Effects of Topography in Nano-Structured Thin Films: A Lorentz Transmission Electron Microscopy and Electron Holography Study

This paper aims at applying advanced transmission electron microscopy (TEM) to functional materials, such as ultra-soft magnetic films for high-frequency inductors, to reveal the structure-property relationship. The ultimate goal is to delineate a more quantitative way to obtain information of the magnetic induction and local magnetization. Nano-crystalline Fe-Zr-N films have been prepared by DC magnetron reactive sputtering with a thickness between 50 and 500 nm. Conventional TEM and selected area diffraction (SAD), reveal crystallites of sizes ranging between 2 and 30 nm. The films showed a granular or hillock type of roughness with an rms amplitude of 5 nm. In particular this paper concentrates on an analysis of phase maps in electron holography and intensity maps in Lorentz transmission electron microscopy including the thickness variation over the sample. For a particular statistical description of the roughness and values for the roughness it is shown that analytical expressions can be obtained. We demonstrate that starting from the concept of the vector potential in classical electrodynamics these results can be achieved assuming independent stationary Gaussian distributions for the height correlation functions.