Effect of Electron Irradiation on Charge Transfer in 2D Gallium Monosulfide

The features of the effect of electron irradiation with an energy of 4 MeV and a dose of 2 × 1012-1013 cm−2 on the dielectric properties and AC-conductivity in alternating current of a 2D layered single GaS crystal in a frequency range of 5 × 104−3.5 × 107 Hz are established. It is shown that the electron irradiation of a single GaS crystal increases the real component of the complex dielectric constant, decreases its imaginary component, causes the dielectric loss tangent and AC-conductivity across the layers. Both before and after the electron irradiation, the conductivity varies according to a law characteristic of the hopping mechanism of charge transfer over states localized near the Fermi level. It is shown that at 140–238 K in the layered single GaS crystals across their natural layers in the constant electric field there is also a hopping conductivity (DC-conductivity) with a variable jump length along the states localized near the Fermi level. The effect of electron irradiation on the electrical conductivity of single GaS crystals and the parameters of the states localized in their forbidden gap was studied. Taking into account the experimental data obtained in alternating and direct currents the density of states near the Fermi level and their energy spread, average hopping distances in the area of activation hopping conductivity, as well as the activation energy of jumps, are estimated in both pure and electron irradiated GaS crystals.


INTRODUCTION
In recent years, various applications of semiconductor low-dimensional materials rapidly extend, in particular, those of 2D chalcogenides in micro-and nanoelectronics, photonics, and spinotronics [1][2][3][4][5][6][7]. Layered А III В VI -based crystals are known to possess anisotropic properties, which result from the presence of two types of atomic bonds in a crystal. Each layer, e.g., that of gallium sulfide, contains four S-Ga-Ga-S atomic planes localized perpendicular to axis C of a crystal. Inside the layers this bond has an ion-covalent character, the neighboring layers are connected with weak bonds of the Van der Waals type [8,9].
The urgent problem is to study the laws of the effects of the X-ray, gamma rays, as well as the stream of charged particles of high energies, on the physical properties of А III В VI semiconductors. In this respect the 2D chalcogenides of gallium have not yet been studied sufficiently.
According to the published data, the 2D materials, the binary sulfides among them, exhibited good potential applications in field transistors, in digital electron devices, and in nano-and optoelectronics [10][11][12][13][14]. For example, the MoS 2 -based field transistor with mobility of 200 cm 2 V -1 s -1 has a high coefficient of switching the current on or off, 10 8 [15].
Few studies were carried out to reveal the electrotransport properties of the 2D binary sulfides. Moreover, in these materials the electron transport properties and their mechanisms are not sufficiently examined yet.
We consider that our work devoted to the study of the electric transport features of 2D materials based on binary chalcogenides can have various potential promising applications in optoelectron devices. In this work we investigate the electric transport mechanisms in electron-irradiated GaS monocrystals.
On the basis of the measurements of conductivity at the forbidden zone of the crystal a valuable information on localized states can be obtained. The layered monocrystals of gallium sulfide are characterized with a fairly high specific resistance and a wide forbidden zone (E g ≈ 2.5 eV) at 300 К. The results of investigation of the electric, photoelectric and optical properties of the 2D of GaS and GaSe crystals we described in [16][17][18][19][20][21][22][23][24].
The purpose of this work is to study the effect of the electron (e -) irradiation on the electric properties of GaS monocrystals, to clarify the mechanism of the charge transport in them under the alternating (AC) and direct (DC) currents, and to determine the parameters of the states localized in the forbidden zone.

EXPERIMENTAL
The single GaS crystals studied were grown using the Bridgman method [9] and were of р-type conductivity. They had a hexagonal structure; the lattice parameters were а = 3.58 Å; с = 15.47 Å.
To measure the electric and dielectric parameters in the alternating current from the single GaS crystals the ~500 μm thick plates were sheared off which were then coated with a silver paste. The silver coat area was 0.2 cm 2 . The GaS condensers were localized in a screened measurement cell. The frequency dependences of the dielectric permittivity (ε'), tangent of the angle of the dielectric losses (tanδ) and AC-conductivity (σ ac ) in the frequency range of f = 5 × 10 4 -3.5 × 10 7 Hz were obtained with a ВМ-560 Q-meter at room temperature. The accuracy of the determination of the resonance values of the capacity and quality factor (Q = 1/tanδ) of the measuring circuit was restricted by the errors was connected to the level of resolution of calculations of the apparatuses. The graduation of the condenser accuracy was ±0.1 pF. The reproducibility of the resonance position was ±0.2 pF with respect to capacity and ±1.0-1.5 of the scale graduation with respect to the quality factor. In addition, the largest deviations from the average values were 3-4% for ε and 7% for tanδ [25].
For the measurements of the electric parameters in the direct current, the ~300 μm thick plates were sheared off from the single GaS crystals, which were plated with the silver past contacts. The samples were produced in a sandwich-structure, so as the direct electric field was supplied along the crystallographic axis C of the crystals, i.e., across their natural layers. The amplitude of the direct electric field supplied to the samples was relevant to the ohmic area of the voltampere characteristics. The electric measurements were performed in a temperature region of 116-294 K. In the process of the measurements the samples were localized in a cryostat with a system of temperature stabilization (the accuracy of stabilization was 0.02 K) [26].
The source of eirradiation was an ELU-4 electronic linear accelerator. The samples of a single GaS crystal were irradiated with 4 MeV stream of electrons.

RESULTS AND DISCUSSION
First, let us examine the results of the charge transfer in the alternating current (σ ac ). Figure 1 shows the frequency dependences of the real component of (ε ) of the dielectric permittivity of the GaS sample prior to and after eirradiation. The observed experimental monotonous decrease in dielectric permittivity of a single GaS crystal with an increase in frequency attests to a relaxation dispersion both before and after eirradiation. At frequencies of f > 10 7 Hz, the value was independent of frequency. In the range of frequencies 5 × 10 4 -10 7 Hz resulting from the electron irradiation the dielectric permittivity of GaS increases and at f > 10 7 Hz eirradiation involves no changes in the ε' value. With an increase in the dose of eirradiation, a marked dielectric dispersion was detected in the GaS.
Unlike ε' the imaginary component (ε″) of the complex dielectric permittivity of the single GaS crystal decreased after eirradiation (Fig. 2). With the increase in the dose of eirradiation, the dispersion of ε″ decreased as well. Figure 3 shows the dependences of ε' and ε″ of a single GaS crystal on the dose of eirradiation (D) at f = 10 5 Hz. The effect of eirradiation on the value of ε″ at high frequencies (f > 10 7 Hz) was slight.
After the electron irradiation, tangent of angle of the dielectric losses in GaS decreased within all examined range of frequencies (Fig. 4). A marked decrease  in tanδ caused by the eirradiation was observed at f = 5 × 10 4 Hz, whereas at f > 10 7 Hz, the change in tanδ was less notable. The character of the frequency dependence of tanδ in a single GaS crystal prior to and after eirradiation attested to the losses of a through conductivity. Figure 5 shows the frequency dependences of ACconductivity across the layers of the single GaS crystal before (curve 1) and after eirradiation by different doses (curves 2 and 3). As can be seen in Fig. 5, as a result of the eirradiation, the σ ac of the single GaS crystal is decreased. The decrease in electroconductiv-ity of irradiated semiconductors can be attributed to compensation of the initially existing electrically active impurity centers by deeper energy levels of radiation defects [27]. In semiconductors with deep energy levels of radiation defects, the compensation of conductivity can be sharply expressed. This phenomenon can probably occur also in a single GaS crystal.
In the region of frequencies of f = 5 × 10 4 -10 7 Hz, the AC-conductivity of a single GaS crystal both before and after eirradiation changes according to the law of σ ac ∞ f n , where n = 0.8, and at f > 10 7 Hz the linear dependence of σ ac on f is present. The depen-  dence of σ ac ∞ f 0.8 established attests to the fact that the conductivity of a single GaS crystal in the frequency region of f = 5 × 10 4 -10 7 Hz is caused by the hops of the charge carriers between the states localized in the forbidden zone. Those states can be localized both near the edges of the allowed zones and near the Fermi level. In both cases the hopping of the charge carriers in those localized states leads to f 0.8 , which is the law for AC-conductivity, according to the theory described in [28].
However, theoretically the frequency dependence of the hopping conductivity near the edges of the zones of material passes into the asymptotic limit f 0.8 at higher frequencies, than the hopping conductivity near the Fermi level. That is, under the experimental conditions, hopping conductivity near the Fermi level in the material always predominates over the conductivity of the states near the edges of the zones. Therefore, the f 0.8 law that we obtained attests to a hopping mechanism of the charge transfer with respect to the states which are localized near the Fermi level of the single GaS crystal. We have found that the following expression corresponds to the above mechanism of charge transfer [29]: (1) where e is the electron charge; k is the Boltzmann constant; N F is the density of the localized states near the Fermi level; a l is the radius of localization; and ν ph is the phonon frequency.
In accordance with the experimental values of σ ac (f) using (1) the GaS density of the localized states near the Fermi level was calculated. The values of N F for GaS prior to and after eirradiation are listed in Table 1. To calculate N F for the GaS radius of localization was taken to be a l = 14 Å [30]. The value of ν ph for GaS was of the order of 10 12 Hz. As is seen from Table 1, N F in GaS decreased with increases in the dose of eirradiation.
The frequency range, in which there is the hopping conductivity in GaS, remained unchanged for curves 1-3 in Fig. 5 and was 5 × 10 4 -10 7 Hz. This experimental fact suggests that the average distance (R) and time of hops (τ) suffer no changes under the eirradiation of the GaS sample.
According to the theory of the hopping conductivity in the alternating current, the average distance of the hops is defined by the following formula: where α is the constant of the decay of the wave function of the localized charge carrier of ψ ~ e -αr , α = 1/a l ; 1/f = τ is the time of hops. The R value for the single GaS crystal calculated using (2) was 87 Å. That is, the R value exceeds by about 6 times the average distance between the centers of localization of the GaS charge carriers. The average time of the hops in GaS was τ = 2 × 10 -7 s.
Using the formula from [28] ( we estimated the energy spread of the states (ΔE) in GaS localized near the Fermi level before and after the eirradiation ( Table 1). The table data show that with the accumulation of the dose of eirradiation in the sample, the energy band of the states localized near the Fermi level expands.
The irradiation of the sample not only induces the radiation defects, but also stimulates burning and migration of the defects present in the crystal [27]. In GaS this obviously leads to the energy redistribution of the local states near the Fermi level, in particular, to their diffusion.
The concentration of deep traps in GaS responsible for the AC-conductivity defined by the following formula (4) was 7.2 × 10 17 cm -3 .
Thus, irradiation of a single GaS crystal with a stream of electrons with energy 4 MeV and doses 2 × 10 12 and 10 13 cm -2 leads to the occurrence of radiation defects, which, obviously, compensate the initial defects of the single crystal structure. As a result, the dielectric permittivity of the single GaS crystal with an increase in the concentration of dose of eirradiation grows, whereas the values of ε″, tanδ and that of conductivity in the alternating current decrease. It follows from this that eirradiation of the single GaS crystal makes it possible to control its dielectric coefficients, as well as the value of conductivity in the alternating current. The latter implies that the single GaS crystals are a promising material for the semiconductor detectors of elementary particles. Now let us study the results of examination of the charge transfer in the direct current (σ dc ). Figure 6 shows the temperature dependences of conductivity in the direct current (σ dc ) of the single GaS crystal both prior to the electron irradiation (curve 1) and after the irradiation with doses 2 × 10 12 (curve 2) and 10 13 cm -2 (curve 3). Unlike the case for AC-conductivity, under the electron irradiation occurs an increase in the DCconductivity in the whole studied region of temperatures. As is seen from Fig. 6, the dependences σ dc (10 3 /T) in all three cases (curves 1-3) were characterized first by the monotonous decay and then at low temperatures became temperature-independent.
The above experimental facts show that, in the single GaS crystals in a direct current, a hopping conductivity with an alternating length of hop appears in states that are localized in the narrow band of energies ΔE near the Fermi level. At this type of conductivity, dependence σ dc = f(T -1/4 ), in accordance with the theory, is a straight line with a slope T 0 [28]: Figure 7 shows the dependences σ dc = f (T -1/4 ) for the single GaS crystal. As is seen in this figure, the temperature dependences of DC-conductivity plotted in the Mott coordinates, in the temperature region of 140-238 K present straight lines. Experimental values of the slopes of those straight lines (T 0 ) before and after the electron irradiation are listed in Table 2. At temperatures T = 116-140 К, as was shown above, now temperature dependence of GaS DC-conductivity both prior to and after the electron irradiation was found, which attests to the presence of an activationless hopping conductivity in the single crystals studied.
Using formula (6), the density of states near the Fermi level was estimated in the single GaS crystal. The obtained for N F values are listed in Table 2 as well, which show that after the eirradiation of the single GaS crystal the density of the states localized near the  Fermi level decreases. This can be attributed to the fact that at the eirradiation doses ranged from 2 × 10 12 to 10 13 cm -2 in the single GaS crystal the annealing of defects obviously occurs. The decrease in value N F in GaS after eirradiation related to the dose 2 × 10 12 -10 13 cm -2 agrees with the above experimental values of conductivity in AC. Using the following formula from [28] (7) we determined the distance of the hops of the charge carriers in the direct current. The obtained for R a average values in the range of temperatures of 140-238 K before and after the eirradiation for the single GaS crystal ( the energy of activation of the hops in the single GaS crystal is estimated. The values of ΔW calculated at 200 K are listed in the last column of Table 2. The values of ΔW were somewhat smaller than those of ΔE.
With increases in the accumulation of the dose of electron irradiation, the activation energy of hops in the single GaS crystal increased. Thus, the irradiation of the single GaS crystal by the stream of electrons with the energy of 4 MeV and doses of 2 × 10 12 and 10 13 cm -2 causes radiation defects, which compensate for the initial defects in the single crystal structure. As a result, the DC-conductivity of the single GaS crystal in the direct current grows with an increase in the accumulation of the irradiation dose, and the parameters of the localized states in the forbidden zone change, correspondingly.

CONCLUSIONS
The regularities of the effect of the electron (e -) irradiation on the dielectric properties and AC-conductivity of the layered single crystal GaS were established in the range of frequencies of 5 × 10 4 -3.5 × 10 7 Hz. Electron irradiation with an energy of 4 MeV of the single GaS crystal by the doses of 2 × 10 12 and 10 13 cm -2 increases the real component of the complex dielectric permittivity, decreases its imaginary component, tangent of the angle of dielectric losses and the AC-con- ductivity across the layers. At the irradiation doses of 2 × 10 12 -10 13 cm -2 in GaS, loss of through conductivity occurs. In the region of frequencies f = 5 × 10 4 -10 7 Hz the AC-conductivity of the single GaS crystal both prior to and after eirradiation varied according to the law of σ ac ∞ f n (where n = 0.7-0.8), typical for the hopping mechanism of charge transfer across the states localized near the Fermi level. It was found that at 140-238 K in the layered single GaS crystals across their natural layers in the direct electric field the hopping conductivity occurs with an alternating length in the localized states near the Fermi level. At T < 140 К in the single GaS crystals the presence of activationless hopping conductivity is found. The data of investigations of DC-and AC-conductivities made it possible to calculate the density of states near the Fermi level and their energy spread, the average distances of hops in the region of activation hopping conductivity, the energy of activation of the hops. The effect of the electron irradiation was studied as well on the AC-and DC-conductivities of the single GaS crystals and parameters of the states localized in their forbidden zone.