Comparison of thermal conductivity, _{1} and _{P} of the three flakes for _{g} mode.

## Abstract

Transition metal dichalcogenides (TMDCs) are emerging to be an exciting class of 2D materials apart from graphene or hexagonal boron nitride (h-BN). They are a class of layered materials that exhibit inspiring properties which are worth exploring, among them PtSe2 is fairly a new addition. Although bulk PtSe2 was first synthesized more than a century ago, the study of its layer-dependent properties is still at a nascent stage. The monolayer of PtSe2 exhibits a band gap between 1.2 and 1.8 eV, the band gap starts to decrease with an increase in the number of layers thus transforming into semimetal type. Among all other 2D materials it shows the highest electron mobility of about 3000 cm2 V−1 s−1 and unlike other TMDCs, it is strikingly stable in ambient conditions. Owing to its stability and tunable properties, it has great potential in the fields of optoelectronics, spintronics, sensorics, and many more. In this book chapter, we report the thickness dependent spectroscopic properties of mechanically exfoliated PtSe2. We have explored low temperature Raman spectroscopy as well as polarized Raman spectroscopy to study in detail the vibrational properties of PtSe2. Raman spectroscopy is also employed to determine its thermal conductivity. We hope that this work will provide a fresh overview of PtSe2 from a spectroscopic perspective.

### Keywords

- transition metal dichalcogenides
- PtSe2
- raman spectroscopy
- electronic band structure
- thermal conductivity

## 1. Introduction

Once a forbidden material, one atom thick material came into existence with the discovery of graphene in 2004 by Novoselov et al. [1]. Unsurprisingly due to the unique properties and momentous potential of 2D materials, the research world jumped into the foray. Interestingly the term “graphene” was coined in 1986 by Boehm and the electronic band structure of single layer graphite is studied since 1942 [2]. The surge of discovery didn’t stop with graphene, it gathered pace, and “2D materials” like * h*-BN, transition metal dichalcogenides (TMDCs), and several other layered materials came into existence. This present work deals with one of the less explored TMDCs, i.e. PtSe

_{2}. Its unique and exciting properties are worth exploring. It has a wide range of applications like photodetectors, gas sensing, electronics, piezoresistive sensors, and electrocatalysis [3, 4, 5, 6]. Another interesting fact about PtSe

_{2}is that it can be grown under relatively low temperatures when compared to other TMDCs via vapour phase synthesis process. This increases the choice of substrates. It has been reported to be grown at temperatures as low as 100°C [7]. Although PtSe

_{2}emerged more than a century ago, its layer dependent properties and their respective applications are hardly explored. This chapter gives an outline of Raman spectroscopic studies of PtSe

_{2}of different thicknesses, both at room temperature and low temperature. It also deals with the task of using Raman spectroscopy to measure in-plane thermal conductivity. Theoretical calculation of electronic band structure and density of states of the monolayer, bilayer, tri layer, and bulk PtSe

_{2}has also been incorporated in this chapter.

The 1T phase of PtSe_{2} belongs to space group P_{2} is hexagonal and has D_{3d} point group symmetry. The monolayer is made up of three atomic sub layers, Pt layer is being sandwiched between two Se layers. The reported lattice vectors are * a*(

*(*a

_{2}, i.e. top view (a) and side view (b). The calculated lattice constant of the primitive unit cell of monolayer PtSe

_{2}is 3.70 Å which matches with the measured value of the same by STEM (scanning tunneling electron microscope) measurement [8, 10]. The primitive unit cell contains three atoms. The Pt-Se bond length for 1T phase is 2.52 Å and the distance between the top and bottom Se sub layers is 2.68 Å [10].

In monolayer 1T-PtSe_{2} phase the bonding is completely covalent in nature with no net transfer of charge between the bonded atoms. The work function of single layer PtSe_{2} is 5.36 eV and the values for other dichalcogenides like MoSe_{2} and WSe_{2} are 4.57 and 4.21 eV [8, 11]. The monolayer behaves as a semiconductor whereas the bulk behaves as a semi-metal [12, 13]. The phonon spectrum of mono layer 1T-PtSe_{2} consists of nine phonon modes out of which six are optical and three are acoustic. Figure 2a shows the phonon modes in 1L1 T-PtSe_{2}. The six optical modes can be decomposed into - Γ = 2_{g} + 2_{u} + _{1g} + _{2u}. The in-plane modes (169 cm^{−1} for _{g} and 218 cm^{−1} for _{u}) are doubly degenerate and out of plane modes (200 cm^{−1} for _{1g} and 223 cm^{−1} for _{2u}) are singly degenerate, the (_{1g} + _{g}) modes are Raman active, 2_{u} is infrared active and 2_{u} is both infrared and Raman active. Out of these four modes, only two of them (_{g} mode at 169 cm^{−1} and _{1g} at 200 cm^{−1}) are prominent. Figure 2b shows their calculated relative intensities along with the modes of vibration [8]. The strong covalent nature of the Pt-Se bond makes the in plane vibrational modes more intense when compared to out of plane modes.

Figure 3 shows the Raman spectra of both bilayer and multilayer (~5 nm thick) CVD grown PtSe_{2} [14]. In bilayer PtSe_{2}, two prominent peaks are observed which are centred at 179 and 207 cm^{−1}. These peaks are associated with first order phonon emission of in-plane and out of plane vibrational modes i.e. _{g} and _{1g} modes. Additionally, another less prominent peak is recorded at 235 cm^{−1}. This low intensity peak arises due to the longitudinal optical mode and can be separated into two vibrations. These two vibrations correspond to first order two phonon emission for out of plane (_{2u}) and in plane (_{u}) vibrations of Pt and Se atoms [14]. O’Brien et al. [15], reported the above mentioned peaks to be centred at 175 cm^{−1} (_{g}), 205 cm^{−1} (_{1g}), and 230 cm^{−1} (LO), and they also showed that these modes have approximately constant peak position for laser excitation of 488, 532, and 633 nm. The differences between theoretically derived (previously discussed) phonon modes and experimentally recorded ones can be attributed to the fact that PtSe_{2} layers are not pristine with definite thickness [15].

## 2. Density functional theory study of layered PtSe_{2}

We employed density functional theory (DFT) to calculate the electronic band structure and density of states of mono layer, bi-layer, tri-layer, and bulk 1T -phase PtSe_{2}. This section deals with the theoretical calculations. DFT is a quantum modeling method used to investigate the properties of chemical systems, including atoms and molecules (i.e., many body systems), particularly the electronic structure properties. It is an ab inito method for solving the Schrodinger equations for many-electron systems which are defined by the electron density. The approach taken is, instead of using a many-body wave function, one-body density is used as the fundamental variable. Since the electron density * n*(

*) is a function of only three spatial coordinates, rather than 3N coordinates of the wave function, DFT is computationally feasible for small to large systems. The root of DFT comes from two theorems given by Hohenberg and Kohn who considered interacting electrons in an external field [16, 17]. The theorems state that the ground state energy is a unique function of electron density, allowing us to work in three dimensions than in 3N dimensions. Only the electron density that minimizes the energy of functional is taken, with the assumption that the function is known. HK theorems sound simple but can be applied only under certain circumstances but they are not considered in practice as densities of atoms do not obey these constraints. Taking into consideration some of the fundamental issues, Kohn and Sham reduce the problem to noninteracting electrons moving in an effective potential, leading to a set of self-consistent, single particle equations known as Kohn-Sham equations that contains exchange correlation potential. The result of DFT calculations depends on the choice of exchange-correlation functional. In terms of increasing accuracy, we have LDA, GGA, meta-GGA, and hybrid functionals. Some functionals give good results for one system and some for another. More accurate functionals consume more computational resources with a trade-off between accuracy and speed of calculation.*r

### 2.1 Computational methods

All the computational calculations were performed using the DFT with the projector augmented wave (PAW) pseudopotentials available with quantum-espresso [18]. Which is an integrated suite of open-source codes for the electronic structure calculation and materials modeling at the nanoscale. We used the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional for the calculation of exchange and correlation potential. The van der Waals correction for the layered structures was taken into account using the DFT-D_{2} method as proposed by Grimme [19]. The arrangement of layers was taken such that it has the lowest ground state energy value and the top-to-top (AA) stacking order is the most favorable one with the interlayer distance calculated to be 2.44 Å. The kinetic energy cut-off for a plane-wave basis set was taken to be 800 eV.

The convergence criteria for self-consistent calculations for electronic structures were set to 10^{−6} eV. For the optimized geometrical configurations, the energy convergence criterion was set to 10^{−5} eV, structure relaxations were conducted until the residual force acting on each atom is less than 0.01 eV/Å and pressure values less than 1 kbar. The sampling of the first Brillouin zone was done using Г-centered * k*-point mesh of 15 × 15 × 15 and 15 × 15 × 1 for bulk and thin film structures, respectively. A region of at least 14 Å vacuum space was added in the

*-direction to minimize the interaction between the neighboring atomic layers.*z

### 2.2 Structure and electronic properties

The bulk phase of PtSe_{2} has 1T phase with tetragonal symmetry having space group P-3 m1 and the lattice constant, after optimization, found to be * a* = 3.77 Å,

*= 5.52 Å, a significant close to the experimental value and similar other reported values as discussed earlier. The monolayer structure is composed of three atomic sublayers with a Pt layer sandwiched between two Se layers. The lattice constant is calculated to be 3.70 Å which is in agreement with previously reported data, and the vertical distance between the upper and lowermost layer of Se is about 2.65 Å close to the reported value of 2.53 Å [12]. While moving from bilayer to bulk structure, the interlayer distance also decreases, along with the trend of increasing layer-layer interaction which enlarges the covalent Pt-Se bond. The lattice constant of monolayer, bilayer and trilayer is found to be 3.70 Å, 3.73 Å and 3.74 Å respectively and for bulk it is 3.78 Å.*c

Figure 4 shows the electronic band structure of 1L,2L, 3L and bulk PtSe_{2}.The electronic structure calculations using the PBE functional show the transition from semiconductor to (semi)metal behavior of the material. The calculated bandgap of monolayer is around 1.39 eV, close to the experimental value [20]. While moving from monolayer to bilayer, the electronic band gap rapidly decreases to 0.38 eV. It is also found that PtSe_{2} crystals having a thickness larger than two layers exhibit metallic behavior. Looking at the band structures, one can see that 1T-PtSe_{2} monolayer has its valence band maximum (VBM) at Г point and conduction band minimum (CBM) within Г-M point. While going from monolayer to bilayer and higher layers, we observe that position of CBM at Г-M point is fixed and VBM shifted from Г point to within K-Г high symmetry point. The reason behind this shift might be due to the non-periodicity of layered structure along the growth direction which is different from the band structure of bulk 3D structure of same material, as the energy band structure is strongly dependent on the crystal periodicity. The decrease in band energy of CB states and increase in VB states leads to metallization starting from trilayer [21, 22].

The DOS variation with different layers is shown in Figure 5a–d. In the DOS plots, for monolayer (Figure 5a), peak appears for the VBM, depicting a greater number of bands near the VBM, and flat near 0 eV. For the bilayer (Figure 5b), the peak disappears near the VBM, where the band involves two peaks near Г point. This remains until peak appears around fermi energy when it comes to more than three layers. It is also noticed that DOS under VBM is small for multilayers due to the large splitting between the first valence band with the second valence band [23, 24]. In this study, we were able to observe an increase in band gap with the decrease in layer numbers from bulk down to monolayer structures. Unlike other TMDs like MX_{2} (M = Mo and W; X = S and Se) which are direct bandgap semiconductors at monolayer, there is no shift from indirect-to-direct band gap with decrease in number layers from bulk to monolayer limit. This may be due to the difference in crystal structure i.e. – MX_{2} has 2H structure and PtSe_{2} has 1T structure. We were able to observe the inverse relationship between the band gap and number of layers, which is governed by factors such as quantum confinement effect and interlayer interaction.

## 3. In plane thermal conductivity of layered PtSe_{2}

The thermal conductivity of layered materials can be measured by employing Raman spectroscopy which is non-destructive in nature. It is fairly common to employ this method to measure the in-plane thermal conductivity in many 2D materials like graphene, * h*-BN and other TMDCs [25, 26, 27, 28]. There are several advantages for this method, such as measurement can be done for 2D material of different thicknesses over any substrates and also on suspended ones. In addition, the effect of substrate on the thermal conductivity can also be studied. Here, we employed Raman spectroscopy to study the thermal conductivity of multilayer mechanically exfoliated PtSe

_{2}. The parent crystal used for mechanical exfoliation was sourced from 2D semiconductors, USA. Exfoliation was done over SiO

_{2}/Si substrate with SiO

_{2}layer being 290 nm thick. A Horiba HR800 UV Raman spectrometer was used to acquire all Raman spectra which had 1800 lines/mm grating and 100X objective (0.9 NA) with a spot size of ~1 μm. The excitation wavelength was 488 nm f0r all the recorded Raman spectra. For low temperature Raman spectroscopy, Linkam liquid nitrogen cooling stage was used. During low temperature measurement, a long working distance 50× objective with 0.5 NA was used. The Raman plots are fitted with the Lorentzian function where the solid lines are fitted data and dots are raw data. We measured the thickness of the flakes by using atomic force microscopy (AFM), which was done by using a Park systems NX10 model. The AFM images were recorded in non-contact mode. Tip radius was less than 10 nm having a force constant of 42 N/m and frequency of 330 kHz. The height has been measured at 10 places to estimate the standard deviation in the measurement. The optical micrographs were taken by using a Nikon Eclipse LV100ND microscope.

We used three differently thick multilayer flakes (named as flake 1, flake 2 and flake 3) for this study. The Raman spectra of flake 1 at different laser power and at different temperatures is depicted in Figure 6a and b respectively. The laser power was varied from 0.227 to 1.08 mW whereas the temperature was varied from 107 to 293 K. Both the in-plane (_{g}) and out of plane (_{1g}) modes shifted to lower wave numbers with the rise in temperature. This shift is due to the thermally bond softening [29]. With higher power both the modes shifted to higher wavelength. Figure 7a and b shows the AFM and optical micrograph of flake 1 respectively. Although the optical image shows a uniform contrast over the whole flake, it is clear from the AFM image that the edges have different thicknesses. The inset of the AFM image shows the height profile, the thickness is about 42 nm ± 2 nm (at the middle part where the thickness is uniform). Which corresponds to approximately 54 layers, each layer being 0.8 nm thick [10]. The Raman spectra in Figure 6 don’t show the LO mode, as the flake is about 42 nm in thickness whereas the LO mode is suppressed due to the bulk nature of the flake.

The variation of the _{g} and _{1g} (for flake 1) with laser power and temperature is shown in Figure 7c and d respectively. Both the plot is linearly fitted and have a negative slope. The range of power was chosen such that the excitation laser doesn’t damage the flake [30, 31]. The negative slope in power dependent Raman spectra for both _{g} and _{1g} implies that the peaks shift to lower wave numbers. This is due to the fact that with increase in power local heating increases and the Pt-Se bonds softens. The thermal conductivity can be deduced by using these two plots (Figure 7a and d). The power (* P*) dependent peak position (

*) is linear in the low power range and is governed by [32]:*ω

So, the power coefficient is given by

The power coefficient of both the _{g} and _{1g} modes have been calculated through a linear fit of power dependent peak shift of these modes (as depicted in Figure 7c). The temperature dependence of both the in-plane (_{g}) and out of plane (_{1g}) Raman modes can be stated as [32, 33]:

Where _{0} is the frequency of _{g} and _{1g} at * T* = 0 K,

α

_{1}and

α

_{2}are the first and second order temperature coefficients. The second order coefficient is applicable at high temperatures, so for the present case, this can be neglected. After neglecting the second order coefficient, the equation was used to linearly fit the evolution Raman peak position with temperature in Figure 7b. The first order temperature and power coefficient can be used to get the thermal conductivity (

*) arising from a particular mode of vibration. For 2D materials the expression used by using*K

α

_{1}and

χ

_{P}and is given by [34]:

where * h*is the thickness of the flake.

The slope of linear fit corresponding to _{g} mode in Figure 7c and d i.e. _{P} and _{1} is −1.654 cm^{−1}/mW and −0.017 cm^{−1}/K respectively. Applying these values to Eq. (3) we get in-plane thermal conductivity for flake 1, which is –38.90 W/mK ± 17.43 W/mK. The error in thermal conductivity was calculated by taking into consideration the error of the slopes in Figure 7c and d and also for the thickness of flake 1. The range of error is consistent with the current literature for this method [35].

We investigated another two flakes named flake 2 and flake 3. The Raman spectra of flake 2 at different laser power and at different temperature is shown in Figure 8a and b respectively. Figure 8c shows the AFM image, with the optical micrograph and height profile in the inset. The thickness of flake 2 as derived from the height profile is 59 nm ±2 nm. Here too the absence of the LO mode is due to the bulk nature of the flake. The evolution of the _{g} and _{1g} Raman modes with power and temperature is depicted in Figure 9a and b respectively.

The plots are linearly fitted as discussed in previous section. Employing Eq. (3) we find the thermal conductivity of flake 2 is 40.42 W/mK ± 16.37 W/mK. Figure 10a and b shows the AFM, optical micrographs and evolution of the _{g} and _{1g} modes with power and temperature (Figure 10c and d respectively) of flake 3. The thickness of flake 3 is 119 nm ± 3 nm. Using _{1} and _{P} from Eq. (3) we get the thermal conductivity, which is 39.30 W/mK ± 14.96 W/mK.

Table 1 shows the comparison between the thermal conductivity, _{1} and _{P} of the three flakes. The thermal conductivity of all the flakes is approximately similar. This shows that PtSe_{2} over 40 nm thick has almost constant thermal conductivity. The first order temperature coefficient is also fairly constant for all three flakes. The calculated thermal conductivity at 300 K for monolayer PtSe_{2} is about 18 W/mK [36]. The saturation value for thicker PtSe_{2} over SiO_{2}/Si substrates can be approximately taken as 40 W/mK.

Flake | (nm) | _{1} (cm^{−1}/K) | _{P} (cm^{−1}/mW) | (W/mK) |
---|---|---|---|---|

1 | 42 | −0.017 | −1.654 | 38.90 |

2 | 59 | −0.011 | −0.734 | 40.42 |

3 | 119 | −0.015 | −0.511 | 39.30 |

## 4. Effect of laser polarization over different thicknesses of PtSe_{2}

The state of laser polarisation during Raman spectroscopy affects the two prominent modes of vibration i.e., _{g} (in plane) and _{1g} (out of plane) mode. Figure 11a and b shows the 1 nm (a) and 5 nm CVD grown PtSe_{2} under vertical (Z(YY)-Z) and horizontal (Z(YX)-Z) polarization [15]. For the 1 nm film, the intensity out of plane (_{1g}) mode significantly varies under vertical and horizontal polarization, whereas the 5 nm film has considerably less variation. When the thickness is increased to 59 nm (flake 2, Figure 11c) the intensity is almost similar under both states of polarization. This is because for the thicker film, the contribution from the bottom layers is more prominent and makes the intensities similar. The state of polarization has no effect over the intensity of the in-plane mode for 1 nm and 59 nm, this is because of it’s planar nature of vibration.

## 5. Conclusion

2D PtSe_{2} is an excellent material, its unique layer dependent properties. The fact that it is stable under ambient conditions unlike most other TMDCs makes it a great choice for scientific study. This book chapter gives an overview of the layer dependent properties of PtSe_{2} like band gap, density of states and thermal conductivity. DFT was employed to study the electronic band structure of 1L, 2L, 3L and bulk PtSe_{2}, which showed that there is a drastic reduction of band gap when moving from monolayer to bilayer.

Optothermal method by using Raman spectroscopy was employed to explore the thermal conductivity of PtSe_{2} flakes. The Raman study was carried out by both varying the power and temperature of the sample. The incident laser power was varied from 0.25 to 2.27 mW and the temperature of the sample was varied from 107 to 353 K, the power coefficient (_{2} with thickness more than 40 nm is about 39–41 W/mK. Perpendicular and parallel polarization study was done for 59 nm thick flake, which reveals that both the in plane and out of plane modes didn’t suffer any change in intensity in contrast with thinner flake (5 nm thick). The authors hope this book chapter shall aid the exploration endeavour regarding PtSe_{2}.

## Acknowledgments

PKN acknowledges the financial support from the Department of Science and Technology, Government of India (DST-GoI), with sanction Order No. SB/S2/RJN-043/2017 under Ramanujan Fellowship. This work was also partially supported by Indian Institute of Technology Madras to the 2D Materials Research and Innovation Group and Micro-Nano and Bio-Fluidics Group under the funding for Institutions of Eminence scheme of Ministry of Education, GoI [Sanction. No: 11/9/2019-U.3 (A)]

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