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Boston University · Aeronautics and Astronautics
Active 1965–2026
Eytan Barouch, PhD, is a Professor in the Department of Mechanical Engineering at Boston University College of Engineering. His main current interest is a combination of numerical analysis with specific practical problems of electromagnetic applications. His research includes simulations of microchip fabrications using non-uniform grid transforms to reduce storage and file size requirements, enabling real-time practical results without sacrificing accuracy. Additionally, he works on electromagnetic inverse scattering of complex material compositions and shapes, particularly involving metals and lossy materials to enhance or reduce scattered beams for identification or disguise purposes. His expertise also extends to material properties identification, including non-linear responses using auxiliary differential equations (ADE) for each term in the materials' permittivity function.
Optical proximity correction based on the direct use of rigorous electromagnetic simulation
2026-04-10
Rigorous electromagnetic simulations are very time-consuming and thus are seldom used directly for optical proximity correction (OPC). To avoid the direct use of rigorous EM simulations, many OPC algorithms rely on approximate M3D models. Such a model may predict the near field accurately, but it may not work well for predicting the gradient of the cost function with respect to the mask pixels. Hence, it is desirable to develop a more accurate method for the computation of the gradient in OPC. In this paper, a rigorous OPC formulation based on the direct use of rigorous EM simulation is presented. It employs the adjoint method for the efficient computation of the gradient of the cost function. Numerical results are presented which show significant differences between the rigorous and approximate gradients. The rigorous OPC formulation is then applied to examples from high-NA EUV lithography to highlight the advantages and disadvantages of the rigorous OPC formulation. Lastly, a hybrid OPC formulation is presented which combines the advantages of the both the rigorous and the approximate OPC methods.
Binary solution for optimization of pixelated EUV source using constrained mathematical programming
2023 · 1 citations
In this paper, we present a new approach to EUV source optimization which automatically generates a binary solution for the intensities of almost all the pixels. The benefit of such a binary solution is that the source power is distributed evenly over all the illuminated pixels, thus avoiding large intensity spikes which can lead to accelerated, radiation-induced degradation of certain parts of the imaging system.
Development of fast rigorous simulator for large-area EUV lithography simulation
2019-03-26 · 7 citations
In this paper, we first explain why the original pseudo-spectral time-domain (PSTD) formulation, as given in a well-know book on computational electromagnetics, is numerically unstable for curvilinear geometries. Then we explain how this problem can be fixed by a simple but crucial modification to the original formulation. The new formulation has allowed us to construct a very accurate and extremely fast rigorous simulator for DUV and EUV lithography. Benchmarks are presented to demonstrate the high accuracy and great speed of the new simulator. This brings us one step closer to achieving the goal full-chip, rigorous simulation for DUV and EUV lithography.
Long-Time Instability of Pseudospectral Time-Domain Method in Curvilinear Coordinates
IEEE Transactions on Antennas and Propagation · 2019-11-11 · 2 citations
We found that the pseudospectral time-domain (PSTD) formulation discussed in the literature exhibits long-time instability when applied to problems with curvilinear geometry. To overcome this problem, we have developed a provably stable PSTD formulation in curvilinear coordinates. In this article, we discuss the new PSTD formulation and present a rigorous proof of stability. Numerical results are given to validate the new formulation. The new formulation requires only a simple change in the form of the spatial-derivative operators in curvilinear coordinates and so can easily be implemented in the existing PSTD codes.
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2017-03-24 · 3 citations
EUV lithography is one of the promising technologies for 1X nm patterning. EUV lithography has high resolution capability because of short wavelength of source but it has some particular patterning problems which are not appeared a t optical lithography. Owing to reflective optics, EUV light incidents obliquely in mask and oblique incidence of EUV lithography leads shadow effect and arc-shaped exposure slit. The study of these particular optical problems are required for optical proximity correction (OPC). Arc-shaped exposure slit leads azimuthal angle variation, incident angle variation , and variation of shadow width. With these variations along exposure slit, patterning result is varied along the exposure slit. With understanding of these particular optical problems, lots of EUV OPC studies have been presented with 0.33 conventional NA system. However, suggested anamorphic high NA system has not only elliptical shaped mask NA and also different angle distribution. The incident angle variation as a function of azimuthal angle is different between isomorphic and anamorphic NA systems. In case of anamorphic NA system, incident angle distribution is decreased on horizontal direction but it is larger on vertical direction compared with case of isomorphic NA system. These differences make different arc-shaped slit effect. CD variation as a function of azimuthal angle is different between isomorphic and a namorphic NA systems. The study of CD variation along the exposure slit is very helpful for OPC in EUV lithography.
Microelectronic Engineering · 2017-01-26 · 9 citations
Impact of a deformed extreme ultraviolet pellicle in terms of the critical dimension uniformity
Journal of Micro/Nanolithography MEMS and MOEMS · 2016-01-29 · 11 citations
The usage of an extreme ultraviolet (EUV) pellicle is regarded as a potential solution for defect control because it can protect the mask from airborne debris. However, some obstacles disrupt realistic application of the pellicle, such as its structural weakness, the risk of thermal damage, and so on. For these reasons, flawless fabrication of the pellicle is impossible. We discuss the influence of a deformed pellicle in terms of the nonuniform intensity distribution and the critical dimension (CD) uniformity. When we consider a 16-nm periodic pattern with dipole illumination, a transmission difference (max-min) of 0.7% causes CD uniformity of 0.1 nm. The deflection of the aerial image caused by gravity is small enough to ignore. CD uniformity is <0.1 nm, even for the current gap of 2 mm between the mask and pellicle. However, wrinkling of the EUV pellicle, caused by heat, can cause serious image distortion because a wrinkled EUV pellicle experiences both transmission loss variation as well as CD nonuniformity. The local angle of a wrinkle (as opposed to the period or amplitude of a wrinkle) is the main factor that influences CD uniformity, and a local angle of <∼16 deg is needed to achieve 0.1-nm CD uniformity for a 16-nm L/S pattern.
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2016-03-18
Even though EUV lithography has extremely short wavelength source, a high numerical aperture(NA) system larger than 0.5 is required to make fine pattern of 1X nm and below. In order to avoid reflective efficiency loss and increase of chief ray angle of incident light, anamorphic high NA is suggested. Suggested anamorphic NA system has non-isotropic magnification which is varied 4X to 8X and the mask NA shape is ellipse due to non-isotropic magnification distribution. Anamorphic NA system has a non-conventional shadow effect due to non-isotropic incident angle distribution and magnification. These non-isotropic characteristics leads the reduction of asymmetric shadow distribution and it involves the reduction of horizontal-vertical bias. As a result anamorphic NA system can achieve balanced patterning results regardless of pattern direction and incident direction.
Influence of non-uniform intensity distribution of deformed pellicle for N7 patterning
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2016-09-26
For protecting mask from debris, EUV pellicle is considered as a most effective solution. EUV pellicle can avoid contamination on mask by covering mask. Usage of EUV pellicle can reduce mask damage caused by contamination but the pellicle involves transmission loss due to absorption of EUV light. To get high transmission, pellicle made with thin thickness but it can be deformed easily due to weak structure. Deformation of pellicle such as wrinkle leads transmission non-uniformity and transmission non-uniformity will involve CD non-uniformity. For real-application at lithography process, the optical study of deformed pellicle is required to avoid degradation of CD uniformity. In this paper, we discuss transmission non-uniformity with various off-axis-illumination (OAI) conditions. Then we studied CD nonuniformity caused by wrinkled pellicle with various patterns. By increasing spatial coherence, transmission nonuniformity is decrease at small wrinkle region. However, transmission non-uniformity variation is independent with illumination conditions at large wrinkle which has large period. Not only wrinkled pellicle imaging but also CD variation caused by non-uniform transmission is also dependent on illumination conditions. In contrast with transmission nonuniformity, CD non-uniformity with high coherent light is smaller than the result with low coherent light. With all of results, we find that the allowable local tilt angle is varied with wrinkle size and illumination conditions and smallest size of allowable local tilt angle is about 250 mrad for both illuminations.
Journal of Micro/Nanolithography MEMS and MOEMS · 2016-08-01 · 3 citations
A high numerical aperture (NA) system with an NA larger than 0.5 is required to make patterns of 1X nm and below, even though extreme ultraviolet lithography uses a 13.5-nm wavelength source. To avoid the reflective efficiency loss and to avoid an increase in the chief ray angle of incident light, use of an anamorphic high-NA system is suggested. The suggested anamorphic NA system has nonisotropic magnification, x-magnification of 4× and y-magnification of 8×, and the mask NA shape is an ellipse due to the nonisotropic magnification distribution. Anamorphic NA systems have a nonconventional shadow effect due to nonisotropic incident angle distribution and magnification. These nonisotropic characteristics lead to the reduction of asymmetric shadow distribution and a reduction of horizontal–vertical bias. As a result, anamorphic NA systems can achieve balanced patterning results regardless of pattern direction and incident direction.
Michael S. Yeung
Barry M. McCoy
The University of Tokyo
Steven A. Orszag
Uwe Hollerbach
Mentor Technologies
Giovanni Gallavotti
Anders Martin‐Löf
Stockholm University
Ph.D., Mechanical Engineering
Massachusetts Institute of Technology (MIT)
M.S., Mechanical Engineering
Massachusetts Institute of Technology (MIT)
B.S., Mechanical Engineering
Technion - Israel Institute of Technology
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D. B. Abraham
University of Oxford
Hye-Keun Oh