Electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) are widely used experimental techniques for characterization of nanoparticles. The discrete dipole approximation (DDA) is a numerically exact method for simulating the interaction of electromagnetic waves with particles of arbitrary shape and internal structure. In this work, we extend the DDA to simulate EELS and CL for particles embedded into arbitrary (even absorbing) unbounded host medium. The latter includes the case of the dense medium, supporting the Cherenkov radiation of the electron, which has never been considered in EELS simulations before. We build a rigorous theoretical framework based on the volume integral equation, final expressions from which are implemented in the open-source software package ADDA. This implementation agrees with both the Lorenz−Mie theory and the boundary-element method for spheres in vacuum and moderately dense host medium. And it successfully reproduces the published experiments for particles encapsulated in finite substrates. The latter is shown for both moderately dense and Cherenkov cases�a gold nanorod in SiO 2 and a silver sphere in SiN x , respectively. For the nanorod, we successfully reproduced the EELS plasmon maps (scans across the particle cross section), although the developed theory is not fully rigorous for electron trajectories intersecting a particle.
To simulate the interaction of a nanoparticle with an electron beam, we previously developed a theoretical description for the general case of a particle fully embedded in an infinite arbitrary host medium. The theory is based on the volume-integral variant of frequency-domain Maxwell’s equations and, therefore, is naturally applicable in the discrete-dipole approximation. The fully-embedded approximation allows fast numerical simulations of the experiments for particles inside a substrate since the host medium discretization is not needed. In this work, we study how applicable the fully-embedded approach is for realistic scenarios with relatively thin substrates. In particular, we performed test simulations for a silver sphere both inside an infinite host medium and inside a finite box or sphere. For the host medium, we considered two non-absorbing cases (the denser one causes Cherenkov radiation), as well as an absorbing case. The peak positions in the obtained spectra approximately agree between substrates a few times thicker than the sphere and the infinite one. However, a much thicker substrate (of the order of μm) would be required to have a qualitative agreement for absolute peak amplitudes. The developed algorithm is implemented in the open-source code ADDA, allowing one to rigorously and efficiently simulate electron-energy-loss spectroscopy and cathodoluminescence by particles of arbitrary shape and internal structure embedded into any homogeneous host medium.
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