Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Mark-Alexander Henn: On numerical reconstructions of lithographic masks in DUV scatterometry

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

The solution of the inverse problem in scatterometry is discussed, i.e. the determination of periodic surface structures from UV or light diffraction patterns. With decreasing size of features of lithography masks, increasing demands on wafer metrology technique arises. Scatterometry as a non-imaging indirect optical method is applied to such periodic line structures in order to determine their critical dimensions (CD) like side-wall angles, heights, top and bottom widths in the range of several ten nanometers for quality evaluation of the manufacturing process. In DUV scatterometry a wave length of 193 nm is applied to determine the profile parameters of a mask. The numerical simulation of diffraction for periodic 2D structures is based on the finite element solution of the Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated as non-linear operator equation in Euclidean spaces. The operator maps the grating parameters to special efficiencies of diffracted plane wave modes. We employ a 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 simulated ones. The reconstruction quality surely depends on the angles of incidence, on the wave lengths and/or the number of propagating scattered wave modes. Moreover, the uncertainties of the measured efficiencies or phase shifts and the uncertainties of the model parameters determine the uncertainties of the reconstructed critical dimensions. Therefore a careful sensitivity analysis to find an optimal measurement configuration for scatterometry is crucial and will be discussed by numerical examples and first experiences with measured DUV data.

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