178
F. Vallée and N. Del Fatti
small sizes, reaching for instance about 450 K for a 3 nm diameter gold sphere and
ω e = 1.3 eV, an effect that must be taken into account in interpreting experimental
data [37].
5.3.2.1 Electron Gas Thermalization
The computed time dependent electron distribution function is illustrated in Fig. 5.3
in the case of gold for weak excitation, ωT me
e = 100 K, and pulse duration t p = 25 fs
and 250 fs. In both cases, an athermal electron population is created, reflecting in
a broad energy extension of the distribution change ω f (E, t) = f (E, t) − f 0 (E).
Fast electron-electron energy redistribution subsequently leads to build up of ω f
around E F as the electron gas internally thermalizes, i.e., f reaches a Fermi-Dirac
distribution with temperature T e . This takes place concurrently with excitation by the
pulse leading to a narrower athermal distribution when using longer pulses (Fig. 5.3).
Internal thermalization kinetics takes place with characteristic thermalization times
of about 500 fs and 350 fs in gold and silver respectively, this slow kinetics being
determined by e-e collisions around the Fermi surface. Their probabilities are strongly
reduced by the Pauli exclusion principle effects, making them the slowest scattering
processes involved in the internal thermalization process [26, 29]. Experimental
results have been found to be in quantitative agreement with the computed ones
the reduced thermalization time in silver as compared to gold being due to larger
screening by the bound electrons in the latter [26]. This kinetics is almost independent
of the injected energy in the weak perturbation regime, i.e., for ωT me
e
≤ 200 −
300 K and becomes faster for larger excitations due to weakening of the effects of
Pauli exclusion increased smearing of the electron distribution around the Fermi
energy [26].
Internal electron gas thermalization has been shown to be faster in nanospheres
with diameter smaller than 10 nm (the thermalization time being about 300 fs in 5
nm gold spheres) [51, 52]. Using a bulk-like model, this size dependence has been
ascribed to confinement induced fastening of the electron-electron energy exchanges,
due to less efficient screening of the e-e Coulomb interactions close to a surface [52].
However, other processes associated to quantum confinement of the electrons, such
as relaxation of momentum conservation or electron state quantization, can play a
role, especially in the very small size regime. For large excitation, other effects can
also influence the observed kinetics, as resonant dynamic screening modification
[105–107].
5.3.2.2 Electron-Lattice Energy Exchanges
Light being selectively absorbed by the electrons, they are out of equilibrium with
the lattice and cools down by electron-lattice energy transfer. After establishment
of an electronic temperature, the electron cooling kinetics can be simply described
using the electron temperature and using the two-temperature model [25, 70, 108].
F. Vallée and N. Del Fatti
small sizes, reaching for instance about 450 K for a 3 nm diameter gold sphere and
ω e = 1.3 eV, an effect that must be taken into account in interpreting experimental
data [37].
5.3.2.1 Electron Gas Thermalization
The computed time dependent electron distribution function is illustrated in Fig. 5.3
in the case of gold for weak excitation, ωT me
e = 100 K, and pulse duration t p = 25 fs
and 250 fs. In both cases, an athermal electron population is created, reflecting in
a broad energy extension of the distribution change ω f (E, t) = f (E, t) − f 0 (E).
Fast electron-electron energy redistribution subsequently leads to build up of ω f
around E F as the electron gas internally thermalizes, i.e., f reaches a Fermi-Dirac
distribution with temperature T e . This takes place concurrently with excitation by the
pulse leading to a narrower athermal distribution when using longer pulses (Fig. 5.3).
Internal thermalization kinetics takes place with characteristic thermalization times
of about 500 fs and 350 fs in gold and silver respectively, this slow kinetics being
determined by e-e collisions around the Fermi surface. Their probabilities are strongly
reduced by the Pauli exclusion principle effects, making them the slowest scattering
processes involved in the internal thermalization process [26, 29]. Experimental
results have been found to be in quantitative agreement with the computed ones
the reduced thermalization time in silver as compared to gold being due to larger
screening by the bound electrons in the latter [26]. This kinetics is almost independent
of the injected energy in the weak perturbation regime, i.e., for ωT me
e
≤ 200 −
300 K and becomes faster for larger excitations due to weakening of the effects of
Pauli exclusion increased smearing of the electron distribution around the Fermi
energy [26].
Internal electron gas thermalization has been shown to be faster in nanospheres
with diameter smaller than 10 nm (the thermalization time being about 300 fs in 5
nm gold spheres) [51, 52]. Using a bulk-like model, this size dependence has been
ascribed to confinement induced fastening of the electron-electron energy exchanges,
due to less efficient screening of the e-e Coulomb interactions close to a surface [52].
However, other processes associated to quantum confinement of the electrons, such
as relaxation of momentum conservation or electron state quantization, can play a
role, especially in the very small size regime. For large excitation, other effects can
also influence the observed kinetics, as resonant dynamic screening modification
[105–107].
5.3.2.2 Electron-Lattice Energy Exchanges
Light being selectively absorbed by the electrons, they are out of equilibrium with
the lattice and cools down by electron-lattice energy transfer. After establishment
of an electronic temperature, the electron cooling kinetics can be simply described
using the electron temperature and using the two-temperature model [25, 70, 108].