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In this work, Mie resonances in single Si nanoparticles (NPs) of different sizes have been systematically studied, using dark field (DF) and cathodoluminescence (CL) spectroscopy. An analytical method has been developed to compare experiment with theory.
Experimental CL spectra are averaged over entire Si NPs, allowing for direct comparison to DF spectra of identical NPs. Theoretical spectra clarify the assignment of Mie resonances within the NP which contribute with different intensity in DF and CL, resulting in an apparent spectral shift. Furthermore, a substrate effect appears. A 100 nm-Si NP on 15 nm SiN results in a broad peak, spectrally in between that of the calculated electric and magnetic dipole, a NP on 50 nm SiN exhibits two separated peaks as theoretically predicted. High spatial resolution of electron beam excitation allows to study the spectral CL changes at varying beam impact parameters. Theory and experiment agree that depending on beam position within a small Si NP, relative intensity of electric and magnetic dipole change; electric dipole vanishing in the center of the NP. Similar results are found for larger (d = 210 nm) Si NPs although the mode assignment is challenging as higher order modes appear and overlap with others.
In conclusion, comparison of CL and DF spectra is not trivial, in fact, excitation/radiation of distinct Mie resonances within a single Si NP are dependent on beam placement. However, substrate effects need to be considered in CL.
The fabrication of nanostructures with ever-decreasing sizes has increased the demand of suitable characterization methods which allow to determine their shape and size at the true nanoscale, and similarly important, enable the investigation of their optical properties beyond the diffraction limit. Due to its high spectral and spatial resolution down to the (sub-) nanometer range, electron beam-based techniques, namely cathodoluminescence (CL) has become a powerful characterization tool, particularly to study plasmonic and dielectric nanostructures. However, the interpretation of the resulting spectral CL maps is not always unambiguously straightforward.
In this work, Mie resonances in single Si nanospheres of different sizes have been systematically studied, using experimental CL spectroscopy and an analytical CL model. For smaller spheres (r ~ 75 nm), the eigenmodes can be unequivocally identified, with relative changes in intensity of the electric and magnetic dipole depending on the electron beam position within the sphere. However, in larger spheres (r ~ 105 nm), the modal assignment becomes increasingly difficult due to a larger number of Mie modes in the visible spectral range. Additionally, penetrating electron beams generate two radiating dipoles at the two Si interfaces – due to the electron and its image charge collapsing at those interfaces – which can, depending on the electron beam’s velocity and its path length inside the particle, produce distinct resonances or dips (constructive or destructive interference of those two radiative dipoles). It is demonstrated that superimposed on the eigenmodes of the studied nanospheres, these resonances can distort the recorded spectrum and lead to potentially erroneous assignment of modal characters to the spectral features. An intuitive analogy is developed to unambiguously distinguish those resonance induced by transition radiation from the nanoparticle-specific Mie resonances.