Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Hermann Gross: Uncertainty estimates for inverse methods in EUV scatterometry

Tue, 21 July, 2009, 17:15-18:15, Foyer

We discuss the solution of the inverse problem in scatterometry, i.e. the determination of geometrical profiles of periodic surface structures from light diffraction patterns. Scatterometry is a non-imaging indirect optical method in wafer metrology and is also relevant to lithography masks designed for Extreme Ultraviolet Lithography, where light with wavelengths in the range of 13 nm is applied. The determination of the sought profile parameters, such as line widths and heights or side-wall angles, is incomplete without knowledge of the uncertainties associated with the reconstructed parameters. With decreasing feature sizes of lithography masks, increasing demands on metrology techniques and their uncertainties arise.

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. For typical EUV masks the ratio period over wave length is so large, that a generalized finite element method has to be used to ensure reliable results. The inverse problem can be formulated as a non-linear operator equation. The operator maps the sought mask parameters to the efficiencies of diffracted plane wave modes. We employ a Gauss-Newton type iterative method to solve this operator equation and end up minimizing the deviation of the measured efficiency or phase shift values from the calculated ones.

Clearly, the uncertainties of the reconstructed geometric parameters essentially depend on the uncertainties of the input data and can be estimated by various methods. We apply a Monte Carlo procedure and an approximative covariance method to evaluate the reconstruction algorithm and to get first estimates for the uncertainties of the reconstructed profile parameters in dependence of different perturbations of the input data. The subject under test is a typical EUV mask composed of TaN absorber lines of about 80 nm height and 140 nm width, a period of 420 nm resp. 840 nm, and with an underlying MoSi-multilayer stack of 300 nm thickness.

Presentation slides (pdf, 840 KB)

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