In-Plane Anisotropic Raman Response and Electrical Conductivity

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

In-Plane Anisotropic Raman Response and Electrical Conductivity with Robust Electron-Photon, ElectronPhonon Interactions of Air Stable MoO Nanosheets 2

Qi Zheng, Pinyun Ren, Yuehua Peng, Weichang Zhou, Yanling Yin, Hao Wu, Wentao Gong, Weike Wang, Dongsheng Tang, and Bingsuo Zou J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00455 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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The Journal of Physical Chemistry Letters

In-Plane Anisotropic Raman Response and Electrical Conductivity with Robust ElectronPhoton, Electron-Phonon Interactions of Air Stable MoO2 Nanosheets Qi Zheng,†,# Pinyun Ren,‡,# Yuehua Peng,† Weichang Zhou,†,* Yanling Yin,† Hao Wu,† Wentao Gong,† Weike Wang,† Dongsheng Tang,†,* Bingsuo Zou§,* †

Synergetic Innovation Center for Quantum Effects and Application, Key Laboratory of Low-

dimensional Quantum Structures and Quantum Control of Ministry of Education, School of Physics and Electronics, Hunan Normal University, Changsha 410081, People’s Republic of China. ‡

Institute of Physics and Electronic Engineering, Sichuan University of Science and Engineering,

Zigong 643000, People’s Republic of China. §

Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics,

Beijing Institute of Technology, Beijing 100081, People’s Republic of China. *

Corresponding Author. E-mail: [email protected] (W. Z.), [email protected] (D.

T.), [email protected] (B. Z.)

ACS Paragon Plus Environment

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ABSTRACT: The monoclinic MoO2 (m-MoO2) has attracted particular attention recently due to its potential applications in electronics and energy storage/conversions. Specially, m-MoO2 shows strong in-plane anisotropy. The in-depth harnessing of anisotropy that is essential to design anisotropicthe diverse angle-dependent nano-devices. However, there is not yet detailed study on the anisotropy of m-MoO2 nanostructures so far. Here, the in-plane anisotropic Raman spectra and electrical conductivity of single-crystal m-MoO2 nanosheets were investigated systematically for the first time. The intensities of different phonon modes and profiles of angleresolved polarized Raman spectroscopy (ARPRS) show distinct dependence on the excitation laser wavelength and sample thickness, demonstrating the robust wavelength dependent optical absorption, electron-photon/electron-phonon interactions and anisotropic phonon polarization in the m-MoO2 nanosheets. Such results are in agreement well with the semi-classical Placzek model. Moreover, The the angle-dependent electrical conductivity of starburst-like m-MoO2 nanosheet devices shows a strong anisotropy with conductivity ratio (σmax/σmin) of up to 10.1, which is the largest value in the previously reported 2D materials. This work underscores the importance of understanding the in-plane anisotropic light-matter interactions for the design and application of m-MoO2 nanosheets in anisotropic plasmonics and artificial synapse.

TOC GRAPHICS


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KEYWORDS: MoO2 nanosheets, in-plane anisotropy, polarization Raman spectra, angledependent electrical conductivity, light-matter interaction.

T

he discovery of graphene has sparked a worldwide research interesting in the single or few layers van der Waals two-dimensional (vdW-2D) materials that cover a broad range

from metal to insulator.1,2 These emerged appealing materials can be mechanical exfoliated easily from their corresponding bulk crystals and show unique layer-number and valley degree of freedom dependent energy band structure and spin-orbit coupling, which can be used to develop novel valley-electronics and opto-electronics devices.3-5 In generally, many of the common 2D materials, such as graphene, transition metal dichalcogenides (TMDCs, MX2, M=Mo, W; X=S, Se), hexagonal boron nitride (h-BN), have high crystal lattice symmetry and isotropic properties along different crystal orientations. Recently, another type 2D materials such as, black phosphorus/arsenic (BPs/B-As), Re(S/Se)2, IV-VI (SnSe, GeSe2, etc.), Ge(P/As), MoTe2, GaTe, (Hf/Zr/Ti)S3, MP15 (M=Li, Na, K), had low symmetrical crystal lattice and attracted much attention of the research community.6-16 Typically, the structural anisotropy could lead to strong anisotropy in electronic energy band structure. Therefore, the electrical, optical, thermal, magnet and phonon properties of these anisotropic materials are diverse along the different in-plane crystal directions.17-24 Moreover, the anisotropy shows an intricate dependence on flake thickness, photon and phonon energy due to the thickness dependent energy band structure and energy level symmetry. This provides another new degree of freedom to tune the previous unexplored properties and supplies a tremendous opportunity to develop new devices, such as: polarizationsensitive photodetector and artificial synapse that are highly desired in the integration logic circuits.25-27


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Raman spectroscopy is one of the most conventional while powerful tools to characterize the crystal structure, material composition, phonon scattering dynamics, bond strength, electronic density of state. It also can be used to measure the layer-number (thickness), intra-layer atom vibration symmetry and inter-layer information (such as: charge exchange, screening, coupling) of 2D materials.28 Specially, based on the crystal symmetry and Raman selection rule, angleresolved polarized Raman spectroscopy (ARPRS) is of great important for the determination of crystallographic orientation, designation of Raman active mode, and investigation of photonphonon/electron-phonon interaction in 2D materials.29,30 Recently, there is a review on the anisotropic Raman spectra of 2D materials.31 However, these above mentioned low symmetrical 2D materials are mainly chalcogenides that are sensitive and fast oxidized to ambient environment. Their anisotropy can degrade quickly to isotropy when exposure to atmosphere for only several hours, affecting seriously the further application.32 As a result, there is an increasing effort to explore others appealing new members of layered-materials family with distinct anisotropic property and excellent air stability.33 As a common metal oxide, MoO2 nanostructures exhibit preeminent light, air and thermal stability, without any concerning over the structural damage.34 Moreover, monoclinic MoO2 (m-MoO2) belongs to layered materials and shows metallic-like transport property due to the formation of Mo-Mo metallic bonds, although it is a typical wide band gap semiconductor.35-37 In addition, due to the nontoxicity and earth-abundant constituent elements, m-MoO2 was often applied in the fields of field emission devices, lithium ion batteries, hydrogen energy, plasmonics, surface enhanced Raman spectroscopy (SERS).38-40 So, it is urgent and crucial to study the distinct electrical, optical, phonon anisotropy of m-MoO2 in detail for optimization the fundamental electronics devices and


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energy conversions application. As far as our knowledge, there has not yet report about the inplane anisotropic Raman spectra and electrical conductivity of 2D m-MoO2 single crystal. In this paper, we study the intricate in-plane anisotropic Raman spectra of high environment stable 2D m-MoO2 nanosheets with different thicknesses (10 nm, 20 nm, 50 nm) under diverse excitation laser wavelengths (532 nm, 632.8 nm, 785 nm) for the first time. By rotating the samples while keeping the parallelism of incident laser polarization to scattered light, we identify the crystalline orientation carefully according to the varied intensity of Raman modes. The polar plots of intensity for the all detected Raman modes exhibit a robust anisotropic electron-phonon and electron-photon interaction in the m-MoO2 nanosheets. The semi-classical model based on the Placzek approximation is adopted to understand such thickness and excitation wavelength dependent Raman modes polarization response. Moreover, we fabricated starburst-like nanodevices to measure the anisotropic electrical conductivity. The angle dependent in-plane conductivity ratio (σmax/σmin) is up to 10.1, which is the highest value in the reported 2D materials. These intriguing results indicate that MoO2 nanosheets have excellent in-plane anisotropy and can act as exceptional candidate for tunable plasmonics devices, SERS and bioinspired electronics. Comparison with the tape exfoliation to obtain ultrathin vdW-2D materials, cChemical vapor deposition (CVD) is more an effective method to growth large scale sample with high productivity, controllable morphology and uniform thickness.41 In this study, CVD was adopted to synthesize the m-MoO2 nanosheets with different thicknesses by evaporating MoO3 powder at 800 oC. 1×1 cm2 SiO2 (300 nm)/Si was selected as growth substrate, which can be directly used for the device fabrication and electrical measurement. The detailed experimental method is described in the Supporting Information. As shown in Figure S1a-c, the typical optical images


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exhibit uniform morphology and size of MoO2 nanosheets under the growth time of 20 min, 30 min, 40 min. The color changes from purple to light yellow with increasing the growth time. The extension of growth time during CVD synthesis can increase the thickness of 2D materials. So, the variety of color might indicate the thickness change. Atomic force microscopy (AFM) was used to measure accurately the thickness of the three MoO2 nanosheets. Insets in Figure S1a-c show the measured AFM images and height profiles, demonstrating the corresponding samples thickness of 10 nm, 20 nm, 50 nm to the growth time of 20 min, 30 min, 40 min. Figure 1a shows the crystal structure of distorted rutile-type MoO2 that has a space group of P21/c and a monoclinic phase with lattice constants of a=5.6109 Å, b=4.8562 Å, c=5.6285 Å. This m-MoO2 is built of layers of oxide and molybdenum atoms alternating along the c axis. In such structure, O atoms are closely packed into octahedrons and Mo atoms occupy half space of the octahedral void to form MoO6 octahedron units (Inset), which connect with each other to form a kind of deformed rutile structure by sharing the common edges and vertices in the direction of metal(Mo)-metal(Mo) bonds.36 Those chains form zigzag along the b axis while alternating layers along the c axis (indicated as light green and tan polyhedral in Figure 1a). More detailed 3D view, a-b and a-c projections of m-MoO2 structure are shown in Figure S2a-c. Figure 1b is the low-magnification transmission electron microscope (TEM) image of single MoO2 nanosheet (10 nm), which was transferred to the micro-grid of copper from as-grown SiO2(300 nm)/Si substrate by KOH solution etching method. The MoO2 nanosheet shows clearly a rhomboid shape with edge lengths of tens of micrometer and corner angles of about 82o and 108o98o. The selected area electron diffraction (SAED) pattern (Figure 1c) exhibits a distinct rhomboid symmetry, consistent with the morphology and demonstrating the single-crystalline nature of asprepared MoO2 nanosheets. The corresponding high resolution TEM (HRTEM) is shown in


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Figure 1d, showing exhibiting the clear lattice fringes and further indicating the high-quality crystallinity of MoO2 nanosheets. The spacings of lattice fringes are measured to be 0.28 nm and 0.55 nm, in agreement with the expected value for the (200) and (001) planes of MoO2.

82o

0.28nm

0.55nm

Figure 1. (a) Crystal structure and b-c plane projection of m-MoO2, composing of MoO6 octahedrons joined by edges and vertices sharing. Inset is the structure of MoO6 octahedron. (b-d) The TEM, SAED and HRTEM image of m-MoO2 nanosheet, respectively. Raman spectroscopy is an effective and non-destructive method to characterize the crystal structure and phonon mode dynamics. According to the group theory, the first order Ramanactive modes of m-MoO2 are expressed as: =15 Ag  12B1g  15B2 g  12B3g . Figure 2a shows the unpolarized Raman spectra of m-MoO2 with thickness of 10 nm, 20 nm, 50 nm, under the same excitation and collection conditions (such as excitation wavelength/power, objective lens


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multiplier, integration time, etc.). Several main modes (125, 202, 228, 343, 360, 423, 458, 466, 495, 569, 585, and 741 cm-1) were observed and the line shapes were almost same for different thicknesses. These peaks are consistent well with the lattice vibration modes of m-MoO2.40 For more detailed information, the narrow wavenumber range between 180 cm-1 and 220 cm-1 were extracted from Figure 2a. As shown in Figure 2b, by fitting the corresponding curves, it can be seen that there are two components (202 cm-1 and 208 cm-1) in the magnified zone, consistent well with the calculated Raman mode frequencies in literature.36 We also observe that the intensity ratio of such two components (I208/I202) increase with the thickness of MoO2 nanosheets. That is to say, the intensity of 208 cm-1 mode is more sensitive to the thickness than that of 202 cm-1 due to their different mode symmetry. Although M. Lerch et al. proposed a tentative modesymmetry assignment of 200 cm-1 to Ag mode under high pressure,36 there is no paper about the mode-symmetry assignment of m-MoO2 in experiment under atmosphere condition, especially for the high resolution 202 cm-1 and 208 cm-1 modes. We further executed polarization dependent Raman responses on the different thickness MoO2 nanosheets with 532 nm, 632.8 nm, 785 nm CW laser as excitation light sources to explore the influence of optical absorption/transition to on Raman modes and understand the lattice dynamics and electronphonon/electron-photon interaction in MoO2 nanosheets. As far as we know, this should be the first report on the polarization dependent Raman response of m-MoO2 single crystal nanostructures.


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Figure 2. (a) Unpolarized Raman spectra of m-MoO2 nanosheets with thickness of 10 nm, 20 nm, 50 nm. (b) Enlarged Raman spectra in the range of 180-220 cm-1 and the corresponding fitting curves. The polarization configuration used for measurement the ARPRS and anisotropy of single mMoO2 nanosheet is shown in Figure S2S3, where the polarization direction of incident and scattered light were fixed to along the y axis in a parallel way while the m-MoO2 nanosheet was rotated to form a variable angle from 0o to 360o with the polarization of incident laser. The ARPRS of m-MoO2 nanosheets with different thicknesses (10 nm, 20 nm, 50 nm) under incident laser wavelength of 532 nm, 632.8 nm, 785 nm are shown in Figure 3a-i, indicating a variety of anisotropy levels. The detailed angle dependence of all Raman modes intensities are plotted in polar coordinate and are summarized in Table 1 and Table S1. The Raman peak intensities of 10 nm MoO2 nanosheets under 785 nm laser excitation are low due to the weak light-matter interaction, similar with the case of GaTe 2D flakes.14 It can be seen from Figure 3 and Table 1 and Table S1 that the angle dependence of peak intensities of 125, 202, 348, 360, 458, and 569 cm-1 are different obviously from that of 208, 228, 343, 423, 466, 495, 585, and 741 cm-1 modes. The maximum intensity of 208, 228, 343, 423, 466, 495, 585, and 741 cm-1 modes show a period


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of 90o for the 532 nm laser excitation, yielding a four-lobed shape with four maxima intensity angles. The two orientation of maximum intensity (blue arrows for the 208 cm-1 mode in Table 1) coincide with the two edges of rhombic m-MoO2 nanosheets (blue dot lines for the 208 cm-1 mode in Table 1). However, the 125, 202, 348, 360, 458, and 569 cm-1 modes show a period of 180o with a two-lobed shape. The orientation of maximum intensity is agreement with the diagonal line of rhombic m-MoO2 nanosheets (green arrow for the 125 cm-1 in Table 1). These phenomena indicate that the 125, 202, 348, 360, 458, and 569 cm-1 modes have different phonon symmetry from the 208, 228, 343, 423, 466, 495, 585, and 741 cm-1 modes. The anisotropic polarization of the Raman intensities relate strongly to the mode symmetry and crystal orientation. Similar phenomena have also been reported in other 2D materials with strong inplane anisotropy.42,43 The thickness shows variable long range polarization and has an important influence on the ARPRS profile. Such as the 343 cm-1 mode (Table S1), the four-lobed shape is more evident with increasing the nanosheets thicknesses from 10 nm to 50 nm. Compared with the excitation of 532 nm laser, the ARPRS of 208, 228, 343, 423, 466, 495, 585, and 741 cm -1 modes show no evident change while the 125, 202, 348, 360, 458, and 569 cm-1 modes demonstrate distinct variation under excitation of 632.8 nm and 785 nm laser. The 202, 348, 360, and 458 cm-1 modes exhibit weak anisotropy under 532 nm laser excitation while relatively stronger anisotropy under excitation of 632.8 nm laser, indicating the different transition process of MoO2 absorption band under variable excitation wavelength.


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Figure 3. (a-i) ARPRS of m-MoO2 nanosheets with thickness of 10 nm, 20 nm, 50 nm under excitation of 532 nm, 632.8 nm, 785 nm laser. Table 1. Polar plots of the angle-dependent Raman intensity of the representative 125 cm-1, 202 cm-1 and 208 cm-1 phonon modes in the m-MoO2 nanosheets with different thicknesses under varied excitation wavelengths.

Mode

532 nm Laser

632.8 nm Laser

Thickness

Thickness

10 nm

20 nm

50 nm

10 nm

20 nm

50 nm

785 nm Laser Thickness 10 nm

20 nm

50 nm

125 cm-1


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202 cm-1 208 cm-1

It is worth to note that, for the 125 cm-1 mode, the major main-axis (maximum Raman intensity) is parallel to the short diagonal line direction of rhombic m-MoO2 nanosheets and the ARPRS profile shows a perfect two-lobed shape under the 532 nm laser excitation (green arrows in Table 1). Although the major main-axis is still parallel to the short diagonal line orientation, there appears a new secondary maximal Raman intensity perpendicular to the short diagonal line direction under the 632.8 nm laser excitation, depicting a four-lobed shape (short black arrows in Table 1). On further increasing the excitation wavelength to 785 nm, the secondary maximal Raman intensity increases greatly to comparable or even exceed to the major main-axis maximal Raman intensity (long black arrows in Table 1). These results indicate that the 125 cm-1 is unidirectional vibration mode under excitation of 532 nm laser, showing maximum and minimum (nearly to zero) Raman intensity when the nanosheets orientation is parallel and perpendicular to the phonon vibration. However, under the excitation of 632.8 nm and 785 nm laser, this mode is always present at any orientation of nanosheets, demonstrating some more electron states contribution to the scattering process. The change trend of ARPRS profile of 348 cm-1 mode is similar and its secondary maxima Raman intensity even exceeds the major maximum value under 632.8 nm laser excitation (Table S1). Therefore, there is a robust lightmatter interaction in the MoO2 nanosheets, yielding peculiar polarization behaviors and scattering process that depend on the different excitation wavelength (photon energy), sample thickness, phonon mode symmetry and phonon frequency (phonon energy).44,45 About this


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electron states involved scattering process, both 785 nm and 632.8 nm laser can excite the electron-phonon coupling modes while the 532 nm laser can only excite the phonon modes in the Raman spectra, similar with the resonant Raman effect in BP flakes.46 We further observe that the main-axis orientation of the four-lobed shape of 125 cm-1 mode under the 785 nm laser excitation is different from that of 208 cm-1 mode, indicating the phonon energy dependent ARPRS profile. So, although the angle-dependent Raman spectroscopy can provide an all-optical method to identify the crystal orientation and determine the Raman mode symmetry, caution is required because there is a strong relationship between the orientation of ARPRS and the photon energy, phonon energy, phonon symmetry, sample thickness.47 46 About this electron states involved scattering process, both 785 nm and 632.8 nm laser can excite the electron-phonon coupling modes while the 532 nm laser can only excite the phonon modes in the Raman spectra, indicating the probable contribution from resonant Raman effect, similar with the case of BP flakes.47 The resonance enhancement profile is benefit to understand the intricate light-matter interaction in m-MoO2. When considering the electron-phonon and electron-photon I ( ) 



i ,m,n

interaction,

the

f H op (s ) n n H ep ( ) m m H op (i ) i ( Elaser  Emi )( Elaser    Eni )

Raman 2

where

intensity I ( )

is is

expressed

the

scatting

as:14,44 intensity,

,

Emi =Em  Ei  i , i , f , m and n are the initial, final, two excited intermediate states, Em ( n ) and  m ( n ) are the energy and damping constant of intermediate states, m H op i

f H op n and

are the electron-photon interaction matrixes, n H ep m is the electron-phonon

interaction matrix. From this formula, the resonance enhanced Raman mode relies strongly on the laser energy, optical absorption coefficient (  ), optical excited electronic transition and electron-phonon coupling. We know that  is proportional to m H op i , which describes the 2


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optical transition from state i to m, and is expressed by the inner product of dipole vector

m  i and light polarization vector.14,44 This optical transition selection rule determined the variable electron transition process, as well as the coupling with phonon when both the wavelength/polarization of incident light and sample thickness related state m(i) were changed. However, the calculated band structure showed that both the valence band and conduction band of MoO2 cross the Fermi level and no obvious band gap was found,48 which is different from the BPs, SnSe, GaTe, GeAs semiconductor that have an evident bandgap.10,12,14,47 Such electronic band structure suggests that m-MoO2 possesses a high density of free d-electron and metallic characteristics. Actually, M. Dieterle and G. Mestl have reported the resonance enhanced Raman spectra of MoO2 and Mo4O11 under the excitation of He-Ne laser (632.8 nm) in contrast to the excitation of 532/514 nm laser.49 They deduced that the coupling of laser frequency to intervalence charge transfer (IVCT) band plays an critical role on this resonant enhancement Raman profile. This deduction is reasonable since there has no pocket-like band structure at the band edge and the excited electron must transfer through the inter/intra-bands. Due to the anisotropic electronic band structure, the electron transfer behavior is diverse along the different crystal orientations, leading to distinct enhancement Raman intensity. In addition, as a common absorbing medium, m-MoO2 exhibits a strong absorption from near-ultraviolet to near-infrared due to the collective oscillation of d-orbital free electron in the electromagnetic field.37 So, the re-adsorption of the emitted Raman scattered light strongly influences the Raman cross section. For the short excitation wavelength (532 nm), the re-absorption efficiency is higher than the long excitation wavelength (632.8 nm), which explains why the 632.8/785 nm laser can induce resonant behavior while the 532 nm laser can’t in the experiment. The observed thickness


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dependent polarization Raman spectra should be due to the variable interference effect along the vertical direction and involved electronic states with thickness.14 These angle-dependent Raman intensities can be quantitatively described by the semiclassical Placzek model, which was expressed as:4850,4951 I  ei  R  es

2

(1)

where ei and es are the electric polarization unitary vectors of incident and scattered light, respectively, R is the Raman tensor. For m-MoO2 crystal structure with space group of P21/c, the 3  3 Raman tensor R of Raman active modes are expressed as:

R( A )

 a eia   0  d eid 

0 b eib 0

d eid   0  c eic 

(2)

e eie

R( B

 0    e eie   0

 i  f e f  0 

(3)

g

g)

0 f e

i f

0

in which a, b, c, d , e, f are constants of the Raman tensor, and  j ( j  a, b, c, d , e, f ) represents the phase of corresponding tensor element. According to the polarization configuration in the experiment, ei and es can be expressed as the same vector (cosθ, sinθ, 0), where θ is the angle of the polarization of incident laser relative to the short diagonal line of rhombic m-MoO2 nanosheets. Thus, we can obtain the angle-dependent Raman intensity expressions for the Ag and Bg modes of m-MoO2 as follows:  b  I ( Ag )  ( sin 2   cos 2  cos ba )2  cos 4  sin 2 ba   a 

(4)


15


I ( Bg )  e sin 2 (2 ) 2

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(5)

Therefore, the observed 208, 228, 343, 423, 466, 495, 585, and 741 cm -1 are assigned to be Bg modes showing a period of 90o while those 125, 202, 348, 360, 458, and 569 cm-1 modes are assigned to be Ag modes with the period of 180o. It is worth noting that the absorption of semiconductor shows complex elements of each component of the dielectric function tensor, which usually has real and imaginary parts (  ij   ij ,   ij ,, ).50 52 So, the element of Raman tensors also has real and imaginary parts that are dependent on the photon energy of incident laser. Here the term ϕba is the phase difference (ϕb-ϕa). The polar plots of angle-dependent Raman intensities of the experiment detected modes can be well fitted with equations (4) and (5), as shown in Table 1 and Table S1, yielding the corresponding cosϕba and |b|/|a| for the Ag modes (125, 202, 348, 458, and 569 cm-1). These values are summarized in Table S2. We also measure the in-plane angle-resolved polarized Raman spectra by rotating the incident laser polarization orientation while fix the sample and polarization direction of scattered light. The schematic diagram of configuration is shown in Figure S3S4. These results demonstrated that the main axis of both Ag and Bg Raman modes does not depend on the diagonal line of rhombic m-MoO2 nanosheets (Figure S4S5). With this incident laser polarization rotation method, the variety of Raman mode intensity is complicated. In this situation, the main-axis orientation of the two-lobed Ag and Bg mode is a function of crystal orientation, |b|/|a| and phase difference ϕba.46

45

However, the 125

cm-1 is an unordinary Raman mode. Its direction of main axis coincided exactly with the short diagonal line of rhombic m-MoO2 nanosheets. So, the 125 cm-1 mode still can be used to determine the crystal orientation of m-MoO2 nanosheets by using the rotating incident laser method.


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We further analysed the cosϕba and |b|/|a| in Table S2 to understand the change of ARPRS profile under different excitation wavelength (532 nm, 632.8 nm, 785 nm) and sample thickness (10 nm, 20 nm, 50 nm). Under excitation of 532 nm laser, the cosϕba approaches to zero (such as 125 cm-1 mode, -0.005, -0.04, -0.03 for thickness of 10 nm, 20 nm, 50 nm), corresponding to the two-lobed ARPRS profiles. The non-zero cosϕba of 125 cm-1 mode under excitation of 632.8 nm and 785 nm laser indicate the appearing of secondary maxima Raman intensity and then formation of four-lobed ARPRS profiles. In the layered GeAs 2D crystals, Ajayan P. M. et al. also observed the obvious secondary maxima of Ag modes when the cosϕba is relatively large under both parallel and cross configurations.12 So, the cosϕba is a crucial factor to determine the ARPRS profile, consistent with the equation (4) that the polar plots of Ag modes depend not only on the polarization configuration but also on the phase difference of Raman tensor. The value of |b|/|a| is another key element to determine the orientation of the maximum Raman intensity main axis. Our results show that the maximum Raman intensity orientates to the short diagonal line under short-wavelength laser excitation (532 nm), which yields |b|/|a|>1. However, the maximum Raman intensity orientates to the long diagonal line under long-wavelength laser (785 nm) excitation that yields |b|/|a|

In-Plane Anisotropic Raman Response and Electrical Conductivity

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