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P Schattschneider

Publications and source records attributed to P Schattschneider.

At least 19 recordsLinked to original sources

Inelastic electron holography as a variant of the Feynman thought experiment.

Using a combination of electron holography and energy filtering, interference fringes produced after inelastic interaction of electrons with hydrogen molecules are examined. Surprisingly, the coherence of inelastic scattering increases when moving from the surface of a hydrogen-containing bubble to the vacuum. This phenomenon can be understood in terms of the Feynman two-slit thought experiment with a variable ambiguity of the which-way registration.

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Short note on parallel illumination in the TEM.

Parallel illumination conditions are required for several experiments in the transmission electron microscope (TEM). The image rotation induced by the helical trajectory of electrons passing through the magnetic field of the TEM lenses inevitably induces an inclination of the beam relative to the optical axis in the object plane--even for an electron which travels parallel to the optical axis in the far field. This angle (shear angle) is vectorially added to the convergence angle; it depends both on the distance to the optical axis and the magnetic field. By using a beam tilt compensation method, the minimum shear angle is found to be of the order of 1 mrad for a field of view of 2 microm in a 200 kV TEM. In practice, "parallel illumination" can only be obtained for fields of view 1 microm.

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ELNES at magic angle conditions.

If one needs to cancel the effects of the anisotropy of the sample in a EELS experiment in the TEM, a particular couple of values for the collection and convergence angle must be used, called magic angle conditions (MAC). Recent developments in the theory have shown that a full relativistic treatment is mandatory to correctly describe this effect and that the MAC are strongly dependent on the acceleration voltage. We show how the analytical formula can be derived and give the exact analytical solution for the MAC which can then be easily applied to every practical case. We show the consequences of the energy dependence of the magic angle and that the parallelity of the beam will be the limiting factor for high acceleration voltages while for low acceleration voltages the contribution coming from Bragg spots may make it impossible to reach MAC.

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Detection of magnetic circular dichroism using a transmission electron microscope.

A material is said to exhibit dichroism if its photon absorption spectrum depends on the polarization of the incident radiation. In the case of X-ray magnetic circular dichroism (XMCD), the absorption cross-section of a ferromagnet or a paramagnet in a magnetic field changes when the helicity of a circularly polarized photon is reversed relative to the magnetization direction. Although similarities between X-ray absorption and electron energy-loss spectroscopy in a transmission electron microscope (TEM) have long been recognized, it has been assumed that extending such equivalence to circular dichroism would require the electron beam in the TEM to be spin-polarized. Recently, it was argued on theoretical grounds that this assumption is probably wrong. Here we report the direct experimental detection of magnetic circular dichroism in a TEM. We compare our measurements of electron energy-loss magnetic chiral dichroism (EMCD) with XMCD spectra obtained from the same specimen that, together with theoretical calculations, show that chiral atomic transitions in a specimen are accessible with inelastic electron scattering under particular scattering conditions. This finding could have important consequences for the study of magnetism on the nanometre and subnanometre scales, as EMCD offers the potential for such spatial resolution down to the nanometre scale while providing depth information--in contrast to X-ray methods, which are mainly surface-sensitive.

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Cerenkov losses: a limit for bandgap determination and Kramers-Kronig analysis.

Measuring low energy losses in semiconductors and insulators with high spatial resolution becomes attractive with the increasing availability of modern transmission electron microscopes (TEMs) equipped with monochromators, C(s) correctors and energy filters. In this paper, we demonstrate that Cerenkov losses pose a limit for the interpretation of low energy loss spectra (EELS) in terms of interband transistions and bandgap determination for many materials. If the velocity of a charged particle in a medium exceeds the velocity of light, photons are emitted leading to a corresponding energy loss of a few electronvolt. Since these losses are strong for energies below the onset of interband transitions, they change the apparent loss function of semiconductors and insulators, with the risk of erroneous interpretation of spectra. We measured low energy losses of Si and GaAs with a monochromated TEM demonstrating the effect of sample thickness on Cerenkov losses. Angle resolved EELS and energy filtered diffraction patterns (taken without a monochromator) show the extremely narrow angular distribution of Cerenkov losses. The latter experiment provides a method that allows to decide whether Cerenkov radiation masks the very low loss signal in EELS.

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Plasmon holographic experiments: theoretical framework.

A theoretical framework is described to understand the results of plasmon holography experiments leading to insight in the meaning of the experimental results and pointing out directions for future experiments. The framework is based on the formalism of mutual intensity to describe how coherence is transferred through an optical system. For the inelastic interaction with the object, an expression for the volume plasmon excitations in a free electron gas is used as a model for the behaviour of aluminium. The formalism leads to a clear graphical intuitive tool for understanding the experiments. It becomes evident that the measured coherence is solely related to the angular distribution of the plasmon scattering in the case of bulk plasmons. After describing the framework, the special case of coherence outside a spherical particle is treated and the seemingly controversial idea of a plasmon with a limited coherence length obtained from experiments is clarified.

Holography↗

The magic angle: a solved mystery.

We resolve the long-standing mysterious discrepancy between the experimental magic angle in EELS--approximately 2theta(E)--and the quantum mechanical prediction of approximately 4theta(E). A relativistic approach surpassing the usually applied kinematic correction yields a magic angle close to the experimental value. The reason is that the relativistic correction of the inelastic scattering cross section in anisotropic systems is significantly higher than in isotropic ones.

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Channeling, localization and the density matrix in inelastic electron scattering.

Building on the relationship between the mixed dynamic form factor (MDFF) for inelastic electron scattering and the one-particle density matrices of the initial and final states of the scatterer it is shown that the MDFF contains information both on the spatial density and the spatial coherence of excitations. We discuss how the MDFF can-at least partly-be measured in scattering geometries invoking channeling conditions. Therefrom, the localization of inelastic events can be determined.

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A proposal for dichroic experiments in the electron microscope.

Building upon the similarities between inelastic electron scattering and X-ray absorption we show that dichroism can be observed in electron energy loss spectrometry (EELS) in the transmission electron microscope (TEM). Natural or magnetic linear dichroism can be studied in electron scattering experiment with definite wave vector transfer in the interaction.The detection of circular dichroism in the TEM relies on interferometric EELS in a particular scattering geometry that allows extraction of the mixed dynamic form factor from energy loss spectra. Similarities between dichroic signals in energy loss near edge structures and X-ray absorption near edge structures are discussed, and a new experimental setup for dichroic measurements in the TEM is proposed.

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Improvement of energy loss near edge structure calculation using Wien2k.

The density functional theory (DFT) is a recognised method for the calculation of electronic properties of materials. As such it can also be used for the calculation of energy loss near edge structures. Some care has to be taken since the DFT is intended for ground state calculation. The effect of the core hole left by the excited electron is different in an insulator and in a metal and can be observed in both cases. For an insulator (MgO, Si), a supercell calculation is needed while in the case of copper, extremely good agreement with experiment can be obtained with a partial core hole calculation. In the particular case of the WIEN code (APW method) we show that calculation of low lying edges (Si L at 99eV) where the initial state is not strongly localised can only be done within the dipole approximation and with some care. Random alloys (CuNi) have been calculated previously using a supercell; we show that a particular version of the virtual crystal approximation gives promising results.

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The separation of surface and bulk contributions in ELNES spectra.

We present a method to separate surface from volume contributions in the fine structure of ionization edges in electron energy loss spectrometry (ELNES). It is based on spectra taken at two positions with different surface-to-volume ratio. Contrary to the similar spatial difference method it uses well defined scaling factors, allowing an estimate of the errors propagated into the result.

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Separation of pure elemental and oxygen influenced signal in ELNES.

The energy loss near edge structure (ELNES) of many elements is strongly influenced by the presence of oxygen or other elements at surfaces, grain boundaries, or in the bulk material. The presented investigation deals mainly with the influence of oxygen at the surface. A method for the separation of both, the pure bulk signal and the oxidized surface signal, was evaluated and tested on Al, Cu, Mg, and Si. A comparison of experimental data with ab initio bandstructure calculations and other proofs of the accuracy of ELNES separation are presented. Influences of error propagations were tested and are exemplarily given for Al and Si.

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Orientation dependence of ionization edges in EELS.

Anisotropy in the density of unoccupied states can be detected in the fine structure of ionization edges in angle-resolved EELS. It is shown that in a crystal an interference term occurs in the inelastic signal, and how it relates to electron channeling and site selection. The combination of orientation and site selection induces subtle variations in the ELNES. It is shown how this technique can be used to analyze local anisotropy related to the point group of the target atom. A second example shows how to extract non-dipole transitions at small scattering angles.

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Energy loss near edge structure of sulfur in non-stoichiometric CuInS(2)

Non-stoichiometric CuInS(2) is a novel material for thin film solar cells. Electron energy loss spectrometry analysis shows that there are considerable lateral inhomogeneities on a scale of less than 100nm. It is as yet unknown whether the Cu or In surplus comes in nanoprecipitates irregularly distributed in the otherwise stoichiometric matrix, or forms supercells where particular atoms are replaced by their complements. This question bears important consequences for the understanding of the local electronic structure and the mechanism of undesired recombination processes in the cell. Since the energy-loss near edge structure of ionisation edges (ELNES) mirrors the local density of unoccupied states it should be different in the two cases. We compare the sulfur L(2,3) ELNES of a Cu-rich and of an In-rich specimen with simulations of supercells based on the TELNES/WIEN97 code. Faint differences in the edge shape can be made visible using difference spectra. They agree reasonably well with simulations. The results show that the surplus species exists as a separate non-stoichiometric phase and not merely as a precipitate of elemental Cu or In.

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Observation of ionization in a crystal interferometer

We present a new interferometric setup where interference of a fast probe electron affects the ionization cross section of an atom. Interference is detected in the intensity of the inelastically scattered electrons at the Bragg scattering angle in transmission. The crystal serves both as a target for core ionization and as a beam-splitting and phase-shifting device.

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The orientation-dependent simulation of ELNES

We describe a program that allows the simulation of energy-loss near edge structure (ELNES). As an extension to the WIEN97 package (a full potential linearized augmented plane wave package for calculating crystal properties) [1] it permits to separate different contributions to the inelastic scattering cross section according to the character of the final state, explicitly taking into account projection onto scattering vector and integration over collection and convergence angle. Thus the program facilitates analysis of ELNES under precisely defined experimental conditions, and allows the investigation of anisotropic effects in ELNES from crystal structures. Dipole-allowed as well as dipole-forbidden transitions can be analyzed with this program.

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The physical significance of the mixed dynamic form factor

We show that the mixed dynamic form factor for inelastic scattering of fast electrons in crystals is closely related to the density matrix of the probe electron and to that of the scatterer. With this insight it is possible to calculate both energy filtered diffraction patterns and energy spectroscopic high-resolution images. As an example we discuss the Si-K and -L edges.

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