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Raman spectra of few-layer phosphorene studied from first-principles calculations
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 185302 (http://iopscience.iop.org/0953-8984/27/18/185302) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.192.114.19 This content was downloaded on 28/05/2015 at 13:35
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 185302 (6pp)
doi:10.1088/0953-8984/27/18/185302
Raman spectra of few-layer phosphorene studied from first-principles calculations Yanqing Feng1 , Jian Zhou2 , Yongping Du1 , Feng Miao1 , Chun-Gang Duan3 , Baigeng Wang1 and Xiangang Wan1 1 Department of Physics and National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China 2 Department of Materials Sciences and Engineering and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China 3 Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, People’s Republic of China
E-mail: [email protected] Received 20 January 2015, revised 22 March 2015 Accepted for publication 26 March 2015 Published 20 April 2015 Abstract
Raman spectra of few-layer phosphorene have been systematically studied using density functional theory calculations. We find that due to the interlayer van der Waals interactions, the low-frequency rigid layer Ag breathing mode and B1g shear mode can shift by as much as 45.1 cm−1 and 38.5 cm−1 , respectively, as the layer numbers increase from 2L to 5L. In addition, a typical characteristic for the experimentally observable A2g mode (∼460 cm−1 in bulk) is identified. Interestingly, this mode changes from coupled in-plane and out-of-plane vibrations in single layer to pure in-plane vibrations in a few layers and the corresponding frequencies vary by as much as over 10 cm−1 . We argue that this Raman frequency variation might be used to experimentally characterize the thickness of this intriguing 2D layered material. Keywords: Raman spectra, density functional theory calculations, few-layer phosphorene (Some figures may appear in colour only in the online journal)
Two-dimensional (2D) materials have attracted a large amount of attention due to their rich physics and promising potential applications [1–3]. The most extensively studied 2D material is graphene [1, 2]. However, a disadvantage for graphene is that it has no band gap, which restrains its applications a lot. Therefore, finding new 2D materials with a finite band gap and high carrier mobility is of both fundamental and technological importance. Single-layer transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS2 ), are promising. Single-layer MoS2 has a direct band gap of 1.75 eV, which allows the fabrication of single-layer MoS2 -based transistors with room temperature on-off current ratios of 1 × 108 [4–7]. Unfortunately, its carrier mobility is quite low [4, 8]. Hence, the synthesis of new 2D materials with novel physical properties and great potential for technological applications is on the way for scientists. Very recently, the 2D layered material phosphorene was found to have an appreciable thickness-dependent direct band 0953-8984/15/185302+06$33.00
gap (increasing from 0.3 eV for bulk to 1.45 eV for single layer with decreasing numbers of layers) [9–12]. The carrier mobility of thin film phosphorene at room temperature is up to 1000 cm2 Vs−1 [9]. Field effect transistors using thin film phosphorene (2 to 15 nm) as channel materials exhibit an onoff current ratio exceeding 1 × 105 , a field-effect mobility of over 200 cm2 Vs−1 and good saturation properties at room temperature [9, 10]. This brings atomic layer phosphorene a tremendous advantage in optoelectronic, electronic and nano-mechanical applications. Thus, the accurate and easy identification of the layer numbers of atomic thick phosphorene is essential. As a nondestructive and powerful technique for characterizing the Brillion zone center ( point) phonon properties of materials, Raman spectroscopy has been widely used to understand the electronic and vibrational properties, as well as their dependence on the thickness of various 2D layered materials [7, 13, 14]. For example, in MoS2 , the redshift of 1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
1 the E2g (∼380 cm−1 ) and the blueshift of A1g (∼400 cm−1 ) on increasing the thickness can conveniently identify the layer numbers [7]. Consequently, a systematic study about the Raman spectra of 2D layered phosphorene is in high demand. In this paper, we present a detailed theoretical study about the Raman spectra of few-layer (labeled as NL, where N is the layer number = 1, 2, 3, 4, 5) and bulk phosphorene by first-principles calculations. We find that the van der Waals (vdW)-corrected calculation method well reproduces the experimentally observed equilibrium geometry and Raman frequencies; the low-frequency rigid layer Ag breathing mode and B1g shear mode can shift by as much as 45.1 cm−1 and 38.5 cm−1 , respectively, as the layer numbers increase from 2L to 5L. Such results verify the importance of considering interlayer vdW interactions in this layered phosphorene. Moreover, with increasing layer numbers, the eigenvectors of the experimentally observable A2g mode (∼460 cm−1 in bulk) change from coupled in-plane and out-of-plane vibrations in 1L to in-plane vibrations in NL (N 2). Their corresponding frequencies vary obviously with the difference between the maximum and minimum over 10 cm−1 , due to stiffer inplane covalent bonding forces than the puckered bonding and interlayer vdW forces. This typical characteristic is critically lacking in this emerging research area and may be a powerful tool to get an accurate and unambiguous identification of the phosphorene layer numbers in experiment. The calculations were performed within the framework of density functional theory (DFT), using the projector augmented wave (PAW) method [15], as implemented in the VASP (Vienna ab-initio Simulation Package) [16]. Different exchange-correlation functions such as the local density approximation (LDA) scheme of Perdew and Zunger (PZ) [17] and the generalized gradient approximation (GGA) scheme of Perdew–Burke–Ernzerhof (PBE) [18] were tested. To check the influence of vdW, we also included the vdW-corrected functions, Grimme correction [19] (vdW-2D) to PBE in the theoretical calculations. This correction adds a semi-empirical dispersion potential to the conventional Kohn–Sham DFT energy for each pair (ij ) of atoms separated by a distance Rij : ij ij EDFT-D = EKS-D + Edis , Edis = i,j f (Rij , R0 ) × C6 × Rij−6 , ij
j
Figure 1. (a) Lattice structure of bulk phosphorene. (b) The projection of puckered layers on the xz plane. (c) Lattice structure of single-layer phosphorene. (d) Lattice structure of two-layer phosphorene. The blue shadow plane is the mirror plane and I is the inversion center.
the inversion center located in the midpoint of the puckered bond. The in-plane (xz plane) crystallographic axis are a (x direction) and c (z direction) and the interlayer crystallographic axis b is along the y direction. Each P atom covalently bonds with three adjacent atoms, with two in-plane covalent bonds and a puckered covalent bond. Each layer is stacked together by vdW interactions. Its puckered layers project onto the xz plane, as shown in figure 1(b), developing a quasi-honeycomb sheet. The lattice structure of the single-layer phosphorene is shown in figure 1(c) and its symmetry space group is Pmna7 D2h with inversion symmetry. The inversion center also lies on the midpoint of the puckered bond, the same as the bulk phosphorene. For the two-layer phosphorene, the space group 11 is D2h and the inversion center lies on the mirror plane midpoint of the two layers, as shown in figure 1(d). At the point of BZ, the point group is isomorphic to D2h (the Schoenies character tables for the point groups can be found in [23]) for bulk and all of the ultrathin-layer phosphorene. The optimized lattice parameters of bulk and singlelayer phosphorene are shown in table 1. We can see that for bulk phosphorene the largest discrepancy of the three calculated lattice parameters with different methods is b, which is along the interlayer stacking direction. The vdW-D method gives the best result comparable with the experimental result. The LDA underestimates b a lot by 4.40% and the GGA overestimates b by 0.64%. The same situation also occurs in the calculated Raman frequencies, as shown in table 2. We find that the vdW-D method indeed provides the most accurate
ij
R0 = R0i + R0 . Here, f (Rij , R0 ) is a damping function, R0i is ij the vdW radii for the i atom, C6 is the dispersion coefficient. In our calculations, the controlled parameters R0i are 1.705 Å and ij C6 is 7.84 Jnm6 mol−1 [19]. The planewave cutoff energy is 550 eV. The NL (N = 1, 2, 3, 4, 5) phosphorene were simulated with a vacuum of 15 Å in the layer stacking direction to ensure negligible interactions between their periodic images. The BZ integration was done on uniform Monkhorst–Pack grids [20] of 24 × 1 × 24 for NL (N = 1, 2, 3, 4, 5) phosphorene and 24 × 6 × 24 for bulk phosphorene. The convergence criterion of self-consistent calculations was 10−5 eV between two consecutive steps. The convergence criterion of relaxation was that the Hellman–Feynman forces on the ions were less than 0.006 eV Å−1 . Bulk phosphorene crystallizes in a base-centered orthorhombic structure, as shown in figure 1(a), with the space 18 group of Cmca-D2h [21, 22]. It owns inversion symmetry with 2
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
1 Table 1. The calculated lattice constants (in unit of Å) as well as the intra-plane P–P bond length (dP−P ) and puckered P–P bond length 2 ) of bulk and single-layer phosphorene with different methods. (dP−P
Bulk
Method
a
b
c
1 dP−P
2 dP−P
1L
LDA GGA vdW-D vdW-D [21] HSE03 [24] Exp. [25] Method
3.256 3.326 3.323 3.300 3.284 3.314 a
10.017 10.545 10.468 10.430 11.135 10.478 b
4.192 4.442 4.423 4.440 4.527 4.376 c
2.223 2.229 2.222 2.225 2.202 2.224 1 dP−P
2.248 2.259 2.260 2.259 2.234 2.244 2 dP−P
LDA GGA DFT-PBE [10]
3.248 3.324 3.35
— — —
4.302 4.457 4.62
2.183 2.229 —
2.210 2.257 —
Note: Previous theoretical data and experiment results are also listed for comparison. Table 2. The Raman frequencies (in unit of cm−1 ) of bulk and single-layer phosphorene with different calculation methods.
Bulk
Method
B1g
1 B3g
A1g
2 B3g
B2g
A2g
1L
LDA GGA vdW-D vdW-D [21] Exp. [26] Method
182.0 181.6 190.7 187.6 192.4 B1g
220.8 220.2 230.7 224.8 227.7 1 B3g
354.1 343.1 360.7 347.2 361.7 A1g
415.2 417.0 418.1 418.3 — 2 B3g
424.6 426.6 435.5 435.2 438.9 B2g
450.1 446.2 460.1 459.8 465.9 A2g
LDA GGA LDA [28] Exp [10]
191.7 190.6 — —
225.8 224.1 — —
368.9 366.3 368 360
427.2 424.0 — —
441.6 434.8 433 440
459.1 453.2 456 465
Note: The related reference data and experiment results are also listed for comparison.
Figure 2. Raman active modes for single-layer phosphorene. The out-of-plane direction is along y; the in-plane directions are x (zigzag direction) and z (armchair direction). The denoted frequencies are the results of the first-principle calculations with the LDA method.
frequencies for bulk phosphorene. And it also matches well with the results of Appalakondaiah et al [21]. Therefore, the interlayer vdW interactions need to be taken into account in this material.
Based on the above obtained structures, we then carry out the lattice dynamic study. A bulk phosphorene primitive cell contains four atoms leading to 12 vibrational modes. According to the group theory [27], the irreducible 3
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
18 representations of point phonons can be written as: D2h = (acoustic ) + (optical ) = (B1u + B2u + B3u ) + (B1u + B2u + Au + 2Ag +B1g +B2g +2B3g ), among which there are three acoustical modes (B1u , B2u , B3u ) and two infrared active optical modes (B1u , B2u ) as well as one silent mode (Au ). The other modes, 1 2Ag (denoted as A1g , A2g ), B1g and B2g , 2B3g (denoted as B3g , 2 B3g ), are first-order Raman active modes and are all nondegenerate. As shown in table 2, there are no low frequency Raman modes below 100 cm−1 . Through an analysis of the vibration eigenvectors, we find that A1g and A2g modes involve coupled in-plane and out-of-plane vibrations. A1g mode has a large component along the out-of-plane direction and A2g mode has a large component along the in-plane armchair direction. B1g and B2g modes move along the in-plane zigzag direction, 1 2 while the B3g mode moves along the armchair direction. B3g mode forms out-of-plane vibrations along the out-of-plane direction, in good agreement with the previous work [21]. For NL phosphorene (N = 1, 2, 3, 4, 5, . . .), the primitive cell contains 4N atoms leading to 12N vibration modes. = 2N(B1u +B2u +Ag +B3g )+N(B3u +Au +B1g +B2g ) and Raman = N(2Ag + 2B3g + B1g + B2g ). There are 6N nondegenerate Raman active modes in NL phosphorene. The six Raman vibration modes for single layer are shown in figure 2, which are similar to that of bulk phosphorene. For NL (N 2) phosphorene, in a low frequency range below 100 cm−1 , there 1 appear rigid-layer vibration Raman modes (Ag , B1g , B3g ) with each layer moving as one unit, which are shown in figure 3. As shown in figure 3, Ag are out-of-plane breathing modes; B1g (moving along the zigzag direction (x direction)) and 1 B3g (moving along the armchair direction (z direction)) are in-plane shear modes. For the modes in the (a) rows, NL can be divided into two groups, with each group being inphase vibrations. Wheres for the modes in the (b) rows, all the adjacent layers are out-of-phase vibrations. The vdW-D method calculated Raman frequencies with their symmetry labels of 2–5L and bulk phosphorene are shown in table 3. For single-layer phosphorene with an absence of interlayer vdW interactions, the pure LDA gives the best Raman frequencies matching with the experiment values (as shown in table 2). Thus, we use the LDA results. Now we discuss the frequency shift tendency with layer numbers for low-frequency rigid-layer Raman modes (as shown in figure 3). The Ag breathing mode in (a) row redshifts by 45.1 cm−1 as the numbers of the layers increase from 2L (74.7 cm−1 ) to 5L (29.6 cm−1 ) and in (b) row redshifts by 9.4 cm−1 from 4L (92.5 cm−1 ) to 5L (83.1 cm−1 ). The B1g shear mode in (a) row redshifts by 38.5 cm−1 from 2L to 5L and 1 in (b) row redshifts by 8.1 cm−1 from 4L to 5L. The B3g shear mode in (a) row changes randomly from 2L to 5L, but in (b) row redshifts by 4.7 cm−1 from 4L to 5L. All these frequency shift tendencies can be explained by considering the linearchain model, assuming that a layer interacts strongly only with adjacent layers and that the strength of the interlayer coupling is characterized by an interlayer vdW force. This model has been used to explain the low-frequency shift tendency of multilayer MoS2 and graphene [29–31]. For Ag breathing mode, in the case of (a) row, a larger N implies more inphase layer vibrations with a larger mass, leading to redshift;
Figure 3. Low-frequency rigid-layer breathing (Ag ) and shear (B1g , 1 ) Raman modes for NL (N = 2, 3, 4, 5) phosphorene. The B3g denoted frequencies are the results of the first-principles calculations with the vdW-D method, in which each black transverse line denotes a rigid single layer moving as one unit and each red arrow indicates the movement direction of the rigid single layer.
while in the case of (b) row, the stable layer in the middle weakens the interlayer vdW force and a larger N means a larger mass, leading to a decreased frequencies tendency. The same 1 shear modes. explanations are also applied to B1g and B3g From the data analysis above, we find that the frequency shift tendency with the layer numbers is somewhat larger than those of multilayer MoS2 and graphene. For MoS2 , as the 4
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
Table 3. Raman frequencies (in unit of cm−1 ) and their corresponding symmetry representations for NL (N = 1, 2, 3, 4, 5) and bulk phosphorene.
Symmetry B1g 1 B3g 1 B3g B1g Ag B1g Ag 2 B3g 2 B3g B1g B1g B1g 1 B3g 1 B3g 1 B3g 1 Ag A1g A1g 2 B3g 2 B3g B2g 2 B3g B2g B2g B2g B2g A2g A2g A2g Ag Ag
1L
2L
3L
9.2
6.3
4L
10.2 11.7 43.3 26.0 15.9 74.7 52.0 40.2 51.1 92.5 137.7 152.3 146.4 174.8 191.7 188.2 190.5 190.8 192.9 192.1 225.8 224.0 223.9 225.7 231.7 231.4 368.9 360.3 363.1 361.0 364.9 364.3 427.2 426.3 422.4 424.6 441.6 438.0 434.4 435.0 439.3 435.3 435.9
429.4 431.3 432.1 434.2 435.0
459.1 455.6 454.9 451.3 456.0 454.4 457.2 469.3 468.9 468.7
5L
to distinguish in the Raman spectrum, thus only one Raman peak in thin film phosphorene remains at around 440 cm−1 under Raman spectroscopy with no significant position change [10, 11, 32]. Whereas for A2g modes, the frequency of the increased modes seems to be able to be divided into two groups (460 cm−1 for the other group) and their frequency differences of the increased modes are quite obvious with the differences between the maximum and minimum being over 10 cm−1 . A further analysis shows that the eigenvectors of A2g modes change from coupled in-plane and out-of-plane vibrations in 1L to in-plane vibrations (denoted as Ag modes, as shown in table 3) in NL (N 2) with increasing layer numbers. The covalent intralayer bonds are much stiffer than the puckered covalent bonds and interlayer vdW interaction [33], which renders higher phonon frequencies for Ag modes than A2g modes, leading to obvious frequency differences of the increased modes. Thus, the numbers of the linearly increased A2g and Ag subpeaks may make it possible to experimentally probe the layer numbers of this layered material under certain wavelength excitations with high resolution. In summary, we have presented a detailed study about the Raman spectra of single-layer, few-layer (N = 1, 2, 3, 4, 5) and bulk phosphorene by first-principles calculations. We find that the interlayer vdW interactions are dominated along the stacking direction in this material. We have also revealed that a typical characteristic for the coupled in-plane and out-of-plane A2g modes at around 460 cm−1 in single-layer phosphorene can evolve into in-plane vibration Ag modes with high phonon frequency in few layers with increasing layer numbers. Due to the fact that covalent intralayer bonds are stiffer than the puckered covalent bonds and interlayer vdW interaction, the frequency differences of the increased A2g modes and Ag modes are significant. We expect our theoretical calculations and analysis will provide a way to the unambiguous identification of layer numbers for 2D phosphorene in experiment.
Bulk
4.8 5.5 7.0 29.6 43.4 83.1 143.2 169.1 189.3 189.6 192.2 221.7 227.1 231.2 360.9 362.5 365.0 419.5 423.8 430.6 431.6 433.1 434.0 434.6 434.8 441.9 449.3 453.0 467.0 468.7
190.7 230.7
360.7
418.1 435.5
460.1
2 thickness increases from 2L to bulk, the E2g shear mode 2 −1 blueshifts ∼10 cm and the B2g breathing mode redshifts ∼30 cm−1 [30]. For graphene, the E2g shear mode scales ∼12 cm−1 from 2L to bulk [29]. These results further confirm that interlayer vdW interactions in phosphorene are dominated along the layer stacking direction. Such an obvious frequency shift tendency with layer numbers for low-frequency rigidlayer Raman modes may be observed in Raman experiments and provide a direct probe of interlayer interactions, given that the low-frequency rigid-layer Raman modes of multilayer MoS2 [30] and graphene [29] have been probed in Raman experiments in recent years. Next, we focus on the high-frequency Raman modes above 100 cm−1 . As shown in table 3, for all the high-frequency Raman modes, we do not observe a considerable and regular frequency shift tendency with increasing layer numbers, while each Raman mode in the single layer evolves into more and more Raman modes with similar frequencies in NL (N 2). We notice that the numbers of the experimentally observable B2g and A2g modes around 440 and 460 cm−1 increase linearly with N, with one mode in 1L and five modes in 5L. Among the increased modes, the frequency differences for B2g modes are tiny (< 5 cm−1 for the maximal difference). These small frequency differences imply that the two modes would be hard
Acknowledgments
The work was supported by the National Key Project for Basic Research of China (Grants No. 2011CB922101, 2014CB921104), NSFC under Grants No. 11474150 and 61125403. We also acknowledge the support for the computational resources by the High Performance Computing Center of Nanjing University. References [1] Novoselov K S, Jiang D, Shedin F, Booth T J, Khot-kevich V V, Morozov S V and Geim A K 2005 Proc. Natl Acad. Sci. USA 102 10451 [2] Castro A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2011 Rev. Mod. Phys. 81 109 [3] Chhowalla M, Shin H S, Eda G, Li L J, Loh K P and Zhang H 2010 Nat. Nanotechnol. 5 487 [4] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and KisL A 2011 Nat. Nanotechnol. 6 147 [5] Mak K F, Lee C and Hone J 2010 Phys. Rev. Lett. 105 136805 [6] Splendiani 2010 Nano Lett. 10 1271 5
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
[7] Lee C, Yan H, Brus L E, Heinz T F, Hone J and Ryu S 2010 ACS Nano 4 2695 [8] Fuhrer M S and Hone J 2013 Nat. Nanotechnol. 8 146 Kis A and Radisavljevic B 2013 Nat. Nanotechnol. 8 147 [9] Li L K, Yu Y J, Ye G J, Ge Q Q, Ou X D, Wu H, Feng D L, Chen X H and Zhang Y B 2014 Nat. Nanotechnol. 9 372 [10] Liu H, Neal A T, Zhu Z, Luo Z, Xu X F, Tom´anek D and Ye P D 2014 ACS Nano 8 4033 [11] Zhang S, Yang J, Xu R, Wang F, Li W, Ghufran M, Zhang Y-W, Yu Z, Zhang G and Qin Q 2014 ACS Nano 8 9590 [12] Tran V, Soklaski R, Liang Y F and Yang L 2014 Phys. Rev. B 89 235319 [13] Ferrari A C 2007 Solid State Commun. 143 47 [14] Lui C H, Leandro M M, Kim S H, Lantz G, Laverge F E, Saito R and Heinz T F 2012 Nano Lett. 12 5539 [15] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [16] Kresse G and Hafner J 1993 Phys. Rev. B 47 558 [17] Perdew J P and Zunger A 1981 Phys. Rev. B 23 5048 [18] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[19] Grimme S 2006 J. Comput. Chem. 27 1787 [20] Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188 [21] Appalakondaiah S and Vaitheeswaran G 2012 Phys. Rev. B 86 035105 [22] Brown A and Rundqvist S 1965 Acta Cryst. 19 684 [23] Dresselhaus M S, Dresselhaus G and Jorio A 1986 Group Theory (Application to the Physics of Condensed Matter) (Berlin: Springer) [24] Prytz E and Flage-Larsen E 2010 J. Phys.: Condens. Matter. 22 015502 [25] Takao Y and Morita A 1981 Physica B+C 105 93 [26] Akahama Y, Kobayashi M and Kawamura H 1997 Solid State Commun. 104 311 [27] Tuinstra F and Koenig J L 1970 J. Chem. Phys. 53 1126 [28] Fei R X and Yang L 2014 Appl. Phys. Lett. 105 083120 [29] Tan P H et al 2012 Nat. Mater. 11 294 [30] Zhao Y Y et al 2013 Nano Lett. 13 1007 [31] Michel K H and Verberck B 2012 Phys. Rev. B 85 094303 [32] Xia F N, Wang H and Jia Y C 2014 Nat. Commun. 5 4458 [33] Wei Q and Peng X H 2014 Appl. Phys. Lett. 104 251915
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Raman spectra of few-layer phosphorene studied from first-principles calculations
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 185302 (http://iopscience.iop.org/0953-8984/27/18/185302) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.192.114.19 This content was downloaded on 28/05/2015 at 13:35
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 185302 (6pp)
doi:10.1088/0953-8984/27/18/185302
Raman spectra of few-layer phosphorene studied from first-principles calculations Yanqing Feng1 , Jian Zhou2 , Yongping Du1 , Feng Miao1 , Chun-Gang Duan3 , Baigeng Wang1 and Xiangang Wan1 1 Department of Physics and National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China 2 Department of Materials Sciences and Engineering and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China 3 Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, People’s Republic of China
E-mail: [email protected] Received 20 January 2015, revised 22 March 2015 Accepted for publication 26 March 2015 Published 20 April 2015 Abstract
Raman spectra of few-layer phosphorene have been systematically studied using density functional theory calculations. We find that due to the interlayer van der Waals interactions, the low-frequency rigid layer Ag breathing mode and B1g shear mode can shift by as much as 45.1 cm−1 and 38.5 cm−1 , respectively, as the layer numbers increase from 2L to 5L. In addition, a typical characteristic for the experimentally observable A2g mode (∼460 cm−1 in bulk) is identified. Interestingly, this mode changes from coupled in-plane and out-of-plane vibrations in single layer to pure in-plane vibrations in a few layers and the corresponding frequencies vary by as much as over 10 cm−1 . We argue that this Raman frequency variation might be used to experimentally characterize the thickness of this intriguing 2D layered material. Keywords: Raman spectra, density functional theory calculations, few-layer phosphorene (Some figures may appear in colour only in the online journal)
Two-dimensional (2D) materials have attracted a large amount of attention due to their rich physics and promising potential applications [1–3]. The most extensively studied 2D material is graphene [1, 2]. However, a disadvantage for graphene is that it has no band gap, which restrains its applications a lot. Therefore, finding new 2D materials with a finite band gap and high carrier mobility is of both fundamental and technological importance. Single-layer transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS2 ), are promising. Single-layer MoS2 has a direct band gap of 1.75 eV, which allows the fabrication of single-layer MoS2 -based transistors with room temperature on-off current ratios of 1 × 108 [4–7]. Unfortunately, its carrier mobility is quite low [4, 8]. Hence, the synthesis of new 2D materials with novel physical properties and great potential for technological applications is on the way for scientists. Very recently, the 2D layered material phosphorene was found to have an appreciable thickness-dependent direct band 0953-8984/15/185302+06$33.00
gap (increasing from 0.3 eV for bulk to 1.45 eV for single layer with decreasing numbers of layers) [9–12]. The carrier mobility of thin film phosphorene at room temperature is up to 1000 cm2 Vs−1 [9]. Field effect transistors using thin film phosphorene (2 to 15 nm) as channel materials exhibit an onoff current ratio exceeding 1 × 105 , a field-effect mobility of over 200 cm2 Vs−1 and good saturation properties at room temperature [9, 10]. This brings atomic layer phosphorene a tremendous advantage in optoelectronic, electronic and nano-mechanical applications. Thus, the accurate and easy identification of the layer numbers of atomic thick phosphorene is essential. As a nondestructive and powerful technique for characterizing the Brillion zone center ( point) phonon properties of materials, Raman spectroscopy has been widely used to understand the electronic and vibrational properties, as well as their dependence on the thickness of various 2D layered materials [7, 13, 14]. For example, in MoS2 , the redshift of 1
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J. Phys.: Condens. Matter 27 (2015) 185302
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1 the E2g (∼380 cm−1 ) and the blueshift of A1g (∼400 cm−1 ) on increasing the thickness can conveniently identify the layer numbers [7]. Consequently, a systematic study about the Raman spectra of 2D layered phosphorene is in high demand. In this paper, we present a detailed theoretical study about the Raman spectra of few-layer (labeled as NL, where N is the layer number = 1, 2, 3, 4, 5) and bulk phosphorene by first-principles calculations. We find that the van der Waals (vdW)-corrected calculation method well reproduces the experimentally observed equilibrium geometry and Raman frequencies; the low-frequency rigid layer Ag breathing mode and B1g shear mode can shift by as much as 45.1 cm−1 and 38.5 cm−1 , respectively, as the layer numbers increase from 2L to 5L. Such results verify the importance of considering interlayer vdW interactions in this layered phosphorene. Moreover, with increasing layer numbers, the eigenvectors of the experimentally observable A2g mode (∼460 cm−1 in bulk) change from coupled in-plane and out-of-plane vibrations in 1L to in-plane vibrations in NL (N 2). Their corresponding frequencies vary obviously with the difference between the maximum and minimum over 10 cm−1 , due to stiffer inplane covalent bonding forces than the puckered bonding and interlayer vdW forces. This typical characteristic is critically lacking in this emerging research area and may be a powerful tool to get an accurate and unambiguous identification of the phosphorene layer numbers in experiment. The calculations were performed within the framework of density functional theory (DFT), using the projector augmented wave (PAW) method [15], as implemented in the VASP (Vienna ab-initio Simulation Package) [16]. Different exchange-correlation functions such as the local density approximation (LDA) scheme of Perdew and Zunger (PZ) [17] and the generalized gradient approximation (GGA) scheme of Perdew–Burke–Ernzerhof (PBE) [18] were tested. To check the influence of vdW, we also included the vdW-corrected functions, Grimme correction [19] (vdW-2D) to PBE in the theoretical calculations. This correction adds a semi-empirical dispersion potential to the conventional Kohn–Sham DFT energy for each pair (ij ) of atoms separated by a distance Rij : ij ij EDFT-D = EKS-D + Edis , Edis = i,j f (Rij , R0 ) × C6 × Rij−6 , ij
j
Figure 1. (a) Lattice structure of bulk phosphorene. (b) The projection of puckered layers on the xz plane. (c) Lattice structure of single-layer phosphorene. (d) Lattice structure of two-layer phosphorene. The blue shadow plane is the mirror plane and I is the inversion center.
the inversion center located in the midpoint of the puckered bond. The in-plane (xz plane) crystallographic axis are a (x direction) and c (z direction) and the interlayer crystallographic axis b is along the y direction. Each P atom covalently bonds with three adjacent atoms, with two in-plane covalent bonds and a puckered covalent bond. Each layer is stacked together by vdW interactions. Its puckered layers project onto the xz plane, as shown in figure 1(b), developing a quasi-honeycomb sheet. The lattice structure of the single-layer phosphorene is shown in figure 1(c) and its symmetry space group is Pmna7 D2h with inversion symmetry. The inversion center also lies on the midpoint of the puckered bond, the same as the bulk phosphorene. For the two-layer phosphorene, the space group 11 is D2h and the inversion center lies on the mirror plane midpoint of the two layers, as shown in figure 1(d). At the point of BZ, the point group is isomorphic to D2h (the Schoenies character tables for the point groups can be found in [23]) for bulk and all of the ultrathin-layer phosphorene. The optimized lattice parameters of bulk and singlelayer phosphorene are shown in table 1. We can see that for bulk phosphorene the largest discrepancy of the three calculated lattice parameters with different methods is b, which is along the interlayer stacking direction. The vdW-D method gives the best result comparable with the experimental result. The LDA underestimates b a lot by 4.40% and the GGA overestimates b by 0.64%. The same situation also occurs in the calculated Raman frequencies, as shown in table 2. We find that the vdW-D method indeed provides the most accurate
ij
R0 = R0i + R0 . Here, f (Rij , R0 ) is a damping function, R0i is ij the vdW radii for the i atom, C6 is the dispersion coefficient. In our calculations, the controlled parameters R0i are 1.705 Å and ij C6 is 7.84 Jnm6 mol−1 [19]. The planewave cutoff energy is 550 eV. The NL (N = 1, 2, 3, 4, 5) phosphorene were simulated with a vacuum of 15 Å in the layer stacking direction to ensure negligible interactions between their periodic images. The BZ integration was done on uniform Monkhorst–Pack grids [20] of 24 × 1 × 24 for NL (N = 1, 2, 3, 4, 5) phosphorene and 24 × 6 × 24 for bulk phosphorene. The convergence criterion of self-consistent calculations was 10−5 eV between two consecutive steps. The convergence criterion of relaxation was that the Hellman–Feynman forces on the ions were less than 0.006 eV Å−1 . Bulk phosphorene crystallizes in a base-centered orthorhombic structure, as shown in figure 1(a), with the space 18 group of Cmca-D2h [21, 22]. It owns inversion symmetry with 2
J. Phys.: Condens. Matter 27 (2015) 185302
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1 Table 1. The calculated lattice constants (in unit of Å) as well as the intra-plane P–P bond length (dP−P ) and puckered P–P bond length 2 ) of bulk and single-layer phosphorene with different methods. (dP−P
Bulk
Method
a
b
c
1 dP−P
2 dP−P
1L
LDA GGA vdW-D vdW-D [21] HSE03 [24] Exp. [25] Method
3.256 3.326 3.323 3.300 3.284 3.314 a
10.017 10.545 10.468 10.430 11.135 10.478 b
4.192 4.442 4.423 4.440 4.527 4.376 c
2.223 2.229 2.222 2.225 2.202 2.224 1 dP−P
2.248 2.259 2.260 2.259 2.234 2.244 2 dP−P
LDA GGA DFT-PBE [10]
3.248 3.324 3.35
— — —
4.302 4.457 4.62
2.183 2.229 —
2.210 2.257 —
Note: Previous theoretical data and experiment results are also listed for comparison. Table 2. The Raman frequencies (in unit of cm−1 ) of bulk and single-layer phosphorene with different calculation methods.
Bulk
Method
B1g
1 B3g
A1g
2 B3g
B2g
A2g
1L
LDA GGA vdW-D vdW-D [21] Exp. [26] Method
182.0 181.6 190.7 187.6 192.4 B1g
220.8 220.2 230.7 224.8 227.7 1 B3g
354.1 343.1 360.7 347.2 361.7 A1g
415.2 417.0 418.1 418.3 — 2 B3g
424.6 426.6 435.5 435.2 438.9 B2g
450.1 446.2 460.1 459.8 465.9 A2g
LDA GGA LDA [28] Exp [10]
191.7 190.6 — —
225.8 224.1 — —
368.9 366.3 368 360
427.2 424.0 — —
441.6 434.8 433 440
459.1 453.2 456 465
Note: The related reference data and experiment results are also listed for comparison.
Figure 2. Raman active modes for single-layer phosphorene. The out-of-plane direction is along y; the in-plane directions are x (zigzag direction) and z (armchair direction). The denoted frequencies are the results of the first-principle calculations with the LDA method.
frequencies for bulk phosphorene. And it also matches well with the results of Appalakondaiah et al [21]. Therefore, the interlayer vdW interactions need to be taken into account in this material.
Based on the above obtained structures, we then carry out the lattice dynamic study. A bulk phosphorene primitive cell contains four atoms leading to 12 vibrational modes. According to the group theory [27], the irreducible 3
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18 representations of point phonons can be written as: D2h = (acoustic ) + (optical ) = (B1u + B2u + B3u ) + (B1u + B2u + Au + 2Ag +B1g +B2g +2B3g ), among which there are three acoustical modes (B1u , B2u , B3u ) and two infrared active optical modes (B1u , B2u ) as well as one silent mode (Au ). The other modes, 1 2Ag (denoted as A1g , A2g ), B1g and B2g , 2B3g (denoted as B3g , 2 B3g ), are first-order Raman active modes and are all nondegenerate. As shown in table 2, there are no low frequency Raman modes below 100 cm−1 . Through an analysis of the vibration eigenvectors, we find that A1g and A2g modes involve coupled in-plane and out-of-plane vibrations. A1g mode has a large component along the out-of-plane direction and A2g mode has a large component along the in-plane armchair direction. B1g and B2g modes move along the in-plane zigzag direction, 1 2 while the B3g mode moves along the armchair direction. B3g mode forms out-of-plane vibrations along the out-of-plane direction, in good agreement with the previous work [21]. For NL phosphorene (N = 1, 2, 3, 4, 5, . . .), the primitive cell contains 4N atoms leading to 12N vibration modes. = 2N(B1u +B2u +Ag +B3g )+N(B3u +Au +B1g +B2g ) and Raman = N(2Ag + 2B3g + B1g + B2g ). There are 6N nondegenerate Raman active modes in NL phosphorene. The six Raman vibration modes for single layer are shown in figure 2, which are similar to that of bulk phosphorene. For NL (N 2) phosphorene, in a low frequency range below 100 cm−1 , there 1 appear rigid-layer vibration Raman modes (Ag , B1g , B3g ) with each layer moving as one unit, which are shown in figure 3. As shown in figure 3, Ag are out-of-plane breathing modes; B1g (moving along the zigzag direction (x direction)) and 1 B3g (moving along the armchair direction (z direction)) are in-plane shear modes. For the modes in the (a) rows, NL can be divided into two groups, with each group being inphase vibrations. Wheres for the modes in the (b) rows, all the adjacent layers are out-of-phase vibrations. The vdW-D method calculated Raman frequencies with their symmetry labels of 2–5L and bulk phosphorene are shown in table 3. For single-layer phosphorene with an absence of interlayer vdW interactions, the pure LDA gives the best Raman frequencies matching with the experiment values (as shown in table 2). Thus, we use the LDA results. Now we discuss the frequency shift tendency with layer numbers for low-frequency rigid-layer Raman modes (as shown in figure 3). The Ag breathing mode in (a) row redshifts by 45.1 cm−1 as the numbers of the layers increase from 2L (74.7 cm−1 ) to 5L (29.6 cm−1 ) and in (b) row redshifts by 9.4 cm−1 from 4L (92.5 cm−1 ) to 5L (83.1 cm−1 ). The B1g shear mode in (a) row redshifts by 38.5 cm−1 from 2L to 5L and 1 in (b) row redshifts by 8.1 cm−1 from 4L to 5L. The B3g shear mode in (a) row changes randomly from 2L to 5L, but in (b) row redshifts by 4.7 cm−1 from 4L to 5L. All these frequency shift tendencies can be explained by considering the linearchain model, assuming that a layer interacts strongly only with adjacent layers and that the strength of the interlayer coupling is characterized by an interlayer vdW force. This model has been used to explain the low-frequency shift tendency of multilayer MoS2 and graphene [29–31]. For Ag breathing mode, in the case of (a) row, a larger N implies more inphase layer vibrations with a larger mass, leading to redshift;
Figure 3. Low-frequency rigid-layer breathing (Ag ) and shear (B1g , 1 ) Raman modes for NL (N = 2, 3, 4, 5) phosphorene. The B3g denoted frequencies are the results of the first-principles calculations with the vdW-D method, in which each black transverse line denotes a rigid single layer moving as one unit and each red arrow indicates the movement direction of the rigid single layer.
while in the case of (b) row, the stable layer in the middle weakens the interlayer vdW force and a larger N means a larger mass, leading to a decreased frequencies tendency. The same 1 shear modes. explanations are also applied to B1g and B3g From the data analysis above, we find that the frequency shift tendency with the layer numbers is somewhat larger than those of multilayer MoS2 and graphene. For MoS2 , as the 4
J. Phys.: Condens. Matter 27 (2015) 185302
Y Feng et al
Table 3. Raman frequencies (in unit of cm−1 ) and their corresponding symmetry representations for NL (N = 1, 2, 3, 4, 5) and bulk phosphorene.
Symmetry B1g 1 B3g 1 B3g B1g Ag B1g Ag 2 B3g 2 B3g B1g B1g B1g 1 B3g 1 B3g 1 B3g 1 Ag A1g A1g 2 B3g 2 B3g B2g 2 B3g B2g B2g B2g B2g A2g A2g A2g Ag Ag
1L
2L
3L
9.2
6.3
4L
10.2 11.7 43.3 26.0 15.9 74.7 52.0 40.2 51.1 92.5 137.7 152.3 146.4 174.8 191.7 188.2 190.5 190.8 192.9 192.1 225.8 224.0 223.9 225.7 231.7 231.4 368.9 360.3 363.1 361.0 364.9 364.3 427.2 426.3 422.4 424.6 441.6 438.0 434.4 435.0 439.3 435.3 435.9
429.4 431.3 432.1 434.2 435.0
459.1 455.6 454.9 451.3 456.0 454.4 457.2 469.3 468.9 468.7
5L
to distinguish in the Raman spectrum, thus only one Raman peak in thin film phosphorene remains at around 440 cm−1 under Raman spectroscopy with no significant position change [10, 11, 32]. Whereas for A2g modes, the frequency of the increased modes seems to be able to be divided into two groups (460 cm−1 for the other group) and their frequency differences of the increased modes are quite obvious with the differences between the maximum and minimum being over 10 cm−1 . A further analysis shows that the eigenvectors of A2g modes change from coupled in-plane and out-of-plane vibrations in 1L to in-plane vibrations (denoted as Ag modes, as shown in table 3) in NL (N 2) with increasing layer numbers. The covalent intralayer bonds are much stiffer than the puckered covalent bonds and interlayer vdW interaction [33], which renders higher phonon frequencies for Ag modes than A2g modes, leading to obvious frequency differences of the increased modes. Thus, the numbers of the linearly increased A2g and Ag subpeaks may make it possible to experimentally probe the layer numbers of this layered material under certain wavelength excitations with high resolution. In summary, we have presented a detailed study about the Raman spectra of single-layer, few-layer (N = 1, 2, 3, 4, 5) and bulk phosphorene by first-principles calculations. We find that the interlayer vdW interactions are dominated along the stacking direction in this material. We have also revealed that a typical characteristic for the coupled in-plane and out-of-plane A2g modes at around 460 cm−1 in single-layer phosphorene can evolve into in-plane vibration Ag modes with high phonon frequency in few layers with increasing layer numbers. Due to the fact that covalent intralayer bonds are stiffer than the puckered covalent bonds and interlayer vdW interaction, the frequency differences of the increased A2g modes and Ag modes are significant. We expect our theoretical calculations and analysis will provide a way to the unambiguous identification of layer numbers for 2D phosphorene in experiment.
Bulk
4.8 5.5 7.0 29.6 43.4 83.1 143.2 169.1 189.3 189.6 192.2 221.7 227.1 231.2 360.9 362.5 365.0 419.5 423.8 430.6 431.6 433.1 434.0 434.6 434.8 441.9 449.3 453.0 467.0 468.7
190.7 230.7
360.7
418.1 435.5
460.1
2 thickness increases from 2L to bulk, the E2g shear mode 2 −1 blueshifts ∼10 cm and the B2g breathing mode redshifts ∼30 cm−1 [30]. For graphene, the E2g shear mode scales ∼12 cm−1 from 2L to bulk [29]. These results further confirm that interlayer vdW interactions in phosphorene are dominated along the layer stacking direction. Such an obvious frequency shift tendency with layer numbers for low-frequency rigidlayer Raman modes may be observed in Raman experiments and provide a direct probe of interlayer interactions, given that the low-frequency rigid-layer Raman modes of multilayer MoS2 [30] and graphene [29] have been probed in Raman experiments in recent years. Next, we focus on the high-frequency Raman modes above 100 cm−1 . As shown in table 3, for all the high-frequency Raman modes, we do not observe a considerable and regular frequency shift tendency with increasing layer numbers, while each Raman mode in the single layer evolves into more and more Raman modes with similar frequencies in NL (N 2). We notice that the numbers of the experimentally observable B2g and A2g modes around 440 and 460 cm−1 increase linearly with N, with one mode in 1L and five modes in 5L. Among the increased modes, the frequency differences for B2g modes are tiny (< 5 cm−1 for the maximal difference). These small frequency differences imply that the two modes would be hard
Acknowledgments
The work was supported by the National Key Project for Basic Research of China (Grants No. 2011CB922101, 2014CB921104), NSFC under Grants No. 11474150 and 61125403. We also acknowledge the support for the computational resources by the High Performance Computing Center of Nanjing University. References [1] Novoselov K S, Jiang D, Shedin F, Booth T J, Khot-kevich V V, Morozov S V and Geim A K 2005 Proc. Natl Acad. Sci. USA 102 10451 [2] Castro A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2011 Rev. Mod. Phys. 81 109 [3] Chhowalla M, Shin H S, Eda G, Li L J, Loh K P and Zhang H 2010 Nat. Nanotechnol. 5 487 [4] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and KisL A 2011 Nat. Nanotechnol. 6 147 [5] Mak K F, Lee C and Hone J 2010 Phys. Rev. Lett. 105 136805 [6] Splendiani 2010 Nano Lett. 10 1271 5
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Y Feng et al
[7] Lee C, Yan H, Brus L E, Heinz T F, Hone J and Ryu S 2010 ACS Nano 4 2695 [8] Fuhrer M S and Hone J 2013 Nat. Nanotechnol. 8 146 Kis A and Radisavljevic B 2013 Nat. Nanotechnol. 8 147 [9] Li L K, Yu Y J, Ye G J, Ge Q Q, Ou X D, Wu H, Feng D L, Chen X H and Zhang Y B 2014 Nat. Nanotechnol. 9 372 [10] Liu H, Neal A T, Zhu Z, Luo Z, Xu X F, Tom´anek D and Ye P D 2014 ACS Nano 8 4033 [11] Zhang S, Yang J, Xu R, Wang F, Li W, Ghufran M, Zhang Y-W, Yu Z, Zhang G and Qin Q 2014 ACS Nano 8 9590 [12] Tran V, Soklaski R, Liang Y F and Yang L 2014 Phys. Rev. B 89 235319 [13] Ferrari A C 2007 Solid State Commun. 143 47 [14] Lui C H, Leandro M M, Kim S H, Lantz G, Laverge F E, Saito R and Heinz T F 2012 Nano Lett. 12 5539 [15] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [16] Kresse G and Hafner J 1993 Phys. Rev. B 47 558 [17] Perdew J P and Zunger A 1981 Phys. Rev. B 23 5048 [18] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[19] Grimme S 2006 J. Comput. Chem. 27 1787 [20] Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188 [21] Appalakondaiah S and Vaitheeswaran G 2012 Phys. Rev. B 86 035105 [22] Brown A and Rundqvist S 1965 Acta Cryst. 19 684 [23] Dresselhaus M S, Dresselhaus G and Jorio A 1986 Group Theory (Application to the Physics of Condensed Matter) (Berlin: Springer) [24] Prytz E and Flage-Larsen E 2010 J. Phys.: Condens. Matter. 22 015502 [25] Takao Y and Morita A 1981 Physica B+C 105 93 [26] Akahama Y, Kobayashi M and Kawamura H 1997 Solid State Commun. 104 311 [27] Tuinstra F and Koenig J L 1970 J. Chem. Phys. 53 1126 [28] Fei R X and Yang L 2014 Appl. Phys. Lett. 105 083120 [29] Tan P H et al 2012 Nat. Mater. 11 294 [30] Zhao Y Y et al 2013 Nano Lett. 13 1007 [31] Michel K H and Verberck B 2012 Phys. Rev. B 85 094303 [32] Xia F N, Wang H and Jia Y C 2014 Nat. Commun. 5 4458 [33] Wei Q and Peng X H 2014 Appl. Phys. Lett. 104 251915
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