Electron holography—basics and applications

Abstract

Despite the huge progress achieved recently by means of the corrector for aberrations, allowing now a true atomic resolution of 0.1 nm, hence making it an unrivalled tool for nanoscience, transmission electron microscopy (TEM) suffers from a severe drawback: in a conventional electron micrograph only a poor phase contrast can be achieved, i.e. phase structures are virtually invisible. Therefore, conventional TEM is nearly blind for electric and magnetic fields, which are pure phase objects. Since such fields provoked by the atomic structure, e.g. of semiconductors and ferroelectrics, largely determine the solid state properties, hence the importance for high technology applications, substantial object information is missing. Electron holography in TEM offers the solution: by superposition with a coherent reference wave, a hologram is recorded, from which the image wave can be completely reconstructed by amplitude and phase. Now the object is displayed quantitatively in two separate images: one representing the amplitude, the other the phase. From the phase image, electric and magnetic fields can be determined quantitatively in the range from micrometre down to atomic dimensions by all wave optical methods that one can think of, both in real space and in Fourier space. Electron holography is pure wave optics. Therefore, we discuss the basics of coherence and interference, the implementation into a TEM, the path of rays for recording holograms as well as the limits in lateral and signal resolution. We outline the methods of reconstructing the wave by numerical image processing and procedures for extracting the object properties of interest. Furthermore, we present a broad spectrum of applications both at mesoscopic and atomic dimensions. This paper gives an overview of the state of the art pointing at the needs for further development. It is also meant as encouragement for those who refrain from holography, thinking that it can only be performed by specialists in highly specialized laboratories. In fact, a modern TEM built for atomic resolution and equipped with a field emitter or a Schottky emitter, well aligned by a skilled operator, can deliver good holograms. Running commercially available image processing software and mathematics programs on a laptop-computer is sufficient for reconstruction of the amplitude and phase images and extracting desirable object information.

In situ electron holography study of charge distribution in high-κ charge-trapping memory

“…As discussed below, using electron beam from Al gate as reference wave will not confuse the analysis of charge-induced phase modulation in the high-k dielectric film. It also avoids the risk of stray field disturbance in the conventional scheme where the phase of the vacuum reference wave could be distorted by the stray field of gate or electrode 49 but the phase resolution is sacrificed because of the coherence deterioration of the penetrating wave 50 . Thus, at least 20 retrieved phase images for each bias were averaged to obtain the final phase distribution, including 0 V image, which was subtracted as the 'background' from the phase maps under bias.…”

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

“…(1), C E is a constant that depends on the microscope accelerating voltage and takes a value of 6.53 Â 10 6 rad V À1 m À1 at 300 kV, while V and A z are the electrostatic potential and the component of the magnetic vector potential in the electron beam direction z, respectively. [14][15][16] Recently, Beleggia et al 17 showed that the magnitude and direction of the electric field around the tip of an electrically biased ellipsoidal metallic needle can be measured by fitting simulations based on theoretical models for the charge density distribution along the needle to electron holographic phase images or Lorentz micrographs. Here, we use a modelindependent approach 18 to determine the charge density distribution along an electrically biased Fe APT needle directly from recorded phase images.…”

Thin-Film Phase Plates for Transmission Electron Microscopy Fabricated from Metallic Glasses

“…In the image plane, a hologram is formed, from which φ PP can be extracted. Details on the experimental procedure and the hologram evaluation are described in review articles [23,24]. substrate.…”