Plasmonic Nanostars with Hot Spots for Efficient Generation of Hot Electrons under Solar Illumination

Abstract

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...

Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms

“…We now comment on the striking difference between the excitation rates for Au and Ag NCs in Figure 6. Overall, a sharper plasmon resonance will produce more hot electrons with high energies, 46 , both denominators and numerators are enhanced. However, these ratios are typically larger in Ag NCs than those in the Au system because of the appearance of stronger quantum effects in metals with a longer mean free path of electron.…”

“…48,49 Later the hot-spot effect was invoked to explain the photochemical performance of NCs of different shapes 50,51 and also a plasmonic experiment with an unusual ultrafast response. 52 According to our previous theoretical modeling, 40,42,46 two mechanisms can contribute to the enhanced generation of energetic electrons in NCs with hot spots: (1) The effect of field enhancement, which is typical for the plasmonic systems, and (2) the effect of nonconservation of linear momentum of electrons owing to surfaces and hot spot regions. The first mechanism is a classical phenomenon, whereas the second one needs a quantum treatment.…”

“…The present study has a number of new, important developments as compared to our previous papers on this topic. 28,29,[40][41][42]46 (1) In this study, we introduce the quantum detailedbalance equation for the density matrix and then treat the hot-electron processes using the spectral rate of generation. This allows us to obtain results that are independent of relaxation mechanisms.…”

“…This mechanism of generation of hot electrons in NCs is also strongly shape-dependent. 40,42,46 As one can see from Figure 2a, a plasmon decays into high-and low-energy electrons and holes in the Fermi sea. In the following step, these hot and warm electrons emit phonons and locally increase the lattice temperature.…”

“…Along with computer simulations, this paper contains simple, useful analytical equations for the generation rates of hot carriers. In particular, the rate of generation of hot carriers at the surface of NCs with simple shapes is given by the integral (see ref 46 and Supporting Information):…”