**3. In plane thermal conductivity of layered PtSe2**

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 [25–28]. 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 PtSe2. The parent crystal used for mechanical exfoliation was sourced from 2D semiconductors, USA. Exfoliation was done over SiO2/Si substrate with SiO2 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 (*E*g) and out of plane (*A*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

#### **Figure 6.**

*Power dependent Raman spectra (a) and temperature dependent Raman spectra (b) of flake 1 measured at fixed power of 2.27 mW.*

#### **Figure 7.**

*(a) AFM image of the flake 1, inset showing the height profile, (b) Optical micrograph of the same flake. (c) and (d) Variation of the in plane (Eg) and out of plane (A1g) with power and temperature respectively.*

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 *E*g and *A*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 *E*<sup>g</sup> and *A*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 (*ω*) is linear in the low power range and is governed by [32]:

$$
\Delta o = o(P\_2) - o(P\_1) = \mathcal{Y} \left( P\_2 - P\_1 \right) = \mathcal{Y}\_\mathbb{P} \text{ } \Delta P \tag{1}
$$

So, the power coefficient is given by .

*Thickness Dependent Spectroscopic Studies in 2D PtSe2 DOI: http://dx.doi.org/10.5772/intechopen.103101*

The power coefficient of both the *E*g and *A*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 (*E*g) and out of plane (*A*1g) Raman modes can be stated as [32, 33]:

$$
\alpha(T) = \alpha\_0 + \alpha\_1 T + \alpha\_2 T^2 \tag{2}
$$

Where *ω*0 is the frequency of *E*g and *A*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 (*K*) arising from a particular mode of vibration. For 2D materials the expression used by using *α*1 and *χ*P and is given by [34]:

$$K = \alpha\_1 \mathcal{Z}\_{\mathbb{P}}^{-1} \left( \frac{\mathbf{1}}{2\pi h} \right) \tag{3}$$

where *h* is the thickness of the flake.

The slope of linear fit corresponding to *E*g mode in **Figure 7c** and **d** i.e. *χ*P and *α*<sup>1</sup> 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 *E*g and *A*1g Raman modes with power and temperature is depicted in **Figure 9a** and **b** respectively.

#### **Figure 8.**

*(a) Raman spectra at different laser power, (b) at different temperature with fixed laser power of 2.27 mW. (c) AFM image, inset shows the optical micrograph and the height profile of flake 2.*

#### **Figure 9.**

*Dependence of Raman peak shift (both Eg and A1g) with (a) power and (b) with temperature of flake 2.*

#### **Figure 10.**

*(a) and (b) AFM and optical micrograph of flake 3, inset showing the height profile. (c) and (d) Variation of the Raman peak shift (both Eg and A1g) with laser power and temperature 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 *E*g and *A*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 *α*1 and *χ*P from Eq. (3) we get the thermal conductivity, which is 39.30 W/mK ± 14.96 W/mK.

*Thickness Dependent Spectroscopic Studies in 2D PtSe2 DOI: http://dx.doi.org/10.5772/intechopen.103101*


#### **Table 1.**

*Comparison of thermal conductivity, α1 and χP of the three flakes for Eg mode.*

**Table 1** shows the comparison between the thermal conductivity, *α*1 and *χ*P of the three flakes. The thermal conductivity of all the flakes is approximately similar. This shows that PtSe2 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 PtSe2 is about 18 W/mK [36]. The saturation value for thicker PtSe2 over SiO2/Si substrates can be approximately taken as 40 W/mK.
