Phonon transport on two-dimensional graphene/boron nitride superlattices

Using nonequilibrium molecular dynamics and lattice dynamics, we investigate phonon conduction on two-dimensional graphene/boron nitride superlattices with varying periods and interface structures. As the period of superlattice increases to a critical value near 5 nm the lattice thermal conductivity drops sharply to a minimum, and beyond that it smoothly increases with the period. We show that the minimum in the thermal conductivity arises from a competition between lattice dispersion and anharmonic effects such as interface scattering. The initial reduction of thermal conductivity can partially be accounted for by harmonic wave effects induced by interfacial modulation, such as the opening of phononic band gaps and reduction of group velocity. Beyond the minimum, reduced inelastic interface scattering is responsible for the recovery. The overall range of thermal conductivity exhibited by the superlattices is substantially reduced with respect to the parent materials. A universal scaling of the thermal conductivity with total superlattice length is found, suggesting that the critical period is independent of total length and that long-wavelength phonons are dominant carriers. Furthermore, we demonstrate the ultrasensitivity of thermal conductivity to interfacial defects and superlattice periodicity disorder.

Figure 1

(a) Schematic of a five-period G/h-BN superlattice with $P=2$ unit cells and $L=5$ unit cells, where a unit cell has dimensions 0.246 and 0.426 nm parallel and perpendicular to the interface, respectively. Inset is reciprocal space and $k$ locus used in this work; (b) Temperature profile of G/h-BN superlattice with $L=700$ unit cells and $P=140$ unit cells, which corresponds to local Knudsen number $\mathrm{K}{\mathrm{n}}_{\mathrm{BN}}\approx 7,\mathrm{K}{\mathrm{n}}_{\mathrm{C}}\approx 10$ and thus phonon flow features transition regime characteristics (note that the superlattice image on top is illustrative, the plotted data correspond to a larger period than depicted).

Figure 2

Thermal conductivity of ideal G/h-BN superlattices: (a) molecular dynamics results for varying $P$ and $L$, minima occur at $P_c=10-20$ unit cells; (b) thermal conductivity normalized by respective minima, showing a general valley trend and thus signifying universal critical length scales: coherence length $\lambda \approx 14\pm 4$ unit cells and mean free path ${\Lambda }_G\approx 1400$ unit cells; (c) thermal conductivity versus total length $L$, where linear dependence indicates the ballistic nature of predominant carriers.

Figure 3

Calculated phononic coherence length λ as a function of the superlattice period $P$; the fluctuations are largely induced by Bose-Einstein weighting.

Figure 4

(a) Lattice dynamics calculation of modified dispersion curves of ideal G/h-BN and (b) spectral contribution to heat conductivity for varying periods. Increasing the pitch results in phonon band gaps and reduced group velocities, inducing a reduction of thermal conductivity, as shown in (b) inset (where MS means Simkin and Mahan's model [35]).

Figure 5

Comparison of normalized thermal conductivity calculated via NEMD and LD. The initial reduction of the thermal conductivity arises from wave effects, while reduced interfacial scattering is responsible for the recovery. The interface scattering model shown here is fitted to the NEMD results, using an interfacial conductance of $1/R_I=2.562\times {10}^9/{\mathrm{m}}^2\mathrm{K}$.

Figure 6

(a) Thermal conductivity of G/h-BN superlattices with (b) interface defects and (c) pseudoperiodicity. Thermal conductivity of pseudoperiodic G/h-BN increases monotonically with period $P$, ranging between (d) the alloy limit and ideal superlattices.