Large tunability of lattice thermal conductivity of monolayer silicene via mechanical strain

Strain engineering is one of the most promising and effective routes toward continuously tuning the electronic and optic properties of materials, while thermal properties are generally believed to be insensitive to mechanical strain. In this paper, the strain-dependent thermal conductivity of monolayer silicene under uniform biaxial tension is computed by solving the phonon Boltzmann transport equation with interatomic force constants extracted from first-principles calculations. Unlike the commonly believed understanding that thermal conductivity only slightly decreases with increased tensile strain for bulk materials, it is found that the thermal conductivity of silicene can increase dramatically with strain. Depending on the size, the maximum thermal conductivity of strained silicene can be a few times higher than that of the unstrained case. Such an unusual strain dependence is mainly attributed to the dramatic enhancement in the acoustic phonon lifetime. Such enhancement plausibly originates from the flattening of the buckling of the silicene structure upon stretching, which is unique for silicene as compared with other common two-dimensional materials. Our findings offer perspectives on modulating the thermal properties of low-dimensional structures for applications such as thermoelectrics, thermal circuits, and nanoelectronics.

Figure 1

Bond length and buckling distance as a function of strain. Inset: Primitive unit cell structures for unstrained and 10% strained silicene.

Figure 2

Phonon dispersion curves of unstrained silicene and strained silicene under 4% and 10% tensile strain.

Figure 3

Thermal conductivity of infinite ($101\times 101\times 1$ and $201\times 201\times 1 q$ mesh) and finite-size (0.3, 3, and $30 \mu \mathrm{m}$) silicene as a function of strain computed with RTA and iterative method. Note that since RTA and iterative method give similar thermal conductivity values for different cases, we only show the iterative results for the $201\times 201\times 1$ infinite and the $0.3 \mu \mathrm{m}$ size cases.

Figure 4

Normalized thermal conductivity accumulation function with respect to phonon mean free path for 0%, 4%, and 10% strain.

Figure 5

The branch contribution of optical phonons, TA/LA phonons, and FA phonons to the total thermal conductivity computed with RTA.

Figure 6

Thermal conductivity as a function of strain computed with RTA and cross-calculated thermal conductivity with $c_{ph},v_x$, or $\tau$ replaced with strained values.

Figure 7

Top panel: Lifetime of FA phonons as a function of frequency for 0%, 2%, 4%, 6%, and 10% strain. Bottom panel: Lifetime of LA/TA phonons as a function of frequency for 0%, 2%, 4%, 6%, and 10% strain.

Figure 8

Scattering rates of acoustic phonons from $\mathrm{\Gamma }$ to M: FA phonons for (a) unstrained silicene, (b) 4% strained silicene, (c) 10% strained silicene. TA phonons for (d) unstrained silicene, (e) 4% strained silicene, (f) 10% strained silicene. LA phonons for (g) unstrained silicene, (h) 4% strained silicene, (i) 10% strained silicene. (Please note the difference in the scales for scattering rates in the panels.)

Figure 9

Thermal conductivity of unstrained silicene vs nearest neighbors computed with RTA and iterative method.

Figure 10

Thermal conductivity of unstrained silicene for different $q$ mesh and different sizes computed with RTA and iterative method.