Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

Abstract

We ascertain the anisotropic thermal conductivity of passivated black phosphorus (BP), a reactive 2D nanomaterial with strong in-plane anisotropy. We measure the room temperature thermal conductivity by time-domain thermoreflectance for three crystalline axes of exfoliated BP. The thermal conductivity along the zigzag direction (86 ± 8 W m −1 K −1 ) is ~2.5 times higher than that of the armchair direction (34 ± 4 W m −1 K −1 ). TOC Figure 2Black phosphorus (BP), a stable phosphorus allotrope at ambient temperature and pressure, [1] is a two-dimensional electronic material with desirable properties for transistor, [2, 3] thermoelectric, [4] and optical sensing [5] applications. 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. [1] Understanding an electronic material's thermal conductivity is critical for the thermal management of small-scale devices and for exploring potential thermoelectric applications.Despite extensive electrical characterization of exfoliated BP, experimental measurements of BP's thermal properties are few. [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. Of this, the electronic contribution to the thermal conductivity is markedly small, less than 3 W m −1 K −1 , even at a high carrier concentration of ~10 12 cm −2 . [11] Experimentally, Slack found the thermal conductivity of bulk, polycrystalline BP to be 10 W m −1 K −1 at room temperature, [13] but no anisotropic effects were examined. 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. By contrast, thermal measurements on thicker (>100 nm) BP flakes, especially those protected against ambient oxidation, provide an intrinsic ...

Revealing the Origins of 3D Anisotropic Thermal Conductivities of Black Phosphorus

“…Summary of the anisotropic thermal conductivities: highlighted in gray are for bulk and BP from both our measurements and simulations at 300 K. The available literature values (theoretical for monolayer BP [ 9,10,12,13 ] and experimental for BP thin fi lms [14][15][16] ) are also plotted for comparison.…”

“…Under SMRTA, the relaxation times should be positive. When the iterative approach was used, the negative relaxation time Ref [14] Ref [16] Ref [15] BP-2…”

“…[ 27 ] Thus, despite the fact that theoretical investigations on the thermal transport in BP have been conducted only for monolayer, the very few experimental studies so far have merely focused on BP thin fi lms and have large deviations. [14][15][16] The measured thermal conductivities of BP thin fi lms span from 20 to 86 W m −1 K −1 for the zigzag direction, and from 10 to 36 W m −1 K −1 for the armchair direction. [14][15][16] Such discrepancies in measurement results are presumably caused by different sample conditions, includng surface contamination due to adsorbates and oxidation, [ 14,15 ] or sample damage during the fabrication process.…”

“…[14][15][16] The measured thermal conductivities of BP thin fi lms span from 20 to 86 W m −1 K −1 for the zigzag direction, and from 10 to 36 W m −1 K −1 for the armchair direction. [14][15][16] Such discrepancies in measurement results are presumably caused by different sample conditions, includng surface contamination due to adsorbates and oxidation, [ 14,15 ] or sample damage during the fabrication process. [ 14,16 ] On the other hand, the wide range of the theoretically predicted values calls for experimental validation.…”

Recent advances in synthesis, properties, and applications of phosphorene

“…[26][27][28] This is the reason for a strong orientation-dependent shear modulus 29 and thermal transport. 30 Strong anisotropic behavior, showing thickness and spectral dependence, is also observed for electron-photon and electron-phonon interactions. 31 The anisotropy of phosphorene's magnetic properties has also been predicted.…”