Determination of layer-thickness fluctuations in Mo/Si multilayers by cross-sectional HR-TEM and X-ray diffraction

We present a method of deriving single layer thickness fluctuations of Mo/Si EUV multilayers from cross-sectional high-resolution transmission electron microscopy micrographs. The obtained thickness values for each layer are used in a layer model to calculate the grazing-incidence X-ray reflectivity (GIXRR) and the corresponding at-wavelength-reflectivity curves. Comparison with XRR measurements shows the strong effect of thickness fluctuations on the intensity of the secondary Kiessig fringes and the main Bragg maxima. This model results in substantially better reflectivity simulations than the standard periodic four-layer model or the assumption of statistically distributed (random) thickness errors. Results for reflectivity curves at 13-nm wavelength are discussed in terms of peak reflectivity, peak shift and further changes in the shape of the reflectivity curve. PACS 68.65.Ac; 68.37.Lp; 41.50.+h