A model for the interpretation of holographic and Lorentz images of tilted reverse-biased p-n junctions in a finite specimen

Design of electrostatic phase elements for sorting the orbital angular momentum of electrons

The orbital angular momentum (OAM) sorter is a new electron optical device for measuring an electron's OAM. It is based on two phase elements, which are referred to as the "unwrapper" and "corrector" and are placed in Fourier-conjugate planes in an electron microscope. The most convenient implementation of this concept is based on the use of electrostatic phase elements, such as a charged needle as the unwrapper and a set of electrodes with alternating charges as the corrector. Here, we use simulations to assess the role of imperfections in such a device, in comparison to an ideal sorter. We show that the finite length of the needle and the boundary conditions introduce astigmatism, which leads to detrimental cross-talk in the OAM spectrum. We demonstrate that an improved setup comprising three charged needles can be used to compensate for this aberration, allowing measurements with a level of cross-talk in the OAM spectrum that is comparable to the ideal case.

Phase contrast image simulations for electron holography of magnetic and electric fields

The research on flux line lattices and pancake vortices in superconducting materials, carried out within a long and fruitful collaboration with Akira Tonomura and his group at the Hitachi Advanced Research Laboratory, led us to develop a mathematical framework, based on the reciprocal representation of the magnetic vector potential, that enables us to simulate realistic phase images of fluxons. The aim of this paper is to review the main ideas underpinning our computational framework and the results we have obtained throughout the collaboration. Furthermore, we outline how to generalize the approach to model other samples and structures of interest, in particular thin ferromagnetic films, ferromagnetic nanoparticles and p-n junctions.

Electron optical phase-shifts by Fourier methods: Analytical versus numerical calculations

The theoretical framework for the computation of electromagnetic fields and electron optical phase-shifts in Fourier space has been recently applied to objects with long-range fringing fields, such as reverse-biased p-n junctions and magnetic stripe domains near a specimen edge. In addition to new analytical results, in this work, we present a critical comparison between numerical and analytical computations. The influence of explicit and implicit boundary conditions on the phase shifts and phase-contrast images is also investigated in detail.

Electron microscope calibration for the Lorentz mode

The calibration of a modern electron microscope for Lorentz microscopy observations has been performed using diffractogram, Fresnel diffraction fringe analysis and low-angle electron diffraction methods. An example related to the observations of electrostatic fields associated to a thinned reverse-biased p-n junction is also reported.

A Fourier approach to fields and electron optical phase-shifts calculations

The Fourier method is applied to calculate fields and electron optical phase shifts in specimens having long-range electromagnetic fields, like reverse biased p-n junctions or stripe magnetic domains. It is shown that this approach not only allows to take into account rather easily the effect of the fringing fields protruding in the space around the specimen, but also to obtain solutions to interesting models in analytical form.

Quantitative electron holography of biased semiconductor devices

Electron holography is used to measure electrostatic potential profiles across reverse-biased Si p-n junctions in situ in the transmission electron microscope. A novel sample geometry based on focused ion-beam milling is developed, and results are obtained for a range of sample thicknesses and bias voltages to allow the holographic contrast to be interpreted. The physical and electrical nature of the sample surface, which is affected by sample preparation and electron beam irradiation, is discussed.