GRAPHENE/HEXAGONAL BORON NITRITE IN PLANE HETERO-STRUCTURE SIMULATIONS

By

PEICHEN WU

A THESIS PRESENTED TO THE GRADUATE SCHOOL

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2019

© 2019 Peichen Wu

To my parents and my grandparents

4

ACKNOWLEDGMENTS

I would like to express my gratitude to Dr. Chen who shared her precious

experience with me and gave me a lot of help and advices. My thanks also go to Dr.

Weixuan Li, Dr. Zexi Zheng, Dr. Yang Li, Mr. Shihao Xu and all other members in

Atomic and Multiscale Mechanics laboratory. I am grateful for their patience and help in

this period. It is my honor to study here. I would also like to extend my gratitude to my

committee member Dr. Kumar.

At last, I want to thank my parents, my grandparents and my girlfriend for their

endless love and selfless support. They are my spiritual support.

5

TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 6

LIST OF FIGURES .......................................................................................................... 7

ABSTRACT ..................................................................................................................... 8

CHAPTER

1 GENERAL INTRODUCTION ..................................................................................... 9

Introduction to Graphene and its Heterostructures ................................................... 9 Synthetic Method for H-BN/Graphene Heterostructures ......................................... 12

Molecular Dynamics................................................................................................ 14 Nonequilibrium Molecular Dynamics Method .......................................................... 16

Graphene/hBN Lateral Interface ............................................................................. 20

2 SIMULATION .......................................................................................................... 21

Potential for Graphene/hBN .................................................................................... 21

Relaxing Process .................................................................................................... 22

Simulation Details and Result ................................................................................. 23 Part 1: Investigate the Effect of Interface Density on Interface Thermal

Conductance ................................................................................................. 23

Part 2: Investigate the Effect of Defects Density on Interface Thermal Conductance ................................................................................................. 27

Part 3: Heat Pulse Simulation on Two Lateral Interface Graphene/hBN .......... 31

3 CONCLUSION AND IMPROVMENTS .................................................................... 33

LIST OF REFERENCES ............................................................................................... 34

BIOGRAPHICAL SKETCH ............................................................................................ 36

6

LIST OF TABLES

Table page 2-1 Specifications of models and thermal conductance result .................................. 24

2-2 Defected interface thermal conductance ............................................................ 28

7

LIST OF FIGURES

Figure page 1-1 Graphene’s atomic structure............................................................................... 10

1-2 Graphite’s atomic structure ................................................................................. 11

1-3 MoS2/Graphene Van der Waals hetero-structure............................................... 11

1-4 WS2/Graphene Van der Waals hetero-structure. ............................................... 11

1-5 h-BN/Graphene van der Waals superlattice. ...................................................... 12

1-6 h-BN/Graphene lateral and vertical hetero-structures. ....................................... 12

1-7 In-site CVD method for synthesizing lateral Graphene-hBN hetero-structure .... 13

1-8 Synthesis process for vertical stacked hBN/Graphene ....................................... 13

1-9 NEMD method .................................................................................................... 18

1-10 Temperature graph of hexagonal boron nitride .................................................. 19

1-11 Temperature jump at graphene/hexagonal boron nitride interface ..................... 19

1-12 Topological defects ............................................................................................. 20

1-13 5|7 defects .......................................................................................................... 20

2-1 Optimized Tersoff potential parameter ............................................................... 22

2-2 Simulation models for part 1 ............................................................................... 25

2-3 Temperature gradient graphs ............................................................................. 26

2-4 Zoom-in image of graphene/hBN 5|7 defects interface ...................................... 29

2-5 Out of plane deformation around 5|7 defects...................................................... 30

2-6 Stress distribution of coherent interface and defected interface ......................... 30

2-7 Heat pulse model ................................................................................................ 31

2-8 The process of heat pulse going through the interface ....................................... 32

8

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science

GRAPHENE/HEXAGONAL BORON NITRITE IN PLANE HETERO-STRUCTURE

SIMULATIONS

By

Peichen Wu

May 2019 Chair: Youping Chen Major: Mechanical Engineering

The purpose of this research is to investigate the effect of interface density and

defects density on graphene/hexagonal boron nitride interface thermal conductance.

This research is doing simulations on nanoscale. Molecular dynamics is the main

method used in this research and direct method (NEMD) is also used to calculate the

interface thermal conductance.

In this thesis, the effect of defects density and interface density on

graphene/hexagonal boron nitride interface is quantified. The process of heat pulse

goes through the interface is also simulated.

9

CHAPTER 1 GENERAL INTRODUCTION

Introduction to Graphene and its Heterostructures

[1] Graphene has attracted a lot of scientific attention since it is firstly isolated

from graphite at 2004. Graphene has many fascinating properties, such as superhigh

electron carrier mobility, ultra-high thermal conductivity, excellent mechanical strength,

elasticity and stiffness, which has a great potential for future Nano-electronic devices

applications. Combining graphene and hexagonal boron nitride (hBN) to form lateral

heterostructure can reveal some new properties, such as tunable electronic and

magnetic properties, which can extend the applications of graphene can be used.

Graphene/hBN can be used in various nano-electrical devices and the interface thermal

conductance is main factor that limit the heat dissipation of nano-devices. Thus, finding

ways to enhance the interface thermal conductance is very important. What’s more,

combining graphene with other materials can also reduce the whole materials’ thermal

conductivity which is good for thermal-electric applications.

Figure 1 shows the atomic structure of Graphene. Graphene consists of many

hexagonal carbon lattices and all the carbon atoms are arranged in a single layer. When

many layers of graphene stacked together in an out-of-plane direction, the materials will

become graphite. The graphite’s atomic structure is showed in figure 2.

Graphene’s lattice constant is 2.46 A and it can be combined with other materials

to form in plane and vertical heterostructures, such as MoS2/graphene, WS2/graphene,

Germanene/graphene, hBN (hexagonal boron nitride)/graphene and so on. [2] [3]

Figure 3 and 4 shows MoS2/Graphene Van der Waals hetero-structure and

WS2/graphene van der Waals heterostructures. What’s more, these heterostructures

10

can also form superlattice if they are repeated periodically on vertical or lateral direction,

such as hbn/graphene van der Waals superlattice.

h-BN (hexagonal boron nitride)’s atomic structure is very similar to graphene. It

consists of boron and nitride atoms, which are arranged in a hexagonal lattice. h-BN’s

lattice constant is 2.5 A which is very similar to graphene. It can form lateral and vertical

hetero-structures with graphene like figure 6. [4] Some theoretical calculations show

that Graphene/h-BN lateral hetero-structure can have a relatively high electron carrier

mobility and lateral Gr/h-BN also exhibit some other excellent properties, such as [5] low

thermal conductivity and [6] metallic behavior. As for vertical van der Waals hetero-

structures, Gr/hbn has a high electron carrier mobility and shows a [7] Hofstadter

butterfly effect. Thus, Gr/h-BN is promising combination for graphene hetero-structures.

Figure 1-1. Graphene’s atomic structure (yellow atom is carbon atom)

11

Figure 1-2. Graphite’s atomic structure

Figure 1-3. MoS2/Graphene Van der Waals hetero-structure

Figure 1-4. WS2/Graphene Van der Waals hetero-structure.

12

Figure 1-5. h-BN (hexagonal boron nitride)/Graphene van der Waals superlattice. (Yellow atom is carbon, purple is boron atom and blue are nitride atom.)

Figure 1-6. h-BN/Graphene lateral and vertical hetero-structures. (Yellow atom is carbon, red atom is boron and blue atom is nitride atom)

Synthetic Method for H-BN/Graphene Heterostructures

Lateral hBN/Graphene hetero-structure mainly use in situ chemical vapor

deposition (CVD) synthesis method. Graphene is firstly put on a super-flat substrate and

hexagonal boron nitride then grows on the substrate by CVD. The in-situ CVD method

is shown on [8] figure 7. Synthesizing vertically stacked hBN/Graphene usually use ex-

13

situ CVD method to grow hBN on the Graphene. What’s more, the growing order can

also be changed. Graphene can also grow on hBN by a copper substrate. H-

BN/Graphene/hBN/graphene can also be synthesized if we use above method

sequentially. The synthesis process for vertically stacked hBN/Graphene is showed on

[9] Figure 8.

Figure 1-7. In-site CVD method for synthesizing lateral Graphene-hBN hetero-structure

Figure 1-8. Synthesis process for vertical stacked hBN/Graphene

14

Molecular Dynamics

Molecular dynamics (MD) is a simulation method, which is very useful in

nanoscale. This method mainly simulates the reaction between different atoms by

introducing potential energy function to the whole system.

In real materials, atoms always have reactions with each other. So, the atoms

are always in a dynamic state and using a function of potential energy has the most

probability to show the motion of atoms. The force between atoms at any given position

can be calculated by the potential function. Then force can determine the motion of

atoms according to newton’s law.

The basic idea behind MD is that simulation time is divided into many time steps

and each time step is less than 10^-15 second. Using the potential function to calculate

the force acting on each atom at each time step. Then MD will update each atom’s

position and velocity by using Newton’s law.

Newton’s second law is

F = ma (1-1)

F(x) = −∇U(x) (1-2)

Where x is the position of each atoms, U is the potential function, F is force on

each atom, m is atom mass and a is acceleration of atom.

The derivative of atom position is equal to velocity and the derivative of atom

velocity is equal to acceleration. So, [10] the equations of motion are written in the

following form.

𝑑𝑥

𝑑𝑡= 𝑣

(1-3)

15

𝑑𝑣

𝑑𝑡=

𝐹(𝑥)

𝑚

(1-4)

Where x is the position of each atom and it has a value on x, y and z direction.

So, the equation will have 3n coordinates and 3n velocity for n atoms. [10] Solving the

equation can get the following result:

𝑥𝑖+1 = 𝑥𝑖 + 𝛿𝑡𝑣𝑖 (1-5)

𝑣𝑖+1 = 𝑣𝑖 +𝛿𝑡𝐹(𝑥𝑖)

𝑚

(1-6)

By using [10] Leapfrog Verlet integration method, a more accurate form of result

can be obtained:

𝑥𝑖+1 = 𝑥𝑖 + 𝛿𝑡𝑣𝑖+1/2 (1-7)

𝑣𝑖+1/2 = 𝑣𝑖−1/2 +𝛿𝑡𝐹(𝑥𝑖)

𝑚 (1-8)

Boundary conditions for MD simulation has 4 four type which are p, f, s and m. (s

is periodic, f is non-periodic and fixed, s is non-periodic and shrink-wrapped, m is non-

periodic and shrink-wrapped with a minimum value). Normally, the boundary conditions

for simulations are periodic due to the simulation size is very small.

There are many different types of potentials in MD, such as SW, tersoff,

Charmm, Amber, Lennard-Jones and so on. As for simulations in this research, main

type of potential is tersoff and Lennard-Jones potential.

Generally, there are 4 procedures for MD simulations. First, construct the

materials structure and set atom mass and velocity. Second, set the boundary

16

conditions and choose the potential. Third, give command to the model, such as, set

simulation time, temperature, region, velocity, heat and so on. Fourth, output the

quantities, such as, coordinates of atoms, velocity, temperature, energy and so on.

Nonequilibrium Molecular Dynamics Method

J = −𝜆∇𝑇 (1-9)

[11] Where J is heat flux vector and it is defined as the energy at a given unit

time going in the system through a given surface area. The unit of heat flux is J/(s*m^2).

∇𝑇 is the gradient of temperature. In 2D materials, the heat flux only moves in in-plane

direction and no heat flux on z direction. The heat flux is collinear to the gradient of

temperature. Thus, the thermal conductivity or conductance is scalar.

Assuming the temperature gradient is along the x direction, the thermal

conductivity can be defined in [12] equation 10:

𝜆 = lim𝑑𝑡/𝑑𝑧→0

lim𝑡→∞

−𝐽𝑧(𝑡)

𝜕𝑇𝜕𝑧

(1-10)

In real experiment, the temperature gradient will be set on the system first. Then

calculating the heat flux in the temperature gradient’s direction and getting the thermal

conductivity by equation 10. However, it will have problems if we calculate the thermal

conductivity by simulating the real experiment process. The problem is that heat flux

has lots of fluctuations which leads to slow convergence and it require the temperature

gradient to be large enough to distinguish itself from the noise. Thus, NEMD method will

be conducted in a reverse direction from real experiment. The heat flux will be set first

and measure the temperature gradient next. This method can avoid calculating heat flux

17

and the value of heat flux is accurate because you control how many heats added into

the system.

The model box will be cut into many identical slabs along x direction like [13]

figure 9. Then set the heat source and sink on the model. (The position of heat source

sink is flexible. Heat source can be set in the middle and set sinks on model’s each end

or set heat source on right end and sink on left end.) After the temperature reach

equilibrium, [13] Florian Mu ̈ller-Plathe use equation 10 to calculate the energy

transferred in the system.

E =∑

𝑚2 (𝑣ℎ

2 − 𝑣𝑐2)𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟

2 (1-11)

Florian Mu ̈ller-Plathe consider the energy transferred in the system by

exchanging unphysical velocity, which is offset equally by the heat flux. So, the energy

transferred in the system can simply calculated by add velocity energy of heat source

and sink together and divided by 2 like equation 11. However, Langevin method can

directly output the energy of heat source and sink in lammps. So, [13] equation 11 will

not be needed.

J =𝐸

𝑡𝐴 (1-12)

Where J is heat flux, t is time and A is cross-section area of the model. As for

temperature gradient, the temperature of each slab will be used to plot the temperature

graph. The temperature graph is shown in figure 10 and calculate the line’s gradient to

get temperature gradient. Then J divided by temperature gradient can get the thermal

conductivity. Thermal conductivity is used to measure how efficient of heat transferring

18

through the system and larger thermal conductivity will lead to smaller temperature

gradient.

In this research, the interface thermal conductance will be mainly investigated

and the formula for thermal conductance is very similar to thermal conductivity. The

difference is that ∆𝑇 in equation 12 means the temperature difference at the interface

and ∆𝑇 in equation 8 means temperature gradient. The unit for thermal conductivity is

W/(m*K) and unit for thermal conductance is W/(K*m^2). The temperature difference ∆𝑇

at interface can also be calculated by using temperature graph. Figure 11 shows the

graphene/hBN temperature difference at the interface.

C =𝑞

∆𝑇 (1-13)

Figure 1-9. NEMD method (N/2 is the heat source and 0 is the sink.)

19

Figure 1-10. Temperature graph of hexagonal boron nitride

Figure 1-11. Temperature jump at graphene/hexagonal boron nitride interface

20

Graphene/hBN Lateral Interface

For the lateral graphene/hBN hetero-structure, the lateral interface has two types

which are coherent interface and incoherent interface. Incoherent interface is also called

defected interface. [14] Jiong Lu reported that they observed the topological defects on

graphene/hBN interface. [14] Figure 12 shows the defected interface and zoom in on

the defect core. Due to 1.8% lattice mismatch, graphene side will have a compression

and hBN side will have a tension if they form a coherent interface. So, there are strain

energy exist on the interface and the coherent interface can be formed before the

defects or breakage appears to relieve the interface strain. Forming incoherent interface

is inevitable and defects effect on interface thermal conductance will be investigated in

this research. The most common observed topological defects are 5|7 defects which

have a shape of pentagon combined with heptagon. [15] Figure 13 shows the 5|7

defects interface.

A) B)

Figure 1-12. Topological defects. A) Topological defects on the interface. B) Zoom in on the defects core. (MD means the misfit dislocation)

Figure 1-13. 5|7 defects

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CHAPTER 2 SIMULATION

Potential for Graphene/hBN

All simulations are using the tersoff potential which is developed by [16] Tersoff.

Tersoff potential has the following form:

𝑉𝑖𝑗 = 𝑓𝑐(𝑟𝑖𝑗)[𝑓𝑅(𝑟𝑖𝑗) + 𝑏𝑖𝑗𝑓𝐴(𝑟𝑖𝑗)],

𝑓𝑐 (𝑟) = 𝑓(𝑥) = {1

2−

1

2sin (

𝜋

2

𝑟 − 𝑅

𝐷) ,

1, 𝑟 < 𝑅 − 𝐷,𝑅 − 𝐷 < 𝑟 < 𝑅 + 𝐷,

0, 𝑟 > 𝑅 + 𝐷,

𝑓𝑅(𝑟) = 𝐴𝑒𝑥𝑝(−𝜆1𝑟),

𝑓𝐴(𝑟) = −𝐵𝑒𝑥𝑝(−𝜆2𝑟),

𝑏𝑖𝑗 = (1 + 𝛽𝑛𝜁𝑖𝑗𝑛)−

12𝑛,

𝜁𝑖𝑗 = ∑ 𝑓𝐶(𝑟𝑖𝑘)𝑔(𝜃𝑖𝑗𝑘) exp [𝜆33(𝑟𝑖𝑗 − 𝑟𝑖𝑘)

3] ,

𝑘≠𝑖,𝑗

g(θ) = (1 +𝑐2

𝑑2−

𝑐2

[𝑑2 + (𝑐𝑜𝑠𝜃 − ℎ2)])

(2-1)

[16] Where 𝑓𝐴 is a three-body term, 𝑓𝑅 is two-body interactions and 𝑓𝐶 is a cutoff

term. 𝑏𝑖𝑗 is the bond angle term.

[17] Cem Srvik and Alpher Kinaci optimized the tersoff interatomic potential and

table 2-1 shows their result.

22

Figure 2-1. Optimized Tersoff potential parameter

Acoustic phonon has a relatively high group velocity comparing optical phonons.

Therefore, acoustic phonon is very important for measuring lattice thermal conductivity.

Their parameter enables to accurately track acoustic phonon (LA, ZA and TA)

dispersion and their group velocity. [17] They also used their potential to measure the

boron nitride nanotube’s thermal conductivity which matches the experimental and first

principle result. That’s why choose this optimized tersoff potential to measure

graphene/hBN interface thermal conductance.

Relaxing Process

Before running the simulation, all the models went through relaxing process first.

The purpose of relaxing process is to see if the materials’ structure is stable at room

temperature. I first fix NVT to hold the materials at 10 K for 5*10^5 timesteps. Then

gradually change the temperature from 10 K to 300 K and run one million timesteps.

Thirdly, holding the materials at 300K for another one million timesteps. The last step is

to fix NVE to run one million timesteps again. After this relaxing process, output the

materials structure data and using Ovito to see if the structure is stable. Timestep is

0.001 ps. (NVT in lammps means system’s number of atoms, volume and temperature

23

will not change and NVE in lammps means system’s number of atoms, volume and

energy will not change.)

Simulation Details and Result

This research mainly has three parts: investigate the interface density effect on

interface thermal conductance, investigate the defects density’s effect on interface

thermal conductance and heat pulse simulation on two lateral interface graphene/hbn.

Then each part’s simulation models will be introduced in the following paragraphs.

Part 1: Investigate the Effect of Interface Density on Interface Thermal Conductance

First part’s main purpose is to see the relationship between middle interface

thermal conductance and materials interface density. So, five model had been created,

which have same length and width but different number of interfaces. Each model has

921600 atoms. The length and width of these five models is 4855.65 A and 525.6 A.

The cross-section area is 1787.01 A^2 and potential function is BNC.tersoff whose

parameter has been introduced in section 2.1. Boundary condition for y direction is

periodic and non-periodic for x and z direction. Figure 14 shows the five models.

Then using NEMD method and thermal conductance equation to calculate five models’

middle interface thermal conductance.

J =𝐸

𝑡𝐴 (2-2)

C =𝑞

∆𝑇 (2-3)

Timestep for five models are all 0.001 ps and the total timestep is 1*10^6. Thus,

the total simulation time for running NEMD method is 1000 ps. According to equation 2-

2 and 2-3, the value of energy 𝐸 transferred in the system and temperature jump ∆𝑇

24

cross the interface need to be obtained. When the whole system reaches the

temperature equilibrium, using lammps to output the energy of heat source and sink.

The energy transferred in the system is equal to heat source energy plus sink energy

divided by 2. (NEMD method and thermal conductance equation is introduced in section

1.4)

According to NEMD method, each model is cut into 200 slabs along the x

direction and output put 200 slabs’ temperature to draw the temperature gradient graph.

The value of temperature jump can get from the temperature gradient graph. Figure 15

shows five models’ temperature gradient graph. Temperature jumps for each model are

4.884K, 3.7082K, 2.4835K, 1.7324K and 1.0923 K respectively. All the specifications of

the models and result is shown in table 2-2.

From the result, thermal conductance of middle interface increases as the

interface density increase.

Table 2-1. Specifications of models and thermal conductance result

model No. 1 2 3 4 5

total atoms number 921600 921600 921600 921600 921600 Interface density (A^-1) 4.12*10^-4 8.237*10-4 16.48*10^-4 32.95*10^-4 65.90*10^-4 number of interfaces 1 3 7 15 31 cross-section area (A^2) 1787.04 1787.04 1787.04 1787.04 1787.04

time (ps) 1000 1000 1000 1000 1000

energy (eV) 10802.853 9375.6739 8198.0052 7089.5422 6225.1238 temperature difference at middle interface (K) 4.884 3.7082 2.4835 1.7324 1.0923 Thermal conductance at middle interface (W/K*m^2)

1.983076*10^10

2.266814*10^10

2.959512*10^10

3.668987*10^10

5.109545*10^10

25

A)

B)

Figure 2-2. Simulation models for part 1. A) Five models with different interface density. B) Zoom in on the graphene/hBN interface

26

A) B)

C) D)

E)

Figure 2-3. Temperature gradient graphs. A) Temperature gradient for model 1 B) Temperature gradient for model 2 C) Temperature gradient for model 3 D) Temperature gradient for model 4 E) Temperature gradient for model 5

27

Part 2: Investigate the Effect of Defects Density on Interface Thermal Conductance

The purpose of second part simulation is to see how the defect density will affect

the graphene/hBN interface thermal conductance. On section 1.5, topological defects

on the lateral graphene/hBN interface are introduced. Due to there is strain energy on

the interface, materials need to form defects or break to relieve the energy. Therefore,

defects on the interface is inevitable and that’s why it is important to understand how the

defects will affect the interface thermal conductance. 5|7 defects are most common

observed type of topological defect and 5|7 type of defects will be used in my model.

Figure 16 shows my model.

Then 4 models were constructed and they have same length and width, but

different 5|7 defects density on the interface. Another model with coherent

graphene/hBN interface was also constructed for comparison. In y direction, the

boundary condition is periodic and boundary conditions are non-periodic in z and x

direction. The length and width of each model is 1322.836 A and 622.8186 A. The

thickness of the model is 3.4 A. Potential is BNC.tersoff. Timestep is 0.001 ps and total

timestep is 5*10^5.

The potential for this simulation is Tersoff potential. Using same method as part

1, get the temperature jump and heat flux to calculate the thermal conductance. The

result shows on table 2-3.

According to result, add 10 and 15 defects into the interface can increase the

interface thermal conductance. Comparing to coherent interface, there are 9.997%

thermal conductance improvement for 10 defects interface and 12.82% improvement for

28

15 defects interface. As for the 20 and 30 defects interface, the interface thermal

conductance decrease comparing to coherent interface.

In normal sense, the defects on the interface will promote phonon scattering

which lead to low thermal conductance. However, this simulation results show low

defects density will enhance the interface thermal conductance, which contrasts with the

common sense. So, explanation need to be produced for this result.

Table 2-2. Defected interface thermal conductance

Number of defects on the interface 0 10 15 20 30

defects density (A^-1) 0 7.56*10^-3 11.3*10^-3 15.1*10^-3 22.7*10^-3 total number of interfaces 1 1 1 1 1 cross-section area (A^2) 4509.764 4509.764 4509.764 4509.764 4509.764

time (ps) 500 500 500 500 500

energy (eV) 31006.092 34320.532 35101.845 32010.722 29011.293 temperature difference at middle interface (K) 16.1887 16.1296 16.0838 16.1 15.7794 Thermal conductance at middle interface (W/K*m^2)

1.37447*10^10

1.51188*10^10

1.55070*10^10

1.41272*10^10

1.30636*10^10

After running the relaxing process, there are some small out of plane

deformations around the defects. Figure 17 shows the out of plane deformation around

the defects.

According to the result table, the temperature jump in each result is almost same.

So enhanced thermal conductance is related to the increased heat flux. The increased

heat flux across the interface may relate to the interface stress change. According to

stress distribution graph showed in figure 18, stress on the interface is extreme high and

the amplitude of stress decreases rapidly with the distance away from the interface for

29

coherent interface. As for the defected interface, the stress mainly concentrated on the

defects. Due to the lattice constant difference between graphene and hexagonal boron

nitride, forming 5|7 defects can largely relieve the mismatch strain. Then out of plane

deformation around the defects can further reduce the strain at the interface. As a

result, the stress on the position without defects will decrease.

Then future work need to find out the relationship between heat flux and stress

on the interface. This research failed to get the local heat flux on the defect position and

position without defects. So, the conclusion is that low 5|7 defects density on the

interface can enhance the interface thermal conductance.

Figure 2-4. Zoom-in image of graphene/hBN 5|7 defects interface

30

Figure 2-5. Out of plane deformation around 5|7 defects

Figure 2-6. Stress distribution of coherent interface and defected interface (defects density is 88.189 A per defect). (Stress unit is GPa)

31

Part 3: Heat Pulse Simulation on Two Lateral Interface Graphene/hBN

The graphene and hexagonal boron nitride are combined laterally. The length

and width of this model are 227.4 nm and 876nm. The thickness of this model is 3.4 A.

Then 20eV heat are loaded on the middle of this model for 0.3 ps.

Combining the graphene and hexagonal boron nitride (hbn) laterally can reduce

the thermal conductivity. The decreased conductivity may relate to the interface

between graphene and hbn. So, heat pulse simulation is used to prove my speculation

and see how the heat across the interface. The heat pulse is set to the center of model

and interfaces are located at heat pulse’s two sides. The heat pulse model is showing

on figure 19 and the process of heat pulse go through the interface is shown on figure

20.

According to the heat pulse simulation, part of heat cannot go through the

interface was observed by using Ovito’s temperature color coding. Further work need to

explain the phenomenon by using phonon lnowledge

Figure 2-7. Heat pulse model

32

Figure 2-8. The process of heat pulse going through the interface

33

CHAPTER 3 CONCLUSION AND IMPROVMENTS

This research mainly has done about three part of simulations. The first and

second part test how the interface density will affect the graphene/hexagonal boron

nitride lateral interface’s thermal conductance and how the 5|7 defects density on the

interface will affect the graphene/hexagonal boron nitride lateral interface’s thermal

conductance. Third part also have done a simulation about simulating heat pulse across

the lateral graphene/hexagonal boron nitride interface. From the first part, the

conclusion is that increasing interface density can increase the graphene/hexagonal

boron nitride’s interface thermal conductance. According to the second part, the

conclusion is that low 5|7 defects density on the interface can also enhance the

graphene/hexagonal boron nitride interface thermal conductance. From the third part,

further work need to be done to explain the phenomenon.

As for the improvement, the value of model thickness needs to be considered.

Due to the simulation materials is 2D materials, it is very easy to get deformation and

the thickeness at the interface may change. When calculate the interface thermal

conductance, heat flux will be divided by cross-section area. So, thickness will directly

affect the precision of the result. Further work needs to be done on the value of material

thickness. The second part failed to get local heat flux at defected position and position

without defects. If the local heat flux can be get, the mechanism behind enhanced

interface thermal conductance can be explained.

34

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36

BIOGRAPHICAL SKETCH

Peichen Wu was born in Henan, China. He got his bachelor’s degree in

manufacturing system engineering from University of Shanghai for Science and

Technology in 2017. In the August the same year, he started his Master of Science

study in the Department of Mechanical and Aerospace Engineering in University of

Florida and began his thesis degree under the advising of Dr. Youping Chen in Jan,

2018. He received his Master of Science degree in May 2019.