Falk Röder

Electron holography for fields in solids: problems and progress.

Electron holography initially was invented by Dennis Gabor for solving the problems raised by the aberrations of electron lenses in Transmission Electron Microscopy. Nowadays, after hardware correction of aberrations allows true atomic resolution of the structure, for comprehensive understanding of solids, determination of electric and magnetic nanofields is the most challenging task. Since fields are phase objects in the TEM, electron holography is the unrivaled method of choice. After more than 40 years of experimental realization and steady improvement, holography is increasingly contributing to these highly sophisticated and essential questions in materials science, as well to the understanding of electron waves and their interaction with matter.

Interconnection of Nanoparticles within 2D Superlattices of PbS/Oleic Acid Thin Films

Make it connected! 2D close-packed layers of inorganic nanoparticles are interconnected by organic fibrils of oleic acid as clearly visualized by electron holography. These fibrils can be mineralised by PbS to transform an organic-inorganic framework to a completely interconnected inorganic semiconducting 2D array.

Noise estimation for off-axis electron holography

Off-axis electron holography provides access to the phase of the elastically scattered wave in a transmission electron microscope at scales ranging from several hundreds of nanometres down to 0.1nm. In many cases the reconstructed phase shift is directly proportional to projected electric and magnetic potentials rendering electron holography a useful and established characterisation method for materials science. However, quantitative interpretation of experimental phase shifts requires quantitative knowledge about the noise, which has been previously established for some limiting cases only. Here, we present a general noise transfer formalism for off-axis electron holography allowing to compute the covariance (noise) of reconstructed amplitude and phase from characteristic detector functions and general properties of the reconstruction process. Experimentally, we verify the presented noise transfer formulas for two different cameras with and without objects within the errors given by the experimental noise determination.

A new linear transfer theory and characterization method for image detectors. Part II: experiment.

A novel generalized linear transfer theory describing the signal and noise transfer in image detectors has been developed in Part I (Niermann, this issue, [1]) of this paper. Similar to the existing notion of a point spread function (PSF) describing the transfer of the first statistical moment (the average), a noise spread function (NSF) was introduced to characterize the spatially resolved transfer of noise (central second moment, covariance). Following the theoretic results developed in Part I (Niermann, this issue, [1]), a new experimental method based on single spot illumination has been developed and applied to measure 2D point and 4D noise spread functions of CCD cameras used in TEM. A dedicated oversampling method has been used to suppress aliasing in the measured quantities. We analyze the 4D noise spread with respect to electronic and photonic noise contributions.

A new linear transfer theory and characterization method for image detectors. Part I: theory.

A new generalized linear transfer theory describing the signal and noise transfer in image detectors is presented, which can be applied to calculate the pixelwise first and second statistical moment of arbitrary experimental images including correlation between pixels. Similar to the existing notion of a point spread function describing the transfer of the first statistical moment (the average), a noise spread function is introduced to characterize the spatially resolved transfer and generation of noise (second central moment, covariance). It is also shown that previously used noise characteristics like the noise power spectrum and detection quantum efficiency, derived from plainly illuminated images, contain only partial information of the complete noise transfer.

Transfer and reconstruction of the density matrix in off-axis electron holography

The reduced density matrix completely describes the quantum state of an electron scattered by an object in transmission electron microscopy. However, the detection process restricts access to the diagonal elements only. The off-diagonal elements, determining the coherence of the scattered electron, may be obtained from electron holography. In order to extract the influence of the object from the off-diagonals, however, a rigorous consideration of the electron microscope influences like aberrations of the objective lens and the Möllenstedt biprism in the presence of partial coherence is required. Here, we derive a holographic transfer theory based on the generalization of the transmission cross-coefficient including all known holographic phenomena. We furthermore apply a particular simplification of the theory to the experimental analysis of aloof beam electrons scattered by plane silicon surfaces.

Direct Depth- and Lateral- Imaging of Nanoscale Magnets Generated by Ion Impact

Nanomagnets form the building blocks for a variety of spin-transport, spin-wave and data storage devices. In this work we generated nanoscale magnets by exploiting the phenomenon of disorder-induced ferromagnetism; disorder was induced locally on a chemically ordered, initially non-ferromagnetic, Fe60Al40 precursor film using  nm diameter beam of Ne+ ions at 25 keV energy. The beam of energetic ions randomized the atomic arrangement locally, leading to the formation of ferromagnetism in the ion-affected regime. The interaction of a penetrating ion with host atoms is known to be spatially inhomogeneous, raising questions on the magnetic homogeneity of nanostructures caused by ion-induced collision cascades. Direct holographic observations of the flux-lines emergent from the disorder-induced magnetic nanostructures were made in order to measure the depth- and lateral- magnetization variation at ferromagnetic/non-ferromagnetic interfaces. Our results suggest that high-resolution nanomagnets of practically any desired 2-dimensional geometry can be directly written onto selected alloy thin films using a nano-focussed ion-beam stylus, thus enabling the rapid prototyping and testing of novel magnetization configurations for their magneto-coupling and spin-wave properties.

Nanoscale three-dimensional reconstruction of elastic and inelastic mean free path lengths by electron holographic tomography

Electron holography at medium resolution simultaneously probes projected electrostatic and magnetostatic potentials as well as elastic and inelastic attenuation coefficients with a spatial resolution of a few nanometers. In this work, we derive how the elastic and inelastic attenuation can be disentangled. Using that result, we perform the first three dimensional tomographic reconstruction of potential and (in)elastic attenuation in parallel. The technique can be applied to distinguish between functional potentials and composition changes in nanostructures, as demonstrated using the example of a GaAs—Al0.33Ga0.67As core-shell nanowire.

Semiclassical TEM image formation in phase space

Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Millers semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity.

Quantitative Imaging of the Magnetic Configuration of Modulated Nanostructures by Electron Holography

By means of off-axis electron holography the local distribution of the magnetic induction within and around a poly-crystalline Permalloy (Ni81Fe19) thin film is studied. In addition the stray field above the sample is measured by magnetic force microscopy on a larger area. The film is deposited on a periodically nanostructured (rippled) Si substrate, which was formed by Xe(+) ion beam erosion. This introduces the periodical ripple shape to the Permalloy film. The created ripple morphology is expected to modify the magnetization distribution within the Permalloy and to induce dipolar stray fields. These stray fields play an important role in spinwave dynamics of periodic nanostructures like magnonic crystals. Micromagnetic simulations estimate those stray fields in the order of only 10 mT. Consequently, their experimental determination at nanometer spatial resolution is highly demanding and requires advanced acquisition and reconstruction techniques such as electron holography. The reconstructed magnetic phase images show the magnetized thin film, in which the magnetization direction follows mainly the given morphology. Furthermore, a closer look to the Permalloy/carbon interface reveals stray fields at the detection limit of the method in the order of 10 mT, which is in qualitative agreement with the micromagnetic simulations.