Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus

Abstract

Black phosphorus has been revisited recently as a new two-dimensional material showing potential applications in electronics and optoelectronics. Here we report the anisotropic in-plane thermal conductivity of suspended few-layer black phosphorus measured by micro-Raman spectroscopy. The armchair and zigzag thermal conductivities are ∼20 and ∼40 W m−1 K−1 for black phosphorus films thicker than 15 nm, respectively, and decrease to ∼10 and ∼20 W m−1 K−1 as the film thickness is reduced, exhibiting significant anisotropy. The thermal conductivity anisotropic ratio is found to be ∼2 for thick black phosphorus films and drops to ∼1.5 for the thinnest 9.5-nm-thick film. Theoretical modelling reveals that the observed anisotropy is primarily related to the anisotropic phonon dispersion, whereas the intrinsic phonon scattering rates are found to be similar along the armchair and zigzag directions. Surface scattering in the black phosphorus films is shown to strongly suppress the contribution of long mean-free-path acoustic phonons.

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

“…Only mechanically exfoliated BP flakes, with defined symmetry axes, allow an assessment of anisotropic thermal properties in all three high symmetry directions of the crystal. A recent preprint [12] reports the in-plane, anisotropic thermal transport for exfoliated, few-layer BP using micro-Raman spectroscopy; still, the extracted values were much smaller than theoretically predicted for phosphorene. For thinner (<15 nm) BP samples, the measured BP thermal conductivity is modified by phonon scattering from oxidized regions, substrates, and surface imperfections.…”

“…Few-layer BP flakes can be exfoliated from bulk crystals due to weak interlayer bonding. [2, 3,6] In contrast to the planar character of graphite and transition metal dichalcogenides, BP has a puckered, honeycomb structure, leading to heightened chemical reactivity [7] and pronounced in-plane anisotropy.Experimental and theoretical examinations of the electrical, [3, 4,6] optical, [3,8] mechanical, [9] and thermal [4,10,11,12] properties reveal distinct anisotropy along BP's two high-symmetry, inplane directions. These symmetry axes are commonly referred to as the zigzag and armchair directions, with lattice constants of a = 3.314 Å and c = 4.376 Å, respectively.…”

“…[10,11] Therein, the phosphorene thickness is set to the inter-layer (b axis) separation of 5.25 Å. [11] Additionally, in a preprint, Luo et al reported [12] the thermal conductivity data for few-layer BP, where they reconciled the thickness dependence of the thermal conductivity through a boundary scattering term to the intrinsic three-phonon scattering rate. Due to the large thickness of the BP flakes we studied in our work, surface scattering should be less significant in our experiments than in those of ref.…”

“…Experimental and theoretical examinations of the electrical, [3, 4,6] optical, [3,8] mechanical, [9] and thermal [4,10,11,12] properties reveal distinct anisotropy along BP's two high-symmetry, inplane directions. These symmetry axes are commonly referred to as the zigzag and armchair directions, with lattice constants of a = 3.314 Å and c = 4.376 Å, respectively.…”

“…[12,13] First-principles calculations of the anisotropic thermal conductivity of monolayer BP, that is, phosphorene, predict that the thermal conductivity along the zigzag direction is two-or three-fold higher [10,11] than along the armchair direction; for example, ref. 11 finds 110 and 36 W m −1 K −1 , respectively, in the two directions.…”