Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Spatially mapping thermal transport in graphene by an opto-thermal method

Spatially mapping thermal transport in graphene by an opto-thermal method www.nature.com/npj2dmaterials ARTICLE OPEN Spatially mapping thermal transport in graphene by an opto- thermal method 1,2 1 1 1,4 1 2 1,2,3 Oliver Braun , Roman Furrer , Pascal Butti , Kishan Thodkar , Ivan Shorubalko , Ilaria Zardo , Michel Calame and Mickael L. Perrin Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working principle of our method by extracting the two-dimensional thermal conductivity map of one pristine suspended single-layer graphene sheet and one irradiated using helium ions. Our method paves the way for spatially resolving the thermal conductivity of other types of layered materials. This is particularly relevant for the design and engineering of nanoscale thermal circuits (e.g. thermal diodes). npj 2D Materials and Applications (2022) 6:6 ; https://doi.org/10.1038/s41699-021-00277-2 INTRODUCTION extensively used in literature since. Alternatives based on the intensity ratio of Stokes to anti-Stokes Raman scattering or the Thermal properties of materials are of crucial importance for Raman 2D-band have also been reported. optimizing heat management in nanoscale devices, with the 1,2 Using this opto-thermal method, the influence of the quality thermal conductivity as key material property . The thermal and structure of the graphene, as well as the environment have conductivity is typically determined by monitoring the sample been extensively investigated. For instance, Cai et al. reported temperature and/or heat flow in response to a local heat source, in −1 −1 values for κ exceeding ~2500 Wm K for suspended graphene combination with an analytical expression or a numerical model. 3,4 20 For instance, for bulk materials, the well-known 3ω technique is grown by chemical vapor deposition (CVD), and Chen et al. used, while for nanoscale materials, methods such as the thermal studied the influence of environment on thermal conductivity of 5–7 8–11 12 13 bridge method and micro-Raman spectroscopy provide the graphene. Isotopically pure C (0.01 % C) graphene has been −1 −1 thermal conductivity of the material. shown to exhibit κ = 4000 Wm K , a factor of two higher than κ 12 13 21 Of particular interest are the thermal properties of layered in graphene composed of a 1:1 mixture of C and C . Also, the materials. Due to their broad range of conductivity values and influence of CVD-graphene’s polycrystallinity on the thermal their atomically thin nature, such materials are highly relevant for conductivity was studied by Lee et al. and Ma et al., revealing 12,13 heat management at the nanoscale . One of the most that smaller grain sizes drastically reduce κ due to grain boundary appealing materials is graphene, with extraordinarily high thermal 22,23 24 scattering . Along similar lines, wrinkles , oxygen-plasma conductivity values. However, extracting the thermal properties of 25 26 induced defects , and electron beam irradiation have shown 2D materials is challenging, in particular when suspended to to reduce the thermal conductivity. reduce the influence of the substrate. For example, time-domain In all the above-mentioned studies, the one-dimensional heat thermoreflectance cannot be applied to 2D materials as the equation is used to fit the experimental temperature and extract material is too thin . Scanning thermal probe microscopy, on the the thermal conductivity. However, such approaches yield an other hand, despite possessing nanometer resolution, is highly average value of thermal conductivity value, not a spatially delicate to perform on suspended 2D materials. Moreover, both resolved map. This implied that local variations caused by defects, techniques rely on on-chip heaters for channeling heat into the folds, contaminants, etc. are neglected. system. Raman spectroscopy can overcome these difficulties, as it For going beyond the average material property value, can utilize the excitation laser to locally heat the device, while at approaches mapping the temperature distribution in the sample the same time measuring the local temperature. Moreover, Raman are necessary, combined with multi-dimensional analytical or spectroscopy can be conveniently performed on suspended numerical model. A range of techniques has been developed for graphene films for eliminating the influence of the substrate. 15,16 nanoscale thermometry, such as time-domain thermoreflec- Using Raman spectroscopy, Balandin and Ghosh et al. 27 15,16 tance , Raman spectroscopy , scanning thermal probe micro- determined the thermal conductivity of suspended graphene to 28–30 31 −1 −1 scopy , polymer imprint thermal mapping and electron be as high as ~5000 Wm K at room temperature. Their opto- energy loss spectroscopy , providing means to locally map the thermal method, measuring the shift of the Raman G-band upon sample temperature. laser irradiation for estimating the local temperature, has been Empa, Swiss Federal Laboratories for Materials Science and Technology, Transport at Nanoscale Interfaces Laboratory, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland. 2 3 Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland. Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland. Present address: Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, CH-8092 Zurich, Switzerland. email: Mickael.Perrin@Empa.ch Published in partnership with FCT NOVA with the support of E-MRS 1234567890():,; O. Braun et al. a) b) Laser for Experimental Finite-element model Raman mapping Graphene (suspended) ... Raman map T Raman map T Low laser power Initial guess  map 1 n Au Si3N4 Si ... Fitting 2D peak Fitting 2D peak Calculated T map Scanning d/dK map Comparison T map Raman map T High laser power Fitted map Hotplate Fig. 1 Experimental and finite-element method description. a Schematic drawing of the suspended graphene membrane. b Experimental workflow to obtain a temperature map upon laser illumination and computational workflow to fit the corresponding thermal conductivity map. Here, we introduce an opto-thermal method that allows for showing substantial spatial variations. Once this calibration map is two-dimensional mapping of thermal conductivity of suspended acquired, a Raman map of the graphene membrane is acquired at graphene membranes. The presented method relies on a high laser power (4 mW), as shown in Fig. 2d. The high laser power combination of scanning μ-Raman spectroscopy finite-element causes the graphene to locally heat, resulting in a shift in the method (FEM) calculations. The workflow for our approach is Raman peak position. We assume steady state conditions for all presented in Fig. 1. In the first experimental stage, a series of two- data interpretations as the thermal time constant is short (τ < dimensional Raman spectroscopy maps are used to construct a 34 300 ns) in suspended graphene . temperature map of the membrane upon illumination. More By combining this high-power measurement with the dω /dT 2D specifically, Raman maps are recorded at low laser power for map obtained at low laser power, a map of the average various hotplate temperatures. This series of maps is used to temperature within the laser spot is obtained for each laser construct a calibration map of the Raman peak shifts with position, as shown in Fig. 2b. We note that local variations in the temperature. Then, another Raman map is recorded at high laser- temperature upon illumination on the order of 50–100 K are power, which, combined with the calibration map, is used to observed, highlighting the importance of spatially mapping the construct a temperature map of the membrane upon laser temperature and its superiority over other techniques that extract heating. thermal conductivity from a single spot. The constructed experimental temperature map is then used as an input for the FEM-based fit procedure. For a given initial guess of the thermal conductivity, the lattice temperature upon laser FEM calculations illumination is calculated. The thermal conductivity is then FEM calculations are employed for the computation of the iteratively adjusted, until the computed temperature map temperature map of the system upon laser illumination for a matches the experimental one. We apply this fit procedure to extract the thermal conductivity of a pristine graphene membrane given spatial thermal conductivity distribution. This concept is that is suspended over a silicon nitride frame. Finally, we illustrated in Fig. 3. As an input, a two-dimensional map of the demonstrate that the thermal conductivity of the graphene thermal conductivity is provided, of which an example is shown membrane can be tuned in a controlled way by the introduction Fig. 3a. Figure 3b presents the layout of the system (not to scale). of helium-ion (He -ion) induced defects in the membrane. A detailed description of the FEM calculation and the implemen- tation thereof is provided in Supplementary Note 3. While scanning the laser across the membrane, the full temperature RESULTS distribution is calculated for each laser spot position on the Experimental temperature maps membrane (three examples are provided in Fig. 3b). The CVD-graphene membranes are prepared as described in the For each of these temperature distributions, the average methods section. We applied Raman spectroscopy to obtain the temperature within the laser spot is calculated, from which all lattice temperature of the suspended graphene membranes (for values are combined to obtain a two-dimensional map of the details see Methods and Supplementary Notes 1 and 3). Here, we graphene temperature upon illumination. This induced- focus on the 2D-band due to its high sensitivity to temperature temperature map is presented in Fig. 3c and represents the same 20,22 −1 −1 changes of around −0.07 cm K . Alternatively, one can also temperature map that is obtained experimentally upon illumina- rely on the G-peak due to its high linearity in peak shift versus tion of the sample with high laser power. 16,19,33 temperature. . To obtain the thermal conductivity map, an iterative minimization Figure 2a presents maps of the Lorentzian-fitted 2D-peaks procedure is employed. More information can be found in acquired at temperatures T –T ranging between 298 and 425 K. 1 7 Supplementary Note 2, in which we also validate the numerical The Raman spectra have been acquired at low laser power method on a simulated system with a known thermal conductivity (0.25 mW) to limit any heating effects using a 532 nm excitation map. The starting point is an initial (typically uniform) guess of the laser (for details see Methods and Supplementary Note 3). For thermal conductivity. In each iteration of the process, the correspond- each pixel, the peak shift with hot plate temperature (dω /dT)is 2D ing induced temperature map is compared to the experimental fitted using a first-order polynomial, as shown in Fig. 2b. The inset temperature map, after which the thermal conductivity is adjusted presents a histogram of the slopes, showing a Gaussian −1 −1 distribution centered around −0.07 cm K . The spatial distribu- pixel-wise according to the temperature difference. This process is tion of the peak shifts with temperature is displayed in Fig. 2c, repeated until convergence is reached. npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS 1234567890():,; adjust  O. Braun et al. low laserpower high laserpower a) 5 2685 d) 5 2685 T1=298K T7=425K T=298K T2=317K 2675 2675 T =337K ... ... T4=358K 0 0 T5=378K 2665 2665 T6=402K -5 -5 2655 2655 -5 0 5 -5 0 5 -5 0 5 Position [m] Position [m] Position [m] b) c) e) 5 2685 high 5 0 450 center T=298K edge linear fits -0.02 2675 400 -0.04 -0.06 2665 350 0 -0.08 -0.1 0 -1 Slope [cm /K] -5 -0.10 -5 300 300 350 400 -5 0 5 -5 0 5 Position [m] Position [m] Temperature [K] Fig. 2 Experimental determination of temperature map. Spatially resolved mapping of laser-induced temperature rise of graphene. a Raman 2D-peak position obtained with P = 0.25 mW at different hot plate temperatures T and T . The dashed circle is a guide to the eye laser 1 7 for the support edge. b Density plot of the temperature evolution of the 2D-peak frequency. Two spatial points (center and edge, see dots in c are highlighted to represent the method. The inset shows a histogram of dω /dT of the complete membrane. c Spatial distribution of 2D change in Raman shift per temperature change dω /dT obtained from linear fits to the data shown in b). d Raman 2D-peak position obtained 2D with P = 4 mW at 297 K. e Temperature distribution obtained by combining the results from c, d. laser a) b) c) 3) Supported Thermal conductivity Temperature upon graphene -1 -1 [W·m ·K ] illumination [K] Suspended 0 500 1000 300 400 500 graphene 5 5 Laser spot 0 0 -5 1) 2) -5 -5 0 5 -5 0 5 Position [m] Position [m] Fig. 3 Finite-element method description. a Input thermal conductivity map. b Schematic representation of the sample and the calculation mesh. Temperature profiles of the graphene membrane with the heating laser spot at three different positions (1–3). c Temperature profile upon laser illumination. Thermal conductivity map based on fitted experimental supporting part, the thermal coupling to the substrate, as well as the temperature map convection parameter are taken from literature . Finally,wenotethat The induced temperature map obtained in Fig. 2 is used as input for it is challenging to model the transition from the suspended graphene to the supported graphene once the laser spot is in the the iterative procedure to obtain the thermal conductivity map. Here, as clarified in Supplementary Note 3, we use a uniform absorption of vicinity of the edge due to (1) reflection from of the laser excitation at the edges of the support may lead to an increase in the deposited 2.7 % for the suspended graphene and double that value (5.4 %) for laser power, (2) quenching of the Raman scattered light on the the supported graphene. Moreover, all the employed model substrate may lead to an overestimation of the local temperature as parameters are summarized in Supplementary Table 1. Importantly, the 2D peak of the suspended graphene is more pronounced than in the model, a spot size of 370 nm is considered, based on a measurement shown in Supplementary Note 3. This value is larger that of the supported graphene. To circumvent this issue, the thermal conductivity of the first 0.5 μm of the membranes away from the than the diffraction-limit, based on the Abbe criterion d= λ/2NA, where d is the spotsize, λ is the wavelength and NA is the numerical support are not fitted and kept at a fixedvalue.Finally,the thermal conductivity is fitted for 100 iterations, after which the absorption is aperture . Moreover, the thermal conductivity of graphene on the Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6 -1 Raman shift [cm ] Position [m] Counts Position [m] Density [arb. u.] Position [m] -1 -1 -1 dω /dT [cm ·K ] Raman shift [cm ] 2D Position [m] Position [m] Position [m] -1 Temperature [K] Raman shift [cm ] O. Braun et al. a) 5 450 c) 5 2000 e) Experimental - 298K 298 K 1500 100 0 0 1000 337 K -5 300 -5 0 -5 0 5 -5 0 5 Position [m] Position [m] 379 K b) 450 d) 5 5 5 Fit 100 400 4 0 0 425 K 350 3 -5 300 -5 2 0 1000 2000 -5 0 5 -5 0 5 -1 -1 Position [m] Position [m]  [W·m ·K ] Fig. 4 Thermal conductivity map based on fitted experimental data. a Experimentally determined temperature map. b Fitted temperature map. c Fitted thermal conductivity map. d Converged absorption map. e Histogram of the thermal conductivity for various hot plate temperatures. Arrows indicate the mode of the smoothed distributions. fitted for the same number of cycles. More details about this the extraction of the temperature. Figure 5b presents the induced procedure can be found in Supplementary Note 2. For numerical temperature map upon a 4 mW laser illumination. In this plot, the stability reasons, we put a lower value on the thermal conductivity at four quadrants are visible, with the lowest temperatures recorded −1 −1 100 Wm K . in the (unexposed) lower left section of the membrane, and the Figure 4a presents the experimental temperature map, as highest one in the upper left (most exposed). This temperature obtained in Fig. 2e, alongside the fitted temperature map in Fig. map is used as input for the iterative FEM-based fitting procedure, resulting in the fitted thermal conductivity map in Fig. 5c and the 4b. The two maps closely resemble each other. The corresponding corresponding fitted temperature map shown in Fig. 5d. Figure 5e thermal conductivity map is presented in Fig. 4c. We find that the −1 −1 presents a histogram of the thermal conductivity of each of the local thermal conductivity values range from 500 to 2000 Wm K −1 −1 four quadrants. A steady decrease in average conductivity is with an average value of 1224 ± 387 Wm K highlighting the −1 −1 + observed, from ~1200 Wm K for the no He -ion irradiation, to importance of spatially resolving the thermal conductivity. The −1 −1 + ~300 Wm K for the highest He -ion dose. This decrease in average value is in agreement with previously reported values for thermal conductivity with increasing defect density is in agree- CVD-graphene, where typical defects like polymer residues, grain 25,26 36–39 ment with previous reports . boundaries, etc. are present .InFig. 4e, we present a histogram of the fitted thermal conductivity map for increasing hot plate temperatures. The bar plots show that for increasing temperature a DISCUSSION gradual decrease in thermal conductivity is observed. This behavior 20–22 The FEM calculations employed here assume that the heat follows the trend observed by others . transport through the system is following Fourier’s Law. This assumption implies that the phonon mean free path is much Thermal conductivity of defect-engineered graphene smaller than the membrane size. Indeed, ballistic phonon As a final demonstration of the capability of the presented transport has been reported in several nanosystems at room method, we study the thermal conductivity of a graphene temperature: In substrate-supported graphene the phonon mean membrane that is exposed to He -ions using focused ion beam free path is ~100 nm ; for suspended graphene discs, the (FIB) lithography. As shown previously, He -ions can be used to transition from ballistic to diffusive transport occurs at induce, in a controlled fashion, defects in suspended graphene ~775 nm while in ultra-thin nanowires phonon mean free paths 40,41 membranes and other two-dimensional materials . of several micrometers have been observed . Therefore, the Figure 5a presents the exposure pattern as well as the used resolution of the presented method is limited by the phonon irradiation doses. The membrane is divided into four quadrants, mean free path as a spatial mapping of the thermal conductivity with the He -ion irradiation steadily increasing in the counter- below this length scale would require a heat transport description 47–49 clockwise direction, starting in the lower left with no He -ion based on the Boltzmann transport equation . Given this dose. Manually selected representative Raman spectra of each boundary condition, the resolution of 250 nm used in this study is quadrant are presented in Supplementary Note 4, exhibiting all close to the ultimate resolution this FEM-based method allows. the characteristic graphene peaks. The selection of the represen- A limitation of the presented method is the time consumption tative Raman spectra can also be done by an advanced clustering of the temperature calibration, reducing its use in high- approach to avoid any human bias as described elsewhere . throughput applications. As the laser power is low, acquiring the Upon an increase of the He -ion dose, the D-band intensity two-dimensional Raman map at each temperature requires several steadily increases. The intensity ratio of the D and D' band I(D)/I(D') hours. This long acquisition time can also lead to a drift in the upon irradiation, is indicative of the type of defect. . We extract sample position during the measurement. To reduce this drift, this ratio by fitting the ratios I(D)/I(G) versus I(D')/I(G) for various clamping of the sample and a good thermalization of the sample He -ion doses. We find an intensity ratio of ~11.7 for the defect- with the environment is crucial. Furthermore, as changing the hot engineered graphene. This value is comparable to the reported plate temperature leads to shifts of the sample position, the intensity ratio of ~13 for sp type of defects (see Supplementary Raman maps acquired at various temperatures need to be aligned Note 4). We employ the same procedure as presented in Fig. 2 for one versus the other. npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS Position [m] Position [m] Temperature [K] Temperature [K] Position [m] Position [m] -1 -1 Absorption [%]  [W·m ·K ] Counts O. Braun et al. c) 5 2000 a) e) He-ion dose 15 -2 (×10 cm ) 40 He: None 0 None 0 1000 0.1 Low 0.25 Medium He: Low 0.5 High -5 0 -5 0 5 Position [m] d) He: b) 5 Fit Experimental - 317K Medium 0 He: High 400 20 -5 300 -5 300 0 1000 2000 -5 0 5 -5 0 5 -1 -1 [W·m ·K ] Position [m] Position [m] Fig. 5 Thermal conductivity of defect-engineered graphene. a Schematic image of a suspended graphene membrane. The areas where the membrane was exposed to He -ions and their corresponding dose is indicated with different colors. b Experimentally observed temperature map. c Fitted thermal conductivity map. d Fitted temperature map. e Histogram of the thermal conductivity for various defect densities. A second limitation is the fixed value for the absorption of 2.7 % conductivity averaged across the entire sample. On the patterned that is used for the first 100 cycles of the fitting procedure, after membrane, we demonstrate controlled engineering of the which the absorption is fitted as well. The accuracy of the model thermal conductivity by He -ion irradiation. As Raman spectro- may be improved by experimentally determining the absorption scopy is widely used in the two-dimensional materials community, at the various hot plate temperatures. Ideally, the absorption our method is ideally suited for studying the thermal properties of would be measured by simultaneously monitoring the trans- other layered materials. Moreover, the working principle of the mitted, and reflected laser power while scanning across the FEM method can easily be extended to more complex geometries sample. We stress that simultaneously measuring both compo- or interfaces, in particular combined with alternative measure- nents is crucial, as contaminations and residues on the membrane ment techniques for providing a temperature map. Our method may scatter the laser light, leading to a reduction in the enables spatially resolving the thermal conductivity of atomically transmitted light, but not to an increase in absorption. However, thin materials, a prerequisite for optimizing and engineering such a measurement is challenging and technically unfeasible in thermal stewardship in nanoscale devices. our current setup. Despite the previously mentioned limitations, our method is well suited for studying the thermal properties of two-dimensional METHODS materials, in particular for materials with an anisotropic thermal Preparation of the SiN membrane 50–52 conductivity . The method can also be extended to character- Two types of Si/Si N -membranes were used. First, commercially available 3 4 ize van der Waals materials consisting of multiple layers. Si/Si N -membranes (Norcada Inc., NORCADA Low Stress SiNx Membrane 3 4 Furthermore, the method is extensible from two to three NX5200D) were patterned with arrays of holes of various diameters using dimensions, allowing for modeling of more complex device Gallium-FIB (FEI, Strata), see Supplementary Note 1. Second, silicon nitrite geometries, including, for instance, stacks of 2D-materials, or the frames are fabricated using dry and wet etch processes as described presence of contact electrodes of finite thickness. As such, it could elsewhere . Further, a Ti/Au (5/40 nm) layer is deposited using an electron beam evaporator to ensure thermal anchoring. be used for assessing the material quality after device integration. Also, as the individual two-dimensional materials in a stacked geometry each have a distinct Raman signature, it is possible to Synthesis and transfer of graphene 40,54,55 investigate the subsurface thermal properties of materials, such as, The CVD-graphene is synthetized as described here and previously . for instance, graphene embedded in a thin hexagonal boron The single-layer graphene samples were synthesized using a Cu metal nitride layer. Alternatively, when the material under study is on a catalyst by CVD. A 25 μm thick Cu-foil was cleaned with acetic acid for substrate or thick enough, other means of determining the 20 min and rinsed with DI-water and ethanol. The Cu-foil was then heated up to 1000 C inside a quartz tube under Ar atmosphere for 3 h, and the temperature map may be used, like time-domain thermoreflec- graphene was then grown with flowing gas mixtures of Ar:H :CH = tance, for reduced measurement time and improve throughput. 2 4 200:20:0.1 (sccm) for 60 min. After synthesizing the graphene, the We have introduced a method for spatially mapping the polymethyl-methacrylate (PMMA) was coated on the graphene at 3000 thermal conductivity of single-layer graphene using a combina- RPM for 30 s. Using reactive ion etching (Ar/O -Plasma, 60 s) the graphene tion of Raman spectroscopy and finite-element calculations at on the back-side of the PMMA/graphene/metal catalyst was removed. The ultimate resolution. We anticipate that this method can be applied metal catalyst was then etched by floating on a 0.1 M ammonium to other single- and few layer materials. We applied the method to persulfate solution overnight. After rinsing the PMMA/graphene with DI- obtain the thermal conductivity of a pristine and He -ion water, the PMMA/graphene was transferred onto the target substrate and patterned suspended single-layer graphene film. For the unpat- ∘ ∘ baked at 110 C for 30 min with an intermediate step at 80 C for 10 min, terned film, large variations of the extracted thermal conductivity increasing the adhesion between the graphene and target substrate. The are observed and attributed to local irregularities such as PMMA was removed with acetone, IPA followed by DI-water. For this study contamination, defects, or folds. These findings highlight the also graphene grown with a slightly different recipe as reported elsewhere importance of spatial mapping of the thermal conductivity, in was used. Besides graphene grown by us, also commercially available contrast to measurement approaches that yield a thermal graphene (Easy Transfer, Graphenea and graphene grown and transferred Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6 Position [m] Temperature [K] Position [m] Position [m] Temperature [K] -1 -1 [W·m ·K ] Counts O. Braun et al. by Applied Nanolayers) was used. A scanning electron micrograph is 11. Neogi, S. et al. Tuning thermal transport in ultrathin silicon membranes by sur- provided in Supplementary Fig. 1. face nanoscale engineering. ACS Nano 9, 3820–3828 (2015). 12. Shahil, K. M. & Balandin, A. A. Thermal properties of graphene and multilayer graphene: Applications in thermal interface materials. Solid State Commun. 152, Raman setup and spectra analysis 1331–1340 (2012). Raman spectra were acquired with a confocal Raman microscope (WITec, 13. Balandin, A. A. Phononics of graphene and related materials. ACS Nano 14, Alpha 300 R) in backscattering geometry, equipped with a 100× (NA = 0.9) 5170–5178 (2020). and a 50× (NA= 0.55, long working distance) objective lenses. The 14. Kasirga, T. S. Thermal Conductivity Measurements in Atomically Thin Materials and backscattered light was coupled to a 300 mm lens-based spectrometer Devices. Springer Singapore, Singapore (2020). −1 −1 with gratings of 600 g mm or 1800 g mm equipped with a thermo- 15. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano electrically cooled CCD. The excitation laser with a wavelength of 532 nm Lett. 8, 902–907 (2008). from a diode laser was used for all Raman measurements. The laser power 16. Ghosh, S. et al. Extremely high thermal conductivity of graphene: Prospects for was set using WITec TruePower. The 2D-peak properties were extracted thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, from the full-spectrum mapping results by fitting a single Lorentz after 151911 (2008). linear background subtraction. 17. Faugeras, C. et al. Thermal conductivity of graphene in corbino membrane geometry. ACS Nano 4, 1889–1892 (2010). 18. Lee, J.-U., Yoon, D., Kim, H., Lee, S. W. & Cheong, H. Thermal conductivity of Temperature calibration suspended pristine graphene measured by Raman spectroscopy. Phys. Rev. B 83, Measurements were carried out under ambient conditions by placing the 081419(R) (2011). sample on a hotplate (Kammrath & Weiss GmbH, LNT 250). The prepared 19. Cai, W. et al. Thermal transport in suspended and supported monolayer graphene membranes are clamped on a hot plate fixed on the piezo stage of the grown by chemical vapor deposition. Nano Lett. 10, 1645–1651 (2010). Raman microscope for mapping. To ensure thermalization of the 20. Chen, S. et al. Raman measurements of thermal transport in suspended mono- membrane, a waiting time of ~45 min is considered before each Raman layer graphene of variable sizes in vacuum and gaseous environments. ACS Nano map is acquired. 5, 321–328 (2011). 21. Chen, S. et al. Thermal conductivity of isotopically modified graphene. Nat. Mater. 11, 203–207 (2012). He -ion irradiation 22. Lee, W. et al. In-plane thermal conductivity of polycrystalline chemical vapor For the irradiation of freestanding graphene membranes, we used a He ion deposition graphene with controlled grain sizes. Nano Lett. 17, 2361–2366 (2017). microscope (Orion, Zeiss) equipped with a pattern generator (Elphy 23. Ma, T. et al. Tailoring the thermal and electrical transport properties of graphene MultiBeam, Raith) operated at 30 keV using a probe current of ~0.5 pA at a −5 films by grain size engineering. Nat. Commun. 8, 14486 (2017). chamber pressure of ~7×10 mbar. The ion dose was controlled by the 24. Chen, S. et al. Thermal conductivity measurements of suspended graphene with exposure dwell time of each pixel ranging from 0.3 to 1.5 ms. and without wrinkles by micro-Raman mapping. Nanotechnology 23, 365701 (2012). 25. Zhao, W. et al. Defect-engineered heat transport in graphene: a route to high DATA AVAILABILITY efficient thermal rectification. Sci. Rep. 5, 11962 (2015). The datasets analysed during the current study are available in the GitHub repository, 26. Malekpour, H. et al. Thermal conductivity of graphene with defects induced by https://github.com/MickaelPerrin74/ThermalconductivityMapping. electron beam irradiation. Nanoscale 8, 14608–14616 (2016). 27. Ziabari, A. et al. Full-field thermal imaging of quasiballistic crosstalk reduction in nanoscale devices. Nat. Commun. 9, 255 (2018). CODE AVAILABILITY 28. Majumdar, A. Scanning thermal microscopy. Annu. Rev. Mater. Sci. 29, 505–585 The code used during the current study is available in the GitHub repository, https:// (1999). github.com/MickaelPerrin74/ThermalconductivityMapping. 29. Kim, K., Jeong, W., Lee, W. & Reddy, P. Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry. ACS Nano 6, 4248–4257 (2012). Received: 15 April 2021; Accepted: 30 November 2021; 30. Menges, F. et al. Temperature mapping of operating nanoscale devices by scanning probe thermometry. Nat. Commun. 7, 10874 (2016). 31. Kinkhabwala, A. A., Staffaroni, M., Suzer, O., Burgos, S. & Stipe, B. Nanoscale thermal mapping of HAMR heads using polymer imprint thermal mapping. IEEE Trans. Magn. 52,1–4 (2016). REFERENCES 32. Mecklenburg, M. et al. Thermal measurement. nanoscale temperature mapping 1. Shi, L. et al. Evaluating broader impacts of nanoscale thermal transport research. in operating microelectronic devices. Science 347, 629–632 (2015). Nanoscale Microscale Thermophys. Eng. 19, 127–165 (2015). 33. Calizo, I., Balandin, A. A., Bao, W., Miao, F. & Lau, C. N. Temperature dependence of 2. Song, H. et al. Two-dimensional materials for thermal management applications. the Raman spectra of graphene and graphene multilayers. Nano Lett. 7, Joule 2, 442–463 (2018). 2645–2649 (2007). 3. Corbino, O. M. Thermal oscillations in lamps of thin fibers with alternating 34. Dolleman, R. J. et al. Optomechanics for thermal characterization of suspended current flowing through them and the resulting effect on the rectifier as a graphene. Phys. Rev. B 96, 475 (2017). result of the presence of even-numbered harmonics. Phys. Z. 11, 413–417 35. Abbe, E. K. Beiträge zur theorie des mikroskops und der mikroskopischen (1910). wahrnehmung. Arch. Mikrosk. Anat. 9, 413–468 (1873). 4. Corbino, O. M. Periodic resistance changes of fine metal threads which are 36. Pettes, M. T., Jo, I., Yao, Z. & Shi, L. Influence of polymeric residue on the thermal brought together by alternating streams as well as deduction of their thermo conductivity of suspended bilayer graphene. Nano Lett. 11, 1195–1200 (2011). characteristics at high temperatures. Phys. Z. 12, 292–295 (1911). 37. Jo, I. et al. Reexamination of basal plane thermal conductivity of suspended 5. Seol, J. H. et al. Two-dimensional phonon transport in supported graphene. Sci- graphene samples measured by electro-thermal micro-bridge methods. AIP Adv. ence 328, 213–216 (2010). 5, 053206 (2015). 6. Swinkels, M. Y. et al. Diameter dependence of the thermal conductivity of InAs 38. Xu, X. et al. Length-dependent thermal conductivity in suspended single-layer nanowires. Nanotechnology 26, 385401 (2015). graphene. Nat. Commun. 5, 3689 (2014). 7. Yazji, S. et al. Assessing the thermoelectric properties of single InSb nanowires: 39. Mercado, E., Anaya, J. & Kuball, M. Impact of polymer residue level on the in-plane The role of thermal contact resistance. Semicond. Sci. Technol. 31, 064001 (2016). thermal conductivity of suspended large-area graphene sheets. ACS Appl. Mater. 8. Deshpande, V. V., Hsieh, S., Bushmaker, A. W., Bockrath, M. & Cronin, S. B. Spatially Interfaces 13, 17910–17919 (2021). resolved temperature measurements of electrically heated carbon nanotubes. 40. Buchheim, J., Wyss, R. M., Shorubalko, I. & Park, H. G. Understanding the inter- Phys. Rev. Lett. 102, 105501 (2009). action between energetic ions and freestanding graphene towards practical 2D 9. Soini, M. et al. Thermal conductivity of GaAs nanowires studied by micro-Raman perforation. Nanoscale 8, 8345–8354 (2016). spectroscopy combined with laser heating. Appl. Phys. Lett. 97, 263107 (2010). 41. Iberi, V. et al. Nanoforging single layer MoSe through defect engineering with 10. Reparaz, J. S. et al. A novel contactless technique for thermal field mapping and focused helium ion beams. Sci. Rep. 6, 30481 (2016). thermal conductivity determination: two-laser Raman thermometry. Rev. Sci. 42. El Abbassi, M. et al. Benchmark and application of unsupervised classification Instrum. 85, 034901 (2014). approaches for univariate data. Commun. Phys. 4, 85 (2021). npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS O. Braun et al. 43. Eckmann, A. et al. Probing the nature of defects in graphene by Raman spec- AUTHOR CONTRIBUTIONS troscopy. Nano Lett. 12, 3925–3930 (2012). O.B., I.S., M.C., and M.L.P. conceived and designed the experiments. K.T. developed the 44. Bae, M.-H. et al. Ballistic to diffusive crossover of heat flow in graphene ribbons. graphene growth recipe and transfer process. R.F. performed the graphene growth. O.B Nat. Commun. 4, 1734 (2013). and I.S. prepared the SiN frame and performed the defect engineering using FIB. O.B. 45. El Sachat, A. et al. Crossover from ballistic to diffusive thermal transport in sus- performed the Raman measurements. O.B., M.L.P., M.C., and I.Z. did the Raman pended graphene membranes. 2D Mater. 6, 025034 (2019). spectroscopy analysis. P.B. developed the finite-element model to calculate the 46. Vakulov, D. et al. Ballistic phonons in ultrathin nanowires. Nano Lett. 20, temperature distribution for a single laser spot position. M.L.P. extended the model to 2703–2709 (2020). construct the temperature map upon illumination by the Raman laser and developed 47. Fugallo, G. et al. Thermal conductivity of graphene and graphite: collective the procedure to fit the thermal conductivity. M.L.P. performed all finite-element excitations and mean free paths. Nano Lett. 14, 6109–6114 (2014). calculations in the manuscript and supervised the study. O.B., M.L.P., and M.C. wrote the 48. Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nat. manuscript. All authors discussed the results and implications and commented on the Commun. 6, 6400 (2015). manuscript. 49. Simoncelli, M., Marzari, N. & Cepellotti, A. Generalization of Fourier’s law into viscous heat equations. Phys. Rev. X 10, 66 (2020). 50. Luo, Z. et al. Anisotropic in-plane thermal conductivity observed in few-layer COMPETING INTERESTS black phosphorus. Nat. Commun. 6, 8572 (2015). The authors declare no competing interests. 51. Kang, J. S., Wu, H. & Hu, Y. Thermal properties and phonon spectral character- ization of synthetic boron phosphide for high thermal conductivity applications. Nano Lett. 17, 7507–7514 (2017). ADDITIONAL INFORMATION 52. Islam, A., van den Akker, A. & Feng, P. X.-L. Anisotropic thermal conductivity of Supplementary information The online version contains supplementary material suspended black phosphorus probed by opto-thermomechanical resonance available at https://doi.org/10.1038/s41699-021-00277-2. spectromicroscopy. Nano Lett. 18, 7683–7691 (2018). 53. Celebi, K. et al. Ultimate permeation across atomically thin porous graphene. Correspondence and requests for materials should be addressed to Mickael L. Perrin. Science 344, 289–292 (2014). 54. Thodkar, K. et al. Comparative study of single and multi domain CVD graphene Reprints and permission information is available at http://www.nature.com/ using large-area Raman mapping and electrical transport characterization. Phys. reprints Status Solidi RRL 10, 807–811 (2016). 55. Braun, O. et al. Optimized graphene electrodes for contacting graphene nanor- Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims ibbons. Carbon 184, 331–339 (2021). in published maps and institutional affiliations. ACKNOWLEDGEMENTS This work was supported by the EC H2020 FET Open project no. 767187 (QuIET). M.L.P. Open Access This article is licensed under a Creative Commons acknowledges funding by the EMPAPOSTDOCS-II program, which has received Attribution 4.0 International License, which permits use, sharing, funding from the European Union’s Horizon 2020 research and innovation program adaptation, distribution and reproduction in any medium or format, as long as you give under the Marie Skłodowska-Curie Grant Agreement no. 754364. M.L.P. also appropriate credit to the original author(s) and the source, provide a link to the Creative acknowledges funding from the Swiss National Science Foundation under the Spark Commons license, and indicate if changes were made. The images or other third party grant no. 196795. I.Z. and M.C. acknowledge funding from the Swiss National Science material in this article are included in the article’s Creative Commons license, unless Foundation under the Sinergia grant no. 189924 (Hydronics). I.Z. acknowledges indicated otherwise in a credit line to the material. If material is not included in the funding from the European Research Council (ERC) under the European Union’s article’s Creative Commons license and your intended use is not permitted by statutory Horizon 2020 research and innovation program (Grant Agreement 756365). The regulation or exceeds the permitted use, you will need to obtain permission directly author acknowledge support from the Multiphysics Hub @ Empa for the COMSOL from the copyright holder. To view a copy of this license, visit http://creativecommons. Multiphyics calculations. We thank the Cleanroom Operations Team of the Binnig and org/licenses/by/4.0/. Rohrer Nanotechnology Center (BRNC) for their help and support, and Roman M. Wyss for fruitful discussions and supply of Si N frames. We further thank Jan Overbeck, 3 4 Maria El Abbassi, Marta De Luca and Milo Y. Swinkels for fruitful discussions. © The Author(s) 2022 Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj 2D Materials and Applications Springer Journals

Spatially mapping thermal transport in graphene by an opto-thermal method

Download PDF
7 pages

Loading next page...
 
/lp/springer-journals/spatially-mapping-thermal-transport-in-graphene-by-an-opto-thermal-0m0LNT59r3

References (60)

Publisher
Springer Journals
Copyright
Copyright © The Author(s) 2022
eISSN
2397-7132
DOI
10.1038/s41699-021-00277-2
Publisher site
See Article on Publisher Site

Abstract

www.nature.com/npj2dmaterials ARTICLE OPEN Spatially mapping thermal transport in graphene by an opto- thermal method 1,2 1 1 1,4 1 2 1,2,3 Oliver Braun , Roman Furrer , Pascal Butti , Kishan Thodkar , Ivan Shorubalko , Ilaria Zardo , Michel Calame and Mickael L. Perrin Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed, most of them yielding an average value across the sample, thereby disregarding the role of local variations. Here, we present a method for the spatially resolved assessment of the thermal conductivity of suspended graphene by using a combination of confocal Raman thermometry and a finite-element calculations-based fitting procedure. We demonstrate the working principle of our method by extracting the two-dimensional thermal conductivity map of one pristine suspended single-layer graphene sheet and one irradiated using helium ions. Our method paves the way for spatially resolving the thermal conductivity of other types of layered materials. This is particularly relevant for the design and engineering of nanoscale thermal circuits (e.g. thermal diodes). npj 2D Materials and Applications (2022) 6:6 ; https://doi.org/10.1038/s41699-021-00277-2 INTRODUCTION extensively used in literature since. Alternatives based on the intensity ratio of Stokes to anti-Stokes Raman scattering or the Thermal properties of materials are of crucial importance for Raman 2D-band have also been reported. optimizing heat management in nanoscale devices, with the 1,2 Using this opto-thermal method, the influence of the quality thermal conductivity as key material property . The thermal and structure of the graphene, as well as the environment have conductivity is typically determined by monitoring the sample been extensively investigated. For instance, Cai et al. reported temperature and/or heat flow in response to a local heat source, in −1 −1 values for κ exceeding ~2500 Wm K for suspended graphene combination with an analytical expression or a numerical model. 3,4 20 For instance, for bulk materials, the well-known 3ω technique is grown by chemical vapor deposition (CVD), and Chen et al. used, while for nanoscale materials, methods such as the thermal studied the influence of environment on thermal conductivity of 5–7 8–11 12 13 bridge method and micro-Raman spectroscopy provide the graphene. Isotopically pure C (0.01 % C) graphene has been −1 −1 thermal conductivity of the material. shown to exhibit κ = 4000 Wm K , a factor of two higher than κ 12 13 21 Of particular interest are the thermal properties of layered in graphene composed of a 1:1 mixture of C and C . Also, the materials. Due to their broad range of conductivity values and influence of CVD-graphene’s polycrystallinity on the thermal their atomically thin nature, such materials are highly relevant for conductivity was studied by Lee et al. and Ma et al., revealing 12,13 heat management at the nanoscale . One of the most that smaller grain sizes drastically reduce κ due to grain boundary appealing materials is graphene, with extraordinarily high thermal 22,23 24 scattering . Along similar lines, wrinkles , oxygen-plasma conductivity values. However, extracting the thermal properties of 25 26 induced defects , and electron beam irradiation have shown 2D materials is challenging, in particular when suspended to to reduce the thermal conductivity. reduce the influence of the substrate. For example, time-domain In all the above-mentioned studies, the one-dimensional heat thermoreflectance cannot be applied to 2D materials as the equation is used to fit the experimental temperature and extract material is too thin . Scanning thermal probe microscopy, on the the thermal conductivity. However, such approaches yield an other hand, despite possessing nanometer resolution, is highly average value of thermal conductivity value, not a spatially delicate to perform on suspended 2D materials. Moreover, both resolved map. This implied that local variations caused by defects, techniques rely on on-chip heaters for channeling heat into the folds, contaminants, etc. are neglected. system. Raman spectroscopy can overcome these difficulties, as it For going beyond the average material property value, can utilize the excitation laser to locally heat the device, while at approaches mapping the temperature distribution in the sample the same time measuring the local temperature. Moreover, Raman are necessary, combined with multi-dimensional analytical or spectroscopy can be conveniently performed on suspended numerical model. A range of techniques has been developed for graphene films for eliminating the influence of the substrate. 15,16 nanoscale thermometry, such as time-domain thermoreflec- Using Raman spectroscopy, Balandin and Ghosh et al. 27 15,16 tance , Raman spectroscopy , scanning thermal probe micro- determined the thermal conductivity of suspended graphene to 28–30 31 −1 −1 scopy , polymer imprint thermal mapping and electron be as high as ~5000 Wm K at room temperature. Their opto- energy loss spectroscopy , providing means to locally map the thermal method, measuring the shift of the Raman G-band upon sample temperature. laser irradiation for estimating the local temperature, has been Empa, Swiss Federal Laboratories for Materials Science and Technology, Transport at Nanoscale Interfaces Laboratory, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland. 2 3 Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland. Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland. Present address: Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, CH-8092 Zurich, Switzerland. email: Mickael.Perrin@Empa.ch Published in partnership with FCT NOVA with the support of E-MRS 1234567890():,; O. Braun et al. a) b) Laser for Experimental Finite-element model Raman mapping Graphene (suspended) ... Raman map T Raman map T Low laser power Initial guess  map 1 n Au Si3N4 Si ... Fitting 2D peak Fitting 2D peak Calculated T map Scanning d/dK map Comparison T map Raman map T High laser power Fitted map Hotplate Fig. 1 Experimental and finite-element method description. a Schematic drawing of the suspended graphene membrane. b Experimental workflow to obtain a temperature map upon laser illumination and computational workflow to fit the corresponding thermal conductivity map. Here, we introduce an opto-thermal method that allows for showing substantial spatial variations. Once this calibration map is two-dimensional mapping of thermal conductivity of suspended acquired, a Raman map of the graphene membrane is acquired at graphene membranes. The presented method relies on a high laser power (4 mW), as shown in Fig. 2d. The high laser power combination of scanning μ-Raman spectroscopy finite-element causes the graphene to locally heat, resulting in a shift in the method (FEM) calculations. The workflow for our approach is Raman peak position. We assume steady state conditions for all presented in Fig. 1. In the first experimental stage, a series of two- data interpretations as the thermal time constant is short (τ < dimensional Raman spectroscopy maps are used to construct a 34 300 ns) in suspended graphene . temperature map of the membrane upon illumination. More By combining this high-power measurement with the dω /dT 2D specifically, Raman maps are recorded at low laser power for map obtained at low laser power, a map of the average various hotplate temperatures. This series of maps is used to temperature within the laser spot is obtained for each laser construct a calibration map of the Raman peak shifts with position, as shown in Fig. 2b. We note that local variations in the temperature. Then, another Raman map is recorded at high laser- temperature upon illumination on the order of 50–100 K are power, which, combined with the calibration map, is used to observed, highlighting the importance of spatially mapping the construct a temperature map of the membrane upon laser temperature and its superiority over other techniques that extract heating. thermal conductivity from a single spot. The constructed experimental temperature map is then used as an input for the FEM-based fit procedure. For a given initial guess of the thermal conductivity, the lattice temperature upon laser FEM calculations illumination is calculated. The thermal conductivity is then FEM calculations are employed for the computation of the iteratively adjusted, until the computed temperature map temperature map of the system upon laser illumination for a matches the experimental one. We apply this fit procedure to extract the thermal conductivity of a pristine graphene membrane given spatial thermal conductivity distribution. This concept is that is suspended over a silicon nitride frame. Finally, we illustrated in Fig. 3. As an input, a two-dimensional map of the demonstrate that the thermal conductivity of the graphene thermal conductivity is provided, of which an example is shown membrane can be tuned in a controlled way by the introduction Fig. 3a. Figure 3b presents the layout of the system (not to scale). of helium-ion (He -ion) induced defects in the membrane. A detailed description of the FEM calculation and the implemen- tation thereof is provided in Supplementary Note 3. While scanning the laser across the membrane, the full temperature RESULTS distribution is calculated for each laser spot position on the Experimental temperature maps membrane (three examples are provided in Fig. 3b). The CVD-graphene membranes are prepared as described in the For each of these temperature distributions, the average methods section. We applied Raman spectroscopy to obtain the temperature within the laser spot is calculated, from which all lattice temperature of the suspended graphene membranes (for values are combined to obtain a two-dimensional map of the details see Methods and Supplementary Notes 1 and 3). Here, we graphene temperature upon illumination. This induced- focus on the 2D-band due to its high sensitivity to temperature temperature map is presented in Fig. 3c and represents the same 20,22 −1 −1 changes of around −0.07 cm K . Alternatively, one can also temperature map that is obtained experimentally upon illumina- rely on the G-peak due to its high linearity in peak shift versus tion of the sample with high laser power. 16,19,33 temperature. . To obtain the thermal conductivity map, an iterative minimization Figure 2a presents maps of the Lorentzian-fitted 2D-peaks procedure is employed. More information can be found in acquired at temperatures T –T ranging between 298 and 425 K. 1 7 Supplementary Note 2, in which we also validate the numerical The Raman spectra have been acquired at low laser power method on a simulated system with a known thermal conductivity (0.25 mW) to limit any heating effects using a 532 nm excitation map. The starting point is an initial (typically uniform) guess of the laser (for details see Methods and Supplementary Note 3). For thermal conductivity. In each iteration of the process, the correspond- each pixel, the peak shift with hot plate temperature (dω /dT)is 2D ing induced temperature map is compared to the experimental fitted using a first-order polynomial, as shown in Fig. 2b. The inset temperature map, after which the thermal conductivity is adjusted presents a histogram of the slopes, showing a Gaussian −1 −1 distribution centered around −0.07 cm K . The spatial distribu- pixel-wise according to the temperature difference. This process is tion of the peak shifts with temperature is displayed in Fig. 2c, repeated until convergence is reached. npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS 1234567890():,; adjust  O. Braun et al. low laserpower high laserpower a) 5 2685 d) 5 2685 T1=298K T7=425K T=298K T2=317K 2675 2675 T =337K ... ... T4=358K 0 0 T5=378K 2665 2665 T6=402K -5 -5 2655 2655 -5 0 5 -5 0 5 -5 0 5 Position [m] Position [m] Position [m] b) c) e) 5 2685 high 5 0 450 center T=298K edge linear fits -0.02 2675 400 -0.04 -0.06 2665 350 0 -0.08 -0.1 0 -1 Slope [cm /K] -5 -0.10 -5 300 300 350 400 -5 0 5 -5 0 5 Position [m] Position [m] Temperature [K] Fig. 2 Experimental determination of temperature map. Spatially resolved mapping of laser-induced temperature rise of graphene. a Raman 2D-peak position obtained with P = 0.25 mW at different hot plate temperatures T and T . The dashed circle is a guide to the eye laser 1 7 for the support edge. b Density plot of the temperature evolution of the 2D-peak frequency. Two spatial points (center and edge, see dots in c are highlighted to represent the method. The inset shows a histogram of dω /dT of the complete membrane. c Spatial distribution of 2D change in Raman shift per temperature change dω /dT obtained from linear fits to the data shown in b). d Raman 2D-peak position obtained 2D with P = 4 mW at 297 K. e Temperature distribution obtained by combining the results from c, d. laser a) b) c) 3) Supported Thermal conductivity Temperature upon graphene -1 -1 [W·m ·K ] illumination [K] Suspended 0 500 1000 300 400 500 graphene 5 5 Laser spot 0 0 -5 1) 2) -5 -5 0 5 -5 0 5 Position [m] Position [m] Fig. 3 Finite-element method description. a Input thermal conductivity map. b Schematic representation of the sample and the calculation mesh. Temperature profiles of the graphene membrane with the heating laser spot at three different positions (1–3). c Temperature profile upon laser illumination. Thermal conductivity map based on fitted experimental supporting part, the thermal coupling to the substrate, as well as the temperature map convection parameter are taken from literature . Finally,wenotethat The induced temperature map obtained in Fig. 2 is used as input for it is challenging to model the transition from the suspended graphene to the supported graphene once the laser spot is in the the iterative procedure to obtain the thermal conductivity map. Here, as clarified in Supplementary Note 3, we use a uniform absorption of vicinity of the edge due to (1) reflection from of the laser excitation at the edges of the support may lead to an increase in the deposited 2.7 % for the suspended graphene and double that value (5.4 %) for laser power, (2) quenching of the Raman scattered light on the the supported graphene. Moreover, all the employed model substrate may lead to an overestimation of the local temperature as parameters are summarized in Supplementary Table 1. Importantly, the 2D peak of the suspended graphene is more pronounced than in the model, a spot size of 370 nm is considered, based on a measurement shown in Supplementary Note 3. This value is larger that of the supported graphene. To circumvent this issue, the thermal conductivity of the first 0.5 μm of the membranes away from the than the diffraction-limit, based on the Abbe criterion d= λ/2NA, where d is the spotsize, λ is the wavelength and NA is the numerical support are not fitted and kept at a fixedvalue.Finally,the thermal conductivity is fitted for 100 iterations, after which the absorption is aperture . Moreover, the thermal conductivity of graphene on the Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6 -1 Raman shift [cm ] Position [m] Counts Position [m] Density [arb. u.] Position [m] -1 -1 -1 dω /dT [cm ·K ] Raman shift [cm ] 2D Position [m] Position [m] Position [m] -1 Temperature [K] Raman shift [cm ] O. Braun et al. a) 5 450 c) 5 2000 e) Experimental - 298K 298 K 1500 100 0 0 1000 337 K -5 300 -5 0 -5 0 5 -5 0 5 Position [m] Position [m] 379 K b) 450 d) 5 5 5 Fit 100 400 4 0 0 425 K 350 3 -5 300 -5 2 0 1000 2000 -5 0 5 -5 0 5 -1 -1 Position [m] Position [m]  [W·m ·K ] Fig. 4 Thermal conductivity map based on fitted experimental data. a Experimentally determined temperature map. b Fitted temperature map. c Fitted thermal conductivity map. d Converged absorption map. e Histogram of the thermal conductivity for various hot plate temperatures. Arrows indicate the mode of the smoothed distributions. fitted for the same number of cycles. More details about this the extraction of the temperature. Figure 5b presents the induced procedure can be found in Supplementary Note 2. For numerical temperature map upon a 4 mW laser illumination. In this plot, the stability reasons, we put a lower value on the thermal conductivity at four quadrants are visible, with the lowest temperatures recorded −1 −1 100 Wm K . in the (unexposed) lower left section of the membrane, and the Figure 4a presents the experimental temperature map, as highest one in the upper left (most exposed). This temperature obtained in Fig. 2e, alongside the fitted temperature map in Fig. map is used as input for the iterative FEM-based fitting procedure, resulting in the fitted thermal conductivity map in Fig. 5c and the 4b. The two maps closely resemble each other. The corresponding corresponding fitted temperature map shown in Fig. 5d. Figure 5e thermal conductivity map is presented in Fig. 4c. We find that the −1 −1 presents a histogram of the thermal conductivity of each of the local thermal conductivity values range from 500 to 2000 Wm K −1 −1 four quadrants. A steady decrease in average conductivity is with an average value of 1224 ± 387 Wm K highlighting the −1 −1 + observed, from ~1200 Wm K for the no He -ion irradiation, to importance of spatially resolving the thermal conductivity. The −1 −1 + ~300 Wm K for the highest He -ion dose. This decrease in average value is in agreement with previously reported values for thermal conductivity with increasing defect density is in agree- CVD-graphene, where typical defects like polymer residues, grain 25,26 36–39 ment with previous reports . boundaries, etc. are present .InFig. 4e, we present a histogram of the fitted thermal conductivity map for increasing hot plate temperatures. The bar plots show that for increasing temperature a DISCUSSION gradual decrease in thermal conductivity is observed. This behavior 20–22 The FEM calculations employed here assume that the heat follows the trend observed by others . transport through the system is following Fourier’s Law. This assumption implies that the phonon mean free path is much Thermal conductivity of defect-engineered graphene smaller than the membrane size. Indeed, ballistic phonon As a final demonstration of the capability of the presented transport has been reported in several nanosystems at room method, we study the thermal conductivity of a graphene temperature: In substrate-supported graphene the phonon mean membrane that is exposed to He -ions using focused ion beam free path is ~100 nm ; for suspended graphene discs, the (FIB) lithography. As shown previously, He -ions can be used to transition from ballistic to diffusive transport occurs at induce, in a controlled fashion, defects in suspended graphene ~775 nm while in ultra-thin nanowires phonon mean free paths 40,41 membranes and other two-dimensional materials . of several micrometers have been observed . Therefore, the Figure 5a presents the exposure pattern as well as the used resolution of the presented method is limited by the phonon irradiation doses. The membrane is divided into four quadrants, mean free path as a spatial mapping of the thermal conductivity with the He -ion irradiation steadily increasing in the counter- below this length scale would require a heat transport description 47–49 clockwise direction, starting in the lower left with no He -ion based on the Boltzmann transport equation . Given this dose. Manually selected representative Raman spectra of each boundary condition, the resolution of 250 nm used in this study is quadrant are presented in Supplementary Note 4, exhibiting all close to the ultimate resolution this FEM-based method allows. the characteristic graphene peaks. The selection of the represen- A limitation of the presented method is the time consumption tative Raman spectra can also be done by an advanced clustering of the temperature calibration, reducing its use in high- approach to avoid any human bias as described elsewhere . throughput applications. As the laser power is low, acquiring the Upon an increase of the He -ion dose, the D-band intensity two-dimensional Raman map at each temperature requires several steadily increases. The intensity ratio of the D and D' band I(D)/I(D') hours. This long acquisition time can also lead to a drift in the upon irradiation, is indicative of the type of defect. . We extract sample position during the measurement. To reduce this drift, this ratio by fitting the ratios I(D)/I(G) versus I(D')/I(G) for various clamping of the sample and a good thermalization of the sample He -ion doses. We find an intensity ratio of ~11.7 for the defect- with the environment is crucial. Furthermore, as changing the hot engineered graphene. This value is comparable to the reported plate temperature leads to shifts of the sample position, the intensity ratio of ~13 for sp type of defects (see Supplementary Raman maps acquired at various temperatures need to be aligned Note 4). We employ the same procedure as presented in Fig. 2 for one versus the other. npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS Position [m] Position [m] Temperature [K] Temperature [K] Position [m] Position [m] -1 -1 Absorption [%]  [W·m ·K ] Counts O. Braun et al. c) 5 2000 a) e) He-ion dose 15 -2 (×10 cm ) 40 He: None 0 None 0 1000 0.1 Low 0.25 Medium He: Low 0.5 High -5 0 -5 0 5 Position [m] d) He: b) 5 Fit Experimental - 317K Medium 0 He: High 400 20 -5 300 -5 300 0 1000 2000 -5 0 5 -5 0 5 -1 -1 [W·m ·K ] Position [m] Position [m] Fig. 5 Thermal conductivity of defect-engineered graphene. a Schematic image of a suspended graphene membrane. The areas where the membrane was exposed to He -ions and their corresponding dose is indicated with different colors. b Experimentally observed temperature map. c Fitted thermal conductivity map. d Fitted temperature map. e Histogram of the thermal conductivity for various defect densities. A second limitation is the fixed value for the absorption of 2.7 % conductivity averaged across the entire sample. On the patterned that is used for the first 100 cycles of the fitting procedure, after membrane, we demonstrate controlled engineering of the which the absorption is fitted as well. The accuracy of the model thermal conductivity by He -ion irradiation. As Raman spectro- may be improved by experimentally determining the absorption scopy is widely used in the two-dimensional materials community, at the various hot plate temperatures. Ideally, the absorption our method is ideally suited for studying the thermal properties of would be measured by simultaneously monitoring the trans- other layered materials. Moreover, the working principle of the mitted, and reflected laser power while scanning across the FEM method can easily be extended to more complex geometries sample. We stress that simultaneously measuring both compo- or interfaces, in particular combined with alternative measure- nents is crucial, as contaminations and residues on the membrane ment techniques for providing a temperature map. Our method may scatter the laser light, leading to a reduction in the enables spatially resolving the thermal conductivity of atomically transmitted light, but not to an increase in absorption. However, thin materials, a prerequisite for optimizing and engineering such a measurement is challenging and technically unfeasible in thermal stewardship in nanoscale devices. our current setup. Despite the previously mentioned limitations, our method is well suited for studying the thermal properties of two-dimensional METHODS materials, in particular for materials with an anisotropic thermal Preparation of the SiN membrane 50–52 conductivity . The method can also be extended to character- Two types of Si/Si N -membranes were used. First, commercially available 3 4 ize van der Waals materials consisting of multiple layers. Si/Si N -membranes (Norcada Inc., NORCADA Low Stress SiNx Membrane 3 4 Furthermore, the method is extensible from two to three NX5200D) were patterned with arrays of holes of various diameters using dimensions, allowing for modeling of more complex device Gallium-FIB (FEI, Strata), see Supplementary Note 1. Second, silicon nitrite geometries, including, for instance, stacks of 2D-materials, or the frames are fabricated using dry and wet etch processes as described presence of contact electrodes of finite thickness. As such, it could elsewhere . Further, a Ti/Au (5/40 nm) layer is deposited using an electron beam evaporator to ensure thermal anchoring. be used for assessing the material quality after device integration. Also, as the individual two-dimensional materials in a stacked geometry each have a distinct Raman signature, it is possible to Synthesis and transfer of graphene 40,54,55 investigate the subsurface thermal properties of materials, such as, The CVD-graphene is synthetized as described here and previously . for instance, graphene embedded in a thin hexagonal boron The single-layer graphene samples were synthesized using a Cu metal nitride layer. Alternatively, when the material under study is on a catalyst by CVD. A 25 μm thick Cu-foil was cleaned with acetic acid for substrate or thick enough, other means of determining the 20 min and rinsed with DI-water and ethanol. The Cu-foil was then heated up to 1000 C inside a quartz tube under Ar atmosphere for 3 h, and the temperature map may be used, like time-domain thermoreflec- graphene was then grown with flowing gas mixtures of Ar:H :CH = tance, for reduced measurement time and improve throughput. 2 4 200:20:0.1 (sccm) for 60 min. After synthesizing the graphene, the We have introduced a method for spatially mapping the polymethyl-methacrylate (PMMA) was coated on the graphene at 3000 thermal conductivity of single-layer graphene using a combina- RPM for 30 s. Using reactive ion etching (Ar/O -Plasma, 60 s) the graphene tion of Raman spectroscopy and finite-element calculations at on the back-side of the PMMA/graphene/metal catalyst was removed. The ultimate resolution. We anticipate that this method can be applied metal catalyst was then etched by floating on a 0.1 M ammonium to other single- and few layer materials. We applied the method to persulfate solution overnight. After rinsing the PMMA/graphene with DI- obtain the thermal conductivity of a pristine and He -ion water, the PMMA/graphene was transferred onto the target substrate and patterned suspended single-layer graphene film. For the unpat- ∘ ∘ baked at 110 C for 30 min with an intermediate step at 80 C for 10 min, terned film, large variations of the extracted thermal conductivity increasing the adhesion between the graphene and target substrate. The are observed and attributed to local irregularities such as PMMA was removed with acetone, IPA followed by DI-water. For this study contamination, defects, or folds. These findings highlight the also graphene grown with a slightly different recipe as reported elsewhere importance of spatial mapping of the thermal conductivity, in was used. Besides graphene grown by us, also commercially available contrast to measurement approaches that yield a thermal graphene (Easy Transfer, Graphenea and graphene grown and transferred Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6 Position [m] Temperature [K] Position [m] Position [m] Temperature [K] -1 -1 [W·m ·K ] Counts O. Braun et al. by Applied Nanolayers) was used. A scanning electron micrograph is 11. Neogi, S. et al. Tuning thermal transport in ultrathin silicon membranes by sur- provided in Supplementary Fig. 1. face nanoscale engineering. ACS Nano 9, 3820–3828 (2015). 12. Shahil, K. M. & Balandin, A. A. Thermal properties of graphene and multilayer graphene: Applications in thermal interface materials. Solid State Commun. 152, Raman setup and spectra analysis 1331–1340 (2012). Raman spectra were acquired with a confocal Raman microscope (WITec, 13. Balandin, A. A. Phononics of graphene and related materials. ACS Nano 14, Alpha 300 R) in backscattering geometry, equipped with a 100× (NA = 0.9) 5170–5178 (2020). and a 50× (NA= 0.55, long working distance) objective lenses. The 14. Kasirga, T. S. Thermal Conductivity Measurements in Atomically Thin Materials and backscattered light was coupled to a 300 mm lens-based spectrometer Devices. Springer Singapore, Singapore (2020). −1 −1 with gratings of 600 g mm or 1800 g mm equipped with a thermo- 15. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano electrically cooled CCD. The excitation laser with a wavelength of 532 nm Lett. 8, 902–907 (2008). from a diode laser was used for all Raman measurements. The laser power 16. Ghosh, S. et al. Extremely high thermal conductivity of graphene: Prospects for was set using WITec TruePower. The 2D-peak properties were extracted thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, from the full-spectrum mapping results by fitting a single Lorentz after 151911 (2008). linear background subtraction. 17. Faugeras, C. et al. Thermal conductivity of graphene in corbino membrane geometry. ACS Nano 4, 1889–1892 (2010). 18. Lee, J.-U., Yoon, D., Kim, H., Lee, S. W. & Cheong, H. Thermal conductivity of Temperature calibration suspended pristine graphene measured by Raman spectroscopy. Phys. Rev. B 83, Measurements were carried out under ambient conditions by placing the 081419(R) (2011). sample on a hotplate (Kammrath & Weiss GmbH, LNT 250). The prepared 19. Cai, W. et al. Thermal transport in suspended and supported monolayer graphene membranes are clamped on a hot plate fixed on the piezo stage of the grown by chemical vapor deposition. Nano Lett. 10, 1645–1651 (2010). Raman microscope for mapping. To ensure thermalization of the 20. Chen, S. et al. Raman measurements of thermal transport in suspended mono- membrane, a waiting time of ~45 min is considered before each Raman layer graphene of variable sizes in vacuum and gaseous environments. ACS Nano map is acquired. 5, 321–328 (2011). 21. Chen, S. et al. Thermal conductivity of isotopically modified graphene. Nat. Mater. 11, 203–207 (2012). He -ion irradiation 22. Lee, W. et al. In-plane thermal conductivity of polycrystalline chemical vapor For the irradiation of freestanding graphene membranes, we used a He ion deposition graphene with controlled grain sizes. Nano Lett. 17, 2361–2366 (2017). microscope (Orion, Zeiss) equipped with a pattern generator (Elphy 23. Ma, T. et al. Tailoring the thermal and electrical transport properties of graphene MultiBeam, Raith) operated at 30 keV using a probe current of ~0.5 pA at a −5 films by grain size engineering. Nat. Commun. 8, 14486 (2017). chamber pressure of ~7×10 mbar. The ion dose was controlled by the 24. Chen, S. et al. Thermal conductivity measurements of suspended graphene with exposure dwell time of each pixel ranging from 0.3 to 1.5 ms. and without wrinkles by micro-Raman mapping. Nanotechnology 23, 365701 (2012). 25. Zhao, W. et al. Defect-engineered heat transport in graphene: a route to high DATA AVAILABILITY efficient thermal rectification. Sci. Rep. 5, 11962 (2015). The datasets analysed during the current study are available in the GitHub repository, 26. Malekpour, H. et al. Thermal conductivity of graphene with defects induced by https://github.com/MickaelPerrin74/ThermalconductivityMapping. electron beam irradiation. Nanoscale 8, 14608–14616 (2016). 27. Ziabari, A. et al. Full-field thermal imaging of quasiballistic crosstalk reduction in nanoscale devices. Nat. Commun. 9, 255 (2018). CODE AVAILABILITY 28. Majumdar, A. Scanning thermal microscopy. Annu. Rev. Mater. Sci. 29, 505–585 The code used during the current study is available in the GitHub repository, https:// (1999). github.com/MickaelPerrin74/ThermalconductivityMapping. 29. Kim, K., Jeong, W., Lee, W. & Reddy, P. Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry. ACS Nano 6, 4248–4257 (2012). Received: 15 April 2021; Accepted: 30 November 2021; 30. Menges, F. et al. Temperature mapping of operating nanoscale devices by scanning probe thermometry. Nat. Commun. 7, 10874 (2016). 31. Kinkhabwala, A. A., Staffaroni, M., Suzer, O., Burgos, S. & Stipe, B. Nanoscale thermal mapping of HAMR heads using polymer imprint thermal mapping. IEEE Trans. Magn. 52,1–4 (2016). REFERENCES 32. Mecklenburg, M. et al. Thermal measurement. nanoscale temperature mapping 1. Shi, L. et al. Evaluating broader impacts of nanoscale thermal transport research. in operating microelectronic devices. Science 347, 629–632 (2015). Nanoscale Microscale Thermophys. Eng. 19, 127–165 (2015). 33. Calizo, I., Balandin, A. A., Bao, W., Miao, F. & Lau, C. N. Temperature dependence of 2. Song, H. et al. Two-dimensional materials for thermal management applications. the Raman spectra of graphene and graphene multilayers. Nano Lett. 7, Joule 2, 442–463 (2018). 2645–2649 (2007). 3. Corbino, O. M. Thermal oscillations in lamps of thin fibers with alternating 34. Dolleman, R. J. et al. Optomechanics for thermal characterization of suspended current flowing through them and the resulting effect on the rectifier as a graphene. Phys. Rev. B 96, 475 (2017). result of the presence of even-numbered harmonics. Phys. Z. 11, 413–417 35. Abbe, E. K. Beiträge zur theorie des mikroskops und der mikroskopischen (1910). wahrnehmung. Arch. Mikrosk. Anat. 9, 413–468 (1873). 4. Corbino, O. M. Periodic resistance changes of fine metal threads which are 36. Pettes, M. T., Jo, I., Yao, Z. & Shi, L. Influence of polymeric residue on the thermal brought together by alternating streams as well as deduction of their thermo conductivity of suspended bilayer graphene. Nano Lett. 11, 1195–1200 (2011). characteristics at high temperatures. Phys. Z. 12, 292–295 (1911). 37. Jo, I. et al. Reexamination of basal plane thermal conductivity of suspended 5. Seol, J. H. et al. Two-dimensional phonon transport in supported graphene. Sci- graphene samples measured by electro-thermal micro-bridge methods. AIP Adv. ence 328, 213–216 (2010). 5, 053206 (2015). 6. Swinkels, M. Y. et al. Diameter dependence of the thermal conductivity of InAs 38. Xu, X. et al. Length-dependent thermal conductivity in suspended single-layer nanowires. Nanotechnology 26, 385401 (2015). graphene. Nat. Commun. 5, 3689 (2014). 7. Yazji, S. et al. Assessing the thermoelectric properties of single InSb nanowires: 39. Mercado, E., Anaya, J. & Kuball, M. Impact of polymer residue level on the in-plane The role of thermal contact resistance. Semicond. Sci. Technol. 31, 064001 (2016). thermal conductivity of suspended large-area graphene sheets. ACS Appl. Mater. 8. Deshpande, V. V., Hsieh, S., Bushmaker, A. W., Bockrath, M. & Cronin, S. B. Spatially Interfaces 13, 17910–17919 (2021). resolved temperature measurements of electrically heated carbon nanotubes. 40. Buchheim, J., Wyss, R. M., Shorubalko, I. & Park, H. G. Understanding the inter- Phys. Rev. Lett. 102, 105501 (2009). action between energetic ions and freestanding graphene towards practical 2D 9. Soini, M. et al. Thermal conductivity of GaAs nanowires studied by micro-Raman perforation. Nanoscale 8, 8345–8354 (2016). spectroscopy combined with laser heating. Appl. Phys. Lett. 97, 263107 (2010). 41. Iberi, V. et al. Nanoforging single layer MoSe through defect engineering with 10. Reparaz, J. S. et al. A novel contactless technique for thermal field mapping and focused helium ion beams. Sci. Rep. 6, 30481 (2016). thermal conductivity determination: two-laser Raman thermometry. Rev. Sci. 42. El Abbassi, M. et al. Benchmark and application of unsupervised classification Instrum. 85, 034901 (2014). approaches for univariate data. Commun. Phys. 4, 85 (2021). npj 2D Materials and Applications (2022) 6 Published in partnership with FCT NOVA with the support of E-MRS O. Braun et al. 43. Eckmann, A. et al. Probing the nature of defects in graphene by Raman spec- AUTHOR CONTRIBUTIONS troscopy. Nano Lett. 12, 3925–3930 (2012). O.B., I.S., M.C., and M.L.P. conceived and designed the experiments. K.T. developed the 44. Bae, M.-H. et al. Ballistic to diffusive crossover of heat flow in graphene ribbons. graphene growth recipe and transfer process. R.F. performed the graphene growth. O.B Nat. Commun. 4, 1734 (2013). and I.S. prepared the SiN frame and performed the defect engineering using FIB. O.B. 45. El Sachat, A. et al. Crossover from ballistic to diffusive thermal transport in sus- performed the Raman measurements. O.B., M.L.P., M.C., and I.Z. did the Raman pended graphene membranes. 2D Mater. 6, 025034 (2019). spectroscopy analysis. P.B. developed the finite-element model to calculate the 46. Vakulov, D. et al. Ballistic phonons in ultrathin nanowires. Nano Lett. 20, temperature distribution for a single laser spot position. M.L.P. extended the model to 2703–2709 (2020). construct the temperature map upon illumination by the Raman laser and developed 47. Fugallo, G. et al. Thermal conductivity of graphene and graphite: collective the procedure to fit the thermal conductivity. M.L.P. performed all finite-element excitations and mean free paths. Nano Lett. 14, 6109–6114 (2014). calculations in the manuscript and supervised the study. O.B., M.L.P., and M.C. wrote the 48. Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nat. manuscript. All authors discussed the results and implications and commented on the Commun. 6, 6400 (2015). manuscript. 49. Simoncelli, M., Marzari, N. & Cepellotti, A. Generalization of Fourier’s law into viscous heat equations. Phys. Rev. X 10, 66 (2020). 50. Luo, Z. et al. Anisotropic in-plane thermal conductivity observed in few-layer COMPETING INTERESTS black phosphorus. Nat. Commun. 6, 8572 (2015). The authors declare no competing interests. 51. Kang, J. S., Wu, H. & Hu, Y. Thermal properties and phonon spectral character- ization of synthetic boron phosphide for high thermal conductivity applications. Nano Lett. 17, 7507–7514 (2017). ADDITIONAL INFORMATION 52. Islam, A., van den Akker, A. & Feng, P. X.-L. Anisotropic thermal conductivity of Supplementary information The online version contains supplementary material suspended black phosphorus probed by opto-thermomechanical resonance available at https://doi.org/10.1038/s41699-021-00277-2. spectromicroscopy. Nano Lett. 18, 7683–7691 (2018). 53. Celebi, K. et al. Ultimate permeation across atomically thin porous graphene. Correspondence and requests for materials should be addressed to Mickael L. Perrin. Science 344, 289–292 (2014). 54. Thodkar, K. et al. Comparative study of single and multi domain CVD graphene Reprints and permission information is available at http://www.nature.com/ using large-area Raman mapping and electrical transport characterization. Phys. reprints Status Solidi RRL 10, 807–811 (2016). 55. Braun, O. et al. Optimized graphene electrodes for contacting graphene nanor- Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims ibbons. Carbon 184, 331–339 (2021). in published maps and institutional affiliations. ACKNOWLEDGEMENTS This work was supported by the EC H2020 FET Open project no. 767187 (QuIET). M.L.P. Open Access This article is licensed under a Creative Commons acknowledges funding by the EMPAPOSTDOCS-II program, which has received Attribution 4.0 International License, which permits use, sharing, funding from the European Union’s Horizon 2020 research and innovation program adaptation, distribution and reproduction in any medium or format, as long as you give under the Marie Skłodowska-Curie Grant Agreement no. 754364. M.L.P. also appropriate credit to the original author(s) and the source, provide a link to the Creative acknowledges funding from the Swiss National Science Foundation under the Spark Commons license, and indicate if changes were made. The images or other third party grant no. 196795. I.Z. and M.C. acknowledge funding from the Swiss National Science material in this article are included in the article’s Creative Commons license, unless Foundation under the Sinergia grant no. 189924 (Hydronics). I.Z. acknowledges indicated otherwise in a credit line to the material. If material is not included in the funding from the European Research Council (ERC) under the European Union’s article’s Creative Commons license and your intended use is not permitted by statutory Horizon 2020 research and innovation program (Grant Agreement 756365). The regulation or exceeds the permitted use, you will need to obtain permission directly author acknowledge support from the Multiphysics Hub @ Empa for the COMSOL from the copyright holder. To view a copy of this license, visit http://creativecommons. Multiphyics calculations. We thank the Cleanroom Operations Team of the Binnig and org/licenses/by/4.0/. Rohrer Nanotechnology Center (BRNC) for their help and support, and Roman M. Wyss for fruitful discussions and supply of Si N frames. We further thank Jan Overbeck, 3 4 Maria El Abbassi, Marta De Luca and Milo Y. Swinkels for fruitful discussions. © The Author(s) 2022 Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022) 6

Journal

npj 2D Materials and Applications – Springer Journals

Published: Jan 17, 2022

There are no references for this article.