Length-dependent lattice thermal conductivity of single-layer and multilayer hexagonal boron nitride: A first-principles study using the Callaway-Klemens and real-space supercell methods

The phonon dispersion, density of states, Grüneisen parameters, and the lattice thermal conductivity of single-layer and multilayer boron nitride were calculated using first-principles methods. For the bulk $h$-BN we also report the two-phonon density of states. We also present simple analytical solutions to the acoustic vibrational mode-dependent lattice thermal conductivity. Moreover, computations based on the elaborate Callaway-Klemens and the real-space supercell methods are presented to calculate the sample length and temperature-dependent lattice thermal conductivity of single-layer and multilayer hexagonal boron nitride which shows good agreement with experimental data.

Figure 1

The calculated phonon dispersion (left) and phonon density of states (right) of (a) SLBN, (b) BLBN, (c) 5LBN, and (d) bulk $h$-BN along with experimental data (orange circles) [43]. The phonon dispersion was calculated along the high-symmetry points of the 2D Brillouin zone $\left(q_z=0\right)$ corresponding to the hexagonal cell for SLBN, BLBN, and bulk $h$-BN and orthorhombic cell for 5LBN. We also plot in (d) the two-phonon DOS shown for bulk $h$-BN in red dashed line. The cyan, magenta, and green curves in (a)–(d) are the best linear fit to the LA and TA phonon modes, and quadratic fit to the ZA modes, respectively.

Figure 2

Calculated thermal conductivity of single-layer and multilayer BN shown as a function of (a) temperature and (b) length, using the real-space approach. In (a) the curves refer to the thermodynamic limit $\left(L\to \infty \right)$. In (b) the sample length is in logarithmic scale. The square and triangle data points refer to experimental measurements for BLBN [50] and 5LBN [20], respectively.

Figure 3

Calculated thermal conductivity of single-layer and multilayer BN shown as a function of temperature at a constant length, using the real-space approach. The square, circle, triangle data points refer to experimental measurements for BLBN [50], bulk $h$-BN [51], and 5LBN [20], respectively.

Figure 4

Contribution to the thermal conductivity of single-layer and multilayer BN from the acoustic modes: (a) ZA, (b) TA, and (c) LA, shown as a function of temperature in the thermodynamic limit $\left(L\to \infty \right)$, and as a function sample length at $T=300\mathrm{K}$ (d)–(f) using the real-space approach.

Figure 5

Grüenisen parameters of each mode for (a) SLBN, (b) BLBN, (c) 5LBN, and (d) bulk h-BN. The color representation of each mode and fit are shown on the right. The magenta curves are the best fit to the ZA mode along the direction in the BZ chosen to calculate the lattice thermal conductivity.

Figure 6

Acoustic modes and temperature dependence of lattice thermal conductivity for (a) SLBN, (b) BLBN, (c) 5LBN, and (d) bulk h-BN at a constant length. The theoretical calculations are carried out by using Eq. (15) for the LA and TA modes, while Eq. (18) was used for the ZA mode. The parameters used in our calculations are shown in Table 2. The color representations for each mode are shown on the right. The black dots are the experimental measurements [20, 50, 51]. Length dependence is worked out by varying $L$ in Eq. (16).

Figure 7

Acoustic modes and temperature dependence of lattice thermal conductivity for (a) SLBN, (b) BLBN, (c) 5LBN, and (d) bulk h-BN at a constant length. The theoretical calculations are carried out by solving Eq. (8) numerically for each of the modes. The color representations for each mode are shown on the right. The black dots are the experimental measurements [20, 50, 51]. Length dependence is worked out by varying $L$ in Eq. (16).