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The solution of the inverse problem in scatterometry employing deep ultraviolet light (DUV) is discussed, i.e. we
consider the determination of periodic surface structures from light diffraction patterns. With decreasing dimensions
of the structures on photo lithography masks and wafers, increasing demands on the required metrology
techniques arise. Scatterometry as a non-imaging indirect optical method is applied to periodic line structures
in order to determine the sidewall angles, heights, and critical dimensions (CD), i.e., the top and bottom widths.
The latter quantities are typically in the range of tens of nanometers. All these angles, heights, and CDs are the
fundamental figures in order to evaluate the quality of the manufacturing process. To measure those quantities
a DUV scatterometer is used, which typically operates at a wavelength of 193 nm. The diffraction of light by
periodic 2D structures can be simulated using the finite element method for the Helmholtz equation. The corresponding
inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Fixing
the class of gratings and the set of measurements, this inverse problem reduces to a finite dimensional nonlinear
operator equation. Reformulating the problem as an optimization problem, a vast number of numerical schemes
can be applied. Our tool is a sequential quadratic programing (SQP) variant of the Gauss-Newton iteration. In
a first step, in which we use a simulated data set, we investigate how accurate the geometrical parameters of an
EUV mask can be reconstructed, using light in the DUV range. We then determine the expected uncertainties
of geometric parameters by reconstructing from simulated input data perturbed by noise representing the estimated
uncertainties of input data. In the last step, we use the measurement data obtained from the new DUV
scatterometer at PTB to determine the geometrical parameters of a typical EUV mask with our reconstruction
algorithm. The results are compared to the outcome of investigations with two alternative methods namely EUV
scatterometry and SEM measurements.
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