A "Phase Scrambling" Algorithm for Parallel Multislice Simulation of Multiple Phonon and Plasmon Scattering Configurations.

Multislice simulations of 4D scanning transmission electron microscopy (4D STEM) data are computationally demanding due to the large number of STEM probe positions that must be calculated. For accurate analysis, inelastic scattering from phonons and plasmons must also be included. However, current frozen phonon and Monte Carlo plasmon techniques require a separate calculation for each different phonon/plasmon configuration, and are therefore not suitable for scaling up to 4D STEM. Here a phase scrambling algorithm (PSA) is proposed, which treats all phonon/plasmon configurations simultaneously. A random phase is introduced to maintain incoherence between the different inelastic scattering events; this is the phase scrambling part of the algorithm. While for most applications, a few tens of frozen phonon iterations are sufficient for convergence, in the case of plasmon scattering as many as tens of thousands of iterations may be required. A PSA is statistically more representative of inelastic scattering, and achieves significant savings in computation time for plasmons. The increase in speed is a pre-requisite for 4D STEM inelastic scattering simulations.

Electron Compton scattering and the measurement of electron momentum distributions in solids.

Electron Compton scattering is a technique that gives information on the electron momentum density of states and is used to characterize the ground state electronic structure in solids. Extracting the momentum density of states requires us to assume the so-called 'impulse approximation', which is valid for large energy losses. Here, the robustness of the impulse approximation in the low energy transfer regime is tested and confirmed on amorphous carbon films. Compared to traditional Compton measurements, this provides additional benefits of more efficient data collection and a simplified way to probe valence electrons, which govern solid state bonding. However, a potential complication is the increased background from the plasmon signal. To overcome this, a novel plasmon background subtraction routine is proposed for samples that are resistant to beam damage. LAY DESCRIPTION: Properties of solids depend on their electronic structure which can be studied using electron Compton scattering technique. Here, an electron beam is used to penetrate a very thin sample. During the interaction between the electrons in the beam and electrons in the sample, the former transfer a part of their energy to the latter, resulting in a measurable energy loss of the transmitted beam. The amount of the energy transfer depends on the angle of incidence between the beam and the sample. Typically, the experiments are carried out using high tilt angles and high energy transfer; however, in this work, we show that even smaller angles of incidence are suitable, which improve the signal quality and ease data processing procedures.

Long Lifetime Hole Traps at Grain Boundaries in CdTe Thin-Film Photovoltaics.

A novel time-resolved cathodoluminescence method, where a pulsed electron beam is generated via the photoelectric effect, is used to probe individual CdTe grain boundaries. Excitons have a short lifetime (≤100 ps) within the grains and are rapidly quenched at the grain boundary. However, a ~47 meV shallow acceptor, believed to be due to oxygen, can act as a long lifetime hole trap, even at the grain boundaries where their concentration is higher. This provides direct evidence supporting recent observations of hopping conduction across grain boundaries in highly doped CdTe at low temperature.

Microstructure and point defects in CdTe nanowires for photovoltaic applications.

Defects in Au-catalysed CdTe nanowires vapour-liquid-solid-grown on polycrystalline underlayers have been critically evaluated. Their low-temperature photoluminescence spectra were dominated by excitonic emission with rarely observed above-gap emission also being recorded. While acceptor bound exciton lines due to monovalent metallic impurities (Ag, Cu or Na) were seen, only deeper, donor-acceptor-pair emission could be attributed to the Au contamination that is expected from the catalyst. Annealing under nitrogen acted to enhance the single crystal-like PL emission, whilst oxidizing and reducing anneals of the type that is used in solar cell device processing caused it to degrade. The incidence of stacking faults, polytypes and twins was related only to the growth axes of the wires (<111> 50%, <112> 30% and <110> 20%), and was not influenced by annealing. The potential electrical activity of the point and extended defects, and the suitability of these nanowire materials (including processing steps) for solar cell applications, is discussed. Overall they have a quality that is superior to that of thin polycrystalline films, although questions remain about recombination due to Au.

Coherent electron Compton scattering and the non-diagonal electron momentum density of solids.

Experimental techniques that probe the electronic structure of crystalline solids are vital for exploring novel condensed matter phenomena. In coherent Compton scattering the Compton signal due to interference of an incident and Bragg diffracted beam is measured. This gives the projected, non-diagonal electron momentum density of the solid, a quantity that is sensitive to both the amplitude and phase of the electron wavefunction. Here coherent electron Compton scattering is demonstrated using electron energy loss spectroscopy in the transmission electron microscope. The technique has several advantages over coherent X-ray Compton scattering, such as a superior spatial resolution and the use of smaller specimens to generate Bragg beams of sufficient intensity. The conditions for a directly interpretable coherent electron Compton signal are established. Results are presented for the projected, non-diagonal electron momentum density for silicon under 004 and 2¯20 Bragg beam set ups.

Quantifying Molecular Disorder in Tri-Isopropyl Silane (TIPS) Pentacene Using Variable Coherence Transmission Electron Microscopy.

Structural disorder in molecular crystals is a fundamental limitation for achieving high charge carrier mobilities. Quantifying and uncovering the mechanistic origins of disorder are, however, extremely challenging. Here we use variable coherence transmission electron microscopy to analyze disorder in tri-isopropyl silane pentacene films, utilizing diffuse scattering that is present both as linear streaks and as a slowly varying, isotropic background. The former is due to thermal vibration of the pentacene molecules along their long axis, while the latter is due to static defects kinetically frozen during film deposition. The thermal vibrational amplitude is ∼0.4 Å, while the static displacement parameter in our simplified analysis is much larger (1.0 Å), because it represents the cumulative scattering of all defect configurations that are frozen in the film. Thin film fabrication therefore has an important effect on crystallinity; our technique can be readily used to compare samples prepared under different conditions.

Quantum theory of magnon excitation by high energy electron beams.

The role of magnon inelastic scattering in high energy electron diffraction of spin unpolarised electron beams, including vortex beams, is investigated theoretically for a Heisenberg ferromagnet. The interaction is between the atomic magnetic dipoles in the specimen and orbital angular momentum (OAM) of the electron beam. Magnon inelastic scattering by vortex beams is allowed despite many atoms along the magnon spin wave experiencing mixed OAM states. The scattering cross-section is however independent of the vortex beam winding number. In the case of planes waves in ferromagnetic iron, the magnon diffuse scattered intensity is significantly smaller than phonons in the energy loss range currently accessible by state-of-the-art monochromated electron energy loss spectroscopy (EELS). Nevertheless, it is shown that the long-range magnetic field of the atomic dipoles has a similar role to dipole scattering in phonon excitation. This means that magnons could, in principle, be detected using aloof beam EELS, where long acquisition times can be realised without any specimen beam damage, an important pre-requisite for detecting the weak magnon signal.

Background subtraction in electron Compton spectroscopy.

Compton scattering in electron energy loss spectroscopy (EELS) is used to quantify the momentum distribution of occupied electronic states in a solid. The Compton signal is a broad feature with a width of several hundred eV. Furthermore, the weak intensity results in a low peak-to-background ratio. Removing the background under the Compton profile is therefore particularly challenging, especially if there is an overlap with EELS core loss edges. Here an empirical background subtraction routine is proposed that uses input data from a bright-field EELS spectrum that does not have a Compton signal. The routine allows for multiple elastic-inelastic scattering within the EELS collection angles. Background subtraction is demonstrated on a Compton profile in silicon that overlaps with the Si L-edge. Systematic errors in the method are also discussed.

A semi-classical theory of magnetic inelastic scattering in transmission electron energy loss spectroscopy.

The feasibility of detecting magnetic excitations using monochromated electron energy loss spectroscopy in the transmission electron microscope is examined. Inelastic scattering cross-sections are derived using a semi-classical electrodynamic model, and applied to AC magnetic susceptibility measurements and magnon characterization. Consideration is given to electron probes with a magnetic moment, such as vortex beams, where additional inelastic scattering can take place due to the change in magnetic potential energy of the incident electron in a non-uniform magnetic field. This so-called 'Stern-Gerlach' energy loss can be used to enhance the strength of the scattering by increasing the orbital angular momentum of the vortex beam, and enables separation of magnetic from non-magnetic (i.e. dielectric) energy losses, thus providing a promising experimental route for detecting magnons. AC magnetic susceptibility measurements are however not feasible using Stern-Gerlach energy losses for a vortex beam.

Theory underpinning multislice simulations with plasmon energy losses.

The theoretical conditions for small-angle inelastic scattering where the incident electron can effectively be treated as a particle moving in a uniform potential is examined. The motivation for this work is the recent development of a multislice method that combines plasmon energy losses with elastic scattering using Monte Carlo methods. Since plasmon excitation is delocalized, it was assumed that the Bloch wave nature of the incident electron in the crystal does not affect the scattering cross-section. It is shown here that for a delocalized excitation the mixed dynamic form factor term of the scattering cross-section is zero and the scattered intensities follow a Poisson distribution. These features are characteristic of particle-like scattering and validate the use of Monte Carlo methods to model plasmon losses in multislice simulations.

Planck's generalised radiation law and its implications for cathodoluminescence spectra.

Cathodoluminescence (CL) is an important analytical technique for probing the optical properties of materials at high spatial resolution. Interpretation of CL spectra is however complicated by the fact that the spectrum depends on the carrier injection density of the incident electron beam. Here a generalised version of Planck's radiation law is used to uncover the evolution of CL spectra with injection under steady-state conditions. The importance of the quasi-Fermi level is highlighted and it is shown that steady-state luminescence is suppressed when the carrier distributions undergo a population inversion. The theory is consistent with some well-known luminescence phenomena, such as the blue shifting of donor-acceptor pair transitions with increased injection, and its predictions are experimentally verified on CdTe and GaN, which are exemplar thin-film solar cell and light emitting diode materials respectively. Furthermore, the discussion is broadened to include pulsed illumination in time resolved CL, where the carrier distribution is dynamically evolving with time.

An inelastic multislice simulation method incorporating plasmon energy losses.

Quantitative electron microscopy requires accurate simulation methods that take into account both elastic and inelastic scattering of the high energy electrons within the specimen. Here a method to combine plasmon excitations, the dominant energy loss mechanism in a solid, with conventional frozen phonon, multislice simulations is presented. The Monte Carlo based method estimates the plasmon scattering path length and scattering angle using random numbers and modifies the transmission and propagator functions in the multislice calculation accordingly. Comparison of energy filtered, convergent beam electron diffraction patterns in [110]-Si show good agreement between simulation and experiment. Simulations also show that plasmon excitation decreases the high angle annular dark field signal from atom columns, due to the plasmon scattering angle suppressing electron beam channeling along the atom columns. The effect on resolution and peak-to-background ratio of the atom columns is however small.

Bloch wave analysis of the Eshelby twist contrast around end-on screw dislocations in bcc Mo.

In high-resolution electron microscopy (HREM), dislocation core structures are examined by tilting the dislocation end-on along the appropriate zone axis. For end-on screw dislocations diffraction contrast is largely due to surface relaxation in the form of the Eshelby twist. In this paper, simulated, many-beam images of end-on, 1/2<111> Mo screw dislocations in a thin TEM foil are presented. The diffraction contrast is found to be rotationally symmetric and of very low value. Bloch waves are used to explain the physical origin of the contrast. Diffraction contrast is, however, significantly enhanced by using an annular aperture which includes only the diffracted beams. Annular aperture contrast is largest for foil thicknesses corresponding to minima in the dark-field pendellösung.

The role of transition radiation in cathodoluminescence imaging and spectroscopy of thin-foils.

There is renewed interest in cathodoluminescence (CL) in the transmission electron microscope, since it can be combined with low energy loss spectroscopy measurements and can also be used to probe defects, such as grain boundaries and dislocations, at high spatial resolution. Transition radiation (TR), which is emitted when the incident electron crosses the vacuum-specimen interface, is however an important artefact that has received very little attention. The importance of TR is demonstrated on a wedge shaped CdTe specimen of varying thickness. For small specimen thicknesses (<250nm) grain boundaries are not visible in the panchromatic CL image. Grain boundary contrast is produced by electron-hole recombination within the foil, and a large fraction of that light is lost to multiple-beam interference, so that thicker specimens are required before the grain boundary signal is above the TR background. This is undesirable for high spatial resolution. Furthermore, the CL spectrum contains additional features due to TR which are not part of the 'bulk' specimen. Strategies to minimise the effects of TR are also discussed.

Dynamic scattering of electron vortex beams--a Bloch wave analysis.

Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (〈Lz〉) transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the 〈Lz〉 pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±h angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in 〈Lz〉. This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the 〈Lz〉 pendellösung.

On the electron vortex beam wavefunction within a crystal.

Electron vortex beams are distorted by scattering within a crystal, so that the wavefunction can effectively be decomposed into many vortex components. Using a Bloch wave approach equations are derived for vortex beam decomposition at any given depth and with respect to any frame of reference. In the kinematic limit (small specimen thickness) scattering largely takes place at the neighbouring atom columns with a local phase change of π/2rad. When viewed along the beam propagation direction only one vortex component is present at the specimen entrance surface (i.e. the 'free space' vortex in vacuum), but at larger depths the probe is in a mixed state due to Bragg scattering. Simulations show that there is no direct correlation between vortex components and the 〈Lz〉 pendellösung, i.e. at a given depth probes with relatively constant 〈Lz〉 can be in a more mixed state compared to those with more rapidly varying 〈Lz〉. This suggests that minimising oscillations in the 〈Lz〉 pendellösung by probe channelling is not the only criterion for generating a strong electron energy loss magnetic circular dichroism (EMCD) signal.

Prospects for electron microscopy characterisation of solar cells: opportunities and challenges.

Several electron microscopy techniques available for characterising thin-film solar cells are described, including recent advances in instrumentation, such as aberration-correction, monochromators, time-resolved cathodoluminescence and focused ion-beam microscopy. Two generic problems in thin-film solar cell characterisation, namely electrical activity of grain boundaries and 3D morphology of excitionic solar cells, are also discussed from the standpoint of electron microscopy. The opportunities as well as challenges facing application of these techniques to thin-film and excitonic solar cells are highlighted.

Characterising the surface and interior chemistry of core-shell nanoparticles using scanning transmission electron microscopy.

A method for extracting core and shell spectra from core-shell particles with varying core to shell volume fractions is described. The method extracts the information from a single EELS spectrum image of the particle. The distribution of O and N was correctly reproduced for a nanoparticle with a TiN core and Ti-oxide shell. In addition, the O distribution from a nanoparticle with a Cu core and a Cu-oxide shell was obtained, and the extracted Cu L(2,3)-core and shell spectra showed the required change in EELS near edge fine structure. The extracted spectra can be used for multiple linear least squares fitting to the raw data in the spectrum image. The effect of certain approximations on numerical accuracy, such as treating the nanoparticle as a perfect sphere, as well as the intrinsic detection limits of the technique have also been explored. The technique is most suitable for qualitative, rather than quantitative, work.

Electron beam-specimen interactions and their effect on high-angle annular dark-field imaging of dopant atoms within a crystal.

A Bloch wave model based on perturbation theory is used to analyse high-angle annular dark-field (HAADF) imaging of a substitutional and interstitial W atom in [111]-oriented body-centred-cubic Fe. For the substitutional atom the 1s Bloch state is scattered to high angles thereby producing HAADF dopant atom contrast. Intraband scattering of the 1s state is the strongest individual Bloch wave transition but collective interband scattering of the non-1s states to the 1s state leads to variations in the high-angle scattering with depth of the dopant atom. The non-1s states are Coulomb attracted towards the W atom thereby giving rise to an 'atom focusing' effect similar to channelling. For the interstitial atom, which in the [111] orientation does not overlap with an atom column of the host lattice, high-angle scattering and Coulomb attraction takes place through the non-1s states. Scattering of the 1s state is, however, negligible.