X-ray absorption in pillar shaped transmission electron microscopy specimens

The dependence of the X-ray absorption on the position in a pillar shaped transmission electron microscopy specimen is modeled for X-ray analysis with single and multiple detector configurations and for different pillar orientations relative to the detectors. Universal curves, applicable to any pillar diameter, are derived for the relative intensities between weak and medium or strongly absorbed X-ray emission. For the configuration as used in 360° X-ray tomography, the absorption correction for weak and medium absorbed X-rays is shown to be nearly constant along the pillar diameter. Absorption effects in pillars are about a factor 3 less important than in planar specimens with thickness equal to the pillar diameter. A practical approach for the absorption correction in pillar shaped samples is proposed and its limitations discussed. The modeled absorption dependences are verified experimentally for pillars with HfO2 and SiGe stacks.