Electron ptychography achieves atomic-resolution limits set by lattice vibrations (2101.00465v1)

Abstract: Transmission electron microscopes use electrons with wavelengths of a few picometers, potentially capable of imaging individual atoms in solids at a resolution ultimately set by the intrinsic size of an atom. Unfortunately, due to imperfections in the imaging lenses and multiple scattering of electrons in the sample, the image resolution reached is 3 to 10 times worse. Here, by inversely solving the multiple scattering problem and overcoming the aberrations of the electron probe using electron ptychography to recover a linear phase response in thick samples, we demonstrate an instrumental blurring of under 20 picometers. The widths of atomic columns in the measured electrostatic potential are now no longer limited by the imaging system, but instead by the thermal fluctuations of the atoms. We also demonstrate that electron ptychography can potentially reach a sub-nanometer depth resolution and locate embedded atomic dopants in all three dimensions with only a single projection measurement.

• The paper introduces multislice electron ptychography to overcome traditional electron scattering, achieving atomic resolution limited only by thermal lattice vibrations.
• It employs high-dynamic pixel array detectors with multislice reconstruction, attaining spatial resolution finer than 0.59 Å even in samples up to 50 nm thick.
• The study reveals that this approach enables precise 3D mapping of atomic dopants, significantly advancing materials characterization in nanotechnology.

An Analytical Essay on Electron Ptychography as a Tool for Achieving Atomic-Resolution Limits

This paper explores the potential of electron ptychography to achieve atomic-resolution limits in transmission electron microscopy (TEM) by overcoming traditional barriers such as lens aberrations and multiple electron scattering. The authors introduce multislice electron ptychography, a methodology that refines electron imaging by deconvoluting complex sample interactions in thicker samples. This approach drastically enhances the spatial resolution, achieving a level limited primarily by the thermal fluctuations of atoms, as opposed to the precision of the imaging system.

The paper delineates the theoretical and practical advancements that allow electron ptychography to reach under 20 picometers resolution in thicker samples. Existing methods have been constrained by the scattering of electrons due to the Coulombic interactions with atoms in thick samples, imposing nonlinear contrast limitations. The researchers present innovative applications of ptychography that solve these issues by leveraging the Cowley-Moodie multislice solution to model electron dynamical scattering. By dissecting samples into slices, the phase response remains linear over varying thicknesses—a critical factor for three-dimensional reconstructions.

The experimental setup, leveraging high-dynamic pixel array detectors and multislice reconstruction, achieved remarkable results. The demonstrated resolution breaches traditional limits and achieves spatial resolution finer than 0.59 Å by precisely solving the inverse multiple scattering problem. Furthermore, a sub-nanometer depth resolution was noted, revealing the structure along the optical axis with unprecedented detail.

Notably, the results underscore the importance of sample thickness, showing a substantial improvement in multislice ptychography's resolution compared to conventional single-slice approaches, particularly in simulating and imaging crystalline PrScO. Even as the thickness increases towards 50 nm, the authors effectively manage sampling constraints and achieve accurate structure retrieval.

A crucial implication of this work is its substantial impact on atomic-scale characterization of materials, notably in identifying atomic dopants with fine precision. The methods described show potential for identifying single dopant atoms in three-dimensional space through multislice ptychography, outperforming conventional projection methods that often miss such details in thicker matrices.

In summary, the research provides a significant leap in TEM capabilities, particularly for analyzing bulk and non-periodic structures, aligning closely with modern needs in physics, chemistry, and materials science. Looking forward, the integration of multislice electron ptychography could accelerate the pace of nanotechnology advancements, offering enhanced precision in materials characterization. Future developments may include further refinement in computational algorithms to enhance reconstruction speeds and integrate this powerful method into routine TEM applications. The work may also pave the way for uncovering complex three-dimensional nanostructures, pushing the frontier of materials discovery and engineering.