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In-plane anisotropic optical and mechanical properties of two-dimensional MoO3
Results . Crystal structure study . We have grown MoO 3 flakes in atmospheric conditions using a modified version of the hot plate-based physical vapor transport method described in ref. 56 . Briefly, a molybdenum foil was oxidized on a hotplate at 540?°C, then a silicon wafer was placed on top. At this temperature, the molybdenum oxide sublimes and re-crystallizes on the surface of the Si wafer, which is at a slightly lower temperature, forming MoO 3 flakes. Then, a Gel-Film (Gel-Pak WF x4 6.0?mil) stamp is used to pick-up and exfoliate the MoO 3 flakes. These flakes can be then transferred onto a target substrate (e.g., a holey Si 3 N 4 TEM grid or a 297?nm SiO 2 /Si substrate) using deterministic transfer set up (see Materials and Methods section for more information). Figure 1a shows the layered crystal structure of α-MoO 3 57 , 58 , 59 , belonging to the Pbnm space group. It consists of a double-layer stacking of linked distorted MoO 6 octahedra in the b direction, along which the adjacent layers are linked by weak van der Waals forces, while in-plane atoms are strongly bonded. This configuration leads to lattice parameters: a?=?3.96??, b?=?13.86?? and c?=?3.70?? (JCPDS file: 05-0508) 44 , 53 , 56 , 59 , 60 . We characterized the structure and composition of the grown MoO 3 flakes using scanning transmission electron microscopy (STEM) along with energy dispersive x-ray spectroscopy (EDS) and scanning electron microscopy (see Supplementary Fig. 4 in the Supporting Information). A thin flake was transferred into a porous Si 3 N 4 membrane, as shown in Fig. 1b . Atomic resolution high angle annular dark field (HAADF) imaging shows an orthorhombic α-MoO 3 structure with a difference in the a - c lattice parameters, as depicted also in a selected area diffraction pattern (SAED) acquired at the same flake (Fig. 1c, d ) 44 , 53 , 56 , 59 , 60 . The chemical composition of the flake was determined by EDS, Fig. 1e shows the spectrum of MoO 3 used for quantification, where we find a small oxygen deficiency. Fig. 1: Anisotropic structure of MoO 3 flakes. a Crystal structure of MoO 3 in Pbnm notation, spheres in blue (red) represent Mo (O) atoms, the two different views belong to ca (top), and ba plane projection (bottom). b Low magnification HAADF image of a mechanically exfoliated MoO 3 flake transferred over a porous SiN membrane, scale bar is of 1?μm. c Atomic resolution HAADF image depicting the anisotropy between the in-plane ( a – c ) lattice parameters, scale bar is of 5?nm. d SAED pattern characteristic of the orthorhombic α- MoO 3 . e EDS spectrum taken at the flake shown in b . Full size image Angle-resolved polarized Raman spectroscopy analysis . We have used angle-resolved polarized Raman spectroscopy technique to identify the different crystal directions in our MoO 3 flakes. Using a linearly polarized laser in a Raman system (see Materials and Methods section) and setting the analyzer and polarizer in a parallel configuration, while we rotate the sample, we obtain the spectra shown in Fig. 2a . The system set up is depicted in Supplementary Fig. 1 in the Supplementary Information and it is explained in detail by Liu et al. 61 . Typical MoO 3 Raman modes are A g and B g 62 and no correlation has been found between the Raman modes and the MoO 3 thickness 63 . We highlight the peaks centered at 282?cm ?1 , assigned to B 2g mode, and at 156 and 818?cm ?1 , assigned to A g c and A g a mode, respectively. The A g c peak corresponds to the translation vibration of the rigid MoO 6 octahedra chains along the c-axis, and the A g a mode is the asymmetric stretching vibration of O-Mo-O atoms along the a-axis 53 , 62 . Fig. 2: Determining the crystal orientation of MoO 3 through Raman spectroscopy. a Raman spectra at 0° (blue), 45° (black) and 90° (red) angles with respect to the horizontal axis. A g c , B 2g and A g a Raman modes are highlighted with vertical dashed lines. Inset: Microscopy image of the sample placed in the initial position (0°) and the a and c axes, determined from the angle-resolved Raman measurements, are shown. b Polar plots, in light red; and fittings, in dark red, of angle-resolved normalized Raman intensities of the A g c (left), B 2g (middle) and A g a (right) modes. Full size image We have carried out angle-resolved polarized Raman measurements in a MoO 3 flake of 28?nm of thickness from 0° to 360°, with a step of 4°. The thickness has been determined by combination of atomic force microscopy with recently developed optical microscopy based techniques 64 . In Fig. 2a three of these measurements at different angles (0°, 45° and 90°) are displayed. Notice the difference in intensity of each mode, revealing how the relative orientation between the incident laser polarization angle and the direction of the crystalline axes plays an important role in the Raman process. In fact, previous works have shown how the A g and B 2g mode intensities can be fitted to 53 , 62 : $$I\left( {A_g} \right) \propto \left( {A\cos ^2\beta + C\sin ^2\beta } \right)^2$$ (1) $$I\left( {B_{2g}} \right) \propto E^2\sin ^22\beta$$ (2) where β is the relative angle between the a-axis crystal direction and the linear polarization direction of the laser. Figure 2b shows the normalized intensity angle-resolved polarized Raman measurements of each mode (light red), with the resulting fit to Eqs. ( 1 ) and ( 2 ) (in dark red), showing an excellent agreement. Note, the A g c and A g a modes are useful to extract the crystal structure of the sample due to their 180-degree periodicity. The inset in Fig. 2a shows a microscopy image of the MoO 3 flake on SiO 2 /Si, studied with the Raman spectroscopy. The a- and c-axes, determined from the Raman measurements are depicted in the figure and coincide with the straight edges produced during the exfoliation of the MoO 3 flake. Polarized micro-reflectance analysis . In order to gain an insight about the in-plane anisotropic optical properties of MoO 3 flakes we carried out micro-reflectance measurements employing linearly polarized incident light. Figure 3 shows the optical contrast spectra acquired for different alignment between the crystal axis and the incident linear polarization (see the bottom inset). The optical contrast C is defined as: $$C = \frac{{I_{fl} - I_{sub}}}{{I_{fl} + I_{sub}}}$$ (3) where I fl and I sub are the intensity measured on the MoO 3 flake and on the bare substrate, respectively. Interestingly, it has been demonstrated how one can use a simple Fresnel law-based model to accurately reproduce the measured optical contrast spectra 64 . Moreover, given the known refractive indexes of air, SiO 2 and Si and the known thickness of the SiO 2 film and MoO 3 flake one can determine the refractive index of the MoO 3 flake for different alignment between the incident linearly polarized light and the crystal directions by using the refractive index as a fitting parameter to achieve the best fit of the Fresnel law-based model to the experimental data. The top inset in Fig. 3 shows the resulting in-plane angular dependence of the refractive index displaying a marked anisotropy (birefringence). While along the a-axis the refractive index of MoO 3 is n a ?=?2.21?+?0i, along the c-axis the refractive index increases up to n c ?=?2.30?+?0i. The difference Δ n between n c and n a , is ~0.1. This value is comparable to that of well-known strongly birefringent materials like calcite (?0.17) and barium borate (?0.12) 65 , 66 . If we compare it with other anisotropic 2D materials, the birefringence of MoO 3 is larger than that of ReS 2 and ReSe 2 (~0.04) 6 but substantially lower than the values reported for black phosphorus (0.25) 6 or TiS 3 (0.3) 67 . However, note that, unlike MoO 3 , all these anisotropic 2D materials are rather opaque in the visible range of the electromagnetic spectrum, limiting their application in polarization optics applications. Therefore, the birefringence value of MoO 3 , although more modest in comparison with TiS 3 or black phosphorus, can have a stronger impact in future ultrathin polarization optics applications. These experimental results for MoO 3 are confirmed by theoretical ab-initio calculations through the solution of the Bethe–Salpeter’s equation, in which we have obtained refractive index values of n a ?=?2.40 and n c ?=?2.60 at small frequency, with a difference Δn ~?0.2. We find these theoretical values close to the ones obtained experimentally. We attribute the lower birefringence experimental value to the presence of defects in the MoO 3 flakes, not considered in the calculations, that can effectively reduce the anisotropy of the lattice. Fig. 3: Birefringence of MoO 3 flakes. Optical contrast vs . wavelength spectra, measured for the 28?nm thick MoO 3 flake shown in the bottom inset, as function of the angle formed between the incident linearly polarized light and the crystal a-axis. Top inset: Polar plot of the change in refractive index as a function of the relative orientation between the incident linearly polarized light and the a-axis of the crystal. Full size image Mechanical anisotropy study . In the following we focus on the characterization of the anisotropy of the Young’s modulus, one of the fundamental magnitudes that govern the mechanical properties of materials, of MoO 3 flakes. We use buckling induced metrology method, which has been proved to be an easy, but reliable way to study the Young’s modulus of thin films 54 , 55 and 2D materials 68 , 69 , 70 , 71 , 72 . The method relies on studying the buckling instability that arises when a thin film is deposited onto an adhesive compliant substrate, and it is subjected to in-plane uniaxial compression 73 . Because of this compression, there is a trade-off in the energy related to the adhesion forces between film and substrate and the bending rigidity of the film. This trade-off leads to a rippling pattern of the thin film, which is characteristic of the film and substrate properties (in the Supplementary Information it can be found an animated GIF, Supplementary GIF , of a α-MoO 3 flake compressed in this way). To perform the buckling metrology measurements, the MoO 3 flakes were transferred onto a flat (unstrained) Gel-Film substrate that is mounted on a rotation stage under the inspection of an optical microscope. Then the flakes were subjected to compressive strain along different crystal directions by pinching the surface of the Gel-Film with two glass slides and pictures of the obtained ripple patterns are acquired with a digital camera attached to the microscope. The MoO 3 flakes are then transferred to a SiO 2 /Si substrate to determine their crystal orientation, through Raman spectroscopy and micro-reflectance, and thickness through AFM (see Supplementary Figs. 2 and 3 of the Supporting Information). The wavelength, λ , of the rippling pattern can be used to determine the Young’s modulus: $$E_f = 3\left( {\frac{\lambda }{{2\pi h}}} \right)^3\frac{{1 - \nu _{fa}\nu _{fc}}}{{1 - \nu _s^2}}E_s$$ (4) being h the flake thickness, v s , v f , E s and E f the Poisson’s ratio and Young’s Modulus of substrate and flake, respectively. The Poisson’s ratio of α-MoO 3 must be taken along the two axes. Using density functional theory (more details available in the Supplementary Information) we calculate Poisson’s ratios of α-MoO 3 correspond to ν fa ?=?0.147 and ν fc ?=?0.06. In our experiment we used a Gel-Film substrate as compliant substrate, with v sub ?=?0.5 74 and its Young’s Modulus is E sub ?=?492?±?11 kPa 68 . Figure 4a shows optical images of a 24?nm thick MoO 3 flake (thickness and orientation obtained with optical microscopy based technique, shown in Supplementary Fig. 2 ) when it is subjected to compression along the a- and c-axes. Upon compression along different orientations the MoO 3 develops a rippled pattern whose periodicity depends on the direction. In Fig. 4b , a statistical study is shown with 14 different samples with thicknesses ranging from 18 to 62?nm (white circles), from which we obtain the mean Young’s Modulus values and their standard deviation along the a- and c-axis. We use histograms to show the flake-to-flake variability of these results and we fit them with a normalized Gaussian distribution function. Moreover, we plot the corresponding two-dimensional normalized Gaussian distribution function in a 2D gray colormap, in which the density of datapoints is associated with the colorbar, set as inset. The obtained Young’s modulus values along the a- and c-axes directions are E a-axis ?=?44?±?8?GPa and E c-axis ?=?86?±?15?GPa, respectively. Interestingly the anisotropy ratio ( E c-axis / E a-axis ) is ~2 among the largest value reported in the literature for anisotropic 2D materials: black phosphorus ~2.7 17 , for orpiment (As 2 S 3 ) is ~1.7 75 . Our DFT calculations predict even higher Young’s modulus values (91.9?GPa and 216.9?GPa for the a- and c-axis respectively) in relatively good agreement with the values reported for bulk-like MoO 3 (~200?nm thick) crystals through Brillouin scattering. Note that the presence of defects in the synthesized MoO 3 samples, like the oxygen vacancies found in the STEM-EDS analysis, could explain the lower Young’s modulus values obtained in our experiments. Fig. 4: Anisotropic mechanical properties of MoO 3 flakes. a Optical images of a MoO 3 flake on Gel-Film substrate applying compression along a and c axes (top images), inset: process of ripples formation; determination of the wavelength of periodic ripples (bottom figure). b Scatter density plot of Young’s modulus values along the two directions obtained from 14 different samples, white circles with black edges, and fitted with a multivariate Gaussian normal distribution function, in gray. Inset: Histogram plots of Young’s modulus along the a-axis (blue) and the c-axis (red), fitted with a Gaussian distribution. Full size image .
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