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Fourier optics for investigating the impact of roughness to scatterometry

Author(s): H. Gross, S. Heidenreich and M. Baer
Journal: Proc SPIE
Year: 2016
Event name: International Conference on Circuits, Systems, Signal Processing, Communications and Computers (CSSCC '14): Recent Advances in Electrical and Computer Engineering: (2014)
ISBN: 978-1-61804-228-6
Abstract: Efficient algorithms are proposed for stochastical investigations of the impact of structure roughness on light diffraction pattern of photo masks. This is important for the scatterometry, i.e. the accurate, indirect determination of geometry parameters from scattered light intensities in wafer metrology. The sensitivity to roughness increases the smaller the wavelengths of the incident light are. For EUV scatterometry at 13.5 nm, many higher diffraction orders can be measured and they are sensitive to structure details. We calculate the light diffraction patterns of apertures with many rough slits in the far field. Applying Fraunhofer approximation, a 2D-Fourier transform of the light distribution of the aperture plane yields the sought diffraction pattern. The rough edges of the aperture are created by means of power spectrum density (PSD) functions used with a random complex exponential phase term. The comparison of the calculated light intensities to those of the undisturbed, ’non-rough’ aperture, whose edges are straight lines, reveal a systematic decrease in terms of the diffraction order and the standard deviation of the roughness amplitude. Ensembles of rough apertures with different values for the imposed standard deviation of the roughness amplitude, the linear correlation length, and the roughness exponent were examined. Former results, obtained by rigorous calculations with computational expensive finite element methods (FEM) have been confirmed. The sensitivity of the method is demonstrated for bi-periodic arrays of hole-space structures too.

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