Effect of Defects on the Thermal Transport Across the Graphene

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C: Physical Processes in Nanomaterials and Nanostructures

Effect of Defects on the Thermal Transport Across the Graphene/Hexagonal Boron Nitride Interface Maoyuan Li, Bing Zheng, Ke Duan, Yun Zhang, Zhigao Huang, and Huamin Zhou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02750 • Publication Date (Web): 06 Jun 2018 Downloaded from http://pubs.acs.org on June 7, 2018

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The Journal of Physical Chemistry

Effect of Defects on the Thermal Transport across the Graphene/Hexagonal Boron Nitride Interface Maoyuan Lia, Bing Zheng a,Ke Duanb, Yun Zhang a, *, Zhigao Huanga, Huamin Zhoua a

State Key Laboratory of Material Processing and Die & Mold Technology, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China

b

State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

* Corresponding author: Tel: 86-27-87543492. E-mail: [email protected] (Yun Zhang);

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Abstract Owing to its extraordinary physical properties and potential for next generation nanoelectronics,

the

in-plane

graphene/hexagonal

boron

nitride

(Gr/h-BN)

heterostructure has been fabricated recently and gained a lot of attention. The defects located at the interface such as vacancies, topological defects are inevitable during the growth process. However, the effects of the defects on the interfacial thermal conductance between the Gr/h-BN interface have not well understood. In this work, the effects of defects on the interfacial thermal conductance across the Gr/h-BN interface have been systematically investigated by using nonequilibrium molecular dynamic simulations. The different types of single-vacancy and Stone-Wales defects were considered. The simulation results showed that the interfacial thermal conductance would decrease linearly with the increase of single-vacancy concentrations and it decreased with the existence of Stone-Wales defects, then reached a platform as concentration increased, the value of which was close to the interfacial thermal conductance of Gr/h-BN with the line defect formed by Stone-Wales defects. The analyses on the phonon vibration power spectrums and the stress analysis indicated that the degradation in the in-plane modes accounted for the decrease caused by single-vacancy, while the stress concentration distribution and the ripple appeared near the interface dominated the degradation caused by Stone-Wales defects. Additionally, the effects of system dimensions and temperature on the interfacial thermal conductance were investigated.

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1. Introduction In recent years, graphene and its heterostructures have attracted tremendous attentions due to their unusual electronic, mechanical, optical and thermal properties1-6. Since graphene is a zero-bandgap semimetal while the hexagonal boron nitride( h-BN) possesses a wide bandgap (5.9 eV)7 and a similar lattice constant with graphene, the graphene/hexagonal boron nitride (Gr/h-BN) in-plane heterostructure has been successfully fabricated using chemical vapor deposition method

2, 4, 8

and

predicted theoretically to possess fascinating physical properties, such as negative differential resistance behavior9, unique electrical rectifying effect10 and minimum thermal conductance

11

. These novel properties are strongly dependent on the mass

ratio, shapes of the two compositions, especially the interface between graphene and h-BN domains12. For example, it has been demonstrated that the graphene nanoribbons embedded in h-BN with zigzag interface are half-metallic, while those with armchair interface are semiconducting10, 13. Using the non-equilibrium Green’s function method and density functional theory, An et al10. found that the Gr/h-BN heterostructure with a left-right type interface displayed a rectifying effect, while possessed a negative differential resistance effect with an up-down type interface. In addition to the above studies about electronic properties, the thermal transport properties across the interface is also of great interest due to its key role in determining the overall thermal conductance of the heterostructure14-15. Using molecular dynamics (MD) method, Hong et al.16 found that the interfacial thermal conductance (ITC) increased with the increasing length and temperature of the 3



Gr/h-BN heterostructures. Ong et al.17 showed that the longitudinal tensile strain led to significant enhancement in ITC caused by the improved alignment of the flexural acoustic phonon bands in both graphene and h-BN. The thermal transport behavior3, 18 and mechanical properties19 in coplanar polycrystalline Gr/h-BN heterostructures have also been investigated and exhibited a grain size/distribution-dependent behavior. These previous studies have improved our understanding of the interfacial thermal transport across the Gr/h-BN interface. Nevertheless, most of the previous simulation works about thermal transport properties of Gr/h-BN heterostructures have focused on the interface without any defect15, 20. However, several defects such as single-vacancy (SV), Stone-Wales(SW) are unavoidably introduced into the interface during the growth process4,

21-23

. Recently, discontinuities and misfit dislocations2 near the

interface have clearly been observed using scanning tunneling microscope by Lu et al 23

. Using density function theory, Ding et al.24-25 have investigated the effect of

defects at the interface on the electronic and mechanical properties of Gr/h-BN, which depended on the type and concentration of defects. More recently, Gao et al.26 showed that the introduction of Stone-Wales defects at the interface could control the asymmetry and direction of thermal transport with the similar effect of applying mechanical tensile strain. In addition, previous experimental and theoretical researches have indicated that the defects have significant impacts on the thermal properties of the pristine graphene or h-BN5,

27-30

. However, the effects of defects at the interface on the interfacial 4


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thermal properties of Gr/h-BN interface have not been well understood31-32. It is of great significance to fully understand the (a) relationship between the defects at the interface and the ITC of Gr/h-BN and (b) the underlying enhancement or degradation mechanism of the defects on the interfacial thermal properties. In this work, we have conducted a series of nonequilibrium molecular dynamics (NEMD) simulations to investigate the effects of defects on the ITC of Gr/h-BN heterostructures. Different types of SV and SW defects were randomly dispersed at the interface. The phonon vibration power spectrums and stress distributions were analyzed and compared to understand the mechanism of the interfacial thermal transport between graphene and h-BN. Additionally, the effects of system dimensions and temperature were also studied.

2. Computational Methods 2.1 Molecular model of Gr/h-BN heterostructure

MD simulations were conducted to evaluate the thermal transport across the Gr/h-BN interface, and the molecular models were first constructed. Since previous experimental results21-22 have showed that the formation of Gr/h-BN with zigzag interface was more preferred than that with armchair interface, only the zigzag interface was studied. The Gr/h-BN heterostructures with zigzag interface, which have the type of the C-B and C-N bonding, are shown in Fig.1(a)-(b). Since the two types have the similar interfacial thermal properties as evaluated by previous studies17,

5



32

and the present work focused on the effects of defects, the Gr/h-BN heterostructure

with C-N bonding was used. The Gr/h-BN heterostructure without any defect at the interface was constructed, as shown in Fig.1(c). The cross-section dimension of the system was 220 Å × 60 Å. Two common types of defects at the interface, including SV and SW-5577 defect were considered (as shown in Fig.1(c)), which have been observed in many experimental studies22-23,

33

. The SV defect was created by

removing one carbon atom or nitride atom at the interface, which were named as SV-C and SV-N, respectively. The SW-5577 was created by rotating one of the C-C or the C-N bonds by 90° at the interface, which were named as SW-CC and SW-CN, respectively. The defect concentration of SV was defined as the number density of atoms removed from the interface. The concentration of SW was defined by considering two defective atoms for each defect. The two kinds of defects were randomly distributed at the interface, respectively. All the MD simulations were conducted by The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)34, and the velocity-Verlet method was used to integrate the equation of motions. The atoms at both ends in the x-direction were fixed, the free boundary condition is applied both in y- and z-directions. The optimized C-B-N parameters35 for the Tersoff potential (see detailed descriptions in Supplementary Information Section I) given in Ref. [35] are used to simulate inter-atomic interaction between C, N and B atoms as it has been successfully employed to study the thermal properties in graphene-boron nitride systems16, 32. A time step of 0.25 fs was used in the whole stages. 6


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Figure 1. Molecular model of (a) the Gr/h-BN zigzag interface for C-B bonding and (b) C-N bonding (c) Gr/h-BN heterostructure.

Figure 2. Types of defect studied in this work, Single vacancy with (a) carbon atoms and (b) nitride atoms; Stone-Wales with (c) C-N bond rotated and (d) C-C bond rotated.

2.2 Calculation of ITC

After the initial models were established, the ITC was calculated by using NEMD methods. The system was first relaxed to reach an equilibrium state, the relaxation involved three different steps. At the beginning, an energy minimization was performed using the conjugate gradient algorithm. The system was then relaxed in a 7



canonical NVT ensemble (i.e., constant number of atoms, volume and temperature) at temperature T=300K for 1 ns followed by relaxation using a microcanonical NVE ensemble (i.e., constant number of atoms, volume and energy) for another 2.5 ns. The total energy was conserved and the temperature of the whole system fluctuated slightly around 300K, which indicated that the equilibrium stage was reached. In the NEMD method, the atoms near the left end (graphene) and the right end (h-BN) were treated as the heat baths, the temperature of which was set to be TH =310 K and TC =290 K by Langevin thermostat, respectively. The accumulated energies added to the hot bath and removed from the cold bath as a function of time are calculated. The sum of added/removed energy is equal to zero, and thus the total energy is conserved. The heat flux along the x-direction Jx can be expressed by:

Jx =

dE / dt (1) A

where E is the accumulated energy, t is the simulation time in NVE ensemble and

A is the cross-section area given by the width multiplied by thickness. The thickness was around 3.35 Å for all the sheets in present study, which is the average value between the Van der Waals thickness of freestanding graphene (i.e., 3.4 Å) and

h-boron nitride (i.e., 3.3 Å) sheet. Once the steady state temperature profiles along the heat flux were reached, a discontinuous temperature ∆T that is, would exist at the interface. Then, the ITC Gk can be calculated by the expression: Gk = J x ∆T

(2)

After the steady state was reached and the temperature profile was found to be 8


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stable, an additional 10 ns was performed. The values Gk were obtained from the last ten different time blocks, and the final value was the average of all calculated values. The error bars were determined by the standard deviation.

2.3 Phonon density of states (PDOS)

The phonon transport across two interface materials can be determined by the overlap of the PDOS between them. Many previous studies have shown that the PDOS is a useful method to understand the thermal transport behavior at the Gr/h-BN interface9,

29, 32, 36

. The PDOS can be obtained by calculating the Fourier

transformation of atomic velocities autocorrelation function at the equilibrium state: τ

D (ω ) = ∫ Γ ( t ) cos (ωt )dt

(3)

0

where ω is frequency, D(ω) is vibration density of state at frequency ω, τ is the total time, and Γ(t) is the velocity autocorrelation function of atoms, and it is given by:

Γ (t ) = v (t ) ⋅ v ( 0)

(4)

where v(t) is the atom velocity at time t, denotes time and atom number-averaged velocity autocorrelation function. In this study, the velocity was correlated every 5 fs with a total integration time τ=25 ps. To quantify the degree of match in the PDOS, an overlap factor S is adopted and calculated by37:

9



S=

∫

∞

0

∫

∞

0

DGr (ω ) Dh − BN (ω )d ω ∞

DGr (ω ) d ω ∫ Dh − BN (ω ) d ω

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(5)

0

where DGr(ω) and Dh-BN(ω) denotes the PDOS at frequency ω of graphene and

h-BN, respectively.

3.Results and discussion 3.1 Interfacial thermal conductance

Based on the NEMD methods described in Section 2, the ITC between Gr/h-BN without any defect was calculated first. The steady-state temperature file along the heat flux direction is shown in Fig.3(a). A discontinuous temperature ∆T at the interface is caused by the thermal contact resistance between graphene and h-BN. By neglecting the jumps near the hot/cold bath, a linear temperature gradient is estimated for the graphene and h-BN domains, and the end value are adopted for the ∆T calculation. The energies added to/ removed from the hot/cold bath as a function of time are shown in Fig.3(b). Based on the equation (1) -(2), the ITC value is about 14.86 GW/m2K at 300K with a dimension of 220 Å × 60 Å, which is in a reasonable range for the simulation results observed by other researchers3, 9, 16-17, 36 (i.e., ~ 3 to 15

GW/m2K). The difference was due to the different system dimension, force field and the Gr/h-BN interface types. This value is much higher than some other graphene-based in-plane heterostructure, such as Gr/silicene (~0.26 GW/m2K)38, Gr/MoS2(~0.25GW/m2K)31 and indicates that the Gr/h-BN in-plane heterostructure

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transports heat efficiently. Besides, the ITC between graphene and h-BN in the vertical heterostructure via van der Waals interactions has also been calculated using NEMD simulations, and the value was only 3.37 MW/m2K39. The higher ITC in the Gr/h-BN in-plane heterostructure (three orders of magnitude higher than that in the vertical heterostructure) is due to the stronger interfacial covalent bond compared with the van der Waals forces.

Figure 3. (a) Steady-state temperature profile of Gr/h-BN heterostructure without any defect obtained using the NEMD approach at 300 K. The color bars highlight the hot/cold bath in simulation. (b) Energies added to the hot bath and removed from the cold bath according to the time.

To further understand the thermal transport behavior across Gr/h-BN interface, the PDOS for the graphene and h-BN are calculated and displayed in Fig4(a). The good overlap of their PDOS curves indicate the efficient heat transport across the interface, thus leading to the high ITC. Since the graphene is highly anisotropic, its PDOS is further decomposed into the in-plane and out-of-plane modes, as shown in Fig4(b). The PDOS peaks of graphene appear at ~50 THZ and lower frequencies (~10 and 25 THZ), which represent the in-plane and out-of-plane modes, respectively. It is 11



observed that the overlaps between the PDOS of graphene and h-BN are distributed in the overall frequency range, especially at the low frequency (

Effect of Defects on the Thermal Transport Across the Graphene

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