Adaptive Finite Element Method for Simulation of Optical Nano Structures

We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components into the unbounded and possibly heterogeneous exterior. We apply the finite element method to the optimization of the design of a hollow core photonic crystal fiber. Thereby we look at the convergence of the method and discuss automatic and adaptive grid refinement and the performance of higher order elements

Finite Element Simulation of Light Propagation in Non-Periodic Mask Patterns

Rigorous electromagnetic field simulations are an essential part for scatterometry and mask pattern design. Today mainly periodic structures are considered in simulations. Non-periodic structures are typically modeled by large, artificially periodified computational domains. For systems with a large radius of influence this leads to very large computational domains to keep the error sufficiently small. In this paper we review recent advances in the rigorous simulation of isolated structures embedded into a surrounding media. We especially address the situation of a layered surrounding media (mask or wafer) with additional infinite inhomogeneities such as resist lines. Further we detail how to extract the far field information needed for the aerial image computation in the non-periodic setting.Comment: Proceedings SPIE conference Photomask Japan (2008

Rigorous Simulations of 3D Patterns on Extreme Ultraviolet Lithography Masks

Simulations of light scattering off an extreme ultraviolet lithography mask with a 2D-periodic absorber pattern are presented. In a detailed convergence study it is shown that accurate results can be attained for relatively large 3D computational domains and in the presence of sidewall-angles and corner-roundings.Comment: SPIE Europe Optical Metrology, Conference Proceeding

Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures

We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.Comment: 24 page

Reduced basis method for computational lithography

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times for different values of geometrical parameters. The reduced basis method allows to split up the solution process of a parameterized model into an expensive offline and a cheap online part. After constructing the reduced basis offline, the reduced model can be solved online very fast in the order of seconds or below. Error estimators assure the reliability of the reduced basis solution and are used for self adaptive construction of the reduced system. We explain the idea of reduced basis and use the finite element solver JCMsuite constructing the reduced basis system. We present a 3D optimization application from optical proximity correction (OPC).Comment: BACUS Photomask Technology 200

Numerical analysis of nanostructures for enhanced light extraction from OLEDs

Nanostructures, like periodic arrays of scatters or low-index gratings, are used to improve the light outcoupling from organic light-emitting diodes (OLED). In order to optimize geometrical and material properties of such structures, simulations of the outcoupling process are very helpful. The finite element method is best suited for an accurate discretization of the geometry and the singular-like field profile within the structured layer and the emitting layer. However, a finite element simulation of the overall OLED stack is often beyond available computer resources. The main focus of this paper is the simulation of a single dipole source embedded into a twofold infinitely periodic OLED structure. To overcome the numerical burden we apply the Floquet transform, so that the computational domain reduces to the unit cell. The relevant outcoupling data are then gained by inverse Flouqet transforming. This step requires a careful numerical treatment as reported in this paper

Finite-Element Simulations of Light Propagation through Circular Subwavelength Apertures

Light transmission through circular subwavelength apertures in metallic films with surrounding nanostructures is investigated numerically. Numerical results are obtained with a frequency-domain finite-element method. Convergence of the obtained observables to very low levels of numerical error is demonstrated. Very good agreement to experimental results from the literature is reached, and the utility of the method is demonstrated in the investigation of the influence of geometrical parameters on enhanced transmission through the apertures