Rigorous Electromagnetic Field Research Articles

Topography reconstruction of high aspect ratio silicon trench array via near-infrared coherence scanning interferometry

Topography measurement of high aspect ratio trench array using coherence scanning interferometry presents significant challenges because the numerical aperture of detection light is constrained by the trenches. Altering the detection light to penetrate the sample like near-infrared light for silicon could overcome this obstacle, but the trench array spreads the detection light. This study introduces a coherence scanning interferometry model based on three-dimensional point spread function and assuming sample is transparent to detection light, which is realized by integrating rigorous numerical electromagnetic field solution to quantify the modulation aberrations of detection light by transparent trench arrays, and theoretical angular spectrum diffraction utilized for far-field interference imaging. This model facilitates a thorough analysis of the aberrations introduced by trench arrays, encompassing comparisons between trench arrays and a single trench, as well as between the symmetric region of the array and the asymmetric region at the edge. Additionally, an investigation into the impact of unified compensation for low-order aberrations on the topography reconstruction is presented, and we find the sample-induced aberration compensation method utilizing a deformable mirror that we previously proposed for a single trench is still effective confronting trench array. Experimental measurements are performed on silicon trench arrays with the aspect ratio of up to 20:1 and the period of approximately 10 µm to validate the effectiveness of our model and measurement methods, thus providing valuable insights for enhancing high aspect ratio manufacturing.

Accurate inverse design for high-efficiency and broadband terahertz devices by co-simulation with genetic algorithms

In this study, we combined MATLAB with the rigorous electromagnetic field simulation software Computer Simulation Technology to perform a co-simulation method for inverse design of high-efficiency and broadband THz metasurface devices. In the proposed design method, genetic algorithm (GA) is embedded to realize automatic and inverse design. Aiming toward the different requirements of high-efficiency and broadband THz metasurface devices, different objective functions are set to optimize the design of different types of THz metasurface devices. Based on the rigorous electromagnetic simulation and genetic algorithm, the proposed design method can realize automatic and inverse design with high reliability, compared to the theoretical model based on catenary e-field theory. This study provides an important guiding role and an efficient method for designing and optimizing required metasurface devices with practical applied value.

Fast diffraction model of lithography mask based on improved pixel-to-pixel generative adversarial network.

Mask three-dimensional (3D) effect is a vital influence factor of imaging performance in the advanced extreme ultraviolet (EUV) lithography system. However, the rigorous 3D mask diffraction model is very time-consuming and brings a great computational burden. This paper develops a fast and accurate method to calculate the mask diffraction near-field (DNF) based on an improved pixel-to-pixel generative adversarial network, where the deformable convolution is introduced for fitting the crosstalk effect between mask feature edges. The long short-term memory model is added to the generator network to fuse and exchange information between the real parts and imaginary parts of DNF matrices. In addition, the simulation accuracy of DNF is enhanced by using the subpixel super-resolution method in the up-sampling step. The calculation accuracy is improved by more than 50% compared to the traditional network, and the calculational efficiency is improved by 128-folds compared to the rigorous electromagnetic field simulation method.

Decomposition-learning-based thick-mask model for partially coherent lithography system.

The simulation of thick-mask diffraction near-field (DNF) is an indispensable process in aerial image calculation of immersion lithography. In practical lithography tools, the partially coherent illumination (PCI) is applied since it can improve the pattern fidelity. Therefore, it is necessary to precisely simulate the DNFs under PCI. In this paper, a learning-based thick-mask model proposed in our previous work is extended from the coherent illumination condition to PCI condition. The training library of DNF under oblique illumination is established based on the rigorous electromagnetic field (EMF) simulator. The simulation accuracy of the proposed model is also analyzed based on the mask patterns with different critical dimensions (CD). The proposed thick-mask model is shown to obtain high-precise DNF simulation results under PCI, and thus is suitable for 14 nm or larger technology nodes. Meanwhile, the computational efficiency of the proposed model is improved up to two orders of magnitude compared to the EMF simulator.

Light transport through a magneto-optical medium: simple theory revealing fruitful phenomena.

Electromagnetic wave transmission in a magneto-optical (MO) medium is a basic and old topic but has raised new interest in recent years, because MO medium plays a vital role in optical isolator, topological optics, electromagnetic field regulation, microwave engineering, and many other technological applications. Here, we describe several fascinating physical images and classical physical variables in MO medium by using a simple and rigorous electromagnetic field solution approach. We can easily obtain explicit formulations for all relevant physical quantities, such as the electromagnetic field distribution, energy flux, reflection/transmission phase, reflection/transmission coefficients, and Goos-Hänchen (GH) shift in MO medium. This theory can help to deepen and broaden our physical understanding of basic electromagnetics, optics, and electrodynamics in application to gyromagnetic and MO homogeneous medium and microstructures, and might help to disclose and develop new ways and routes to high technologies in optics and microwave.

Accurate prediction of EUV lithographic images and 3D mask effects using generative networks

Background: As extreme ultraviolet lithography (EUV) lithography has progressed toward feature dimensions smaller than the wavelength, electromagnetic field (EMF) solvers have become indispensable for EUV simulations. Although numerous approximations such as the Kirchhoff method and compact mask models exist, computationally heavy EMF simulations have been largely the sole viable method of accurately representing the process variations dictated by mask topography effects in EUV lithography. Aim: Accurately modeling EUV lithographic imaging using deep learning while taking into account 3D mask effects and EUV process variations, to surpass the computational bottleneck posed by EMF simulations. Approach: Train an efficient generative network model on 2D and 3D model aerial images of a variety of mask layouts in a manner that highlights the discrepancies and non-linearities caused by the mask topography. Results: The trained model is capable of predicting 3D mask model aerial images from a given 2D model aerial image for varied mask layout patterns. Moreover, the model accurately predicts the EUV process variations as dictated by the mask topography effects. Conclusions: The utilization of such deep learning frameworks to supplement or ultimately substitute rigorous EMF simulations unlocks possibilities of more efficient process optimizations and advancements in EUV lithography.

A 2D Waveguide Method for Lithography Simulation of Thick SU-8 Photoresist.

Due to the increasing complexity of microelectromechanical system (MEMS) devices, the accuracy and precision of two-dimensional microstructures of SU-8 negative thick photoresist have drawn more attention with the rapid development of UV lithography technology. This paper presents a high-precision lithography simulation model for thick SU-8 photoresist based on waveguide method to calculate light intensity in the photoresist and predict the profiles of developed SU-8 structures in two dimension. This method is based on rigorous electromagnetic field theory. The parameters that have significant influence on profile quality were studied. Using this model, the light intensity distribution was calculated, and the final resist morphology corresponding to the simulation results was examined. A series of simulations and experiments were conducted to verify the validity of the model. The simulation results were found to be in good agreement with the experimental results, and the simulation system demonstrated high accuracy and efficiency, with complex cases being efficiently handled.

Fast extreme ultraviolet lithography mask near-field calculation method based on machine learning.

Near-field calculation for a three-dimensional (3D) mask is a fundamental task in extreme ultraviolet (EUV) lithography simulations. This paper develops a fast 3D mask near-field calculation method based on machine learning for EUV lithography. First, the training libraries of rigorous mask near fields are built based on a set of representative mask samples and reference source points. In the testing stage, the mask under consideration is first segmented into a set of non-overlapped patches. Then the local near field of each patch is calculated based on the non-parametric regression and data fusion techniques. Finally, the entire mask near field is synthesized based on the image stitching and data fitting methods. The proposed method is shown to achieve higher accuracy compared to the traditional domain decomposition method. In addition, the computational efficiency is improved up to an order of magnitude compared to the rigorous electromagnetic field simulator.

Tunable Resonator as the Load of a Microstrip Line

A microstrip resonator is studied in which frequency tuning is carried out by micromechanical movements of the signal electrode above the substrate. The investigated resonator can be used as a component of a tunable antenna element, turned on as the load of the line. It is shown that the effective dielectric permittivity, which determines the resonant frequency, significantly decreases as a result of the movement of the signal electrode at a distance of several percents from the thickness of the substrate. Absolute values of the displacement usually stand tens or hundreds of micrometers depending on substrate thickness. Such displacements are available for modern piezoelectric or electrostrictive actuators. It opens an opportunity to implement the electrical type of tuning. For resonator performed on the substrate with dielectric permittivity about 10, resonant frequency tuning achieves more than 30 percent while the displacement of the signal electrode above the substrate does not exceed 10 percent. It is established that the variation range and sensitivity of the resonant frequency tuning can be increased by increasing the dielectric permittivity and decreasing the height of the microstrip line's substrate. Although the ratio between the width and the length of the resonator affects the tuning characteristics, the choice of these parameters is conditioned by the requirement for the formation of the required radiation pattern of the antenna element, the component of which is the viewed resonator. An equivalent circuit of a microstrip resonator as an element of a tunable antenna is proposed. The equivalent circuit model gives results that are satisfactorily consistent with those obtained based on a rigorous electromagnetic field model and a three-dimensional finite element method. At the same time, the schematic model simplifies the analysis of the influence of the geometric and electrophysical parameters of the resonant element on its characteristics and allows simplifying the design process of the antenna element and optimize its characteristics. The need to find the optimal parameters at the stage of designing the antenna element, in particular, arises during the matching of the feeder's and the radiator's characteristics and to provide the necessary range of the center frequency tuning.

Electromagnetic Fields Due to the Wake of a Moving Slender Body in a Finite-Depth Ocean with Density Stratification

Weak electric currents are induced in moving seawater by cutting the geomagnetic fields. These electric currents can produce measurable electromagnetic fields that may be used for some purposes such as monitoring of ocean internal waves. This article is aimed at presenting the procedure to calculate the electromagnetic fields owing to the wake raised by an undersea moving slender body. A pair of Havelock point sources are introduced to model the moving body, which generate the similar wake at places far from the body. The ocean is taken to be of finite-depth with density stratification due to thermocline. Three distinct forms of water-flow wake can be identified, the free-surface Kelvin wake, the internal interfacial wake, and the localized volume wake. The electric currents evoked by the motional wake may produce observable electromagnetic fields, which may be solved using rigorous electromagnetic field theory. At the sea level, the magnitudes of the induced electric field and magnetic field are on the order of a few microvolts per meter and one nano-Tesla, respectively, which are appreciable in terms of nowadays marine electric and magnetic sensors.

Large area manufacturing of plasmonic colour filters using substrate conformal imprint lithography

This work presents the large area fabrication of plasmonic colour filters consisting of subwavelength apertures in aluminium films of different thicknesses. Wafer-scale pattern transfer was realized by a soft lithography technique (substrate conformal imprint lithography). The fabricated colour filters have an active area of up to 145 cm2 which presents a considerable increase compared to previously published results. In addition to experimental investigations, simulations of the transmission behaviour were performed using a rigorous electromagnetic field solver based on an extended RCWA approach. Furthermore, the use of a spin-coated cover layer consisting of the UV-curable hybrid polymer OrmoComp® instead of often applied PECVD-SiO2 was investigated.

Contribution to calculating the impedance of grounding electrodes using circuit equivalents

In this paper the dynamic behavior of grounding electrodes is investigated by calculating their impedance to ground. The calculations are performed by implementing popular modelling approaches including circuit, transmission line, and electromagnetic field (EMF) model. The attention of this paper is given to the circuit based (CBM) method. The results from the rigorous EMF model are used as reference in the process of validity range determination of the other models. Numerically obtained curves for the frequency-dependent impedance to ground are presented in several figures for various electrode lengths and soil characteristics.

基于严格电磁场模型的光学光刻仿

基于严格电磁场模型的光学光刻仿

Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling

Purpose – The purpose of this paper is to find an optimized thin-film amorphous silicon solar cell design by numerically optimizing the light trapping efficiency of a pyramid-structured back-reflector using a frequency-domain finite element Maxwell solver. For this purpose short circuit current densities and absorption spectra within the investigated solar cell model are systematically analyzed. Furthermore, the authors employ a topology simulation method to accurately predict the material layer interfaces within the investigated solar cell model. The method simulates the chemical vapor deposition (CVD) process that is typically used to fabricate thin-film solar cells by combining a ballistic transport and reaction model (BTRM) with a level-set method in an iterative approach. Predicted solar cell models are far more realistic compared to solar cell models created assuming conformal material growth. The purpose of the topology simulation method is to increase the accuracy of thin-film solar cell models in order to facilitate highly accurate simulation results in solar cell design optimizations. Design/methodology/approach – The authors perform numeric optimizations using a frequency domain finite element Maxwell solver. Topology simulations are carried out using a BTRM combined with a level-set method in an iterative fashion. Findings – The simulation results reveal that the employed pyramid structured back-reflectors effectively increase the light path in the absorber mainly by exciting photonic waveguide modes. In using the optimization approach, the authors have identified solar cell models with cell periodicities around 480 nm and pyramid base widths around 450 nm to yield the highest short circuit current densities. Compared to equivalent solar cell models with flat back-reflectors, computed short circuit current densities are significantly increased. Furthermore, the paper finds that the solar cell models computed using the topology simulation approach represent a far more realistic approximation to a real solar cell stack compared to solar cell models computed by a conformal material growth assumption. Research limitations/implications – So far in the topology simulation approach the authors assume CVD as the material deposition process for all material layers. However, during the fabrication process sputtering (i.e. physical vapor deposition) will be employed for the Al:ZnO and ITO layers. In the framework of this ongoing research project the authors will extend the topology simulation approach to take the different material deposition processes into account. The differences in predicted material interfaces will presumably be only minor compared to the results shown here and certainly be insignificant relative to the differences the authors observe for solar cell models computed assuming conformal material growth. Originality/value – The authors systematically investigate and optimize the light trapping efficiency of a pyramid nano-structured back-reflector using rigorous electromagnetic field computations with a 3D finite element Maxwell solver. To the authors’ knowledge such an investigation has not been carried out yet in the solar cell research literature. The topology simulation approach (to the best of the authors’ knowledge) has previously not been applied to the modelling of solar cells. Typically a conformal layer growth assumption is used instead.

Insight of limitations of effective media theory for metal–dielectric multilayer metamaterials

Effective media theory (EMT) is usually used in the simulations and descriptions of one type of metamaterials which are composed of metal–dielectric multilayer films because of its simplicity and intuitiveness. It is consistent with the rigorous electromagnetic field analysis when the approximation conditions are strictly satisfied. However, there are several noticeable, and sometimes significant failures for the predicted properties that are caused by the approximation dealing with the finite layer of metal/dielectric multilayer structures. These inaccuracies and errors including surface plasmon polaritons (SPPs) spreading angles, reflection properties and interference patterns for SPPs lithography, originate from the differences of isofrequency contours between ideal hyperbolic multilayer structures and the actually fabricated multilayer structures with finite layer of films. Simulation results of EMT with metal/dielectric multilayer structures are analyzed and compared with the rigorous field analysis approach. Being aware of these issues can help to reduce the errors and improve the designs of the plasmonic devices for many applications.

Simulation of the polarization effects induced by the bilayer absorber alternating phase-shift mask in conical diffraction

Hyper numerical aperture (NA) and off-axis illumination enable extension of ArF lithography for 45 nm technology node and beyond. Also, rigorous electromagnetic field modeling is taken into account for the optical and topographical properties of the mask. A rigorous three-dimensional mask model for bilayer absorber alternating phase shift mask (AltPSM) with the rigorous coupled-wave analysis (RCWA) is established. First, the harmonic waves are expanded based on the least common multiple of the periods in order to model the diffraction of multiple grating layers with different periods. Second, Lalanne’s formulation is used to improve the convergence of RCWA for multiple grating layers in conical diffraction. Third, the enhanced transmittance matrix approach is also extended to conical diffraction to avoid the numerical instability. Given the chromium oxide/chromium AltPSM, the change of polarization state as a function of mask and incident light properties is investigated. When the linewidth is below 30 nm, the mask acts as a transverse magnetic field polarizer, which is not preferred in terms of image quality, so the mask-induced polarization effects must be considered in the hyper NA lithography.

微谐振环结构体内太赫兹增强效应

Based on the rigorous electromagnetic field theory, the rigorous expression of terahertz waves in micro-ring resonators with shape and fishnet structure is given in this paper. With the boundary conditions of electromagnetic field, the enhancement effect of the spatial distribution of terahertz waves in the micro-ring resonator with shape and fishnet structure is analyzed. The numerical results show that the electric field is greater than the magnetic field near the ring resonator metal strips. The electric field near the metal strips is obviously stronger than that in other regions, especially in the opening. The THz electric and magnetic fields in the peak position of electromagnetic field in fishnet structure are symmetry with respect to x. The extremum of the electric field appears in the four up and down corners of the large cross, while the extremum of the magnetic field appears in the upper and lower ends of the small cross. The physical interpretation of these phenomena is also given in the point view of the theory of electromagnetic field transmission lines.

Electromagnetic Modeling of Quantum Well Infrared Photodetectors

Rigorous electromagnetic field modeling is applied to calculate the quantum efficiency of various quantum well infrared photodetector (QWIP) geometries. We found quantitative agreement between theory and experiment for corrugated-QWIPs, grating-coupled QWIPs, and enhanced-QWIPs, and the model explains adequately the spectral lineshapes of the quantum grid infrared photodetectors. After establishing our theoretical approach, we used the model to optimize the detector structures for 12-micron pixel pitch focal plane arrays.

Rigorous electromagnetic field simulation of the impact of photomask line-edge and line-width roughness on lithographic processes

The impact of edge profile roughness of the absorber lines on an optical photomask has been studied by means of rigorous electro-magnetic field (EMF) simulation for the mask diffraction spectrum and subsequent imaging. Roughness has been modeled using two different approaches, a sinusoidal description and an algorithm known from literature-based on Fourier transformation. The latter can arbitrarily create rough profiles and surfaces based on the three morphological parameters standard deviation σ, roughness exponent α, and correlation length ξ. In this study, the standard deviation has been kept fixed while varying the remaining two morphological parameters, still showing impact on the lithographic process. A software interface for use of the generated profiles with the Waveguide EMF solver of the Dr.LiTHO lithography simulation suite has been implemented. It was shown by means of image analysis and study of the resulting process windows that mask roughness is partially transferred to the aerial image. Isolated and dense features behave differently, leading inter alia to an iso-dense bias different to that of ideal lines. Due to the roughness, process windows now depend on the position along the line. Determing process windows at multiple positions for statistical analysis implies a reduction of the effective process window. Correlation length ξ has shown to be an important parameter and, thus, morphology should not be ignored in the modeling of rough lines. Tapered sidewalls can add to the shift of the process windows in the same order of magnitude.

Behaviour of grounding systems: A quasi-static EMTP model and its validation

The transient behaviour of grounding systems subject to lightning strokes may be studied by means of approaches based to simple and approximated circuit models or to the more rigorous electromagnetic field theory. Both philosophies have pros and cons.In the paper a circuit model, developed by the authors in the past years and implemented with modern simulation software, is presented. The model is suitable to describe with sufficient accuracy the behaviour of complex and realistic grounding systems under surge condition, and, in particular, the peculiarity of this model is the inclusion of current controlled voltage sources into the classical RLC circuit, in order to take into account the resistive coupling among the elementary electrodes of a complex grounding system.In order to validate the model and to identify the frequency range of applicability, simulation results have been compared to ones based on electromagnetic field theory available in literature.