# Also in the Article

Thermo-optical response calculation
This protocol is extracted from research article:
Tracking ultrafast hot-electron diffusion in space and time by ultrafast thermomodulation microscopy
Sci Adv, May 10, 2019;

Procedure

We modeled the complex permittivity at the infrared probe wavelength with a Drude model permittivity (41)$ε=ε∞−ωp2(Tl)ω(ω+iγre(Te,Tl))$Here, ε = 9.5 is the high-frequency permittivity (41). The plasma frequency ωp depends on the lattice temperature Tl due to volume expansion affecting the free conduction band electron density ne. Namely, $ωp(Tl)=(e2/ε0meff)×ne(T0)/(1+βΔTl)$, where β = 4.23 × 10−5 K−1 is the thermal expansion coefficient (42), ne(T0) = 5.9 × 1022 cm−3 is the unperturbed density (42), meffme is the effective electron mass, ε0 is the vacuum permittivity, and me and e and are the elementary charge and mass, respectively. Further, γre represents the total rate of relaxation collisions that conserve momentum and energy of the electron subsystem, given by$γre(Te,Tl)=γe−ph(Tl)+γe−eUm(Te)$, where γe−ph is the electron-phonon collision rate, depending on the lattice temperature as γe−ph(Tl) = BTl, and $γe−eUm$ is the Umklapp electron-electron collision rate, depending on Te as$γe−eUm(Te)=Δ(Um)ATe2$, with A = 1.7 × 107 K−2 s−1, B = 1.45 × 1011 K−1 s−1, and ΔUm = 0.77 (see note S3 and fig. S2) (43, 44).

Note: The content above has been extracted from a research article, so it may not display correctly.

Q&A