17 June 2009 Evaluation of measurement uncertainties in EUV scatterometry
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Abstract
Scatterometry, the analysis of light diffracted from a periodic structure, is a versatile metrology tool for characterizing periodic surface structures, regarding the critical dimension (CD) and other properties of the surface profile. For extreme ultraviolet (EUV) masks, only EUV radiation provides direct information on the mask performance comparable to the operating regime in an EUV lithography tool. With respect to the small feature dimensions on EUV masks, the short wavelength of EUV is also advantageous since it provides a large number of diffraction orders from the periodic structures irradiated. We present measurements at a prototype EUV mask with large fields of periodic lines-space structures using an EUV reflectometer at the Berlin storage ring BESSY II and discuss the corresponding reconstruction results with respect to their measurement uncertainties. As a non-imaging indirect optical method scatterometry requires the solution of the inverse problem, i.e., the determination of the geometry parameters describing the surface profile from the measured light diffraction patterns. In the time-harmonic case the numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. Restricting the solutions to a class of surface profiles and fixing the set of measurements, the inverse problem can be formulated as a nonlinear operator equation in Euclidean space. The operator maps the profile parameters to special efficiencies of diffracted plane wave modes. We employ a Gauss-Newton type iterative method to solve this operator equation, i.e., we minimize the deviation of the calculated efficiencies from the measured ones by variation of the geometry parameters. The uncertainties of the reconstructed geometry parameters depend on the uncertainties of the input data and can be estimated by statistical methods like Monte Carlo or the covariance method applied to the reconstruction algorithm. The input data of the reconstruction are very complex, i.e., they consists not only of the measured efficiencies, but furthermore of fixed and presumed model parameters such as the widths of the layers in the Mo/Si multilayer mirror beneath the line-space structure. Beside the impact of the uncertainties on the measured efficiencies, we analyze the influence of deviations in the thickness and periodicity of the multilayer stack on the measurement uncertainties of the critical dimensions.
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H. Gross, F. Scholze, A. Rathsfeld, M. Bär, "Evaluation of measurement uncertainties in EUV scatterometry", Proc. SPIE 7390, Modeling Aspects in Optical Metrology II, 73900T (17 June 2009); doi: 10.1117/12.827018; https://doi.org/10.1117/12.827018
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