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Fano resonance energy (ER in Table I) does not change with photoreduction. The very large q Fano parameter required to fit the most oxidized rGO1 samples suggests the sp2 hybridized regions are not extensively delocalized and retain a molecular-like character. B. Hot-electron cooling rates in reduced graphene oxide Figure 4 fits the hot electron cooling TA kinetics in progressively reduced GO as the TA probe energy is in- creased from 1.2 (top) to 1.8 eV (bottom). Specifically, the hot-electron cooling rate (τSC) is extracted. Unlike the exponential rate τ2 from Fig. 2, τSC is analogous to the recombination rate as the electron cool near the Fermi energy, and is independent of probe energy (Eprobe). To connect the above phenomenological exponential relax- ation models of GO to this first-principle hot-electron cooling model, the fits in Figure 4 models our TA re- laxation kinetics using a hot electron heat dissipation rate H = Ce (dTe /dt), where Ce and Te are the elec- tronic heat capacity and temperature respectively. The top-panel of Fig. 4a contains first-principle hot electron cooling model fits (solid lines) to the normalized TA ki- netics of the rGO samples. Hot electron cooling rates in rGO can be qualitatively understood by comparing to CVD ml-graphene kinetics (black dotted line). The low- est energy probe (Epr=1.2 eV) in the top panel of Fig. 4a shows the hot electron cooling rate response of ml- graphene (dashed line) is identical to rGO1, rGO2 and rGO3. Interestingly, rGO4,5 dissipates heat even faster than CVD ml-graphene. The mechanism for fast energy dissipation or hot- electron cooling in graphene has been widely debated in the past. The optical phonon dissipation model28,43,44 evolves on the sub-ps relaxation timescale of the τ1 component. At longer relaxation times, the disorder- mediated acoustic phonon decay pathway or supercol- lision (SC) hot electron cooling model are the primary factor limiting cooling of the photoexcited hot elec- tron temperature, Te(t).45 Experimental studies demon- strate the SC-model45 successfully predicts graphene’s photocurrent29, optical46 and electrical47 heating re- sponse. However, the applicability of the SC-model to more disordered lattice of GO and rGO has not been considered. To understand hot electron cooling in rGO, we apply the acoustic phonon SC-model illustrated in Fig. 4b (in- set). In the SC model, hot electron cooling near the Fermi level occurs without crystal momentum conserva- tion. Instead, higher-energy (∼ kB Te ) acoustic phonons are emitted with the momentum imbalance, qrecoil ac- counted for by disorder-induced intrinsic lattice recoil.45 This SC- hot electron is illustrated in Fig. 4b (inset), and gives in a faster hot electron cooling rate than a hot- phonon model that is given by,29,45 dt αTe α Te where A/α is the SC rate coefficient, Tl and Te are the lattice and electron temperatures, respectively. Solving Eq. 2, Te(t) ∼= To when Te(t) ≫ Tl, where To is 1+ATo t/α the initial electron temperature. Since all data shown is at Tl =292 K, the transient change in Te(t) is small compared to Tl, or Te(t) − Tl ≪ Tl such that we can approximate Eq. 2 by expanding the leading terms to arrive at the room-temperature hot electron tempera- ture, Te(t) ∼= Tl + (To − Tl)e−t/τSC , to get the expression τ−1 = 3AT /α.29 The TA response is obtained using the hot electron (or hole) temperature (Te) through analytically fitting to the transient interband optical conductivity, ∆σ(E , t) = o dT H AT3 −T3 e=−=−el. (2) −e2/4~ fe/h(Te(t),Epr)−fe/h(Tl,Epr) .34 The Fermi- Dirac hot-electron occupancy function, fe/h(Te(t),Epr) at the probe energy (Epr) equations are given in the Sup- plementary Materials as a change in interband optical conductivity ∆σ(t,Epr).34,48 In Fig. 4b the hot electron cooling rates (τ−1) for rGO are extracted by fitting the SC data in Fig. 4a to the analytical SC-model solution (Eq. 2), allowing for two additional exponential components (τ1 and τ3). This fast component, τ1 ∼= 0.34 ps, averages over the initial electron thermalization and optic phonon emission timescale and is discussed elsewhere.49,50 Any molecular-like π − π∗ transitions present are captured by τ3∼61ps. The accelerating TA relaxation kinetics in Fig. 4a are consistent with the idea that photoreduction of GO creates more disorder and defects on the graphene sub- lattice. Figure 4b shows an increase in the rate of hot electron cooling, τ−1. Unlike the earlier exponential fits, SC the rate τ−1 is independent of the probe energy and is SC the rate at which the hot-electron Fermi-Dirac distribu- tion cools. The hot electron cooling time for the com- parison monolayer CVD -grown graphene (dashed line in Fig. 4b) at 292 K is 3.1 ps. τ−1 increases by a factor of SC ∼6 as the samples are reduced. This suggests the xenon arc lamp used to reduce GO is a largely destructive pro- cess to underlying sp2 sub-lattice. At the highest level of photoreduction, Fig. 4b suggests the increased lat- tice disorder destroys the desired graphene-like extended lattice by creating to many point-defects. The τ−1 = 3ATl/α expression is a direct measure of SC lattice disorder by the expression A ∼= 2 λ kB , where α 3kFl ~ the mean free scattering path is kFl.45 The electron- phonon coupling strength can be approximated as λ = D2 2EF , where both the deformation potential, D and ρs2 π(~vF )2 Fermi energy EF are the experimental variable that in- crease the hot electron cooling rate. Figure 4b shows that Aα ∼= 0.3 ns−1 K−1 for rGO1−3 , which matches the monolayer CVD graphene values in literature.46 How- ever, further photoreduction increases Aα upto 6×, sug- gesting the graphene sub-lattice is being damaged. If the 6 SC lPDF Image | Graphene Oxide Photoreduction Recovers Graphene
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