Enhanced Heat Dissipation for Macroscopic Metals Achieved by a Single‐Layer Graphene

The increasing demand for high‐performance devices on heat dissipation makes it approach the bottleneck even for metals with high thermal conductivities. The coating of only one layer of graphene, the heat dissipation performances of Cu, Ag, and Al can be further enhanced, e.g., with a maximum temperature reduction by ≈9% for a Cu foil is demonstrated. Molecular dynamics (MD) analysis of spectral phonon transmission reveals that low‐frequency phonons play a significant role in the thermal transport within the Cu/single‐layer graphene (SLG) system, and the high‐frequency phonons exhibit substantial mismatch. It suggests that the thermal anisotropy of graphene enables a rapid heat dispersion in the in‐plane direction and provides an effective thermal insulation in the out‐of‐plane direction. The thermal conductivity calculations demonstrate an enhanced participation of phonons in heat conduction by the graphene layer, indicating a novel heat conduction mechanism in the Cu/single‐layer graphene system. These findings highlight the positive impact of graphene on the heat conduction of metals, and they will hold crucial implications for the design and application of graphene‐based thermal devices is believed.


Introduction
Effective heat dissipation is becoming increasingly critical to thermal management for different applications such as power semiconductors and interconnects. [1]Low-efficient or nonuniform DOI: 10.1002/admi.202300877heat dissipation can cause an overheat in the device, negatively impacting its performance and lifespan. [2]To disperse heat from the hot spots, metals such as Cu and Al with high thermal conductivities (200-400 W•m −1 •K −1 ) are commonly used, but for certain applications such as interconnects, the significantly reduced thickness of metal leads to a ≈80% reduction in the thermal conductivity compared to its bulk, due to electrons contributing more to the thermal conductivity than phonons, hindering the heat dissipation in microelectronics. [3]raphene is a one-atom-thick material with superb thermal conductivity. [4]he thermal conductivity of suspended single-layer graphene (SLG) has been reported to be as high as 5300 W•m −1 •K −1 , [5] whereas that of graphene supported in SiO 2 would be drastically reduced but still as high as 600 W•m −1 •K −1 , [6] indicating the great potential for graphene in heat dissipation applications.[9] Exfoliated graphene quilts have also been used in the thermal management of high-power transistors, with a ≈20 °C reduction in hot spot temperature when the transistor is operating at ≈13 W•mm −1 , extending the transistor's lifespan by an order of magnitude. [10]Gao et al. [2] used the chemical vapor deposition (CVD) method to grow SLG and applied it as a heat spreader, resulting in a ≈13 °C decrease (from 121 to 108 °C) in the hot spot with a heat flux of 430 W•cm −2 on Si chips.Moreover, graphene-reinforced metal composites appear to be a promising alternative to overcome the thin film limitation of metals mentioned above. [11,12]Among these composites, Cu is widely used in thermal management due to its inherent thermal conductivity and lower cost compared to Ag, the metal with the highest thermal conductivity.For instance, a composite formed by Cu and a large-sized graphene flake was synthesized by reduced graphene oxide film and continuously rolled followed by magnetron sputtering of Cu.It exhibits an ultrahigh thermal conductivity of over 1932.73 (± 63.07) W•m −1 •K −1 and excellent electrical conductivity. [13]Similarly, recent research on the thermal conductivity of graphene/Cu composites are using oxide graphene or graphene nanosheets as well. [13,14]However, for wafer scale procession using the complementary metal oxide semiconductor (CMOS) fabrication techniques, uniform graphene deposition is necessary, [15,16] making the CVD method a viable option for generating large areas of graphene and enabling the mass production of graphene heat spreaders. [17,18]Balandin et al. [19] first reported the effect of the graphene deposition on Cu on its thermal properties, which caused a ≈24% enhancement in the thermal conductivity near room temperature for graphene-Cu-graphene sandwich films grown by the CVD method compared to reference Cu films.They demonstrated the contribution of reducing substrate roughness and improving grain size to thermal performance but did not verify the importance of graphene.In addition to the Cu film or foils, graphene was also deposited on the Cu nanowires to form composites by plasma CVD, which outperform uncoated nanowires in both electrical and thermal conductivities. [20]n this work, we study the effect of continuous graphene layer coated on macroscopic metal surfaces for heat dissipation.Taking Cu as an example, with only SLG on its surface to separate the heat source, the heat transferred through the metal can be significantly reduced, evident from the decreased temperature of the other Cu surface.This enhanced heat dissipation performance by SLG is also applicable to Ag and Al.We also explore the underlying mechanism through the vibrational density of states (DOS) spectrum of the Cu/SLG interface using the molecular dynamics (MD), as well as the thermal conductivities of the Cu and Cu/SLG systems.We believe that this work will help improve the heat dissipation performance of the interconnects and heat-sinks in electronic devices as well as other related thermal management applications.

Graphene Synthesis
A series of metal foils with graphene coating was prepared for the experiments.For Cu/SLG samples, Cu foils with a thickness of 25 μm were directly used as the catalytic substrate to synthesize graphene by the CVD method. [18]For details, the temperature of the furnace was set as rising to 1060 °C within 40 min followed by maintaining it for 30 min.During this process, the Cu foil was annealing using 300 standard-cubic-centimeter-per-minute (sccm) H 2 to eliminate the oxides on the Cu surface.Then, 1 sccm CH 4 was introduced for 30 min as the carbon source for graphene deposition, and the temperature of the furnace was then cooled to room temperature.As a reference, the same H 2 annealing temperature, atmosphere and time were carried out to prepare the only-annealed Cu samples, and no CH 4 was introduced into the furnace for the graphene synthesis.

Graphene Transfer
For the samples of graphene coating on 25 μm Ag and Al foils (Alfa Aesar China Chemical Co.Ltd.), due to the fact that these metals are not the catalysts usually used for graphene synthesis, a chemical process was adopted to transfer the graphene onto the metal substrate.Polymethyl methacrylate (PMMA, 4 wt% in anisole, AR-P 679.04,Allresist GmbH, Germany) was spincoated to as-synthesized Cu/graphene as a protective film, then put the Cu foil in FeCl 3 (1 m) solution until the Cu was completely etched.The PMMA supported graphene was rinsed by the deionized water, and transferred to the target metal substrate.Finally, the PMMA was dissolved in acetone for 30 min.

Characterizations
The morphologies and quality of graphene and its metal composites were characterized using an optical microscope (OM, Olympus BXFM-ILHS, Olympus Co., Ltd.), scanning electron microscopy (SEM, S-3400 I, Hitachi Co., Ltd.) and Micro-Raman spectroscopy (LabRAM HR Evolution, Horiba Co., Ltd.).An IR thermal detector (GTC 400C, BOSCH GmbH) was used for the temperature monitoring of the metal and metal-graphene composites.Due to the poor IR emissivity of Cu, a layer of thermal grease with a high emissivity of 0.97 and a thermal conductivity of 6 W•m −1 •K −1 is uniformly coated for the temperature measurements, for both the only-annealed Cu and the Cu/SLG systems, as shown in Figure S1a (Supporting Information).The schematics of the sample placements relative to the heat flow are shown in Figure S1b,c (Supporting Information) as well.

Results and Discussion
Figure 1a illustrates the experimental setup for characterizing the thermal properties of the metals and metal-graphene composites.The system consists of a heating stage, a steel column with a diameter of 8.5 mm placed on the heating stage, an IR detector, and a sample holder (Figure 1b).A 12-mm-diameter hole in the sample holder facilitates the contact of the column with the lower surface of the sample, and conducts different amounts of heat flows to it by setting the temperatures of the heating stage.It is known that an interfacial thermal resistance exists at the solid-solid interface, and the presence of the sample holder avoids film bending and results in a more uniform contact between the column and sample, maintaining a stable interfacial thermal resistance with the same input temperature in each test.In order to verify the contact between the sample and the heat source, we calibrated it with an optical noncontact method, as shown in Figure S3 (Supporting Information).Repeated temperature measurements with an error less than 0.5% also confirm the use of above setups (Figure S4, Supporting Information).The thermal performance of the sample is finally evaluated based on the hot spot temperature of its upper surface measured by the IR detector.To mitigate the influence of environment, all tests were conducted under controlled room temperature conditions.Figure 1c displays the OM images of the surface morphologies of the Cu/SLG and Cu samples after the thermal tests at 180 °C.After the test, the Cu/SLG surface maintains the metallic luster of Cu due to the complete coverage of graphene for oxygen isolation.In contrast, the only-annealed Cu sample has changed its color to dark red as the formation of a thin Cu x O y layer oxidized in the air.Moreover, the SEM image in the upper panel of Figure 1d demonstrates that the graphene is wrinkled, which is a common phenomenon in 2D membranes.For large-scale growth of graphene on Cu, high densities of wrinkles are usually caused by the different thermal expansion coefficients between Cu and graphene, [18] which causes a slight decrease in the thermal conductivity of graphene, [21] but still exhibits the extremely high thermal conductivity of over 1400 W•m −1 •K.−1 [21] Raman spectroscopy with a wavelength of 532 nm was also adopted to characterize the samples, as presented in Figure 1e.Although both Raman spectra are partially lifted by the fluorescence signals of the Cu substrate, the clear G (≈1580 cm −1 ) and 2D (≈2670 cm −1 ) peaks detected from the Cu/SLG sample indicate the existence of graphene, with an overall high quality evaluated from the negligible D peak (≈1350 cm −1 ).
The hot spot temperature variations in Cu/SLG and onlyannealed Cu at different temperatures ranging from 100 to 300 °C are presented in Figure 2(a-e).The measurements of onlyannealed Cu were repeated for the three times and the error bars  Here we take the temperatures of the last three minutes to evaluate the thermal equilibrium process.Although Cu has already exhibited a high thermal conductivity of ≈300 W•m −1 •K −1 , when its surface is fully covered by graphene, compared with the only-annealed state (T Cu ), the peak temperatures at these hot spots (T Cu/SLG ) decrease by 5-6 °C (ΔT = T Cu − T Cu/SLG ), except for the temperature input at 100 °C that the temperature decreases by only 3 °C.Moreover, graphene coating causes a temperature drop by up to 5.6 °C with a 150 °C input, corresponding to a maximum ΔT/T Cu value of 9%, and with increased temperature, the ΔT/T Cu value shows a downward trend with an exception with a 100 °C input as well, as displayed in Figure 2f.A possible mechanism is interpreted as follows.As the temperature increases, the lattice vibrational scattering becomes more significant, leading to a decrease in the thermal conductivity of graphene. [22]However, with a 100 °C input the resultant temperature in the sample is closer to the ambient room temperature, resulting in a much less amount of heat exchange between it and the environment, which can also be proved by the large fluctuation of the measured temperature profile in Figure 2a.
The above result clearly demonstrates the ability of graphene in improving the heat dispassion performance of Cu, a metal that already exhibits a very high thermal conductivity.The thermal transport in solids is characterized by thermal conductivity K, as described by the following Fourier's law of heat conduction: where J denotes the heat flux along the heat flow direction and ∇T is the temperature gradient.A is the cross-sectional area.Although limited studies have focused on the temperature distribution during the heating process, the in-plane heat distributions were captured here using an IR detector (Figure 3).This enables us to visualize the in-plane heat conduction of the samples, where the isotherms approximately formed circles with the hot spot as the center.Apparently, the thermography of Cu/SLG demonstrate a smaller temperature gradient (∇T = dT/dr), exhibiting a transition from high to low temperatures and a slower heating rate.As the heat source and heating temperature are held the same, the different temperatures in the samples indicate that Cu/SLG exhibits an enhanced in-plane thermal conductivity compared to only-annealed Cu, confirming that Cu's heat dissipation performance can be effectively improved through the coating of only one layer of graphene.
The mechanism of the significant enhancement in the thermal properties of Cu/SLG, compared to the reference of onlyannealed Cu, needs to be discussed.Cu recrystallizes at a temperature of 227°C, [23] which is considerably lower than the temperature of 1060 °C required for CVD annealing and synthesis of graphene.Consequently, during CVD the Cu recrystallization increases its grain sizes, reduces its defect density, and enhances its mechanical characteristics. [24]SEM images in Figure S5 (Supporting Information) confirm the increased grain size of Cu by the CVD process of graphene.Balandin et al. [19] suggest that the observed significant enhancement in the thermal properties of Cu after CVD is primarily related to the influence from the increased Cu grains during the graphene synthesis, and the role played by graphene itself is negligible.To reveal that graphene is a primary factor contributing to the improved thermal properties instead of the increased Cu grain sizes, we studied the thermal properties of Cu with graphene removal.Considering that graphene was first peeled off from graphite using Scotch tape, [25,26] we also used this tape to remove graphene from the Cu surface of Cu film, and this peeling process at ambient conditions does not change the Cu's grain size.The Raman spectrum in Figure S6 (Supporting Information) confirms the absence of the G and 2D peaks of graphene, indicating the successful removal of graphene from the Cu surface.Figure 4a illustrates the temperature rising profiles at the hot spots in Cu/SLG and Cu with graphene removal with a heat input of 200 °C, and the former also exhibits a faster heating rate and a lower equilibrium temperature by ΔT = 5.8°C.Because the only difference between the two Cu samples is the presence of graphene, this result strongly suggests that graphene is the key factor for the enhancement of thermal properties.Figure 4b illustrates a possible mechanism, that heat can be efficiently propagated in the additional in-plane channels created by graphene, due to the superior thermal conductivity of supported graphene.Moreover, the out-of-plane thermal conductivity (K ⊥ ) of graphene is extremely low, 3-4 orders of magnitude lower than that roe its in-plane direction, [4] leading to a large thermal resistance at the interface, [27] owing to the new phonon channels created by the interlayer coupling between graphene and the substrate. [28]This also helps improve the heat dissipation efficiency from the in-plane direction of graphene.Therefore, the above two factors enable graphene to afford and dissipate a substantial amount of heat, and only a portion of heat is transferred to Cu, resulting in a lower temperature and more uniform temperature distribution at the other surface of the Cu.
To verify the ability of graphene on enhancing the heat dissipation for other metals, we conducted additional experiments using two other metals with high thermal conductivities: Al (237 W•m −1 •K −1 ) and Ag (≈429 W•m −1 •K −1 ).These metals differ significantly from Cu in terms of physical properties such as density and atomic size, but they all belong to metals with the highest thermal conductivities (Ag, Cu, Au, and Al).Due to the lack of synthesis methods for large-scale and uniform graphene on Ag and Al, we employed a transfer process to obtain metal-graphene composites on the respective substrates, as described in the Experimental Section.The temperature rising profiles of Al and Ag with a heat input of 200 °C, as well as those for their composites with SLG, are present in Figure 4c,d.The results indicate that at the thermal equilibrium, the temperature at the hot spot of Al decreased from 82.1 to 75.4 °C (ΔT/T Al ≈ 8%), whereas that of Ag decreased from 75.4 to 71.1 °C (ΔT/T Ag ≈ 6%).These temperature reductions demonstrate that graphene enhances the heat dissipation performances of Al and Ag as well, confirming the general applicability of graphene in improving the thermal properties of metals.
We also conducted a water vaporization experiment to demonstrate the heat dissipation performance of the Cu-graphene composite, as shown in Figure 5.For both Cu and Cu/SLG samples, we pipetted 100 μL of deionized water onto the Cu surface without graphene, and set the heat source at 200 °C.The vaporization of liquids can generally be categorized into the evaporation and boiling processes.Evaporation, which occurs at the liquid surface, can transpire at any temperature, therefore its rate plays a crucial role in both the fundamental study of droplet evaporation and many practical industrial processes.In our experiment, we considered the pressure of the ambient condition as a constant parameter, focusing on the temperature as the primary factor affecting the evaporation rate.The result indicates that the water droplets evaporate significantly slower on Cu/SLG, with an evaporation rate approximately 16% slower than that on onlyannealed Cu.Even when the water droplets on only-annealed Cu have completely evaporated, approximately 14% of the droplet remains on Cu/SLG.Figure 5c illustrates the spatiotemporal distribution of hot spot temperatures within the droplets.The temperature of the Cu/SLG composite remains consistently lower than that of the only-annealed Cu throughout the entire test.Moreover, a distinct difference can be observed after 5-min heating, where the temperature profile of the Cu/SLG begins to exhibit a declining trend but the only-annealed Cu still persists an increase in temperature over the same period.This observation suggests that there is a reduced heat transfer to the Cu part, as heat is efficiently directed away by the graphene layer, resulting in a significantly cooler surface of Cu.The details for calculating the volume of a water droplet are provided in the Supporting Information.
The involvement of graphene in enhancing the thermal properties of metals indicates the presence of new mechanisms, rather than originating from the grain changes in Cu.We conducted MD simulations to investigate the mechanism of heat conduction of Cu/SLG, all simulations were performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package. [29]The interactions between the metal atoms were described by the embedded-atom-method (EAM) interatomic potential, [25] which accounts for electron density contributions from the atoms.The covalent interaction between the carbon atoms was described by the Tersoff potential. [30,31]At the interface between the C and Cu atoms, the Lennard-Jones (L-J) potential [32] V ij (r) = 4ɛ ij [( ij /r) 12 − ( ij /r) 6 ] was utilized with ɛ = 25.78 meV and  = 3.0825 Å, based on the previous literature. [32,33]We used the experimentally derived values of the facecentered cubic (FCC) lattice constants for Cu (3.61 Å) and the C-C bond length (1.42 Å).
We considered the model consist of a Cu substrate, a graphene layer and a heat source shown in the insert of Figure 6a, in which the Cu (111) surface was covered with a graphene layer in its most stable configuration to impede heat transport from a 127 °C heat source.The dimensions of the Cu substrate were approximately 50 × 50 × 10 Å, and a time step of 0.5 fs was used for all simulations.Besides, we calculated the phonon vibration spectra of the atoms in the graphene layer and the Cu substrate.The vibrational DOS P() at a frequency  can be obtained by performing the Fourier transform on the velocity auto-correlation function as [34,35] First, we focused on assessing the influence of graphene on heat dissipation of Cu.The system was initially placed in the NVT ensemble at 27 °C and allowed to relax for 1 ns to reach the equilibrium.Subsequently, the Cu and graphene systems were subjected to heating using the 127 °C heat source to observe the effect of graphene on heat dissipation.As depicted in Figure 6a, when bare Cu is exposed to the heat source, its temperature rises by approximately 46 °C.However, when a single layer of graphene covers the Cu substrate, the temperature of Cu drops by around 10 °C.The significant temperature drop is attributed to the interface thermal resistance of Cu/SLG and the extremely high thermal anisotropy of SLG, as well as the overall increase in the thermal conductivity.Because of the limited size for the MD simulation, the interface thermal resistance of Cu/SLG cannot be neglected, which acts as an impediment to out-of-plane heat transfer.Besides, the thermal anisotropy of SLG allows a rapid heat conduction in the in-plane direction and provides an effective thermal insulation in the out-of-plane direction. [10,36]It is noted that the weak van der Waals interaction between graphene and Cu, as well as graphene's susceptibility to ambient conditions, causes significant perturbation in the temperature of Cu when graphene is attached to its surface.This behavior is a characteristic feature of 2D nanomaterials.However, in our experimental setup, the size of graphene is much larger compared to the simulation, resulting in the fading away of this phenomenon.To further explore the heat conduction of the interlayer of graphene and Cu, we calculated the vibrational spectra of graphene and Cu.As shown in Figure 6b, it can be noted that the vibration modes of Cu are mainly concentrated in the low-frequency region ( < 8 THz), while graphene exists in the whole frequency region, and has the highest peak at 50 THz. [35]As shown in the insert of Figure 6b, the vibrational DOS spectrum between Cu and graphene appears a substantial overlap in the low-frequency region below 8 THz, whereas the high-frequency phonon is highly mismatched.Thus, above 8 THz, the phonon transport at the Cu/SLG interface becomes negligible, it is easier for the lowfrequency phonons to propagate through the interface, [37] allowing phonons in low-frequencies dominate the interface heat transport.
Moreover, to obtain a comprehensive understanding of the heat conduction process for Cu/SLG systems, we performed nonequilibrium molecular dynamics (NEMD) to derive the thermal conductivities of pure Cu and Cu/SLG, with a volume of 7.229 × 36.147× 7.229 nm 3 for the former and that of 7.229 × 36.147× 7.909 nm 3 for the latter.Considering that a graphene-covered Cu in MD simulation often experiences atom loss and fails to achieve equilibrium state, we selected a Cu/SLG/Cu sandwich structure to ensure a more stable and reliable system configuration for accurate analysis of thermal conductivity.As shown in Figure 6c, a 1D heat flux is applied along the length direction of the structures, and the heat source (425 K) and heat sink (375 K) are located at the hot and cold sides, respectively.After the energy minimization of the initial structures, an equilibrium state is achieved at t = 100 ps by their progressive relaxation using the Langevin thermostat [38] along the axial direction at 300 K and 0 GPa.The results show that, for Cu/SLG and Cu systems, their temperature gradients extracted from Figure 6c are 0.128 and 0.133 K per Å, respectively, and the corresponding heat flows of them are 6.172 and 2.627 eV per ps, respectively, as shown in Figure 6d.A thermal conductivity value of 6.04 W•m −1 •K −1 for Cu can be further extracted using Equation 1, and when considering a Cu/SLG sandwich structure, the thermal conductivity increases to 13.54 W•m −1 •K −1 .The calculated results of thermal conductivity of above samples are comparable with previous results, for instance, that of Cu with a value of ≈5.7 W•m −1 •K −1 by Richardson et al [39] using an EAM potential and the same NEMD method.The significant discrepancy between the values obtained from MD simulations and from the experiments for Cu can be attributed to the inherent limitation of MD in adequately capturing the role of electrons, as well as the considerably smaller modeling sizes than the testing samples.To further investigate the underlying mechanism of the thermal conductivity enhancement, we calculate the vibrational DOS of bare Cu and Cu in Cu/SLG as shown in Figure S8 (Supporting Information).The low-frequency peaks for bare Cu and the Cu in Cu/SLG are located at almost the same frequencies.However, the intensities are significantly increased from 214.0 for bare Cu to 272.6 for Cu in Cu/SLG, indicating an increase in the low-frequency phonons for Cu in Cu/SLG.As the low-frequency phonon dominates the heat conduction process, an increase of low-frequency phonons leads to an improvement in the thermal conductivity of Cu/SLG as well.
The contact between graphene and metal leads to the concentration of charge carriers, which does not contribute to the heat conduction across the interface. [40]However, combined with the increased in-plane thermal conductivity of Cu/SLG film, we conjecture that the contact between graphene and metal causes phonon-electron coupling, which results in the excitation of phonons in the Cu, brings a significant contribution to the heat conduction.According to this result, it is far different from Ref. [19], which reported that the improvement of thermal properties for the graphene/Cu/graphene system results primarily from the change in Cu grain during the CVD process.

Conclusion
In conclusion, owing to the Cu/SLG structure, the hot spot temperature of Cu with graphene decreased by ≈9% compared to annealed Cu.Because of the thermal anisotropy of graphene, heat is quickly dispersed in in-plane direction and provides thermal insulation along the out-of-plane direction.Our results indicate that graphene can facilitate a new mechanism of heat conduction between graphene and metal interface.The spectral phonon transmission analysis reveals that thermal transport in Cu/SLG is mainly contributed by the low-frequency phonons, and is highly mismatched in the high-frequency region.The MD simulations demonstrate that the presence of graphene provokes the excitation of phonons in the Cu substrate, facilitating an increased phonon contribution to the thermal conductivity.These findings show the positive effect of graphene on the heat conduction of metals and are crucial for the design and application of graphenebased electronic devices.

Figure 1 .
Figure 1.a) Experimental setups for the characterization of the thermal properties.b) Schematics of the design of the sample holder.The sizes of all samples are 2 × 2 cm.c,d) OM images, SEM images, and typical Raman spectra of the Cu/SLG (upper panel) and only-annealed Cu (lower panel) samples after the thermal tests, respectively.e) Typical Raman spectra of the Cu/SLG (black) and only-annealed Cu (red) samples.

Figure 2 .
Figure 2. Hot spot temperature rising profiles of only-annealed Cu and Cu/SLG with inputs at a) 100 °C; b) 150 °C; c) 200 °C; d) 250 °C and e) 300 °C.f) The ΔT/T Cu ratio between the only-annealed Cu and Cu/SLG samples as a function of the input temperature.

Figure 3 .
Figure 3.Comparison of the in-plane temperature distribution of only-annealed Cu and Cu/SLG with the same heat input at 200 °C.

Figure 4 .
Figure 4. a) Hot spot temperature rising profile of Cu/SLG and Cu after graphene removal.b) Illustration of the heat transfer process in Cu enhanced by graphene coating.Hot spot temperature rising profiles of c) Al and Al/SLG and d) Ag and Ag/SLG.

Figure 5 .
Figure 5. a) Evaporation process of water droplets on the Cu surface without graphene for the only-annealed Cu and Cu/SLG samples, both with a heat input at 200 °C.Note that the scales represent 5 mm b) Remaining percentage of the volumes of the water droplets in (a).c) The surface temperature of the water droplets measured by an IR detector.

Figure 6 .
Figure 6.a) The impact of the graphene layer in heat dissipation performance of the Cu substrate.The dotted lines represent the average temperatures of Cu at equilibrium for Cu and Cu/SLG configurations.b) The vibrational DOS between Cu and graphene.The insert shows a magnified view of vibrational DOS in the low-frequency region.c) The temperature profiles along the heat flux direction of Cu/SLG and Cu, obtained after the system reaches a non-equilibrium steady state via the NEMD method.d) The accumulated energy between the heat source and sink as a function of time in Cu/SLG and Cu.