The solution of the inverse problem in scatterometry, i.e. the determination of periodic surface structures from light
diffraction patterns, is incomplete without knowledge of the uncertainties associated with the reconstructed surface
parameters. With decreasing feature sizes of lithography masks, increasing demands on metrology techniques arise.
Scatterometry as a non-imaging indirect optical method is applied to periodic line-space structures in order to determine
geometric parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the
manufacturing process. The numerical simulation of the diffraction process 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 a non-linear
operator equation in Euclidean spaces. The operator maps the grating 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 simulated ones. The reconstruction properties and
the convergence of the algorithm, however, is controlled by the local conditioning of the non-linear mapping and the
uncertainties of the measured efficiencies or phase shifts. In particular, the uncertainties of the reconstructed geometric
parameters essentially depend on the uncertainties of the input data and can be estimated by various methods. We
compare the results obtained from a Monte Carlo procedure to the estimations gained from the approximative covariance
matrix of the profile parameters close to the optimal solution and apply them to EUV masks illuminated by plane waves
with wavelengths in the range of 13 nm.