Controlling the thermal conductance of $\text{graphene}/h-\mathrm{BN}$ lateral interface with strain and structure engineering

Although phonon-mediated thermal conduction in pristine graphene and hexagonal boron nitride is well understood, less is known about phonon transport in single-sheet graphene-hexagonal boron nitride ($\mathrm{Gr}/h-\mathrm{BN}$) lateral heterostructures, where the thermal resistance of the interfaces plays an important role in the overall thermal conductivity. We apply the newly developed extended atomistic Green's function method to analyze with detail the effect of strain and structure engineering on the thermal conductance $G_{\mathrm{int}}$ of the $\mathrm{Gr}/h-\mathrm{BN}$ interface. Our calculations show that longitudinal tensile strain leads to significant $G_{\mathrm{int}}$ enhancement (up to $25\%$ at 300 K) primarily through the improved alignment of the flexural acoustic phonon bands, despite the reduction in the longitudinal acoustic (LA) and transverse acoustic phonon velocities. In addition, we find that alternating C-N zigzag bonds along the zigzag interface lead to a greater $G_{\mathrm{int}}$ than C-B bonds through more effective transmission of high-frequency LA and transverse optical phonons, especially at high strain levels. We also demonstrate how the interfacial structure dramatically affects the orientation of the transmitted optical phonons, a phenomenon that is neither seen for acoustic phonons nor predictable from conventional acoustic wave scattering theory. Insights from our paper can provide the basis for manipulating the interfacial thermal conductance in other two-dimensional heterostructures.

Figure 1

Schematic of the $\mathrm{Gr}/h$-BN (a) armchair interface and the zigzag interface for (b) C-N zigzag, (c) C-N bridge, (d) C-B zigzag, and (e) C-B bridge bonding at the interface.

Figure 2

The interfacial thermal conductance $G_{\mathrm{int}}$ as a function of temperature with increasing strain, from 0 to $7\%$ in the (a) $x$ and (b) $y$ direction. The arrow indicates the direction of increasing strain. (c) The cross-sectional phonon transmission spectrum ($\mathrm{n}{\mathrm{m}}^{-2}$) for strain in the zigzag ($x$) and armchair ($y$) direction.

Figure 3

Phonon dispersion in the longitudinal (zigzag) or $x$ direction for graphene and BN, on the left and right half of the ($k_x, \omega$) plane, respectively, at (a) $0\%$ and (b) $5\%$ longitudinal strain. The transmission probabilities of the modes are indicated in color. The corresponding distribution of modes on the ($k_x, k_y$) plane at $\omega =200\mathrm{c}{\mathrm{m}}^{-1}$ for (c) $0\%$ and (d) $5\%$ longitudinal strain are shown below. As a visual guide, we connect with the intersecting points between (a), (b) and (c), (d) with dotted lines. The transmission frequency cutoff for the ZA phonons is around 325 and $392\mathrm{c}{\mathrm{m}}^{-1}$ for (a) and (b), respectively, and is indicated by the dashed lines. We also show the transmission probability spectra for the graphene out-of-plane phonon modes at (e) $0\%$ and (f) $5\%$ longitudinal strain in reciprocal and frequency space. (g) and (h) Corresponding transmission probability spectra for graphene in-plane (transverse and longitudinal acoustic) phonon modes at $0\%$ and $5\%$ strain, respectively. The dashed lines indicate the position of the transmission frequency cutoff.

Figure 4

Interfacial thermal conductance $G_{\mathrm{int}}$ as a function of temperature with increasing strain, from 0 to $7\%$, for the (a), (b) C-N and (c), (d) C-B zigzag interface, in the (a), (c) $x$ direction and (b), (d) $y$ direction. We have C-N or C-B zigzag bonds at the interface.

Figure 5

Transmission probability spectra at normal incidence ($k_x=0$) for BN and graphene at 0 and $5\%$ longitudinal ($x$) strain, similar to that given in Figs. 3 and 3, corresponding to the (a), (b) C-N and (c), (d) C-B zigzag bonds, over the frequency range of $0-1600\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 6

Cross-sectional phonon transmission as a function of strain in the armchair direction (normal to the zigzag interface) for (a) the C-N and (b) the C-B interfacial bond. (c) and (d) Corresponding BN phonon transmission probability spectra at $0\%$ strain in ($\omega , k_x, k_y$) space and in the $800-1350\mathrm{c}{\mathrm{m}}^{-1}$ range, which includes the LA and TO phonon bands. (e) The phonon dispersion in the direction normal to the interface showing the phonon transmission probabilities. The dashed lines show the lower and upper bound of the $800-1350\mathrm{c}{\mathrm{m}}^{-1}$ frequency range. We also label the LA, TA, ZA, LO, TO, and ZO bands in BN. There are 12 phonon branches instead of six because we define the unit cell with four atoms in our AGF computational scheme. However, it is straightforward to identify the branches because they are connected at $k_x=0$.

Figure 7

(a) and (b) Corresponding BN phonon transmission probability spectra at $5\%$ strain in ($k_x, k_y, \omega$ space and in the $700-1250\mathrm{c}{\mathrm{m}}^{-1}$ range, which includes the LA and TO phonon bands. (c) and (d) The same BN phonon transmission probability spectra but at $10\%$ strain.

Figure 8

(a) Interfacial thermal conductance $G_{\mathrm{int}}$ as a function of temperature from 0–800 K for C-N/C-B zigzag and bridge bonds. We calculate the temperature-weighted phonon transmission at (b) 100, (c) 300, and (d) 800 K.

Figure 9

Transmission probability spectra at normal incidence ($k_x=0$) for BN and graphene at 0 percent strain, corresponding to the (a) C-N and (b) C-B zigzag bonds as well as to the (c) C-N and (d) C-B bridge bonds, over the frequency range of 0–1600 ${\mathrm{cm}}^{-1}$.