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In all investigations that we performed over the past years; it has been clearly demonstrated that the off-line mask-to-mask overlay as determined on the Zeiss PROVE  tool correlates very well with the on-wafer measurements. It all started off with a correlation study utilizing wafer alignment marks. Wafer alignment marks are metrology structures that can be read out inside ASML scanners by the wafer alignment sensor. In that work, the impact of the reticle alignment marks required to align the mask inside the scanner was incorporated as well. An excellent correlation (R 2 > 0.96) was shown with an accuracy of 0.58-nm. This result was achieved after carefully setting up an experiment in photoresist and by ruling out any other additional overlay contributors other than mask and the scanner baseline overlay performance.After this initial success, we continued the investigation by considering µ-DBO (Diffraction Based Overlay) metrology targets that can be read out on an ASML Yieldstar (YS:375) overlay metrology tool. In this work, the complexity of the experiment was increased. Instead of using only photo resist, an industry relevant process Litho-Etch process flow was selected. The mask was written on a state-of-the-art writing tool (EBM-9000). Again, excellent correlation coefficients (R 2 > 0.92) were obtained. This time within the sub-nanometer range at wafer level.During the execution of that work, an error source that contributes to the small mismatch (< 0.14-nm) between mask and on-wafer measurements was addressed: the sampling scheme difference of the signal generating areas. While the PROVE  tool has been designed to measure local (feature) placement errors, this is not the case for an overlay metrology tool or the scanner wafer alignment sensor. For the latter two metrology systems, a position is obtained from a much larger region of interest (ROI) for which local placement errors are averaged out. The observed mismatch can easily be mitigated by increasing the number of PROVE  measurements with a small ROI to match it with the ROI of the overlay metrology tool or the wafer alignment sensor.While studying the increasing number of local registration measurements by the PROVE  tool, an interesting observation was made. The way the mask had been written on the mask e-beam writer seemed to be reflected in the residual local registration measurements! Stripes were observed that appear to be running across the full width of the mask. Since the typical dimensions of the stripes at wafer level are small compared to the areas that are used for overlay measurements and/or wafer alignment measurements, they are hard to detect on wafer by using optical techniques.In this follow-up work, we explore the correlation between mask registration measurements and the on-wafer measurement for individual device features. This means that we make another step-in complexity, the length scales of interest are now significantly below the typical dimensions of an overlay metrology target. To continue the correlation study, a larg...

An investigation of the chromatic effects in refracting optical systems naturally shows that all five Seidel aberrations vary in wavelength because they are all dependent on the refractive index. In general, the color variation of spherical aberration is denoted as spherochromatism. Besides the chromatic variation of 1st-order paraxial parameters, e.g., focal length and magnification, described by axial and lateral color, spherochromatism can also strongly affect the color correction of an optical system. However, to the best of our knowledge, the literature shows no exact analytical formula available, specifying this effect. Actually, a general 3rd-order description based on the chromatic variation of Seidel's surface contribution for spherical aberration has not yet been considered. Therefore, this paper deals with this mentioned analytical gap and provides a description of a 3rd-order surface contribution for spherochromatism. Based on this, the result is analyzed and discussed concerning the differentiating between intrinsic and induced aberration parts. In the case of spherochromatism, its 3rd-order contribution shows induced effects caused by prior summed-up primary color aberrations of the system.