Charge Transfer Processes In Granulated Mg 3 Sb 2 Particles

In the article, temperature dependence of speci�c resistance ( ρ ), concentration of charge carriers (n) and mobility (µ) was studied experimentally at T = 300–700 K to study charge transfer processes in granulated Mg 3 Sb 2 particles. The research results were explained on the basis of the charge transfer mechanism in Mg 3 Sb 2 particles. In particular, at the initial stage of temperature increase, Т ≤ 375 К , localized traps with energy level E in appear in the interparticle boundary areas of the heated part of the sample. When charge carriers are trapped in them, ρ increases sharply, and n decreases. In the later stages of temperature increase, the thermal phenomenon increases along the length of the sample. In this process, localized traps with energy level E in appear successively in the interparticle boundary regions located along the length of the sample. In relation to the charges held in them, the concentration of the generated charge carriers n increases in accordance with the increase in temperature, in this case ρ changes steadily. The increase of the potential barrier height in the interparticle boundary regions from ϕ ∼ 0.411 eV to 0.91 eV con�rms the above considerations. In addition, under the in�uence of temperature, the particle size and impurity ionization in the interparticle boundary areas or thermal �uctuations of the crystal lattice decrease the free movement path of the carriers. This leads to a decrease in µ at T = 300– 700 K.


Introduction
Mg3Sb2 semiconductor materials are widely studied as thermoelectric materials in the world energy sector. In most studies, it is recognized that it allows to create effective thermoelectric materials due to its low thermal conductivity. Therefore, in recent years, interest in studying the electrophysical and thermoelectric properties of Mg 3 Sb 2 type semiconductor materials has increased. In works [1][2][3][4][5][6][7], it was shown that the main thermoelectric parameters of Mg 3 Sb 2 type semiconductors depend on the crystallographic structure of the material, temperature, and introduced atoms. In its band gap, impurity states create wide energy levels, and with an increase in temperature, the formation of electron-hole pairs in them leads to an increase in electrical conductivity (σ) and the Seebeck coe cient (α), on the contrary, a decrease in the motion of phonons in the crystal lattice leads to a decrease in thermal conductivity (λ), which in turn, as has been observed, leads to an increase in ZT.
Theoretical and practical studies show that it is recognized that such a result can be achieved by controlling the structure of the material and the in uence of external or introduced atoms and the method of obtaining Mg 3 Sb 2 . For example, in the process of pressing Mg 3 Sb 2 particles under vacuum conditions, it was observed that the amount of Mg atoms in the pressed sample was reduced [1][2][3][4][5][6][7]. The thermoelectric parameters of Mg 3 Sb 2 were improved by introducing additional Mg atoms into it. However, the electrophysical or thermoelectric properties of Mg 3 Sb 2 material in the particulate state are one of the unexplored areas.
It should be noted that in recent years, much attention has been paid to the preparation of thermoelectric materials based on micro-and nano-sized granular semiconductor particles and to the study of their properties [8][9][10][11][12]. Thermoelectric materials made on the basis of granulated semiconductor particles consist of a heterogeneous medium [11,12], parameters σ, α, λ have been observed to depend on the charge transfer process in granulated particles [13][14][15]. In connection with these, it is interesting to study the formation of heterogeneous environment in granulated particles of Mg 3 Sb 2 type and charge transfer processes in them.

Materials And Research Method
Granular Mg 3 Sb 2 particles obtained by synthesis of Mg and Sb elements were selected for conducting research. The novelty of the research is that, for the rst time, the formation of a heterogeneous environment in granulated Mg 3 Sb 2 particles and the processes of charge transfer in them were carried out during the temperature change at T = 300-700 K based on the method of Egor and Disselkhorsta [9][10][11][12]. Figure 1 illustrates the research method and a simpli ed scheme of the sample. When heat Q is applied to the sample, the charges generated in area A move to area В, and an electric driving force is generated due to the temperature difference between M A and M В contacts. The temperature difference was controlled using T A and T В thermocouples. It should be noted that all studies were conducted in the process of temperature increase and decrease.

Results And Discussion
Temperature dependence of speci c resistance (ρ), concentration of charge carriers (n) and mobility (µ) was studied at T = 300-700 K to study charge transfer processes in granulated Mg 3 Sb 2 particles.  and (b-c). That is, if at T≤375 K (a-b) decreases sharply, then (b-c) changes steadily. The same situation was observed in the dependence of n on temperature (Fig. 4).
It is known from the physics of semiconductors that the dependence of ρ on temperature is represented by µ and n. As a result of the vibration of the crystal lattice due to the thermal phenomenon under the in uence of temperature, the free path of carriers decreases. In this case, a decrease in µ leads to an increase in ρ (Fig. 2, case a-b). The change of ρ depending on the temperature con rms the above considerations. However, it was observed that the results of this study are signi cantly different from the results obtained by other scientists on the Mg 3 Sb 2 material. For example, in works [1][2][3][4][5], it was observed that electrical conductivity takes values of MOm and increases with temperature. In our case, varies in the range of ρ∼300-625 Oh . sm. Also, in works [4,6,7], n∼10 19 -10 20 sm − 3 and µ∼20-160 sm 2 /Vsek change with temperature. From Figs. 3 and 4, we can clearly see that these results are also very different from our results. The reason for this is the technology of Mg 3 Sb 2 material preparation. That is, the results obtained in works [1][2][3][4][5][6][7] refer to the Mg 3 Sb 2 material prepared by pressing under vacuum conditions. And our results refer to granular Mg 3 Sb 2 particles.
It should be noted that the temperature dependence of ρ, µ and n in granular semiconductor particles depends on the charge transfer processes in the particles [13][14][15]. Charge transfer processes in granular particles can be explained as follows depending on the structure of the particles and their charge transfer mechanisms.

Structure Of Mg3sb2 Particles And Charge Transfer Mechanisms In Them
It is known that the structure and morphology of granulated semiconductor particles depends on their production technology [16,17]. For example, the structure of particles obtained on the basis of powder technology can be conditionally divided into 3 parts (Fig. 5a). It is known from the powder technology that the powdering process is performed mechanically. In a mechanical method, the phenomenon of friction causes the powder particles to heat up. In our opinion, the heating process does not occur uniformly throughout the volume of the powder particle. That is, there is a temperature difference along the size of the particle. As a result, due to heating, the surface temperature of the particle is higher than that in the volume (Т 3 ≤Т 2 ≤Т 1 , Fig. 5a). In addition, in the process of rubbing, surface defects appear in the atomic structure of the powder particle surface, forming complex-shaped bumps (area 1 with temperature T 1 , Fig. 5a). Atomic crystallographic distortions increase to the surface. This causes the phases of each eld to change. Accordingly, the reactivity of each eld increases from the particle core to the surface [18]. For example, in works [11,12] it was determined that silicon oxide with a thickness of 10 nanometers is formed on the surface of silicon particles taken in the atmosphere of the atomosphere. This is explained on the basis of the high reactivity of the atomic state on the surface of the silicon particle.
Therefore, according to the surface defects formed on the surface of the particle, the reactivity of each eld, and the temperature difference, we can conditionally divide the particle structure into 3 parts, as shown in Fig. 5a. Rough surface (1) area with relatively high temperature and reactivity, and area (2) separating it from the particle core (3). With this, the structure of particles creates a multi-layer heterogeneous environment [11,12].
Thus, a simpli ed arrangement scheme of particles can be depicted in the form of particles arranged in series and parallel to each other, as in Fig. 1a. Its magni ed state is also shown in Fig. 5b. Through metal contacts M A and M В , Mg 3 Sb 2 particles are pressed together with a speci ed force from both sides (Fig. 1a). The compressive strength was selected by measuring the sample resistance. In this case, the smallest resistance was around ∼1 kOhm, which was achieved when pressed together with a force of 30-50 kG. Interparticle boundary zones are formed between the particles located in series and parallel to each other (zones 3 and 4 in Fig. 1a and 5b). These areas are rich in defects and crystallographic distortions consistent with the particle structure (Fig. 5a). They create a barrier effect consisting of E in -level localized traps for charge carriers (Fig. 5c). Therefore, the process of charge transfer in such located particles can be divided into two parts. If the particles are located in a series with each other, the process of charge transfer from the rst particle to the second particle takes place through the interparticle boundary areas formed between them (area 3, Fig. 5b). If the particles are located parallel to each other, the charge transfer process takes place mainly along the 4th region, which is parallel to each other. Now let's try to explain the results of the research based on the given considerations.
If the charge transfer process is carried out from the rst particle to the second particle through area 3, the charge carriers are trapped in localized traps with the energy level Ein appearing in sequence (Fig. 5s).
This process leads to an increase in the height of the potential barrier (ϕ) in the interparticle boundary region. Based on the Setto model, the dependence of ϕ on ρ can be expressed as follows [1]: Figure 6 shows the dependence of the height of the potential barrier on temperature. Studies show that during the temperature change of T = 300-700 K, ϕ ∼0.411 eV to 0.91 eV was found to increase. It is known that ϕ depends on the amount of charges trapped in localized traps ( ): where, N G is the concentration of electrically active alloying elements, ε and ε о are the relative and absolute dielectric constants of the medium and vacuum, respectively.
So, it can be seen from expression (2) that the increase of charges ( ) trapped in localized traps leads to an increase of ϕ, which in turn leads to an increase of ρ (case a-b). Based on this, the charge transfer processes in Mg 3 Sb 2 particles can be explained as follows. For this, we use the simpli ed scheme of the sample presented in Fig. 1a. We conditionally divide the sample into parts I, II, III, VI. At the initial stage of temperature increase T≤375 K, localized traps with energy level E in appear in the interparticle boundary regions of the sample I. An increase in the amount of charges () captured in them leads to an increase in ρ (case a-b, Fig. 2) and a decrease in n (case a-b, Fig. 4). In this case, the traps localized in parts II, III, VI of the sample will not be ionized yet. In the later stages of temperature increase, localized traps with E in energy level are lled. In parts II, III, VI of the sample, localized traps with E in energy level appear in a row [17,19]. Compared to localized traps, ρ changes steadily (case b-s, Fig. 2) due to the higher n formed in area A (case b-s, Fig. 4). Also, µ decreases due to thermal phenomena in the interparticle boundary regions (Fig. 3).
Temperature dependence of speci c resistance (ρ), concentration of charge carriers (n) and mobility (µ) was studied at T = 300-700 K to study charge transfer processes in granulated Mg 3 Sb 2 particles. Figures 2-4 show the temperature dependence of ρ, n and µ, respectively.

Conclusions
Thus, the results obtained for Mg 3 Sb 2 particles differ signi cantly from the results obtained for Mg 3   Dependence of relative resistance on temperature.

Figure 3
Dependence of the mobility of charge carriers on temperature.

Figure 4
Dependence of the concentration of charge carriers on temperature.