Coherent Fourier Scatterometry (CFS) is a powerful optical metrology technique for the precise characterisation of nanostructures. Conventional CFS systems rely on piezo-based scanning stages for raster scanning, which limits throughput due to slow scanning speeds. In this work, we present a high-speed CFS system incorporating a galvanometric (galvo) mirror for beam scanning. This approach significantly enhances scanning speed while maintaining measurement accuracy. Although galvo mirrors are widely used in optical systems, their implementation in CFS has unique challenges such as off-axis beam aberrations and angle-dependent beam shifts at the split detector. These issues are analysed and mitigated through optical design, alignment and system calibration. Additionally, we derive the minimum detector bandwidth required to capture high-frequency signals generated by the fast scanning. The effectiveness of the system is demonstrated through the calibration of pits with various diameters that are etched onto a silicon wafer. Results show a substantial improvement in scanning speed as compared with piezo-based systems without compromising measurement precision, making this approach highly suitable for high-throughput metrology applications.

We present a digital micro-mirror device (DMD)-enabled scan head for coherent Fourier scatterometry (CFS) that performs lateral scanning without macroscopic moving parts, while maintaining a diffraction-limited probe. A binary Fresnel zone plate (FZP) is displayed and translated on the DMD to steer a single focused spot across the sample, providing an electronically programmable alternative to scanning using piezo-based translation devices. To the best of our knowledge, this is the first published CFS implementation in which a DMD is the primary lateral scanning element. Furthermore, the DMD programmability is used to compensate for the scan-position-dependent aberrations using an iterative optimisation algorithm. Across a 400 × 200 DMD-pixel scan area, the peak-intensity coefficient of variation improves from 39.4% (uncorrected) to 16.1% (after correction) and to 4.47% with additional power normalisation, demonstrating substantially improved probe uniformity. Finally, we demonstrate particle detection on a Si wafer with 1 μm polystyrene latex particles, achieving an signal-to-noise ratio of 16.04 ± 1.11dB. The results establish DMD-FZP scanning with integrated aberration correction as a compact, fast, and scalable CFS architecture, with a clear pathway to higher throughput via multi-spot parallelisation.

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.

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 very sensitive optical metrology technique that has been applied for detection and characterisation of nanostructures. It is a scanning-based technique where the samplie is illuminated with a focused light spot. However, in practical CFS systems, residual optical aberrations can distort the focused spot and degrade the signal-to-noise ratio during measurements. Here, we present a systematic study of the influence of low-order aberrations: defocus, spherical, astigmatism, oblique astigmatism, and coma on the differential split-detector CFS signal. Controlled amounts of each aberration, described by Zernike polynomials, were introduced into the Fourier plane via a spatial light modulator. Two-dimensional differential scattering maps were recorded on a reference sample of 425 nm diameter, 150 nm deep pits etched in silicon, and the peak-to-peak differential signal was quantified as a function of peak-valley (PV) wavefront error. We find that defocus has the strongest impact, halving the signal at just 0.27λ PV, followed by spherical (0.32λ) and coma (0.40λ), whereas astigmatism and oblique astigmatism require larger wavefront errors (> 0.6λ) to produce comparable signal loss. These results define quantitative aberration tolerances for CFS systems. The insights gained here can guide the design and optimisation of different CFS implementations for in-line process control and nanostructure metrology.

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.

We show a general method to estimate with optimum precision, i.e., the best precision determined by the light-matter interaction process, a set of parameters that characterize a phase object. The method is derived from ideas presented by Pezze et al. [Phys. Rev. Lett. 119, 130504 (2017)0031-900710.1103/PhysRevLett.119.130504]. Our goal is to illuminate the main characteristics of this method as well as its applications to the physics community probably not familiar with the formal quantum language usually employed in works related to quantum estimation theory. First, we derive precision bounds for the estimation of the set of parameters characterizing the phase object. We compute the Crámer-Rao lower bound for two experimentally relevant types of illumination: a multimode coherent state with mean photon number N and N copies of a multimode single-photon quantum state. We show under which conditions these two models are equivalent. Second, we show that the optimum precision can be achieved by projecting the light reflected or transmitted from the object onto a set of modes with engineered spatial shape. We describe how to construct these modes and demonstrate explicitly that the precision of the estimation using these measurements is optimum. As an example, we apply these results to the estimation of the height and sidewall angle of a cliff-like nanostructure, an object relevant in the semiconductor industry for the evaluation of nanofabrication techniques.

We exploit quantum correlations to enhance quantitative phase retrieval of an object in a non-interferometric setting, only measuring the propagated intensity pattern after interaction with the object.

Achieving high degree of tunability in photonic devices has been a focal point in the field of integrated photonics for several decades, enabling a wide range of applications from telecommunication and biochemical sensing to fundamental quantum photonic experiments. We introduce a novel technique to engineer the thermal response of photonic devices resulting in large and deterministic wavelength shifts across various photonic platforms, such as amorphous Silicon Carbide (a-SiC), Silicon Nitride (SiN) and Silicon-On-Insulator (SOI). In this paper, we demonstrate bi-directional thermal tuning of photonic devices fabricated on a single chip. Our method can be used to design high-sensitivity photonic temperature sensors, low-power Mach-Zehnder interferometers and more complex photonics circuits.