Direct structure inversion from exit waves

Atomically resolved 3D structural reconstruction of small quantum dots

Semiconducting quantum dots (QDs) have potential applications in light-emitting diodes, single-photon sources and quantum computing due to shape-dependent (opto) electronic properties. Atomic resolution 3D-structure determination is important in understanding growth kinetics and improving device performance. 3D-reconstruction of large QDs was reported using characterization techniques like atomic force microscopy, atom probe tomography and tilt series electron tomography, but, still, atomic resolution tomography of QDs, especially those sized below 10 nm, is a challenge. Inline-3D-holography is an emerging and promising technique to perform atomic resolution tomography at low electron doses. In the present study, atomically resolved 3D structures of QDs were reconstructed using inline-3D-holography, implemented on InN QDs (<10 nm) grown on a Si substrate. The residual amorphous glue distorts the exit surface geometry; hence an error correction method was proposed. This is the first experimental evidence of pre-pyramid shaped 3D structure of QDs sized below 10 nm that supports theoretical predictions.

Atomically resolved tomographic reconstruction of nanoparticles from single projection: Influence of amorphous carbon support

Nanoparticles have a wide range of applications due to their unique geometry and arrangement of atoms. For a precise structure-property correlation, information regarding atomically resolved 3D structures of nanoparticles is utmost beneficial. Though modern aberration-corrected transmission electron microscopes can resolve atoms with the sub-angstrom resolution, an atomic-scale 3D reconstruction of a nanoparticle using Scanning Transmission Electron Microscopy (STEM) based tomographic method faces hurdles due to high electron irradiation damage and "missing-wedge". Instead, inline 3D holography based tomographic reconstructions from single projection registered at low electron doses is more suitable for defining atomic positions at nanostructures. Nanoparticles are generally supported on amorphous carbon film for Transmission Electron Microscopy (TEM) experiments. However, neglecting the influence of carbon film on the tomographic reconstruction of the nanoparticle may lead to ambiguity. To address this issue, the effect of amorphous carbon support was quantitatively studied using simulations and experiments and it was revealed that increasing thickness and/or density of carbon support increases distortion in tomograms.

Feasible atomic-resolution electron tomography for general crystal surfaces by quantitative reconstruction from a high-resolution image

Whether or not the 3-dimensional surface morphologies of a crystal sample can be reconstructed at atomic-scale from a single 2-dimensional image becomes an interesting issue in high-resolution transmission electron microscopy, after the work by Jia et al. [1]. Here we propose an improved and self-validated algorithm to enhance such an electron tomography method and to make it applicable to more general crystal surfaces even with thin amorphous layers. Our study shows that a resolution in the beam (z) direction and a confidence level have to be defined and estimated after performing tomographic reconstruction in order to evaluate the quality and the reliability of its result. Applying the proposed procedure to the Si[110] image to recover the surface morphologies of a silicon crystal with amorphous contamination, the obtained results show that an atomic-resolution of 0.384 nm in the z-direction and a high confidence level of 95% are achieved for imaging the Si-surface structures, quantitatively described by tomographic parameters, i.e., the height (defocus) and the thickness (atom number) of Si-atomic columns.

Prospects for atomic resolution in-line holography for a 3D determination of atomic structures from single projections

It is now established that the 3D structure of homogeneous nanocrystals can be recovered from in-line hologram of single projections. The method builds on a quantitative contrast interpretation of electron exit wave functions. Since simulated exit wave functions of single and bilayers of graphene reveal the atomic structure of carbon-based materials with sufficient resolution, we explore theoretically how the approach can be expanded beyond periodic carbon-based materials to include non-periodic molecular structures. We show here theoretically that the 3D atomic structure of randomly oriented oleic acid molecules can be recovered from a single projection.

Atomic Resolution Imaging of Halide Perovskites

The radiation-sensitive nature of halide perovskites has hindered structural studies at the atomic scale. We overcome this obstacle by applying low dose-rate in-line holography, which combines aberration-corrected high-resolution transmission electron microscopy with exit-wave reconstruction. This technique successfully yields the genuine atomic structure of ultrathin two-dimensional CsPbBr₃ halide perovskites, and a quantitative structure determination was achieved atom column by atom column using the phase information of the reconstructed exit-wave function without causing electron beam-induced sample alterations. An extraordinarily high image quality enables an unambiguous structural analysis of coexisting high-temperature and low-temperature phases of CsPbBr₃ in single particles. On a broader level, our approach offers unprecedented opportunities to better understand halide perovskites at the atomic level as well as other radiation-sensitive materials.

In-line three-dimensional holography of nanocrystalline objects at atomic resolution

Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons. Such unprecedented performance allows expansion of electron microscopic investigations with atomic resolution into the third dimension. Here we report a general tomographic method to recover the three-dimensional shape of a crystalline particle from high-resolution images of a single projection without the need for sample rotation. The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces. We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1–2 Å, which is smaller than inter-atomic distances.

The resolution of transmission electron microscopes allows the imaging of single atoms and determination of their locations in a plane. Here, the authors present a tomographic method to recover the three-dimensional shape of a crystalline particle without the need for sample rotation.

Depth-resolution imaging of crystalline nanoclusters attached on and embedded in amorphous films using aberration-corrected TEM

For observations of crystalline nanoclusters, the features and capabilities of depth-resolution imaging by aberration-corrected transmission electron microscopy (TEM) were investigated using image simulations and experiments for two types of samples. The first sample was gold clusters attached on an amorphous carbon film. The experimental through-focal series indicated that the focal plane for the cluster was shifted 3 nm from that for the supporting film. This difference is due to the depth-resolution imaging of the cluster and film, the mid-planes of which are separated by 3 nm along the depth direction (the electron incident direction). On the basis of this information, the three-dimensional configuration of the sample, such as the film thickness of 2 nm, was successfully illustrated. The second sample was a Zr₆₆.₇Ni₃₃.₃ metallic glass including a medium-range-order (MRO) structure, which was approximately considered to be a crystalline cluster with a diameter of 1.6 nm. In the experimental through-focal series, the lattice fringe of the MRO cluster was visible at limited focal conditions. Image simulations reproduced well the focal conditions and also indicated a structural condition for the visualization that the embedded cluster must be apart from the mid-plane of the matrix film. Similar to the case of the first sample, this result can be explained by the idea that the "effective focal planes" for the film and cluster are at different heights. This type of depth-resolution phase contrast imaging is possible only in aberration-corrected TEM and when the sample has a simple structure and is sufficiently thin for the kinematical scattering approximation.

Determination of the 3D shape of a nanoscale crystal with atomic resolution from a single image

Although the overall atomic structure of a nanoscale crystal is in principle accessible by modern transmission electron microscopy, the precise determination of its surface structure is an intricate problem. Here, we show that aberration-corrected transmission electron microscopy, combined with dedicated numerical evaluation procedures, allows the three-dimensional shape of a thin MgO crystal to be determined from only one single high-resolution image. The sensitivity of the reconstruction procedure is not only sufficient to reveal the surface morphology of the crystal with atomic resolution, but also to detect the presence of adsorbed impurity atoms. The single-image approach that we introduce offers important advantages for three-dimensional studies of radiation-sensitive crystals.

Keyhole electron diffractive imaging (KEDI)

Electron diffractive imaging (EDI) relies on combining information from the high-resolution transmission electron microscopy image of an isolated kinematically diffracting nano-particle with the corresponding nano-electron diffraction pattern. Phase-retrieval algorithms allow one to derive the phase, lost in the acquisition of the diffraction pattern, to visualize the actual atomic projected potential within the specimen at sub-ångström resolution, overcoming limitations due to the electron lens aberrations. Here the approach is generalized to study extended crystalline specimens. The new technique has been called keyhole electron diffractive imaging (KEDI) because it aims to investigate nano-regions of extended specimens at sub-ångström resolution by properly confining the illuminated area. Some basic issues of retrieving phase information from the EDI/KEDI measured diffracted amplitudes are discussed. By using the generalized Shannon sampling theorem it is shown that whenever suitable oversampling conditions are satisfied, EDI/KEDI diffraction patterns can contain enough information to lead to reliable phase retrieval of the unknown specimen electrostatic potential. Hence, the KEDI method has been demonstrated by simulations and experiments performed on an Si crystal cross section in the [112] zone-axis orientation, achieving a resolution of 71 pm.

A method to determine the local surface profile from reconstructed exit waves

Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.