Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus

Ling, Xi; Liang, Liangbo; Huang, Shengxi; Puretzky, Alexander A.; Geohegan, David B.; Sumpter, Bobby G.; Kong, Jing; Meunier, Vincent; Dresselhaus, M. S.

doi:10.1021/acs.nanolett.5b01117

Cited by 186 publications

(300 citation statements)

References 86 publications

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“…Further, unlike ref. 12, our BP flakes are encapsulated by both AlOx and NbV, making ambient oxidation [7] or photodegradation [27] less significant, giving us an intrinsic measurement of BP's anisotropic thermal conductivities.We briefly note our thermal conductivity results for ambient oxidized BP samples.One BP sample (h > 600 nm thick) was coated with NbV three months after AlOx encapsulation and measured two weeks after NbV deposition. This sample exhibits much we observe BP degradation from under both the NbV and AlOx encapsulants ( Figure S5).…”

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Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

et al. 2015

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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 ...

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Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

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“…31,32 Because the accumulated intensity of a Raman mode is determined by the Raman cross-section, which is proportional to | × × | 2 , the intensities are related to the Raman tensor R and the scattering geometry in polarization configuration e. 34,35 According to Eq. (S1), the Raman tensor parameter c is larger than the parameter a under 532 nm laser excitation, consistent with the recently obtained theoretical result.…”

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Probing the anisotropic behaviors of black phosphorus by transmission electron microscopy, angular-dependent Raman spectra, and electronic transport measurements

Fei

et al. 2015

Applied Physics Letters

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In this study, we correlated the angular dependence of the Raman response of black phosphorus to its crystallographic orientation by using transmission electron microscopy and Raman spectroscopy. It was found that the intensity of the 2 mode reached a maximum when the polarization direction of the incident light was parallel to the zigzag crystallographic orientation. Notably, it was further confirmed that the zigzag crystallographic direction exhibited superior conductance and carrier mobility. Because of the lattice extension along the armchair direction, an intensification of the anisotropic Raman response was observed. This work provides direct evidence of the correlation between anisotropic properties and crystallographic direction and represents a turning point in the discussion of the angular-dependent electronic properties of black phosphorus.♯ These authors contributed equally to this work

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“…6,[14][15][16][17][18][19] The accidental degeneracy discussed above has not been reported in these previous DFT calculations. It is also worth mentioning that LDA usually overbinds the atomic structure yielding smaller bond lengths and lattice constants than experiment.…”

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confidence: 76%

“…However, it is quite uncommon that for BP, even LDA significantly underestimates the Raman frequency of the A g 2 mode. 6,15,16,18 As will be discussed below, the commonly used Perdew-Burke-Ernzerhof (PBE) functional also underestimates the frequency of the A g 2 mode, even including the dispersion force correction.…”

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Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene

Sun

Zhang

2016

The Journal of Chemical Physics

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Bulk black phosphorus has two optical phonon modes labeled as Ag2 and B2u, respectively, that are nearly degenerate in frequency. However, density functional theory calculations using local or semi-local functionals cannot reproduce this degeneracy. Here, we propose a hybrid functional approach aided by van der Waals (vdW) force fields, which can accurately describe the lattice dynamic and electronic properties of both bulk and few-layer black phosphorus (phosphorene). Using this approach we show that in bilayer phosphorene, the two Raman modes derived from the B2u and Ag2 modes could exhibit strong resonance as a result of the accidental degeneracy so that both modes could be observed in Raman experiment. Without the mode degeneracy, however, the Raman intensity of the B2u-derived mode would be too weak to be observed. We further show that the accidental degeneracy is correlated to the applied strain, which enables Raman spectroscopy to be a powerful tool for characterizing built-in strains in 2D materials, e.g., due to the interaction with substrates, which has emerged as an important issue in vdW epitaxy.

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Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus

Cited by 186 publications

References 86 publications

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus

Probing the anisotropic behaviors of black phosphorus by transmission electron microscopy, angular-dependent Raman spectra, and electronic transport measurements

Communication: Effect of accidental mode degeneracy on Raman intensity in 2D materials: Hybrid functional study of bilayer phosphorene

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