Rigorous electromagnetic field mask modeling and related lithographic effects in the low &lt;inline-formula&gt;&lt;math altimg="none" display="inline" overflow="scroll"&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/inline-formula&gt; and ultrahigh numerical aperture regime

Erdmann, Andreas; Evanschitzky, Peter

doi:10.1117/1.2778447

Cited by 27 publications

(5 citation statements)

References 31 publications

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“…In order to implement OPC for generating the conjugate illumination light field, we use vectorial diffraction theory to rigorously model the propagation of the electromagnetic field in the projection system that has a high magnification factor and a high numerical aperture (NA). 32,33 The intensity in the sample plane can be expressed as…”

Section: ■ Methodologymentioning

confidence: 99%

“…This facilitates the simplification of the generation of the conjugate structured light field by using an SLM or a DMD, which could enable grayscale programming of the light field that is not achievable by a physical photomask. In order to implement OPC for generating the conjugate illumination light field, we use vectorial diffraction theory to rigorously model the propagation of the electromagnetic field in the projection system that has a high magnification factor and a high numerical aperture (NA). , The intensity in the sample plane can be expressed as bold-italicI image = prefix∑ p = x , y , z || H p ⊗ M || 2 2 Here, H is the function of the projection system, M is a pixelated representation of the input mask pattern, and ⊗ is the symbol of two-dimensional convolution (see Section S2 for the unabridged description of the vector diffraction imaging theory). To inspect the deep subwavelength nanostructure, the feature size of the structured light field should be much smaller than the diffraction barrier.…”

Section: Methodsmentioning

confidence: 99%

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Optical Far-Field Detection of Sub-λ/14 Wide Defects by Conjugate Structured Light-Field Microscopy (c-SIM)

Zhang,

Liu,

Jiang

et al. 2023

ACS Photonics

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Optical far-field detection and imaging of deep-subwavelength objects in a large-area wafer is challenging because of the well-known diffraction barrier and weak Rayleigh scattering. Although the scattering signal of deep subwavelength defects can be enhanced by various methods, such as using a high full-well-capacity camera and increasing the exposure time, the accurate classification of various defects and the precise positioning of defects in a subwavelength domain is rather challenging. In this letter, we report a theoretical framework that the optical bright-field imaging microscopy, coupled with an optical proximity correction-based structured light-field illumination mode, could pinpoint and classify various sub-λ/14 wide defects in a subwavelength domain in a large-area wafer. The underlying physics is that the illuminated structured light field, which is customized to mimic the geometrical feature of the background pattern in the wafer, creates the defect-induced breakdown of geometrical and electromagnetic symmetry. We believe that this work not only paves the route for optical wafer defect inspection and classification at advanced technology nodes but also could potentially be extended to many other areas, such as biosensing, lithographic mask inspection, material characterization, and nanoscale metrology.

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Section: ■ Methodologymentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Optical Far-Field Detection of Sub-λ/14 Wide Defects by Conjugate Structured Light-Field Microscopy (c-SIM)

Zhang,

Liu,

Jiang

et al. 2023

ACS Photonics

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“…Modeling of EUV light interaction with such a thick mask comprises various optical and imaging effects that cannot be adequately predicted by a Kirchhoff approach. This includes light amplitude and phase deformation at the mask, mask-induced 3D effects [4], polarization effects [5], wave aberrations [6], and others. To effectively simulate the scattering and diffraction of EUV light from a typical EUV mask and comprehend the corresponding effects, rigorous electromagnetic field (EMF) modeling approaches are essential.…”

Section: Introductionmentioning

confidence: 99%

3d mask simulation and lithographic imaging using physics-informed neural networks

Medvedev,

Erdmann,

Rosskopf

2024

Optical and EUV Nanolithography XXXVII

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Background: The increasing demands on computational lithography and computational imaging in the design and optimization of lithography processes necessitate rigorous modeling of EUV light diffracted from the mask. Traditional electromagnetic field (EMF) solvers are inefficient for large-scale technology problems, while deep neural networks rely on a huge amount of expensive rigorously simulated or measured data [1].Aim: In order to overcome these constraints, we explore the potential of physics-informed neural networks (PINN)[2] as a promising solution for addressing complex optical problems in the field of EUV lithography.Approach: We extend the existing MaxwellNet[3] to simulate the light diffraction from typical reflective EUV masks. The coupling of the predicted diffraction spectrum with image simulations enables the evaluation of PINN performance in predicting relevant lithographic metrics and typical mask 3D effects. Results:The results of modeling near-and far-field diffraction using PINN showcase a good performance in terms of convergence behavior, stability, accuracy, and a significant speed-up (up to ×10000) compared to the rigorous 3D mask simulation using an established numerical EMF solver. In contrast to other machine learning approaches, PINN is able to accurately simulate the near field, learns the involved physics, and captures the optical and mask-induced 3D effects. PINNs can predict lithographic process windows with sufficient accuracy. Conclusions: Differently from numerical solvers, once trained, generalized PINN can simulate light scattering in several milliseconds without re-training and independently of problem complexity. This opens up the capabilities for partially coherent imaging simulations without the Hopkins approach, source optimization, and fast investigation of mask 3D effects.

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“…Continuous reduction of mask and feature size enabled by high NA projection systems exhibit complex polarization, interference, diffraction, and oblique illumination effects. The Kirchhoff approach, which assumes an infinitely thin mask, can not accurately predict resulting light amplitude and phase deformation at the mask, mask-induced 3D effects [3], wave aberrations [4], and polarization effects [5]. In order to accurately model the diffraction of EUV light from a typical EUV mask and the corresponding polarization effects, rigorous electromagnetic field (EMF) modeling methods are required.…”

Section: Introductionmentioning

confidence: 99%

3D EUV mask simulator based on physics-informed neural networks: effects of polarization and illumination

Medvedev,

Erdmann,

Rosskopf

2024

Computational Optics 2024

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Background: To enable the manufacturing of advanced semiconductor devices, EUV lithography has been continuously shrinking the lateral dimensions of the mask and features. Resulting complex diffraction, polarization, and oblique illumination effects require rigorous modeling of EUV light diffracted from the mask. Traditional electromagnetic field (EMF) solvers are inefficient for large field-of-view simulations, while deep neural networks rely on a huge amount of expensive rigorously simulated or measured data. [1] Aim: Building upon our prior research [2], which revealed the PINN's potential and enabled sufficient aerial image simulation of small features, this study aims to broaden the scope of PINN's applications. Specifically, we extend this work towards the investigation of polarization effects and variable illumination settings.Approach: The established PINN model [2] was employed for EUV mask simulations under various illumination directions to investigate the orientation dependence of lithographic patterning. Expressing the residual of 3D Maxwell's equations, we effectively decoupled the transverse electric (TE) and transverse magnetic (TM) modes of EUV light. Employing a vectorial formulation of the wave equation, we investigated the ability of the PINN approach to predict the generation of additional electric field components resulting from the scattering at the absorber edges.Results: PINN accurately predicts the polarization effects that are relatively small, but still notable close to the absorber edges and inside the multilayer. The generalized PINN-based solver, adapted for arbitrary illumination settings, demonstrates the significant impact of the illumination direction and exposure wavelength on the reflected EUV light. PINN captures asymmetries in the near field caused by off-axis illumination and the significant drop in the intensity of the reflected light for larger incidence angles.Conclusions: By pushing the application limits of the existing PINN approach, we demonstrated its capability to accurately model oblique illumination effects, polychromatic effects, and even the weak polarization effects in the EUV spectral range. Different from numerical solvers, a universal PINN-based mask solver can simulate light scattering response in several milliseconds for arbitrary mask geometries and illumination settings without re-training.

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Rigorous electromagnetic field mask modeling and related lithographic effects in the low <inline-formula><math altimg="none" display="inline" overflow="scroll"><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></math></inline-formula> and ultrahigh numerical aperture regime

Cited by 27 publications

References 31 publications

Optical Far-Field Detection of Sub-λ/14 Wide Defects by Conjugate Structured Light-Field Microscopy (c-SIM)

Optical Far-Field Detection of Sub-λ/14 Wide Defects by Conjugate Structured Light-Field Microscopy (c-SIM)

3d mask simulation and lithographic imaging using physics-informed neural networks

3D EUV mask simulator based on physics-informed neural networks: effects of polarization and illumination

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