Article www.acsnano.org Hot-Carrier Cooling in High-Quality Graphene Is Intrinsically Limited by Optical Phonons Eva A. A. Pogna, Xiaoyu Jia, Alessandro Principi, Alexander Block, Luca Banszerus, Jincan Zhang, Xiaoting Liu, Thibault Sohier, Stiven Forti, Karuppasamy Soundarapandian, Bernat Terrés, Jake D. Mehew, Chiara Trovatello, Camilla Coletti, Frank H. L. Koppens, Mischa Bonn, Hai I. Wang, Niek van Hulst, Matthieu J. Verstraete, Hailin Peng, Zhongfan Liu, Christoph Stampfer, Giulio Cerullo, and Klaas-Jan Tielrooij* Cite This: ACS Nano 2021, 15, 11285−11295 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Many promising optoelectronic devices, such as broadband photodetectors, nonlinear frequency converters, and building blocks for data communication systems, exploit photoexcited charge carriers in graphene. For these systems, it is essential to understand the relaxation dynamics after photoexcitation. These dynamics contain a sub-100 fs thermal- ization phase, which occurs through carrier−carrier scattering and leads to a carrier distribution with an elevated temperature. This is followed by a picosecond cooling phase, where different phonon systems play a role: graphene acoustic and optical phonons, and substrate phonons. Here, we address the cooling pathway of two technologically relevant systems, both consisting of high-quality graphene with a mobility >10 000 cm2 V−1 s−1 and environments that do not efficiently take up electronic heat from graphene: WSe2-encapsulated graphene and suspended graphene. We study the cooling dynamics using ultrafast pump−probe spectroscopy at room temperature. Cooling via disorder-assisted acoustic phonon scattering and out-of-plane heat transfer to substrate phonons is relatively inefficient in these systems, suggesting a cooling time of tens of picoseconds. However, we observe much faster cooling, on a time scale of a few picoseconds. We attribute this to an intrinsic cooling mechanism, where carriers in the high-energy tail of the hot-carrier distribution emit optical phonons. This creates a permanent heat sink, as carriers efficiently rethermalize. We develop a macroscopic model that explains the observed dynamics, where cooling is eventually limited by optical-to-acoustic phonon coupling. These fundamental insights will guide the development of graphene-based optoelectronic devices. KEYWORDS: graphene, cooling dynamics, hot electrons, transient absorption microscopy, optical phonons, phonon bottleneck INTRODUCTION instance photodetectors and receivers, exploit the ultrafast The ultrafast dynamics of photoexcited charge carriers in photothermoelectric effect in graphene,18,19 where a longer graphene have received ample attention, initially driven by hot-carrier cooling time leads to an increased photoresponse. fundamental scientific interest in the intriguing electron− Other applications, such as modulators, could instead benefit electron and electron−phonon interactions; cf. refs 1−5. More from a short cooling time, as this can lead to a higher recently, interest has multiplied as a result of the emergence of modulation speed, i.e., to a broader bandwidth. Generally, highly promising technological applications that exploit these these applications require high-quality graphene with a high ultrafast dynamics. One example is ultrafast photodetection of visible (VIS) and infrared light,6,7 and even terahertz (THz) radiation.8−10 The ultrafast electronic response of graphene to Received: December 28, 2020 incoming light has also led to the development of several Accepted: June 3, 2021 concepts with relevance for data communication technologies, Published: June 17, 2021 including modulators and receivers,11−13 and is demonstrated to be crucial for tailoring nonlinear photonics applica- tions.14−17 Part of the aforementioned applications, for © 2021 The Authors. Published by American Chemical Society https://doi.org/10.1021/acsnano.0c10864 11285 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article Figure 1. Characterization of the WSe2-encapsulated graphene sample. (a) Sketch of the encapsulated graphene prepared by exfoliation and dry transfer of two flakes of WSe2 and monolayer graphene.41 (b) Atomic force microscopy image of the sample, used to determine the thicknesses of the WSe2 flakes. (c) Raman spectra of fully encapsulated graphene (blue line) and of semiencapsulated graphene (black line) obtained with 532 nm laser source. Encapsulation gives rise to a background, reduced graphene Raman signatures’ (G and 2D peaks) intensity, and a clear blue shift of the 2D peak. (d, e) Maps of the 2D peak frequency ω2D (d) and width Γ2D (e) extracted from Raman spectra at different positions on the sample fitted with a Voigt function centered in ω2D. (f, g) Statistical distribution of ω2D (f) and Γ2D (g) in the encapsulated graphene obtained from the maps in panels d and e. The narrow width suggests a high electrical mobility. electrical mobility. Clearly, it is crucial to properly understand range.27 In the case of graphene with significant disorder, the cooling dynamics of hot carriers in graphene, and in however, coupling to acoustic phonons becomes much more particular to identify the intrinsic mechanism that ultimately efficient through disorder-assisted scattering. By scattering with determines the cooling process in high-quality systems. defects, the large momentum mismatch between electrons and The decay of photoexcited charges in graphene occurs acoustic phonons is overcome.28 This disorder-assisted “super- through a variety of dynamical processes that are the result of collision” cooling process leads to typical cooling times of a few the specific properties of Dirac electrons and graphene picoseconds at room temperature, as measured by electrical,29 phonons. Photoexcited charge carriers in graphene first optical,30,31 and optoelectronic32 techniques. Since disorder undergo thermalization on a <100 fs time scale, which occurs also limits the electrical mobility, this disorder-assisted cooling through carrier−carrier scattering and leads to a state with an mechanism tends to play an increasingly important role for elevated carrier temperature, i.e., a broadened Fermi−Dirac graphene with lower electrical mobility. Currently, there are distribution.2−4,20 This photoinduced heating process is very contrasting views in the literature regarding the role of efficient5,21 and, due to the small electronic heat capacity of different cooling mechanisms. In particular, some studies, such graphene,22 the electron temperature Te can be increased as ref 26, question the role of supercollision cooling. significantly (Te ≫ 500 K). The hot-carrier state then relaxes In the case of graphene with a mobility above 10 000 cm2 −1 −1 back to the ground state with the electronic system at ambient V s , which we here refer to as “high-quality graphene”, the temperature. This cooling process occurs through the disorder density is low enough that disorder-assisted cooling interaction between charge carriers and graphene optical will not play an important role. Recent experiments on high- phonons, graphene acoustic phonons, and substrate phonons quality hBN-encapsulated graphene with a mobility above in nearby materials. These phonon-induced relaxation 30 000 cm2 V−1 s−1, however, did not show a strong increase in mechanisms have intricate dependencies on intrinsic (sam- cooling time.33 This is because a parallel relaxation mechanism ple-dependent) parameters (such as disorder density and emerges in these heterostructures: hot carriers in graphene can intrinsic doping), as well as extrinsic experimental parameters decay through near-field interaction with hyperbolic phonon (such as photon energy, incident fluence, and ambient polaritons of the hBN.33−35 Hyperbolic phonon polaritons temperature). Thus, determining the dominant cooling occur in spectral regions, where the in- and out-of-plane channel(s) for excited graphene charge carriers has been permittivities (ϵ∥ and ϵ⊥, respectively) have opposite signs, i.e., challenging. the permittivity product ϵ∥·ϵ⊥ is negative.36 These hyperbolic It is generally believed that charge carriers with enough spectral regions contain a high density of optical modes, which kinetic energy can relax on an ultrafast time scale of a few are accessible via near-field interaction with a large range of hundred femtoseconds by interacting with strongly coupled momentum vectors. As a result, out-of-plane super-Planckian optical phonons.2,23,24 These are the optical phonons at the Γ cooling for hBN-encapsulated graphene occurs with a decay and K points with an energy of 0.2 and 0.16 eV, respectively.25 time of a few picoseconds at room temperature.33−35 Thus, charge carriers with an excess energy >0.16 eV above the Here, we aim to unveil the intrinsic physical mechanism that chemical potential can efficiently cool by optical phonon ultimately limits the cooling of hot carriers in high-quality emission.26 Carriers with an excess energy <0.16 eV can only graphene. We address this question using time-resolved optical couple to acoustic phonons, generally resulting in very measurements of the cooling dynamics in two specifically inefficient cooling with decay times up to the nanosecond chosen material systems: WSe2-encapsulated graphene and 11286 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article Figure 2. Hot-carrier cooling dynamics of WSe2-encapsulated graphene. (a) Transient transmission ΔT/T maps at a fixed time delay t = 100 fs between pump and probe pulses acquired with pump at 0.8 eV (1550 nm) and probe at 0.729 eV (1700 nm). White lines indicate the edges of WSe2 flakes extracted from an optical image. The panel on the right shows a zoom of the left panel, and the black cross indicates the location in the fully encapsulated region, where the ΔT/T dynamics are measured. (b) Comparison of normalized ΔT/T relaxation dynamics of graphene encapsulated by WSe2 (blue dots) and hBN (black dots), using a pump fluence of ∼1 μJ/cm2 in both cases. Encapsulation with hBN gives rise to faster dynamics, which we attribute to out-of-plane cooling to hyperbolic phonons of hBN.33−35 This cooling mechanism is much less efficient for WSe2 encapsulation. (c) ΔT/T dynamics (dots) for WSe2-encapsulated graphene at five different pump fluences from 0.2 to 2 μJ/cm2. The positive ΔT/T is due to pump-induced heating, leading to Pauli blocking of probe interband transitions. The solid lines are the calculated ΔT/T dynamics, based on the intrinsic hot-electron cooling mechanism via the combination of optical-phonon emission, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (d) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel c. Here, fast decay due to the electron-optical-phonon coupling is followed by slower decay via optical-to-acoustic phonon coupling. The former component shows up very strongly in the TA signal as a consequence of the strongly superlinear relation between the TA signal ΔT/T and the change in carrier temperature ΔTe. suspended graphene. Both systems contain “high-quality” encapsulated graphene (see Figure 1a). Encapsulation with graphene, according to our definition of having a mobility materials offering atomically planar surfaces via van der Waals >10 000 cm2 V−1 s−1, which is high enough to make stacking, is a successful route for obtaining high-quality “supercollision” cooling inefficient. Furthermore, they have graphene, suppressing rippling, preserving high carrier basically nonhyperbolic environments, such that out-of-plane mobility37 and partially screening long-distance Coulomb cooling to hyperbolic phonons does not play any role. We scattering with substrate charges.38 Besides hBN, WSe2 is show that, despite eliminating these two relaxation channels, arguably one of the most promising encapsulation materials for cooling still happens on a time scale of a few picoseconds. We various technological applications of graphene.39 One of the attribute this to the high-energy tail of the hot-carrier main reasons is that it leads to a very high room-temperature distribution, where electrons with an energy >0.16 eV above mobility, which in a recent study reached up to 350 000 cm2 the chemical potential reside. These electrons lose energy by V−1 s−1 for hBN/graphene/WSe2.40 Our sample of WSe2- coupling to optical phonons, which in turn couple to graphene encapsulated monolayer graphene was prepared using acoustic phonons, while the electronic system continuously exfoliation and dry transfer. The WSe2 flakes were obtained rethermalizes. Probing the transient optical properties of by adhesive tape exfoliation of WSe2 crystals in the trigonal graphene in the VIS, near-infrared (NIR), and THz ranges, prismatic phase synthesized by chemical vapor transport, as we will show that this cooling mechanism is consistent with the detailed in the Methods. Bottom and top WSe2 flakes are 63 experimentally obtained cooling dynamics. and 61 nm thick, respectively, as measured by atomic force microscopy (see Figure 1b and the Supporting Information). The WSe2/graphene/WSe2 heterostructure was transferred RESULTS AND DISCUSSION onto a 280 μm thick CaF2 substrate that is transparent for VIS Cooling Dynamics in High-Quality WSe2-Encapsu- and NIR light and allows for pump−probe measurements in lated Graphene. The first material system we study is WSe2- transmission geometry. 11287 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article We first characterize the WSe2-encapsulated graphene using decays to 10% of the initial value (at time zero) after a time Raman spectroscopy with a 532 nm laser source (see Methods delay of ∼5.5 ps for WSe2-encapsulated graphene, instead of a for details), in order to assess the quality of graphene and delay of ∼2 ps for the hBN-encapsulated graphene. As shown extract an estimation of its Fermi energy and charge mobility. recently, in high-quality, hBN-encapsulated graphene, hot- In the regions where graphene is semiencapsulated, the Raman carrier cooling is dominated by out-of-plane coupling to fingerprints of graphene, the G-peak and 2D-peak, are clearly hyperbolic phonons in hBN.33−35 Since the hyperbolic nature visible (see Figure 1c). In the fully encapsulated region, the of hBN is crucial for making this cooling channel efficient,34 we spectrum is dominated by a large background. Nevertheless, by study the hyperbolicity of WSe2 using ab initio density extending the exposure time, we can identify the G-peak with functional theory calculations. The comparison of in-plane center frequency of ωG ∼ 1584 cm−1 and width of ΓG ∼ 20 and out-of-plane permittivities of WSe2 and hBN, reported in cm−1 (spectra in the Supporting Information). From the G- the Supporting Information, shows that WSe2 is much less peak position and width we estimate that |EF| ≤ 0.1 eV, in hyperbolic than hBN. Therefore, out-of-plane cooling to the agreement with a previous observation for graphene supported phonons in the encapsulant will be relatively inefficient in by single-layer WSe2.40 Examining the 2D-peak at many WSe2-encapsulated graphene, in qualitative agreement with the positions in the encapsulated portion of graphene, we find that slower cooling that we observe. Quantitatively, however, both it is blue-shifted from ∼2689 to ∼2710 cm −1 after disorder-assisted “supercollision” cooling and out-of-plane encapsulation; see Figure 1d. The distribution of the 2D- cooling to the encapsulant would predict longer cooling peak widths Γ2D in Figure 1 is centered at 18 cm−1, indicating times (see Supporting Information), well above 10 ps for the that WSe2-encapsulated graphene has a rather homogeneous WSe2-encapsulated graphene sample, which is not what we strain distribution, with little intravalley scattering and high observe. mobility.42 On the basis of the empirical correlation of ref 43, In order to explain the relatively fast cooling dynamics the measured Γ2D corresponds to a mobility of ∼80 000 cm2 observed in the WSe2-encapsulated graphene, we therefore V−1 s−1. In order to verify this estimate, we measured the consider an intrinsic cooling mechanism, based on the transport properties at room temperature of a similar WSe2- coupling of electrons with energy >0.16 eV above the chemical encapsulated graphene heterostructure with two metal contacts potential to optical phonons. The optical phonons, at the Γ and a backgate. We obtained an electron (hole) mobility of and K points, in turn, are anharmonically coupled to acoustic ∼39 000 cm2 V−1 s−1 (∼36 000 cm2 V−1 s−1, see Supporting phonons. An important ingredient for this cooling channel is Information). With such high mobility values, disorder-assisted the continuous rethermalization of the electronic system. “supercollision” cooling predicts a characteristic cooling time Microscopically, this means that once the electrons with high scale of >10 ps (see Supporting Information). enough energy (more than 0.16 eV above the chemical Having established the high quality of our WSe 2 - potential) have relaxed by coupling to optical phonons, the encapsulated graphene sample, we now study its hot-carrier remaining electrons will rethermalize through carrier−carrier cooling dynamics. We perform time-resolved transient scattering. This means that some electrons will end up with an absorption (TA) measurements in the NIR range using a energy that is high enough to emit optical phonons. Even at an high-sensitivity microscope (see Methods for details on the electron temperature of 300 K, there is a significant fraction of experimental setup), which effectively serves as an ultrafast electrons that can emit optical phonons. As a result, this is a electronic thermometer. All experiments are performed under rather efficient cooling channel for graphene at room ambient conditions and at room temperature, monitoring the temperature. We will describe the analytical model of this time-dependent differential transmission ΔT/T(t). We use cooling mechanism in more detail in the following discussion pump pulses at 1550 nm (0.8 eV) with a 40 MHz repetition and in the Supporting Information. rate and probe pulses at 1700 nm (0.729 eV). These photon We calculate the cooling dynamics and compare the results energies are chosen well below the band gap of WSe2 (∼1.35 to the experimental data. In the calculation, we also take into eV for multilayer WSe2), to avoid photoexcitation of charges in account the superlinear relation connecting the ΔT/T signal to the encapsulant (see reflectance measurements in the the change in carrier temperature. As shown in Figure 2c, the Supporting Information). Thus, the role of the WSe2 is solely experimental data and calculated signal are in good agreement that of a dielectric environment. The pump pulses are absorbed when we use an optical-to-acoustic phonon decay time of 2 ps in graphene, where they induce carrier heating, i.e., a and a Fermi energy of 0.1 eV. This optical phonon lifetime lies broadening of the Fermi−Dirac distribution of the electronic within the range 1.2−2.55 ps, previously reported44−48 for system. The probe pulses are sensitive to this because the graphene. Figure 2d shows the temperature dynamics broadening leads to Pauli blocking of the interband transitions corresponding to the calculated transient signals in Figure 2c, at the probe photon energy. Therefore, the pump-induced which are clearly nonexponential. The fast initial decay increase in probe transmission is a measure of the electronic corresponds to efficient coupling to optical phonons, whereas temperature. Accordingly, the ΔT/T signal in Figure 2a is the slower subsequent decay is the result of the hot-phonon positive, indicating pump-induced transmission increase, i.e., bottleneck, where optical phonons are cooling to acoustic absorption bleaching. We can distinguish between fully phonons. encapsulated and semiencapsulated graphene regions in Figure Cooling Dynamics in High-Quality Suspended Gra- 2a, as the former gives rise to a lower transient signal (at a time phene. In order to determine if this cooling mechanism is delay of ∼100 fs), which is likely the result of strong Fresnel intrinsic to graphene, we study a second technologically reflections at the air−WSe2 and WSe2−graphene interfaces. relevant material system in which any thermal exchange with Figure 2b shows the relaxation dynamics of the ΔT/T signal the environment is inherently excluded: high-quality sus- of WSe2-encapsulated graphene and compares it to the pended graphene. This sample contains large-area graphene dynamics for hBN-encapsulated graphene. The decay in grown by chemical vapor deposition (CVD), which was then WSe2-encapsulated graphene is significantly slower: the signal transferred onto a transmission electron microscopy (TEM) 11288 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article Figure 3. Characterization of suspended high-quality graphene. (a) Sketch of graphene suspended on a holey carbon film. (b) Scanning electron microscopy images of suspended graphene on holey carbon, showing relatively large hole sizes and high yield. (c) TEM image of the suspended graphene, showing the absence of disorder. (d) Plot of 2D peak frequency ω2D as a function of G peak frequency ωG. Dashed lines represent the expected dependence in the strain-free (red dot-dot-dashed line) and doping-free (blue dot-dashed line) material. (e) Fermi energy EF distribution extracted from vector decomposition of peaks positions in panel d,51 and centered at |EF| ≈ 0.18 eV. (f) Obtained distribution of 2D-peak widths, indicating a mobility of >17 000 cm2 V−1 s−1, following calculations of ref 43. Figure 4. Hot-carrier cooling dynamics of suspended graphene. (a) Transient transmission ΔT/T map at time zero, showing individual holes where graphene is suspended, acquired with pump tuned at 3.1 eV (400 nm) and probe at 1.55 eV (800 nm). (b) ΔT/T dynamics (colored dots) for suspended graphene at five different pump fluences from 3 to 38 μJ/cm2. The positive ΔT/T results from the pump-induced carrier heating that leads to decreased interband conductivity due to Pauli blocking, and thus decreased absorption of the NIR probe light. The colored lines are the calculated ΔT/T dynamics, based on the intrinsic cooling mechanism where hot electrons cool via the combination of emission of optical phonons, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (c) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel b. Here, a fast decay due to electron-optical-phonon coupling is followed by a slower decay due to optical-to-acoustic phonon coupling. grid; see Figure 3a. This was achieved through a polymer-free furthermore show an atomically perfect lattice (see Figure 3c). approach, using the method described in ref 49. As a TEM grid We then perform Raman spectroscopy, in order to estimate the we used holey carbon, which is convenient as it has locations Fermi energy and charge mobility of the suspended graphene. with relatively large holes with a diameter exceeding 10 μm. It Performing a strain-doping analysis of the G-peak and 2D- has been shown that the graphene in such samples has a peak, obtained from several positions on the sample (see mobility well over 10 000 cm2 V−1 s−1.50 Given the large area Figure 3d), we obtain a distribution of carrier densities (see and high quality of graphene prepared by this fabrication Figure 3e), which corresponds to an average Fermi energy of approach, which is furthermore scalable, this is a highly ∼0.18 eV. Using the measured width of the 2D-peaks in Figure promising material system for a broad range of electronic and 3e and the empirical correlation of ref 43, we extract a mobility optoelectronic applications. of >17 000 cm2 V−1 s−1. This result is in agreement with We characterize our suspended graphene sample using electrical measurements performed on a sample of suspended various microscopic techniques; see Figure 3. First, we show an graphene, prepared in an identical way; see ref 50. The image taken using scanning electron microscopy, evidencing extracted mobility confirms the high quality of the sample, for excellent graphene coverage of the holes and providing an which disorder-assisted ”supercollision” cooling predicts a indication of hole sizes (see Figure 3b). TEM measurements cooling time >10 ps (see Supporting Information). 11289 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article Figure 5. Hot-carrier cooling dynamics in high-quality graphene. (a) Process of electronic cooling explained through schematics of the carrier density N as a function of carrier energy for three electron temperatures (1200, 800, and 400 K). Cooling occurs through a combination of (i) optical phonon emission by electrons with energy >0.16 eV above the chemical potential (red-shaded area), (ii) rethermalization of the electronic distribution, and (iii) anharmonic coupling of optical phonons to acoustic phonons. (b) Calculated “instantaneous” cooling time for a given initial electron temperature for three different Fermi energies. (c) Calculated cooling time as a function of lattice temperature TL for a very small ΔTe and EF = 0.03 eV. For panels b and c, cooling occurs through optical phonon emission and continuous rethermalization of the electronic system. The hot-phonon bottleneck is not included. Having established the high quality of our suspended Supporting Information. Despite the different optical tran- graphene sample, we now study its hot-carrier cooling sitions that are probed, both techniques essentially function as dynamics using time-resolved transient absorption microscopy ultrafast electrical thermometers for graphene. This is because (see Methods for details on the experimental setup). We use a in both cases the probe absorption is affected by pump- pump tuned at 400 nm (3.1 eV) and a probe at 800 nm (1.55 induced changes in the carrier temperature. The observed eV). Similar to the NIR TA measurements, we observe OPTP dynamics, reported in the Supporting Information, can photoinduced bleaching (ΔT/T > 0) of the probe, due to be described with the same model as before, confirming the heating-induced Pauli blocking. The ΔT/T map at zero time validity of this intrinsic cooling mechanism. delay (overlapping pump and probe pulses) in Figure 4a shows We now discuss in more detail the cooling mechanism that that we can resolve the individual holes spatially and that a we have used to describe the experimentally obtained cooling clearly distinctive transient signal comes from insidefrom the dynamics (schematically shown in Figure 5a). First, we note suspended graphene. For this experiment we use relatively that in many early time-resolved studies on graphene the small spot sizes (see Methods), in order to resolve individual dynamics were explained using a qualitatively similar suspended regions. mechanism involving electrons decaying to optical phonons, The experimental TA dynamics of our high-quality and a hot-phonon bottleneck; cf. refs 24, 46, 52, and 53. Some suspended graphene sample are shown in Figure 4b for five of these studies applied a phenomenological two- (or three-) different fluences. Similar transient optical responses were temperature model for electron cooling via optical phonons observed in suspended graphene prepared by exfoliation, in the (and acoustic phonons), which is (implicitly) based on VIS (400 nm pump, 800 nm probe),52 and in the NIR (830 (re)thermalization of the electronic system. Also using nm pump, 1100−1400 nm probe).24 We describe the electrical transport measurements, signatures of cooling via dynamics with the same cooling mechanism as for WSe2- optical phonons were identified (for bilayer graphene).54 This encapsulated graphene, with the same optical-to-acoustic cooling mechanism, however, was often thought to only phonon coupling time of 2 ps (details in the Supporting mediate cooling for carriers with high enough energy to couple Information). For this sample we use an EF = 0.15 eV, close to directly to optical phonons55 and was typically used for the experimentally determined average value. Figure 4c reports experiments with relatively high fluence and therefore relatively the temperature dynamics corresponding to the ΔT/T high electron temperatures. For the rest of the carriers in the dynamics in Figure 4b, again showing an initial fast decay hot-carrier distribution, and for cooling of systems with due to coupling between electrons and optical phonons, relatively low electron temperature, alternative cooling followed by slower decay due to optical phonons coupling to channels were considered. In particular, for cooling below a acoustic phonons. carrier temperature of ∼1500 K, disorder-assisted “super- As a final experimental test, we complement our TA collision cooling” to graphene acoustic phonons28−30,32 and measurements on suspended graphene, which probe interband out-of-plane cooling to (hyperbolic) substrate phonons,33−35 transitions, with optical-pump THz probe (OPTP) measure- which can both give rise to picosecond cooling at room ments, which probe intraband transitions; see Figure S3 of temperature, were thought to be the dominant mechanisms. In 11290 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article 2016, a microscopic, numerical, simulation of the cooling describes the decay of optical phonons to acoustic phonons, dynamics of hot carriers in graphene was presented, based on where T(0)α is the equilibrium phonon temperature, i.e., the electron-to-optical phonon coupling, and including rethermal- lattice temperature TL. For the optical phonon decay term, we ization of the carrier system.26 The calculated cooling times use the parameter γα as a phenomenological damping rate. were used to explain qualitative trends in decay times There are essentially two adjustable parameters in our measured by OPTP in samples of multilayer epitaxial graphene calculations: the optical phonon lifetime γα−1, and the on SiC and monolayer graphene grown by CVD. These results parameter v that governs the temperature dependence of the motivated us to (re)consider cooling via optical phonons as phonon number density (see Supporting Information). We the intrinsic cooling pathway for high-quality graphene, where note that this thermodynamic model, characterized by a single disorder-assisted cooling and out-of-plane cooling are electronic temperature and chemical potential, is based on inefficient. The cooling mechanism is schematically explained underlying microscopic carrier−carrier interactions that lead to in Figure 5a. We consider two phonon baths, Γ and K carrier (re)thermalization, as well as carrier−phonon and phonons, and we capture qualitatively the effect of temperature phonon−phonon interactions that lead to carrier cooling. smearing of the electron Fermi surface in the phonon density We have seen that this analytical model is able to accurately of states. The latter is important, because we are dealing with describe the experimentally obtained cooling dynamics. The elevated temperatures that lead to a smeared-out Fermi hot-phonon bottleneck, occurring when the density of emitted surface. optical phonons is so high that they cannot completely decay We developed an analytical model to describe the hot-carrier into acoustic phonons and part of their energy is scattered back cooling dynamics in graphene. The details of the derivation are to the electronic system, becomes more and more important shown in the Supporting Information. Briefly, we solve the with increasing initial Te, and it leads to an overall slower following rate equations for the electron temperature Te(t), cooling of the graphene hot carriers. For applications operating and phonon temperature Tα(t): with a small heating ΔTe, however, cooling is ultimately l o o o determined by electron-optical-phonon cooling. This regime is o o o o Ce(Te(t )) ∂tTe(t ) = −ℏ ∑ ωα 9 α(Te(t ), Tα(t )) likely relevant for applications that require low power o o o o consumption with low light intensities. Therefore, we analyti- m +(ω , T (t )) ∂ T (t ) = 9 α(Te(t ), Tα(t )) α o o cally study the cooling in the absence of the hot-phonon o o o bottleneck, i.e., when γα → ∞. We calculate that in this case, o o o α α t α o cooling at room temperature takes between ∼500 fs, for EF = o Mα(Te(t )) o n 0.3 eV, and ∼1.4 ps for 0.1 eV. Cooling to optical phonons will − γα[nα(Tα(t )) − nα(Tα(0))] (1) quickly become less efficient upon decreasing the lattice temperature TL. Around 200 K, we find a cooling time around The left-hand side of the first rate equation contains the 5 ps, whereas this increases to ∼4 ns at 100 K (see Figure 5c). electronic heat capacity Ce(Te(t)) and the temporal derivative We note that when ΔTe is not small, the effect of increased of the electron temperature. For each electronic temperature, cooling time with decreased lattice temperature is much the chemical potential is obtained by imposing that the total weaker. Thus, obtaining a longer intrinsic cooling time requires carrier density is fixed. The description of electrons in terms of a reduction of both TL and ΔTe. a single temperature and chemical potential implicitly assumes As a final discussion, we mention another physical that electron−electron interband scattering processes occur on mechanism that can play a significant role in the cooling a much shorter time scale than the electron−phonon process of hot carriers in high-mobility graphene (see dynamics. The dependence of the chemical potential on Supporting Information for details). This mechanism is carrier temperature that we use (see Supporting Information) “diffusive cooling”, where the electron system cools down by correspond to those that follow from conservation of total in-plane heat diffusion out of the initially heated spot. Until carrier density, where both intraband and interband carrier− now, this mechanism was mainly considered in the case of carrier scattering are taken into account. The right-hand side of micron-sized channels of ultrahigh-quality graphene (≫10 000 eq 1 describes the emission of optical phonons, where the sum cm2/(V s)) and at cryogenic temperatures.22,57 Cooling via is over the two optical phonon modes (labeled by α), at the Γ diffusion depends on the electronic heat diffusivity D, which and K point, ωα is the frequency of mode α, and 9 α(Te , Tα) is increases with charge mobility and Fermi energy.58 In the case the rate of α-phonon emission. We calculate this rate of pump−probe measurements, the observed evolution of the analytically using a Boltzmann-equation approach, which electron temperature increase due to lateral heat diffusion contains one important input parameter, namely, the depends on both pump and probe spot sizes (σpump and σpr, electron−phonon coupling strength. For this, we use the respectively), according to (see Supporting Information): value 11.4 eV/Å, obtained by density functional theory calculations, and verified by experiments.56 The left-hand σpump2σpr 2 ΔTe,probed(t ) ∝ side of the second rate equation contains σpump2 + σpr 2 + 2Dt (2) +(ωα , Tα) = ∂nα(Tα)/(∂Tα), where nα(Tα) is the phonon occupation function. Its right-hand side contains a first term Using this equation, we calculate that, for spot sizes below 1 due to the emission of optical phonons by electrons, where the μm, “diffusive cooling” can become the dominant cooling parameter Mα(Te) measures the size of the portion (an channel in high-mobility graphene samples, even at room annulus) of the phonon Brillouin zone that is heated in the temperature. In the measurements we performed on WSe2- electron-cooling process. This parameter depends, assuming encapsulated graphene, “diffusive cooling” does not play a large the phonon dispersion to be flat, on the maximum momentum role, due to the relatively large spot sizes that we used (see that can be exchanged between electrons and phonons, and Figure S12 of the Supporting Information). However, for the thus on the electron temperature Te. The second term measurements on suspended graphene, with smaller spot sizes, 11291 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article it is very likely that “diffusive cooling” contributes to the NPXYZ100). Image size of 120 × 120 pixels is used in the probed cooling dynamics, in particular in the tail of the experiment. The width of the cross-correlation between pump and dynamics. It is also conceivable that this leads to an probe pulses at the sample is ∼210 fs. overestimation of the optical phonon decay rate γα. We do The transient absorption measurements in the VIS on suspended graphene are performed using 400 nm pump and 800 nm probe note that this “diffusive cooling” is not an intrinsic cooling pulses with 150 fs pulses at 76 MHz repetition rate. Both pump and mechanism, since its contribution becomes negligible for probe pulses are carefully overlapped and focused at the same focal sufficiently large spot sizes. plane with a 40×/0.6 NA objective to focal spot sizes of 1.35 and 0.9 μm, respectively. The pump beam is modulated with an optical CONCLUSION chopper at 6.4 kHz. The probe is delayed temporally with a mechanical delay line and detected in transmission on a balanced Using three different time-resolved measurement techniques photodiode via lock-in detection. Further details of the setup are (NIR TA, VIS TA, and OPTP) and two different high-quality, described in ref 59. technologically relevant, graphene systems (WSe2-encapsulated Raman Spectroscopy. For Raman characterization, we used an and suspended CVD graphene), we have shown that hot inVia confocal Raman spectrometer from Renishaw plc, equipped carriers decay through an intrinsic mechanism involving optical with 473 and 532 nm CW laser sources. The laser beam was focused phonon emission and constant rethermalization of the onto the sample through a 100× objective lens, with 0.89 NA. The electronic system. Electrons with an energy >0.16 eV above nominal fwhm of the Gaussian beam at the focus is estimated to be the chemical potential couple to optical phonons, which in ∼1 μm, and the step size for the maps is set to 4 μm. The laser power turn decay to acoustic phonons while the electronic system hitting the sample in the selected configurations for the measurements were 1.6 mW for the 473 nm laser and 0.7 mW for the 532 nm. With continuously rethermalizes. The electron-to-optical-phonon an exposure time per pixel of 60 s, the fluence was 122 and 53 mJ/ cooling component gives rise to subpicosecond cooling. Due μm2, respectively. Depending on the measurement, a 1800 lines/mm to the hot-phonon bottleneck governed by the anharmonic grating or a denser 2400 lines/mm were used. The spectra are coupling of optical to acoustic phonons, an approximately calibrated with respect to the Si peak at 520 cm−1. biexponential cooling occurs, where the second decay component has a characteristic time scale of a few picoseconds. ASSOCIATED CONTENT The overall decay becomes slower for increasing initial * sı Supporting Information electron temperature (higher incident fluence) due to the The Supporting Information is available free of charge at hot-phonon bottleneck. Whereas previous studies considered a https://pubs.acs.org/doi/10.1021/acsnano.0c10864. similar mechanism for cooling of high-energy carriers, we here show that this is the intrinsically limiting cooling mechanism Hyperbolic cooling model, cooling dynamics probed for high-mobility graphene, also under relatively low incident with terahertz pulses, topography of encapsulated fluences and therefore lower electron temperatures. Our graphene, electron mobility of WSe2-encapsulated analytical model suggests that this mechanism will quickly graphene, Raman characterization of WSe2-encapsulated become less efficient upon decreasing the ambient temperature graphene, fully encapsulated vs semiencapsulated gra- TL, provided that also the amount of heating is small ΔTe < TL. phene, differential reflectance of WSe2-encapsulated Thus, operating graphene with low incident fluence and at graphene, cooling due to lateral heat diffusion, cooling reduced ambient temperatures is likely a promising approach via disorder-assisted acoustic phonon scattering, cooling to optimize optoelectronic applications exploiting hot carriers via optical phonons (PDF) in graphene. AUTHOR INFORMATION METHODS Corresponding Author High-Sensitivity Transient Absorption Microscopy. The Klaas-Jan Tielrooij − Catalan Institute of Nanoscience and transient absorption microscope for measurements in the NIR is Nanotechnology (ICN2), BIST & CSIC, Barcelona 08193, custom-built starting from a Er-doped fiber laser (Toptica-Femto fiber Spain; orcid.org/0000-0002-0055-6231; pro) generating 300 mW, 150 fs pulses centered at 1550 nm with 40 Email: klaas.tielrooij@icn2.cat MHz repetition rate. A portion of the output of the laser is used as the pump pulse, and it is modulated with an acousto-optic modulator Authors operating at 1 MHz. The NIR probe pulse is obtained by a Eva A. A. Pogna − NEST, Istituto Nanoscienze-CNR and supercontinuum (SC) generation focusing part of the laser Scuola Normale Superiore, 56127 Pisa, Italy; Department of fundamental in a highly nonlinear fiber. The high-energy component Physics, Politecnico di Milano, 20133 Milan, Italy; of the SC and the fundamental frequency are filtered out with a long- pass filter cutting at 1600 nm, and the component at 1700 nm is orcid.org/0000-0003-4779-3549 selected with a double-grating monochromator with 5 nm spectral Xiaoyu Jia − Max-Planck-Institut für Polymerforschung, resolution. The pump and the probe are collinearly focused on the 55128 Mainz, Germany sample with an objective (Olympus-LCPLN-IR with magnification Alessandro Principi − School of Physics and Astronomy, 100× and NA = 0.85) over a spot size of 2.8 (3.0) μm for the probe University of Manchester, M13 9PL Manchester, U.K. (pump) pulse. The probe transmitted by the sample is collected with Alexander Block − Catalan Institute of Nanoscience and an achromatic doublet with a 8 mm focal length and detected by an Nanotechnology (ICN2), BIST & CSIC, Barcelona 08193, InGaAs balanced amplified photodiode with 4 MHz bandwidth. The Spain component of the probe at the modulation frequency is measured Luca Banszerus − JARA-FIT and second Institute of Physics, with a lock-in amplifier (HFLI, Zurich Instruments) using 300 ms effective time constant resulting in a ΔT/T sensitivity below 10−6. RWTH Aachen University, 52074 Aachen, Germany; Transient transmission dynamics is monitored by changing the orcid.org/0000-0002-1855-1287 pump−probe time delay with an optical delay line, while the pump− Jincan Zhang − Center for Nanochemistry, College of probe maps (images) at fixed time-delay are acquired by moving the Chemistry and Molecular Engineering, Academy for sample with a motorized three-axis piezo-stack linear stage (Newport Advanced Interdisciplinary Studies, Peking University, Beijing 11292 https://doi.org/10.1021/acsnano.0c10864 ACS Nano 2021, 15, 11285−11295 ACS Nano www.acsnano.org Article 100871, China; Beijing Graphene Institute, Beijing 100095, ACKNOWLEDGMENTS P. R. China We would like to thank Andrea Tomadin for discussions. The Xiaoting Liu − Center for Nanochemistry, College of authors acknowledge funding from the European Union Chemistry and Molecular Engineering, Academy for Horizon 2020 Programme under Grant Agreement No. Advanced Interdisciplinary Studies, Peking University, Beijing 881603 Graphene Core 3. ICN2 was supported by the Severo 100871, China; Beijing Graphene Institute, Beijing 100095, Ochoa program from Spanish MINECO (Grant No. SEV- P. R. China 2017-0706). A.P. acknowledges support from the European Thibault Sohier − NanoMat/Q-Mat/CESAM, Université de Commission under the EU Horizon 2020 MSCA-RISE-2019 Liège (B5), B-4000 Liège, Belgium programme (project 873028 HYDROTRONICS) and from Stiven Forti − Center for Nanotechnology Innovation IIT@ the Leverhulme Trust under grant RPG-2019-363. K.J.T. NEST, 56127 Pisa, Italy acknowledges funding from the European Union’s Horizon Karuppasamy Soundarapandian − ICFO - Institut de 2020 research and innovation program under Grant Agree- Ciències Fotòniques, BIST, Barcelona 08860, Spain ment No. 804349 (ERC StG CUHL), RyC fellowship No. Bernat Terrés − ICFO - Institut de Ciències Fotòniques, BIST, RYC-2017-22330, and IAE project PID2019-111673GB-I00 Barcelona 08860, Spain and financial support through the MAINZ Visiting Professor- Jake D. Mehew − Catalan Institute of Nanoscience and ship. X.J. acknowledges the support from the Max Planck Nanotechnology (ICN2), BIST & CSIC, Barcelona 08193, Graduate Center with the Johannes Gutenberg-Universität Spain Mainz (MPGC). J.Z. acknowledges the support from National Chiara Trovatello − Department of Physics, Politecnico di Natural Science Foundation of China (No. 52072042). Z.L. Milano, 20133 Milan, Italy; orcid.org/0000-0002-8150- acknowledges the support from National Natural Science 9743 Foundation of China (No. 51520105003). T.S. acknowledges Camilla Coletti − Center for Nanotechnology Innovation support from the University of Liege under Special Funds for IIT@NEST, 56127 Pisa, Italy; Graphene Laboratories, Research, IPD-STEMA Programme. M.J.V. gratefully acknowl- 16163 Genova, Italy; orcid.org/0000-0002-8134-7633 edges funding from the Belgian Fonds National de la Frank H. L. Koppens − ICFO - Institut de Ciències Recherche Scientifique (FNRS) under PDR grant T.0103.19- Fotòniques, BIST, Barcelona 08860, Spain; ICREA - ALPS. Computational resources were provided by CECI (FRS- Institució Catalana de Reçerca i Estudis Avancats, 08010 FNRS G.A. 2.5020.11) and the Zenobe Tier-1 supercomputer Barcelona, Spain; orcid.org/0000-0001-9764-6120 (Gouvernement Wallon G.A. 1117545) and by a PRACE-3IP Mischa Bonn − Max-Planck-Institut für Polymerforschung, DECI grant 2DSpin and Pylight on Beskow (G.A. 653838 of 55128 Mainz, Germany; orcid.org/0000-0001-6851- H2020). ICFO was supported by the Severo Ochoa program 8453 for Centers of Excellence in R&D (CEX2019-000910-S), Hai I. Wang − Max-Planck-Institut für Polymerforschung, Fundació Privada Cellex, Fundació Privada Mir-Puig, and the 55128 Mainz, Germany; orcid.org/0000-0003-0940- Generalitat de Catalunya through the CERCA program. N.v.H. 3984 acknowledges funding by the European Commission (ERC Niek van Hulst − ICFO - Institut de Ciències Fotòniques, AdG 670949-LightNet), the Spanish Plan Nacional BIST, Barcelona 08860, Spain; ICREA - Institució Catalana (PGC2018-096875-BI00), and the Catalan AGAUR de Reçerca i Estudis Avancats, 08010 Barcelona, Spain; (2017SGR1369). orcid.org/0000-0003-4630-1776 Matthieu J. Verstraete − NanoMat/Q-Mat/CESAM, REFERENCES Université de Liège (B5), B-4000 Liège, Belgium (1) George, P. A.; Strait, J.; Dawlaty, J.; Shivaraman, S.; Hailin Peng − Center for Nanochemistry, College of Chemistry Chandrashekhar, M.; Rana, F.; Spencer, M. G. Ultrafast Optical- and Molecular Engineering, Academy for Advanced Pump Terahertz-Probe Spectroscopy of the Carrier Relaxation and Interdisciplinary Studies, Peking University, Beijing 100871, Recombination Dynamics in Epitaxial Graphene. Nano Lett. 2008, 8, China; Beijing Graphene Institute, Beijing 100095, P. R. 4248−4251. 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