Ultrafast relaxation dynamics of excited carriers in metals: Simplifying the intertwined dependencies upon scattering strengths, phonon temperature, photon energy, and excitation level
Physical Review B(2024)
摘要
Using the Boltzmann transport equation (BTE), we study the evolution of
nonequilibrium carrier distributions in simple (sp) metals, assumed to have
been instantaneously excited by an ultrafast laser pulse with photon energy h
ν. The mathematical structure of the BTE scattering integrals reveals that
h ν is a natural energy scale for describing the dynamics. Normalizing all
energy quantities by h ν leads to a set of three unitless parameters –
β / δ, γ, and α – that control the relaxation
dynamics: β / δ is the normalized ratio of electron-phonon to
electron-electron scattering strengths, γ is the normalized phonon
(lattice) temperature, and α is the normalized absorbed energy density.
Using this theory, we systematically investigate relaxation times for the
high-energy part of the distribution (τ_H), energy transfer to the phonon
subsystem (τ_E), and intracarrier thermalization (τ_th). In the
linear region of response (valid when α is sufficiently small), we offer
heuristic descriptions of each of these relaxation times as functions of β
/ δ and γ. Our results as a function of excitation level α
show that many ultrafast experimental investigations lie in a transition region
between low excitation (where the relaxation times are independent of α)
and high excitation (where the two-temperature model of carrier dynamics is
valid). Approximate boundaries that separate these three regions are described
by simple expressions involving the normalized parameters of our model.
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