Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications in which excited electrons play an important role. However, the central questions in the problem of plasmonic hot electrons are the number of optically-excited energetic electrons in a nanocrystal and how to extract such electrons. Here we develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, 2 hot electrons are generated due to surfaces and hot spots. As expected, the formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly high-energy (hot) electrons. We obtain analytical expressions for the distribution functions of excited carriers for simple shapes. For complex shapes with hot spots and for small quantum nanocrystals, our results are computational.By looking at the energy distributions of electrons in an optically-excited nanocrystal, we see how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coefficients, we formulate a simple scheme describing how the plasmon in a nanocrystal dephases over time. In most nanocrystals, the main decay mechanisms of a plasmon are the Drude friction-like process and the interband electronhole excitation, and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. The hot-electron path strongly depends on the material system and on its shape. Correspondingly, the efficiency of hot-electron production in a nanocrystal strongly varies with size, shape and material. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochemistry and photodetectors. 3Introduction.
The use of plasmonic metal nanoparticles as photosensitizers has undergone a strong development in the last few years given their ability to increase the activity of semiconductors into the visible and near infrared regions. The present work reports an experimental and theoretical study on the critical influence that shape anisotropy of gold nanoparticles exerts on the photocatalytic performance of Au-TiO2 nanoarchitectures. The obtained results show
to the resonant plasmonic effect. It was also observed [24,26,27] and calculated [25] that the plasmonic hot spots in metal nanostructures can generate large numbers of energetic electrons. The design of a plasmonic nanocrystal is crucial to create plasmonic hot spots that generate efficiently energetic electrons. In this study, we will address this problem of hot spots and energetic electrons.Here we investigate theoretically the process of generation of hot electrons in nanocrystals with various shapes, such as nanostars (NSTs), nanorods (NRs), and spherical nanoparticles (NPs). The focus will be on the role of plasmonic hot spots in such NCs. In this study, we show that plasmonic NSTs with multiple hot spots are very efficient for generation of energetic electrons. We also compare NSTs with NRs and NPs and discuss two material systems, gold and silver. Silver NCs exhibit much larger rates of generation since the plasmon enhancement in such silver NCs is much stronger than that in the case of gold. The physical reason for the high rates of generation of hot carriers in the silver NCs are the following: (1) The long mean free path of electrons and (2) the narrow and intensive plasmonic resonances. The effect of generation of hot electrons is an essentially quantum effect and comes from the optical absorption processes near the surfaces of a NC. Such surface absorption is, of course, efficient only in relatively small NCs. We, therefore, examine the quantum efficiencies and the quantum plasmonic parameter for NCs of various sizes and shapes. Using such calculations, we show the quantum nature of the generation of energetic carriers in NCs in general.We also should note that the formalism of the paper focuses on the quantum intraband transitions in the NCs made of gold and silver. Such intraband transitions dominate the optical responses of the plasmonic NCs in the spectral intervals λ > 500 nm (gold) and λ > 400 nm (silver). Simultaneously, these spectral intervals are most interesting for the plasmonic effects since the plasmonic peaks in these spectral regions appear to be narrow and strong. [23] Regarding the role of the interband transitions and generation of hot holes in the d-band, one can look into recent review papers (e.g., ref.[23]).Theoretically, the problem of hot electrons has been addressed using several methods: Density matrix formalism combined with time-dependent DFT, perturbative approach for the injection currents, Fermi's golden rule, nonequilibrium Nanostars (NSTs) are spiky nanocrystals (NCs) with plasmonic hot spots. In this study, it is shown that strong electromagnetic fields localized in the NST tips are able to generate large numbers of energetic (hot) electrons, which can be used for photochemistry. To compute plasmonic NCs with complex shapes, a quantum approach based on the effect of surface generation of hot electrons is developed. This approach is then applied to NSTs, nanorods (NRs) and nanospheres. It is found that the plasmonic NSTs with multiple hot spots have the best charact...
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