Electron holography of thin amorphous carbon films: Measurement of the mean inner potential and a thickness-independent phase shift

The phase shift induced by thin amorphous carbon films with thicknesses between 1 and 16 nm was measured by electron holography in a transmission electron microscope. Large phase shifts Δφ   are observed as the thickness of the amorphous C films decreases which cannot be described by the well-known equation Δφ=CEV0tΔφ=CEV0t (V0: mean inner Coulomb potential of the material, t  : sample thickness). Data plotted in a ΔφΔφ vs. t   diagram can be well-fitted by a modified equation Δφ=CEV0t+φaddΔφ=CEV0t+φadd. The mean inner Coulomb potential of the amorphous carbon with a density of 1.75 g/cm3 was determined to be 9.09 V which is consistent with previous experimental data for amorphous carbon with a higher density. The thickness-independent phase offset φaddφadd of 0.497 rad is large for amorphous carbon under the given experimental conditions. We suggest that a surface-related electrostatic potential is responsible for the thickness-independent contribution φaddφadd.