Effects of nanosized constriction on thermal transport properties of graphene
© Yao et al.; licensee Springer. 2014
Received: 28 May 2014
Accepted: 9 August 2014
Published: 21 August 2014
Thermal transport properties of graphene with nanosized constrictions are investigated using nonequilibrium molecular dynamics simulations. The results show that the nanosized constrictions have a significant influence on the thermal transport properties of graphene. The thermal resistance of the nanosized constrictions is on the order of 107 to 109 K/W at 150 K, which reduces the thermal conductivity by 7.7% to 90.4%. It is also found that the constriction resistance is inversely proportional to the width of the constriction and independent of the heat current. Moreover, we developed an analytical model for the ballistic thermal resistance of the nanosized constrictions in two-dimensional nanosystems. The theoretical prediction agrees well with the simulation results in this paper, which suggests that the thermal transport across the nanosized constrictions in two-dimensional nanosystems is ballistic in nature.
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KeywordsGraphene Ballistic resistance Nanosized constriction Molecular dynamics simulation
Graphene is a two-dimensional (2D) material formed of the honeycomb lattice of sp2-bonded carbon atoms. The strong bonding and perfect lattice structure give its unique thermal properties [1–3]. As Balandin et al. [1, 2] demonstrated, the thermal conductivity of graphene is up to 5,400 W/(m · K), which makes it one of the most promising base materials for next-generation electronics and thermal management [2–6]. Additionally, compared with other high-conductivity materials, such as carbon nanotubes [7–9], graphene is much easier to be fashioned into a broad range of shapes. Such flexibility makes possible the utilization of graphene.
Usually, limited by the synthesis and fabrication procedure, graphene inevitably has a variety of defects, such as vacancies, Stone-Wales defects, and impurities [10, 11]. Many scholars have demonstrated that these defects are obstacles to heat transfer and create additional sources of phonon scattering in graphene [12–16], especially when the characteristic dimension is less than the phonon mean free path (approximately 775 nm at room temperature) . Hao et al.  performed molecular dynamics (MD) simulations on defected graphene sheets. They observed that the increasing defect concentration dramatically reduces the thermal conductivity of graphene. Chien et al.  investigated the effect of impurity atoms in graphene and found a rapid drop in thermal conductivity, where hydrogen coverage down to as little as 2.5% of the carbon atoms reduces the thermal conductivity by about 40%. So we can conclude that the thermal transport properties of graphene are very sensitive to its own structures. Besides these defects, the structural configuration is another important but less studied factor impacting the thermal properties, and thus, it can affect the lifetime and reliability of the graphene-based nanodevices further because these devices have more complex shapes in engineering situations. Therefore, from a practical point of view, the investigation on how to predict or tune the thermal transport properties of graphene with a variety of shapes is especially useful for thermal management.
Recently, Xu et al.  investigated the transport properties of various graphene junctions and quantum dots using nonequilibrium Green's function method and found that the thermal conductance is insensitive to the detailed structure of the contact region but substantially limited by the narrowest part of the system. Huang et al.  constructed a sandwich structure with atomistic Green's function method, where two semi-infinite graphene sheets are bridged by a graphene nanoribbon (GNR). They mainly focused on the phonon transport behavior in GNR and observed that the thermal conductance increases with the width of GNR at fixed length and decreases with GNR length at fixed width.
This paper presents the effect of the nanosized constrictions on the thermal transport properties of graphene studied by the nonequilibrium molecular dynamics (NEMD) simulations. We calculate the thermal transport properties of graphene with those constrictions, and the effects of the heat current and the width of the constriction were explored in detail. Further, based on the phonon dynamics theory, we develop an analytical model for the ballistic resistance of the nanosized constrictions in two-dimensional nanosystems, which agrees well with the simulation results in this paper.
where N is the number of atoms per slab, kB is the Boltzmann constant, and P i is the momentum of the i th atom.
Results and discussion
Nine graphene sheets with different-sized constrictions are simulated in this paper, and the corresponding pristine one is also designed for comparison. The constriction widths of nine cases are 0.216, 0.648, 1.08, 1.512, 1.944, 2.376, 2.808, 3.24, and 3.672 nm, respectively. And four heat currents (i.e., J = 0.2097, 0.3146, 0.4195, and 0.5243 μW) are performed for all the cases.
where ω is the frequency of phonons, ωm is the maximum frequency, ℏ is the reduced Planck constant, is the occupation of phonons given by the Bose-Einstein distribution, D(ω) is the phonon density of states, vg(ω) is the phonon group velocity, τ(ω,θ) is the transmissivity of phonons, θ is the polar angle, and φ is the azimuthal angle. What is more, in the ballistic limit, two limiting cases of phonon transmission behavior are further discussed, which is differentiated depending on the characteristic size of the constriction (a) relative to the dominant phonon wavelength λd. If a is much larger than λd, which is the geometric scattering limit, the transmissivity of phonons is described as τ(ω,θ) = cosθ. If a is near or smaller than λd, which is the Rayleigh scattering limit, the effect of the wave diffraction should be considered and the calculation of the transmissivity is more complex . It can be seen that the theoretical modeling of the constriction resistance is based on the three-dimensional (3D) system so far. But for graphene, a 2D material, it is invalid.
From Equation 9, the ballistic constriction resistance is inversely proportional to the cross section area (A), i.e., the width of the constriction (w), which is consistent with the conclusion of MD. And the predicted results, obtained by substituting cv = 6.81 × 105 J/(m3 · K)  and vg = 17.45 km/s into Equation 9, are compared quantitatively with MD results in Figure 4. It can be seen that the present model predicts well the thermal resistance of the constriction in graphene, which suggests that thermal transport across the nanosized constrictions in 2D nanosystems is ballistic in nature.
Graphene has shown great potential for the applications in high-efficiency thermal management and nanoelectronics due to its exceptional thermal properties in the past few years. Understanding the underlying mechanism of controlling the thermal properties of various structures is of considerable interest. In this paper, systems of rectangular graphene sheets with various nanosized constrictions are constructed by embedding linear vacancy defects and the thermal transport properties are investigated by using nonequilibrium molecular dynamics method. The results show that the nanosized constriction has a significant influence on the thermal transport properties of graphene. And the constriction resistance is on the order of 107 to 109 K/W at 150 K, which reduces the thermal conductivity by 7.7% to 90.4%. Besides, the constriction resistance is inversely proportional to the constriction width and independent of the heat current. These findings indicate that the desired thermal conduction can be achieved via nanosized constrictions. Moreover, we develop a ballistic constriction resistance model for 2D nanosystems, which corresponds to the case when the mean free path of phonon is much larger than the characteristic dimension of the constriction. The predicted values of this model agree well with the simulation results in this paper, which suggests that the thermal transport across nanosized constrictions in 2D nanosystems is ballistic in nature.
nonequilibrium molecular dynamics.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51322603, 51136001, and 51356001), Science Fund for Creative Research Groups (No. 51321002), the Program for New Century Excellent Talents in University, Tsinghua University Initiative Scientific Research Program, the Tsinghua National Laboratory for Information Science and Technology of China, and the Foundation of Key Laboratory of Renewable Energy Utilization Technologies in Buildings of the National Education Ministry in Shandong Jianzhu University (No. KF201301).
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