## 3 Structural Design of Plasmon-Mediated Photocatalysts
### Generating Efficiency Improvement of HCs
#### 3.1.1 Design of Structures with \"Hot Spots\"  
Recently, it has been shown that the plasmonic metals with \"hot spots\", where the EM fields are strongly amplified in small regions, can boost the rates of generation of HCs [54; 55; 56; 57]. Furthermore, this is attributed to two physical reasons [58]: (1) the enhancement of local EM fields in classical effects and (2) the non-conservation of the linear momentum of electrons in quantum formalism. In recent reports, the relations between the rates of generation of HCs and local EM fields were established as follows [59; 60]:  
\[Rate_{high-energy,\varepsilon>\Delta E_{b}}=\frac{2}{\pi^{2}}\times\frac{e^{2} E_{F}^{2}}{\hbar}\frac{\hbar\omega-\Delta E_{b}}{\left(\hbar\omega\right)^{4}} \int_{S_{\rm NC}}\left|E_{normal}(\theta,\varphi)\right|^{2}\!ds \tag{7}\]  
Figure 2: (**a**) The decay of excited surface plasmons (SPs) in plasmonic metal. (**b**) The transitions of hot carriers (HCs) in two ways, Intraband transition and Interband transition. (**c**) The scheme of transportation of HCs in plasmon induced hot-electron transfer (PHET) and (**d**) in plasmon induced metal-to-semiconductor interfacial charge transfer transition (PICTT). (**e**) The diffusions of HCs and the photocatalytic process of the redox reaction in plasmon-mediated heterostructure (PMH). where \(\Delta E_{b}\) is the height of the interfacial barrier, and \(E_{normal}(\theta,\varphi)\) is the normal component of the EM fields near the surface. In this equation, the rate of generation of HCs is proportional to the square of the amplitudes of the local EM field in plasmonic metal. In one way, the plasmonic metals with sharp tips or corners (namely \"tip hot spots\") [61; 62], e.g., nanorods, nanotriangles, and nanocubes, nanostars, are usually designed to be efficient carriers for generating HCs. In such structures, the redistributed electrons are localized near the tips of the metal by perturbing the incident light fields, resulting in several orders of enhancement of the local EM fields. [PERSON] et al. [63] studied the morphology-related generation of HCs by setting up three types of plasmonic metals, nanospheres, nanorods and nanostars, as models (Figure 3a). They proposed that plasmonic metals with tip structures (nanorods and nanostars) were endowed with a higher EM field enhancement when compared to nanospheres, and that the structures with long tips contributed to the highest EM enhancement (see the calculated EM enhancement factor in Figure 3b). To build up relations between this EM field enhancement and HCs effects, they assembled plasmonic metals and TiO\({}_{2}\) on SiO\({}_{2}\) microspheres. Both the theory and the experiments on the catalytic decomposition of RhB indicated that the EM field played a dominant role in the higher generation of HCs (Figure 3c). Such features were also demonstrated in some experimental results. [PERSON] et al. [64] reported Au-TiO\({}_{2}\) dumbbells by fixing amorphous TiO\({}_{2}\) at both ends of Au rods (Figure 3d), differing from Au rods@TiO\({}_{2}\) and Au rods/TiO\({}_{2}\) by simple mixing; the rates of degradation of methyl blue (MB) in these \"hot spots\" mediated heterostructures were improved significantly (Figure 3e). [PERSON] et al. [65] placed the Cu\({}_{2}\)O at the corners of the Au nanocubes (Figure 3f). This site-selective configuration exhibited an 8.1-fold increment in the photocatalytic hydrogen production compared to the Au@Cu\({}_{2}\)O core shell nanostructures (Figure 3g). Another effective way for achieving enhanced EM fields is to design gap \"hot spots\" structures by arranging the numbers of metallic units rationally. In such an integrating system, the EM fields  
Figure 3: “Tip hot spots” effects in plasmon-mediated heterostructures. (**a**) Calculated distributions of electromagnetic (EM) fields in nanospheres, nanorods and nanostars (from left to right). (**b**) Theoretical EM field enhancement factor in three typical metals.