DC-Electrical Properties of TlGaTe 2 Single Crystals under Hydrostatic Pressure

The effect of hydrostatic pressure (up to 0.82 GPa) on the electric properties of chain TlGaTe2 single crystals has been investigated in the temperature range 77–296 K. It has been shown that pressure leads to a considerable increase of conductivity (σ⊥) across the chains of TlGaTe2 single crystals. Parameters of localized states in the band gap of TlGaTe2 single crystal according to the low-temperature electrical measurements were obtained at various pressures.


Introduction
TlGaTe 2 single crystals are typical representatives of chainlayred semiconductors and attract a lot of attention due to their interesting physical properties.These properties include strong anisotropy of the electric parameters related to special features in the crystalline structure.Chain and layered crystals usually contain structural defects, such as vacancies and dislocations.The presence of these defects results in a high density of localized states near the Fermi level.The states localized in the band gap are responsible for most electronic processes occurring in semiconductors.Both dc and ac charge transport in thallium-gallium chalcogenides proceeds via these localized states [1][2][3].Measurements of temperature-dependent conduction of a crystal can give valuable information on the localized states.The physical properties of TlGaTe 2 single crystals are very sensitive to external actions, such as temperature, dc and ac electric fields, laser light, ionizing irradiations, and pressure.Roomtemperature study of the effect of hydrostatic pressure up to 0.9 GPa on the electrical conductivity and Hall coefficient for the TlGaTe 2 crystals have been made in [4].
The work [5] deals with the results of experimental investigation of the effect of hydrostatic pressure up to 0.9 GPa on the kinetic properties of the TlGaTe 2 crystals over temperature range 220 to 295 K.The aim of this work is to study the influence of hydrostatic pressure on the dc-electrical properties of TlGaTe 2 single crystals over the temperature range from 77 to 296 K.

Experimental
The crystals used for our study were grown by the Bridgman method and have tetragonal structure of the TlSe type with space group I4/mcm and lattice parameters: a = (8.430± 0.002) Å, b = (6.858± 0.004) Å at room temperature.The samples for electrical measurements had the shape of rectangular plates.Indium was used as a contact material to the TlGaTe 2 samples.Dc-electric field from Ohmic region of current-voltage characteristic was applied crosswise to the natural chains of a TlGaTe 2 single crystal.
The measurements under pressure (up to 0.82 GPa) were performed in a conventional copper-beryllium vessel with a mixture of dehydrated transformer oil and kerosene (1 : 4) as a pressure transmitting media.This fluid did not cause any irreversible changes in the samples.Pressure was measured with a calibrated manganine gauge with an accuracy not less than 1%.

Results and Discussions
The temperature dependences of electrical conductivity of TlGaTe 2 across the chains (σ ⊥ ) measured at different pressures in the interval 0-0.71GPa are shown in Figure 1.
It is evident from Figure 1 that high-temperature branchs of log σ ⊥ (1/T) dependences are exponential in the temperature range 230-296 K.In this temperature range, the conduction of thermally generated impurity charge carriers in the allowed zone is dominated.The activation energies of impurity charge carriers (E t ) estimated from the slops of the curves log σ ⊥ (1/T) under various pressures, are presented in the last column of Table 1.The activation energy at P = 0 and 3.1•10 8 Pa for TlGaTe 2 E t = 0.29 eV is in satisfactory agreement with that presented in [6] (E t = 0.26 eV).
The characteristic feature is that at T < 230 K, the slope of log σ ⊥ = f (1/T) curves plotted on a semilogarithmic scale is not constant; the activation energy of conductivity decreases monotonically with decreasing temperature.As the pressure increases, the log σ ⊥ (1/T) dependence becomes flatter and, at P = 7.1•10 8 Pa and T < 130 K, the low-temperature conductivity increases with decreasing temperature (Figure 1, curve 4).
The above experimental facts indicate that, in the temperature range 130-220 K, the TlGaTe 2 single crystals exhibit variable range hopping conduction over states lying in a narrow energy band (of width ΔE) near the Fermi level.Such type of hopping conductivity in TlGaTe 2 was observed also in [6].With this type of conductivity, the ln σ ⊥ = f (T −1/4 ) dependence should be a straight line with a slope T 0 [7]: where N F is the density of states near the Fermi level, k is the Boltzmann constant, and a is the localization radius.Figure 2 displays the log σ ⊥ = f (T −1/4 ) dependences for a TlGaTe 2 single crystal at various values of the pressure.The measured values of T 0 at different pressures are presented in Table 1, from which it follows that, as the pressure increases, the T 0 value also increases.
Using (2), we estimated the density of states near the Fermi level.When calculating N F , the localization length for the TlGaTe 2 single crystal was taken as a = 25 Å by analogy with binary gallium telluride [8].The values of N F at different pressures are also listed in Table 1.It can be seen that, as the pressure increases, the density of localized states N F decreases.The N F (P) dependence plotted on a semilogarithmic scale is shown in Figure 3(a).It is obvious that this dependence is exponential.
From the formula [7], one can calculate the carrier jump distance.We found average values of R at temperature interval 130-220 K under various hydrostatic pressures.The obtained values of R av are presented in Table 1.As the pressure increases, R av also increases.From Figure 3(b), it is obvious that dependence R av (P) is linear.As is seen, the average jump distance R av (T) in the TlGaTe 2 single crystal substantially exceeds the distance between the carrier localization centers.From the condition [7], we determined the scatter of trap states near the Fermi level (ΔE).The values of ΔE under different pressures are also listed in Table 1.It can be seen that, as the pressure increases, the range of ΔE energies becomes wider.The dependence ΔE(P) (Figure 3(c)) is linear.Table 1: Parameters of localized states in the band gap of the TlGaTe 2 single crystal according to the temperature electrical measurements at various pressures.Charge carrier jumps occur exactly in this narrow energy band.The temperature dependence of activation energy of hopping conductivity is described by relation [9]: The ΔW(T) values for TlGaTe 2 calculated at T = 130 K and under various pressures from 0 to 7.1•10 8 Pa are presented in Table 1.It is seen from Figure 3(d) that ΔW linearly increases with pressure.The table also presents the concentrations of trapping states in TlGaTe 2 under different pressures, which were calculated according to the formula Since the concentration of localized states in the band gap of TlGaTe 2 is rather high, the energy band structure of the crystals under consideration is similar to that of amorphous semiconductors.The amorphous state is characterized by the presence of strongly deformed or even broken chemical bonds, which have a tendency toward manifestation of acceptor properties.These defects play an especially important role in layered and chain crystals, such as TlGaTe 2 single crystals.The generation of new defects under pressure does not make a significant contribution against the background of the initially high concentration of localized states in the band gap of TlGaTe 2 due to the presence of different types of defects.It seems that the decreasing of N F and N t values in TlGaTe 2 due to pressure is caused by the partial healing of defects.Hydrostatic pressure stimulates also the redistribution of already existing defects in the TlGaTe 2 single crystal, which apparently leads to a spreading of the energy distribution of localized states.Figure 4 represents the pressure dependence of the conductivity of TlGaTe 2 single crystal at room temperature.The characteristic feature of the pressure behavior of the conductivity σ ⊥ may be described as follows: the conductivity increases with increasing pressure from 2•10 −3 to 5.43•10 −2 Ohm −1 •cm −1 .Measurements permitted to evaluate the pressure behavior of σ ⊥ , which may be written as ln σ ⊥ (P) = ln σ ⊥ (0) + βP, ( 7 ) where β = d ln σ ⊥ (P)/dP = 4.02 GPa −1 .
Assuming that the electrical conductivity changes with pressure according to the equation where γ = dE i g /dP is the pressure coefficient of the indirect band gap, one can easily find that One can see that since β > 0 then it follows from (9) that γ should be negative to satisfy (8).Hence, with increasing pressure, the forbidden band gap of TlGaTe 2 should decrease.We found that the dependence of the band gap of TlGaTe 2 on pressure may be written as E i g (P) = E i g (0) − |γ|P, where |γ| = 0.207 eV/GPa.Analogical results have been obtained by us for chain TlInSe 2 single crystals [10], where dE i g /dP = −0.175eV/GPa.As it was shown above in TlGaTe 2 single crystal, the anomaly on log σ ⊥ (1/T)-dependence (Figure 1, curve 4) is observed at low temperatures (T < 130 K) and high pressure (0.71 GPa).It seems to be due to phase transition stimulated by high pressure.About phase transition in TlGaTe 2 at 98.5, 121 and 130 K, it was reported in [11][12][13][14] from investigation of electrical, optical, and thermal properties of these single crystals.The pressure-induced phase transition at P ≈ 0.72 GPa has been observed by us also in TlInSe 1−x S x crystals [10].

Conclusions
The effect of hydrostatic pressure (up to 0.82 GPa) on the electric properties of chain TlGaTe 2 single crystals has been investigated in the temperature range 77-296 K.It has been shown that pressure leads to a considerable increase of conductivity (σ ⊥ ) across the chains of TlGaTe 2 single crystals.The increase of conductivity with pressure is described by the formula σ ⊥ (P) = σ ⊥ (0) exp(−γP/2kT), and the pressure coefficient of the indirect band gap γ = dE i g /dP was found to be −0.207eV/GPa.
Parameters of localized states in the band gap of TlGaTe 2 single crystal according to the low-temperature electrical measurements were obtained at various pressures.It has been established that, as the pressure increases, the density of localized states near the Fermi level decreases exponentially, but average jump distance, energy spread of localized states, and activation energy of hopping conduction in TlGaTe 2 increase linearly.

Figure 3 :
Figure 3: (a) Density of states near the Fermi level, (b) average hopping distance, (c) scatter of trap states near the Fermi level, and (d) jump activation energy in TlGaTe 2 single crystal as a function of pressure.