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Off-axis electron holography has evolved into a powerful electron-microscopy-based technique for characterizing electromagnetic fields with nanometer-scale resolution. In this paper, we present a review of the application of off-axis electron holography to the quantitative measurement of electrostatic potentials and charge density distributions. We begin with a short overview of the theoretical and experimental basis of the technique. Practical aspects of phase imaging, sample preparation and microscope operation are outlined briefly. Applications of off-axis electron holography to a wide range of materials are then described in more detail. Finally, challenges and future opportunities for electron holography investigations of electrostatic fields and charge density distributions are presented., (Copyright © 2019. Published by Elsevier B.V.)

A reconstruction technique for off-axis electron holography not requiring Fourier transformation is presented. Background intensity and amplitude modulation recorded in a hologram are normalized using an envelope function, and a cosine-function image corresponding to interference fringes is retrieved from the hologram. A reconstructed phase image is then calculated from the retrieved cosine image. After phase unwrapping, the phases due to carrier frequency and Fresnel diffraction from the biprism are removed using a reference hologram, and the corrected phase image is obtained. One advantage of this method is that the spatial resolution does not rely on the interference fringe spacing. Another advantage is that the phase image has no artifacts due to windowing of the sideband, which occurs in the usual Fourier-transformation method. Details of the calculation process and demonstrations of the method using a latex sphere particle and self-assembled Co nanoparticles are described.

The three-dimensional (3D) morphology of a nanometer-sized object can be obtained using electron tomography. Variations in composition or density of the object cause variations in the reconstructed intensity. When imaging homogeneous objects, variations in reconstructed intensity are caused by the imaging technique, imaging conditions, and reconstruction. In this paper, we describe data acquisition, image processing, and 3D reconstruction to obtain and compare tomograms of magnetite crystals from bright field (BF) transmission electron microscopy (TEM), annular dark-field (ADF) scanning transmission electron microscopy (STEM), and high-angle annular dark field (HAADF) STEM tilt series. We use histograms, which plot the number of volume elements (voxels) at a given intensity vs. the intensity, to measure and quantitatively compare intensity distributions among different tomograms. In combination with numerical simulations, we determine the influence of maximum tilt angle, tilt increment, contrast changes with tilt (diffraction contrast), and the signal-to-noise ratio (SNR) as well as the choice of the reconstruction approach (weighted backprojection (WB) and sequential iterative reconstruction technique (SIRT)) on the histogram. We conclude that because ADF and HAADF STEM techniques are less affected by diffraction, and because they have a higher SNR than BF TEM, they are better suited for tomography of nanometer-sized crystals.

Off-axis electron holography is used to characterize a linear array of transistors, which was prepared for examination in cross-sectional geometry in the transmission electron microscope (TEM) using focused ion beam (FIB) milling from the substrate side of the semiconductor device. The measured electrostatic potential is compared with results obtained from TEM specimens prepared using the more conventional 'trench' FIB geometry. The use of carbon coating to remove specimen charging effects, which result in electrostatic fringing fields outside 'trench' specimens, is demonstrated. Such fringing fields are not observed after milling from the substrate side of the device. Analysis of the measured holographic phase images suggests that the electrically inactive layer on the surface of each FIB-milled specimen typically has a thickness of 100 nm.

The Gerchberg-Papoulis (GP) iterative algorithm is applied to electron holographic reconstruction to supplement the Fourier-transform method. The GP algorithm can recover the phase to high accuracy using simulated holograms. This method is useful when a region of known amplitude is present, such as a region of vacuum or uniform thickness. Modulations of the phase on the order of 0.1 rad can be corrected significantly using this algorithm.

Silicon wafers with a complex but known dopant profile were used to explore possible methods for improving the reliability of off-axis electron holography for quantitative determination of electrostatic potential profiles in doped semiconductor devices. The variability of results from nominally identical structures was attributed to local charging and associated external fields, forcing the development of a more robust approach to hologram analysis that incorporated an additional phase correction factor rather than rely on vacuum for phase flattening. Consistent results in close agreement with simulated profiles based on measured dopant distributions could then be obtained. Carbon coating was shown to be effective in reducing accumulation of charge caused by emission of secondary electrons. Overall, this work demonstrates that reliable potential profiles from unbiased samples should be obtainable on a routine basis provided that regions suitable for flattening of the phase profile can be identified.