1. Introduction

In recent years, group- VI semiconductors have attracted much interest in their applications particularly in the area of solar cells. WSe2 is a member of the compounds of VI-A and VI-B group. It has stacked layer structure of M-X-M type which is an extra incentive for device research. Here M is transition metal e.g. tungsten and X is chalcogen e.g. Selenium. The crystal structures of the layered TMDC are usually described as belonging to 1T, 2H, 3R, 4H2, 4Hb, 6R phases[1, 2]. TMDCs have been used for many years as solid state lubricants[3], photovoltaic/photo catalytic solar energy converters[4-7]. Transition metal dichalcogenides materials use in photovoltaic and photo electrochemical (PEC) solar cells is because of their inherent resistive nature to photo corrosion.

Looking to potential for such diverse applications of TMDCs, we have chosen to study WSe₂ semi-conducting materials of group VI. Successful growth of single crystals of WSe₂ has been reported earlier[8] for the measurements of photoelectric and electrical properties. Here we report electrical transport parameters of the well characterized grown crystals of WSe₂ have been done. Thermoelectric properties like carrier concentration, Fermi energy, density of states and effective mass of carriers have also been determined and discussed in the paper. Here we report Hall Effect measurements. These investigations can yield valuable information about their electronic properties.

2. Experimental

Crystals of Tungsten dieseline (WSe₂) have been grown by direct vapour transport (DVT) technique using dual zone horizontal furnace. The temperature profile used for the growth of WSe₂ crystal is shown in fig. 1. The crystals grown were found to be in the form of thin platelets having opaque appearance with silver shining surface. The chemical composition was identified using energy dispersive analysis of X-ray (EDAX) (XL–30 ESEM, Netharland) XRD analysis was carried out by X-ray Diffractometer (Philips, X-pert MPD, Netharland) for the determination of structure. The thermoelectric power measurements (TEP) have been carried out on the grown crystals with the help of totally computer controlled TEP measurement setup developed in our laboratory.

Figure 1. The temperature profile used for the growth of WSe2

The sample with area 3x3 mm² was used. The measurements were taken in the temperature range of 333K to 473K and the temperature difference (∆T) between the ends of the sample was kept to be 10K. These crystals were also characterized using Hall effect measurement setup (Lakeshore-7504) in temperature range 10 - 300K to estimate the carrier concentration, hole mobility, Hall coefficient and resistivity.

Figure 2. Block diagram of the equipment setup of thermo electric power measurement

3. Results and Discussion

3.1. EDAX Analysis

The stoichiometry of the grown crystals was analyzed by EDAX and it is found that thegrown crystals possess nearly perfect stoichiometry with chemical formula W_1.03Se_1.97. There are no any impurities were presented in the limit of sensitivity.

Figure 3. EDAX Scan of WSe2 crystal

Table 1. Chemical composition (wt. %) of as grown WSe2 crystals obtained by EDAX analysis with chemical formula

3.2. XRD Study

Figure 4. X-ray diffractogram of WSe2 crystal

The typical X-ray diffractogram of the grown WSe₂ crystal is shown in figure 3.5was obtain with the help of Phillips X’pert MPD X-ray diffractometeremploying Cu, K_α radiation. All the peaks were indexed with the help of "powder X" programme, as depicted in fig.4. The highest intensity peak indicates the most preferred orientation of the crystal grains. The analytical indexing of the pattern thus obtained was done to calculate the lattice parameters for the hexagonal layered structures. The results obtained for as grown crystals of WSe₂ are given in table 2. In order to affirm that these lines belong to tungsten diselenide, the d spacing and relative intensities of these lines were compared with JCPDS data 2H-WSe₂polytypes[6].

The lattice parameters, a and c, were determined for hexagonal structure using the following equation[4, 5].

(1)

where h, k and l represent the Miller indicesand d is the inter planer spacing. Theobserved ‘d’ values and calculated ‘d’values are shown in table 2.

The particle size (D) of the WSe₂Crystals was determined by using the Debye-Scherrer’s formula,

(2)

where λ is the wave length of X –rays used, β is the FWHM, k is a constant (taken as 1) and θ is the angle between the incident and scattered X-rays.[10].

The micro strain (ε) and the dislocation density (ρ) of the deposited films were evaluated using the equations[11]

(3)

and

(4)

The results of these calculations have also been shown in table 2. The data presented in table 2.

3.3. Thermoelectric Power Study

The results of TEP measurements as shown by variation of thermoelectric power (S) with temperature in the range 333K to 750 K have been shown in fig.5. The positive values of ‘S’ shows that the crystals possess p-type conductivity. To analyze the temperature dependence of thermoelectricpower of a p-type semiconductor, the expression given by Mohanchandra and Uchil[12] and H. J. Goldsmid[13] has been used. It is given as

(5)

where k is Boltzmann constant, e is electronic charge, A=(5/2 - C) is the scattering coefficient which varies from 0 to 4 depending on the scattering process , C is the scattering parameter and E_F is the separation of Fermi level from the top of the valance band.

As the carrier concentration depends on E_F in the crystal and for a small temperature range, E_F can be considered as fairly constant, equation (1) can be expressed as[14 – 17]

(6)

Here N_A=[2πm_h^*kT/h²]^3/2is the effective density of states inwhich m_h^* is the effective mass of holes and h is the Plank’s constant.

Considering constant E_F, theplot of thermoelectric power (S) against the reciprocal of temperature gives a straight line as shown in fig. 5.

3.4. Low Temperature Hall Effect

The Ohmic nature of contacts prepared for van der Pauw geometry in case of variouspairs of contacts at 300 K is shown in the Fig. 6. It is seen from here that Ag-pastecontacts exhibit good Ohmic nature for both polarity in a large current range. The average van der Pauw factor for a set of four contacts is found to be 0.7. This deviationfrom ideal requirement of unity probably originates from the anisotropic nature of WSe₂ and not from other conditionsrequired for measurements using van der Pauw technique.The resistivity (p), Hallcoefficient (R_H), carrier density (n) and mobility (u) of WSe₂ single crystals were calculated from the measured I - V values under magnetic field of 3kG using thestandard formula over the temperature rangeof 50K to 300K and the results are tabulated in Table - 4. Figs. 7 and 8 show the variation of Resistivity, Hall Coefficient and Carrier concentration with respect to inverse of temperature. From these figures it is clearly seen that resistivity is decreasing monotonically with increasing temperature above around 90K which confirms the semiconducting nature of WSe₂ crystals.The anomalous semiconducting behavior below 90K is reflected in mobility also andseems to be related to changes in scattering mechanism. However carrier concentration is increasing with increasing temperature.

Table 2. Structural parameter for WSe2 Crystal

Table 3. Carrier Concentration, Fermi Energy, Effective Density of State, Effective Mass, Scattering Parameter of WSe2crystal

Table 4. Measured Hall parameters of WSe2 crystal

Figure 5. Variation of thermoelectric power S of WSe2 single crystal as an inverse function of temperature (ΔT = 10 K)

Figure 6. I-V characteristics between different pair of contacts for p-WSe2 crystal

Figure 7. RH andρ of p-WSe2crystals as a function of 1000/T

Figure 8. Carrier concentration vs. 1000/T for p-WSe2crystal

4. Conclusions

The EDAX analysis shows that the grown crystals are nearly perfect in stoichiometry. The X-ray analysis shows that crystals posses hexagonal structure. The values of the computed lattice parameters for the grown crystals are a = b = 3.28Å and c = 13.00 Å. The single crystals of WSe₂ grown by a direct vapour transport technique are found to have a p- type (WSe₂) semiconducting nature. The value of scattering parameter is nearly ≈ 2.48 which shows that the defect scattering dominates the charge transport mechanism in the grown crystals. The value of effective density of states is found to be around 6.68x1024 m^-3. The effective mass of charge carriers mh* was calculated and is found to be around 7.6x10-31 Kg. All these estimated parameters are in good agreement with the reported values in the literature[11-13].

The sign of Hall coefficient remains positive in the entire range of measurement temperature, indicating the conductivity type of the crystals as p-type and it is in agreement with the TEP measurements. This again shows that the quality of ohmic contacts made for present investigations is good and stable throughout the range of reported measurements. The conductivity of the sample decreases with the temperature and thus again confirms the semiconducting nature of the grown WSe₂ crystals. The measured carrier concentration at room temperature is 1.032x1018 cm^-3. This is in agreement with the reported value of 3.5x1018 cm^-3[14].