Dynamics of fast electron beams and bounded targets

We analyze the full relativistic force experienced by swift electrons moving close to planar films for the experimental conditions commonly used in electron energy loss spectroscopy in STEM. In metals the main effects derive from the dispersion of the surface plasmons, which are clearly observed in the EEL spectra. In insulators we explore the role played by the Cherenkov radiation (CR) emitted in the energy gap window. The focus is placed on the transverse force and different factors which may turn this force into repulsive, as reported in recent experimental and theoretical works.This project was supported by the ETORTEK project NANOIKER from the Basque Government (BG), project FIS2010-19609-C02-01 from the Spanish Ministry of Science and Innovation and Grant IT-75613 from BG-UPV/EHU.Peer Reviewe

Inelastic scattering of fast electrons in nanowires: A dielectric formalism approach

The excitations produced by fast electrons impinging perpendicularly on both metallic and semiconductor cylindrical nanowires are investigated within the framework of dielectric theory. The dependence of the electron energy-loss spectra (EELS) on the nanowire radius is studied in detail, and so is the spatial extension of the induced-charge fluctuations associated to the modes that are excited during the loss process. The limits of applicability of dielectric theory to nanowires are discussed. In particular, comparison between the present theory and EELS measurements performed with silicon nanofibers support the use of dielectric theory at the scale of a few nanometers in diameter, and it is shown that this positive result is justified in terms of the longitudinal pattern of the induced surface plasmons. Finally, the effect of nanowire termination on the electron energy-loss probability for electrons passing near the edge is calculated using the boundary charge method, showing that the range of this effect can extend up to tens of nanometers for low-energy m=0 modes.Support from the Basque government and Basque Country University is acknowledged. One of the authors E.O. also acknowledges the Spanish Ministerio de Educacion y Cultura for financial support under Contract No. PB98-0780-C02.Peer reviewe

Secondary electron emission in the scattering of fast probes by metallic interfaces

In the frame of a nonretarded local density hydrodynamic approach nonlocal effects in the scattering of a fast probe interacting with a metallic interface are studied. In addition to quantal effects in the electron-gas response, effects derived from the interface density profile are taken into account. The relevance in the excitation spectrum of both collective and single electron excitations is studied. For probes at grazing incidence the decay of collective excitations into single electron ones is found. Around the surface plasmon frequency the momentum carried by these excitations allows identifying them as secondary electrons emerging from the target. The recoil associated with them leads to a repulsive force with qualitative agreement with experimental observations. Effects of the momentum transfer in the deflection angle of the beam are also studied.Peer reviewe

Nonlocal effects in the plasmons of nanowires and nanocavities excited by fast electron beams

14 pp.-- PACS: 73.20.Mf, 79.20.Uv, 68.37.Lp, 78.70.-g.The solutions of surface modes in cylindrical metallic wires and cavities are obtained within a nonlocal dielectric formalism. We compare the results with those obtained from standard local approaches. The specular reflection model is applied to describe the nonlocal potentials in the vicinity of the wires and cavities. The external probe exciting the surface plasmons are fast electron beams traveling parallel to the wires and cavities, as those commonly used in electron microscopy and cathodoluminescence. Energy-loss spectra due to surface-plasmon excitation are calculated with use of the nonlocal formalism both for electron trajectories near a metallic nanowire and a metallic nanocavity. When nonlocal effects are considered, the intensity of the plasmon excitation is reduced, and a blueshift of the energy is observed. This effect is more pronounced for very thin wires and cavities where the cylindrical interfaces are strongly interacting. The blueshifts reported here are important for the accurate design of the plasmon response in one-dimensional metallic nanostructures.Peer reviewe

Relativistic force between fast electrons and planar targets

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.The full retarded electromagnetic force experienced by swift electrons moving parallel to planar boundaries is revisited, for both metallic and dielectric targets, with special emphasis on the consequences in electron microscopy experiments. The focus is placed on the sign of the transverse force experienced by the electron beam as a function of the impact parameter. For point probes, the force is found to be always attractive. The contribution of the induced magnetic field and the causality requirements of the target dielectric response, given by the Kramers-Kronig (K-K) relations, prove to be crucial issues at small impact parameters. For spatially extended probes, repulsive forces are predicted for close trajectories, in agreement with previous works. The force experienced by the target is also explored, with the finding that in insulators, the momentum associated to Cherenkov radiation (CR) is relevant at large impact parameters. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.This project was supported by the ETORTEK project NANOIKER from the Basque Government (BG), project FIS2010-19609-C02-01 from the Spanish Ministry of Science and Innovation, and grant IT-75613 from BG-UPV/EHU.Peer Reviewe

Electron spill-out effects in plasmon excitations by fast electrons

A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.Financial supportthrough Projects no. FIS2016-80174-P of Spanish MINECO and Consolidated Groups at UPV/EHU (grant no. IT1164-19) of the BasqueGovernment is acknowledged

Theory of energy loss in scanning transmission electron microscopy of supported small particles

A general expression for the energy loss probability in scanning transmission electron microscopy (STEM) is derived. The method uses a Green’s function for the incident and scattered electrons and then folds the specimen into a local response function. Our expression is appropriate to any target geometry and dielectric response. As an application, the energy loss spectrum of a STEM electron moving close to an Al sphere half-embedded in an Al planar surface is calculated. The coupling between different l modes, neglected in earlier theoretical approaches, is taken into account.The authors thank the Education Department of the Basque Country Government (project PGV9114.1), Guipuzkoako Foru Aldundia and Iberdrola for help and support and Labein for the use of computing facilities.Peer reviewe

Electron energy loss near supported particles

A general expression for the energy-loss probability in scanning transmission electron microscopy valid for complex microstructures is presented in the framework of classical dielectric theory. Calculations are carried out for small particles half embedded in a planar interface. We used experimental data for the dielectric functions that characterize the media and we take into account the coupling among different multipolar terms. Resonances, present neither in the planar-interface nor in the isolated-sphere energy-loss spectra, are found. The results agree with many experimental results reported in the literature of the last few years. A different behavior between conducting and insulator supports is found. The effect of an oxide coating around the spherical particle is also discussed.They thank the Basque Country Government (project PGV9114.1), Gipuzkoako Foru Aldundiaia and Iberdrola for financial help, and Labein for the use of computing facilities.Peer reviewe

Plasmon excitations at diffuse interfaces

Energy losses experienced by a fast electron probe moving through a dielectric medium have been studied both numerically and analytically, where the response function varies continuously with position in one transverse direction. The frequent assumption that the loss spectrum should exhibit a peak determined by the plasmon energy in a homogeneous medium with the composition found locally at the probe position can be incorrect. In free electron systems, inhomogeneous effects can cause spectral shape changes as well as peak shifts. Computations for diffuse interfaces between semiconductors with differing band gaps are also reported. Prospects for improved spatial resolution in valence loss spectroscopy at higher momentum transfer are discussed. © IOP Publishing Ltd.A Howie thanks Professor P Echenique and the staff of the Donostia International Physics Centre for excellent stimulation and hospitality. This work was supported in part by the Spanish MEC (contract No. FIS2004-06490-C03-02) and by the EU (project No. STRP-016881-SPANS).Peer Reviewe

Electron spill-out effects in plasmon excitations by fast electrons

A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.The author would like to thank A. Howie, P. M. Echenique, N. Zabala and P. Apell for many stimulating discussions. Financial support through Projects no. FIS2016-80174-P of Spanish MINECO and Consolidated Groups at UPV/EHU (grant no. IT1164-19) of the Basque Government is acknowledged