Abstract
Localised surface plasmons create a non-equilibrium high-energy electron gas in nanostructures that can be injected into other media in energy harvesting applications. Here, we derive the rate of this localised-surface-plasmon mediated generation of hot electrons in nanorods and the rate of injecting them into other media by considering quantum mechanical motion of the electron gas. Specifically, we use the single-electron wave function of a particle in a cylindrical potential well and the electric field enhancement factor of an elongated ellipsoid to derive the energy distribution of electrons after plasmon excitation. We compare the performance of nanorods with equivolume nanoparticles of other shapes such as nanospheres and nanopallets and report that nanorods exhibit significantly better performance over a broad spectrum. We present a comprehensive theoretical analysis of how different parameters contribute to efficiency of hot-electron harvesting in nanorods and reveal that increasing the aspect ratio can increase the hot-electron generation and injection, but the volume shows an inverse dependency when efficiency per unit volume is considered. Further, the electron thermalisation time shows much less influence on the injection rate. Our derivations and results provide the much needed theoretical insight for optimization of hot-electron harvesting process in highly adaptable metallic nanorods.
Highlights
Addition to photovoltaic applications, such electrons and holes can participate in chemical reactions on the metal or the semiconductor surface[3,4,5,6,7]
We calculated the rate of injection of these hot electrons from the nanorod to a semiconductor in contact with it using the single-electron wave function and the corresponding eigen energy states
We note from the energy distribution of the excited electrons, that a high proportion of generated electrons have energies in the vicinity of the Fermi level, which reduces the injection efficiency
Summary
In this article we have derived the rate of high-energy electron generation for a metallic nanorod illuminated optically such that the external electric field is oriented along the nanorod length. The arrangement we have studied here, a metallic nanorod supported on a semiconductor, allows high degree of contact with the surrounding media, resulting in efficient transfer of electrons from the donor solution to the nanoparticle. The energetic electrons generated inside the nanoparticle have to reach the metal boundaries before they can be transferred to the semiconductor. Even though a nanorod with a high aspect ratio can produce large proportion of high energy electrons, if its length is too long compared to electron’s mean free path, most of the electrons may not reach the boundary. Our derivations and results provide the much needed theoretical background for understanding such a transfer of plasmon-induced hot electrons using nanorod shaped metals. They should provide guidance in the development and optimization of hot-electron harvesting mechanisms operating over a broad spectral range
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