“Hot” electrons in metallic nanostructures—non-thermal carriers or heating?

Abstract

Understanding the interplay between illumination and the electron distribution in metallic nanostructures is a crucial step towards developing applications such as plasmonic photocatalysis for green fuels, nanoscale photodetection and more. Elucidating this interplay is challenging, as it requires taking into account all channels of energy flow in the electronic system. Here, we develop such a theory, which is based on a coupled Boltzmann-heat equations and requires only energy conservation and basic thermodynamics, where the electron distribution, and the electron and phonon (lattice) temperatures are determined uniquely. Applying this theory to realistic illuminated nanoparticle systems, we find that the electron and phonon temperatures are similar, thus justifying the (classical) single-temperature models. We show that while the fraction of high-energy “hot” carriers compared to thermalized carriers grows substantially with illumination intensity, it remains extremely small (on the order of 10−8). Importantly, most of the absorbed illumination power goes into heating rather than generating hot carriers, thus rendering plasmonic hot carrier generation extremely inefficient. Our formulation allows for the first time a unique quantitative comparison of theory and measurements of steady-state electron distributions in metallic nanostructures.

Size-dependence of the photothermal response of a single metal nanosphere

“…This work is critical for the optimization of the photo-thermal effect in all the above mentioned applications. Most importantly, since thermal effects were shown to be responsible for observations of faster chemical reactions in some of the most famous papers on the topic (see discussion in [27][28][29]35]), our work can be used to interpret correctly the differences in chemical reaction enhancements originating from the use of metal particles of different sizes.…”

Thermal effects – an alternative mechanism for plasmon-assisted photocatalysis

“…This pure thermal interpretation is based, initially (see Section II) on our first-principles theory in which the electron distribution and temperatures were computed self-consistently for the first time, see Ref. [10]. This theory showed that the power going to generation of "hot" electrons is an incredibly small fraction of the total absorbed energy, which thus goes in its entirety to heating.…”

Ultrafast Dynamics of Optically Induced Heat Gratings in Metals

“…We assume that the pump illuminates the sample near its plasmon resonance with a local field of ∼ 30MV /m. 4 Importantly, the comparisons below are performed for the same local field (hence, absorbed power density) within a single unit-cell.…”

“…Unfortunately, as well known, the assumption underlying the the TTM is never strictly valid. As a remedy, using a similar model, we derived in [4,5] an extended version of the TTM (referred to below as the eTTM) whereby the early stages of the thermalization of the electron subsystem are accounted for via the total energy of the nonthermal electrons; the latter is then characterized by a fast rise time and slow decay time, corresponding to the thermalization of the electron subsystem 1 ,2 . This derivation confirmed the phenomenological model presented much earlier in [19,20].…”

“…We adopt here the extended Two Temperature Model (eTTM) which describes the spatio-temporal dynamics of the non-thermal electron energy as well as of the electron and phonon (lattice) temperatures [4,5]. In this approach, U N T e , the energy density of the NT electrons is given by 3…”