Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography.

The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams.

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50 nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

Electron-beam-induced charging of an Al2O3 nanotip studied using off-axis electron holography.

Electrostatic charging of specimens during electron, photon or ion irradiation is a complicated and poorly understood phenomenon, which can affect the acquisition and interpretation of experimental data and alter the functional properties of the constituent materials. It is usually linked to secondary electron emission, but also depends on the geometry and electrical properties of the specimen. Here, we use off-axis electron holography in the transmission electron microscope to study electron-beam-induced charging of an insulating Al2O3 nanotip on a conducting support. The measurements are performed under parallel electron illumination conditions as a function of specimen temperature, electron dose, primary electron energy and surface cleanliness. We observe a lack of reproducibility of charge density measurements after cycling the specimen temperature. Surprisingly, we find both positively and negatively charged regions in closely adjacent parts of the specimen.

A sorter for electrons based on magnetic elements.

The orbital angular momentum (OAM) sorter is an electron optical device for the measurement of an electron's OAM. It is based on two phase elements, which are referred to as an "unwrapper" and a "corrector" and are located in Fourier conjugate planes. The simplest implementation of the sorter is based on electrostatic phase elements, such as a charged needle for the unwrapper and electrodes with alternating charges or potentials for the corrector. Here, we use a formal analogy between phase shifts introduced by charges and vertical currents to propose alternative designs for the sorter elements, which are based on phase shifts introduced by magnetic fields. We use this concept to provide a general guide for phase element design, which promises to provide improved reliability of phase control in electron optics.

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.

Quantitative measurement of charge accumulation along a quasi-one-dimensional W5O14 nanowire during electron field emission.

We use an electron holographic method to determine the charge distribution along a quasi-one-dimensional W5O14 nanowire during in situ field emission in a transmission electron microscope. The results show that the continuous charge distribution along the nanowire is not linear, but that there is an additional accumulation of charge at its apex. An analytical expression for this additional contribution to the charge distribution is proposed and its effect on the field enhancement factor and emission current is discussed.

The Young-Feynman controlled double-slit electron interference experiment.

The key features of quantum mechanics are vividly illustrated by the Young-Feynman two-slit thought experiment, whose second part discusses the recording of an electron distribution with one of the two slits partially or totally closed by an aperture. Here, we realize the original Feynman proposal in a modern electron microscope equipped with a high brightness gun and two biprisms, with one of the biprisms used as a mask. By exciting the microscope lenses to conjugate the biprism plane with the slit plane, observations are carried out in the Fraunhofer plane with nearly ideal control of the covering of one of the slits. A second, new experiment is also presented, in which interference phenomena due to partial overlap of the slits are observed in the image plane. This condition is obtained by inserting the second biprism between the two slits and the first biprism and by biasing it in order to overlap their images.

Comment on 'electron holography on dynamic motion of secondary electrons around sciatic nerve tissues'.

We present an alternative interpretation of the holographic phase dislocation loops revealed by Shindo et al. [J. Electron Microsc. 56(1): 1-5 (2007)] around a charged sample. Our interpretation does not involve the motion of secondary electrons around a charged object. It relates, instead, to fluctuating charges on the sample and to the resulting Moiré-type patterns in the hologram.

Fine electron biprism on a Si-on-insulator chip for off-axis electron holography.

Off-axis electron holography allows both the amplitude and the phase shift of an electron wavefield propagating through a specimen in a transmission electron microscope to be recovered. The technique requires the use of an electron biprism to deflect an object wave and a reference wave to form an interference pattern. Here, we introduce an approach based on semiconductor processing technology to fabricate fine electron biprisms with rectangular cross-sections. By performing electrostatic calculations and preliminary experiments, we demonstrate that such biprisms promise improved performance for electron holography experiments.

Tunable Ampere phase plate for low dose imaging of biomolecular complexes.

A novel device that can be used as a tunable support-free phase plate for transmission electron microscopy of weakly scattering specimens is described. The device relies on the generation of a controlled phase shift by the magnetic field of a segment of current-carrying wire that is oriented parallel or antiparallel to the electron beam. The validity of the concept is established using both experimental electron holographic measurements and a theoretical model based on Ampere's law. Computer simulations are used to illustrate the resulting contrast enhancement for studies of biological cells and macromolecules.

Generation of electron vortex beams using line charges via the electrostatic Aharonov-Bohm effect.

It has recently been shown that an electron vortex beam can be generated by the magnetic field surrounding the tip of a dipole-like magnet. This approach can be described using the magnetic Aharonov-Bohm effect and is associated with the fact that the end of a long magnetic rod can be treated approximately as a magnetic monopole. However, it is difficult to vary the magnetisation of the rod in such a setup and the electron beam vorticity is fixed for a given tip shape. Here, we show how a similar behaviour, which has the advantage of easy tuneability, can be achieved by making use of the electrostatic Aharonov-Bohm effect associated with an electrostatic dipole line. We highlight the analogies between the magnetic and electrostatic cases and use simulations of in-focus, Fresnel and Fraunhofer images to show that a device based on two parallel, oppositely charged lines that each have a constant charge density can be used to generate a tuneable electron vortex beam. We assess the effect of using a dipole line that has a finite length and show that if the charge densities on the two lines are different then an additional biprism-like effect is superimposed on the electron-optical phase.

Prospects for quantitative and time-resolved double and continuous exposure off-axis electron holography.

The technique of double exposure electron holography, which is based on the superposition of two off-axis electron holograms, was originally introduced before the availability of digital image processing to allow differences between electron-optical phases encoded in two electron holograms to be visualised directly without the need for holographic reconstruction. Here, we review the original method and show how it can now be extended to permit quantitative studies of phase shifts that oscillate in time. We begin with a description of the theory of off-axis electron hologram formation for a time-dependent electron wave that results from the excitation of a specimen using an external stimulus with a square, sinusoidal, triangular or other temporal dependence. We refer to the more general method as continuous exposure electron holography, present preliminary experimental measurements and discuss how the technique can be used to image electrostatic potentials and magnetic fields during high frequency switching experiments.

Elastic and inelastic electrons in the double-slit experiment: A variant of Feynman's which-way set-up.

Modern nanotechnology tools allowed us to prepare slits of 90 nm width and 450 nm spacing in a screen almost completely opaque to 200 keV electrons. Then by covering both slits with a layer of amorphous material and carrying out the experiment in a conventional transmission electron microscope equipped with an energy filter we can demonstrate that the diffraction pattern, taken by selecting the elastically scattered electrons, shows the presence of interference fringes, but with a bimodal envelope which can be accounted for by taking into account the non-constant thickness of the deposited layer. However, the intensity of the inelastically scattered electrons in the diffraction plane is very broad and at the limit of detectability. Therefore the experiment was repeated using an aluminum film and a microscope also equipped with a Schottky field emission gun. It was thus possible to observe also the image due to the inelastically scattered electron, which does not show interference phenomena both in the Fraunhofer or Fresnel regimes. If we assume that inelastic scattering through the thin layer covering the slits provides the dissipative process of interaction responsible for the localization mechanism, then these experiments can be considered a variant of the Feynman which-way thought experiment.

Tunable caustic phenomena in electron wavefields.

Novel caustic phenomena, which contain fold, butterfly and elliptic umbilic catastrophes, are observed in defocused images of two approximately collinear oppositely biased metallic tips in a transmission electron microscope. The observed patterns depend sensitively on defocus, on the applied voltage between the tips and on their separation and lateral offset. Their main features are interpreted on the basis of a projected electrostatic potential model for the electron-optical phase shift.

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.

Sommerfeld revisited: a new approach to the third-order Seidel aberrations.

In following a suggestion of Sommerfeld, who was able to derive the paraxial properties for points on the optic axis from the existence and continuity of wave fronts satisfying the eikonal equation, it will be shown how the whole set of the third-order Seidel aberrations of a centered optical system made of refracting surfaces of revolution can be obtained if the series expansion in the radial coordinates is continued up to the fourth order.