Research in the area of two-dimensional (2-D) materials such as graphene, hexagonal boron nitride (h-BN), and transition metal dichalcogenides (TMDCs) has heavily increased within the last few years. 2-D materials are promising for a wide range of applications including nano-elecronics, opto-electronics, bio-chemical sensing and water desalination. Researchers have found that the stacking of 2-D materials could lead to exceptional performance in nano-electronic devices, e.g., h-BN, which has similar planar hexagonal lattice structure as grapheme, serves as an excellent dielectric and substrate for graphene electronics, leading to higher carrier mobility compared to any other substrate.

As the size of electronic devices scales down and power density increases, inefficient thermal management is becoming challenging for performance and reliability. The thermal boundary resistance (TBR) at the interface of the 2-D materials and the substrates may play a dominant role in degrading overall device performance. TBR at such interfaces are primarily dominated by phonons which could be understood as atomic vibrations at different frequencies and wave-vectors. Nano-engineering such surfaces for enhanced phonon coupling and reduced TBR requires a good understanding of how atomistic structure and chemistry at the interface affects the phonon transmission. Unfortunately, experimental techniques do not provide frequency and wave-vector dependent phonon transmission for the phonon spectrum of interest.

Today, researchers at the Georgia Institute of Technology, and Oak Ridge National Laboratory (ORNL) have developed a new analysis method based on the first principle density functional theory and atomistic Green’s function to predict the phonon transmission at the interface of 2-D materials. They, for the first time, report both frequency and wave-vector (k space) dependent phonon transmission at interface of single layer graphene (SLG) sandwiched between h-BN layers (h-BN/SLG/h-BN) and analyze the contribution of different phonon modes to TBR considering the effect of atomistic configuration.

The developed method does not use any empirical fitting but computes force constants describing the atomic interactions directly from the first principle density functional theory (DFT) and uses this in a quantum theory based thermal transport model to compute phonon transmission and TBR. This unique feature of the model makes it capable of investigating interfaces of new materials without going through the cumbersome process of devising interatomic potentials. “By allowing us to investigate the effect of bonding, and electrostatics for different interfacial configurations, this numerical technique opens up a whole new direction to investigate phonon transport at junctions and contacts in next generation of nano-materials and their devices,” said Satish Kumar, an associate professor in the George W. Woodruff School of Mechanical Engineering at the Georgia Institute of Technology.

The research was supported by the National Science Foundation and ORNL Laboratory Directed Research and Development funding, and reported in the journal Nanoscale in the January 2016 issue. The research team includes graduate student and first author Zhequan Yan and his adviser Satish Kumar from Georgia Tech, Liang Chen, an assistant professor at Xi’an Jiaotong University and ex-member of Kumar’s group, and Mina Yoon, research scientist at Center for Nanophase Materials Sciences (CNMS) at ORNL.

Researchers found that the atomistic configuration has a significant influence on the phonon transport across the h-BN/SLG/h-BN sandwiched systems. They analyzed five representative and stable configurations of h-BN/SLG/h-BN, which are obtained from the optimization following DFT. In a real sample of h-BN/SLG/h-BN, all these configurations may be present in different grains and separated by the grain boundaries. The structures with the carbon atom located directly on top of the boron atom (C-B matched) are observed to have 50% lower thermal boundary resistance (TBR) compared to the structures with carbon atom directly on top of the nitrogen atom (C-N matched), which is due to the stronger phonon-phonon coupling of C-B matched interface compared with that of the C-N matched interface. The comparison of frequency and wave-vector dependent phonon transmission function reveals that the contribution of in-plane phonon modes are lower in C-N matched interfaces compared to the C-B matched (see Figure below), which is due to the low interfacial distance between graphene and h-BN in C-N matched interfaces leading to high TBR. The low interfacial spacing is a consequence of the differences in the effective atomic volume of N and B atoms and the difference in the local electron density around the N and B atoms.

The findings in this study provide insights in to the mechanism of phonon transport at h-BN/SLG/h-BN interfaces. They will help in explaining the experimental observations using Raman Spectroscopy for probing phonon properties and to engineer these interfaces to enhance heat dissipation in graphene based electronic devices. The developed method is general and could be applied to a wide range of nano-materials to decipher the effect of surface chemistry and bonding on interfacial thermal transport.

“Our simulation and analysis method could be a powerful tool for predicting the interfacial thermal transport of different nano-materials and for providing guidelines to experiments for the growth of stacked layers with favorable properties,” said Satish Kumar. “It provides a quick and effective way to develop and find the new generations of the 2-D materials with a promising thermal properties at their interfaces.”

This work was partially supported by National Science Foundation Grant CBET-1236416. Part of this research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility and supported by the ORNL Laboratory Directed Research and Development funding. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

CITATION: Zhequan Yan, Liang Chen, Mina Yoon, Satish Kumar, “Phonon Transport at the Interfaces of Vertically Stacked Graphene and Hexagonal Boron Nitride Heterostructures,” (Nanoscale, 2016). http://dx.doi.org/10.1039/c5nr06818e