Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.

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Scatterometry as a non-imaging indirect optical method in wafer metrology is also relevant to lithography masks designed for extreme ultraviolet lithography, where light with wavelengths in the range of 13 nm is applied. The solution of the inverse problem, i.e. the determination of periodic surface structures regarding critical dimensions (CD) and other profile properties from light diffraction patterns, is incomplete without knowledge of the uncertainties associated with the reconstructed parameters. 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. The inverse problem can be formulated as a nonlinear operator equation in Euclidean space. 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. We apply our reconstruction algorithm for the measurement of a typical EUV mask composed of TaN absorber lines of about 80 nm height, a period in the range of 420 nm–840 nm, and with an underlying MoSi-multilayer stack of 300 nm thickness. 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. Finally, we analyze the influence of uncertainties in the widths of the multilayer stack by the Monte Carlo method.

Accurate and traceable measurements of critical dimension (CD) and sidewall profile of extreme ultraviolet (EUV) photomask structures using atomic force microscopes (AFMs) are introduced in this paper. An instrument complementarily applied with two kinds of AFM techniques, the CD-AFM and the tilting-AFM, has been developed. High measurement stability of the instrument is demonstrated, for instance, the long-term CD stability is better than 1 nm over 500 successive measurements over 55 h. To traceably calibrate the effective tip geometry, transmission electron microscopes-based method is applied, which uses either the silicon crystal lattice or the structure pitch value calibrated by metrological AFMs as an internal scale. Several grating patterns with different nominal CDs and line/space ratios of an EUV photomask have been measured using the developed methods. A data evaluation method with considered higher order tip effect due to the non-vertical sidewall is introduced. Detailed measurement results of a test EUV photomask, such as middle CD, left and right sidewall angle, feature height, line edge roughness and edge profiles are given. Finally, the AFM results are compared to that of a PTB EUV scatterometer. The comparison of the middle CD yields a linear relation within a spread of only about ±2 nm and an offset of the absolute values below 3 nm. For the sidewall angle, both methods yield consistent results within a range of about 2°.

The real part of the refractive index (RI) of aqueous solutions of human hemoglobin is computed from their absorption spectra in the wavelength range 250 nm-1100 nm using the Kramers-Kronig (KK) relations and the corresponding uncertainty analysis is provided. The strong ultraviolet (UV) and infrared absorbance of the water outside this spectral range were taken into account in a previous study employing KK relations. We improve these results by including the concentration dependence of the water absorbance as well as by modeling the deep UV absorbance of hemoglobin's peptide backbone. The two free parameters of the model for the deep UV absorbance are fixed by a global fit.

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ABSTRACT:Urban terrain reconstruction has many applications in areas of civil engineering, urban planning, surveillance and defense research. Therefore the needs of covering ad-hoc demand and performing a close-range urban terrain reconstruction with miniaturized and relatively inexpensive sensor platforms are constantly growing. Using (miniaturized) unmanned aerial vehicles, (M)UAVs, represents one of the most attractive alternatives to conventional large-scale aerial imagery. We cover in this paper a four-step procedure of obtaining georeferenced 3D urban models from video sequences. The four steps of the procedure -orientation, dense reconstruction, urban terrain modeling and geo-referencing -are robust, straight-forward, and nearly fully-automatic. The two last steps -namely, urban terrain modeling from almost-nadir videos and co-registration of models -represent the main contribution of this work and will therefore be covered with more detail. The essential substeps of the third step include digital terrain model (DTM) extraction, segregation of buildings from vegetation, as well as instantiation of building and tree models. The last step is subdivided into quasiintrasensorial registration of Euclidean reconstructions and intersensorial registration with a geo-referenced orthophoto. Finally, we present reconstruction results from a real data-set and outline ideas for future work.