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2011

Doctoral Thesis

Title

# The finite integration technique (FIT) and the application in lithography simulations

Other Title

Die Finite Integrationstechnik (FIT) und die Anwendung in der Lithographie-Simulation

Abstract

Rigorous electromagnetic field (EMF) simulation of light diffraction from optical lithography masks has become a standard requirement for the optimization of lithographic processes. Firstly, due to an increasing requirement for enhanced image resolution. Secondly, because of the ongoing miniaturization of electronic circuits where feature sizes are in the order or smaller than the wavelength of light used in the projection imaging system. Lithographic masks are produced by various processes, some of which produce complex shapes with some surface roughness on the mask. These shapes affect both light scattering and image formation. For all these reasons, rigorous simulation of light diffraction of masks, in the sub-wavelength range, is an important factor to predict light transmission behavi or. In this thesis, the finite integration technique (FIT) is extended and adapted to the modeling of light diffraction from lithographic masks with complex shapes. This extension, to the standard FIT, models curved interfaces with second order accuracy. The strength of this method is that implementation is carried out on the structured grid which simplifies the grid generation. Also, memory requirements of this method are similar to the classical FIT method and much less than non-orthogonal and unstructured grid implementations. The finite integration technique (FIT) program is used for the simulation of light transmission and diffraction by two- and three-dimensional masks. The influence of mask absorber patterns, on near-field and image, are investigated for complex masks. These geom etries consist of attenuated phase-shift masks with parametrized surface roughness, as well as mask with more realistic surface roughness are simulated in order to extrapolate the effect of the regular and random surface roughness on the resulting image. These simulations involve parallel computing due to the large number of grid points of the complex three-dimensional shape. Moreover, a new iterative algorithm is developed to simulate materials with negative permittivity, such as metals, in the optical spectrum. The proposed approach can be categorized as the finite difference frequency domain (FDFD) method. The main advantages of this algorithm over the existing dispersive approaches are that it does not require an approximation of material properties in the frequency domain and no addit ional unknown is required for problems involving metals.

Thesis Note

Erlangen-Nürnberg, Univ., Diss., 2011

Publishing Place

Erlangen-Nürnberg