Abstract
The exact solution of Maxwell's equations in the presence of arbitrarily shaped dielectrics is expressed in terms of surface-integral equations evaluated at the interfaces. The electromagnetic field induced by the passage of an external electron is then calculated in terms of self-consistently obtained boundary charges and currents. This procedure is shown to be suitable for the simulation of electron energy loss spectra when the materials under consideration are described by local frequency-dependent response functions. The particular cases of translationally invariant interfaces and axially symmetric interfaces are discussed in detail. The versatility of this method is emphasized by examples of energy loss spectra for electrons passing near metallic and dielectric wedges, coupled cylinders, spheres, and tori, and other complex geometries, where retardation aspects and Cherenkov losses can sometimes be significant.
Highlights
Resolved energy loss spectroscopy with fast electrons has proved to be a powerful microscopy technique for determining local chemical and electronic structure, when looking at the excitation of target atomic cores.[1]The relatively more intense low-energy, valence excitation part of the loss spectrum is of considerable interest,[2,3,4,5] but so far has been of less practical importance
Electron energy loss spectra can be simulated by setting the external charge to that of a fast electron.[28]
The contribution to the loss probability coming from the first terms in Eqs. ͑6͒ and7͒ does not contain any information about the interface, and it is the same as if the electron were traveling inside the bulk of an infinite material described by a dielectric function ⑀ j and a magnetic permeability j
Summary
Resolved energy loss spectroscopy with fast electrons has proved to be a powerful microscopy technique for determining local chemical and electronic structure, when looking at the excitation of target atomic cores.[1]. A method for simulating EELS with the incorporation of retardation effects in the presence of arbitrarily shaped interfaces has been recently proposed by the authors.[37] It consists in expressing the three-dimensional dependence of the scalar and vector potentials in terms of interface charges and currents via a set of surface integral equations This is the boundary element method61 ͑BEM, where the only assumption, common to all previously discussed methods, is that the different media involved in the structures under study are described by frequency-dependent local dielectric functions and terminate in abrupt interfaces. Gaussian atomic unitsa.u., that is, បϭmϭeϭ1) will be used on, unless otherwise specified
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