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

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, 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, whereakplasmons 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 toward 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. On the basis of 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 electron hole 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.