Using nonequilibrium molecular dynamics, we investigate the mechanisms of thermal transport across SiC/graphene sheets. In simulations, 3C-, 4H-, and 6H-SiC are considered separately. Interfacial thermal resistances between Bernal stacking graphene sheets and SiC (Si- or C-terminated) are calculated at the ranges of 100 K~700 K. The results indicate, whether Si-terminated or C-terminated interface, the interfacial thermal resistances of 4H- and 6H-SiC have similar trends over temperatures. Si-terminated interfacial thermal resistances of 3C-SiC are higher than those of 4H- and 6H-SiC in a wide temperature range from 100 K to 600 K. But, for C-rich interface, this range is reduced from 350 K to 500 K.
For the atomically thin structure of graphene, it has attracted much attention due to potential applications to thermoelectric and photoelectric devices. Over the past decade, researchers mainly focus on the fabrication of graphene and its physical characteristics. The most common used methods of graphene fabrication are epitaxial growth on silicon carbide (SiC) and chemical vapor deposition (CVD). As to epitaxial growth method, Si atoms sublimate from a single-crystal SiC substrate and create large area graphene sheets. CVD method employs carbon source gas to react with the specific substrate chemically, so as to synthesize graphene sheets. In recent years, the techniques of graphene production have been improved dramatically. Tzalenchuk et al. [
As to theoretical study, researchers usually adopt analytical or numerical approaches to perform nanoscale heat transport simulations, involving molecular dynamics (MD) method, Monte Carlo (MC) method, Boltzmann transport equation, and Green’s function. Compared with other methods, MD is much closer to physical reality, which defines the simulation region with atoms, supposed to the arrangement of chemical structures. Based on Newton’s law, MD sets cut-off radius to build atom groups, in which atoms interact with each other by elastic forces. At the beginning of MD simulation, motion parameters of each atom should be initialized according to the imposed temperatures. After enough circulations, system reaches to an equilibrium and the temperature can be obtained by Boltzman equipartition theorem (BET). According to the different calculation principles, MD can be divided into equilibrium MD (EMD) and nonequilibrium MD (NEMD) methods. As to EMD, thermal conductivity may be obtained by Green-Kubo linear response under equilibrium state [
The key points of NEMD method are the creation of thermal flux and the interaction potential. In order to create thermal flux, we may keep the temperature gap between the hot part and the cold part, which drives thermal flux. Another way is to swap the coldest atoms in the hot part with the hottest ones in cold part. From the computation viewpoint, the latter is more effective, because the number of atoms involved in the calculation is less than the former. Therefore, we utilize the former way to drive thermal flux in NEMD simulations.
In semiconductors, heat transfer mainly depends on the transmission of elastic vibration by interatomic force, which is the derivative of the interaction potential. Hence, whether the right interaction potential is utilized determines the correctness of the results. In this work, Tersoff [
A NEMD ball and stick 3C-SiC film model in our study is depicted in Figure
Ball and stick model of 3C-SiC film in this work.
In Figure
Temperature distributions of 3C-SiC, graphene sheets, and Si across cell serial number. (a) The enlarged figure. (b) The thermal flux.
Exchanging kinetic energy of atoms in hot bath and cold bath, system reaches to an equilibrium state and thermal conductivity can be obtained from the following equation:
In-plane thermal conductivities of monolayer graphene on SiO2 substrate.
Interfacial thermal resistance
Schematic diagram of graphene sheets/SiC.
The lattice parameters used in our work are listed in Table
Lattice parameters of SiC polytypes and graphene [
3C-SiC | 4H-SiC | 6H-SiC | Graphene | |
---|---|---|---|---|
|
4.348 | 3.073 | 3.0813 | 2.552 |
|
4.348 | 10.0848 | 15.1198 | 3.35 |
In Figure
Temperature distribution of 4H-SiC/graphene sheets across the length.
The lattice mismatch of SiC/graphene system can strongly affect the special thermal properties and electronic characteristics. Correspondingly, it is necessary to investigate the influences of different interfacial morphologies on thermal transports. As shown in Figure
Interfacial thermal resistances of Si-teminated SiC films.
In the CVD graphene growing method, we can also use C-rich surface to bond with C atoms. The interface of SiC/graphene becomes different from Si-rich interface as depicted in Figure
Interfacial thermal resistances of C-terminated 3C-, 4H, 6H-SiC/graphene sheets across temperatures.
By chemical method, monolayer graphene and graphene sheets can be synthesized on SiC substrates. Many researchers have studied electrical and thermal properties of graphene; however, few works involve the thermal transport of SiC/graphene sheets. In this work, we apply a dedicated NEMD model to investigate interfacial thermal resistances of SiC/graphene sheets. Three polytypes of SiC (3C-, 4H-, and 6H-SiC) are set as substrates to bond with graphene sheets in simulation. Si-rich and C-rich interfaces between SiC/graphene are also analyzed at the temperatures from 100 K to 700 K. From the results of Si-rich interface, the interfacial thermal resistance of 3C-SiC is larger than those of 4H- and 6H-SiC below 600 K. From 100 K to 700 K, the curve of 6H-SiC is always greater than that of 4H-SiC. By fitting the calculated datum, the peak interfacial thermal resistances of 3C-, 4H-, and 6H-SiC are
However, it should be acknowledged that surface reconstructions of SiC such as
The authors declare that there is no conflict of interests regarding the publication of this paper.
Zan Wang would like to acknowledge the financial support from the National Natural Science Foundation of China (51106043, 51205061, 51373048), and this work is also supported by the basic research project of Henan Provincial Department of Education Science and Technology (13A470176) and Plan For Scientific Innovation Talent of Henan University of Technology.