Ultrafast relaxation of hot phonons in Graphene-hBN Heterostructures

Fast carrier cooling is important for high power graphene based devices. Strongly Coupled Optical Phonons (SCOPs) play a major role in the relaxation of photoexcited carriers in graphene. Heterostructures of graphene and hexagonal boron nitride (hBN) have shown exceptional mobility and high saturation current, which makes them ideal for applications, but the effect of the hBN substrate on carrier cooling mechanisms is not understood. We track the cooling of hot photo-excited carriers in graphene-hBN heterostructures using ultrafast pump-probe spectroscopy. We find that the carriers cool down four times faster in the case of graphene on hBN than on a silicon oxide substrate thus overcoming the hot phonon (HP) bottleneck that plagues cooling in graphene devices.

2 within tens of femtoseconds 8 . This hot thermal population cools further through the emission of optical phonons near the Γ point of the phonon dispersion. When the temperatures of the carriers and optical phonon bath equalize, this cooling channel slows down and this is termed as the Hot Phonon (HP) bottleneck 5,[9][10][11][12][13] . Cooling through direct acoustic phonon emission is not viable because of a vanishingly small phase space for such a scattering process 14 . The hot optical phonons cool down through anharmonic decay to acoustic phonons which are subsequently absorbed into the substrate. Direct cooling of the charge carriers is also predicted to occur through coupling with the surface phonons of the underlying polar substrate 12,15-17 . Theoretical predictions and experiments place the hot optical phonon lifetime in graphene, graphite and CNTs in the 1-5ps range 5,9,[18][19][20][21] . The buildup of optical phonons is detrimental to device performance and the HP bottleneck has been invoked to explain current saturation and negative differential conductance in graphene and CNTs 10,11,22 . The HP bottleneck also affects the photoresponse 23 of optoelectronic devices. It is important to explore cooling channels that can efficiently de-energize the optical phonons and remove the HP bottleneck. In that regard, graphene heterostructures incorporating an appropriate substrate, such as hBN, could offer additional mechanisms for accelerating the cooling process. It has been recently reported that the active cooling efficiency due to the Peltier effect in graphene-hBN devices is more than twice as much as the highest reported room temperature power factors 24 . A comparative study of relaxation dynamics for graphene on hBN and SiO2 is missing from literature. In this letter, we study the relaxation of carriers in graphene-hBN heterostructure devices. Our findings indicate that the substrate interface plays a major role in the carrier cooling process and carriers in graphene devices fabricated on hBN substrates relax significantly faster than those on SiO2 substrates thus providing relief of the HP bottleneck and enabling better device performance.
Hexagonal boron nitride flakes were exfoliated and deposited on silicon chips that have a 285 nm thermally grown oxide. Pristine graphene was grown on copper foil using a low pressure chemical vapor deposition (CVD) method as described in the work by Xuesong Li et al 25 . PMMA was spin coated onto the copper foil before floating it on a mixture of hydrogen peroxide, hydrochloric acid and de-ionized water to etch away the copper. The remaining graphene/PMMA film was transferred to clean de-ionized water. The Si/SiO2 chip with exfoliated hBN was used to gently pick up the floating graphene/PMMA film and then dried. The chip was then placed in acetone to dissolve the PMMA layer. The samples were then subsequently annealed in an atmosphere of argon and hydrogen at 350˚C for 3 hours to get rid of residues, impurities and ensure better adhesion to the substrate. An optical image of one of the samples is shown in Figure 1. The spot marked 1 has graphene on hBN (g-hBN) whereas spot 2 has graphene on SiO2 (g-SiO2). The Raman spectra of g-SiO2 and g-hBN are shown in Figure 1(b). The absence of a D peak means that both the g-SiO2 and g-hBN are defect free. We infer from the G and 2D peak positions that g-SiO2 and g-hBN are p-doped by about 3.5×10 12 −2 and 1×10 12 −2 respectively 26,27 , which is well below the 1.58 eV probing photon energy.
For the pump-probe study we used amplified 780 nm pulses from a Ti-sapphire laser amplifier for both pump and probe. The spot sizes (FWHM) of the pump and probe beams were measured using the knife edge technique to be 154 μm and 23 μm respectively. The FWHM as measured using the FROG technique was 45 fs. The experiment was conducted with a range of pump pulse energies, all of which were below the damage threshold of graphene under irradiation with ultrafast pulses 28 . The pump was chopped using an optical chopper and the probe reflectivity of the sample was measured using lock-in detection. The polarizations of the pump and probe were crossed for better rejection of the pump scatter.
The relaxation of PE carriers is captured by the differential reflectivity, , of the sample. The differential reflectivity shows the opposite trend as the electronic temperature in graphene, which means that a decrease in corresponds to an increase in the electronic temperature. Figure 2 shows as a function of the pump-probe time delay for three different g-hBN structures along with curves for g-SiO2 for comparison. The pump pulse energy is 60 2 . The baseline at large positive pump probe delay is non-zero because of the underlying contribution from silicon base of our samples. This baseline is constant over 100 picoseconds which is far greater timescale than those discussed in this letter. We have independently verified that this baseline does not contribute to the lifetimes extracted from our experiment (section S2 in the supplementary information). It is immediately evident from Figure 2 that the relaxation dynamics of g-hBN are faster than that of g-SiO2.
In order to quantify the timescales observed in the experiment we modeled the temperature dynamics of the heterostructure using a two-temperature model 29,30 . The lateral transport of heat is negligible because the diffusion timescale is of the order of 90 microseconds (section S1 in the supplementary information).
where and denote the electronic and optical phonon temperatures of graphene respectively. The coupling between and is given by the function ( , ). 0 is the ambient room temperature; and denote the phononic and electronic heat capacity of graphene; ( ) is the time profile of the pump pulse which is assumed to be a Gaussian with a FWHM of 45 fs. The thermal relaxation timescale is which denotes the optical phonon lifetime in graphene. We numerically solve the system of differential equations given above for the electronic temperature, which determines the optical conductivity (σ) of graphene as a function of time. We use the optical conductivity calculated in the previous step to determine the total reflectance of the heterostructure using the transfer matrix method. We fit the experimental transient reflectivity curves using the two temperature model to estimate the where, The heat capacity is the effective heat capacity per unit area of the composite graphene-hBN system 32 . The heat capacity and conductance of hBN can be ignored because the limiting term in the vertical heat transport dynamics of the heterostructure is the interfacial thermal conductance between graphene and the substrate. Since the measured phonon lifetime shows a decreasing trend with the temperature differential, we estimate the lower limit of the room temperature interfacial conductance of the graphene-hBN interface from our measured relaxation lifetime for the lowest fluence as 16.25 2 . at room temperature. The corresponding value for the graphene-SiO2 interface is 3.75 2 .
. The value of for g-hBN measured here is higher than that reported in the work by Chen et al. 33  The interaction between the carriers in graphene and the surface plasmon polaritons (SPP) of the polar substrate has been proposed as a possible cooling mechanism for overcoming the HP bottleneck in graphene 15-17, 34 . It has been established that graphene on hBN substrates has lower charge doping level than graphene on SiO2 3 which is also the case in our samples as evidenced by the slightly upshifted (~10 cm -1 ) and narrower G peak 27 for g-SiO2. If SPP interactions were the dominant cooling mechanism, the doping of graphene due to SiO2 will shield this interaction and reduce the efficacy of this channel consequently increasing the relaxation time for phonons in g-SiO2. The interaction between graphene and the substrate also depends on many factors like topographic conformity, coulombic interactions and adhesion energy. The g-hBN interface can be more transparent to heat carrying phonons because of the similar masses of carbon, boron and nitrogen 35 . The curvature of the graphene sheet is an additional contributor to 6 the interface thermal resistance in g-SiO2 36 . Annealing contributes to the graphene sheet conforming to the substrate and hBN being atomically flat means the graphene sheet in g-hBN has lower cumulative curvature than the graphene sheet in g-SiO2 effectively decreasing interfacial resistance in g-hBN.
In conclusion, we have used differential reflectance spectroscopy to study the carrier dynamics of graphene-hBN heterostructures. We extract the optical phonon lifetime and interface thermal conductance using a twotemperature model. The thermal relaxation rates of graphene-hBN are significantly faster than those of graphene-SiO2 thus mitigating the hot phonon bottleneck. We conclude that hBN substrates will enhance the thermal performance of high power graphene devices 39 .

S3. Details of the two temperature model and reflectivity calculation
The two temperature model makes the lumped heat capacity approximation wherein the limiting term in the heat dynamics is the interfacial thermal resistance. This is a reasonable approximation because the atomic layer thickness of graphene ensures a uniform temperature across its depth.
Another factor contributing to the validation of the lumped element model is that the heat capacity per unit area of hBN is much higher than graphene. to the relative permittivity of graphene is denoted as . We calculate the reflectivity of the graphene\hBN\SiO2\Silicon stack using the transfer matrix method of thin film interference 3 . Thus, knowing the electronic temperature ( ) as a function of time delay allows us to calculate reflectivity ( ) as a function of time delay.

S4. Evolution of the electronic and phonon temperature
The following graphs show the evolution of the electron and phonon temperatures extracted from the simulations with incident fluence 60 μJ cm 2 ( Fig S4) and 80 μJ cm 2 (Fig S5) respectively. We note that the maximum electron temperature reached can vary non-linearly with the incident pump fluence due to state filling, localized doping or screening due to the substrate.