In-plane anisotropic optical and mechanical properties of two-dimensional MoO$_3$

Molybdenum trioxide (MoO$_3$) in-plane anisotropy has increasingly attracted the attention of the scientific community in the last few years. Many of the observed in-plane anisotropic properties stem from the anisotropic refractive index and elastic constants of the material but a comprehensive analysis of these fundamental properties is still lacking. Here we employ Raman and micro-reflectance measurements, using polarized light, to determine the angular dependence of the refractive index of thin MoO$_3$ flakes and we study the directional dependence of the MoO$_3$ Young's modulus using the buckling metrology method. We found that MoO$_3$ displays one of the largest in-plane anisotropic mechanical properties reported for 2D materials so far.


Introduction
Recently, two-dimensional (2D) materials with an in-plane anisotropy, such as several transition metal chalcogenides, group-VA, black phosphorus and compounds made of two group-VA elements (so called V-V binary materials), have been extensively studied  . Some of them have demonstrated a great potential in optoelectronics and flexible electronics applications 22-25 , allowing the fabrication of devices with new functionalities (e.g. polarization sensitive photodetectors 22,26 ) and the observation of novel quasi one-dimensional physics phenomena 27 .
Here, using a combination of experiments and density functional theory calculations, we have studied the direction-dependent refractive index (birefringence) and Young's Modulus of α-MoO3 exfoliated flakes, two fundamental quantities that govern the anisotropy observed in Raman and phonon polariton experiments. We studied thin flakes of α-MoO3 by aberration corrected scanning transmission electron microscopy and energy-dispersive x-ray spectroscopy. We then deposited the flakes on SiO2/Si substrates and identified the crystallographic orientation of samples using angle-resolved polarized Raman spectroscopy technique 53 . Then, we determined the in-plane anisotropy of the MoO3 refractive index using angle-resolved polarized microreflectance spectroscopy, finding a remarkably large birefringence. The anisotropic mechanical properties of the MoO3 flakes was experimentally investigated with the buckling metrology method 54,55 , finding one of the largest Young's modulus anisotropy reported so far for 2D materials.

Results and Discussion
We have grown MoO3 flakes in atmospheric conditions using a modified version of the hot platebased 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 MoO3 flakes. Then, a Gel-Film (Gel-Pak WF x4 6.0 mil) stamp is used to pick-up and exfoliate the MoO3 flakes. These flakes can be then transferred onto a target substrate (e.g., a holey Si3N4 TEM grid or a 297 nm SiO2/Si substrate) using deterministic transfer set up (see Materials and Methods section for more information). Figure 1a shows the layered crystal structure of α-MoO3 57-59 , belonging to the Pbnm space group.
It consists of a double-layer stacking of linked distorted MoO6 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 Å, b = 13.86 Å and c = 3.70 Å (JCPDS file: 05-0508) 44,53,56,59,60 . We characterized the structure and composition of the grown MoO3 flakes using scanning transmission electron microscopy (STEM) along with energy dispersive x-ray spectroscopy (EDS) and scanning electron microscopy (see Figure S4 in the Supporting Information). A thin flake was transferred into a porous Si3N4 membrane, as shown in Figure 1b. Atomic resolution high angle annular dark field (HAADF) imaging shows an This is the authors' version (post peer-review) of the manuscript: S Puebla et al. npj 2D Materials and Applications, 5, 37 (2021) https://doi.org/10.1038/s41699-021-00220-5 That has been published in its final form: https://www.nature.com/articles/s41699-021-00220-5 4 orthorhombic α-MoO3 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 (Figure 1 c, d). 44,53,56,59,60 The chemical composition of the flake was determined by EDS, Figure 1e shows the spectrum of MoO3 used for quantification, where we find a small oxygen deficiency. We highlight the peaks centered at 282 cm -1 , assigned to B2g mode, and at 156 and 818 cm -1 , assigned to Ag c and Ag a mode, respectively. The Ag c peak corresponds to the translation vibration This is the authors' version (post peer-review) of the manuscript: S Puebla et al. npj 2D Materials and Applications, 5, 37 (2021) https://doi.org/10.1038/s41699-021-00220-5 That has been published in its final form: https://www.nature.com/articles/s41699-021-00220-5 5 of the rigid MoO6 octahedra chains along the c-axis, and the Ag a mode is the asymmetric stretching vibration of O-Mo-O atoms along the a-axis 53,62 .
We have carried out angle-resolved polarized Raman measurements in a MoO3 flake of 28 nm of thickness from 0º to 360º, with a step of 4º. The thickness has been determined by combination of atomic force microscopy with recently developed optical microscopy based techniques 64 . In ( 2 ) ∝ 2 sin 2 2 (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 equations (1) and (2)  In order to gain an insight about the in-plane anisotropic optical properties of MoO3 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: This is the authors' version (post peer-review) of the manuscript: S Puebla et al. npj 2D Materials and Applications, 5, 37 (2021) https://doi.org/10.1038/s41699-021-00220-5 That has been published in its final form: https://www.nature.com/articles/s41699-021-00220-5 where Ifl and Isub are the intensity measured on the MoO3 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   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 MoO3 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  Raman spectroscopy and micro-reflectance, and thickness through AFM (see Figure S2 and S3 of the Supporting Information).
The wavelength, λ, of the rippling pattern can be used to determine the Young's modulus:   5, 37 (2021) https://doi.org/10.1038/s41699-021-00220-5 That has been published in its final form: https://www.nature.com/articles/s41699-021-00220-5 10 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

Growth and Deposition
We have based our present grown procedure on a modification of the hot plate growth method developed by Molina-Mendoza et. al 56 .
Once the growth of the crystals is finished, the MoO3 flakes are firstly exfoliated onto a polydimethylsiloxane (PDMS) (Gel-Film WF x4 6.0mil, by Gelpak®) and then transferred onto a 297 nm SiO2/Si substrate using a deterministic transfer method 76,77 .

Scanning Transmission Electron Microscopy
For the scanning transmission electron microscope characterization, we used an aberrationcorrected JEOL JEM-ARM 200cF electron microscope operated at 80 kV, equipped with a cold field emission gun and an Oxford Instruments EDS spectrometer.

Optical Microscopy and Spectroscopy
Optical microscopy images were acquired using a Motic BA310 MET-T microscope equipped with a 50× 0.55 NA objective and an AMScope MU1803 CMOS Camera. Reflection spectra were collected from a spot of ~1.5-2 µm diameter with a Thorlabs CCS200/M fiber-coupled spectrometer (Thorlabs Inc., Newton, New Jersey, United States). More details about the microreflectance setup can be found in Reference 78 .

Raman Spectroscopy
Raman characterization of MoO3 flakes on 297 nm SiO2/Si substrates were carried out with a confocal Raman microscopy system (MonoVista CRS+ from Spectroscopy & Imaging GmbH) using a 532 nm excitation laser with an incident power of 1.234 mW and a 100× objective with the integration time of 20 s.

Numerical methods
We have analyzed the optical and elastic properties of MoO3 using the YAMBO and Quantum Espresso suite of programs [79][80][81] . For the electronic structure calculation we have used the generalized gradient approximation in the PBE parametrization for the exchange-correlation energy with a plane wave cut-off of 60 Ry 82 . The electronic structure calculations are performed This is the authors' version (post peer-review) of the manuscript: S Puebla et al. npj 2D Materials and Applications, 5, 37 (2021) https://doi.org/10.1038/s41699-021-00220-5 That has been published in its final form: https://www.nature.com/articles/s41699-021-00220-5 13 on a Monkhorst-Pack grid of 8x8x8 points. We have chosen norm-conserving pseudo potentials in the SG15 database 83 .
For the elastic properties, we have used the thermo_pw code from the Quantum Espresso suite 84 .
The elastic properties agree when we used either norm-converting or ultra-soft pseudo potentials.

Data Availability
Data presented in this study are available on request from the authors.