Phonon thermal transport in $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ monolayers: A first-principles study of the interplay between harmonic and anharmonic phonon properties

The investigation of the thermal properties of recently emerged two-dimensional materials is a necessary step towards fulfilling their potential applications in nanoelectronics devices. In this study, the thermal conductivities $\mathrm{of}\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ monolayers are investigated using a first-principles density-functional theory approach based on the full solution of the linearized Peierls-Boltzmann transport equation. The results show that the room-temperature thermal conductivities of $\beta$-NP, $\beta$-NAs, and $\beta$-NSb are about 1.1, 5.5, and 34.0 times higher than those of their single-element $\beta$-P, $\beta$-As, and $\beta$-Sb monolayers, respectively. The phonon transport analysis reveals that higher phonon group velocities, as well as higher phonon lifetimes, are responsible for such an enhancement in the lattice thermal conductivities of $\beta \text{−}\mathrm{N}X$ binary compounds compared to their single-element group-VA monolayers. We found that $\beta$-NP has the minimum thermal conductivity among $\beta \text{−}\mathrm{N}X$ monolayers, while it has the minimum average atomic mass, which is in contrast with the common assumption that lower-mass systems exhibit higher thermal conductivities. This work demonstrates the tradeoff between harmonic and anharmonic phonon properties in determining the variation of the thermal conductivity among $\beta \text{−}\mathrm{N}X$ monolayers. The higher anharmonicity in $\beta$-NP is found to be responsible for the lower thermal conductivity of this monolayer.

Figure 1

Top and side view of monolayers (a) $\beta \text{−}\mathrm{N}X$ and (b) $\beta \text{−}X$.

Figure 2

Variation of the thermal conductivity with temperature in 20-Å-thick layers of (a) $\beta$-NP and $\beta$-P, (b) $\beta$-NAs and $\beta$-As, (c) $\beta$-NSb and $\beta$-Sb, and (d) $\beta$-NP, $\beta$-NAs, and $\beta$-NSb.

Figure 3

Room-temperature thermal conductivity versus the average atomic mass of unit cells for 20-Å-thick layers of $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ and $\beta \text{−}X$ monolayers.

Figure 4

Contribution of each phonon mode towards the total thermal conductivity in $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ and $\beta \text{−}X$ monolayers at room temperature.

Figure 5

Phonon-dispersion curves of (a) $\beta$-NP and $\beta$-P, (b) $\beta$-NAs and $\beta$-As, and (c) $\beta$-NSb and $\beta$-Sb.

Figure 6

Phonon group velocity of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NP and $\beta$-P.

Figure 7

Phonon group velocity of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NAs and $\beta$-As.

Figure 8

Phonon group velocity of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NSb and $\beta$-Sb.

Figure 9

Phonon group velocity of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NP, $\beta$-NAs, and $\beta$-NSb.

Figure 10

Scattering phase space of the (a) $\mathrm{ZA}$, (b) $\mathrm{TA}$, and (c) $\mathrm{LA}$ modes in $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ monolayers.

Figure 11

Phonon lifetime of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NP and $\beta$-P at 300 K.

Figure 12

Phonon lifetime of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NAs and $\beta$-As at 300 K.

Figure 13

Phonon lifetime of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NSb and $\beta$-Sb at 300 K.

Figure 14

Phonon lifetime of (a) ZA mode, (b) TA mode, and (c) LA mode in $\beta$-NP, $\beta$-NAs, and $\beta$-NSb at 300 K.

Figure 15

(a) Grüneisen parameters in $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ monolayers. (b) Positive values of the Grüneisen parameters.

Figure 16

Normalized thermal conductivity accumulation at 300 K for $\beta \text{−}\mathrm{N}X\left(X=\mathrm{P},\mathrm{As},\mathrm{Sb}\right)$ and $\beta \text{−}X$.