Ozsoy Keskinbora, Cigdem (2016)
Recovering Low Spatial Frequency Phase Information by Electron Holography: Challenges, Solutions and Application to Materials Science.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (Abstract)

Bi2Se3 is a narrow band gap semiconductor, which has the peculiarity to host a single degenerate surface state consisting of a Dirac cone.1 Since the discovery of its surface state using angle resolved photoemission spectroscopy (ARPES), Bi2Se3 has been considered as a simple model system for topological insulators (TIs). As expected for TIs, the Bi2Se3 surface state stays robust against adsorption of adatoms even after exposure to air. However, as a semiconductor, atomic or molecular adsorption creates an electrical potential, which induces bending of energy bands at the surface. ARPES measurements showed that exposing Bi2Se3 to air results in the appearance of new parabolic bands at the surface. These states are imputed to the presence of a two dimensional electron gas (2DEG), resulting from downward bending of the conduction band at the (110) surface.2 However, ARPES experiments are carried out in reciprocal state, and so cannot “see” the 2DEG whereas it can be directly observed by electron holography in a transmission electron microscope (TEM). Holography - originally developed for correcting spherical aberration in transmission electron microscopes3 - is now used in a wide range of disciplines that involve the propagation of waves, including light optics,4 electron microscopy,5 acoustics6 and seismology.7 In electron microscopy, the two primary modes of holography are Gabor’s original in-line setup and an off-axis approach that was developed subsequently. Electron holography is a powerful technique for characterizing electrostatic potentials,8 charge order, electric9 and magnetic10 fields, strain distributions,11,12 and semiconductor dopant distributions13 with nm spatial resolution. One of the main electron holography methods, in-line electron holography, suffers from inefficient low spatial frequency recovery but has the advantage of high phase sensitivity at high spatial frequencies. In contrast, off-axis electron holography can cover the low spatial frequencies but cannot achieve currently the performance of in-line holography at high spatial frequencies. These two techniques are highly complementary, offering superior phase sensitivity at high and low spatial resolution, respectively. All previous investigations have focused on improving each method individually. This dissertation summarizes two alternative approaches. The first approach focuses on the in-line electron holography method and shows the first examples of how gradient-flipping enhances the low spatial frequency recovery of the existing flux preserving non-linear wave reconstruction algorithm. The second approach, called hybrid electron holography, shows how the two methods can be combined in a synergetic fashion to provide phase information with excellent sensitivity across all spatial frequencies, low noise and an efficient use of electron dose. These principles are expected to be widely applicable also to holography in light optics, X-ray optics, acoustics, ultra-sound, terahertz imaging, etc. High spatial resolution and high phase sensitivity are crucial for investigating low dimensional materials and challenging when the aim is full quantifiability. Therefore, gold nanoparticles and some preliminary result from Bi2Se3 are presented as an example, showcasing the suitability of hybrid electron holography for addressing such questions.

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