Inverse optical scatterometry using sketch-guided deep learning.

Optical scatterometry, also referred to as optical critical dimension (OCD) metrology, is a widely used technique for characterizing nanostructures in semiconductor industry. As a model-based optical metrology, the measurement in optical scatterometry is not straightforward but involves solving a complicated inverse problem. So far, the methods for solving the inverse scattering problem, whether traditional or deep-learning-based, necessitate a predefined geometric model, but they are also constrained by this model with poor applicability. Here, we demonstrate a sketch-guided neural network (SGNN) for nanostructure reconstruction in optical scatterometry. By learning from training data based on the designed generic profile model, the neural network acquires not only scattering knowledge but also sketching techniques, that allows it to draw the profiles corresponding to the input optical signature, regardless of whether the sample structure is the same as the generic profile model or not. The accuracy and strong generalizability of proposed approach is validated by using a series of one-dimensional gratings. Experiments have also demonstrated that it is comparable to nonlinear regression methods and outperforms traditional deep learning methods. To our best knowledge, this is the first time that the concept of sketching has been introduced into deep learning for solving the inverse scattering problem. We believe that our method will provide a novel solution for semiconductor metrology, enabling fast and accurate reconstruction of nanostructures.

Frequency properties of channeled spectropolarimetry: an information theory perspective.

Channeled spectropolarimetry (CSP) has emerged as a notable technique due to its unique capacity to instantaneously measure either the polarization state of light or the Mueller matrix of a sample over a broad spectral range. Leveraging the quasi-linear relation between phase retardances of thick birefringent retarders and wavenumber, the target signal undergoes wavelength encoding. For the first time, we present a theoretical framework for the general CSP from a perspective of information theory. This framework comprehensively addresses the frequency properties of CSP, encompassing signal bandwidth, modulation frequency, sampling relationships, and filter window width during the demodulation process. Drawing from the frequency properties of CSP, we establish a theoretical foundation that informs the design of versatile CSPs and evaluates their measurement capabilities. Simulations for both Stokes CSP and Mueller CSP validate the efficacy of the proposed approach.

X-ray-based overlay metrology using reciprocal space slicing analysis.

Overlay serves as the pivotal performance indicator for lithography tools, and its prompt and precise measurement significantly underpins the process yield control. At present, diffraction-based overlay metrology employing optical wavelengths encounters constraints in terms of measurement sensitivity. When transitioning to x-ray wavelengths, the critical-dimension small-angle x-ray scattering (CDSAXS) method for nanostructure characterization necessitates reciprocal space mapping (RSM) and inverse problem solving, resulting in substantial throughput constraints. In this work, we propose an x-ray-based overlay metrology using reciprocal space slicing analysis (RSS), yielding high-precision overlay measurement at one single angle of incidence (AOI). Moreover, we examine the robustness of the proposed method against errors stemming from overlay target grating fabrication and measurement processes, substantiating its efficacy as a novel x-ray-based overlay metrology and unveiling the potential application of x-ray-based techniques within the realm of integrated circuit metrology.

Multi-spectral snapshot diffraction-based overlay metrology.

Diffraction-based overlay (DBO) metrology has been successfully introduced to deal with the tighter overlay control in modern semiconductor manufacturing. Moreover, DBO metrology typically needs to be performed at multiple wavelengths to achieve accurate and robust measurement in the presence of overlay target deformations. In this Letter, we outline a proposal for multi-spectral DBO metrology based on the linear relation between the overlay errors and the combinations of off-diagonal-block Mueller matrix elements ΔM = Mij - ( - 1)jMji (i = 1, 2; j = 3, 4) associated with the zeroth-order diffraction of overlay target gratings. We propose an approach that can realize snapshot and direct measurement of ΔM over a broad spectral range without any rotating or active polarization component. The simulation results demonstrate the capability of the proposed method for multi-spectral overlay metrology in a single shot.

Application value of CT-guided localization using a coil in combination with medical adhesive in sublobar resection.

PURPOSE: To explore the application value of CT-guided localization using a coil in combination with medical adhesive in sublobar resection. METHODS: The clinical data of 90 patients who had small pulmonary nodules and received thoracoscopic sublobar resection during the period from September 2021 to October 2022 in the Department of Thoracic Surgery, Juxian People's Hospital, Shandong Province, were retrospectively analyzed. RESULTS: The diameters of 95 pulmonary nodules in the 90 patients in the whole group ranged from 0.40 to 1.24 cm, and their distances from the visceral pleura ranged from 0.51 to 2.15 cm. In these patients, percutaneous lung puncture was successfully performed under local anesthesia, through which coils were implanted in the nodules and medical adhesive was injected around the nodules, with a success rate of localization of 100%. Localization complications included 10 cases of asymptomatic pneumothorax, 9 cases of intrapulmonary hemorrhage, 5 cases of severe pain, and 1 case of pleural reaction, all of which required no special treatment. After preoperative localization, the success rate of resection of pulmonary nodules was 100%, and sufficient surgical margins were obtained. CONCLUSION: CT-guided localization using a coil in combination with medical adhesive is a safe, effective, and simple localization method that can meet the requirements of thoracic surgeons for intraoperative localization; for small pulmonary nodules, especially those small-sized and deep-located ground-glass nodules containing few solid mass, this method has important clinical application value, which is a preoperative localization technique worthy of wide application in clinical practice.

Monitoring sidewall tilting of pixelated nanogratings in 3D display.

Sidewall tilting is an important parameter to describe the grating morphology and would affect the diffraction efficiency of three-dimensional (3D) display devices based on pixelated nanogratings. However, there is currently a lack of a non-destructive measurement method that can accurately measure the sidewall tilting of the pixelated nanogratings. This is mainly because the kind of nanograting is manufactured in a micron-scale pixel region and the grating lines generally have various directions to ensure that the display device can display images smoothly. In this work, we propose to use a home-made imaging Mueller matrix ellipsometer (IMME) to monitor sidewall tilting of pixelated nanogratings. Simulation and experiments were carried out to characterize the sidewall tilting angle. Through the combination of Mueller matrix elements, we can quickly and qualitatively identify the tilting angle for the purpose of on-line quality monitoring of the device. Through the inverse calculation of the Mueller matrix, we can accurately and quantitatively obtain the value of the tilting, so as to meet the demands of the device design. It is expected the proposed method can provide guidance for the identification and detection of tilting in 3D display elements based on pixelated gratings.

Characterization of pixelated nanogratings in 3D holographic display by an imaging Mueller matrix ellipsometry.

The diffraction grating, as an element that can control the direction of the emitted light, is the key component used in holographic sampling three-dimensional (3D) displays. The structural accuracy of nanogratings greatly affects the precision of light modulation, thus influencing the cross talk and resolution in 3D displays. It is of great significance for the nondestructive measurement of nanogratings. However, existing measurement methods have certain limitations such as destructiveness and low measurement efficiency in the face of measuring such pixelated nanogratings. In this work, aimed at the measurement requirements and challenges of pixelated nanogratings in 3D displays, we propose to use a self-designed imaging Mueller matrix ellipsometer (IMME) for grating characterization. A sample containing 6 periods and 10 orientations of pixelated gratings is investigated to verify the effectiveness of the method used. Through the measurement and fitting data, the measurement data obtained by using the IMME can be well matched with the theoretical results. At the same time, the extraction results of the structural parameters, periods, and orientations are also consistent with the measurement results from scanning electron microscopy. It is expected that the IMME will provide a guarantee for the accurate display of 3D holography.

Superachromatic polarization modulator for stable and complete polarization measurement over an ultra-wide spectral range.

The polarization measurement system deals with polarized light-matter interactions, and has been a kind of powerful optical metrology applied in wide fields of physics and material. In this paper, we address several general theoretical aspects related to the system model and optimization for linear polarization systems from a view of the matrix algebra. Based on these theories, we propose a new framework of superachromatic polarization modulator (PM) by combining a linear polarizer and a sequence of parallel linear retarders (LRs) for a typical kind of linear polarization system based on the rotating compensator (RC) principle. In the proposed PM, the LRs are made of quarter-wave plates and as a whole act as the RC. Compared with conventional achromatic/superachromatic composite waveplates, the LR sequence has general axis orientations and is optimized by the condition number of the instrument matrix of the PM, which thereby provide much more flexibility to achieve uniform, stable and complete polarization modulation over ultra-wide spectral range. The intrinsic mechanisms, including the working principle, optimization strategy and in-situ calibration method of the proposed PM, are presented and revealed mathematically by the matrix algebra. Results on several prototypes of the PM demonstrate the validity and capability of the proposed methods for applications in broadband polarization measurement systems. The fabricated PM is further applied to a home-made dual RC Mueller matrix ellipsometer, and the accuracy and precision in the full Mueller matrix measurement are better than 2‰ and 0.6‰ respectively over the ultra-wide spectral range of 200∼1000 nm. Compared with existing techniques, the proposed PM has advantages due to superachromatic performances over ultra-wide spectral ranges, stable and complete modulation of the polarized light, and convenience for adjustment and calibration.

Reconstruction of finite deep sub-wavelength nanostructures by Mueller-matrix scattered-field microscopy.

Computational super-resolution is a novel approach to break the diffraction limit. The Mueller matrix, which contains full-polarization information about the morphology and structure of a sample, can add super-resolution information and be a promising way to further enhance the resolution. Here we proposed a new approach called Mueller-matrix scattered-field microscopy (MSM) that relies on a computational reconstruction strategy to quantitatively determine the geometrical parameters of finite deep sub-wavelength nanostructures. The MSM adopts a high numerical-aperture objective lens to collect a broad range of spatial frequencies of the scattered field of a sample in terms of Mueller-matrix images. A rigorous forward scattering model is established for MSM, which takes into account the vectorial nature of the scattered field when passing through the imaging system and the effect of defocus in the measurement process. The experimental results performed on a series of isolated Si lines have demonstrated that MSM can resolve a feature size of λ/16 with a sub-7 nm accuracy. The MSM is fast and has a great measurement accuracy for nanostructures, which is expected to have a great potential application for future nanotechnology and nanoelectronics manufacturing.

Imaging Mueller matrix ellipsometry with sub-micron resolution based on back focal plane scanning.

The development of nanotechnology and nanomaterials has put forward higher requirements and challenges for precision measurement or nanometer measurement technology. In order to cope with this situation, a new type of imaging Mueller matrix ellipsometer (IMME) has been developed. A back focal plane scanning method is designed to make the IMME have the ability to measure multiple incident angles. A two-step calibration method is proposed to ensure the measurement accuracy of IMME. After calibration, the IMME can achieve measurement with wavelengths from 410 nm to 700 nm and incident angles from 0° to 65°. The lateral resolution of the IMME is demonstrated to be 0.8 µm over the entire measurement wavelength range. In addition, a Hadamard imaging mode is proposed to significantly improve the imaging contrast compared with the Mueller matrix imaging mode. Subsequently, the IMME is applied for the measurement of isotropic and anisotropic samples. Experimental results have demonstrated that the proposed IMME has the ability to characterize materials with complex features of lateral micron-distribution, vertical nano-thickness, optical anisotropy, etc., by virtue of its advantages of high lateral resolution and high precision ellipsometric measurement.

Unsupervised learning polarimetric underwater image recovery under nonuniform optical fields.

Turbid media will lead to a sharp decline in image quality. Polarization imaging is an effective method to obtain clear images in turbid media. In this paper, we propose an improved method that combines unsupervised learning and polarization imaging theory, which can be applied in a variety of nonuniform optical fields. We treat the background light as a spatially variable parameter, so we designed an end-to-end unsupervised generative network to inpaint the background light, which produces an adversarial loss with the discriminative network to improve the performance. And we use the angle of polarization to estimate the polarization parameters. The experimental results have demonstrated the effectiveness and generalization ability of our method. Compared with other works, our method shows a better real-time performance and has a lower cost in preparing the training dataset.

Eigenvalue calibration method for dual rotating-compensator Mueller matrix polarimetry.

Dual rotating-compensator Mueller matrix polarimetry (DRC-MMP) has achieved wide spread applications in material characterization, nano-scale measurement, and biomedical diagnostics. However, the traditional calibration method for DRC-MMP relies on establishing an accurate system model, making its implementation cumbersome, especially in the presence of polarizing components that are to complex to be modeled. We propose a novel, to the best of our knowledge, eigenvalue calibration method for DRC-MMP without system modeling. Two specific basis vectors are introduced in order to transform the continuously modulated light intensity in DRC-MMP into a 5×5 projection matrix. Eigenvalue analysis is then performed based on the light intensity projection matrix to obtain the modulation matrix and the analysis matrix associated with the polarization state generator and the polarization state analyzer, respectively. The method is applied for DRC-MMP in both single-pass and double-pass setups. The experimental results have verified the proposed calibration method.

Multi-objective collaborative optimization strategy for efficiency and chromaticity of stratified OLEDs based on an optical simulation method and sensitivity analysis.

The low efficiency and dissatisfactory chromaticity remain as important challenges on the road to the OLED commercialization. In this paper, we propose a multi-objective collaborative optimization strategy to simultaneously improve the efficiency and ameliorate the chromaticity of the stratified OLED devices. Based on the formulations derived for the current efficiency and the chromaticity Commission International de L'Eclairage (CIE) of OLEDs, an optical sensitivity model is presented to quantitatively analyze the influence of the layer thickness on the current efficiency and the CIE. Subsequently, an evaluation function is defined to effectively balance the current efficiency as well as the CIE, and a collaborative optimization strategy is further proposed to simultaneously improve both of them. Simulations are comprehensively performed on a typical top-emitting blue OLED to demonstrate the necessity and the effectivity of the proposed strategy. The influences of the layer thickness incorporated in the blue OLED are ranked based on the sensitivity analysis method, and by optimizing the relative sensitive layer thicknesses in the optical views, a 16% improvement can be achieved for the current efficiency of the OLED with desired CIE meantime. Hence, the proposed multi-objective collaborative optimization strategy can be well applied to design high-performance OLED devices by improving the efficiency without chromaticity quality degradation.

Fast reconstruction of the aberrated scanning lithographic image by a quadratic imaging model and an integral transfer function.

Since the pupil function is defined as a time-invariant system, the traditional partially coherent imaging model is time-consuming to calculate the effect of spatially varying wavefront aberrations on the scanning image. A fast reconstruction method of the aberrated scanning aerial image is presented for the scanning projection lithographic tool. In the proposed method, the principal components (PCs) are used to decompose and reconstruct the aberrated aerial image. Due to the exact quadratic relationship between the PC coefficients and the Zernike coefficients, the integration of the PCs in the intensity domain can be transformed into the integration of quadratic Zernike vectors when reconstructing the scanning aerial image. An integral transfer function is introduced to describe this process. This method can not only reconstruct the aberrated scanning image quickly but can also obtain the explicit relationship between the Zernike coefficients and the aberrated scanning aerial image.

High-speed Mueller matrix ellipsometer with microsecond temporal resolution.

A high-speed Mueller matrix ellipsometer (MME) based on photoelastic modulator (PEM) polarization modulation and division-of-amplitude polarization demodulation has been developed, with which a temporal resolution of 11 µs has been achieved for a Mueller matrix measurement. To ensure the accuracy and stability, a novel approach combining a fast Fourier transform algorithm and Bessel function expansion is proposed for the in-situ calibration of PEM. With the proposed calibration method, the peak retardance and static retardance of the PEM can be calibrated with high accuracy and sensitivity over an ultra large retardance variation range. Both static and dynamic measurement experiments have been carried out to show the high accuracy and stability of the developed MME, which can be expected to pave the way for in-situ and real-time monitoring for rapid reaction processes.

On the limits of low-numerical-aperture imaging scatterometry.

Although imaging scatterometry has been demonstrated to be a powerful technique for characterization of nano-gratings when high lateral resolution is required, some limits of this novel technique are still undisclosed yet, such as the constraint for the imaging numerical aperture (NA), the number of unit cells for accurate grating reconstruction, and the analyzability of image pixels associated with the grating region. To this end, we establish a vectorial image formation (VIF) model for imaging scatterometry based on the finite-difference time-domain (FDTD) method and vectorial diffraction theory. According to the established VIF model and the simulation results of a Si grating sample with finite numbers of unit cells, we find that accurate grating reconstruction by routine RCWA (rigorous coupled-wave analysis) -based data analysis requires an upper limit for the NA of the employed objective. And enough numbers of unit cells are also required to be covered in the illumination spot. Only in these conditions, the zeroth-order diffraction information of the grating under test can be exclusively and completely collected by the imaging system. Moreover, only the image pixels off the edge of the grating region are analyzable by routine RCWA-based data analysis due to the effect of edge scattering. The required number of grating unit cells and the size of the analyzable region are closely related with the imaging NA and the ratio between the illumination spot size and the size of the grating region D/L. Higher imaging NA or smaller D/L typically requires fewer grating unit cells and meanwhile allows a larger analyzable region. The investigation in this paper promises to provide valuable insights into the application of imaging scatterometry.

Multiobjective optimization for target design in diffraction-based overlay metrology.

Overlay target design is an important issue in overlay metrology, whose aim is to probe the optimal overlay target to achieve good performance on measurement precision and accuracy even in the presence of process variation. In this paper, the target design problem is first formulated as a multiobjective optimization problem and then solved by the multiobjective genetic algorithm. The feasibility of the proposed method is verified based on simulations carried out on two overlay targets. The results reveal that measurements with high precision, accuracy, and process robustness could be achieved on the targets designed by the proposed method.

Nonuniform depolarization properties of typical nanostructures and potential applications.

Nonuniform depolarization properties of ${\text{SiO}_2}$SiO2 thin film, two-dimensional (2D) Si grating, and three-dimensional Si cylinder grating, were systematically investigated by Lu-Chipman decomposition. We find that introducing surface profiles with dimensions comparable to the detecting wavelengths can lead to obvious nonuniform depolarization, and control of the sample azimuth can manipulate the uniformity of the depolarizer components. The results indicate that the 2D nanostructure shows obvious nonuniform depolarization at 0° and 90° azimuths, while almost uniform depolarization at 45° azimuth. These discovered phenomena may give rise to some potential applications, such as the detection of the existence of nanostructures without a priori information about the sample, and the design of a uniform or nonuniform depolarizer.

Attitude metrology based on the field-of-view effect of birefringence using high-speed polarimetry.

A novel, to the best of our knowledge, optical method using a high-speed polarimetry is proposed for real-time attitude tracking in an ultra-large measurement range. The attitude metrology utilizes the field-of-view effect in birefringent crystals, which is known as the birefringence deviates with the field-of-view angle of polarized light. The basic principle of the metrology is presented via theoretical derivation and has been verified in the static retardance measurement experiments. With a resolution test, a temporal resolution of 0.4 ms per attitude measurement and an angular resolution up to 0.0025°are achieved. With the help of a bubble level, the attitude angles of an object attached with a birefringent wave plate are obtained in the dynamic experiments, which have achieved an accuracy better than 0.02°. Additionally, the angular velocity and acceleration of the real-time measured roll angle can be extracted simultaneously. The experimental results demonstrate that the proposed metrology has great potential and advantages in the real-time attitude sensing.

Performance optimization of tandem organic solar cells at varying incident angles based on optical analysis method.

Tandem organic solar cells (OSCs) show great potential due to advantages such as the utilization of wide-spectrum light and low thermalization loss. The current mismatch between sub-cells is one of the major issues reducing the final output efficiency of a tandem device. In this paper, we focus on the current mismatch of tandem OSCs at oblique incidence and aim to reduce its adverse effect on the performances of realistic devices working at varying incident angle. Firstly, we propose an optical analysis method based on the 4×4 matrix formalism to analyze and optimize the performance of tandem solar cells at arbitrary incident angles. Compared with those optimal designs via matching the currents of sub-cells only at normal incidence, the proposed method chooses the optimal structure of the tandem device by maximizing the generated energy density per day with considering the current match at different incident angles during daytime. With the proposed method, a typical tandem organic solar cell is optimized as an example, and the optimized tandem device has a balanced current match at all incident angles during a whole day. Experimental results demonstrate that the generated energy density per day of the optimized tandem device has increased by 4.9% compared to the conventional device optimized only at normal incidence. The proposed method and results are expected to provide some new insights for the performance analysis and optimization of tandem or multi-junction solar cells, especially those devices exhibiting serious current mismatch between sub-cells at varying incident angles in practical applications.