Towards understanding of charging effects of thin‐film phase plates
Authors: Janzen Roland , Schundelmeier Jonas , Hettler Simon , Dries Manuel , Gerthsen Dagmar 
Published: December 2016

In the past few years, physical phase plates (PP) have become a viable tool to enhance the contrast of weak‐phase objects in transmission electron microscopy (TEM). Here we focus on thin‐film PPs where the mean inner potential is exploited to impose a phase shift on electrons propagating through the PP [1]. The application of thin‐film PPs is hampered by deviations of the phase shift from its desired value which occur due to charging of the thin film. Our experimental approach to overcome charging of thin‐film PPs was using the metallic glass alloy Pd77.5Cu6.0Si16.5 (PCS) with a high specific conductivity of 1.18×10
6
S/m [2] as PP material. However, Hilbert PPs fabricated from thin PCS films nevertheless show pronounced distortions of the Thon‐ring system during illumination with 200 keV electrons. These observations initiated the development of a theoretical model to obtain an improved understanding of charging, which is presented in this work.

Charging is described by assuming a charge‐dipole layer to be present at the PP. A possible source for such a dipole layer could be an insulating contamination layer on top of the PCS film in the illuminated PP region which could capture and fix low‐energy secondary electrons generated by the primary electrons in the PCS film. Together with its positive mirror charge in the grounded electrically conducting PCS film this fixed charge would form a dipole layer. The dipole strength is assumed to be proportional to the current density distribution in the back focal plane which can be qualitatively obtained from a diffraction pattern. The proportionality factor for the dipole strength is a fit parameter denoted as phase mask amplitude in the following.
As a test of our model we compare power spectra obtained from an experimental image of an amorphous carbon (aC) thin‐film test object with a simulation based on our model. The experimental reference image was obtained by using a PCS film‐based Hilbert PP installed in the back focal plane of a Philips CM 200 FEG/ST transmission electron microscope. In the simulation we assume the Hilbert PP to be illuminated by the current density distribution given by the diffraction pattern and calculate the phase shift in the back focal plane. The resulting dipole strength distribution is then fed into an image simulation procedure which yields simulated power spectra as a function of the phase mask amplitude. The latter is optimized by a comparison with the experimental reference. The experimental reference and calculated power spectra are compared pixel by pixel. The sum of all pixel comparisons belonging to one pair of power spectra serves as measure of agreement, which is plotted for different phase mask amplitudes in Figure 1 for the region below the cut‐on frequency. Best agreement of almost 75% is obtained. This is remarkable taking into account that experimental and simulated spectra (based on noisy input for the illumination data) contain noise.
Figure 2 shows a montage of a simulated and experimental power spectrum. Two regions, below and above the cut‐on frequency, can be distinguished in the power spectra. The cut‐on frequency is given by the distance between the PP edge and the zero‐order beam and is marked by vertical white lines. Note the good agreement between experimental and simulated spectra, especially below the cut‐on frequency.
Overall our method seems to be a promising approach to analyze and explain phase shift distortions due to charging in thin‐film PP applications.