GRAPHENE BASED HIGH-PERFORMANCE THERMAL INTERFACE MATERIALS

Transcription

1 Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea ACTS GRAPHENE BASED HIGH-PERFORMANCE THERMAL INTERFACE MATERIALS Jie Chen 1 * 1 Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai , China * Presenting and Corresponding Author: jie@tongji.edu.cn ABSTRACT Thermal properties of graphene have attracted intensive investigations in recent years. In this study, we present our recent progress on developing graphene based high-performance thermal interface materials using molecular dynamics simulations. By applying mechanical strain that can tailor the phonon spectrum, we demonstrate that the inter-layer thermal resistance in few-layer graphene can be reduced by 85%. Furthermore, we show that by replacing the inter-layer van der Waals interaction with the covalent sp 2 bond with the carbon nanotube, the graphene-carbon nanotube hybrid outperforms few-layer graphene by more than 2 orders of magnitude for the c-axis heat transfer, while its thermal resistance is 3 orders of magnitude lower than the state-of-the-art TIMs. When immersed in water, the hybrid structure can provide sustainable cooling of high temperature and high heat flux hot surfaces via the solidliquid interaction. Our study provides useful insights to the application of graphene for thermal management. KEYWORDS: Thermal interface material, graphene, carbon nanotube, strain engineering, covalently bonded hybrid, Kapitza resistance, solid-liquid interface 1. INTRODUCTION Thermal conductivity of graphene has been the focus of intense investigations [1] in recent years because of its extensive fascinating properties, such as the recorded superior high thermal conductivity [2]. Based on Raman spectroscope measurement, room temperature thermal conductivity of suspended single-layer graphene (SLG) is found to reach a high value of ~ 2,500-5,300 W/m-K [2-4]. Compared to the suspended SLG, the in-plane thermal conductivity of suspended few-layer graphene (FLG) is lower, which decreases with the layer number and converges to that of the graphite ~ 1,000-2,000 W/m-K after a few atomic layers [5]. The high in-plane thermal conductivity of suspended graphene has raised the exciting prospect that the high-efficiency heat dissipation devices can be realized with graphene. However, the cross-plane thermal conductivity of suspended graphite is more than two orders of magnitude smaller than the in-plane thermal conductivity [1]. Recent experimental study on suspended FLG with thickness ~ 35 nm reported the cross-plane thermal conductivity ~ 0.7 W/m-K at room temperature [6]. This large anisotropy in thermal conductivity reduces the applicability of graphene for rapid heat dissipation, which makes the cross-plane heat transport a bottleneck for efficient heat dissipation in graphene. In this regard, reducing the interfacial thermal resistance between graphene sheets and therefore facilitating cross-plane heat transport is the key towards the design of graphene-based high-performance heat dissipation device. 2. METHOD Non-equilibrium molecular dynamics (NEMD) simulations are used to calculate the Kapitza resistance of graphene. As shown in Fig. 1, multiple layers of Nosé-Hoover heat bath with high temperature T + (red box) are applied to the center of the simulation domain as heat source, while low temperature heat bath T _ (blue box) is 1

2 applied to both ends of the simulation domain as heat sink. Periodic boundary condidtions are used in all directions. This particular setup avoids the use of fixed boundary conditions, and therefore allows for structure relaxation during thermal equilibration and deformation during strain loading process. In this setup, heat flows in both directions (red arrow) away from the center, and the effective domain (dashed black box) is about half of the whole simulation domain. Figure 1. Setup of the non-equilibrium molecular dynamics simulations. The dashed black box depicts the effective domain. The red and blue box denotes the heat bath regions with high temperature (T+) and low temperature (T-), respectively. In-plane directions are in XY plane, and the cross-plane direction is in the z-axis. Periodic boundary conditions are applied in all directions. All MD simulations in our study are performed by using LAMMPS package [7]. Optimized Tersoff potential [8] for graphene is used to model the C-C bond within the same graphene sheet, while Lennard-Jones (LJ) potential with optimized parameters for graphene [9] is used to model the inter-layer C-C interactions between different layers. The cut-off distance in LJ potential is set as 2.5σ. Moreover, the neighbor list is dynamically updated every ten time steps, and each time step is set as 0.2 fs in our simulations. Thermal conductivity is computed based on Fourier s law κ=-j/ T, where J is the heat flux computed as the energy induced by the thermostat across unit area per unit time, and T is the temperature gradient computed based on the linear regression analysis of the temperature profile. We run NEMD simulation long enough to ensure the steady state that temperature gradient and heat flux is independent with time. All results presented in the paper have been averaged over six independent runs with different initial conditions. 2

3 3.1 STRAIN ENGINEERING 3. RESULTS AND DISCUSSION To study the strain effect on the cross-plane heat transport in FLG, we apply uniaxial strain to the fully relax graphene sheets after thermal equilibration. The uniaxial strain is define as e = l l 0 l 0, (1) where l 0 and l is, respectively, the length of the simulation box in the strain loading direction for the unstrained and strained graphene. To load strain in the specified direction, the size of simulation domain in the strain loading direction is deformed at a constant strain rate. Moreover, the size of the plane perpendicular to the strain loading direction is fixed (NVT ensemble) so that strain is truly uniaxially loaded in our simulations. Figure 2. Normalized Kapitza resistance R of few-layer graphene versus uniaxial cross-plane strain e c at Room temperature. Symbols denote raw data for different number of graphene layers in the effective domain, and lines draw the exponential fit to the raw data. The relative value is normalized by Kapitza resitance of unstrained graphene. After applying the cross-plane strain to FLG, we calculate its Kapitza resistance using NEMD simulations. Figure 2 shows the dependence of Kapitza resistance R on uniaxial cross-plane strain e c at room temperature. It is found the compressive cross-plane strain reduces R, while the tensile cross-plane strain leads to the increase of R. When the cross-plane varies from compressive to tensile, R increases monotonically, showing an exponential trend with the variation of e c for different layer numbers (lines in Fig. 2). More interestingly, we found the relative variation of R, which is normizelid by R of unstrained graphene at each layer number, follows the same exponential dependence on e c, regardless of the thickness of the FLG. This result suggests that the exponential dependence of Kapitza resistance on cross-plane strain might be a generic feature in FLG, which offers a quite robust measure to tailor Kapitza 3

4 resistance of FLG. Moreover, our simulation results show that with 5% compressive cross-plane strain, Kapitza resistance of FLG can be reduced by 50%. In our simulation, the maximum stress induced by cross-plane strain is less than 40 GPa, which is much lower than the extreme stress of graphene ~ 130 GPa measured in experiment [10]. Therefore, our study suggests that strain engineering is a practical approach that can be realized in experiment to reduce Kapitza resistance of graphene. To understand the physical mechanism responsible for the strain effect on heat transport, we calculate in both unstrained and strained FLG the vibrational density of states (DOS) as DOS(ω ) = v(0)iv(t) e iωt dt. (2) For the unstrained FLG, the characteristic G peak at ~ 1600 cm -1 (~48 THz) [11] is well reproduced by our calculations. Compared to the unstrained FLG, the total DOS of strained FLG exhibits a blue/red shift for lowfrequency phonons near Brillouin zone center when subjected to compressive/tensile uniaxial cross-plane strain, while the G peak is almost unaffected by the cross-plane strain (Fig. 3(a)). The polarized DOS further reveals that the frequency shift of zone-center low-frequency phonons (less than 10 THz) induced by the the cross-plane strain stems from the low-frequency out-of-plane vibration (Fig. 3(b)), which corresponds to the flexual acoustic (ZA) phonons [11] ], while DOS for in-plane phonons is independent with the cross-plane strain (Fig. 3(c)). Figure 3. Vibrational density of states (DOS) of few-layer graphene under different uniaxial cross-plane strain e c. (a) Total DOS. The inset zooms in for the low-frequency phonons. (b) DOS for out-of-plane vibration. (c) DOS for inplane vibration. 4

5 The strain effect on Kapitza resistance of FLG can be understood from the kinetic theory, in which thermal conductivity of a solid can be expressed as κ = C λv λ l λ. Here λ(k,p) is the phonon mode index, depending on λ wavevector k and polarization p. C, v and l denotes specific heat, group velocity, and mean-free path of each phonon mode, respectively. Using lattice dynamics calculations, Li et al. studied the effect of strain on phonon dispersion relation for bulk silicon and diamond [12]. They found compressive/tensile strain causes the blue/red shift of phonon spectrum, which is consistent with our MD simulation results. Such frequency-shift of phonon spectrum induced by compressive/tensile strain results in the increase/decrease of both phonon group velocity and specific heat, thus leading to the increase/decrease of thermal conducitivty [12]. The Kapitza resistance R of FLG is related to the cross-plane thermal conductivity κ as R=L 0 / κ, where L 0 is the inter-layer distance. Since the compressive/tensile cross-plane strain causes the decrease/increase of L 0 and increase/decrease of κ, R is reduced/increased consequently. 3.2 GRAPHENE-CARBON NANOTUBE HYBRID By applying mechanical strain, we find Kapitza resistance in FLG can be reduced by 85%. Further improvement based on strain is difficult due to the non-covalent van der Waals (vdw) interaction between FLG. An alternative is the use of high thermal conductivity materials that can modify the heat propagation across graphene. Carbon nanotube (CNT) is a carbon allotrope formed by sp 2 covalent bonding, and has high axial thermal conductivity [13]. We construct graphene-cnt hybrid structure by seamlessly connecting two graphene sheets with varying numbers of (6,6) CNT through sp 2 covalent bonding, with the careful design of the interfacial structure based on Euler s rule for polygons [14]. In our simulation, we first consider two graphene sheets with a fixed cross section about 10 nm 10 nm connected by CNTs with fixed length L=16 nm. Using the setup shown in Fig. 4(a), thermal conductivity of the hybrid structure is computed with NEMD simulation, where the high temperature and low temperature thermostats are applied to the top and bottom graphene layer, respectively. For a consistent comparison with the pure graphene, we consider two definitions of the cross section when computing the heat flux: (a) the constant cross section S 0 =D 2, (b) the effective cross section excluding the hollow area S E =S 0 *(1-ρ). Here ρ is the density of CNT defined as ρ= N*π*R 2 /S 0, where N is the number of CNTs and R is the CNT radius. Even with one CNT, the hybrid structure shows almost one order of magnitude improvement in c-axis thermal conductivity κ compared to the pure graphene (Fig. 4(b)). For multiple CNTs, κ increases monotonically with ρ. In the low CNT density region (ρ<15%), the inter-cnt interaction is negligible so that κ is independent of the specific CNT arrangement for a given density. Moreover, two definitions of cross section gives equivalent results, so the enhancement in c-axis thermal conductivity can only be attributed to the replacement of non-covalent interaction with covalent bonding. When ρ is below 5%, κ depends linearly on the CNT density (dashed line in Fig. 4(b)). With about 10% CNT, the c-axis thermal conductivity is increased more than 2 orders of magnitude compared to that of pure graphene. In the high CNT density region (ρ>15%), κ is underestimated with S 0 as there are significantly less atoms actually conducting heat in the holey graphene sheet compared to the full graphene sheet. Moreover, κ is below the linear dependence on ρ at high CNT density, suggesting greatly enhanced phonon scatterings at the graphene- CNT junctions. In addition to the CNT density, we find the inter-cnt interaction also plays a role in affecting the c- axis heat transfer. The onset of inter-cnt interaction leads to the reduction of κ in the hybrid structure, and the further increase of the inter-cnt interaction strength is found to decrease κ monotonically (Fig. 4(c)). This result is consistent with the previous study on multi-walled CNT. Previous experimental studies [13, 15] found inter-cnt interaction in multi-walled CNT causes reduction of axial thermal conductivity, leading to the diameter-dependent thermal conductivity. 5

6 Figure 4. Cross-plane thermal conductivity κ of graphene-cnt hybrid structure at room temperature. (a) Schematic setup of the non-equilibrium molecular dynamics simulations. Langevin thermostat with temperature T + and T - is applied to the top (red) and bottom (blue) graphene sheet, respectively, resulting in the heat flow in z-direction. (b) Dependence of κ on CNT density ρ with D=10 nm and L=16 nm. Two definitions of cross section (S 0 and S E ) are used for comparison. The c-axis thermal conductivity in multi-layer graphene from literature is also plotted for reference. (c) Effect of inter-cnt interaction strength χ for a CNT array (inset) with ρ=0.32, D=10 nm, and L=16 nm. S E is used in the calculation. (d) Length dependence of κ for individual CNT and graphene-cnt hybrid structure with D=10 nm. S 0 is used for both graphene-cnt hybrid structure and individual CNT. We further compare the thermal properties of the hybrid structure with the pure CNT. To make a reasonable comparison, a constant cross section S 0 is used for both hybrid structure and pure CNT when computing the heat flux. Surprisingly, we find the rescaled thermal conductivity of individual CNT is identical to that of hybrid structure with one CNT (Fig. 4(d)). This suggests that the high thermal conductivity of CNT can be inherited by the hybrid structure. More interestingly, κ of the hybrid structure can be increased proportionally by adding more CNTs, while the multi-walled CNT is known to have lower thermal conductivity than single-walled CNT [13, 15]. Therefore, the hybrid structure essentially provides an useful platform to parallelize the heat transfer capability of CNT. Furthermore, due to the power law dependence κ~l α (α<1), κ of individual CNT is less than doubled when the length is doubled. In contrast, κ of the hybrid structure is proportional to the number of CNTs at small ρ. This creates a novel material that has thermal conductivity several times of that of individual CNT. For the purpose of enhancing the axial thermal conductivity, the hybrid structure is more efficient than increasing the length of individual CNT, thus provides a new avenue to utilize the high thermal conductivity of CNT. 6

7 3.3 COOLING OF HOT SURFACE Figure 5. Cooling high temperature hot surface by G-CNT hybrid structure and water. (a) The G-CNT hybrid immersed in water. (b) Averaged temperature of the two hot surfaces cooled down by the G-CNT with/without water surrounded. The cooling performance for FLG is also plotted for comparison. The symbols show the initial temperature of the hot surface. The proposed G-CNT structure is compatible with the multiple stackings envisioned for the next generation 3D IC chips. The G-CNT can serve as a thermal interface material to dissipate the heat from two hot surfaces through the contact with its graphene layers, and it can be immersed in a circulating liquid (Fig. 5a) for the sustained cooling of IC chips. To demonstrate this idea, we simulate the transient cooling process of the hot surface by G-CNT. The top and bottom graphene layers are initially heated to high temperature to represent the hot surfaces. The G-CNT and the FLG have the same dimension of 12 nm 10 nm 13 nm, and the G-CNT has a CNT density about 14%. To fill in the empty space between the CNTs in the G-CNT, water molecules are used to reproduce the bulk water density in the regions away from the CNT and graphene surface. As shown in Fig. 5(b), the G-CNT hybrid can cool down the hot surfaces much faster than the FLG. Following Ref. [16], we fit the temperature decay of the hot surface according to the exponential function. The computed 7

8 temperature relaxation time is τ=0.7 ps and τ=126.6 ps for the G-CNT and FLG, respectively, exhibiting more than 2 orders of magnitude speed up by the G-CNT. We then immerse the G-CNT in a large water reservoir. Interestingly, the water does not affect the fast heat dissipation path through the solid G-CNT matrix. Furthermore, it removes the heat away from the solid matrix through the solid-liquid interaction, and further cools down the hot surface to the ambient temperature. 4. CONCLUSIONS We find the mechanical strain is an effective way to control the inter-layer thermal resistance in few-layer graphene. The thermal resistance in few-layer graphene increases monotonically when the uniaxial cross-plane strain varies from compressive to tensile. Maximum reduction in thermal resistance by the strain is about 85%. We further present a covalently bonded graphene-cnt (G-CNT) hybrid structure that is shown to outperform the heat disssipation properties of both carbon nanotubes and few-layer graphene. Through molecular dynamics simulations, we demonstrate that the G-CNT enhances the c-axis heat transfer of individual CNTs through their parallel arrangement. The G-CNT is shown to outperform by 2 to 3 orders of magnitude the heat transfer capabilities of state-of-the-art TIMs. When immersed in a liquid, we show that the G-CNT can provide sustained and rapid cooling of the hot surfaces. Our results provide novel insights to the thermal management in IC chips. ACKNOWLEDGMENT J.C. acknowledges support as an ETH Zurich Fellow, the National Natural Science Foundation of China (Grant No ), and the National Youth 1000 Talents Program in China. NOMENCLATURE A short nomenclature defining unusual or non-standard symbols can be placed immediately above the REFERENCES, if necessary. SI Units must be used. R Kapitza resistance (m 2 K/W) e strain ratio (-) S cross sectional area (m 2 ) ρ density of carbon nanotube (-) κ thermal conductivity (W/m-K) T temperature (K) REFERENCE [1] A.A. Balandin, Thermal properties of graphene and nanostructured carbon materials, Nat. Mater., 10 (2011) [2] A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene, Nano Lett, 8(3) (2008) [3] S. Ghosh, I. Calizo, D. Teweldebrhan, E.P. Pokatilov, D.L. Nika, A.A. Balandin, W. Bao, F. Miao, C.N. Lau, Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits, Appl. Phys. Lett., 92(15) (2008) [4] W. Cai, A.L. Moore, Y. Zhu, X. Li, S. Chen, L. Shi, R.S. Ruoff, Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition, Nano Lett, 10(5) (2010) [5] S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau, A.A. Balandin, Dimensional crossover of thermal transport in few-layer graphene, Nat. Mater., 9 (2010) [6] M. Harb, C. von Korff Schmising, H. Enquist, A. Jurgilaitis, I. Maximov, P.V. Shvets, A.N. Obraztsov, D. Khakhulin, M. Wulff, J. Larsson, The c-axis thermal conductivity of graphite film of nanometer thickness measured by time resolved X-ray diffraction, Appl. Phys. Lett., 101(23) (2012) [7] S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys., 117 (1995) [8] L. Lindsay, D.A. Broido, Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene, Phys. Rev. B, 81(20) (2010) [9] L.A. Girifalco, M. Hodak, R.S. Lee, Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential, Phys. Rev. B, 62(19) (2000) 8

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