Skip to main content

Advanced Holographic Tomographies for Nanoscale Materials: Revealing Electromagnetic and Deformation Fields, Chemical Composition and Quantum States at Atomic Resolution.

Periodic Reporting for period 2 - ATOM (Advanced Holographic Tomographies for Nanoscale Materials: Revealing Electromagnetic and Deformation Fields, Chemical Composition and Quantum States at Atomic Resolution.)

Reporting period: 2018-07-01 to 2019-12-31

The ongoing miniaturization in nanotechnology and functional materials puts an ever increasing
focus on the development of three-dimensional (3D) nanostructures, such as quantum dot arrays,
structured nanowires, nanoantennas or nanomagnetic textures such as skyrmions, which permit
a better performance of optical or electronic devices in terms of speed and energy efficiency. To
develop and advance such technologies and to improve the understanding of the underlying
fundamental physical effects, the nondestructive and quantitative 3D characterization of
physical, e.g. electric or magnetic, fields down to atomic resolution is indispensable. Current
nanoscale characterization methods only inadequately convey this information, e.g. because they probe
surfaces, record projections, or lack resolution. AToM will provide a ground-breaking
tomographic methodology for current nanotechnology by mapping electric and magnetic
fields as well as crucial properties of the underlying atomic structure in solids, such as the
chemical composition, mechanical strain or spin configuration in 3D down to atomic
resolution. To achieve that goal, advanced holographic and tomographic setups in the Transmission
Electron Microscope (TEM) are combined with novel computational methods, e.g. taking into
account the ramifications of electron diffraction. Moreover, fundamental application limits are
overcome (A) by extending the holographic principle, requiring coherent electron beams, to
quantum state reconstructions applicable to electrons of any (in)coherence; and (B) by adapting a
unique in-situ TEM with a very large sample chamber to facilitate holographic field sensing down
to very low temperatures (6 K) under application of external, e.g. electric, stimuli. The joint
development of AToM in response to current problems of nanotechnology, including the previously
mentioned ones, is anticipated to immediately and sustainably advance nanotechnology in its
various aspects.
The project is divided into two main areas: Holographic tomography of physical fields in materials and Quantum state reconstruction of inelastically scattered electrons for comprehensive analysis of dielectric response. Progress has been achieved in both, with the details pertaining the several subareas listed below.

Area 1:

In order achieve atomic-resolution in the 3D reconstruction of electrostatic fields we combined two ideas. First, we use to maximal information extractable from an elastic scattering experiment, i.e. the (holographically reconstructed) electron wave function and record a tilt series of that. Second, we identified a suitable (nonlinear) mapping of that holographic tilt series into a projection series linearly depending on the 3D electrostatic potential (based on Rytov approximation and diffraction tomography). These principles have been implemented in a very flexible reconstruction algorithm for atomic scattering potentials capable of dealing with large tomographic datasets. Key features of the implementation are the possibility to reconstruct from multiple non-orthogonal tilt series, the possibility to deliberately exclude certain parts of the data (e.g. corrupted by erroneous phase unwrapping or sample modifications during the tilt series), and the possibility to incorporate additional constraints (such as maximal or minimal potential values). This algorithm has been successfully applied to simulated tilt series of wave functions, which had been scattered on nanoobjects, such as WS2 nanotubes. More recently, we acquired atomic resolution holographic tilt series of W nanotips to be used as experimental proof-of-principle of the novel method. It turned out that the alignment of the atomic-resolution holographic tilt series as well as modification of the sample occurring while tilting (e.g. adsorbates) require additional efforts in the preprocessing, which we are currently addressing.

Several major breakthroughs have been accomplished in the development of magnetic vector field tomography for nanoscale magnetic textures. We developed dedicated multiple tilt holographic series acquisition routines, holographic and tomographic reconstruction algorithms, and a 3 translation + 3 rotation axis specimen holder; dedicated to the reconstruction of all three Cartesian components of the magnetization texture in non-trivial 3D nanomagnets (such as vortices, bubbles, skyrmions, Bloch points, etc.). Amongst others we were able to show that the current scheme of employing two perpendicular tilt series and Maxwell's third law imposes a non-isotropic band filter on the reconstructed vector field independent of the reconstruction algorithm (e.g. whether rooted in the field or potential calcul), which provided a major stimulus for the development of the unique 6-axis tomography holder, overcoming this fundamental restriction. We demonstrated the model-base-free reconstruction of all three Cartesian components of the magnetic induction as well as pertaining magnetic properties such as the bound current or parts of the exchange energy density in various magnetic nanowire configurations (Fig. 1) and made the first steps into extending the method to cryogenic conditions (as required for a large class of fundamental magnetic phenomena).

The problem of 3D strain field reconstruction as been tackled through a close collaboration with our ERC project partner from the TU Berlin, Prof. Dr. M. Lehmann, Dr. T. Niermann and PhD candidate Laura Meißner, who developed and tested tomographic schemes for the 3D reconstruction of strain fields based on the beam tilt method proposed in AToM. In a first step a precise control of the beam tilt (and hence the excitation error) has been developed. In a second step beam tilt series of various strained semiconductor structures (containing buried quantum dots and wells) have been acquired and evaluated employing dynamic scattering simulations and the analytic weighting function approximation providing the basis for a direct tomographic reconstruction. It has been demonstrated that 3D information can be extracted from these data albeit with a rather restricted spatial resolution along the beam axis as of now (several tens of nanometer). Moreover, it has been revealed that large strains, such as occurring at interfaces between semiconductors of different lattice constant, require additional extensions beyond the weighting function approach.

Concerning the reconstruction of attenuation coefficients, we developed a novel method, which allows to distinguish between mesoscale potentials due to space charge regions (purely electronic potentials) and atomic potentials reflecting the chemical composition (i.e. mean inner potentials), by combining electron holographic tomography and high-angle annular dark field tomography. This method has been applied to multi-quantum-well semiconductor nanowires, where the 3D morphology of the wells (i.e. thickness variations) and the tapered tip of the nanowire determine its optical properties (e.g. in novel sensors). Subsequently we started to work intensively on the mapping of elastic and inelastic attenuation at atomic resolution. To that end high-resolution holograms of various 2D materials (h-BN, graphene, WS2) have been recorded at spatial and chromatic aberration corrected TEMs (e.g. TEAM 1.0 at NCEM Berkeley). We developed a novel automatic residual aberration determination and correction scheme using only the acquired hologram data, which allows to largely remove the impact of imperfect imaging in a dose optimized way (no extra acquisition required). We showed how to evaluate this data in terms of 3D charge delocalization. Currently a detailed analysis in terms of inelastic attenuation attenuation (mainly through excitation of vibrational degrees of freedom) is underway.

In the first year of the project we completed the development of the JEOL 2010F JEM Dresden-special insitu TEM. We installed the continuous-flow liquid He cryostat, aligned the instrument and set up several dedicated aberration corrected imaging modi and aligned several advanced imaging modes (e.g. holography). Subsequently, we characterized the optical performance and performed the first cryogenic experiments on topical materials (e.g. transition metal dichalgogenites containing charge density waves at low temperatures). Subsequently the insitu TEM has been mainly employed in cryogenic studies on low temperature magnetic skyrmion formation (mostly in lacunar spinels). Currently, extensions of the state to allow probing with electrical currents are underway.

Area 2:

One original goal in this area is the measurement of all Cartesian components of the probability current of the inelastically scattered electron beam as a means to measure transient electric and magnetic fields pertaining charge excitations (mainly surface plasmon polaritions) in the sample. With regard of ease of experimental implementation and an extension to a full quantum state reconstruction we decided to use a variant of a differential phase contrast technique, which we dubbed inelastic momentum transfer instead. Here, we scan a focused electron probe over the sample and measure both the deflection of the scattered probe in an energy resolved way. We have demonstrated that small angles in the µrad range can be readily determined using large camera lengths and related to polaritonic electric fields of surface plasmons in plasmonic nanostructures (Fig. 2). We showed how to simulate the experimental signal and showed that the main bottleneck toward a full quantitative analysis is thepresence of notorious aberrations of the probe forming optics in the low magnification mode. is problem is currently addressed in collaboration with CEOS Heidelberg, one of our project partners in the ERC. We have employed the technique to study various aluminum based plasmonic nanostructures, plasmonic wave guides based on nanoparticle chains as well as thin gold networks.

The quantum state of inelastically scattered electrons provides access to the fully non-local dielectric response. We showed, how the fully non-local response can be completely reconstructed by employing inelastic electron ptychography., which is difficult and currently not possible to obtain from other spectroscopic techniques. Moreover, we developed dedicated measurement ptychographic measurement schemes, including an automated recording of the ptychographic dataset on the TEM and independent measurements of the probe phase space distribution. Building on the IMT technique of discussed above (which is based on the same ptychographic dataset), we analyzed various plasmonic nanostructures. However, elastic vignetting and low signal to noise ratio currently complicates the ptychographic reconstruction (i.e. phase space deconvolution). Development of suitable regularization regimes are underway.

In order to develop a fully relativistic inelastic electron scattering code, facilitating the computation of both core and low-loss spectra as well as energy filtered imaging and diffraction, we first elaborated on the theoretical foundations of inelastic electron scattering. We particularly studied the ramifications of 3D effects (typically neglected in current inelastic scattering implementations) and the various approximation levels to relativistic effects (e.g. fully relativistic vs. scalar relativistic vs. quasi static). We could, amongst others, provide a unified framework for core-loss and low-loss scattering incorporating current-current coupling as the leading order relativistic effects in both core-loss and low-loss scattering. The implementation into ab-initio density functional theory based simulation package is underway.
Progress beyond the state of the art has been mainly achieved in two areas so far: (1) Development of vector field tomography as a unique and flexible tool for studying 3D magnetization textures such as vortices or Skyrmions at several nanometer resolution. The successful implementation of the technique includes several hardware and software developments (see above). The proof-of-concept has been carried out at the example of a complex magnetization texture in a magnetic Co-Cu stacked nanowire (Fig. 1). Currently, the technique is extended to be applicable under cryogenic conditions and under the application of a rotatable external magnetic field. With that we expect to resolve the 3D magnetization texture of topical nanomagnetic phenomena such as Skyrmions or Bloch point domain walls until the end of the project. These studies contribute to reveal the crucial impact of spatial confinement, surface and bulk anisotropies and various other parameters on the formation of 3D magnetization textures and their functionalization in devices. (2) Development of a novel nanoscale probing technique for transient electric and magnetic fields of (collective) charge excitations (i.e. surface plasmons). Here, we adapted the conventional differential phase contrast technique such to allow for spectrally resolving time-dependent fields. The technique has been successfully applied to characterize the plasmonic response of several plasmonic nanostructures, albeit with a rather strong artificial impact from geometrical aberrations of the beam forming optics (condenser). We currently work on aberration corrected setups to remedy the latter, facilitating a more quantitative application of the technique, e.g. for characterizing magnetic surface plasmon modes or peculiar magnetoelectric coupling effects in topological insulators (axion plasmonics).
In the field of atomic resolution reconstruction, cryogenic TEM and quantum state reconstruction main milestones have been achieved with respect to reconstruction algorithms, continuous-flow liquid He cooling and inelastic ptychography data acquisition and analysis, respectively. Major breakthroughs are therefore to be expected until the end of the project resulting from the further development and application of the developed methodology.