Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation

Burger, Sven; Köhle, Roderick; Zschiedrich, Lin; Gao, Wenjing; Schmidt, Frank; Marz, R.; Nölscher, Christoph

doi:10.1117/12.631696

Cited by 47 publications

(41 citation statements)

References 14 publications

(20 reference statements)

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“…It relies on the rigorous solution of Maxwell's equations, using a finite element method (FEM). Especially by employing nonstructured, adaptive finite element meshes, and FEM elements of high orders, these programs show clear advantages in convergence, precision, and calculation speed, when compared to other software solutions [41][42][43][44]. In case of cylinder-symmetrical formulations, the use of an appropriate extension of a 2D solver in fact gives full 3D output, but strong reduction of numerical effort.…”

Section: Numerical Calculationsmentioning

confidence: 99%

nm- andμm-Scale Surface Roughness on Glass with Specific Optical Scattering Characteristics on Demand

Fouckhardt

Steingoetter

Brinkmann

et al. 2007

Advances in OptoElectronics

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During maskless ion etching of amorphous glass, self-organization can arise in certain etch parameter ranges, which leads to dense-lying dots/cones with typical diameters and heights in the 30-300 nm range. Another phenomenon, which results in cone sizes around 1 μm or more, is self-masking especially in the case of heterogeneous glasses like borosilicate glass as used in this contribution. Thus, a wide range of characteristic sizes and shapes of individual scatterers on the glass surface, jointly acting as a defined roughness, can be achieved resulting in specific optical scattering characteristics. This contribution gives results on borosilicate thin-glass dry etching. Certain surface morphologies are reported together with experimental results on their optical scattering characteristics.

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Section: Numerical Calculationsmentioning

confidence: 99%

nm- andμm-Scale Surface Roughness on Glass with Specific Optical Scattering Characteristics on Demand

Fouckhardt

Steingoetter

Brinkmann

et al. 2007

Advances in OptoElectronics

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“…The simulation image by using the scalar, vector Hopkins formula and rigorous coupled-wave analysis (RCWA) [24][25][26] Figure 7 shows the 3D intensity distributions of the mask pattern is simulated by scalar, vector Hopkins formula and RCWA, and results are shown in Figures 7(a), (b) and (c), respectively. We find that the diffraction intensity is most centralized by using RCWA, next is using the vector Hopkins formula.…”

Section: Matlab Is Used To Simulationsmentioning

confidence: 99%

Vector Hopkins Model Research Based on Off-Axis Illumination in Nanoscale Lithography

Cao¹,

Cheng²,

Zhang

2009

PIER

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Abstract-Based on vector electromagnetic theory and the Waveguide Model, the vector Hopkins model is deduced. The model contains the vector Hopkins formula and the resist profile model of fast Optical Proximity Correction. The vector Hopkins formula considers incidence angles and azimuth angles of off-axis illumination, which differs from the traditional scalar Hopkins formula. The resist profile model is employed to analyze the effect of the photoresist diffusion under off-axis illumination by using self-adaptive Gaussian filter with scale adjustable, and a new transmission cross coefficient is obtained. The projection system parameters are introduced simultaneously, such as incidence angles, azimuth angles of off-axis illumination and diffusion parameters of photoresist. By simulating the aerial image of 3D mask in the actual lithography process, the optimal angular range of oblique incidence is studied; the image quality by impact with the oblique incidence angle is discussed as well.

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“…5 The performance of our methods is investigated and compared to competing approaches in a number of benchmark studies. [5][6][7] The main ingredients for accurate performance are adaptive methods based on goal-oriented error estimators, higher-order vector elements, and fast direct and iterative numerical methods for solving matrix equations. 8 …”

Section: 1117/212009051629 Page 2/3mentioning

confidence: 99%

Simulation method improves accuracy for optical metrology and nanooptics design

Burger¹

2009

SPIE Newsroom

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A dedicated finite-element solver enables accurate and fast simulations of light interaction with metallic nanostructures.With advances in nanotechnology growing at a fast pace, reliable simulations of nanooptical devices are crucial for research and development. Designing and optimizing the functionality of nanooptical components is typically assisted by computer simulations in combination with optical inspection as a critical step in product development and quality control. Dimensional metrology, for example, relies essentially on a numerical comparison of measurements with simulations. In addition, the latter are used in most scientific nanooptics publications to support theoretical and experimental results.The evolution of electric and magnetic fields in any welldefined nanostructure is described by Maxwell's equations. All information about the classical properties of light is contained in the electromagnetic fields, which is used to solve these differential equations. A variety of methods exist to perform rigorous simulations of Maxwell's equations. These include finite-element, finite-difference time-domain, Fouriermodal, and boundary-element approaches. However, especially (logarithmic scale, blue: low, red: high).for large 3D computational domains and highly conductive materials (like silver or gold), the electromagnetic fields of interest are so complicated that reaching accurate approximations becomes challenging for all numerical methods. It has even been suspected that nearly all published numerical results of light scattering off 3D metal nanostructures are of incorrect accuracy. 1 To approach this challenge, we use dedicated finite-element method (FEM)-based simulation tools, which enable significantly improved accuracy and relatively short computation times. Dedicated FEM solver for nanooptics simulationsIn a joint effort between the Zuse Institute Berlin and JCMwave, we are developing the JCMsuite finite-element solver, a dedicated tool for nanooptical simulations. It has been applied successfully to a wide range of electromagnetic-field computations including metamaterials, 2 photonic-crystal fibers 3 (see Figure 1), Continued on next page

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Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation

Cited by 47 publications

References 14 publications

nm- andμm-Scale Surface Roughness on Glass with Specific Optical Scattering Characteristics on Demand

nm- andμm-Scale Surface Roughness on Glass with Specific Optical Scattering Characteristics on Demand

Vector Hopkins Model Research Based on Off-Axis Illumination in Nanoscale Lithography

Simulation method improves accuracy for optical metrology and nanooptics design

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