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We describe the development, operation, and application of the 4D Camera-a 576 by 576 pixel active pixel sensor for scanning/transmission electron microscopy which operates at 87,000 Hz. The detector generates data at ∼480 Gbit/s which is captured by dedicated receiver computers with a parallelized software infrastructure that has been implemented to process the resulting 10-700 Gigabyte-sized raw datasets. The back illuminated detector provides the ability to detect single electron events at accelerating voltages from 30 to 300 kV. Through electron counting, the resulting sparse data sets are reduced in size by 10--300× compared to the raw data, and open-source sparsity-based processing algorithms offer rapid data analysis. The high frame rate allows for large and complex scanning diffraction experiments to be accomplished with typical scanning transmission electron microscopy scanning parameters.

Nanobeam electron diffraction can probe local structural properties of complex crystalline materials including phase, orientation, tilt, strain, and polarization. Ideally, each diffraction pattern from a projected area of a few unit cells would produce a clear Bragg diffraction pattern, where the reciprocal lattice vectors can be measured from the spacing of the diffracted spots, and the spot intensities are equal to the square of the structure factor amplitudes. However, many samples are too thick for this simple interpretation of their diffraction patterns, as multiple scattering of the electron beam can produce a highly nonlinear relationship between the spot intensities and the underlying structure. Here, we develop a stacked Bloch wave method to model the diffracted intensities from thick samples with structure that varies along the electron beam. Our method reduces the large parameter space of electron scattering to just a few structural variables per probe position, making it fast enough to apply to very large fields of view. We apply our method to SrTiO3/PbTiO3/SrTiO3 multilayer samples, and successfully disentangle specimen tilt from the mean polarization of the PbTiO3 layers. We elucidate the structure of complex vortex topologies in the PbTiO3 layers, demonstrating the promise of our method to extract material properties from thick samples.

Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal series of four-dimensional scanning transmission electron microscopy (4D-STEM) data. We apply the approach to a lead iridate, PbIrO, and yttrium-stabilized zirconia, YZrO, heterostructure from data acquired with the specimen in a single plan-view orientation, with the epitaxial layers stacked along the beam direction. We demonstrate that Pb-Ir atomic columns are visible in the uppermost layers of the reconstructed volume. We compare this approach to the alternative techniques of depth sectioning using differential phase contrast scanning transmission electron microscopy (DPC-STEM) and multislice ptychographic reconstruction.

Scanning transmission electron microscopy (STEM), where a converged electron probe is scanned over a sample's surface and an imaging, diffraction, or spectroscopic signal is measured as a function of probe position, is an extremely powerful tool for materials characterization. The widespread adoption of hardware aberration correction, direct electron detectors, and computational imaging methods have made STEM one of the most important tools for atomic-resolution materials science. Many of these imaging methods rely on accurate imaging and diffraction simulations in order to interpret experimental results. However, STEM simulations have traditionally required large calculation times, as modeling the electron scattering requires a separate simulation for each of the typically millions of probe positions. We have created the Prismatic simulation code for fast simulation of STEM experiments with support for multi-CPU and multi-GPU (graphics processing unit) systems, using both the conventional multislice and our recently-introduced PRISM method. In this paper, we introduce Prismatic version 2.0, which adds many new algorithmic improvements, an updated graphical user interface (GUI), post-processing of simulation data, and additional operating modes such as plane-wave TEM. We review various aspects of the simulation methods and codes in detail and provide various simulation examples. Prismatic 2.0 is freely available both as an open-source package that can be run using a C++ or Python command line interface, or GUI, as well within a Docker container environment.

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles

Three-dimensional phase-contrast imaging of multiply-scattering samples in x-ray and electron microscopy is challenging due to small numerical apertures, the unavailability of wave front shaping optics, and the highly nonlinear inversion required from intensity-only measurements. In this work, we present an algorithm using the scattering matrix formalism to solve the scattering from a noncrystalline medium from scanning diffraction measurements and simultaneously recover the illumination aberrations. We demonstrate our method experimentally in a scanning transmission electron microscope, recovering the scattering matrix of a heterogeneous sample with two layers of multiwall carbon nanotubes filled with TaTe2 core-shell structures, spaced 10nm apart in the axial direction. Our work enables phase contrast imaging and materials characterization in multiply-scattering samples at high resolution for a wide range of materials.

Increasing interest in three-dimensional nanostructures adds impetus toelectron microscopy techniques capable of imaging at or below the nanoscale inthree dimensions. We present a reconstruction algorithm that takes as input afocal series of four-dimensional scanning transmission electron microscopy(4D-STEM) data and transcends the prevalent structure retrieval algorithmassumption of a very thin specimen homogenous along the optic axis. Wedemonstrate this approach by reconstructing the different layers of a leadiridate (Pb$_2$Ir$_2$O$_7$) and yttrium-stabilized zirconia(Y$_{0.095}$Zr$_{0.905}$O$_2$) heterostructure from data acquired with thespecimen in a single plan-view orientation, with the epitaxial layers stackedalong the beam direction.

Increasing interest in three-dimensional nanostructures adds impetus toelectron microscopy techniques capable of imaging at or below the nanoscale inthree dimensions. We present a reconstruction algorithm that takes as input afocal series of four-dimensional scanning transmission electron microscopy(4D-STEM) data. We apply the approach to a lead iridate, Pb$_2$Ir$_2$O$_7$, andyttrium-stabilized zirconia,Y$_{0.095}$Zr$_{0.905}$O$_2$ , heterostructure fromdata acquired with the specimen in a single plan-view orientation, with theepitaxial layers stacked along the beam direction. We demonstrate that Pb-Iratomic columns are visible in the uppermost layers of the reconstructed volume.We compare this approach to the alternative techniques of depth sectioningusing differential phase contrast scanning transmission electron microscopy(DPC-STEM) and multislice ptychographic reconstruction.

Three-dimensional phase contrast imaging of multiply-scattering samples inX-ray and electron microscopy is extremely challenging, due to small numericalapertures, the unavailability of wavefront shaping optics, and the highlynonlinear inversion required from intensity-only measurements. In this work, wepresent a new algorithm using the scattering matrix formalism to solve thescattering from a non-crystalline medium from scanning diffractionmeasurements, and recover the illumination aberrations. Our method will enable3D imaging and materials characterization at high resolution for a wide rangeof materials.

Multiple electron scattering and the nonintuitive nature of image formation with coherent radiation complicate the interpretation of conventional transmission electron microscopy images. Precession of the illuminating beam in transmission electron microscopy (TEM) can lead to more robust and interpretable images with some penalty to image contrast, a technique known as dynamic hollow-cone illumination TEM. We demonstrate direct and robust imaging of light and heavy atoms in a crystalline environment with this technique. This method is similar to the annular bright-field technique in scanning transmission electron microscopy, via the principle of reciprocity. Dynamic hollow-cone illumination TEM is challenging in practice due to sensitivity to the misalignment of the precession axis, microscope objective aperture, and crystal zone axis.

Scanning transmission electron microscopy (STEM) allows for imaging,diffraction, and spectroscopy of materials on length scales ranging frommicrons to atoms. By using a high-speed, direct electron detector, it is nowpossible to record a full 2D image of the diffracted electron beam at eachprobe position, typically a 2D grid of probe positions. These 4D-STEM datasetsare rich in information, including signatures of the local structure,orientation, deformation, electromagnetic fields and other sample-dependentproperties. However, extracting this information requires complex analysispipelines, from data wrangling to calibration to analysis to visualization, allwhile maintaining robustness against imaging distortions and artifacts. In thispaper, we present py4DSTEM, an analysis toolkit for measuring materialproperties from 4D-STEM datasets, written in the Python language and releasedwith an open source license. We describe the algorithmic steps for datasetcalibration and various 4D-STEM property measurements in detail, and presentresults from several experimental datasets. We have also implemented a simpleand universal file format appropriate for electron microscopy data in py4DSTEM,which uses the open source HDF5 standard. We hope this tool will benefit theresearch community, helps to move the developing standards for data andcomputational methods in electron microscopy, and invite the community tocontribute to this ongoing, fully open-source project.

Scanning transmission electron microscopy (STEM) allows for imaging,diffraction, and spectroscopy of materials on length scales ranging frommicrons to atoms. By using a high-speed, direct electron detector, it is nowpossible to record a full 2D image of the diffracted electron beam at eachprobe position, typically a 2D grid of probe positions. These 4D-STEM datasetsare rich in information, including signatures of the local structure,orientation, deformation, electromagnetic fields and other sample-dependentproperties. However, extracting this information requires complex analysispipelines, from data wrangling to calibration to analysis to visualization, allwhile maintaining robustness against imaging distortions and artifacts. In thispaper, we present py4DSTEM, an analysis toolkit for measuring materialproperties from 4D-STEM datasets, written in the Python language and releasedwith an open source license. We describe the algorithmic steps for datasetcalibration and various 4D-STEM property measurements in detail, and presentresults from several experimental datasets. We have also implemented a simpleand universal file format appropriate for electron microscopy data in py4DSTEM,which uses the open source HDF5 standard. We hope this tool will benefit theresearch community, helps to move the developing standards for data andcomputational methods in electron microscopy, and invite the community tocontribute to this ongoing, fully open-source project.

Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss spectroscopy (EELS). These simulations require a full quantum-mechanical treatment of multiple scattering of the electron beam, both before and after a core-level inelastic transition. Current algorithms scale quadratically and can take up to a week to calculate on desktop machines even for simple crystal unit cells and do not scale well to the nanoscale heterogeneous systems that are often of interest to materials science researchers. We introduce an algorithm with linear scaling that typically results in an order of magnitude reduction in computation time for these calculations without introducing additional error and discuss approximations that further improve computational scaling for larger-scale objects with modest penalties in calculation error. We demonstrate these speedups by calculating the atomic resolution STEM-EELS map using the L-edge transition of Fe, for a nanoparticle 80 Å in diameter, in 16 hours, a calculation that would have taken at least 80 days using a conventional multislice approach.