Anharmonic phonon effects in Raman spectra of unsupported vertical graphene sheets

Lin, Jingjing; Guo, Liwei; Huang, Qingsong; Jia, Yue; Li, Kang; Lai, Xiaofang; Chen, Xiaolong

doi:10.1103/physrevb.83.125430

Cited by 73 publications

(124 citation statements)

References 44 publications

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“…5, we linearly fitted the data and considered the first-order temperature coefficient , which has two components leading to the Raman frequency shift. In detail, the temperature dependence of the Raman frequency can be rewritten as = 0 + Δ + Δ = 0 + ( ) ∆ + ( ) ∆ , where the first term ( ) ∆ is the "self-energy" shift, which is the pure temperature effect, and the second term ( ) ∆ is due to the crystal thermal expansion 64,65 . For the out-of-plane B mode of few-layer BP, which is solely due to interlayer coupling, the contribution to the Raman shift from the second term ( ) ∆ depends on the thermal expansion along the out-of-plane direction.…”

Section: Temperature Dependencementioning

confidence: 99%

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

et al. 2015

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As a new two-dimensional layered material, black phosphorus (BP) is a promising material for nanoelectronics and nano-optoelectronics. We use Raman spectroscopy and first-principles theory to report our findings related to low-frequency (LF) interlayer breathing modes (<100 cm -1 ) in few-layer BP for the first time. The breathing modes are assigned to Ag symmetry by the laser polarization dependence study and group theory analysis. Compared to the high-frequency (HF) Raman modes, the LF breathing modes are much more sensitive to interlayer coupling and thus their frequencies show much stronger dependence on the number of layers. Hence, they could be used as effective means to probe both the crystalline orientation and thickness for fewlayer BP. Furthermore, the temperature dependence study shows that the breathing modes have a harmonic behavior, in contrast to HF Raman modes which are known to exhibit anharmonicity. 2 Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.3 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 2Orthorhombic black phosphorus (BP) is the most stable allotrope of phosphorus. It features a layered structure with puckered monolayers stacked by van der Waals (vdW) force 1 . Few-or single-layer BP can be mechanically exfoliated from bulk BP [2][3][4][5] . Due to BP's intrinsic thicknessdependent direct bandgap (ranging from 0.3 eV to 2.0 eV) and relatively high carrier mobility (up to ~1,000 cm 2 V -1 s -1 at room temperature) 2,4,[6][7][8][9] , it is expected to have promising applications in nanoelectronic devices [2][3][4]10 , and near and mid-infrared photodetector [11][12][13][14][15][16][17][18][19] . Recently, high performance thermoelectric devices were also predicted based on BP thin films [20][21][22] . With the surge of interest in two-dimensional (2D) materials (such as graphene and transition metal dichalcogenides (TMDs)) 23,24 , BP has become a new attraction since 2014 because it bridges the gap between graphene and TMDs, and offers the best trade-off between mobility and on-off ratio 3 . Moreover, the unique anisotropic puckered honeycomb lattice of BP leads to many novel in-plane anisotropic properties, which could lead to more applications based on BP 3,9,25,26 .Phonon behaviors play an important role in the diverse properties of materials 27 , which has been intensively studied in vdW layered materials, such as graphene and TMDs [28][29][30][31][32][33][34][35] . Raman spectroscopy is a powerful non-destructive tool to investigate the phonons and their coupling to electrons, and has been successfully applied to vdW layered materials [36][37][38][39][40] . Due to the lattice dynamics of vdW layered compounds, the phonon modes in these materials can be classified as high-frequency (HF) intralayer modes and low-frequency (LF) interlayer modes 27 . Intralayer modes involve vibrations from the intralayer chemical bonds (Fig. 1c), and the associated frequencies ...

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Section: Temperature Dependencementioning

confidence: 99%

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

et al. 2015

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“…The sensitivity of the Raman G and 2D bands to both anharmonic coupling of phonon modes and carboncarbon length make Raman spectroscopy a useful tool for studying the temperature and strain dependence of graphene [5][6][7][8] that the effects of strain and doping cannot be neglected when calibrating the temperature coefficient of the Raman modes of graphene. In this work, we measure the Raman spectra of both suspended and supported graphene before, during, and after thermal cycling from 300K to 700K.…”

mentioning

confidence: 99%

“…The sensitivity of the Raman G and 2D bands to both anharmonic coupling of phonon modes and carboncarbon length make Raman spectroscopy a useful tool for studying the temperature and strain dependence of graphene [5][6][7][8]. Recently, Late et al investigated the Raman spectra of single layer graphene on Si/SiO 2 substrates from 77K to 573K, and calibrated the temperature coefficient of the G and 2D band Raman modes to be ∂ω G /∂T = − 0.016 cm Raman G and 2D bands are also used to estimate the effect of strain in graphene [11][12][13][14].…”

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confidence: 99%

Raman spectroscopy of substrate-induced compression and substrate doping in thermally cycled graphene

et al. 2012

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By thermally cycling single layer graphene in air, we observe irreversible upshifts of the Raman G and 2D bands of 24 cm -1 and 23 cm -1 , respectively. These upshifts are attributed to an in-plane compression of the graphene induced by the mismatch of thermal expansion coefficients between the graphene and the underlying Si/SiO 2 substrate, as well as doping effects from the trapped surface charge in the underlying substrate. Since the G and the 2D band frequencies have different responses to doping, we can separate the effects of compression and doping associated with thermal cycling.By performing the thermal cycling in an argon gas environment and by comparing suspended and on-substrate regions of the graphene, we can separate the effects of gas doping and doping from the underlying substrate. Variations in the ratio of the 2D to G band Raman intensities provide an independent measure of the doping in graphene that occurs during thermal cycling. During subsequent thermal cycles, both the G and 2Dbands downshift linearly with increasing temperature, and then upshift reversibly to their original frequencies after cooling. This indicates that no further compression or doping is 2 induced after the first thermal cycle. The observation of ripple formation in suspended graphene after thermal cycling confirms the induction of in-plane compression. The amplitude and wavelength of these ripples remain unchanged after subsequent thermal cycling, corroborating that no further compression is induced after the first thermal cycle. 3In the study of graphene, Raman spectroscopy is used widely for identifying the thickness, carrier concentration, temperature, and strain [1][2][3][4]. The sensitivity of the Raman G and 2D bands to both anharmonic coupling of phonon modes and carboncarbon length make Raman spectroscopy a useful tool for studying the temperature and strain dependence of graphene [5][6][7][8] that the effects of strain and doping cannot be neglected when calibrating the temperature coefficient of the Raman modes of graphene. In this work, we measure the Raman spectra of both suspended and supported graphene before, during, and after thermal cycling from 300K to 700K. Both the Raman G and 2D bands are studied systematically. Atomic force microscopy (AFM) is used to determine the suspended graphene profile variation before and after thermal cycling. Thermal cycling in air and Ar gas environments enables us to indentify changes associated with gas doping. In doing so, we are able to separate the effects of doping, compression, and temperature in graphene through the interpretation of the resulting Raman spectra.In this work, graphene flakes are deposited on Si/SiO 2 substrates using mechanical exfoliation [22,23]. The number of graphene layers are identified using This G band upshift is consistent with our previous work on suspended graphene, which showed a 25 cm -1 upshift in the supported region, while the suspended region remained constant after thermal cycling [30]. In this previous work, ripple formati...

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“…The quartic anharmonicity to first order only contributes to the phonon frequency, thus showing the importance of analyzing both the lifetime and frequency of the modes versus temperature. In most cases, the cubic anharmonicity dominates and results in softening and broadening the phonon as the temperature rises 12 . However, for materials with high anharmonic potentials (e.g.…”

Section: Temperature Dependence Of Phonon Energymentioning

confidence: 99%

“…High resolution and small sample requirements are provided by temperature dependent Raman spectroscopy, which is well established for measuring the evolution of the lattice structure 8 , phonon dynamics and anharmonicity in a wide range of materials [9][10][11][12][13] . While there have been some studies of Bi 2 Te 3−x Se x using Raman spectroscopy 14,15 , these either were limited to fewer phonon modes or samples were measured just at room temperature.…”

Section: Introductionmentioning

confidence: 99%

Understanding the evolution of anomalous anharmonicity in Bi2Te3−xSex

et al. 2017

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Anharmonic effect in thermoelectrics has been a central topic for decades in both condensed matter physics and material science. However, despite the long believed strong and complex anharmonicity in the Bi2Te3−xSex series, experimental verification of anharmonicity and its evolution with doping remains elusive. We fill this important gap with high resolution, temperature dependent Raman spectroscopy in high quality single crystals of Bi2Te3, Bi2Te2Se and Bi2Se3 over the temperature range from 4 K to 293 K. The Klemens's model was employed to explain the renormalization of their phonon linewidths. The phonon energy of Bi2Se3 and Bi2Te3 are analyzed in detail from three aspects, lattice expansion, cubic and quartic anharmonicity. For the first time, we explain the evolution of the anharmonicity in various phonon modes and across the series. In particular we find the interplay between cubic and quartic anharmonicity is governed by their distinct dependence on the phonon density of states, providing insights into anomalous anharmonicity designing of new thermoelectrics.

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Anharmonic phonon effects in Raman spectra of unsupported vertical graphene sheets

Cited by 73 publications

References 44 publications

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

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

Raman spectroscopy of substrate-induced compression and substrate doping in thermally cycled graphene

Understanding the evolution of anomalous anharmonicity in Bi2Te3−xSex

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