2D Materials PAPER • OPEN ACCESS Crossover from ballistic to diffusive thermal transport in suspended graphene membranes To cite this article: A El Sachat et al 2019 2D Mater. 6 025034 View the article online for updates and enhancements. This content was downloaded from IP address 158.109.11.194 on 02/04/2019 at 10:16 2D Mater. 6 (2019) 025034 https://doi.org/10.1088/2053-1583/ab097d OPEN ACCESS PAPER Crossover from ballistic to diffusive thermal transport in suspended RECEIVED graphene membranes 26 November 2018 RE VISED 7 February 2019 A El Sachat1,4 , F Köenemann2, F Menges2,5, E Del Corro1, J A Garrido1,3, C M Sotomayor Torres1,3, F Alzina1 and B Gotsmann2 ACCEP TED FOR PUBLICATION 1 22 February 2019 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain 2 PUBLISHED IBM Research - Zurich, Säumerstrasse 4,8803 Rüchlikon, Switzerland 3 15 March 2019 ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain 4 Present address: Facultad de Ciencias, Departamento de Física de la Materia Condensada and Condensed Matter. Physics Center (IFIMAC), C/ Francisco Tomás y Valiente 7, Universidad Autónoma de Madrid, 28049, Madrid, Spain Original content from 5 this work may be used Present address: Department of Physics, University of Colorado, CO-80309, Boulder, United States of America under the terms of the E-mail: alexandros.elsachat@uam.es Creative Commons Attribution 3.0 licence. Keywords: graphene, nanoscale thermal transport, nanoscale thermal imaging, ballistic phonon transport, scanning thermal microscopy Any further distribution of this work must Supplementary material for this article is available online maintain attribution to the author(s) and the title of the work, journal citation and DOI. Abstract We report heat transport measurements on suspended single-layer graphene disks with radius of 150–1600 nm using a high-vacuum scanning thermal microscope. The results of this study revealed a radius-dependent thermal contact resistance between tip and graphene, with values between 1.15 and 1.52  ×  108 KW−1. The observed scaling of thermal resistance with radius is interpreted in terms of ballistic phonon transport in suspended graphene discs with radius smaller than 775 nm. In larger suspended graphene discs (radius  >775 nm), the thermal resistance increases with radius, which is attributed to in-plane heat transport being limited by phonon–phonon resistive scattering processes, which resulted in a transition from ballistic to diffusive thermal transport. In addition, by simultaneously mapping topography and steady-state heat flux signals between a self-heated scanning probe sensor and graphene with 17 nm thermal spatial resolution, we demonstrated that the surface quality of the suspended graphene and its connectivity with the Si/SiO2 substrate play a determining role in thermal transport. Our approach allows the investigation of heat transport in suspended graphene at sub-micrometre length scales and overcomes major limitations of conventional experimental methods usually caused by extrinsic thermal contact resistances, assumptions on the value of the graphene’s optical absorbance and limited thermal spatial resolution. 1. Introduction of the fundamentals of heat transport in graphene at sub-micrometre scale still remains an unresolved Graphene is a subject of intense research because of challenge for several reasons. To a certain extent, its unique electronic and thermal transport behavior the lack of understanding arises from technical that makes it attractive for large-scale integration limitations imposed by the experimental methods in future nanoelectronic devices. In particular, available to study heat transport at the nanoscale. For graphene’s high room-temperature carrier mobility instance, current experimental techniques, including [1] and high thermal conductivity [2] makes it a Raman spectroscopy [9–14] and electro-thermal promising candidate for thermal management in methods [15–22], proved to be insufficient for nanoelectronic circuits [3, 4]. However, engineering thermal characterization in nanometer-scale samples. graphene in sub-micrometre size devices requires the Moreover, both methods have shown contradictive understanding of heat dissipation at the nanoscale, results with large uncertainties. In the opto-thermal which is mainly dominated by a ballistic rather than a techniques, in addition to the uncertainties caused diffusive mechanism [2, 5–8]. Despite the enormous by the value of the graphene’s optical absorbance progress over the last few years, the understanding and the limited temperature sensitivity, the relatively © 2019 IOP Publishing Ltd 2D Mater. 6 (2019) 025034 A El Sachat et al large size of the focused laser spot limits the heat elsewhere [34]. By measuring topography and steady- transport studies to micrometre-scale samples. In state heat flux signals between a self-heated scanning the electro-thermal methods besides the difficult probe sensor and suspended graphene micro-discs sample preparation, the high extrinsic thermal of different radius, we quantify the in-plane heat contact resistance (graphene/electrode contacts) in transport, providing in parallel a valuable informa- submicron samples complicates the experimental tion regarding the surface quality and morphology of data interpretation and eventually leads to ambiguous the graphene discs. Therefore, we attribute the differ- results. Recently Nika et al [23, 24] summarized the ences in the measured thermal resistance only to vari- current available experimental heat transport results ations in the sample radius and not to the additional in graphene obtained from the aforementioned scattering that resulted from surface contamination methods, emphasizing the wide discrepancies and or deformation. the issue of accuracy. Consequently, these technique- related restrictions limit the understanding of ballistic 2. Materials and methods thermal transport in graphene, which requires thermal spatial resolution below the phonons mean free path 2.1. Fabrication (MFP). Graphene was grown by chemical vapor deposition on Apart from the difficulties of the measurement a 4.5  ×  7 cm2 copper foil previously electropolished, methods, CVD graphene samples often show sub- followed by a one hour annealing step at 1015 °C, like strate-induced surface corrugations, such as ripples or described elsewhere [35]. For growing times of 15 min at wrinkles, which are formed during the CVD growth 12 mbar (1000 sccm Ar/200 sccm H2/2 sccm CH4) the and retained after the transfer [25]. The origin of these graphene samples consist of a closed monolayer with surface corrugations are related to the morphology of a low density of second nucleation grains, as revealed the substrate on which the graphene layer was grown. by scanning electron microscopy. Graphene samples Calado et al [26] suggested that the water drainage are transferred to the final substrate (Si/SiO2) by a wet between graphene and substrate during the transfer chemical method using poly (methyl methacrylate) process plays an important role in wrinkle formation. as sacrificial polymer and iron chloride for the cooper In addition, it has been shown that the formation of etching. The graphene samples are characterized by wrinkles is particularly related to the adhesion and the Raman spectroscopy before and after the transfer magnitude of strain between graphene and substrate procedure to prove that the quality of the graphene [27]. Although the formation mechanisms respon- is preserved during the process. The Raman spectra sible for such surface corrugations in graphene has (see also figure S2 in the Supporting information (SI) been extensively discussed elsewhere [25], the effect (stacks.iop.org/TDM/6/10.1088/2053-1583/ab097d/ of this kind of surface corrugations on thermal trans- mmedia)) reveal a monolayer graphene sheet free of port remains almost unknown [28]. Furthermore, structural defects [36]. CVD graphene samples often suffer from high surface contamination from polymer residue, which usu- 2.2. Thermal analysis ally formed during the transfer process [29–31], and To quantify the local tip-sample thermal resistance, a may affect graphene’s intrinsic electronic and thermal self-heated scanning thermal microscope cantilever properties [25]. For instance, low quality suspended was used in active mode operation to measure the graphene samples exhibit thermal resistance or ther- heat flux variations caused by the difference in tip- mal conductivity that differ from the intrinsic value sample temperature. The measured heat flux signals predicted for clean suspended graphene [18, 32]. depend on both the temperature difference and the Although several experiments have been developed tip-sample thermal resistance (Rts ) and is equal to over the last decade to study thermal transport in CVD suspended monolayer graphene [1, 11, 20, 32, 33], the Q̇ts = (Tt − Ts )/Rts . The temperature of the integrated effect of graphene’s surface contamination on the heat heater/sensor (Tt = 180 ◦ C), was controlled by transport results is rarely discussed [32]. Therefore applying a DC current to the resistive silicon scanning experimental heat transport data of CVD suspended probe cantilever [37]. The temperature of the sample graphene with defined morphology and high thermal was kept at a room temperature (Ts = RT = 20 ◦ C). spatial resolution are still lacking. The thermal resistance of the cantilever was measured In this work we address the aforementioned chal- from the voltage drop across the heater/sensor while lenges by studying thermal transport in suspended the Rts was extracted by measuring the change of the monolayer graphene in a high-vacuum (10−6 mbar) thermal resistance in contact (Rth,in ) and out of contact −1 scanning thermal microscope, which directly enables (Rth,out ), Rts = (R−1 −1 th,in − Rth,out ) . More details quantitative heat flux measurements and thermal regarding the probe calibration and the quantification mapping with spatial resolution down to few-nano- of the Rts are given elsewhere [34]. Taking into account metre. The tip of the scanning thermal microscope the thermal resistive components at the tip-graphene effectively acts as a point-like heat source. More contacts, the Rts can be described by a series of resistors, details about the experimental setup can be found as follows: 2 2D Mater. 6 (2019) 025034 A El Sachat et al Figure 1. (a) Schematics of the nanoscopic tip-sample contact and the equivalent thermal resistance circuit, (b) a scanning electron microscopy image of the tip apex of the scanning thermal microscope cantilever with a radius of a  =  (5–10) nm and (c) a typical example of the measured thermal conductance signal during several tip-graphene point contacts. The distribution of the selected positions of the contacts in the membrane is shown in the inset of figure 1(c). Rts = Rt + Rc + Rspr (1) graphene areas with a spatial resolution of 17 nm. The estimation of the thermal spatial resolution was where Rt is the thermal resistance of the tip, Rc is the extracted by comparing topography and thermal thermal interface resistance between the tip and resistance data, as described in detail in figure S5 (see graphene (thermal contact resistance) and Rspr is SI). The brighter homogeneous contrast in the cen- the thermal spreading resistance in the graphene tral part of the thermal resistance image (figure 2(b)) membrane and into the substrate. Note, that this equation implies a diffusive transport in the graphene indicates decreased heat flow and an increased tip- sample. If the transport is ballistic in the graphene sample thermal resistance. We attribute this behav- membrane, then the thermal contact between tip and ior to the change in both Rc and Rspr when the tip is graphene is a part of the ballistic transport problem moving from the suspended graphene (brighter and Rc cannot be written as a summand for Rts region) to graphene-SiO2 contacts. The relative varia- independent from Rspr . Figures 1(a) and (b) display tions of the thermal resistance and topography signals schematics of the nanoscopic tip-sample contact, the between tip-graphene-SiO2 and tip-graphene contacts equivalent thermal resistance circuit and a scanning can be directly observed in the profiles of figure 2(c) electron microscopy image of the tip apex with radius (obtained from the line scans shown in figures 2(a) and of a  =  (5–10) nm. In figure 1(c) is shown a typical (b)). Topography-related resistance modulations are example of the measured thermal conductance signal visible in the graphene-SiO2 regions and at the edges of when the tip is brought in and out of contact with a the suspended graphene due to the relatively large var- suspended graphene membrane at different positions. iations of the tip-sample contact geometry. However, in the suspended graphene disc, we observe a rather 3. Results and discussion constant, homogeneous thermal resistance signal due to the flat surface topography. In particular, the topog- First, we obtain topography and thermal resistance raphy variations in the suspended part are smaller than maps of several suspended graphene disks with ~1 nm and the corresponding thermal resistance sig- radius between 150 nm and 1600 nm by simultaneous nal is constant with error less than 1% of the average measuring the local variations in topography and value. This result indicates a clear distinguish of the tip-sample thermal resistance. Figures 2(a) and two measured signal levels in the transferred graphene (b) show typical examples of the topography and and ballistic thermal transport. In addition, in the SI the corresponding thermal resistance image of (figure S3), we show that for relatively large graphene a suspended graphene discs with 150 nm radius. membranes (e.g. r ~ 1.6 µm), a thermal resistance The topography image in figure 2(a) shows a clean gradient appears as the tip-membrane contact moves graphene surface without defects and polymer toward the edge of the membrane. The thermal resist­ residue. However, the graphene membrane exhibits ance decrease, which is not only topography related as pronounced out-of-plane deformation with a height in the case of the graphene membrane with r ~ 150 nm, of approximately 25 nm. This kind of out-of-plane might be related to the dominance of the diffusive deformation is related to the interaction between the transport. substrate and the suspended graphene and usually Note that in few graphene membranes wrinkles arises from a tensile strain that is created during the or contaminated surface were visible both in the sup- fabrication process [29, 38]. Similarly, nanometre- ported and the suspended graphene. In figure S4 (see sized deformations in graphene have been observed in SI), we show examples of graphene membranes with previous studies [25, 30, 31, 39]. wrinkles, defects and contaminated surface from The thermal resistance map (figure 2(b)) shows polymer residue that are detected by our scanning clear differences between supported and suspended thermal microscope. In particular, the thermal resist­ 3 2D Mater. 6 (2019) 025034 A El Sachat et al Figure 2. (a) Topography and (b) thermal resistance maps of a clean suspended graphene disc free of structural defects with approximately 150 nm radius. (c) Topography (black spheres) and thermal resistance (red spheres) profiles obtained from the 400 nm white dashed lines depicted in figures (a) and (b), respectively. ance profile of figure S4(g) shows a 35% decrease of In order to quantify the variation of the thermal the thermal resistance due to a wrinkle that formed in resistance with the size of the suspended graphene, a suspended graphene membrane (see figures S4(c) we have studied a set of samples with varying radius. and (d)). Although this decrease might be attributed For this purpose, we obtain the average Rts for each to the contact area variations when the tip is moving suspended graphene disc by monitoring the heat flux from a lower height level towards the wrinkle, by com- signals transferred from the tip to several nanoscopic paring the cross sectional topography and thermal contacts of the graphene surface. Figure 3(a) displays resistance profiles of figure S4(g), we observe a smooth the average thermal resistance, Rts , as a function of topography change (~3 nm) from the suspended part the radius of the graphene discs. Note that the imag- towards the wrinkle and a relatively large decrease ing of the surface topography of all the membranes of the thermal resistance signal. Note that previous was performed prior to these measurements in order topography changes of approximately similar height to determine the surface quality and morphology of in a suspended graphene with absence of wrinkle did the transferred suspended graphene. Furthermore, not show similar magnitude change of the thermal by measuring the deflection of the cantilever during resistance signal. Therefore, the decrease of the ther- the approach-retract process, we estimated the mean mal resistance in the wrinkle most likely is not related value of the adhesion force for each graphene disc (fig- to the geometrical change of the contact area only. The ure 3(b)). A variation in the adhesion force points to identification of such surface corrugations is a clear a variation of the tip-sample contact through either a demonstration of the general idea of our approach, variation of sample compliance or, more frequently, a which aims to study heat transport in graphene at sub- contamination of the tip. A constant adhesion force is micrometre samples by simultaneously analyzing the therefore an indication of preserved integrity of the tip surface topography of the graphene, and show that it during the experiments. Therefore, in all the tip-gra- is possible to correlate changes in the thermal resist­ phene contacts we ensured that the applied contacting ance to the presence of such surface corrugations in the force, thus the thermal contact was similar. Graphene graphene surface. membranes that showed higher or lower average adhe- Furthermore, in figures S5(a) and (b) in the SI, we sion force and correspondingly higher or lower aver- show the topography and the corresponding thermal age thermal conductance have been excluded from the resistance map of a suspended graphene disc with analysis. Note also that polymer residues (or defects) 550 nm radius, where the thermal contrast between might potentially increase the thermal resistance of suspended and supported graphene has been changed. the graphene membranes. Therefore, it was essential The darker contrast (suspended graphene) in the ther- to compare thermal transport data derived from clean mal resistance image (figure S5(b)) indicates increased graphene membranes with similar morphology. heat flow and a lower thermal resistance. Note that Figure 3(a) shows an approximately linear thermal this is the first indication of the increased in plane resistance decrease with increasing graphene radius heat dissipation with increasing radius. Similarly, until 775 nm. The decrease of Rts with increasing from the thermal resistance profile (figure S5(c)), we radius suggests an increase of the in-plane heat dissi- observe topography-related resistance modulations in pation in the suspended graphene. On the other hand, graphene-SiO2 regions and a homogeneous thermal in graphene discs with a radius larger than 775 nm resistance signal in the suspended graphene. we found that the thermal resistance increases with 4 2D Mater. 6 (2019) 025034 A El Sachat et al Figure 3. The average measured (a) thermal resistance, Rts , and (b) adhesion force, Fad , as a function of the radius of the graphene discs. (c) The thermal resistance maps of the different radius graphene membranes, showing the thermal contrast modulations with increasing length. The experimental errors of the average values of the Rts presented in figure (a) are in the order of 104 KW−1. The error bars in (b) describe the statistical distribution of adhesion values measured. increasing radius. A second set of experimental data exponentially decreases and that for relatively large acquired with a different scanning thermal micro- suspended graphene disks, Rsup becomes negligible. scope cantilever, confirmed the increase of the thermal In particular, by increasing the graphene radius from resistance with graphene radius after 775 nm (see fig- 150 to 775 nm the Rsup is decreasing from 2.9 × 105 ure S7 in the SI). It is worth mentioning also that the to 6.2 × 104 KW−1. The exact values of Rsup as a experimental trend is consistent with the absolute function of different graphene lengths are given in thermal contrast changes with increasing graphene the SI, in Figure S8. Although the effect of the Rsup in radius, as shown in the thermal images in figure 3(c). the measured Rts might be considerable, from the In particular, by increasing the radius of the graphene experimental data in figure 3(a), we can see that the discs from 150 nm to 775 nm the absolute thermal magnitude change of the measured Rts in graphene contrast becomes darker. Then, by increasing fur- discs with radius between 150 and 775 nm is almost ther the radius of the graphene discs (from 775 nm to two order of magnitude larger than the decrease of 1.6 µm), the thermal contrast becomes brighter and the Rsup for the same length range. Therefore, the corre­spondingly the thermal resistance is increasing. contribution of Rsup to the thermal resistance of the Next, we analyze the experimentally observed sample Rspr and to the total thermal resistance Rts is trend of the radius–dependent thermal resistance. As negligible. This leaves us with the thermal resistance the thermal resistance Rts is a sum of different comp­ of the suspended part of the graphene as the main onents, we need to identify the components responsi- candidate for the observed dependence on flake radius. ble for the observed variation. The thermal resistance Next, we consider both ballistic and diffusive ther- of the tip Rt can be safely assumed constant. The heat mal transport in the suspended graphene. The average spreading into the silicon substrate in the region in MFP of thermal phonons in graphene estimated from which the graphene is supported is a function of the measurements ranges from 250 nm [22] to 800 nm [3]. membrane dimension. Using a heat diffusion equa- Regarding calculated values, single-phonon excita- tion in the cylindrical coordinates, we calculate Rsup as tions show typical MFP of about 1 µm [42]. Although follows [11]: an increase of two orders of magnitude was calculated 1 Ko (Zr ) for collective excitations [43], it has been recently Rsup = (2)  shown that the MFP recovers the values similar to the 2πr( gtks ) K1 (Zr ) single-phonon approximation, when four-phonon where g = 8.34 × 107 W m−2 K−1 is the total interface scattering processes are introduced [44]. Since the thermal conductance per unit area between graphene radius (r ) of the measured graphene discs are in the and SiO2 [14, 40], ks = 370 W m−1 K−1 is the thermal range of the expected MFPs, we can expect deviations conductivity of the supported graphene, t = 0.335 nm from a diffusive thermal transport and ballistic trans- is the thickness of graphene [41], Zr = r(g/ks t)1/2 port needs to be considered. [11] and K0, K1 are the zero and the first order Bessel Taking into account the sample geometry, we functions, respectively. From the equation (2) we define a ‘ballistic channel length’ equal to the dis- find that as the graphene’s disk radius increases, Rsup tance between the tip-graphene point contact and the 5 2D Mater. 6 (2019) 025034 A El Sachat et al supported graphene. Thus, by approaching the tip in We point out that in our experimental configura- the center of the graphene discs, the ballistic channel tion the size of the heat source is more than one order length becomes equal to the radius of the disc and a of magnitude smaller than the average MFP of the symmetrical in-plane propagation of ballistic pho- phonons in graphene, thus it was essential to consider nons from the tip apex to the supported graphene is in the analysis a model that explains the heat transport expected. In this transport regime, the ballistic thermal results in the ballistic transport regime. According to resistance (Rb ) is modeled as a constant [45]: previous reports [46, 50, 51] the thermal resistance 1 depends on the Knudsen number Kn = l/a . In the Rb ∝  (3) ballistic regime (Kn  1) an increase in the thermal A λ Cλ |υx,λ | αλ resistance is expected due to the additional ballistic where A is the cross-section of the heated area, λ is resistance. This trend has been observed in our exper­ the number of phonon modes, Cλ is the volumetric imental data in figure 3(a) (see also SI, figure S7), where specific heat contribution, υx,λ is the group velocity it is shown that graphene discs with a radius smaller along the temperature gradient for the phonon mode than 775 nm exhibit increased Rts due to the increase of λ and αλ is the phonon transmission coefficient across the ballistic resistance. the interfaces between the suspended and supported In the suspended graphene discs with a radius graphene. As the transport regime becomes purely comparable with the average MFP of phonons (r ∼ l ), ballistic, the temperature jump at the interface between the thermal transport regime consists of both ballistic suspended and supported graphene increases and the and diffusive features. In such cases the intrinsic ther- absolute temperature gradient inside the suspended mal resistance can often be approximated as a sum graphene decreases. Note that the ballistic resistance in between diffusive and ballistic parts, usually expressed this case is essentially the intrinsic thermal resistance as functions of Kn. The diffusive contribution to the of graphene. On the contrary, in the purely diffusive thermal resistance will increase with increasing gra- regime the thermal resistance increases with increasing phene membrane radius and will dominate the resist­ radius as: ance for large flakes. In this regime, the graphene radius ln ar ˆ r dr becomes much larger than the average MFP of phon- (4) Rd = = ons (r  l), therefore, phonon–phonon Umklapp a 2πrtκ 2πtκ resistive scattering processes become dominant [33, where α is the radius of the heated area, t is the thickness 47] and the heat transport starts to decrease. Note that of graphene and κ the thermal conductivity in the in relatively large graphene samples the contribution Fourier law. The phenomenological transmission Ä ä of the Rb to the intrinsic thermal resistance seems to ln r −1 coefficient in equation (3), αλ = 1 + l a remain a matter of ongoing debate due to the fact that [45], introduces the probability of heat carriers heat transport is significantly affected by the size of the undergo scattering. This results in the smoothing of heat source [52–54]. For instance, according to a pre- the otherwise abrupt transition between the length vious work [54], where a nanometer size heat source dependent diffusive resistance and the pure ballistic was used, an increase of the thermal resistance in rela- limit. tively large graphene samples was observed taking into Considering the high surface quality of the sus- account the contribution of the ballistic resistance. pended graphene micro-discs, thus the absence of Nevertheless, even if the contribution of Rb would phonon scattering on polymer residue and defects, be substantial, it will remain constant in the diffusive this result suggests a ballistic phonon transport up to regime of the membrane conductance and therefore 775 nm (ballistic channel length) approximately and does not conflict with our interpretation. a radius-dependent thermal resistance. The observed This behavior reflects the crossover from ballis- increased in-plane heat dissipation with increasing tic to diffusive thermal transport and is visible in our graphene lateral size can be attributed to the increase experimental data in graphene discs with a radius population of in-plane ballistic phonons at stationary larger than 775 nm. Note that this transition has been non-equilibrium conditions. In other words, as the confirmed also in the second set of measurements (fig- radius increases, more low-frequency acoustic phon- ure S7). We note, that the scaling of the ballistic and ons are excited and contribute to thermal conduction, diffusive resistance of the graphene and of the interface resulting in a length-dependent behavior. Similarly, is not only subject to geometry but a size-dependence it has been shown, that heat transport in suspended of the phonon density of states. The longest phonon graphene can be conducted from ballistic phonons wavelength that can support transport is limited by the [46] and quasi-ballistic heat flow effects should be size of the suspended part of the flake. Low frequency considered in graphene samples shorter than 1 µm / long wavelength phonons contribute significantly to [32, 47]. The importance of the low-frequency acoustic thermal transport in graphene [49, 55], and therefore phonons on heat transport with increasing g­ raphene the unexpected, almost linear scaling of thermal resist­ size has been emphasized also in several theoretical ance versus radius in the ballistic regime may be due to works [48, 49]. both geometry and density of states scaling. 6 2D Mater. 6 (2019) 025034 A El Sachat et al According to a previous work [32], a cross-over (FIS2015-70862-P). ICN2 is supported by the Severo from diffusive to quasi-ballistic regime is expected as Ochoa program from Spanish MINECO (Grants No. the suspended CVD graphene length is reduced below SEV-2013-0295 and No. SEV-2017-0706) and by 1 µm. However, the experimental data presented by Jo the CERCA programme/Generalitat de Catalunya. et al [32] did not show clear signatures of ballistic ther- FK and BG acknowledge funding in through the mal transport at room temperature. The identification H2020 European project CONNECT under the grant of ballistic transport features in CVD graphene sam- agreement number 688612 (www.connect-h2020. ples also was neither possible in recent reported heat eu). FM acknowledges support by The Branco Weiss transport data observed by Xu et al [22], either due to Fellowship–Society in Science administered by the the strong scattering of the low-frequency phonons by ETH Zurich. The authors thank K Moselund and N polymer residue [15, 32] or the limited heat flux reso- Mosso for their support. lution. Moreover, the previous works did not provide any information about the morphology and the sur- Notes face quality of the suspended graphene and the ther- mal measurements performed with the same exper­ The authors declare no competing financial interest. imental method. Note that in the previous studies, the micrometre size heat sources were similar to the length ORCID iDs of the suspended graphene, therefore ballistic heat transport was difficult to be revealed. A El Sachat https://orcid.org/0000-0003-3798-9724 F Alzina https://orcid.org/0000-0002-7082-0624 4. 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