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 Delta phi are observed as the thickness of the amorphous C films decreases which cannot be described by the well-known equation Delta phi = C-E V(0)t (V-0: mean inner Coulomb potential of the material. t: sample thickness). Data plotted in a Delta phi vs. t diagram can be well-fitted by a modified equation Delta phi = C-E V(0)t + phi(add). The mean inner Coulomb potential of the amorphous carbon with a density of 1.75 g/cm(3) 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 phi(add) 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 phi(add). (c) 2005 Elsevier B.V. All rights reserved.