Three-Dimensional Atomic Imaging by Electron Holography

We have presented the principles of three-dimensional atomic imaging by electron-emission holography. Unlike conventional methods which use the Helmholtz-Kirchhoff integral theorem, we invert photoelectron and Auger-electron diffraction patterns to reconstruct three-dimensional images of surface and interface atoms by three-dimensional Fourier transformation. Direct structural information of near -neighbor atoms can be obtained. The structure so determined provides a useful starting point for refinement by diffraction methods, thus avoiding the cumbersome trial-and-error process. With the phase-shift correction, the small-window energy-extension process (SWEEP) is provided for forward -scattering electrons and back-scattering electrons. This method extends the usable range in phase space for three -dimensional image reconstruction. As an extension of the SWEEP method, we introduce a method for spatially resolved imaging of energy-dependent photoelectron diffraction (SRI -EDPD). EDPD spectra are individually Fourier transformed to three-dimensional vector space. The complex transformed intensities are summed over a span of phi angles or over a span of polar angles. The images are, respectively, well resolved in the radial and azimuthal directions, or in the radial and polar directions. The intersections of these real-space maps fix the atomic coordinates. Furthermore, a variable-axis SWEEP method is introduced to eliminate the angular anisotropies in the source wave and the scattering factor. We show that within the small angular cone, the anisotropy of the source wave towards an atom is cancelled by that towards the detector. Also, the cone only samples the flat part of the slope of the scattering factor's phase. The remaining shift in the image position can be quantitatively corrected for the near-neighbor atoms. In this dissertation, we demonstrate image reconstruction for many systems with simulated and experimental data.