Spectral studies on 2D Transition Metal Dichalcogenides (2D TMDCs)

Shreeaishwarya R

Department of Physics, Lady Doak College, Madurai

Dr. Rajeev N. Kini

Department of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram

Abstract

Novel properties emerge as the dimensionality of the materials gets reduced such as graphene which is exfoliated from graphite ^[1]. The lack of band gap being its only limitation in its applications, led to the exploration of Transition Metal Dichalcogenides (TMDCs). TMDCs, denoted by MX₂, are 2D materials comprising of a transition metal layer (group 4-10) and two chalcogen atoms(S, Se, Te) together forming a hexagonal lattice structure. Among them, layered Group 6 TMDCs like MoS₂, MoSe₂, WS₂ and WSe₂ exhibit superconducting, metallic, semiconducting properties. The semiconducting property of TMDC monolayer was revealed by their optoelectronic properties, studied via Photo Luminescence (PL), where there exist an indirect to direct band gap transition from the bulk to monolayer. Raman spectroscopic technique is used to study the thickness dependency of TMDCs. The Carrier dynamics in TMDCs plays a crucial role in improving the performance of optoelectronic devices. The coulombic interactions resulting in tightly bound excitons and large binding energies create changes in the relaxation and recombination process. This photoexcited carrier dynamics can be studied using pump probe spectroscopy. In this project, the mechanical exfoliation (top down) process is done to extract few-layered TMDCs from the bulk ones. The Molybdenum disulphide (MoS₂) sample taken is exfoliated on Si/SiO₂ substrate and the layer thickness is analyzed by Optical Contrast (OC) analysis method by using a Mat-lab program. Our project aims at the Optical Microscopic (OM) studies for accurate and reliable identification of layer thickness of layered 2D TMDCs (MoS₂) and the determination of their fundamental properties using the spectroscopic techniques like Photo Luminescence (PL) spectroscopy.

Keywords: Photo Luminescence spectroscopy, Optical Microscopy, Optical Contrast, MoS₂

Abbreviations

INTRODUCTION

2 Dimensional (2D) materials have greatly attracted the attention in the recent years and offer great opportunities in various fields. Graphene, hexagonal boron nitride (h- BN) and 2D TMDCs comes under the layered 2D material family. Graphene, a 2D material exfoliated from the bulk graphite is a semi metal because of the lack of band gap^[2] and thus graphene’ s success and limitation led to the exploration of 2D Transition Metal Dichalcogenides (TMDCs). Layered TMDCs are atomically thin and each layer has a metal layer and two chalcogen atoms, together forming a hexagonal lattice structure. Each layer is held together by weak Van der Waals forces. It is denoted by MX₂. They have received a great deal of attention due to their extra ordinary optoelectronic, vibrational and electronic properties. However, the monolayers have two polytypes such as trigonal prismatic and octahedral. The monolayers of MoS₂ from the bulk one is obtained by the top down and bottom up approaches. The mechanical exfoliation (top down) process is an effective method of exfoliation done to extract monolayer of TMDCs from the bulk ones at small scale.

Thickness of the sample plays a vital role in determining the properties. The identification of thickness of 2D materials includes the methods like Atomic Force Microscopy (AFM), Raman spectroscopy, Optical Contrast analysis, Transmission Electron Microscopy (TEM). However the methods like Atomic Force Microscopy and Transmission Electron Microscopy (TEM) are expensive and time consuming process. Hence the thickness of the 2D TMDCs is found using the optical imaging technique like Optical Contrast analysis and Raman spectroscopy since they are less time consuming, non-destructive and easy method of identification of thickness.

Objectives of the Research

The main objective of this research is to fabricate monolayers from bulk Transition Metal Dichalcogenide, MoS₂, by mechanical exfoliation and the spectral analysis to determine the number of layers that is more reliable and accurate.

LITERATURE REVIEW

Layered 2 D Transition metal dichalcogenides consist of a metal group (4-7) and two chalcogen atoms such as S, Se, Te, each layer forming a hexagonal lattice structure. Each layer is held together by weak Van der Waals forces. Group 6 TMDCs include MoS₂, WS₂, MoSe₂ and WSe₂ which have opened up a new field of applications due to their layer dependent semiconducting properties to be employed in the optoelectronic applications. The TMDCs exists in different polytypes such as 1T (Octahedral), 2H (Hexagonal) and 3R (Rhombohedral) according to the method of exfoliation done and among which the lack of inversion symmetry in the monolayer 2D TMDCs opens up a new field of interest of study called valleytronics. The coordination of metal atoms in TMDCs determines the semiconducting, semi metal or metallic property. The monolayer of 2H phase of 2D TMDCs are found to be semiconducting and the semiconducting behaviour is explained using the optoelectronic properties. The electronic band structure determines the number of layers. There is an indirect to direct band gap transition from the multilayer to monolayer of TMDCs at k point in the brillouin zones which is revealed by the Photo Luminescence (PL) spectroscopy. The photoluminescence is studied using the near band edge emissions. Near band edge emission is the radiative recombination process of the electron from conduction to valence band resulting in the emission of photon equal to the energy of the band gap. The energy of the band gap of monolayer is found to be 1.9 eV which lies in the visible and near infrared regions making the monolayer TMDCs an ideal candidate for opto electronic applications.

In monolayer MoS₂, the conduction and the valence band are located at the corners of the brillouin zone known as k points. When the right circularly polarized light is shone on the sample, K₊ valley gets excited. Similarly for left circularly polarized light that excites the K_- valley. The excitation of linearly polarized light leads to the spin hall effect and valley hall effect. The strong Spin Orbit Coupling and inversion symmetry breaking of monolayer group 6 TMDCs led to the manipulation of spin and valley degrees of freedom. This made TMDCs, a promising candidate in spintronics and valleytronics. The exfoliation is done to extract the monolayer of different polytypes. This includes two approaches: top down (mechanical exfoliation, liquid exfoliation) and bottom up (Chemical Vapour Deposition (CVD)) approach. However mechanical exfoliation is the best approach to obtain monolayers at small scale. The determination of number of layers involves the thickness identification via optical microscopic techniques. Atomic Force Microscopy is a method for thickness identification which scans the surface of the substrate using the sharp tip but consumes more time, can cause damage and expensive. Hence the alternate way like Optical microscopic techniques are chosen which gives quick results even done at the large scale.

The contrast is the difference in the brightness that is used to distinguish an object. Optical Contrast technique is easy and reliable method of identification of thickness. This involves the analysis of the optical microscopic image using the RGB values of each pixel of substrate and the sample. The visible light incident on the MoS₂ deposited SiO₂/Si substrate results in reflection, transmission at different angles because of the multilayer structure. Thus the reflected intensities are calculated to find the contrast spectrum. The thickness dependence transition can also be identified by the Raman spectroscopic analysis after the optical microscopic techniques. Raman spectroscopy gives more accuracy than the infrared spectroscopy. Raman spectrum has two modes namely in plane (E_2g) and out of plane (A_1g) vibrational modes where the difference between two modes determines the layer thickness. A_1g mode corresponds to the out of plane vibration of sulphur atoms and the E_2g mode corresponds to the in plane vibration of Mo and S atoms. Increase in number of layers at E_2g mode results in decrease in the peak frequencies and hence shifts to lower frequencies. For the A_1g mode there is a shift to higher frequencies. Low frequency Raman modes or interlayer vibrational modes provide the layer number in detail. There are two types of interlayer vibration modes, the shear (S) mode, where the oscillation is parallel to the layer plane, and the layer-breathing (LB) mode, where the oscillation is perpendicular to the layer plane. Photo luminescence spectroscopy is difficult and gives good results if it is a monolayer. Thus Raman spectroscopy is found to be one of the best methods of characterization of layer thickness without any destruction.

METHODOLOGY

The mechanical exfoliation process is done to obtain few layers of TMDCs from the bulk ones. The sample used here is MoS₂. The bulk MoS₂ is exfoliated using scotch tape for 2-3 times to obtain few layers of MoS₂. The SiO₂/Si substrate is cleaned by sonicating it with DI water, acetone and isopropanol followed by the plasma cleaning. This scotch tape method gives thin flakes of MoS₂ is transferred to the cleaned substrate. This is viewed under the optical microscope ‘Olympus 52 BX 53M’ that is equipped with Charge Coupled Device (CCD) and the images are taken. The obtained optical microscopic images of MoS₂ are shown as in fig1.

The layers of the optical contrast image are differentiated using the optical contrast analysis by using mat lab software as shown in the fig1.

Fig 1 (a), (c) and (e) Optical microscopic images of MoS₂ and (b), (d) and (f) representing the corresponding Mat- Lab images

Raman Spectroscopy

The optical contrast gives the number of layers. Yet, there is a need for the determination of number of layers using other techniques. Raman spectroscopy is an alternate reliable method for the characterization of thickness of MoS₂ quantitatively. The Raman spectroscopy setup includes the light source, sample and detector. The setup used is a micro Raman setup. This set up has both Photo Luminescence and Raman spectroscopy and also has the provision of employing both linearly and circularly polarized light to focus on the sample. The micro Raman setup has an image sensor (CCD) which employs the white light to fall on the material to focus the designated flake that is needed to be studied using Raman spectroscopy.

The excitation wavelength is set to 532 nm and power is measured as 3mW using the power meter for 532 nm. The specifications like the slit width of the detector that encloses monochromator is made small for Raman spectroscopy since it includes the vibrational studies and are set to 0.05 mm respectively. The position of CCD is set to 565.

The Raman spectroscopy works in a way that the laser light is focused on the designated flake of the MoS₂ sample and the incident light gets scattered at different directions. The exposure time is set to 5 seconds. The scattered light is focused by the lens and is recorded and detected or sensed by the Charge Coupled Device (CCD). The detector is enclosed with both monochromator and detector. The grating Raman spectroscopy has 1200 rulings. The monochromator scans the wavelength and the intensity (counts) for each wavelength is determined. The intensity peak signal obtained for the designated flake of MoS₂ is along with the generation of signals of Si and the noise which is averaged (average - 10) to get a final signal in terms of intensity (counts) for the visible wavelength region.

Fig 2 Experimental setup for Raman spectroscopy: Abbreviations: M, Mirror; OL, Objective Lens

Data Analysis

Optical Contrast Analysis

i) EXPERIMENTAL THICKNESS IDENTIFICATION:

The thickness identification of MoS₂ is done using optical contrast (OC) analysis using a mat lab programme by reading the R, G, B values of the pixels of the optical images of substrate and sample. The contrast is defined as the difference in the brightness to distinguish an object. The colour contrast of the layers of the sample gives the accurate thickness identification. The optical contrast (for R, G and B) between the substrate and the sample is calculated by,

​ $OC=\;\left|\frac{C_{subsrate}-\;C_{sample}}{C_{substrate}+C_{sample}}\right|$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>C</mi><mo>=</mo><mo>&#xA0;</mo><mfenced open="|" close="|"><mfrac><mrow><msub><mi>C</mi><mrow><mi>s</mi><mi>u</mi><mi>b</mi><mi>s</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi></mrow></msub><mo>-</mo><mo>&#xA0;</mo><msub><mi>C</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msub></mrow><mrow><msub><mi>C</mi><mrow><mi>s</mi><mi>u</mi><mi>b</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi></mrow></msub><mo>+</mo><msub><mi>C</mi><mrow><mi>s</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow></msub></mrow></mfrac></mfenced></math>OC=\;\left|\frac{C_{subsrate}-\;C_{sample}}{C_{substrate}+C_{sample}}\right|

From the experimental results, the green channel’s OC value is chosen because of the exposure of sample to the light source.

ii) THEORETICAL RESULTS:

When a beam enters a multilayer structure, a part of beam gets reflected and transmitted. This results in the change in the reflected light intensities of sample and the substrate. Thus the contrast spectrum between the sample and the substrate is calculated by the Fresnel

equation ^{[3], [4]}

$C(\lambda)=\;\left|\frac{R_0(\lambda)\;-R(\lambda)}{R_0(\lambda)+R(\lambda)}\right|$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo><mo>=</mo><mo>&#xA0;</mo><mfenced open="|" close="|"><mfrac><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo><mo>&#xA0;</mo><mo>-</mo><mi>R</mi><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo></mrow><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo><mo>+</mo><mi>R</mi><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo></mrow></mfrac></mfenced></math>C(\lambda)=\;\left|\frac{R_0(\lambda)\;-R(\lambda)}{R_0(\lambda)+R(\lambda)}\right|

Where,

R₀ (λ) =|r₀ (λ)| ² is the reflected light intensity from air/ (SiO₂ on Si) system and

R (λ) =|r(λ)|² is the reflected light intensity from air/ MoS₂/ SiO₂ / Si system

The total reflected amplitude of air/ (SiO₂ on Si) system is calculated by the equation,

$r_0\left(\lambda \right)=\frac{r_{02}+r_{23}\cdot e^{-2i{\varphi }_2}}{1+r_{02}\cdot r_{23}\cdot e^{-2i{\varphi }_2}}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mn>0</mn></msub><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo><mo>=</mo><mfrac><mrow><msub><mi>r</mi><mn>02</mn></msub><mo>+</mo><msub><mi>r</mi><mn>23</mn></msub><mo>&#x22C5;</mo><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>2</mn></msub></mrow></msup></mrow><mrow><mn>1</mn><mo>+</mo><msub><mi>r</mi><mn>02</mn></msub><mo>&#x22C5;</mo><msub><mi>r</mi><mn>23</mn></msub><mo>&#x22C5;</mo><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>2</mn></msub></mrow></msup></mrow></mfrac></math>r_0(\lambda)=\frac{r_{02}+r_{23}⋅e^{-2i\phi_2}}{1+r_{02}⋅r_{23}⋅e^{-2i\phi_2}}

$r\left(\lambda \right) =\frac{r_{01}+r_{01}{r}_{12}{r}_{23}{e}^{-2i{\varphi }_2}+r_{12}{e}^{-2i{\varphi }_1}+r_{23}{e}^{-2i({\varphi }_1+{\varphi }_2)}}{1+r_{12}{r}_{23}{e}^{-2i{\varphi }_2}+r_{01}{r}_{12}{e}^{-2i{\varphi }_1}+r_{01}{r}_{23}{e}^{-2i({\varphi }_1+{\varphi }_2)}}$<math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mi>&#x3BB;</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mfrac><mrow><msub><mi>r</mi><mn>01</mn></msub><mo>+</mo><msub><mi>r</mi><mn>01</mn></msub><msub><mi>r</mi><mn>12</mn></msub><msub><mi>r</mi><mn>23</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>2</mn></msub></mrow></msup><mo>+</mo><msub><mi>r</mi><mn>12</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>1</mn></msub></mrow></msup><mo>+</mo><msub><mi>r</mi><mn>23</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><mo>(</mo><msub><mi>&#x3D5;</mi><mn>1</mn></msub><mo>+</mo><msub><mi>&#x3D5;</mi><mn>2</mn></msub><mo>)</mo></mrow></msup></mrow><mrow><mn>1</mn><mo>+</mo><msub><mi>r</mi><mn>12</mn></msub><msub><mi>r</mi><mn>23</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>2</mn></msub></mrow></msup><mo>+</mo><msub><mi>r</mi><mn>01</mn></msub><msub><mi>r</mi><mn>12</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><msub><mi>&#x3D5;</mi><mn>1</mn></msub></mrow></msup><mo>+</mo><msub><mi>r</mi><mn>01</mn></msub><msub><mi>r</mi><mn>23</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>i</mi><mo>(</mo><msub><mi>&#x3D5;</mi><mn>1</mn></msub><mo>+</mo><msub><mi>&#x3D5;</mi><mn>2</mn></msub><mo>)</mo></mrow></msup></mrow></mfrac><mo>&#xA0;</mo></math>\style{font-family:'Times New Roman'}{r(\lambda)\;=\frac{r_{01}+r_{01}r_{12}r_{23}e^{-2i\phi_2}+r_{12}e^{-2i\phi_1}+r_{23}e^{-2i(\phi_1+\phi_2)}}{1+r_{12}r_{23}e^{-2i\phi_2}+r_{01}r_{12}e^{-2i\phi_1}+r_{01}r_{23}e^{-2i(\phi_1+\phi_2)}}\;}

Where, r_ij is the reflection coefficient of layer at i and j interface respectively.

At normal incidence, r_ij is calculated by, r_ij = $\frac{\widetilde{n_i}-\widetilde{n_j}}{\widetilde{n_i}+\widetilde{n_j}}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mover><msub><mi>n</mi><mi>i</mi></msub><mo>~</mo></mover><mo>-</mo><mover><msub><mi>n</mi><mi>j</mi></msub><mo>~</mo></mover></mrow><mrow><mover><msub><mi>n</mi><mi>i</mi></msub><mo>~</mo></mover><mo>+</mo><mover><msub><mi>n</mi><mi>j</mi></msub><mo>~</mo></mover></mrow></mfrac></math>\frac{\widetilde{n_i}-\widetilde{n_j}}{\widetilde{n_i}+\widetilde{n_j}}

where, $\widetilde{n_i}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>i</mi></msub><mo>~</mo></mover></math>\widetilde{n_i} and $\widetilde{n_j}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>j</mi></msub><mo>~</mo></mover></math>\widetilde{n_j}represents complex refractive index of i and j layer respectively and the i and j values of $\widetilde{n_i}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>i</mi></msub><mo>~</mo></mover></math>\widetilde{n_i} and $\widetilde{n_j}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>j</mi></msub><mo>~</mo></mover></math>\widetilde{n_j} are designated as i= j= 0,1,2,3. The air in the multilayer structure represents layer 0, MoS₂ to be layer 1 SiO₂ to be layer 2, Si as layer 3.the complex refractive index of,

​ $\begin{array}{l}\widetilde{n_0}=1\\\widetilde{n_1}=n_1-ik_1\\\widetilde{n_2}=n_2\\\widetilde{n_3}=n_3-ik_3\end{array}$<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mn>0</mn></msub><mo>~</mo></mover><mo>=</mo><mn>1</mn><mspace linebreak="newline"/><mover><msub><mi>n</mi><mn>1</mn></msub><mo>~</mo></mover><mo>=</mo><msub><mi>n</mi><mn>1</mn></msub><mo>-</mo><mi>i</mi><msub><mi>k</mi><mn>1</mn></msub><mspace linebreak="newline"/><mover><msub><mi>n</mi><mn>2</mn></msub><mo>~</mo></mover><mo>=</mo><msub><mi>n</mi><mn>2</mn></msub><mspace linebreak="newline"/><mover><msub><mi>n</mi><mn>3</mn></msub><mo>~</mo></mover><mo>=</mo><msub><mi>n</mi><mn>3</mn></msub><mo>-</mo><mi>i</mi><msub><mi>k</mi><mn>3</mn></msub></math>\begin{array}{l}\widetilde{n_0}=1\\\widetilde{n_1}=n_1-ik_1\\\widetilde{n_2}=n_2\\\widetilde{n_3}=n_3-ik_3\end{array}

k represents the absorption coefficient of the corresponding layer. $\phi_{1,2}=\frac{2\mathrm\pi n_{1,2}d_{1,2}}\lambda$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#x3D5;</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">&#x3C0;</mi><msub><mi>n</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><msub><mi>d</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow><mi>&#x3BB;</mi></mfrac></math>\phi_{1,2}=\frac{2\mathrm\pi n_{1,2}d_{1,2}}\lambda, where ${\varphi }_1$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#x3D5;</mi><mn>1</mn></msub></math>\phi_1 and ${\varphi }_2$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&#x3D5;</mi><mn>2</mn></msub></math>\phi_2 are the phase difference when light pass through MoS₂ or SiO₂ layers respectively. n₁ and n₂ are the refractive indices of MoS₂ and SiO₂. d₁ and d₂ are the thickness of MoS₂ and SiO₂ respectively. $d_1=N\times d$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>d</mi><mn>1</mn></msub><mo>=</mo><mi>N</mi><mo>&#xD7;</mo><mi>d</mi></math>d_1=N\times dis the thickness of MoS₂ layers. N represents the number of layers and the thickness of one layer of MoS₂ is d= 0.85nm. λ represents the wavelength. The OC values and the corresponding layer numbers are found for all the visible wavelength from 400-800 nm and the graph is plotted for the wavelength 535 nm.​

iii) COMPARISON:

The theoretically and experimentally obtained optical contrast values with respect to the layer numbers are shown as in fig 3. The experimentally obtained OC values match well with the theoretical results as per the data table shown in table 1.

Fig 3 Graph representing the experimental and theoretically obtained optical contrast and the corresponding layer number of MoS₂ flakes on SiO₂/Si substrate.3

Raman Measurements

The Raman scattering studies of few layer MoS₂ is done to determine the layer dependent properties due to the lattice vibrations. The wavelength is scattered in the directions at specific angles. The wavelength (nm) and the corresponding intensity (counts) of the MoS₂ sample. The data obtained are plotted in the graph as the function of Raman shift (cm^-1) after normalization using origin software. The corresponding graph of the Raman spectra of few layers gives the normalized intensity of as the function of Raman shift is shown as in fig4.

The $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1}and $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g} peak frequencies are determined and compared with the values taken from reference for few layers and bulk MoS₂ at 532nm ^[5]. The data table 2 represents the corresponding peak frequency of $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1}and $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g}modes at 532 nm.

Fig 4 a) Graph representing the modes of MoS₂ with Si peaks after normalization b) Graph representing the two modes of different layers of MoS2 on SiO2/Si substrate.

RESULTS AND DISCUSSION

The aim of mechanical exfoliation is to get monolayer MoS₂. The optical microscopic images taken are done Optical Contrast analysis (OC). The experimentally determined optical contrast values of RGB separately are plotted and optical contrast values of green channel is chosen due to the exposure time of MoS₂ sample on SiO₂/Si substrate to the light source and is compared with the theoretical results at 535 nm. This shows that the experimental contrast values matches with the theoretical results and the layer number is determined. The experimental and theoretical OC values with layer numbers are plotted in the graph using origin software as shown in the fig2. It is found from the graph that, the corresponding layer number increases with an increase in OC values. The least obtained layer is trilayer.

Usually the $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1}and $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g}modes will be in a way that the layer thickness monolayer to 5 layers are dependent on each other and also easy for the identification of layers. The frequency difference $\left(\Delta \omega \right)$<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>&#x394;</mi><mi>&#x3C9;</mi><mo>)</mo></math>(\Delta\omega) between the two peaks is found using the formula as in reference ^[6]. It is found that the increase in the number of layers results in the increase in frequency difference. For the given MoS₂ sample, the frequency shift of $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1}mode decreases with increase in thickness, where for the $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g}mode, the frequency shift increases with increase in the thickness. Hence the mode of vibration is strong at bulk MoS₂ compared to the other few layers. The experimentally determined frequency peak values for trilayer varies slightly with the expected frequency peak for the trilayer which is 382.4 cm^-1 for $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1}and 405.7 cm^-1 for $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g} mode.

The determination of number of layers can also be identified using the intensity of the $E_{{}_{2g}}^{{}^1}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>E</mi><msub><mrow/><mrow><mn>2</mn><mi>g</mi></mrow></msub><msup><mrow/><mn>1</mn></msup></msubsup></math>E_{{}_{2g}}^{{}^1} and $A_{{}_{1}g}$<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><msub><mrow/><mn>1</mn></msub><mi>g</mi></mrow></msub></math>A_{{}_1g}peak modes after normalization. It is seen from the graph of fig 4, the signals are found to be imperfect and not precise due to the presence of more noise signals. Hence, layer number identification using the Raman intensity is less preferred.

CONCLUSION

The mechanical exfoliation is done to extract the few layers of MoS₂ from the bulk MoS₂ sample. The MoS₂ transferred SiO₂/Si substrate is viewed through the optical microscope and the corresponding layer number is determined. Primarily, this is done using the optical contrast analysis. The theoretical and the experimental results of OC values are compared for the identification of the layer number. The secondary method was Raman spectroscopy to determine the number of layers using the vibrational modes. However Raman spectroscopy done here is found to be not a good method for the determination of number of layers since the intensity variation is not significant. Hence optical contrast helps in and suffices to be a good method in the identification of layer thickness and determination of number of layers of the sample MoS₂.

REFERENCES

1. Hualing Zeng. et al. An optical spectroscopic study on two dimensional group-VI transition metal dichalcogenides. Chem. Soc. Rev., (2015), 44, 2629.

2. Kinam Kim. et al. A role for graphene in silicon-based semiconductor devices

Nature (2011), 338, 479 (7373).

3. Ying Ying Wang1. et al. Thickness identification of two-dimensional materials by optical imaging , Nanotechnology (2012), 23, 495713.

4. Dan Bing. et al. Optical contrast for identifying the thickness of two dimensional materials, Optics Communications. (2018), 406, 128-138.

5. Hong Li. et al. From Bulk to Monolayer MoS₂ : Evolution of Raman Scattering Adv. Funct. Mater. (2012), 22, 1385–1390.

6. Fang Liang. et al. Raman spectroscopy characterization of two dimensional materials Chinese Phys. B (2018), 27, 037802

ACKNOWLEDGEMENTS

I would like to thank Indian Academy of Sciences for giving me a great opportunity to work on a project.

I owe my sincere thanks and profound gratitude to my guide, Dr. Rajeev N. Kini, for giving an opportunity to join his lab, admittance to work in the laboratory and for his constant encouragement, support and guidance throughout my internship.

I would like to express my heartfelt gratitude to Mr. Prahlad Kanti Barman for the knowledge he shared, guidance, and for being a moral support to complete the project.

Finally, I extend my special thanks to my lab mates who helped me during this project.