This PDF file contains the front matter associated with SPIE Proceedings Volume 12619, including the Title Page, Copyright information, Table of Contents, and Conference Committee information

The coherence function offers new possibilities for optical metrology not available with conventional wave field sensing. Its measurement involves spatio-temporal sampling of wave fields modulated by the object under investigation. While the evaluation of the coherence function is more elaborate than conventional approaches, an information theoretical treatment shows that it also delivers more information about the object under investigation. In order to achieve efficient information extraction from the coherence function, advanced approaches involving compressed sensing are required to obtain optical metrology techniques that are simultaneously precise, robust and fast as well as suited for complex measurement situations.

Local defects and non-uniformities in optoelectronic materials and devices can have an impact on their quality and performance characteristics. The development of non-destructive optical metrology methods that provide spatially resolved information on defects and inhomogeneities is crucial for multiple industries that rely on high quality semiconductor materials and devices, from power electronics and LEDs to solar cells and photodiodes. Traditional point-by-point scanning approaches for microscopy and spectroscopy offer mapping solutions that can produce invaluable datasets, nevertheless in most cases measurements are time-consuming, require complex measurement setups or give very weak signals. In this work we present how a compressed sensing approach can benefit optical metrology techniques and the principles of how to adopt and implement a compressed sensing optical system in practice for semiconductor metrology. As examples, we demonstrate through a simulation process a proposed compressed sensing spectral photoluminescence measurement methodology for characterization of semiconductor materials and devices. The focus in this work is specifically wide bandgap semiconductor materials. The features, advantages and challenges of this compressed sensing optical measurement approach are discussed, including the minimum noise levels required for experimental implementation. Different approaches for reconstruction of the spectral PL datacubes are presented.

Continued improvement of production-scalable characterisation methods is necessary to support the growth of semiconductor industries. In this work we present the application of compressed sensing for photoluminescence imaging in the temporal and spectral domains. The application can be enabled by using a digital micromirror device to programmatically control the spatial information of the excitation or detection source, allowing the use of single-point detectors for imaging applications, with benefits in terms of reduced measurement time and dark noise. We present the methodology for successful compressed sensing acquisition and reconstruction of spectral and temporal photoluminescence signals, developed through computational modelling work.

All indirect optical metrology techniques, such as spectroscopic ellipsometry, reflectometry or scatterometry, for characterization of surfaces, thin films and complex 2D/3D multilayer structures require an appropriate modeling. Parametric sensitivity analysis (SA) is as an essential prerequisite step in optical metrology data modeling to quantify the relative importance of optical model parameters and to identify those with little influence in order to simplify a model. In our previous studies, we have detailed the use of the Morris or Elementary Effect (EE) method, a screening type SA procedure, applied it to the spectroscopic ellipsometry data processing and investigated different types of its convergence. The present study is a continuation of these investigations, extending the application of the EE method for ellipsometric modeling. The method is a global SA technique and uses a stepping of m parameters along certain so-called “trajectories”, or sequences of points in parameter space, randomly constructed in order to maximally fill the volume of the m-dimensional parameter space. However, it is reputed that the EE method relies heavily on a sampling strategy, or a way of selecting “optimized trajectories” in parameter space, i.e., the selection of a necessary number of trajectories chosen to be well spread over the space to properly cover the entire realistic ranges of all input factors. Here, we test some sampling methods for selecting trajectories with possibly different distributions and investigate their effects on the estimation of various sensitivity measures in spectroscopic ellipsometry data modeling. The results indicate that the performance of the sampling strategy should not be judged only by maximization of the trajectory spread but also by certain convergence criteria for the sensitivity index μ*.

Mueller ellipsometry is one of the most sensitive techniques for accurate measurements of sub-wavelength structures and is an attractive upgrade compared to simple intensity-based scatterometry. In Non-normalized Mueller ellipsometry, all 16 elements of the Mueller matrix are measured. However, most Mueller matrix ellipsometers provide data which are normalized to the first Mueller matrix. In this work, we demonstrate that knowledge about the first Mueller matrix element, which can be acquired from a scatterometry measurement, greatly enhances the measurement accuracy. We demonstrate the advantage of Non-normalized Mueller ellipsometry over normalized Mueller ellipsometry by comparing the results obtained by the the two methods on a set of silicon line gratings with a pitch of 589 nm. The experimental data was acquired at fixed angle of incidence of 70 degrees using wavelengths from 200 to 850 nm. The data analysis involves inverse problem solving, which requires an optical model describing the system. Here we use the Rigorous Coupled Wave Analysis (RCWA) method to simulate the optical response from the grating structures. The combination of Non-normalized Mueller ellipsometry with advanced inverse modelling from rigorous simulations of the optical model structure enables high accuracy measurements of nanostructures. Notably, this approach allows for accurate measurements of grating structures in which the slimness or shape of the grooves make them inadequate for AFM measurements.

Model-based optical scatterometry is a widely utilized non-destructive measuring technique in semiconductor manufacturing for retrieving features on wafers. It offers an attractive solution for quality control and process monitoring. However, the increasing complexity of 3D nanoscale device structures presents significant challenges for optical scatterometry. To address these challenges, it is crucial to integrate different methods and create a hybrid metrology approach that could encompass measurements, modeling, and data analysis techniques. To tackle this objective, we explore in this study two alternative approaches for parameter reconstruction, distinct from the conventional library search method. The first approach utilizes a neural network based on a Resnet architecture, while the second approach employs the Levenberg-Marquardt algorithm, a nonlinear least square fitting technique. By performing a comparative analysis of the two methods, we propose a strategy to combine them for accurate and efficient parameter reconstructions.

Optical metrology faces significant challenges as functional devices continue to shrink in size due to new patterning processes for semiconductor chips. Consequently, there is a growing interest in modeling optical systems to achieve more accurate measurements and to compare measurements from different optical instruments, such as confocal microscopes, white light interference microscopes, and focus-varied microscopes. Previous models have employed either a thin layer approximation or 2D periodic structures to simulate light scattering. However, to accurately simulate more complex structures and compare them with experimental data, there is a need for a physically accurate modeling and simulation tool that can handle large-scale aperiodic 3D surfaces. To address this need, we have developed a simulation tool called SpeckleSim, which utilizes the boundary element method. By incorporating a multi-level fast multiple method, we are able to calculate light scattering from 3D nanostructures within a reasonable timeframe. In this report, we adapt the method to a confocal microscopy model and investigate the extent to which it can reproduce surface profiles for different types of structures. The obtained results will be compared with experimental measurements and the results from other rigorous simulation tools such as rigorous coupled wave analysis (RCWA) method.

Imaging coordinate measuring machines (CMMs) are widely used because of their ability to perform non-contact and high-precision coordinate measurement. Imaging CMMs measures not only the coordinate values but also forms of complex structures. However, the accuracy evaluation of the complex form measurement is not sufficient. ISO10360-7[1] defines the method for evaluating the accuracy of imaging CMMs. In this ISO, the length measurement errors are to be evaluated using a calibrated line scale, and the probing errors are to be evaluated using a calibrated roundness standard. The evaluation of probing errors is important for the accuracy evaluation of complex form measurement. Therefore, we started development of a calibration system for the photomask test circles, which serves as reference roundness standards for imaging CMMs. We constructed a rotary-table-based roundness measuring system. This system consists of an optical microscope and a high-precision rotary table, which equipped with a self-calibrating rotary encoder (SelfA) developed at NMIJ, instead of orthogonal linear stage, to eliminate the influence of geometric errors. To evaluate the validity of the developed method, the roundness of a circular mask with a nominal diameter of 0.22 mm was measured using a multistep method. As a result, a measurement result of 39 nm was obtained with respect to a reference value of 0.02 μm.

The detection of gravitational waves requires a strain sensitivity at unprecedented precision. The planned space observatory LISA overcomes this extreme challenge by heterodyne laser interferometry at picometer-precision based on the exploitation of carrier phase measurements between spacecraft separated by millions of kilometers. In addition, data transmission and absolute ranging, necessary to mitigate effects of laser frequency fluctuations in post-processing, are achieved with direct-sequence spread spectrum signals. The foreseen receivers shall typically operate in a sequential phase-locked loop and delay-locked loop configuration for consecutive phase and distance measurement. Recent analysis observed code tracking delay variations, identified as ranging bias variations, as a result of this sequential arrangement. Hereafter, we present an analytical analysis of these ranging bias variations. Comparisons to numerical simulations reveal the compelling influence of the cross-correlation of the chip sequences on the ranging bias variations for a fixed modulation scheme and thus affirm the necessity of numerical analysis. In addition, a generic model for the quantisation error of a digital delay-locked loop is introduced that may be used for analysis and design of digital code tracking loops in various applications. Finally, comparison to a numerical simulation reveals that at small ranging bias variations, the code tracking error is fully described by the quantisation error, while at high ranging bias variations, this effect is negligible and the code tracking error is dominated by ranging bias variations.

The high-accuracy phase description of the coherent light propagation is important to assess and optimize far-field and astigmatic optical systems, such as interferometric surface test, etc. Usually, the wavefront propagation is simulated by the physical optics theory throughout each optical element, which might be time-consuming and incur computational complexity. In this article, we analyze the wavefront degeneration in the CGH interferometric null test by the complex ray tracing. We sample the wavefront by a series of elliptical Gaussian beamlets, which is consistent with the Eula formula in the differential geometry. The propagation of elliptical Gaussian beamlets through the optical system can be calculated by the tiny ray bundle theory and geometric optics. In the output space, the wavefront can be described by an elliptical Gaussian beam originated from the propagated Gaussian waist through the system. Therefore, the phase distribution at the output space can be characterized by the sum of series of elliptical Gaussian beams, which gives a high-accuracy analytical simulation of phase distribution better than 30mrad with time about 0.2s. As an example, we apply our method to the analysis of the wavefront degeneration in the interferometric null test of a ⌀3m aspheric mirror. After the optimization, the instrumental transfer function increased from 0 to 0.65 at 0.4 Nyquist frequency.

Digital photoelasticity is a non-contact inspection technique, that requires new strategies to unwrap the stresses map based on color images. Therefore, this paper presents a new three-wavelength chromatic-corrected hybrid phase-shift method for single-camera digital photoelasticity applications. For the experiments, the intensities of isochromatic images are simulated considering a birefringent sample compressed and a circular polariscope configured to produce a bright field image that avoids the effects caused by isoclinics. To increase the range of the fringe order, three LEDs with peaks of close wavelengths were used. Additionality, for each LED a RGB color image is simulated. The red channel of each image is used to generate a new synthetic chromatic-corrected image (CCI) thereby: the red channel of λ3 is the red channel of the new CCI, and the green and blue channels of the CCI use the respective red channels of λ2 and λ1; additionally, the wavelengths must satisfy the following condition (λ3 > λ2 < λ1). An inverted image of the CCI is computed. Thus, with the CCI and its inverted image, six images are stored, and with these images and some trigonometric relations proposed by Ekman and Nurse a wrapped phase map is extracted. Finally, an unwrapping algorithm is applied to reconstruct the stresses map. The results show that the method improves the detected maximum order and reduces stress map distortions compared to similar color phase shifting approaches. Furthermore, since the algorithm requires only a camera and a circular polariscope setup, it can be implemented in dynamic experimental applications.

Elastic lenses have been used in various optical systems, such as cameras, microscopes and vision systems, to name a few. A recently reported technique consists of making the lens's optical design, subsequently manufacturing an aluminum mold with the optical parameters of the design obtained, and finally injecting the polymer mixture into it to generate the lens. Where the lens surfaces take the shape of the mold surfaces, it is necessary to verify the finish of the mold surfaces so that the manufactured lenses meet the design requirements. In this work, the null screen technique is presented to evaluate the finish of these surfaces. An analysis of the results obtained and their conclusions is offered.

Devices with a pair of rotational Risley prisms are one of the most common and fastest 2D laser scanners. The present work builds on the novel, graphical method we have developed [Proc. of the Romanian Acad. Series A 19, 2018; Applied Sciences 11, 2021; Symmetry 15, 2023] to simulate and study scan patterns of such devices. Our method has the advantage to generate exact patterns, in contrast to approximate methods. Also, it is easy to use, in contrast to analytical methods. This graphical approach allows for fulfilling the aim of this work: to utilize ghost rays (which are usually avoided in optical systems) in order to increase the fill factor (FF) of scan patterns. Thus, secondary scan patterns are produced and studied. A radiometric threshold is set for such patterns – to maintain the emerging flux from the prisms above a certain minimum level. With this condition, three useful secondary ray trajectories can be identified through the system. One of the four possible configurations of this type of scanner is considered in this study. Dimensions and characteristics of the secondary scan patterns are pointed out, in comparison to the “main” scan pattern, generated when pure refraction is considered throughout the prisms. Simulations, as well as experiments are carried out.

Scientific optical 3D modeling requires the possibility to implement highly flexible and customizable mathematical models as well as high computing power. However, established ray tracing software for optical design and modeling purposes often has limitations in terms of access to underlying mathematical models and the possibility of accelerating the mostly CPU-based computation. To address these limitations, we propose the use of NVIDIA’s OptiX Ray Tracing Engine as a highly flexible and high-performing alternative. OptiX offers a highly customizable ray tracing framework with onboard GPU support for parallel computing, as well as access to optimized ray tracing algorithms for accelerated computation. To demonstrate the capabilities of our approach, a realistic focus variation instrument is modeled, describing optical instrument components (light sources, lenses, detector, etc.) as well as the measuring sample surface mathematically or as meshed files. Using this focus variation instrument model, exemplary virtual measurements of arbitrary and standardized sample surfaces are carried out, generating image stacks of more than 100 images and tracing more than 1E9 light rays per image. The performance and accuracy of the simulations are qualitatively evaluated, and virtually generated detector images are compared with images acquired by a respective physical measuring device.

The rigorous coupled-wave analysis (RCWA) is a semi-analytic solver to Maxwell's equation, which is one of the most successful methods for modeling periodic optical structure. The repetitive nature of semiconductors has made RCWA widely applied in the semiconductor metrology industry. However, devices with high aspect ratio units, such as vertical NANDs(V-NANDs), require lengthy computation times, making them difficult to model in practice even with fully parallelized RCWA applications. This is because RCWA involves a time-consuming process of eigendecomposition and matrix inversion for each layer sliced along the vertical axis. In order to circumvent such computations, we propose a neural network based approach: channel-hole approximating network in the electromagnetic aspect (CHANEL). Based on the characteristic that the horizontal cutting plane is topologically consistent along the vertical axis of the channel-hole, CHANEL directly predicts the scattering matrix of each layer from its structural and optical parameters. In the scattering matrix of each layer, we found salient regions for Jones matrix calculation, which enhanced the accuracy of Jones matrix prediction with intensive learning on that area. In this paper, we demonstrate that CHANEL outperforms the traditional CPU-based RCWA implementations in terms of time, performing diffraction simulation more than 10 times faster.

A new non-integral optical scatterometry technique has been introduced to circumvent issues with traditional methods in the critical dimension (CD) characterization of micro and nano-structures in semiconductor inspections. This method uses the high spatial coherence of the laser source, and an adjustable numerical aperture (NA) for effective beam shaping, enabling precise measurement of high-aspect-ratio structures. It incorporates a model-based approach with a virtual optical system and the Finite- Difference Time-Domain (FDTD) method for multiple CD characterizations, improving measurement precision. Early tests indicate a minimal average bias of 1.74% from calibrated references and standard deviations within 7 nm.

Inspecting the structure of the through silicon via (TSV) with high aspect ratio is important because they are used for 3D IC stacking. In reflectometry, simulation of near field data for TSV hole arrays is used to investigate reflection spectrum for TSV with different geometry parameters such as depth and top critical dimension. We investigate simulation results of electromagnetic field data for different TSV array using the finite-difference time-domain (FDTD) method. Near field simulation data are stored as n by n complex matrices, where n represent the number of simulation region grid points. The matrices are large in dimension, and it is necessary to compress a huge data set by looking for the dominant singular value terms to keep the information as much as possible. We find that the singular value terms shrink fast in the first few terms. It is shown that after using singular value decomposition to compress near field data, the far field reflectivity spectrum is still close to the accurate results. We propose to use data after singular value decomposition for data analysis to investigate the TSV parameters mapping to the near field data.

As the semiconductor industry moves forward towards advanced packaging, through silicon vias (TSVs) with a top Critical Dimension (CD) down to 1 μm and aspect ratio 1:15 or higher are being projected. This poses a major challenge to optical metrology as the dimensions of the lattice get close to the wavelength of the visible light. White-light interferometry is commonly used to measure the depth of the vias, but suffers from decreasing signal-to-noise ratio depending on aspect ratio and diameter. To understand the limitations and develop new approaches for sensing these structures, modelling has proved to be a valuable tool. In this paper, we present results from electromagnetic wave propagation analysis compared to experimental interferometry data from high aspect ratio samples. Effects of via shape, spacing and dimension as well as simulation parameters on the resulting spectra are shown. Simulation can thus be used to predict for which type of vias a successful measurement can be expected.

Microsphere and microcylinder-assisted microscopy (MAM) has grown to an intensively studied optical far-field imaging technique over the last decade that overcomes the fundamental lateral resolution limit of a given microscope. However, the physical effects leading to resolution enhancement are still frequently debated. In addition, various configurations of MAMs operating in transmission as well as reflection mode are examined and results generalized. We present a rigorous simulation model of MAM and present a way to quantify the resolution simulatively. The lateral resolution is compared for microscope arrangements in reflection and transmission mode. Further, we discuss different physical effects with respect to their contribution to resolution enhancement. The results indicate that the effects affecting the resolution as well as the enhancement itself strongly depend on the arrangement of the microscope and the measurement object.

We present a numerical computation scheme for calculation of the reflected and transmitted near- and far-fields arising from the interaction of 2D cylindrical shaped particles with photonic structures. The photonic structures are illuminated with either planar or Gaussian incident fields. The interaction between the cylindrical particle and the photonic structure is generally too complex to be handled analytically, so we will use the semi-analytical Fourier Modal Method (FMM) to calculate the near- and far-fields. The Gaussian field is written as a sum of plane waves with varying amplitudes. We present a very general method for obtaining the plane wave amplitudes by combining the angular spectrum theory, Parseval’s theorem and Shannon’s sampling theorem. We demonstrate the use of this method in our rigorous calculation of reflected and transmitted near- and far-fields of single cylindrical particle located in the vicinity of a periodic photonic structure or a planar silicon surface. The examples demonstrate that the method may be applied to particle counting.

In recent years, tomographic phase microscopy has gained credits as one of the most powerful imaging modality for label-free single-cell analysis in 3D. The conventional tomographic imaging systems probe the sample from different directions, experimentally fixed a priori, and the tomographic reconstruction is performed by well-known techniques. The recent demonstration of such technology in flow cytometry condition, in which cells rotate in a microfluidic channel, permits to achieve high-throughput analysis, but it is needed of a reliable and robust computational processing pipeline. In fact, no a priori information about the rotation angles of cells are available, hence suitable algorithms are designed to recover them. Moreover, the number of such rotating angles is low if compared to the number of orientation directions explored in conventional systems, thus requiring more sophisticated algorithm to reconstruct cells tomograms. Finally, due to the high-throughput modality, the huge amount of data to manage becomes one of the main computational problems to face with. Here we show an efficient computational processing pipeline to achieve reliable tomographic reconstructions based on (i) a fast quantitative phase maps recovery method based on deep learning end-to-end reconstruction, (ii) the modelling of the cells’ 3D pose in microfluidic flow through holographic tracking, (iii) the use of a suitable tomographic reconstruction algorithm, (iv) a new strategy to encode single-cell phase contrast tomograms by using the 3D version of Zernike polynomials, thus allowing an efficient data storage.

Performance characteristics for interferometers that measure surface topography include the ability to resolve closely spaced surface features, referred to as topographic spatial resolution. Within well-defined limits, scalar diffraction theory and classical Fourier optics provide a software model for prediction of the resolution and spatial frequency response for interference phase-based measurements of surface topography. Analytical solutions and adaptive sampling allow for rapid simulation of both the nominal linear transfer function and an estimate of intrinsic residual nonlinearities.

Optical surface topography measurements sometimes suffer from systematic errors. In order to predict such deviations, modeling of optical profilers is a substantial part of the European project TracOptic (Traceable Optics). Within the framework of this project, we recently developed the UFO (Universal Fourier Optics) model, which simulates virtual CSI measurements of surface topographies that fulfill the requirements of the scalar Kirchhoff approximation. The model enables a fast computation of ‘measured’ surface topographies as it is based on discrete Fourier transforms. It treats the surface under investigation as a two-dimensional phase object assuming a linear dependence of the interference phase on surface height and axial spatial frequency. The scattered light field is transferred to the Fourier domain and multiplied by a partial two-dimensional transfer function (TF) representing a horizontal cross section of the three-dimensional TF at a certain axial spatial frequency or evaluation wavelength, respectively. The TF includes parameters of the interference microscope and the reference field distribution. Inverse Fourier transform enables the reconstruction of the phase object. The coherence peak position of an interference signal results from numerical differentiation with respect to the axial spatial frequency and is generally used to overcome the 2π ambiguity of the phase profile. Parameters affecting final results of reconstructed surface topographies are the central wavelength and the spectral bandwidth of the illuminating light as well as the numerical aperture of the objective lens and the chosen evaluation wavelength. We discuss results of the UFO model with respect to the prediction of systematic deviations of measured surface topographies.

One important cause for limited traceability in optical metrology is the presence of systematic measurement errors caused by the interaction of the sensor and the measured object. These effects are complex and influenced by many factors, hence, they may differ significantly even among similar measurement systems. This also implies, that it is usually necessary to model the whole measurement chain including the relevant characteristics of the measured surface. We are currently developing a model of a chromatic confocal point sensor dedicated to simulate object-dependent systematic measurement errors and estimating task-specific measurement uncertainties. The simulations already cover all relevant fundamental aspects of the system, some important details are currently being developed. We recently introduced realistic reflection characteristics based on methods originating in physically based rendering. We show how to phenomenologically describe the light-object-interaction using bidirectional reflectance distribution functions and how the principle of Monte Carlo Ray Tracing can be adopted for this use case. We can already show the general influence of surface curvature and slope and can qualitatively predict systematic effects. However, simulations using the current model still show clear deviations from measurement results. While some effects are caused by non-ideal characteristics of the real system, others are likely caused by the approximations within our model. Therefore, further investigations and model developments are pursued.

A reliable tool for simulations of confocal microscopes shall be developed to enable improved model-based dimensional metrology. To simulate measurements on rough surfaces the boundary element method (BEM) simulation tool SpeckleSim, developed by the ITO of the University of Stuttgart, is combined with a Fourier optics based image formation. SpeckleSim, which calculates the light-structure interaction by solving the Maxwell equations, is compared with the well-known FEM based solver JCMsuite and the FDTD based solver Ansys Lumerical. As an example, a rectangular shaped line is used as an object. Due to different boundary conditions the results show as expected small deviations, which require further investigations. First comparison results and the general concept of the image formation method will be presented.

Coherence scanning interferometry (CSI) is a widely used optical method for surface topography measurement of industrial and biomedical surfaces. The operation of CSI can be modelled using approximate physics-based approaches with minimal computational effort. A critical aspect of CSI modelling is defining the transfer function for the imaging properties of the instrument in order to predict the interference fringes from which topography information is extracted. Approximate methods, for example, elementary Fourier optics, universal Fourier optics and foil models, use scalar diffraction theory and the imaging properties of the optical system to model CSI surface topography measurement. In this paper, the measured topographies of different surfaces, including various sinusoids, two posts and a step height, calculated using the three example methods are compared. The presented results illustrate the agreement between the three example models.

Laser scanning is employed in a variety of modalities, including the most common raster scanning, as well as spiral, Lissajous, or Risley prism-based (the later a type of rhodonea) scanning. The first two can have the advantage of linearity, while the last two are faster, although they are highly non-linear. The present study performs an exploration of such aspects. Thus, we compare the characteristics of the above-mentioned modalities, with an emphasis on parameters such as field of view (FOV), linearity, resolution, and fill factor (FF). Simulations are carried out regarding different types of scanning patterns, as well as some experimental validations. Also, results from some of our recent studies on galvanometer-, polygon mirror-, and Risley prisms-based scanning are utilized. Some of the specific performances of the considered scanning modalities are discussed, highlighting advantages and drawbacks.

Optical inspection systems allow faster detection of defects on semiconductor wafers than scanning electron microscopy (SEM) inspection systems. However, optical detection becomes more challenging as the structure feature size shrinks below the optical diffraction limit with the advancement of technology nodes in semiconductor manufacturing. To overcome this challenge and achieve optimal performance, the optical system must be tailored to the specific characteristics of the wafer sample which requires knowledge of the underlying microscopic and macroscopic optical phenomena. In this work, we proposed a multiphysics simulation workflow to model the microscopic light interaction with the wafer sample using Ansys Lumerical FDTD and the macroscopic optics of the inspection system using Ansys Zemax OpticStudio. The optimum optical system design with maximum defect signal strength could be achieved through defect image analysis. Together, FDTD and OpticStudio facilitate the design of complex optical inspection systems and reduce the cycle time for creating inspection recipes in the development of advanced technology nodes in semiconductor manufacturing.

Further improving the axial resolution is paramount for three-dimensional optical imaging systems. Vortex beams are being widely applied in 3D microscopy techniques. Here we theoretically investigate the ultimate resolution limits using Laguerre-Gauss (LG) beams. Various kinds of superpositions can nowadays be easily prepared by spatial light modulators (SLM). It has been keenly shown that LG beams’ superpositions possess more information than pure LG beams yet do not saturate the ultimate limit with a simple intensity scan. More sophisticated detection schemes based on quantum super-resolution protocols are investigated here to retrieve the discarded information.

For the development of integrated circuits, the accompanying metrology inside the fabrication process is essential. Non-imaging metrology of nanostructure has to be quick and non-destructive. The multilayers are crucial components of today’s microprocessor nanostructures and reflective coatings. Coherent Fourier scatterometry (CFS), which is currently employed as a method for determining certain parameters of nanostructures and isolated particle detection, has not been investigated in the context of multilayer characterization. Retrieving the thickness of many wavelength-thick films using a coherent visible-range source at a full-complex-field measurement is the specific application where CFS might be advantageous. Furthermore, due to polishing in the realistic multilayers, the anticipated optical performance suffers from stochastic changes relating to surface roughness. Few non-imaging metrology methods take into consideration these statistic variances and thus are of interest for this study. Operating in the visible regime, CFS can become a viable candidate to provide cover layer reconstruction in the presence of surface roughness that has a correlation length bigger than the characteristic spot size i.e., in the range of microns. We present forward model results of multilayer structure as measured with visible range CFS modality. The influence of surface roughness is taken into account and the simulation results are discussed. Simulations of micron-sized layers of dielectric on silicon substrate suggest an influence on the far field intensity that motivates a future extended study on experimental multiple wavelength thick cover layer reconstruction in the presence of roughness.

Nowadays, optical systems commonly use either aspheric or free-form surfaces to improve their performance; however, to ensure that the manufactured surfaces become successful in concordance with to the nominal design, some geometrical parameters such as radius of curvature, conic constant, aspheric coefficients, etc., must be measured, including the surface shape under test. In this work, we propose a simple method to evaluate the optical quality of a plano-convex aspheric lens, where the convex face is modeled as an aspheric or free-form surface. We design a non-uniform pattern on the plane face of the plano-convex lens, to obtain a uniform pattern on a predefined detection plane by using the law of refraction in vector form. Additionally, implementing numerical simulations, we calculate the synthetic images produced through a predefined optical surface that we will use as if they were obtained from an experimental test. Finally, we apply an iterative method to retrieve the shape of the surface by using the normal vector field to demonstrate the feasibility of our proposal.