Author Correction: Spatially resolved steady-state negative capacitance.

In this Letter, the first name of author Bhagwati Prasad was misspelled Bhagawati. This error has been corrected online.

Spatially resolved steady-state negative capacitance.

Negative capacitance is a newly discovered state of ferroelectric materials that holds promise for electronics applications by exploiting a region of thermodynamic space that is normally not accessible1-14. Although existing reports of negative capacitance substantiate the importance of this phenomenon, they have focused on its macroscale manifestation. These manifestations demonstrate possible uses of steady-state negative capacitance-for example, enhancing the capacitance of a ferroelectric-dielectric heterostructure4,7,14 or improving the subthreshold swing of a transistor8-12. Yet they constitute only indirect measurements of the local state of negative capacitance in which the ferroelectric resides. Spatial mapping of this phenomenon would help its understanding at a microscopic scale and also help to achieve optimal design of devices with potential technological applications. Here we demonstrate a direct measurement of steady-state negative capacitance in a ferroelectric-dielectric heterostructure. We use electron microscopy complemented by phase-field and first-principles-based (second-principles) simulations in SrTiO3/PbTiO3 superlattices to directly determine, with atomic resolution, the local regions in the ferroelectric material where a state of negative capacitance is stabilized. Simultaneous vector mapping of atomic displacements (related to a complex pattern in the polarization field), in conjunction with reconstruction of the local electric field, identify the negative capacitance regions as those with higher energy density and larger polarizability: the domain walls where the polarization is suppressed.

Correlative imaging reveals physiochemical heterogeneity of microcalcifications in human breast carcinomas.

Microcalcifications (MCs) are routinely used to detect breast cancer in mammography. Little is known, however, about their materials properties and associated organic matrix, or their correlation to breast cancer prognosis. We combine histopathology, Raman microscopy, and electron microscopy to image MCs within snap-frozen human breast tissue and generate micron-scale resolution correlative maps of crystalline phase, trace metals, particle morphology, and organic matrix chemical signatures within high grade ductal carcinoma in situ (DCIS) and invasive cancer. We reveal the heterogeneity of mineral-matrix pairings, including punctate apatitic particles (<2 µm) with associated trace elements (e.g., F, Na, and unexpectedly Al) distributed within the necrotic cores of DCIS, and both apatite and spheroidal whitlockite particles in invasive cancer within a matrix containing spectroscopic signatures of collagen, non-collagen proteins, cholesterol, carotenoids, and DNA. Among the three DCIS samples, we identify key similarities in MC morphology and distribution, supporting a dystrophic mineralization pathway. This multimodal methodology lays the groundwork for establishing MC heterogeneity in the context of breast cancer biology, and could dramatically improve current prognostic models.

Characterization of Sulfur and Nanostructured Sulfur Battery Cathodes in Electron Microscopy Without Sublimation Artifacts.

Lithium sulfur (Li-S) batteries have the potential to provide higher energy storage density at lower cost than conventional lithium ion batteries. A key challenge for Li-S batteries is the loss of sulfur to the electrolyte during cycling. This loss can be mitigated by sequestering the sulfur in nanostructured carbon-sulfur composites. The nanoscale characterization of the sulfur distribution within these complex nanostructured electrodes is normally performed by electron microscopy, but sulfur sublimates and redistributes in the high-vacuum conditions of conventional electron microscopes. The resulting sublimation artifacts render characterization of sulfur in conventional electron microscopes problematic and unreliable. Here, we demonstrate two techniques, cryogenic transmission electron microscopy (cryo-TEM) and scanning electron microscopy in air (airSEM), that enable the reliable characterization of sulfur across multiple length scales by suppressing sulfur sublimation. We use cryo-TEM and airSEM to examine carbon-sulfur composites synthesized for use as Li-S battery cathodes, noting several cases where the commonly employed sulfur melt infusion method is highly inefficient at infiltrating sulfur into porous carbon hosts.

Atomically Thin Graphene Windows That Enable High Contrast Electron Microscopy without a Specimen Vacuum Chamber.

Scanning electron microscopes (SEMs) require a high vacuum environment to generate and shape an electron beam for imaging; however, the vacuum conditions greatly limit the nature of specimens that can be examined. From a purely scattering physics perspective, it is not necessary to place the specimen inside the vacuum chamber-the mean free paths (MFPs) for electron scattering in air at typical SEM beam voltages are 50-100 µm. This is the idea behind the airSEM, which removes the specimen vacuum chamber from the SEM and places the sample in air. The thickness of the gas layer is less than a MFP from an electron-transparent window to preserve the shape and resolution of the incident beam, resulting in comparable imaging quality to an all-vacuum SEM. Present silicon nitride windows scatter far more strongly than the air gap and are currently the contrast and resolution limiting factor in the airSEM. Graphene windows have been used previously to wrap or seal samples in vacuum for imaging. Here we demonstrate the use of a robust bilayer graphene window for sealing the electron optics from the room environment, providing an electron transparent window with only a 2% drop in contrast. There is a 5-fold-increase in signal/noise ratio for imaging compared to multi-MFP-thick silicon nitride windows, enabling high contrast in backscattered, transmission, and surface imaging modes for the new airSEM geometry.

Spatial Resolution in Scanning Electron Microscopy and Scanning Transmission Electron Microscopy Without a Specimen Vacuum Chamber.

A long-standing goal of electron microscopy has been the high-resolution characterization of specimens in their native environment. However, electron optics require high vacuum to maintain an unscattered and focused probe, a challenge for specimens requiring atmospheric or liquid environments. Here, we use an electron-transparent window at the base of a scanning electron microscope's objective lens to separate column vacuum from the specimen, enabling imaging under ambient conditions, without a specimen vacuum chamber. We demonstrate in-air imaging of specimens at nanoscale resolution using backscattered scanning electron microscopy (airSEM) and scanning transmission electron microscopy. We explore resolution and contrast using Monte Carlo simulations and analytical models. We find that nanometer-scale resolution can be obtained at gas path lengths up to 400 µm, although contrast drops with increasing gas path length. As the electron-transparent window scatters considerably more than gas at our operating conditions, we observe that the densities and thicknesses of the electron-transparent window are the dominant limiting factors for image contrast at lower operating voltages. By enabling a variety of detector configurations, the airSEM is applicable to a wide range of environmental experiments including the imaging of hydrated biological specimens and in situ chemical and electrochemical processes.

High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy.

We describe a hybrid pixel array detector (electron microscope pixel array detector, or EMPAD) adapted for use in electron microscope applications, especially as a universal detector for scanning transmission electron microscopy. The 128×128 pixel detector consists of a 500 µm thick silicon diode array bump-bonded pixel-by-pixel to an application-specific integrated circuit. The in-pixel circuitry provides a 1,000,000:1 dynamic range within a single frame, allowing the direct electron beam to be imaged while still maintaining single electron sensitivity. A 1.1 kHz framing rate enables rapid data collection and minimizes sample drift distortions while scanning. By capturing the entire unsaturated diffraction pattern in scanning mode, one can simultaneously capture bright field, dark field, and phase contrast information, as well as being able to analyze the full scattering distribution, allowing true center of mass imaging. The scattering is recorded on an absolute scale, so that information such as local sample thickness can be directly determined. This paper describes the detector architecture, data acquisition system, and preliminary results from experiments with 80-200 keV electron beams.

Achieving sub-0.5-angstrom-resolution ptychography in an uncorrected electron microscope.

Subangstrom resolution has long been limited to aberration-corrected electron microscopy, where it is a powerful tool for understanding the atomic structure and properties of matter. Here, we demonstrate electron ptychography in an uncorrected scanning transmission electron microscope (STEM) with deep subangstrom spatial resolution down to 0.44 angstroms, exceeding the conventional resolution of aberration-corrected tools and rivaling their highest ptychographic resolutions​. Our approach, which we demonstrate on twisted two-dimensional materials in a widely available commercial microscope, far surpasses prior ptychographic resolutions (1 to 5 angstroms) of uncorrected STEMs. We further show how geometric aberrations can create optimized, structured beams for dose-efficient electron ptychography. Our results demonstrate that expensive aberration correctors are no longer required for deep subangstrom resolution.

Angstrom-scale imaging of magnetization in antiferromagnetic Fe2As via 4D-STEM.

We demonstrate a combination of computational tools and experimental 4D-STEM methods to image the local magnetic moment in antiferromagnetic Fe2As with 6 angstrom spatial resolution. Our techniques utilize magnetic diffraction peaks, common in antiferromagnetic materials, to create imaging modes that directly visualize the magnetic lattice. Using this approach, we show that center-of-mass analysis can determine the local magnetization component in the plane perpendicular to the path of the electron beam. Moreover, we develop Magnstem, a quantum mechanical electron scattering simulation code, to model electron scattering of an angstrom-scale probe from magnetic materials. Using these tools, we identify optimal experimental conditions for separating weak magnetic signals from the much stronger interactions of an angstrom-scale probe with electrostatic potentials. Our techniques should be useful for characterizing the local magnetic order in systems such in thin films, interfaces, and domain boundaries of antiferromagnetic materials, which are difficult to probe with existing methods.

Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit.

Nanoscale spin textures, especially magnetic skyrmions, have attracted intense interest as candidate high-density and power-efficient information carriers for spintronic devices1,2. Facilitating a deeper understanding of sub-hundred-nanometre to atomic-scale spin textures requires more advanced magnetic imaging techniques3-5. Here we demonstrate a Lorentz electron ptychography method that can enable high-resolution, high-sensitivity magnetic field imaging for widely available electron microscopes. The resolution of Lorentz electron ptychography is not limited by the usual diffraction limit of lens optics, but instead is determined by the maximum scattering angle at which a statistically meaningful dose can still be recorded-this can be an improvement of up to 2-6 times depending on the allowable dose. Using FeGe as the model system, we realize a more accurate magnetic field measurement of skyrmions with an improved spatial resolution and sensitivity by also correcting the probe-damping effect from the imaging optics via Lorentz electron ptychography. This allows us to directly resolve subtle internal structures of magnetic skyrmions near the skyrmion cores, boundaries and dislocations in an FeGe single crystal. Our study establishes a quantitative, high-resolution magnetic microscopy technique that can reveal nanoscale spin textures, especially magnetization discontinuities and topological defects in nanomagnets6. The technique's high-dose efficiency should also make it well suited for the exploration of magnetic textures in electron radiation-sensitive materials such as organic or molecular magnets7.

Theory and practice of electron diffraction from single atoms and extended objects using an EMPAD.

What does the diffraction pattern from a single atom look like? How does it differ from the scattering from long-range potential? With the development of new high-dynamic range pixel array detectors to measure the complete momentum distribution, these questions have immediate relevance for designing and understanding momentum-resolved imaging modes. We explore the asymptotic limits of long-range and short-range potentials. We use a simple quantum mechanical model to explain the general and asymptotic limits for the probability distribution in both real and reciprocal space. Features in the scattering potential much larger than the probe size cause the bright field (BF) disk to deflect uniformly, while features much smaller than the probe size, instead of a deflection, cause a redistribution of intensity within the BF disk. Because long-range and short-range features are encoded differently in the diffraction pattern, it is possible to separate their contributions in differential phase-contrast (DPC) or center-of-mass (CoM) imaging. The shape profiles for atomic resolution CoM imaging are dominated by the shape of the probe gradient and not the highly singular atomic potentials or their local fields. Instead, only the peak height shows an atomic number sensitivity, whose precise dependence is determined by the convergence angle. At lower convergence angles, the contrast oscillates with increasing atomic number, similar to BF imaging. The range of collection angles impacts DPC and CoM imaging differently, with CoM being more sensitive to the upper cutoff limit, while DPC is more sensitive to the lower cutoff.