Multiple scattering in low-energy electron holography

The theory of the low-energy electron point source (LEEPS) microscope is reformulated in matrix form to readily account for multiple scattering. An algorithm is developed for the storage of the structure matrix and an iterative method is used to solve the matrix equation for the structure factor. Examples of small and large clusters of atoms are given to compare single and multiple scattering. A Kirchhoff-Helmholtz transform is used for the reconstruction. We find that in some cases the multiple scattering is too strong and reconstruction is not possible. We give examples which show that, even when multiple scattering is important, one can still obtain reconstructions that reveal the atomic structure both along and lateral to the optical axis. We also compare our results with those found in LEED.     

Coherent low-energy electron diffraction on individual nanometer sized objects

Today's structural biology techniques require averaging over millions of molecules to obtain detailed structural information. Derivation of the molecular structure from a scattering experiment with just one single 3D-molecule imposes major challenges. Coherent and damage-free radiation is needed to ensure sufficient elastic scattering events before destroying the molecule and a means to solve the phase problem is wanted. We have devised such a scheme using coherent low-energy electrons shaped into a collimated beam by an electrostatic microlens. Initial experiments using a carbon nanotube sample demonstrate the feasibility of coherent low-energy electron diffraction on an individual nanometer-sized object.     

Digital in-line holography on amplitude and phase objects prepared with electron beam lithography

We report on the fabrication and characterization of amplitude and phase samples consisting of well defined Au or Al features formed on ultrathin silicon nitride membranes. The samples were manufactured using electron beam lithography, metallization and a lift-off technique, which allow precise lateral control and thickness of the metal features. The fabricated specimens were evaluated by conventional microscopy, atomic force microscopy and with the digital in-line holography set-up at the Lund Laser Centre. The latter uses high-order harmonic generation as a light source, and is capable of recovering both the shape and phase shifting properties of the samples. We report on the details of the sample production and on the imaging tests with the holography set-up.     

Past,present and future of electron holography

Electron holography, originally devised for improving the resolution of electron microscopes, progressed significantly with the advent of the ‘coherent’ field-emission electron beam. This permitted high-resolution microscopy (Lichte, 1986), and opened up such new fields as high-precision electron interferomentry. This paper briefly describes the developments in electron holography.     

Semiconductor dopant profiling by off-axis electron holography

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.     

Observation of surfaces by reflection electron holography.

Reflection electron holography is described as a method to observe sub-A surface morphology. Phase shift of a Bragg-reflected electron wave was measured by means of holographic interferometry using an electron microscope equipped with a field emission electron gun and an electron biprism. A short wavelength of high energy electrons is the essential key to the high vertical sensitivity of this method, since geometrical path differences produced by the surface topography are measured in units of wavelengths in interferometrical measuring. Phase shift at a monoatomic step and the displacement field around a dislocation emerging on the surface were observed.     

Morphology visualization of irregular shape bacteria by electron holography and tomography

In the current work, irregular morphology of Staphylococcus aureus bacteria has been visualized by phase retrieval employing off‐axis electron holography (EH) and 3D reconstruction electron tomography using high‐angle annular dark field scanning transmission electron microscopy (HAADF‐STEM). Bacteria interacting with gold nanoparticles (AuNP) acquired a shrunken or irregular shape due to air dehydration processing. STEM imaging shows the attachment of AuNP on the surface of cells and suggests an irregular 3D morphology of the specimen. The phase reconstruction demonstrates that off‐axis electron holography can reveal with a single hologram the morphology of the specimen and the distribution of the functionalized AuNPs. In addition, EH reduces significantly the acquisition time and the cumulative radiation damage (in three orders of magnitude) over biological samples in comparison with multiple tilted electron expositions intrinsic to electron tomography, as well as the processing time and the reconstruction artifacts that may arise during tomogram reconstruction.     

Off-axis and inline electron holography: Experimental comparison

Electron holography is a very powerful technique for mapping static electric and magnetic potentials down to atomic resolution. While electron holography is commonly considered synonymous with its off-axis variant in the high energy electron microscopy community, inline electron holography is widely applied in low-energy electron microscopy, where the realization of the off-axis setup is still an experimental challenge. This paper demonstrates that both inline and off-axis holography may be used to recover amplitude and phase shift of the very same object, in our example latex spheres of 90 and 200 nm in diameter, producing very similar results, provided the object does not charge under the electron beam.     

Off-axis and inline electron holography: A quantitative comparison

Capable of quantitatively imaging static magnetic and electric potentials and even strain electron holography is a very versatile and powerful TEM technique. In this paper we compare off-axis electron holography with a recently developed focal series reconstruction algorithm and phase retrieval based on the transport of intensity equation. Based on theoretical considerations and simulations we compare the different techniques with respect to parameters such as the coherence requirements, field of view, resolution, noise properties, and other required experimental conditions.     

Determination of the mean inner potential in III-V semiconductors by electron holography

The mean inner potential of GaAs(14.18V), InAs(14.50V), GaP(14.35V) and InP(14.50V) has been measured by transmission electron holography using the phase shift of the (000)-beam of the first hologram sideband. To provide a defined specimen geometry we used 90 degrees wedges obtained by the cleavage technique. The exact excitation condition as well as the acceleration voltage of the electrons were determined from convergent beam electron diffraction images. The magnification is extracted from two-beam lattice fringe images and dynamical effects are taken into account by Bloch-wave calculations.     

On the interpretation of magnetic and electric fields imaged by low-magnification off-axis electron holography

The interpretation of magnetic and electric fields imaged by off-axis electron holography is not always straightforward. We will demonstrate this by some examples of possible misinterpretations which can result from, for example, comparing a hologram with a second one acquired such that the reference wave travelled on the opposite side of the sample, the diffraction of the electron beam at the biprism fibre, not centring an area to the true centre of the sideband when reconstructing the image wave by Fourier optics, quantification of 'magnetic' and 'electric' phases, procedures to separate electric from magnetic phases and dislocations in the interference fringes of the hologram.     

Off-axis electron holography of magnetic nanowires and chains, rings, and planar arrays of magnetic nanoparticles

A selection of recent results illustrating the application of off-axis electron holography to the study of magnetic microstructure in closely-spaced nanoparticles and nanowires is reviewed. Examples are taken from the characterization of FeNi nanoparticle chains, Co nanoparticle rings, two-dimensional arrays of naturally occurring magnetite crystals in minerals, and single crystalline Co nanowires. Approaches that can be used to separate the magnetic signal of interest from the mean inner potential contribution to the measured holographic phase shift are described, and the spatial and phase resolution that can be achieved are discussed.     

The contribution of phonon scattering to high-resolution images measured by off-axis electron holography

The contribution of electrons that have been phonon scattered to the lattice fringe amplitude and the background intensity of a high-resolution electron microscope (HREM) image is addressed experimentally through the analysis of a defocus series of energy-filtered off-axis electron holograms. It is shown that at a typical specimen thickness used for HREM imaging approximately 15% of the electrons that contribute to an energy-filtered image have been phonon scattered. At this specimen thickness, the phonon-scattered electrons contribute a lattice image of opposite contrast to the elastic lattice image. The overall lattice fringe contrast is then reduced to 70% of the value that it would have in the absence of phonon scattering. At higher specimen thickness, the behaviour is defocus-dependent, with the phonon image having lattice fringe contrast of either the same or the opposite sense to the elastic image as the defocus is varied.     

Determination of the mean inner potential in III-V semiconductors, Si and Ge by density functional theory and electron holography

The mean inner potentials of various III-V semiconductors, Si and Ge have been calculated by density functional theory methods. For that purpose, the Coulomb potential of slabs consisting of a crystal and vacuum region has been computed and averaged inside the crystal region. The computed values are in agreement with experimental values obtained by electron holography for Si and GaAs. For the other semiconductors, the deviations are smaller than 0.8 V. The results from density functional theory are approximately 10% smaller than the values derived from atomic scattering factors computed by Hartree Fock calculations.     

Observation of electrostatic fields by electron holography: The case of reverse-biased p-n junctions

The technique of electron holography is applied to the investigation of microelectric fields such as those associated with reverse-biased p-n junctions. Suitable electron-optical conditions were adopted in order to minimize the effect of the electrostatic fringing field on the reference wave. The electron holograms were optically processed by the method of differential interferometry.     

Precession electron diffraction: observed and calculated intensities

Theory and algorithms have been developed for performing kinematical and dynamical two-beam and multibeam dynamical simulations of precession electron diffraction patterns. Intensities in experimental precession patterns have been quantified and are shown to be less dynamical.     

Compositional analysis based on electron holography and a chemically sensitive reflection

A method for compositional analysis of low-dimensional heterostructures is presented. The suggested procedure is based on electron holography and the exploitation of the chemically sensitive (0 0 2) reflection. We apply an off-axis imaging condition with the (0 0 2) beam strongly excited and centered on the optic axis. The first side band of the hologram is centered using an "empty" reference hologram obtained for a hole of the specimen. From the centered side band we use the phase of the central (0 0 0) and the amplitude of the (0 0 2) reflections to evaluate the local composition and the local specimen thickness in an iterative and self-consistent way. Delocalization effects that lead to a shift of the spatial information of (0 0 0) and (0 0 2) reflections are taken into account. The application of the procedure is demonstrated with an AlAs/GaAs(0 0 1) superlattice with a period of 5 nm. The concentration profiles obtained are discussed in relation to segregation. The measured segregation efficiency is R = 0.51 +/- 0.02.     

Three-dimensional organization of the golgi complex observed by scanning electron microscopy

With the development of new specimen preparation techniques and improvements in instrumental resolution, scanning electron microscopy (SEM) became an effective means of studying the three-dimensional organization of the Golgi complex. When specimens prepared by the osmium-DMSO-osmium method are observed with high-resolution SEMs, cis-most cisternae of Golgi stacks appear as sieve-like plates with many small perforations. In some cell types, larger fenestrations are also present. The trans-most cisternae showed a fenestrated or retucular pattern. At the trans-side of Golgi stacks, distinctive structures, such as a well-developed tubular plexus or a single widely extended cisterna, are observed in some types of cells. In lacrimal gland cells, Golgi stacks are linked by an irregular network of anastomosing branches extending throughout the cytoplasm. In these cells, the piled cisternae seemed to be connected to each other either directly within the stack or via cisternae of other stacks. Connections between Golgi stack and rough endoplasmic reticulum (ER) were often found in our SEM observations. In nerve cells, interconnecting tubules arise from rough ER and most often fuse with the rim of the cis-cisternae of Golgi stacks.     

Simulations of scanning electron microscopy imaging and charging of insulating structures

We present a three‐dimensional simulation of scanning electron microscope (SEM) images and surface charging. First, the field above the sample is calculated using Laplace's equation with the proper boundary conditions; then, the simulation algorithm starts following the electron trajectory outside the sample by using electron ray tracing. When the electron collides with the specimen, the algorithm keeps track of the electron inside the sample by simulating the electron scattering history with a Monte Carlo code. During this phase, secondary and backscattered electrons are emitted to form an image and primary electrons are absorbed; therefore, a charge density is formed in the material. This charge density is used to recalculate the field above and inside the sample by solving the Poisson equation with the proper boundary conditions. Field equation, Monte Carlo scattering simulation, and electron ray tracing are therefore integrated in a self‐consistent fashion to form an algorithm capable of simulating charging and imaging of insulating structures. To maintain generality, this algorithm has been implemented in three dimensions. We shall apply the so‐defined simulation to calculate both the global surface voltage and local microfields induced by the scanning beam. Furthermore, we shall show how charging affects resolution and image formation in general and how its characteristics change when imaging parameters are changed. We shall address magnification, scanning strategy, and applied field. The results, compared with experiments, clearly indicate that charging and the proper boundary conditions must be included in order to simulate images of insulating features. Furthermore, we shall show that a three‐dimensional implementation is mandatory for understanding local field formation.     

Quantitative off-axis electron holography of GaAs p-n junctions prepared by focused ion beam milling

Focused Ion beam (FIB) prepared GaAs p-n junctions have been examined using off-axis electron holography. Initial analysis of the holograms reveals an experimentally determined built-in potential in the junctions that is significantly smaller than predicted from theory. In this paper we show that through combinations of in situ annealing and in situ biasing of the specimens, by varying the intensity of the incident electron beam, and by modifying the FIB operating parameters, we can develop an improved understanding of phenomena such as the electrically 'inactive' thickness and subsequently recover the predicted value of the built-in potential of the junctions.
PACS numbers: 85.30.De