Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract
Gross, Hermann
The characterisation of nanostructured surfaces by scatterometry is an established method in wafer metrology. From measured light diffraction patterns, critical dimensions (CDs) of periodic surface profiles are determined, i.e., line widths, heights and other profile properties in the sub-micrometer range. Along with the values for the reconstructed CDs, the estimation of their uncertainties is essential for evaluating the quality of the method. As structures become smaller and smaller, shorter wavelengths like extreme ultraviolet (EUV) at 13.5 nm ensure that the measured light diffraction pattern is sensitive with regard to the structure details. Obviously, the impact of structure roughness with amplitudes in the range of a few nanometers can no longer be neglected in the course of the profile reconstruction. To model line roughness, i.e., line edge and line width roughness, a rigorous finite element (FEM) approach and complementary simulations of light diffraction patterns based on a 2D-Fourier transform (FTM) are presented. In the FEM approach a large number of simulations are performed for computational domains with large periods, each containing many pairs of line and space with stochastically chosen widths. These structures are composed of TaN-absorber lines with an underlying MoSi-multilayer stack representing a typical EUV mask. Mean efficiencies and the variances of the efficiencies in dependence on different degrees of roughness are calculated. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances are observed. In particular, we obtain a simple analytical expression for the bias in the mean efficiencies and for the additional uncertainty contribution stemming from line roughness. In the 2D FTM approach the diffraction pattern for samples of rough apertures composed of several slits can be calculated very efficiently. The rough apertures are representing binary 2D gratings. The roughness of the edges of the aperture slits is modelled by a power spectrum density (PSD) function, which is often used in metrology of rough geometries. Using the formula for this PSD, the roughness depends on three parameters, namely on the standard deviation, the correlation length and the roughness exponent. Compared to diffraction pattern of the unperturbed aperture, the rough samples are revealing the same systematic decrease of the mean efficiencies as those of the rigorous FEM simulations executed with a relatively crude and simple model of roughness. As a consequence, to provide more reliable values for the reconstructed critical profile parameters and their estimated uncertainties, the observed bias has to be included into the model. We compare different models for EUV scatterometry at a photomask. Using maximum likelihood estimation to reconstruct the parameters of interest, we successively extend our model to compensate for the systematic errors caused by line roughness and further effects. Comparing the reconstructed CDs of the different models and the estimated uncertainties, we demonstrate the improvements in terms of simulated and measurement data. par (joint with M.-A. Henn, S. Heidenreich, A. Rathsfeld and M. Bär)