Atomic resolution imaging of YAlO3: Ce in the chromatic and spherical aberration corrected PICO electron microscope

The influence of chromatic aberration on the dose-limited spatial resolution of transmission electron microscopy

The effect of chromatic aberration (CC) on the spatial resolution in transmission electron microscopy (TEM) was studied in thick specimens in which the sample becomes the limiting factor in the resolution. The sample influences the energy spread of the electron beam, allows only a limited electron dose, and modulates electron scattering events. The experimental set-up consisted of a thin silicon nitride membrane and a silicon wedge containing gold nanoparticles. The resolution was measured as a function of electron dose and sample thickness for different sample configurations and for different microscopy modalities including regular TEM, energy filtered TEM (EFTEM) and CC-corrected TEM. Comparison with an analytical model aided the understanding of the experimental data applied over varied conditions. The general trend for all microscopy modalities was a transition from a noise-limited resolution at low electron dose to a CC-limited resolution at high-dose in the absence of beam blurring. EFTEM required an accurate energy slit offset and an optimal energy spread to energy-slit width ratio to surpass regular TEM. The key advantage of CC correction appeared to be the best possible resolution for larger sample thickness at low electron dose outperforming EFTEM by about fifty percent. Several hypothetical sample configurations relevant to liquid phase electron microscopy were evaluated as well to demonstrate the capabilities of the analytical model and to determine the most optimal microscopy modality for this type of experiment. The analytical model included an automated optimization of the EFTEM settings and may aid in optimizing the sample-limited resolution for experimental analysis and planning.

Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50 nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

Magnetic Cc/Cs-corrector compensating for the chromatic aberration and the spherical aberration of electron lenses

Aberration correction in transmission electron microscopy has proven feasible and useful over a large range of acceleration voltages. The spherical aberration has been corrected for beam energies from 15 kV [1] up to 1.2 MeV [2] while the correction of the chromatic aberration has been achieved for beam energies ranging from 20 kV[3] up to 300 kV[4]. Above this threshold the conventional correction principle based on mixed electric and magnetic focusing elements becomes infeasible with present technology [5]. For conventional electron sources at high voltages the relative energy width of the beam gets so small that chromatic correction becomes less important. Nevertheless, for new applications with pulsed electron sources with energy spreads in the order of 100 eV chromatic aberration will become a limiting factor even at high energies [6]. To enable chromatic aberration correction for such systems a novel type of a feasible, purely magnetic multipole aberration corrector with curved optic axis is proposed which is capable of compensating for the chromatic and spherical aberration up to several MeV.

An improved iterative wave function reconstruction algorithm in high-resolution transmission electron microscopy

Exit wavefunction reconstruction is a powerful image processing technique to enhance the resolution and the signal-to-noise ratio for atomic-resolution imaging in both aberration uncorrected and corrected transmission electron microscopes. The present study aims to improve the performance of the iterative wavefunction reconstruction algorithm in comparison not only with its conventional form but also with the popular commercial Trueimage software for exit wavefunction reconstruction. It is shown that by implementing a wave propagation procedure for refining its image alignment, the iterative wavefunction reconstruction algorithm can be greatly improved in accurately retrieving the wavefunctions while keeping its original advantages, which allow the reconstruction be performed with less images and a larger defocus step in the data set of through-focus image series. In addition, calculations of this algorithm can be accelerated drastically by the graphic processing unit (GPU) hardware programming using the popular computer unified device architecture language, whose computing speed can be 25-38 times as fast as a central processing unit (CPU) program.

Absolute Scale Quantitative Off-Axis Electron Holography at Atomic Resolution

An absolute scale match between experiment and simulation in atomic-resolution off-axis electron holography is demonstrated, with unknown experimental parameters determined directly from the recorded electron wave function using an automated numerical algorithm. We show that the local thickness and tilt of a pristine thin WSe_{2} flake can be measured uniquely, whereas some electron optical aberrations cannot be determined unambiguously for a periodic object. The ability to determine local specimen and imaging parameters directly from electron wave functions is of great importance for quantitative studies of electrostatic potentials in nanoscale materials, in particular when performing in situ experiments and considering that aberrations change over time.

Third-rank chromatic aberrations of electron lenses

In this paper the third-rank chromatic aberration coefficients of round electron lenses are analytically derived and numerically calculated by Mathematica. Furthermore, the numerical results are cross-checked by the differential algebraic (DA) method, which verifies that all the formulas for the third-rank chromatic aberration coefficients are completely correct. It is hoped that this work would be helpful for further chromatic aberration correction in electron microscopy.