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Surface-engineered nanoscale diamond films enable remarkable enhancement in thermal conductivity and anisotropy
CARBON 94 (2015) 760–767
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CARBON journal homepage: www.elsevier.com/locate/carbon
Surface-engineered nanoscale diamond films enable remarkable enhancement in thermal conductivity and anisotropy Xiangjun Liu, Gang Zhang ⇑, Yong-Wei Zhang Institute of High Performance Computing, A⁄STAR, Singapore
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 1 July 2015 Accepted 17 July 2015 Available online 18 July 2015
a b s t r a c t Nanoscale diamond films have attracted increasing attention due to their great potential for coating and thermal management in nanoscale electronic and opto-electronic devices. However, in strong contrast to the ultrahigh thermal conductivity of bulk diamond, nanoscale diamond films with typical 2 1 reconstructed dimer surfaces show rather disappointing thermal characteristics. Here we demonstrate an effective route to significantly enhance the thermal conductivity of nanoscale diamond films via reconstructing their surfaces by forming carbon nanotubes (CNT). For the same film thickness, the film with the CNT-reconstructed surfaces shows a surprising 3-fold enhancement in thermal conductivity compared to that with the typical 2 1 reconstructed dimer surfaces. In addition, a large anisotropy in the in-plane thermal conductivity is observed and remarkably, this strong anisotropy can be effectively tuned by varying the film thickness. We further show that the orientation-dependent lifetime of long wavelength phonons is responsible for the remarkable anisotropy in thermal conductivity. The present work underscores the use of surface engineering to manipulate heat transport at the nanoscale, which provides opportunities for developing effective thermal channeling devices. Ó 2015 Published by Elsevier Ltd.
1. Introduction Diamond has attracted a great deal of interest due to its unique combination of several fascinating properties, such as extreme hardness, chemical inertness, electrical insulating and ultrahigh thermal conductivity, which are originated from its lattice structure and strong carbon-carbon bond [1]. With the fast development of nanotechnology in recent years, nanoscale diamond has attracted increasing attention. Several methods have been developed to synthesize nanoscale diamond, for example, by transforming graphite under high temperature and high pressure, milling microcrystalline diamond and using chemical vapor deposition techniques (CVD) [2–6]. It was shown remarkably that some of the chemical and physical properties of man-made nanoscale diamond can approach those of natural diamond [7–9]. For example, nanoscale diamond was shown to exhibit some intrinsic characteristics, such as chemical inertness, low friction coefficient, high elastic modulus and strength-to-weight ratio, and have found a wide range of technological applications in optical, electronic, and mechanical applications [10,11]. It is well-known that when the sizes of a material reach the nanoscale, its physical and chemical properties can be very ⇑ Corresponding author. E-mail address: [email protected] (G. Zhang). http://dx.doi.org/10.1016/j.carbon.2015.07.061 0008-6223/Ó 2015 Published by Elsevier Ltd.
different from its bulk form. As a material system scales down in sizes, its surfaces can play an increasingly important role. Bulk diamond is in the form of sp3 hybridization; while an unpassivated diamond surface generally exhibits a different bonding characteristic. Among all the low-index diamond surfaces, the {1 0 0} surface is the dominant one in nanoscale crystalline diamond films synthesized by CVD technique [12–14]. Typically, the {1 0 0} surface has two dangling bonds per terminated surface carbon atom. To reduce the surface energy, these dangling bonds on the surface can be eliminated via surface reconstructions which involve the formation of new bonds. A (2 1) reconstruction featuring C@C dimer rows on the {1 0 0} surface was proposed theoretically in 1981 [3] and confirmed experimentally in 2001 [5]. Very recently, a new stable surface reconstruction featuring self-assembled carbon nanotube (CNT) arrays on the (1 0 0) surface of diamond film was predicted based on first-principles density functional theory [15]. It was found that this reconstructed surface is energetically competitive with the well-known (2 1) reconstructed surface under ambient condition, and interestingly, it becomes energetically even more favorable under a small compressive strain or at high temperatures [15]. Although several studies were performed on nanoscale diamond films [15–18], these studies were primarily focused on their structures and electronic properties. Owing to the ultrahigh thermal conductivity of bulk diamond, nanoscale diamond structures
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are expected to address the ‘‘hotspot’’ issue, that is, zones with excessive heat generated in electronic devices, which is a limiting factor currently to the device development [19–22]. Diamond film has been used for a variety of thermal management applications, including heat-dissipating for wide-bandgap semiconductor power electronics [23,24], temperature and heat-flux sensors [25], heat spreaders for high-power laser diodes [26]. Compared to graphene and CNTs, diamond film possesses a supreme hardness, which can be used as a substrate material for multi-chip modules and a submount for integrated circuits. Due to increased boundary phonon scattering, there is a considerable reduction in the thermal conductivity of nanoscale diamond films compared with their bulk counterpart, which becomes a bottleneck for their applications in thermal management. To realize nanoscale diamond films for applications in thermal management, one needs to address the following important issues: (1) Can one engineer the surface structure of nanoscale diamond films to significantly enhance their thermal conductivity? (2) Can such engineered nanoscale diamond films exhibit a strong anisotropy in thermal conductivity? (3). How does the thermal conductivity and anisotropy of such engineered films depend on the film thickness? Clearly, answers to these questions are not only of scientific significance and but also of technological impact on the development of thermal devices and also on the thermal management at the nanoscale. In the present work, using equilibrium molecular dynamics (EMD) simulations, we investigate the thermal transport properties of nanoscale diamond films with surfaces reconstructed in both the (2 1) dimer array and the self-assembled CNT array. For brevity, these two films are respectively named as dimersurface and CNT-surface diamond films. Our simulations show that compared to the dimer-surface, the CNT-surface can significantly enhance the thermal conductivity of nanoscale diamond films. In addition, a strong anisotropy in in-plane thermal conductivity for CNT-surface films is also observed. The present work indicates that the CNT-surface diamond films may play a vital role in thermal management for future nanoscale electronic devices.
2. Computational methods In our study, nanoscale diamond films are constructed from the bulk form. More specifically, the lattice structure of a nanoscale diamond film is extracted by selecting all the carbon atoms that fall within a rectangular slab in the bulk diamond. During the extraction, the top and bottom surfaces of the slab are chosen to be the {0 0 1} planes. Subsequently, the top and bottom surfaces of the film are artificially reconstructed and relaxed to form the 2 1 dimer-reconstruction surfaces and CNT-surfaces as shown in Fig. 1(a) and (b), respectively. In the setting, the x, y, and z directions are respectively the [1 0 0], [0 1 0] and [0 0 1] crystallographic directions. The direction of dimer rows or the CNT is along the y-direction. EMD simulations are employed to study the thermal properties of the diamond thin films using the LAMMPS package [27]. In all MD simulations performed herein, the bond order AIREBO potential [28] is used to describe the reactive, covalent bonding CC interactions. The simulations were carried out with a time step of 0.25 fs throughout. The size of simulation domain is 25.2 Å 25.2 Å in the x and y directions, as shown in Fig. 1. Periodic boundary condition (PBC) is applied in the in-plane (x and y) directions, which mimics the infinite size of diamond films by eliminating the boundary effects during the simulations. Free boundary condition (FBC) is applied in the z direction (the out-of-plane direction). Nosé-Hoover heat bath [29] is used to equilibrate the diamond film at 300 K with the isothermal-isobaric (NPT) ensemble. Once the temperature reaches
the required value, the thermostat is removed; then the heat flux J is calculated with micro-canonical (NVE) ensemble [30],
J¼
N X
ei v i þ
i
N N 1X 1 X ðF ij v i Þr ij þ ðF ijk v i Þðr ij þ r ik Þ; 2 ij;i–j 6 ijk;i–j–k
ð1Þ
where, ei and v i are the energy density and velocity associated with atom i, respectively. Vector rij denotes the interatomic distance between two atoms, and Fij and Fijk denote the two-body and three-body force, respectively. The thermal conductivity of diamond films is calculated based on the Green-Kubo formula (GKF). In GKF, the thermal conductivity is related to heat current autocorrelation function (HCACF) derived from the fluctuation–dissipation theorem and linear response theory [30],
j¼
Z
V kB T
2
1
hJ i ð0ÞJ i ðtÞidt;
ð2Þ
0
where kB is the Boltzmann constant, V is the volume of the system, and hJ i ð0ÞJi ðtÞi is the average heat flux autocorrelation function along the x and y directions, respectively. 3. Results and discussions We first examine a typical diamond film to study the in-plane thermal conductivity along the y-direction (the dimer row or CNT direction), that is, jy. For this case, the film thickness is H = 6a (where a = 3.556 Å is the diamond lattice constant), which is equal to 24 atomic layers. As shown in Fig. 2, the in-plane thermal conductivity jy of the dimer-surface film is 107 W/mK. On the one hand, this value is higher than that of diamond nanorod with a diameter of 1.3 nm (less than 50 W/mK) [7] due to the larger surface versus volume ratio and its resulting high phonon scattering of the nanorod, and also higher than the experimentally measured thermal conductivity of a polycrystalline diamond nano film [31] due to the strong phonon scattering from grain boundaries. On the other hand, this value is significantly lower than that of bulk diamond due to the strong phonon scattering of the film surfaces. Unlike bulk diamond that consists of pure sp3 hybridized single CC bond with a bond length of 1.539 Å [6], the dimer-structured film has surfaces that consist of p-bonded C@C dimers with a bond length of 1.382 Å [6]. The loss of atoms in the surface leads to the reduction in the coordination number. The bond-order–length–strength (BOLS) correlation indicates that when the coordination number of an atom is reduced, the equilibrium atomic distance between the under-coordinated atoms will contract, and the cohesive energy of the shortened bond will increase [32]. These changes will cause the increase in elastic modulus and inter-atomic force constant, which in turn leads to the difference in phonon frequencies in the surface and central sections, additional phonon scattering and reduced thermal conductivity [33,34]. As shown in Fig. 2, the in-plane thermal conductivity jy of the CNT-surface film is 310 W/mK, which is significantly higher (3 times) than the in-plane thermal conductivity jy of the dimer-surface film with the same thickness. The surface structure of the CNT-surface film consists of a large number of sp2 hybridized C atoms, which can be considered as an array of deformed single-wall (2,2) CNT on diamond (0 0 1) surface [15]. The nanotube array possesses eight-membered C rings, with the bottom one being embedded on the diamond (0 0 1) surface. An isolated (2,2) CNT has a thermal conductivity as high as 2436 W/mK [35], which indicates that the array of sp2 hybridized CNT serves as much more efficient paths for thermal energy transport than the dimer array. Although the thermal conductivity of CNT-surfaced diamond nanoscale film is still lower than that of the bulk diamond, it is still significantly higher than that of bulk silicon (140 W/mK at room
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Fig. 1. Schematics of surface-reconstructed diamond thin films. (a) Diamond thin film with dimer structures on the top and bottom surfaces. (b) Diamond thin film with CNT structures on the top and bottom surfaces. Atoms in gray, blue, green, and red are the carbon atoms in bulk, dimer, transition, and CNT region of the film, respectively. Note that the x, y and z direction are along the [1 0 0], [0 1 0] and [0 0 1] crystallographic direction, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperature) [22], and comparable to bulk copper, which is a commonly-used material for efficient thermal conduction. Our results suggest that nanoscale CNT-surface diamond films can be an efficient material for thermal management at the nanoscale. From Fig. 2, it is found remarkably that both the dimer- and CNT-surface diamond thin films exhibit a strong in-plane anisotropy in thermal conduction. For the dimer-surface film with H = 6a, the thermal anisotropy ratio c (= jy/jx) is 1.8 while for the CNT-surface film with the same thickness, it is further increased to 2.7. Such a large thermal anisotropy ratio has rarely been reported in other materials before, especially in bulk materials. Recently, two-dimensional (2D) materials, such as graphene and MoS2, have been suggested for use in nanoscale electronics and photonics devices [36–41]. However, these 2D materials show a nearly isotropic in-plane thermal conductivity. Very recently, phosphorene, another atomically thin 2D material, has been the focus of a considerable interest due to its strong anisotropic
in-plane thermal conductivity [42,43]. For phosphorene, the thermal conductance along the zigzag direction is about 40% larger than that along the armchair direction due to its strongly puckered ridge-accordion structure [43]. Compared to the anisotropy ratio of phosphorene, c = 1.4, the anisotropy ratio of the CNT-surface film, c = 2.7, is much higher. This highly anisotropic thermal property may be useful in the design of thermal channeling devices, thus showing another important advantage of CNT-surfaced diamond films besides the enhanced thermal conductivity. In order to understand the underlying mechanism of this remarkable thermal transport anisotropy in CNT-surfaced films, we have calculated the rescaled heat current autocorrelation function (HCACF), CJJ(t), of the film, which is defined as C JJ ðtÞ ¼ k VT 2 hJ i ð0ÞJ i ðtÞi, and compared with that of the bulk diaB
mond. It is known that the decay of HCACF in bulk material is exponential, following the macroscopic law of relaxation and Onsager’s postulate for microscopic thermal fluctuations [44].
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Fig. 2. The thermal conductivities of surface-reconstructed diamond thin films, that is, the dimer-surface and CNT-surface films. The film thickness H = 6a. The anisotropy ratios are also shown.
Also, the initial fast decay is due to the high frequency phonon modes while the slow decay corresponds to the low frequency phonon modes. From the bulk diamond HCACF as shown in Fig. 3(a), it is seen that there is a rapid initial decay (0.05 ps) followed by a long time exponential decay of the correlation function in bulk diamond, which is consistent with the double exponential function observed for the HCACF of bulk diamond by Che et al. [44]. Here, we have used the same double exponential function to fit the bulk HFACF [45],
C JJ ðtÞ ¼ AS expðt=sS Þ þ AL expðt=sL Þ
ð3Þ
The subscripts S and L refer to the short wavelength phonon modes and long wavelength phonon modes, respectively. The parameters AS, sS, AL, and sL are derived using a nonlinear least-square method, where, sS and sL correspond to the relaxation time of short wavelength and long wavelength phonons, respectively. As shown in Fig. 3(a) and Table 1, it is clear that in the bulk diamond, both sS and sL are weakly direction-dependent. From Fig. 3(b), it is also seen that the HCACF of the CNT-surface diamond film is very different from that of the bulk: the former shows a regular high frequency oscillation while the latter does not. We note that a similar oscillation was also observed in heterogeneous systems with different atomic masses [46,47]. From Table 1, it is also seen that the phonon relaxation time in the CNT-surface film is remarkably anisotropic. Unlike the slight difference in sS along the x and y directions, there is a much larger sL for the long wavelength (low frequency) phonons along the y direction than that along the x direction. In general, short wavelength (high frequency) phonons have limited contribution to thermal conductivity due to their low group velocity. Thus the large difference in relaxation time for the long wavelength phonons along the x and y direction is responsible for the remarkable direction-dependent thermal conductivity in CNT-surface diamond films. Clearly, the surface effect is the dominant factor that causes the anisotropic thermal transport. Below, we perform atomic vibrational analysis in the frequency domain to examine thermal transport in the different regions of the CNT-surface film. The phonon vibrational density of states (VDOS) in the frequency domain is calculated by taking the Fourier transform (FT) of the velocity autocorrelation functions of atoms belonging to the different regions in the system,
DðxÞ ¼
Z s 0
CðtÞ expðixtÞdt;
ð4Þ
Fig. 3. The heat current autocorrelation functions and the double exponential fitting for (a) bulk diamond and (b) CNT-surface film. The parameters obtained by fitting to the double exponential function (blue lines) are given in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Parameters obtained by fitting to the double exponential function of the heat current autocorrelation functions for both the bulk diamond and CNT-surface diamond thin film.
Bulk diamond x-Direction y-Direction
AS (W/mK)
sS (ps)
AL (W/mK)
sL (ps)
0.53 0.50
0.0068 0.0070
0.32 0.31
7.6 7.7
0.0065 0.0073
1.27 1.82
4.3 9.8
CNT-surface diamond film x-Direction 1.60 y-Direction 1.21
where x is the frequency, D(x) is the VDOS at frequency x, and
CðtÞ ¼ hv ðtÞv ð0Þi=hv ð0Þv ð0Þi is the velocity autocorrelation function. v ðtÞ is the atom velocity, h i denotes time and atom number averaged velocity autocorrelation function, and s ¼ 5 ps is the time duration to compute the velocity autocorrelation function and its corresponding discrete Fourier transform in a series of short runs. For comparison, we have also calculated the VDOS of carbon atoms in the bulk diamond. Fig. 4(a) shows the VDOS of carbon atoms in the bulk diamond while Fig. 4(b)–(d) show the VDOS in different regions of the
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CNT-surface film. To avoid the overlap of VDOS in the x and y direction, the VDOS in the y direction is plotted on top of that in the x direction. The carbon atoms in different regions of CNT-surface film are considered separately, as shown in the inset of Fig. 4(b). The C2-type atoms link the sp3 bonded C1-type atoms (in the bulk region of CNT-surface film) and sp2 bonded C3-type atoms (in the CNT). The VDOS of carbon atoms in the bulk diamond along the x direction is the same as that along the y directions, which is consistent with the common understanding that the thermal conductivity in bulk diamond is isotropic. It is found that the vibrational spectrum of C1 atoms is consistent with that in bulk diamond with a major peak at about 43 THz. This shows that the surface reconstruction only affects the lattice vibration locally. On the other hand, the major peak of vibrational spectrum of C3 atoms is at about 50 THz (Fig. 4(d)), which is markedly different from that in bulk diamond, but in good agreement with that in sp2 bonded carbon atoms in graphene [48]. Unlike in the y direction where C2 atoms have the same major spectrum peak as C1 atoms at about 43 THz, there is a large mismatch in vibrational spectrum peaks in the x direction between C2 and C3 atoms (with 36 THz and 50 THz, respectively). In the central region of the CNT-surface film, the VDOS along the x direction is nearly the same as that along the y direction, showing a weak directional dependence in thermal conduction. However, for heat energy transport within the surface region, the situation is distinctively different. As shown in Fig. 1(b), the C2 and C3 atom arrays are arranged alternatively along the x direction, while they are parallel along the y direction. Hence, the heat transport along the y direction is channeled mainly by these parallel heat paths, thus possessing a relatively high thermal conductivity. On the other hand, the heat energy transport along the x direction is channeled by the C2 and C3 atom arrays alternatively, similar to that in superlattice structures [49]. Clearly, the large mismatch in VDOS causes a large resistance in heat flow through the system,
therefore resulting in a low thermal conductivity and high anisotropic ratio. For comparison, the VDOS in different regions of the dimer-surface film are shown in Fig. 4(e) and (f). It is seen that the major peak of vibrational spectrum of Cd1 atoms is at 43 THz, which is consistent with those of atoms in bulk diamond and C1 atom in CNT-surface film. On the other hand, the major peak of vibrational spectrum of Cd2 atoms is at 50 THz, agreeing well with that in sp2 bonded carbon atoms in the CNT-surface film. Thus, the mismatch in vibrational spectrum peaks in the x direction between Cd1 and Cd2 atoms is responsible for the lower thermal conductivity along the x direction than that along the y direction. However, it is apparent that the mismatch in VDOS is not as significant as that in CNT-surface film. This is the reason why a lower anisotropic ratio is observed in the dimer-surface film than that in CNT-surface film. Next, we examine the thickness effect on the thermal conductivity and thermal transport anisotropy of the CNT-surface films. Based on first-principles calculations [15], the CNT arrays on the top and bottom surfaces are arranged in parallel when the number of atom layer is even (2n, where n is an integer). In contrast, when the number of atom layer is odd (2n + 1), the CNT arrays on the top and bottom surfaces are arranged in perpendicular, as shown in Fig. 5(a). Fig. 5(b) shows that for diamond films with an even number of atom layer, both jx and jy increase with the film thickness, while the anisotropy is independent of the thickness. However, for the diamond films with an odd number of atom layer, the thermal conductivity anisotropy disappears, although there is a similar thickness dependence in thermal conductivity. This is because in this type of diamond films, the CNT arrays on the two surfaces are arranged perpendicularly, thus the change in lattice symmetry destroys the orientation-dependent thermal transport. Fig. 5(d) shows the anisotropy ratio jy =jx as a function of the film thickness. Interestingly, the anisotropy ratio shows a strong oscillation where two distinct families ðH ¼ 2n and ðH ¼ 2n þ 1Þ
Fig. 4. The phonon vibrational density of states for (a) carbon atoms Cbulk in bulk diamond, (b) carbon atom C1 in the bulk region of CNT-surface film, (c) carbon atom C2 in the connecting region between the CNT and bulk regions of the CNT-surface film, (d) carbon atom C3 in the CNT region of the CNT-surface film, (e) carbon atom Cd1 in the bulk region of dimer-surface film, and (f) carbon atom Cd2 in the dimer region of the dimer-surface film.
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Fig. 5. (a) Schematics for parallel-arranged and perpendicularly-arranged CNT-surface films; (b) the thermal conductivity of parallel-arranged CNT-surface films along the x and y directions as a function of thickness; (c) the thermal conductivity of perpendicularly-arranged CNT-surface films as a function of thickness; and (d) the thermal anisotropy ratio (jy/jx) of parallel-arranged and perpendicularly arranged CNT-surface films as a function of thickness.
Fig. 6. Potential energy difference between diamond films with CNT-surface (ECNT) and dimer-surface (EDimer) under different conditions of temperature and strain.
are clearly visible. The oscillating behavior in the anisotropy ratio can be explained by the change in the surface symmetry of nanoscale diamond films with thickness. The parallel-arranged CNT-surface films exhibit a large thermal anisotropy with the
reduction of the film thickness. For example, for the film with a thickness of 10.7 Å, its thermal anisotropy ratio c can reach as high as 4.6. This remarkably high anisotropy ratio may be useful in heat channeling devices, such as phononic waveguide, in which a strong directional dependence in thermal conduction is required. Finally, we explore the energetics and structural stability of CNT-surface. Fig. 6 shows the potential energy of the CNT-reconstructed surface compared with that of the dimer reconstruction, with temperature changing from 100 K to 500 K, and strain from 1.2% to 1.6%. It is interesting to find that in the considered ranges of temperature and strain, the potential energy of the CNT surface is always lower than that of the dimer surface, and the difference in potential energy decreases with increasing temperature. At room temperature and zero strain, the potential energy of CNT-surface is about 41 meV/atom lower than that of the dimer-surface, indicating that the CNT-surface is energetically more favorable. This is consistent with the first-principles calculation results that the binding energy of CNT surface is slightly lower than that of the dimer structure [15]. Although the binding energies of dimer-surface and CNT-surface are close to each other [15], there is a 1.6 eV per unit cell (10 atoms) barrier in transition from dimer-surface to CNT-surface. Moreover, the H-terminated dimer is energetically more stable than H-terminated CNT-surface [15]. This is why so far there is no CNT-surface observed in natural diamond surface.
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However, for chemical vapor deposition (CVD) growth of diamond nanofilm, the situation is different. The growth of diamond films has been of great interest because diamond nanoscale film has a wide range of applications in electronic, mechanical, optical and thermal devices. Thermal CVD is an efficient method for growing high quality diamond films with low concentration of defects. CVD of diamond film is typically initiated by dissociation of a gaseous mixture of H2 and hydrocarbon precursor such as methane or acetylene. [50] Kang and Musgrave [51] studied the surface chemistry and reaction path of dimer-opening on the diamond (2 1) surface with adsorbed CH3, and found that the adsorbed CH3 can be converted to CH2 by H abstraction, and the dimer-opening is followed by ring-closing process, which is the rate limiting reaction. Thus in thermal CVD using methane as precursor, dimer-surface should grow continuously. However, if a pair of molecules (each consists of two carbon atoms, for example, acetylene) adsorb on dimer surface of diamond, they will form a bridge state [15]. Rotations of these molecules by 45° and 45° of the bridge site, respectively, will lead to the formation of tube surface structure. From first-principles calculation, the transition from bridge site to CNT-surface is smooth, with no barrier [15]. In contrast, there is an energy barrier of 2–3 eV required for the continuous growth of dimer structure [52]. Thus CNT-surface is expected in thermal CVD growth with carbon rich condition, for example, using acetylene as precursor. 4. Conclusions In summary, we have investigated the thermal transport behavior of surface-reconstructed nanoscale diamond films using molecular dynamics simulation. It is found that for the same film thickness, the film with the CNT-surface shows a 3-fold enhancement in thermal conductivity compared to that with the 2 1 reconstructed dimer surface. In addition, a remarkable thermal anisotropy is observed in the CNT-surface diamond film, with an anisotropy ratio of 2.7 for the 2 nm thick film and 4.6 for the 1 nm thick film. From phonon vibration spectrum analysis, it is understood that this remarkable anisotropy is originated from orientation-dependent lifetime of long wavelength phonons due to the surface CNT structures. The enhanced thermal conductivity and remarkably high anisotropy of the CNT-surface diamond films revealed from the present work highlight an important route to tune the thermal transport of nanoscale structures by surface engineering. The present work also shows that the CNT-surface diamond films may be promising for applications in thermal management and novel phononic devices. Acknowledgment The authors gratefully acknowledge the financial support from the Agency for Science, Technology and Research (A⁄STAR), Singapore and the use of computing resources at the A⁄STAR Computational Resource Centre, Singapore. References [1] K.E. Spear, J.P. Dismukes, E. Society, Synthetic Diamond: Emerging CVD Science and Technology, John Wiley & Sons, New York, 1994. [2] A. Krueger, Diamond nanoparticles: jewels for chemistry and physics, Adv. Mater. 20 (12) (2008) 2445–2449. [3] N.V. Novikov, New trends in high pressure synthesis of diamond, Diamond Relat. Mater. 8 (1999) 1427–1432. [4] J.A. Viecelli, F.H. Ree, Carbon particle phase transformation kinetics in detonation waves, J. Appl. Phys. 88 (2) (2000) 683–690. [5] J.P. Boudou, P.A. Curmi, F. Jelezko, J. Wrachtrup, P. Aubert, M. Sennour, et al., High yield fabrication of fluorescent nanodiamonds, Nanotechnology 20 (23) (2009) 235602–235611.
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Contents lists available at ScienceDirect
CARBON journal homepage: www.elsevier.com/locate/carbon
Surface-engineered nanoscale diamond films enable remarkable enhancement in thermal conductivity and anisotropy Xiangjun Liu, Gang Zhang ⇑, Yong-Wei Zhang Institute of High Performance Computing, A⁄STAR, Singapore
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 1 July 2015 Accepted 17 July 2015 Available online 18 July 2015
a b s t r a c t Nanoscale diamond films have attracted increasing attention due to their great potential for coating and thermal management in nanoscale electronic and opto-electronic devices. However, in strong contrast to the ultrahigh thermal conductivity of bulk diamond, nanoscale diamond films with typical 2 1 reconstructed dimer surfaces show rather disappointing thermal characteristics. Here we demonstrate an effective route to significantly enhance the thermal conductivity of nanoscale diamond films via reconstructing their surfaces by forming carbon nanotubes (CNT). For the same film thickness, the film with the CNT-reconstructed surfaces shows a surprising 3-fold enhancement in thermal conductivity compared to that with the typical 2 1 reconstructed dimer surfaces. In addition, a large anisotropy in the in-plane thermal conductivity is observed and remarkably, this strong anisotropy can be effectively tuned by varying the film thickness. We further show that the orientation-dependent lifetime of long wavelength phonons is responsible for the remarkable anisotropy in thermal conductivity. The present work underscores the use of surface engineering to manipulate heat transport at the nanoscale, which provides opportunities for developing effective thermal channeling devices. Ó 2015 Published by Elsevier Ltd.
1. Introduction Diamond has attracted a great deal of interest due to its unique combination of several fascinating properties, such as extreme hardness, chemical inertness, electrical insulating and ultrahigh thermal conductivity, which are originated from its lattice structure and strong carbon-carbon bond [1]. With the fast development of nanotechnology in recent years, nanoscale diamond has attracted increasing attention. Several methods have been developed to synthesize nanoscale diamond, for example, by transforming graphite under high temperature and high pressure, milling microcrystalline diamond and using chemical vapor deposition techniques (CVD) [2–6]. It was shown remarkably that some of the chemical and physical properties of man-made nanoscale diamond can approach those of natural diamond [7–9]. For example, nanoscale diamond was shown to exhibit some intrinsic characteristics, such as chemical inertness, low friction coefficient, high elastic modulus and strength-to-weight ratio, and have found a wide range of technological applications in optical, electronic, and mechanical applications [10,11]. It is well-known that when the sizes of a material reach the nanoscale, its physical and chemical properties can be very ⇑ Corresponding author. E-mail address: [email protected] (G. Zhang). http://dx.doi.org/10.1016/j.carbon.2015.07.061 0008-6223/Ó 2015 Published by Elsevier Ltd.
different from its bulk form. As a material system scales down in sizes, its surfaces can play an increasingly important role. Bulk diamond is in the form of sp3 hybridization; while an unpassivated diamond surface generally exhibits a different bonding characteristic. Among all the low-index diamond surfaces, the {1 0 0} surface is the dominant one in nanoscale crystalline diamond films synthesized by CVD technique [12–14]. Typically, the {1 0 0} surface has two dangling bonds per terminated surface carbon atom. To reduce the surface energy, these dangling bonds on the surface can be eliminated via surface reconstructions which involve the formation of new bonds. A (2 1) reconstruction featuring C@C dimer rows on the {1 0 0} surface was proposed theoretically in 1981 [3] and confirmed experimentally in 2001 [5]. Very recently, a new stable surface reconstruction featuring self-assembled carbon nanotube (CNT) arrays on the (1 0 0) surface of diamond film was predicted based on first-principles density functional theory [15]. It was found that this reconstructed surface is energetically competitive with the well-known (2 1) reconstructed surface under ambient condition, and interestingly, it becomes energetically even more favorable under a small compressive strain or at high temperatures [15]. Although several studies were performed on nanoscale diamond films [15–18], these studies were primarily focused on their structures and electronic properties. Owing to the ultrahigh thermal conductivity of bulk diamond, nanoscale diamond structures
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are expected to address the ‘‘hotspot’’ issue, that is, zones with excessive heat generated in electronic devices, which is a limiting factor currently to the device development [19–22]. Diamond film has been used for a variety of thermal management applications, including heat-dissipating for wide-bandgap semiconductor power electronics [23,24], temperature and heat-flux sensors [25], heat spreaders for high-power laser diodes [26]. Compared to graphene and CNTs, diamond film possesses a supreme hardness, which can be used as a substrate material for multi-chip modules and a submount for integrated circuits. Due to increased boundary phonon scattering, there is a considerable reduction in the thermal conductivity of nanoscale diamond films compared with their bulk counterpart, which becomes a bottleneck for their applications in thermal management. To realize nanoscale diamond films for applications in thermal management, one needs to address the following important issues: (1) Can one engineer the surface structure of nanoscale diamond films to significantly enhance their thermal conductivity? (2) Can such engineered nanoscale diamond films exhibit a strong anisotropy in thermal conductivity? (3). How does the thermal conductivity and anisotropy of such engineered films depend on the film thickness? Clearly, answers to these questions are not only of scientific significance and but also of technological impact on the development of thermal devices and also on the thermal management at the nanoscale. In the present work, using equilibrium molecular dynamics (EMD) simulations, we investigate the thermal transport properties of nanoscale diamond films with surfaces reconstructed in both the (2 1) dimer array and the self-assembled CNT array. For brevity, these two films are respectively named as dimersurface and CNT-surface diamond films. Our simulations show that compared to the dimer-surface, the CNT-surface can significantly enhance the thermal conductivity of nanoscale diamond films. In addition, a strong anisotropy in in-plane thermal conductivity for CNT-surface films is also observed. The present work indicates that the CNT-surface diamond films may play a vital role in thermal management for future nanoscale electronic devices.
2. Computational methods In our study, nanoscale diamond films are constructed from the bulk form. More specifically, the lattice structure of a nanoscale diamond film is extracted by selecting all the carbon atoms that fall within a rectangular slab in the bulk diamond. During the extraction, the top and bottom surfaces of the slab are chosen to be the {0 0 1} planes. Subsequently, the top and bottom surfaces of the film are artificially reconstructed and relaxed to form the 2 1 dimer-reconstruction surfaces and CNT-surfaces as shown in Fig. 1(a) and (b), respectively. In the setting, the x, y, and z directions are respectively the [1 0 0], [0 1 0] and [0 0 1] crystallographic directions. The direction of dimer rows or the CNT is along the y-direction. EMD simulations are employed to study the thermal properties of the diamond thin films using the LAMMPS package [27]. In all MD simulations performed herein, the bond order AIREBO potential [28] is used to describe the reactive, covalent bonding CC interactions. The simulations were carried out with a time step of 0.25 fs throughout. The size of simulation domain is 25.2 Å 25.2 Å in the x and y directions, as shown in Fig. 1. Periodic boundary condition (PBC) is applied in the in-plane (x and y) directions, which mimics the infinite size of diamond films by eliminating the boundary effects during the simulations. Free boundary condition (FBC) is applied in the z direction (the out-of-plane direction). Nosé-Hoover heat bath [29] is used to equilibrate the diamond film at 300 K with the isothermal-isobaric (NPT) ensemble. Once the temperature reaches
the required value, the thermostat is removed; then the heat flux J is calculated with micro-canonical (NVE) ensemble [30],
J¼
N X
ei v i þ
i
N N 1X 1 X ðF ij v i Þr ij þ ðF ijk v i Þðr ij þ r ik Þ; 2 ij;i–j 6 ijk;i–j–k
ð1Þ
where, ei and v i are the energy density and velocity associated with atom i, respectively. Vector rij denotes the interatomic distance between two atoms, and Fij and Fijk denote the two-body and three-body force, respectively. The thermal conductivity of diamond films is calculated based on the Green-Kubo formula (GKF). In GKF, the thermal conductivity is related to heat current autocorrelation function (HCACF) derived from the fluctuation–dissipation theorem and linear response theory [30],
j¼
Z
V kB T
2
1
hJ i ð0ÞJ i ðtÞidt;
ð2Þ
0
where kB is the Boltzmann constant, V is the volume of the system, and hJ i ð0ÞJi ðtÞi is the average heat flux autocorrelation function along the x and y directions, respectively. 3. Results and discussions We first examine a typical diamond film to study the in-plane thermal conductivity along the y-direction (the dimer row or CNT direction), that is, jy. For this case, the film thickness is H = 6a (where a = 3.556 Å is the diamond lattice constant), which is equal to 24 atomic layers. As shown in Fig. 2, the in-plane thermal conductivity jy of the dimer-surface film is 107 W/mK. On the one hand, this value is higher than that of diamond nanorod with a diameter of 1.3 nm (less than 50 W/mK) [7] due to the larger surface versus volume ratio and its resulting high phonon scattering of the nanorod, and also higher than the experimentally measured thermal conductivity of a polycrystalline diamond nano film [31] due to the strong phonon scattering from grain boundaries. On the other hand, this value is significantly lower than that of bulk diamond due to the strong phonon scattering of the film surfaces. Unlike bulk diamond that consists of pure sp3 hybridized single CC bond with a bond length of 1.539 Å [6], the dimer-structured film has surfaces that consist of p-bonded C@C dimers with a bond length of 1.382 Å [6]. The loss of atoms in the surface leads to the reduction in the coordination number. The bond-order–length–strength (BOLS) correlation indicates that when the coordination number of an atom is reduced, the equilibrium atomic distance between the under-coordinated atoms will contract, and the cohesive energy of the shortened bond will increase [32]. These changes will cause the increase in elastic modulus and inter-atomic force constant, which in turn leads to the difference in phonon frequencies in the surface and central sections, additional phonon scattering and reduced thermal conductivity [33,34]. As shown in Fig. 2, the in-plane thermal conductivity jy of the CNT-surface film is 310 W/mK, which is significantly higher (3 times) than the in-plane thermal conductivity jy of the dimer-surface film with the same thickness. The surface structure of the CNT-surface film consists of a large number of sp2 hybridized C atoms, which can be considered as an array of deformed single-wall (2,2) CNT on diamond (0 0 1) surface [15]. The nanotube array possesses eight-membered C rings, with the bottom one being embedded on the diamond (0 0 1) surface. An isolated (2,2) CNT has a thermal conductivity as high as 2436 W/mK [35], which indicates that the array of sp2 hybridized CNT serves as much more efficient paths for thermal energy transport than the dimer array. Although the thermal conductivity of CNT-surfaced diamond nanoscale film is still lower than that of the bulk diamond, it is still significantly higher than that of bulk silicon (140 W/mK at room
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Fig. 1. Schematics of surface-reconstructed diamond thin films. (a) Diamond thin film with dimer structures on the top and bottom surfaces. (b) Diamond thin film with CNT structures on the top and bottom surfaces. Atoms in gray, blue, green, and red are the carbon atoms in bulk, dimer, transition, and CNT region of the film, respectively. Note that the x, y and z direction are along the [1 0 0], [0 1 0] and [0 0 1] crystallographic direction, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
temperature) [22], and comparable to bulk copper, which is a commonly-used material for efficient thermal conduction. Our results suggest that nanoscale CNT-surface diamond films can be an efficient material for thermal management at the nanoscale. From Fig. 2, it is found remarkably that both the dimer- and CNT-surface diamond thin films exhibit a strong in-plane anisotropy in thermal conduction. For the dimer-surface film with H = 6a, the thermal anisotropy ratio c (= jy/jx) is 1.8 while for the CNT-surface film with the same thickness, it is further increased to 2.7. Such a large thermal anisotropy ratio has rarely been reported in other materials before, especially in bulk materials. Recently, two-dimensional (2D) materials, such as graphene and MoS2, have been suggested for use in nanoscale electronics and photonics devices [36–41]. However, these 2D materials show a nearly isotropic in-plane thermal conductivity. Very recently, phosphorene, another atomically thin 2D material, has been the focus of a considerable interest due to its strong anisotropic
in-plane thermal conductivity [42,43]. For phosphorene, the thermal conductance along the zigzag direction is about 40% larger than that along the armchair direction due to its strongly puckered ridge-accordion structure [43]. Compared to the anisotropy ratio of phosphorene, c = 1.4, the anisotropy ratio of the CNT-surface film, c = 2.7, is much higher. This highly anisotropic thermal property may be useful in the design of thermal channeling devices, thus showing another important advantage of CNT-surfaced diamond films besides the enhanced thermal conductivity. In order to understand the underlying mechanism of this remarkable thermal transport anisotropy in CNT-surfaced films, we have calculated the rescaled heat current autocorrelation function (HCACF), CJJ(t), of the film, which is defined as C JJ ðtÞ ¼ k VT 2 hJ i ð0ÞJ i ðtÞi, and compared with that of the bulk diaB
mond. It is known that the decay of HCACF in bulk material is exponential, following the macroscopic law of relaxation and Onsager’s postulate for microscopic thermal fluctuations [44].
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Fig. 2. The thermal conductivities of surface-reconstructed diamond thin films, that is, the dimer-surface and CNT-surface films. The film thickness H = 6a. The anisotropy ratios are also shown.
Also, the initial fast decay is due to the high frequency phonon modes while the slow decay corresponds to the low frequency phonon modes. From the bulk diamond HCACF as shown in Fig. 3(a), it is seen that there is a rapid initial decay (0.05 ps) followed by a long time exponential decay of the correlation function in bulk diamond, which is consistent with the double exponential function observed for the HCACF of bulk diamond by Che et al. [44]. Here, we have used the same double exponential function to fit the bulk HFACF [45],
C JJ ðtÞ ¼ AS expðt=sS Þ þ AL expðt=sL Þ
ð3Þ
The subscripts S and L refer to the short wavelength phonon modes and long wavelength phonon modes, respectively. The parameters AS, sS, AL, and sL are derived using a nonlinear least-square method, where, sS and sL correspond to the relaxation time of short wavelength and long wavelength phonons, respectively. As shown in Fig. 3(a) and Table 1, it is clear that in the bulk diamond, both sS and sL are weakly direction-dependent. From Fig. 3(b), it is also seen that the HCACF of the CNT-surface diamond film is very different from that of the bulk: the former shows a regular high frequency oscillation while the latter does not. We note that a similar oscillation was also observed in heterogeneous systems with different atomic masses [46,47]. From Table 1, it is also seen that the phonon relaxation time in the CNT-surface film is remarkably anisotropic. Unlike the slight difference in sS along the x and y directions, there is a much larger sL for the long wavelength (low frequency) phonons along the y direction than that along the x direction. In general, short wavelength (high frequency) phonons have limited contribution to thermal conductivity due to their low group velocity. Thus the large difference in relaxation time for the long wavelength phonons along the x and y direction is responsible for the remarkable direction-dependent thermal conductivity in CNT-surface diamond films. Clearly, the surface effect is the dominant factor that causes the anisotropic thermal transport. Below, we perform atomic vibrational analysis in the frequency domain to examine thermal transport in the different regions of the CNT-surface film. The phonon vibrational density of states (VDOS) in the frequency domain is calculated by taking the Fourier transform (FT) of the velocity autocorrelation functions of atoms belonging to the different regions in the system,
DðxÞ ¼
Z s 0
CðtÞ expðixtÞdt;
ð4Þ
Fig. 3. The heat current autocorrelation functions and the double exponential fitting for (a) bulk diamond and (b) CNT-surface film. The parameters obtained by fitting to the double exponential function (blue lines) are given in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Parameters obtained by fitting to the double exponential function of the heat current autocorrelation functions for both the bulk diamond and CNT-surface diamond thin film.
Bulk diamond x-Direction y-Direction
AS (W/mK)
sS (ps)
AL (W/mK)
sL (ps)
0.53 0.50
0.0068 0.0070
0.32 0.31
7.6 7.7
0.0065 0.0073
1.27 1.82
4.3 9.8
CNT-surface diamond film x-Direction 1.60 y-Direction 1.21
where x is the frequency, D(x) is the VDOS at frequency x, and
CðtÞ ¼ hv ðtÞv ð0Þi=hv ð0Þv ð0Þi is the velocity autocorrelation function. v ðtÞ is the atom velocity, h i denotes time and atom number averaged velocity autocorrelation function, and s ¼ 5 ps is the time duration to compute the velocity autocorrelation function and its corresponding discrete Fourier transform in a series of short runs. For comparison, we have also calculated the VDOS of carbon atoms in the bulk diamond. Fig. 4(a) shows the VDOS of carbon atoms in the bulk diamond while Fig. 4(b)–(d) show the VDOS in different regions of the
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CNT-surface film. To avoid the overlap of VDOS in the x and y direction, the VDOS in the y direction is plotted on top of that in the x direction. The carbon atoms in different regions of CNT-surface film are considered separately, as shown in the inset of Fig. 4(b). The C2-type atoms link the sp3 bonded C1-type atoms (in the bulk region of CNT-surface film) and sp2 bonded C3-type atoms (in the CNT). The VDOS of carbon atoms in the bulk diamond along the x direction is the same as that along the y directions, which is consistent with the common understanding that the thermal conductivity in bulk diamond is isotropic. It is found that the vibrational spectrum of C1 atoms is consistent with that in bulk diamond with a major peak at about 43 THz. This shows that the surface reconstruction only affects the lattice vibration locally. On the other hand, the major peak of vibrational spectrum of C3 atoms is at about 50 THz (Fig. 4(d)), which is markedly different from that in bulk diamond, but in good agreement with that in sp2 bonded carbon atoms in graphene [48]. Unlike in the y direction where C2 atoms have the same major spectrum peak as C1 atoms at about 43 THz, there is a large mismatch in vibrational spectrum peaks in the x direction between C2 and C3 atoms (with 36 THz and 50 THz, respectively). In the central region of the CNT-surface film, the VDOS along the x direction is nearly the same as that along the y direction, showing a weak directional dependence in thermal conduction. However, for heat energy transport within the surface region, the situation is distinctively different. As shown in Fig. 1(b), the C2 and C3 atom arrays are arranged alternatively along the x direction, while they are parallel along the y direction. Hence, the heat transport along the y direction is channeled mainly by these parallel heat paths, thus possessing a relatively high thermal conductivity. On the other hand, the heat energy transport along the x direction is channeled by the C2 and C3 atom arrays alternatively, similar to that in superlattice structures [49]. Clearly, the large mismatch in VDOS causes a large resistance in heat flow through the system,
therefore resulting in a low thermal conductivity and high anisotropic ratio. For comparison, the VDOS in different regions of the dimer-surface film are shown in Fig. 4(e) and (f). It is seen that the major peak of vibrational spectrum of Cd1 atoms is at 43 THz, which is consistent with those of atoms in bulk diamond and C1 atom in CNT-surface film. On the other hand, the major peak of vibrational spectrum of Cd2 atoms is at 50 THz, agreeing well with that in sp2 bonded carbon atoms in the CNT-surface film. Thus, the mismatch in vibrational spectrum peaks in the x direction between Cd1 and Cd2 atoms is responsible for the lower thermal conductivity along the x direction than that along the y direction. However, it is apparent that the mismatch in VDOS is not as significant as that in CNT-surface film. This is the reason why a lower anisotropic ratio is observed in the dimer-surface film than that in CNT-surface film. Next, we examine the thickness effect on the thermal conductivity and thermal transport anisotropy of the CNT-surface films. Based on first-principles calculations [15], the CNT arrays on the top and bottom surfaces are arranged in parallel when the number of atom layer is even (2n, where n is an integer). In contrast, when the number of atom layer is odd (2n + 1), the CNT arrays on the top and bottom surfaces are arranged in perpendicular, as shown in Fig. 5(a). Fig. 5(b) shows that for diamond films with an even number of atom layer, both jx and jy increase with the film thickness, while the anisotropy is independent of the thickness. However, for the diamond films with an odd number of atom layer, the thermal conductivity anisotropy disappears, although there is a similar thickness dependence in thermal conductivity. This is because in this type of diamond films, the CNT arrays on the two surfaces are arranged perpendicularly, thus the change in lattice symmetry destroys the orientation-dependent thermal transport. Fig. 5(d) shows the anisotropy ratio jy =jx as a function of the film thickness. Interestingly, the anisotropy ratio shows a strong oscillation where two distinct families ðH ¼ 2n and ðH ¼ 2n þ 1Þ
Fig. 4. The phonon vibrational density of states for (a) carbon atoms Cbulk in bulk diamond, (b) carbon atom C1 in the bulk region of CNT-surface film, (c) carbon atom C2 in the connecting region between the CNT and bulk regions of the CNT-surface film, (d) carbon atom C3 in the CNT region of the CNT-surface film, (e) carbon atom Cd1 in the bulk region of dimer-surface film, and (f) carbon atom Cd2 in the dimer region of the dimer-surface film.
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Fig. 5. (a) Schematics for parallel-arranged and perpendicularly-arranged CNT-surface films; (b) the thermal conductivity of parallel-arranged CNT-surface films along the x and y directions as a function of thickness; (c) the thermal conductivity of perpendicularly-arranged CNT-surface films as a function of thickness; and (d) the thermal anisotropy ratio (jy/jx) of parallel-arranged and perpendicularly arranged CNT-surface films as a function of thickness.
Fig. 6. Potential energy difference between diamond films with CNT-surface (ECNT) and dimer-surface (EDimer) under different conditions of temperature and strain.
are clearly visible. The oscillating behavior in the anisotropy ratio can be explained by the change in the surface symmetry of nanoscale diamond films with thickness. The parallel-arranged CNT-surface films exhibit a large thermal anisotropy with the
reduction of the film thickness. For example, for the film with a thickness of 10.7 Å, its thermal anisotropy ratio c can reach as high as 4.6. This remarkably high anisotropy ratio may be useful in heat channeling devices, such as phononic waveguide, in which a strong directional dependence in thermal conduction is required. Finally, we explore the energetics and structural stability of CNT-surface. Fig. 6 shows the potential energy of the CNT-reconstructed surface compared with that of the dimer reconstruction, with temperature changing from 100 K to 500 K, and strain from 1.2% to 1.6%. It is interesting to find that in the considered ranges of temperature and strain, the potential energy of the CNT surface is always lower than that of the dimer surface, and the difference in potential energy decreases with increasing temperature. At room temperature and zero strain, the potential energy of CNT-surface is about 41 meV/atom lower than that of the dimer-surface, indicating that the CNT-surface is energetically more favorable. This is consistent with the first-principles calculation results that the binding energy of CNT surface is slightly lower than that of the dimer structure [15]. Although the binding energies of dimer-surface and CNT-surface are close to each other [15], there is a 1.6 eV per unit cell (10 atoms) barrier in transition from dimer-surface to CNT-surface. Moreover, the H-terminated dimer is energetically more stable than H-terminated CNT-surface [15]. This is why so far there is no CNT-surface observed in natural diamond surface.
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However, for chemical vapor deposition (CVD) growth of diamond nanofilm, the situation is different. The growth of diamond films has been of great interest because diamond nanoscale film has a wide range of applications in electronic, mechanical, optical and thermal devices. Thermal CVD is an efficient method for growing high quality diamond films with low concentration of defects. CVD of diamond film is typically initiated by dissociation of a gaseous mixture of H2 and hydrocarbon precursor such as methane or acetylene. [50] Kang and Musgrave [51] studied the surface chemistry and reaction path of dimer-opening on the diamond (2 1) surface with adsorbed CH3, and found that the adsorbed CH3 can be converted to CH2 by H abstraction, and the dimer-opening is followed by ring-closing process, which is the rate limiting reaction. Thus in thermal CVD using methane as precursor, dimer-surface should grow continuously. However, if a pair of molecules (each consists of two carbon atoms, for example, acetylene) adsorb on dimer surface of diamond, they will form a bridge state [15]. Rotations of these molecules by 45° and 45° of the bridge site, respectively, will lead to the formation of tube surface structure. From first-principles calculation, the transition from bridge site to CNT-surface is smooth, with no barrier [15]. In contrast, there is an energy barrier of 2–3 eV required for the continuous growth of dimer structure [52]. Thus CNT-surface is expected in thermal CVD growth with carbon rich condition, for example, using acetylene as precursor. 4. Conclusions In summary, we have investigated the thermal transport behavior of surface-reconstructed nanoscale diamond films using molecular dynamics simulation. It is found that for the same film thickness, the film with the CNT-surface shows a 3-fold enhancement in thermal conductivity compared to that with the 2 1 reconstructed dimer surface. In addition, a remarkable thermal anisotropy is observed in the CNT-surface diamond film, with an anisotropy ratio of 2.7 for the 2 nm thick film and 4.6 for the 1 nm thick film. From phonon vibration spectrum analysis, it is understood that this remarkable anisotropy is originated from orientation-dependent lifetime of long wavelength phonons due to the surface CNT structures. The enhanced thermal conductivity and remarkably high anisotropy of the CNT-surface diamond films revealed from the present work highlight an important route to tune the thermal transport of nanoscale structures by surface engineering. The present work also shows that the CNT-surface diamond films may be promising for applications in thermal management and novel phononic devices. Acknowledgment The authors gratefully acknowledge the financial support from the Agency for Science, Technology and Research (A⁄STAR), Singapore and the use of computing resources at the A⁄STAR Computational Resource Centre, Singapore. References [1] K.E. Spear, J.P. Dismukes, E. Society, Synthetic Diamond: Emerging CVD Science and Technology, John Wiley & Sons, New York, 1994. [2] A. Krueger, Diamond nanoparticles: jewels for chemistry and physics, Adv. Mater. 20 (12) (2008) 2445–2449. [3] N.V. Novikov, New trends in high pressure synthesis of diamond, Diamond Relat. Mater. 8 (1999) 1427–1432. [4] J.A. Viecelli, F.H. Ree, Carbon particle phase transformation kinetics in detonation waves, J. Appl. Phys. 88 (2) (2000) 683–690. [5] J.P. Boudou, P.A. Curmi, F. Jelezko, J. Wrachtrup, P. Aubert, M. Sennour, et al., High yield fabrication of fluorescent nanodiamonds, Nanotechnology 20 (23) (2009) 235602–235611.
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