# The UV Plasmonic Behavior of Rhodium Tetrahedrons--A Numerical Analysis
## 3 Results and Discussion
### Rh Tetrahedra: Effect of a Concavity
However, the drop  
Figure 6: (a) Absorption cross-sections (\(C_{abs}\)) of edge length \(L=20\) nm Rh TDs with a concavity with increasing size \(t\) while keeping its depth constant \(d=3\) nm; (b) local field enhancement (\(|\mathbf{E}|^{2}\)) averaged over the TD’s surface; (c) local field enhancement in logarithmic scale (\(|\mathbf{E}|^{2}\)) over the surface of the different TD when illuminated with the corresponding resonant wavelength. in the value of \(\langle|\sigma|\rangle_{in}\) is smaller (from 0.57 to 0.36) than the increase of \(\langle|\sigma|\rangle_{out}\) (from 0.60 to 1.00). Thus, with a intermediate concavity size it is possible to keep a large reactive surfaces with a high values of \(\langle|\sigma|\rangle\) simultaneously inside and outside the concavity. In small concavities, the angle between the inner and inner-outer faces is smaller, leading to an enhancement of the lightning rod effect [24] on those regions, and subsequently, to larger charge concentrations (higher \(\langle|\sigma|\rangle_{in}\)). Figure 7c shows the value \(\sigma\) on the surface of the TDs when illuminated at resonance. The highest surface charge concentrations are located at the external edges and corners of the TDs as evidenced by the high values of \(\langle|\sigma|\rangle_{out}\) in comparison with those of \(\langle|\sigma|\rangle_{in}\). After analyzing the effect of the size of the concavity, now we will address the effect that has its depth on \(C_{abs}\), \(\langle|\mathbf{E}|^{2}\rangle\) and \(\sigma\). As in the previous cases, we will consider a TD with \(L=20\) nm. The concavity size has been fixed to \(t=5\) nm and its depth \(d\) has been varied from 0 to 4 nm. Figure 8 shows the (a) \(C_{abs}\) and (b) \(\langle|\mathbf{E}|^{2}\rangle\) spectra for different values of \(d\). It can be seen how the \(C_{abs}\) peaks red-shift and slightly increase with \(d\) while their width progressively lowers. A similar trend can be seen in the case of \(\langle|\mathbf{E}|^{2}\rangle\)--the wide peak appearing for the perfect TD red-shifts and narrows as \(d\) becomes larger. Again, the red-shift and narrowing of the LSPR peak can be understood in terms of the constrain in the oscillation amplitude of the electrons that the concavity impose. By looking at the local field enhancement on the surface of the TDs (Figure 8c), it is clear that, as concavity becomes deeper, the values of \(|\mathbf{E}|^{2}\), evenly distributed along the edges for the perfect TD, are redistributed into the bottom corners and the inner edges of the concavity. Attending to the normalized surface charge density averaged outside and inside the concavity (\(\langle|\sigma|\rangle_{out}\) and \(\langle|\sigma|\rangle_{in}\)), we have looked at the possibility of simultaneously maximizing both magnitudes in order to increase the reactivity in the external edges and corners as well as in the defect-rich inner surfaces of the concavity. Figure 9 shows the average of the absolute value of the surface charge density (a) outside \(\langle|\sigma|\rangle_{out}\) and (b) inside \(\langle|\sigma|\rangle_{in}\) the concavity. It is clear that, by deepening the concavity, the surface charge density inside and outside increases. Therefore, the deeper the concavity the higher are the values of \(\langle|\sigma|\rangle_{out}\) and \(\langle|\sigma|\rangle_{in}\). The increasing value of \(\langle|\sigma|\rangle_{in}\) with \(d\) can  
Figure 7: **(a)** Normalized spectral values of surface charge distribution (\(\sigma\)) averaged over the exterior faces and (b) over the concavity of the TDs as a function of the concavity size \(t\) while keeping its depth constant \(d=3\) nm. **(c)** Surface charge distribution (\(\sigma\)) over the concave Rh TDs. The red/blue regions represent positive/negative charge densities.