Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals

Abstract

Hot carriers (HC) generated by surface plasmon polaritons (SPPs) in noble metals are promising for application in optoelectronics, plasmonics and renewable energy. However, existing models fail to explain key quantitative details of SPP-to-HC conversion experiments. Here we develop a quantum mechanical framework and apply first-principles calculations to study the energy distribution and scattering processes of HCs generated by SPPs in Au and Ag. We find that the relative positions of the s and d bands of noble metals regulate the energy distribution and mean free path of the HCs, and that the electron–phonon interaction controls HC energy loss and transport. Our results prescribe optimal conditions for HC generation and extraction, and invalidate previously employed free-electron-like models. Our work combines density functional theory, GW and electron–phonon calculations to provide microscopic insight into HC generation and ultrafast dynamics in noble metals.

Plasmonic hot carrier dynamics in solid-state and chemical systems for energy conversion

“…Recently, the decay of surface plasmons via direct transitions in the bulk material has been examined in detail using Fermi's golden rule calculations on relativistic DFT+U band structures [66], and confirmed by subsequent GW calculations [68]. Figure 4 shows the theoretical predictions for the carrier distributions generated by direct transitions in several plasmonic metals, and annotates the dominant transitions on the band structures of the metals [66].…”

Harvesting the loss: surface plasmon-based hot electron photodetection

“…Hot carriers are primarily generated with momentum parallel to the external field [31], which is generally parallel with the semiconductor interface in the case of an antenna, resulting in poor injection. Moreover, hot electron generation is also dependent on the plasmonic material employed [32,72,[76][77][78]. Several groups have explored the effects of the electronic structure of the metal on the generated carrier distributions [32,76] ( Figure 1F), and it has been shown that, in the interband transition regime, the electronic band structure of the metal plays an important role in determining both the energy and the momentum distribution of the generated hot carriers [32].…”

“…Moreover, hot electron generation is also dependent on the plasmonic material employed [32,72,[76][77][78]. Several groups have explored the effects of the electronic structure of the metal on the generated carrier distributions [32,76] ( Figure 1F), and it has been shown that, in the interband transition regime, the electronic band structure of the metal plays an important role in determining both the energy and the momentum distribution of the generated hot carriers [32]. In fact, in this regime, none of the commonly used plasmonic materials, including gold, silver, aluminum, and copper, exhibit the isotropic momentum distribution assumed in Fowler's theory [32].…”

First-principles dynamics of electrons and phonons*

“…For example, the energy loss rate of excited carriers [32][33][34] and the room temperature electrical conductivity in crystals with low impurity concentrations [2,35,36] are both controlled by e-ph scattering. In DFT [20], the Kohn-Sham (KS) potential V KS , computed at the equilibrium atomic positions, is employed to obtain the electronic KS bandstructure nk and wavefunctions φ nk .…”

“…To converge the e-ph RTs, interpolation of the e-ph matrix elements is necessary since the sum in eq. 12 requires 10 4 −10 6 q-points to converge [32][33][34]36], an unrealistic task for direct DFPT calculations due to computational cost. An interpolation approach using maximally localized Wannier functions [40] has been recently developed [41]; alternative interpolation schemes using localized basis sets are being investigated by the author.…”