6 July 2015 Fully-vectorial simulation and tolerancing of optical systems for wafer inspection by field tracing
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Abstract
The simulation, design and tolerancing of optical systems for wafer inspection is a challenging task due to the different feature sizes, which are involved in these systems. On the one hand light is propagated through macroscopic lens systems and on the other hand light is diffracted at microscopic structures with features in the range of the wavelength of light. Due to this variety of scale plenty of different physical effects like refraction, diffraction, interference and polarization have to be taken into account for a realistic analysis of such inspection systems. We show that all of these effects can be included in a system simulation by field tracing, which combines physical and geometrical optics. The main idea is the decomposition of the complex optical setup in a sequence of subdomains. Per subdomain a different approximative or rigorous solution of Maxwell’s equations is applied to propagate the light. In this work the different modeling techniques for the analysis of an exemplary wafer inspection system are discussed in detail. These techniques are mainly geometrical optics for the light propagation through macroscopic lenses, a rigorous Fourier Modal Method (FMM) for the modeling of light diffraction at the wafer microstructure and different free-space diffraction integrals. In combination with a numerically efficient algorithm for the coordinate transformation of electromagnetic fields, field tracing enables position and fabrication tolerancing. As an example different tilt tolerance effects on the polarization state and image contrast of a simple wafer inspection system are shown.
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Daniel Asoubar, Daniel Asoubar, Hagen Schweitzer, Hagen Schweitzer, Christian Hellmann, Christian Hellmann, Michael Kuhn, Michael Kuhn, Frank Wyrowski, Frank Wyrowski, } "Fully-vectorial simulation and tolerancing of optical systems for wafer inspection by field tracing", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260J (6 July 2015); doi: 10.1117/12.2184825; https://doi.org/10.1117/12.2184825
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