Abstract
The effect of hydrostatic pressure (up to 0.82βGPa) on the electric properties of chain TlGaTe2 single crystals has been investigated in the temperature range 77β296βK. It has been shown that pressure leads to a considerable increase of conductivity () 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.
1. Introduction
TlGaTe2 single crystals are typical representatives of chain-layred 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 [1β3]. Measurements of temperature-dependent conduction of a crystal can give valuable information on the localized states. The physical properties of TlGaTe2 single crystals are very sensitive to external actions, such as temperature, dc and ac electric fields, laser light, ionizing irradiations, and pressure. Room-temperature study of the effect of hydrostatic pressure up to 0.9 GPa on the electrical conductivity and Hall coefficient for the TlGaTe2 crystals have been made in [4].
The work [5] deals with the results of experimental investigation of the effect of hydrostatic pressure up to 0.9βGPa on the kinetic properties of the TlGaTe2 crystals over temperature range 220 to 295βK. The aim of this work is to study the influence of hydrostatic pressure on the dc-electrical properties of TlGaTe2 single crystals over the temperature range from 77 to 296βK.
2. 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: βΓ , βΓ at room temperature. The samples for electrical measurements had the shape of rectangular plates. Indium was used as a contact material to the TlGaTe2 samples. Dc-electric field from Ohmic region of current-voltage characteristic was applied crosswise to the natural chains of a TlGaTe2 single crystal.
The measurements under pressure (up to 0.82βGPa) were performed in a conventional copper-beryllium vessel with a mixture of dehydrated transformer oil and kerosene (1β:β4) 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%.
3. Results and Discussions
The temperature dependences of electrical conductivity of TlGaTe2 across the chains measured at different pressures in the interval 0β0.71βGPa are shown in Figure 1.
It is evident from Figure 1 that high-temperature branchs of dependences are exponential in the temperature range 230β296βK. 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 estimated from the slops of the curves under various pressures, are presented in the last column of Table 1. The activation energy at and 3.1Β·108βPa for TlGaTe2βββeV is in satisfactory agreement with that presented in [6] (βeV).
The characteristic feature is that at βK, the slope of log curves plotted on a semilogarithmic scale is not constant; the activation energy of conductivity decreases monotonically with decreasing temperature. As the pressure increases, the dependence becomes flatter and, at βPa and βK, the low-temperature conductivity increases with decreasing temperature (Figure 1, curve 4).
The above experimental facts indicate that, in the temperature range 130β220βK, the TlGaTe2 single crystals exhibit variable range hopping conduction over states lying in a narrow energy band (of width ) near the Fermi level. Such type of hopping conductivity in TlGaTe2 was observed also in [6]. With this type of conductivity, the dependence should be a straight line with a slope [7]: where is the density of states near the Fermi level, is the Boltzmann constant, and is the localization radius.
Figure 2 displays the log dependences for a TlGaTe2 single crystal at various values of the pressure. The measured values of at different pressures are presented in Table 1, from which it follows that, as the pressure increases, the value also increases.
Using (2), we estimated the density of states near the Fermi level. When calculating , the localization length for the TlGaTe2 single crystal was taken as βΓ by analogy with binary gallium telluride [8]. The values of at different pressures are also listed in Table 1. It can be seen that, as the pressure increases, the density of localized states decreases. The dependence plotted on a semilogarithmic scale is shown in Figure 3(a). It is obvious that this dependence is exponential.
(a)
(b)
(c)
(d)
From the formula [7], one can calculate the carrier jump distance. We found average values of at temperature interval 130β220βK under various hydrostatic pressures. The obtained values of are presented in Table 1. As the pressure increases, also increases. From Figure 3(b), it is obvious that dependence is linear. As is seen, the average jump distance in the TlGaTe2 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 . The values of under different pressures are also listed in Table 1. It can be seen that, as the pressure increases, the range of energies becomes wider. The dependence (Figure 3(c)) is linear.
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 values for TlGaTe2 calculated at βK and under various pressures from 0 to 7.1Β·108βPa are presented in Table 1. It is seen from Figure 3(d) that linearly increases with pressure. The table also presents the concentrations of trapping states in TlGaTe2 under different pressures, which were calculated according to the formula
Since the concentration of localized states in the band gap of TlGaTe2 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 TlGaTe2 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 TlGaTe2 due to the presence of different types of defects. It seems that the decreasing of and values in TlGaTe2 due to pressure is caused by the partial healing of defects. Hydrostatic pressure stimulates also the redistribution of already existing defects in the TlGaTe2 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 TlGaTe2 single crystal at room temperature. The characteristic feature of the pressure behavior of the conductivity may be described as follows: the conductivity increases with increasing pressure from 2Β·10-3 to 5.43Β·10-2βOhm-1Β·cm-1. Measurements permitted to evaluate the pressure behavior of , which may be written as where βGPa-1.
Assuming that the electrical conductivity changes with pressure according to the equation where is the pressure coefficient of the indirect band gap, one can easily find that
One can see that since then it follows from (9) that should be negative to satisfy (8). Hence, with increasing pressure, the forbidden band gap of TlGaTe2 should decrease. We found that the dependence of the band gap of TlGaTe2 on pressure may be written as , where βeV/GPa. Analogical results have been obtained by us for chain TlInSe2 single crystals [10], where βeV/GPa.
As it was shown above in TlGaTe2 single crystal, the anomaly on βdependence (Figure 1, curve 4) is observed at low temperatures (βK) and high pressure (0.71βGPa). It seems to be due to phase transition stimulated by high pressure. About phase transition in TlGaTe2 at 98.5, 121 and 130βK, it was reported in [11β14] from investigation of electrical, optical, and thermal properties of these single crystals. The pressure-induced phase transition at βGPa has been observed by us also in TlInSe1-xSx crystals [10].
4. Conclusions
The effect of hydrostatic pressure (up to 0.82βGPa) on the electric properties of chain TlGaTe2 single crystals has been investigated in the temperature range 77β296βK. It has been shown that pressure leads to a considerable increase of conductivity () across the chains of TlGaTe2 single crystals. The increase of conductivity with pressure is described by the formula , and the pressure coefficient of the indirect band gap was found to be β0.207βeV/GPa.
Parameters of localized states in the band gap of TlGaTe2 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 TlGaTe2 increase linearly.