern electronics. In this paper, we demonstrate coherent Fourier scatterometry (CFS) at a near-infrared wavelength (λ=1055 nm) for noninvasive inspection of nanostructures buried within Si. Despite Si's transparency in this spectral range, its high refractive index causes strong Fresnel reflections at the air–Si interface. To eliminate these unwanted signals, we employ two distinct approaches: (i) a split detector to subtract reflections in defect inspection mode, and (ii) a reduced coherence length, below lasing threshold, combined with spatial filtering, for retrieving far-field diffraction patterns in grating inspection mode. We systematically investigate how thickness of overlying Si (without overlying Si wafer, with 300 μm thick Si wafer, and with 500 μm thick Si wafer) affects scattering signals of the buried nanostructures. We demonstrate the detection of low contrast polystyrene nanospheres (down to 400 nm, well below the diffraction limit of λ/(2NA)≈959 nm) buried under 500 μm of Si. Further, we successfully detect nanopillars ≥100 nm and nanopits ≥225 nm. We also analyze the influence of spherical aberrations, which increases linearly with the thickness of the Si layer, resulting in a degradation of the focal spot quality. Beyond isolated defects, we retrieve the diffraction patterns of a 1430 nm period grating under 500 μm of Si, with minimal distortion relative to when no Si layer is present. Overall, these results highlight CFS as a robust, high-sensitivity technique for in-depth inspection in microelectronics and photonic applications, demonstrating potential for failure analysis, process control, and metrology in advanced packaging environments.

Nanopillars are widely used for various applications and require accurate shape characterization to enhance their performance and optimize fabrication processes. In this paper, we employ coherent Fourier scatterometry (CFS) combined with rigorous three-dimensional finite-difference time-domain simulations to accurately determine the shapes of nanopillars with various geometries, including cylindrical, triangular, square, and rectangular shapes. The nanopillars considered here have lateral dimensions (a) ranging from 100 to 1000 nm. Our methodology utilizes the preferential excitation of the nanostructures by a tightly focused beam and leverages their inherent symmetry to capture far-field signatures that vary periodically with rotation. This approach allows us to distinguish between different nanopillar shapes based on these rotational signatures. Our results demonstrate that the CFS method can reliably characterize nanopillars with lateral dimensions a≥300 nm, surpassing the conventional diffraction limit of 351 nm. However, the method reaches its fundamental limits for a≤200 nm, as also confirmed by simulations, where we approach the dipole approximation regime (a≪λ). This constraint is not observed for rectangular nanopillars, owing to their constant breadth (b=1000 nm), which prevents such a regime. Furthermore, our method successfully differentiates nanopillars transitioning from rectangular to square shapes. We also explored the method's limitations concerning nanostructure height (h), finding that triangular and square nanopillars could be characterized accurately for h≥50 nm and h≥150 nm, respectively. Furthermore, the method remains robust against shape distortions such as edge roundness. The method is primarily effective in determining the lateral (top-down) shape of nanopillars, it does not resolve longitudinal features. The ability to accurately characterize nanostructure shapes has significant implications in fields such as photonics and biosensing, where geometry critically influences device performance.

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.

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.