# Plasmonics in the Ultraviolet with Aluminum, Gallium, Magnesium and Rhodium
## 4 Comparison of the Plasmonic Response of Simple Geometries: Oxidation Effects  
In this section, we will compare the plasmonic response in both the near- and far-field regimes of nanostructures made of Al, Mg, Ga and Rh. The parameter of interest in the far-field regime will be the absorption cross-section \(C_{abs}\), while for the near-field we calculate the enhancement of the local intensity averaged over the NP surface \(\langle|E|^{2}\rangle\). From now on, we will refer to \(\langle|E|^{2}\rangle\) as _averaged local enhancement_ for brevity. In the case of Al, Mg and Ga, NPs will be modeled with an oxide thickness of 3, 5 and 1 nm, respectively, to be consistent with previous numerical and experimental studies [20; 22; 49]. Figure 2 shows the complex dielectric permittivity (\(\epsilon=\epsilon_{r}+i\epsilon_{i}\)) of these metals and their corresponding oxides. The values of the complex dielectric permittivity have been taken from different sources in the literature [18; 20; 79]. Note the similar optical behavior shown by Mg and Al oxides, while Ga\({}_{2}\)O\({}_{3}\) shows absorption in the UV region above 3 eV. As in a previous work [80], we have considered tripod stars (\(l=10\) nm, \(w=5\) nm and \(h~{}=~{}5\) nm), cubes (\(L=8.1139\) nm) and spheres (\(R=5.0335\) nm) with equivalent volume. By choosing nanoparticles with the same volume but different shape, it is possible to explore the rela  
Figure 2: Real (solid line) and imaginary (dashed line) parts of the complex relative permittivity (\(\epsilon=\epsilon_{r}+i\epsilon_{i}\)) of Al, Mg, Ga, Rh (**left**) and their corresponding oxides (**right**) as a function of the photon energy of the incident beam. The values of the complex relative permittivities have been taken from different sources from the literature [18; 20; 79]. shape (corners and edges effects included) and the material. Such small NPs are highly demanded in photocatalysis applications. It is well known that small NPs have higher catalytic activity than larger ones due to their increased surface to volume ratio. The hot-electrons produced by LSPR excitation in these small NPs are more likely to reach the surface and enter anti-bonding orbitals of adsorbed molecules, thereby weakening a critical bond and accelerating the reaction [38]. Figure 3 shows the absorption cross-section \(C_{abs}\) (top row) and averaged local enhancement \(\langle|E|^{2}\rangle\) (bottom row) for equivalent tripod stars, spheres, and cubes made of Al + Al\({}_{2}\)O\({}_{3}\), Mg + MgO, Ga + Ga\({}_{2}\)O\({}_{3}\) and Rh. The oxide shell thickness in each case has been set to 3, 5 and 1 nm respectively [22; 24; 49]. The aforementioned dimensions for the tripod stars, cubes and spheres already include the thickness of oxide shell in each case. The percentage of metal content in each nanoparticle is shown in Table 1. This magnitude is defined as \(V(metal)/V(metal+oxide)\times 100\), where \(V\) represents the volume of either metal or metal+oxide within the NP. Figure 4 shows the \(|E|^{2}\) maps (logarithmic scale) at E = 3.82 eV (\(\lambda\) = 325 nm, HeCd laser) for Rh and Ga + Ga\({}_{2}\)O\({}_{3}\) tripod stars (\(l\) = 10 nm, \(w\) = 5 nm and \(h\) = 5 nm), nanoc \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metal** & **Tripod Star** & **Cube** & **Sphere** \\ \hline Al + Al\({}_{2}\)O\({}_{3}\) & 0\% & 1.8\% & 6.6\% \\ Mg + MgO & 0\% & 0\% & 0\% \\ Ga + Ga\({}_{2}\)O\({}_{3}\) & 22\% & 42\% & 51\% \\ Rh & 100\% & 100\% & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Percentage of metal content in each of the studied nanoparticles. Figure 3: Spectral enhancement of the local intensity averaged over the NP surface \(\langle|E|^{2}\rangle\) (left column) and the absorption cross-section \(C_{abs}\) for equivalent tripod stars (\(l\) = 10 nm; \(w\) = \(h\) = 5 nm), cubes (\(L\) = 8.1139 nm) and spheres (\(R\) = 5.0335 nm) composed of Al + Al\({}_{2}\)O\({}_{3}\), Mg + MgO, Ga + Ga\({}_{2}\)O\({}_{3}\) and Rh, illuminated under normal incidence. spheres (\(R=5.0335\) nm).