Linearized EUV mask optimization based on the adjoint method.

Mask optimization, a compensation method for the thick mask effect and the optical proximity effect in projection lithography, is essential for advanced EUV-enabled production nodes. However, owing to high computation costs and the absence of gradient calculations, it is challenging to optimize EUV masks under rigorous consideration of the thick mask effect. In this work, a linearized EUV mask optimization method based on the adjoint method is proposed to provide fast and effective optimizations. The adjoint method is introduced to calculate the gradient of the EUV mask model. Additionally, a linearized gradient is proposed to quickly compensate for wafer pattern distortion caused by the prominent thick mask effect. Two examples of the EUV mask optimization implemented with a two-step strategy were provided, from which it was observed that the linearized gradient can improve the efficiency by about 40% in the coarse optimization step. The proposed method is promising for accurate full-chip EUV mask optimization.

EUV mask model based on modified Born series.

Mask model is a critical part of computational lithography (CL). Owing to the significant 3D mask effects, it is challenging to accurately and efficiently calculate the near field of extreme ultraviolet (EUV) masks with complex patterns. Therefore, a method based on the modified Born series (MBS) was introduced for EUV mask modeling. With comparable accuracy, the MBS method was two orders of magnitude faster than the finite-difference time-domain method for the investigated examples. Furthermore, the time required for MBS was further reduced when the mask pattern was slightly changed. The proposed method shows great potential for constructing an accurate 3D mask model in EUV CL with high efficiency.

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.

Multi-parameter and multi-objective optimization of stratified OLEDs over wide field-of-view considering thickness tolerance.

Poor wide field-of-view (FOV) performances and low production yields are major factors that restrict the application of organic light-emitting diodes (OLEDs) in large-size panels. In this paper, we propose an optimization and analysis method to improve optical performances of stratified OLEDs over wide FOV with consideration of the thickness tolerance in the practical production process. With key optical performance parameters defined using the angle-dependent luminescence spectra, including the external quantum efficiency (EQE), current efficiency (CE), just noticeable color difference (JNCD), and the color coordinates, the optimization of OLEDs over wide FOV is described as a multi-parameter and multi-objective optimization problem which is accomplished by the genetic algorithms (GAs). Further, the thickness tolerance is introduced to improve the structure stability considering thickness fluctuations in the practical production process. Appropriate thickness tolerances can be determined to achieve stable structures for the OLED device by defining and analyzing the distributions of preference regions of the GA output noninferior solutions and the correlation coefficients between the layer thicknesses. Based on the proposed methods, high-throughput simulations are carried out on a typical Green Bottom-emitting OLED (G-BOLED) to design a stable device structure with high-performances. Experimental results demonstrate that compared with the initial device, the performances of the optimized device have been significantly improved, with the CE improved by over 30% in the normal direction, the EQE improved by over 20%, and the JNCD reduced from 4.45 to 1.36 over the whole FOV of 0-60°. In addition, within the thickness fluctuation in the practical process, optimized devices can strictly satisfy the "Best" preferred region, indicating that the structure is more stable against thickness fluctuations in the practical production process. The proposed optimization method can simultaneously improve optical performances over wide FOV and provide a stable structure for stratified OLEDs, and it therefore can be expected to improve the production yields and promote the OLEDs applied to large-size panels.

Strong Second- and Third-Harmonic Generation in 1D Chiral Hybrid Bismuth Halides.

Breaking the symmetry of a crystal structure can enable even-order nonlinear activities, including second-harmonic generation (SHG). The emerging chiral hybrid organic-inorganic metal halides feature unique optical and electronic properties and flexible crystal structures, making them a class of promising nonlinear optical materials. However, their nonlinear response performances are currently inferior to traditional nonlinear crystals, because of the lack of research on resonant enhancement and third-harmonic generation (THG). Herein, we designed chiral hybrid bismuth halides with naturally nonsymmetrical structure to enable SHG. Simultaneously, these chiral compounds preserve 1D crystal structures to create strong free exciton, broad self-trapped exciton (STE), and discrete band energy levels, which facilitate the resonant enhancement of SHG and THG susceptibilities. These new chiral films showcase superior effective SHG susceptibility (χ(2) ∼ 130.5 pm V-1 at an interesting wavelength of 1550 nm), exceeding that of the reference, a commercial LiNbO3 (χ(2) ∼ 83.4 pm V-1) single-crystal film. Furthermore, their THG intensities are even higher than their SHG intensities, with effective THG susceptibility (χ(3)) being ∼9.0 × 106 pm2 V-2 at 1550 nm (37 times that of the reference monolayer WS2). Their high SHG and THG performances indicate the promising future of these 1D chiral hybrid bismuth halides toward nonlinear optical applications.

Birefringence and Dichroism in Quasi-1D Transition Metal Trichalcogenides: Direct Experimental Investigation.

Birefringence and dichroism are very important properties in optical anisotropy. Understanding the intrinsic birefringence and dichroism of a material can provide great help to utilize its optical anisotropy. But the direct experimental investigation of birefringence in nanoscale materials is rarely reported. As typical anisotropic transition metals trichalcogenides (TMTCs) materials with quasi-1D structure, TiS3 and ZrS3 have attracted extensive attention due to their special crystal structure and optical anisotropy characteristics. Here, the optical anisotropy properties such as birefringence and dichroism of two kinds of quasi-1D TMTCs, TiS3 and ZrS3 , are theoretically and experimentally studied. In experimental results, the anisotropic refraction and anisotropic reflection of TiS3 and ZrS3 are studied by polarization-resolved optical microscopy and azimuth-dependent reflectance difference microscopy, respectively. In addition, the birefringence and dichroism of ZrS3 nanoribbon in experiment are directly measured by spectrometric ellipsometry measurements, and a reasonable result is obtained. This work provides the basic optical anisotropy information of TiS3 and ZrS3 . It lays a foundation for the further study of the optical anisotropy of these two materials and provides a feasible method for the study of birefringence and dichroism of other nanomaterials in the future.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Simulation method for study on outcoupling characteristics of stratified anisotropic OLEDs.

We derive explicit power dissipation functions for stratified anisotropic OLEDs based on a radiation model of dipole antennas inside anisotropic microcavity. The dipole field expressed by vector potential is expanded into plane waves whose coefficients are determined by scattering matrix method, and then an explicit expression is derived to calculate the energy flux through arbitrary interfaces. Taking advantage of the formulation, we can easily perform quantitative analysis on outcoupling characteristics of stratified anisotropic OLEDs, including outcoupling efficiency, normalized decay rate and angular emission profile. Simulations are carried out on a prototypic stratified OLED structure to verify the validity and capability of the proposed model. The dependencies of the outcoupling characteristics on various emission feature parameters, including dipole position, dipole orientation, and the intrinsic radiative quantum efficiency, are comprehensively evaluated and discussed. Results demonstrate that the optical anisotropy in different organic layers has nonnegligible influences on the far-field angular emission profile as well as outcoupling efficiency, and thereby highlight the necessity of our method. The proposed model can be expected to guide the optimal design of stratified anisotropic OLED devices, and help to solve the inverse outcoupling problem for determining the emission feature parameters.

Wide field-of-view angle linear retarder with an ultra-flat retardance response.

We propose a universal method for optimal design of a wide field-of-view (FOV) angle linear retarder with an ultra-flat retardance response based on paired positive/negative birefringent plates. The mechanism and rules for the FOV effect compensation are revealed to determine the structure of the proposed retarder by introducing the partial derivative of refractive index with respect to the incident angle. A concrete example based on quartz/sapphire plates is designed and manufactured as a proof-of-concept of the proposed method. The maximum deviation in the retardance of the optimally designed quartz/sapphire wide FOV angle retarder over the concerned FOV angles (incidence: -20°-20°; azimuth: 0°-360°) is only 0.08°, which has been reduced by 3 orders of magnitude compared with the common quartz retarder.

Comprehensive characterization of a general composite waveplate by spectroscopic Mueller matrix polarimetry.

Composite waveplates (CWs) consisting of multiple single waveplates are basic polarization elements and widely used to manipulate the polarized light in optical systems, and their performances affect the final accuracy and precision significantly. This research proposes a method for the comprehensive characterization of an arbitrary CW based on spectroscopic Mueller matrix polarimetry. An analytical model is established to describe a general CW by extending Jones' equivalent theorem with Mueller matrix calculus. In this model, an arbitrary CW is optically equivalent to a cascaded system consisting of a linear retarder with slight diattenuation followed by an optical rotator, and its polarization properties are completely described by four polarization parameters, including the retardance, the fast axis azimuth, the rotation angle, and the diattenuation angle. Analytical relations between the polarization properties, the structure, and the Mueller matrix of the CW are then derived from the established model. By the proposed method, the polarization parameters of an arbitrary CW can be comprehensively characterized over an ultra-wide spectral range via only one measurement. Moreover, the actual structure of the CW, including the thicknesses and fast axis azimuths of the single waveplates, as well as the axis alignment errors, can be completely reconstructed from the polarization spectra. Experiments performed with a house-developed broadband Mueller matrix polarimeter on three typical CWs including a compound zero-order waveplate, an achromatic waveplate and a specially designed biplate have demonstrated the capability of the proposed method.

Robust overlay metrology with differential Mueller matrix calculus.

Overlay control is of vital importance to good device performances in semiconductor manufacturing. In this work, the differential Mueller matrix calculus is introduced to investigate the Mueller matrices of double-patterned gratings with overlay displacements, which helps to reveal six elementary optical properties hidden in the Mueller matrices. We find and demonstrate that, among these six elementary optical properties, the linear birefringence and dichroism, LB' and LD', along the ± 45° axes show a linear response to the overlay displacement and are zero when the overlay displacement is absent at any conical mounting. Although the elements from the two 2 × 2 off-diagonal blocks of the Mueller matrix have a similar property to LB' and LD', as reported in the literature, we demonstrate that it is only valid at a special conical mounting with the plane of incidence parallel to grating lines. The better property of LB' and LD' than the Mueller matrix elements of the off-diagonal blocks in the presence of overlay displacement verifies them to be a more robust indicator for the diffraction-based overlay metrology.