Introduction
The capabilities of conventional transmission electron microscopy (TEM) are limited by the fact that in an electron microscope only the squared amplitude of the electron wave is recorded as intensity, while its phase information is lost. Following Gabor's idea, off-axis electron holography in TEM overcomes the phase problem of imaging by recording an object-modulated interferogram called an electron hologram. Numerical processing reconstructs the quantitative information of the electron wave and, in the case of atomic resolution, subsequently corrects for residual aberrations leading to the amplitude and phase of the object exit wave. Since the phase information of the object is reconstructed without transfer gaps, a wide, unique field opens up for both methodological developments and holographic applications in solid-state physics, materials science, and chemistry.
Special Optics for Electron Holography
By means of a Möllenstedt biprism, which is actually only a small addition to an FEG-based TEM, the reference wave and the object-modulated exit wave are made to superimpose, producing an interference pattern on the detector, the so-called off-axis electron hologram. Based on the fundamental considerations of Lichte [1] and Harada [2], our specially designed FEI Titan 80-300 Holography Special Berlin TEM with two biprisms after the image Cs-corrector provides higher experimental flexibility to adjust the width and fringe spacing of the holograms [3]. In this double biprism setup, where the first biprism serves as a shadow and the second biprism is placed near its optimal position so that the reference and image waves overlap, atomically resolved holograms fringe spacing of about 35 pm are produced while maintaining high fringe contrast. Combined with improved instrument stability, lower Fresnel diffraction, and reduced vignetting effect, complete reconstruction of the object exit wave of a GaN crystal up to the instrument's 75 pm information limit has already been demonstrated without transfer gaps [4].
[1] H. Lichte, Ultramicroscopy 64 (1996) 79.
[2] K. Harada et al. Appl. Phys. Lett. 84 (1994) 3229.
[3] F. Genz u.a., Ultramicroscopy 147 (2014) 33.
[4] T. Niermann und M. Lehmann, Micron 63 (2014) 28.
The Titan TEM was realized within the framework of the DFG project INST 131/508-1 FUGG.
Hologram Acquisition and Statistical Evaluation
By recording a series of electron holograms with 20 or more holograms and then reconstructing them, taking into account the drifts of the sample and biprism throughout the series, an image wave with a high signal-to-noise ratio can be obtained, which is advantageous for further analysis at both medium and atomic resolution [1]. At the atomic scale, quantitative comparison of the full experimentally obtained image waves with wave functions calculated in simulations to model electron-object interaction and wave propagation through the objective lens yields a whole range of important sample and imaging parameters by least-square fitting: In addition to sample thickness, Ádeviations from a low-index zone axis, and distortion fields, imaging parameters such as twofold astigmatism, defocus, and higher orders are extracted, which in turn are used to correct for residual aberrations. Consequently, experimental uncertainties arising from imprecise knowledge of imaging parameters are greatly reduced, allowing object structure to be evaluated with high precision.
[1] T. Niermann und M. Lehmann, Micron 63 (2014) 28.
This method development has been pursued within the DFG CRC 787 subproject A4.
