The bulk nanograined Bi2Te3 material was prepared by the microwave assisted solvothermal method
and cold isostatic pressure method. It was found that above T* ≈ 190 K the temperature dependence of the
specific electrical resistivity of material is of metallic type, while below this temperature a semiconductor
conductivity takes place. Within the temperature ΔT ≈ 90 K-35 K interval the electrical conductivity of material
can be described by the variable-range hopping conductivity mechanism. Negative magnetoresistance
was observed at the same temperature interval

Ivanov, O.N.

Lyubushkin, R.A.

Sudzhanskaya, I.V.

Yaprintsev, M.N.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 7 No 4, 04073(3pp) (2015) Том 7 № 4, 04073(3cc) (2015) 
 
 
2077-6772/2015/7(4)04073(3) 04073-1  2015 Sumy State University 
Hopping Conductivity and Negative Magnetoresistance of the Bulk  
Nanograined Bi2Te3 Material 
 
O.N. Ivanov, R.A. Lyubushkin, M.N. Yaprintsev, I.V. Sudzhanskaya 
 
Belgorod State University, 85, Pobedy St., 308015 Belgorod, Russia 
 
(Received 01 October 2015; published online 24 December 2015) 
 
The bulk nanograined Bi2Te3 material was prepared by the microwave assisted solvothermal method 
and cold isostatic pressure method. It was found that above T* ≈ 190 K the temperature dependence of the 
specific electrical resistivity of material is of metallic type, while below this temperature a semiconductor 
conductivity takes place. Within the temperature ΔT ≈ 90 K-35 K interval the electrical conductivity of ma-
terial can be described by the variable-range hopping conductivity mechanism. Negative magnetore-
sistance was observed at the same temperature interval. 
  
Keywords: Bulk nanograined materials, Hopping conductivity, Magnetoresistance. 
 
 PACS numbers: 72.10.Fk, 72.15. – v 
 
 
1. INTRODUCTION 
 
It is known that the nanograined materials are dis-
ordered and inhomogeneous materials [1-3]. As a rule, 
such kind of materials consists of numerous conducting 
or semiconducting grains separating by insulating inter-
faces [4, 5]. Specific mechanisms of the electrical conduc-
tivity can take place in electrically inhomogeneous solid. 
In particular, hopping conductivity of various types is 
predicted for disordered and inhomogeneous semicon-
ductors at low temperatures [6, 7]. It is important to 
note that unusual physical properties including negative 
magnetoresistance can also observed the hopping con-
ductivity phenomenon [8]. 
The aim of this paper is to find out and analyze the 
features of the specific electrical conductivity of the bulk 
nanograined Bi2Te3 material. 
 
2. EXPERIMENTAL PROCEDURE 
 
Microwave-solvothermal synthesis (closed reactor 
ERTEC model 02-02) was applied to prepare the na-
nosized Bi2Te3 powder. As is known, compared with the 
conventional methods, the microwave-assisted heating 
technique has the advantages of very short time of syn-
thesis, simplicity and energy efficiency, small particle 
size of the products, narrow particle size distribution 
and high purity [9]. 
Analytically pure chemicals were used for the syn-
thesis from LANHIT-LTD (bismuth oxide Bi2O3 with 
99.9 % purity, tellurium oxide TeO2 with 99.9 % purity 
and L-cysteine (cys ≥ 97 %). Ethylene glycol (EG 99,8 % 
purity), nitric acid (HNO3 70 % with purity) and N,N-
dimethylformamide (DMF anhydrous 99.8 % purity), 
were purchased from Sigma-aldrich. 
Oxides of bismuth and tellurium taken in a stoichio-
metric ratio was dissolving in concentrated nitric acid, 
resulting solution was mixed in a ratio of 1 : 1 of eth-
ylene glycol and cosolvent (DMF or DMSO or CAN). 
Then 4.2 mmol of L-cysteine was added to resulting 
solution with stirring for 30 min.  
The microwave-assisted reaction was carried out in 
an ERTEC 02-02 microwave reactor, with a power of 
300 W at 2.45 GHz working frequency. Synthesis was 
carried out for 20 min at temperature of 453 K and pres-
sure of 40 bar. 
The powder after synthesis was cold isostatically 
pressed uder pressure 2800 bar. Then, the pressured 
powder was calcined at 623 K for 2 h in Ar atmosphere. 
X-ray diffraction (XRD) analysis was performed for 
the phase and crystal structure determination by using a 
Rigaku Ultima IV diffractometer with CuKα - radiation 
(a step width of 0.03 and a counting time of 1.6 s/step). 
Transmission electron microscope (TEM), JEM-2100, 
was applied to study morphology of the powders (for an 
accelerating voltage of 200 kV). Scanning electron micro-
scope (SEM), Nova NanoSEM, was used to examine the 
grain structure of the bulk material (for an accelerating 
voltage of 2 kV). 
The specific electrical resistivity, , was measured by 
four-probed method at 0.1 mA dc current using the sin-
tered samples with Ag electrodes. Magnetic field up to 
5 T directed perpendicular to the electrical current can 
be applied to the sample during the  measurements.  
 
3. RESULTS AND DISCUSSION 
 
XRD-analysis confirmed that the synthesized powder 
is the single-phase Bi2Te3 compound (space symmetry 
group is   ̅ ). 
TEM-image in Fig. 1 shows a typical morphology of 
the powder. It is seen that the powder mainly consists of 
irregularly shaped nanoparticles of 20-50 nm in size. 
The bulk Bi2Te3 material has dense, homogeneous 
and porousless structure (Fig. 2). Nano- and microsized 
grains having a crystal faceting can be taken as evidence 
of intense sintering of the nanopowder. 
The temperature dependence of the specific electrical 
resistivity for the sample under study taken for the 
2÷300 K interval is shown in Fig. 3. 
One can see that this dependence is rather 
complicated and can be divided into two temperature 
fields. Above the temperature T*  190 K, the resistivity 
decreases at cooling. Such kind of behavior is typical for 
metals or degenerate semiconductors having T-
independent concentration of charge carriers. Below T* 
the resistivity increases as temperature decreases. This 
(T) dependence is characteristic for semiconductors. 
 
 O.N. IVANOV, R.A. LYUBUSHKIN, ET AL. J. NANO- ELECTRON. PHYS. 7, 04073 (2015) 
 
 
04073-2 
 
 
Fig. 1 – TEM-image of Bi2Te3 nanoparticles 
 
 
 
Fig. 2 – SEM-image of the bulk nanograined Bi2Te3 material 
 
A few mechanisms of the electrical conductivity 
could lead to the (T) dependence like the dependence 
presented in Fig. 3 below T*. 
One can see that this dependence is rather 
complicated and can be divided into two temperature 
fields. Above the temperature T*  190 K, the resistivity 
decreases at cooling. Such kind of behavior is typical for 
metals or degenerate semiconductors having T-
independent concentration of charge carriers. Below T* 
the resistivity increases as temperature decreases. This 
(T) dependence is characteristic for semiconductors. 
A few mechanisms of the electrical conductivity 
could lead to the (T) dependence like the dependence 
presented in Fig. 3 below T*. 
First of all, it should be noted that temperature T* 
is low enough to generate of charge carries via 
transitions of electrons from valence band into 
conduction band. 
Typical mechanism of the electrical conductivity of 
semiconductors is the thermal activation of the charge 
carriers from shallow impurity levels to the conduction 
or valence band. In this case, the (T) dependence will 
satisfy the law 
 
    0 exp /aТ E kT  , (1) 
 
the 0 is the prefactor, k is the Boltzmann constant and 
Ea is the activation energy.  
0 75 150 225 300
4,0
4,5
5,0
T*
T, K

, 
1
0
-3
, 
o
h
m
. m
 
 
Fig. 3 – The (T) dependence for the bulk nanograined Bi2Te3 
material 
 
It was found that the experimental (T) dependence 
cannot be described by the expression (1). So, another 
mechanism of the electrical conductivity explaining the 
experimental data should be applied. 
As was mentioned above the hopping conductivity 
can take place in the bulk nanograiened materials.  
The hopping conductivity can be realized via differ-
ent mechanisms given by a universal equation [10] 
 
    0exp /
ppТ DT T T     
, (2) 
 
where D is a constant, T0 is a characteristic tempera-
ture and p is an exponent depending on regime of the 
localized electrons hopping. 
The case of p  1 corresponds to the regime of near-
est-neighbor hopping (NNH) conductivity and p  1/4 
and 1/2 to the Mott [11] and the Shklovskii-Efros [12] 
types of variable-range hopping conductivity, respec-
tively. 
It was established that the best fitting by the ex-
pression (2) can be achieved at p  1/4 for the tempera-
ture interval from T1  90 K down to T2  35 K (Fig. 4). 
 
0,32 0,40 0,48 0,56
-6,6
-6,3
-6,0
T2ln
(
/T
1
/4
)
T-1/4, K-1/4
T1
 
 
Fig. 4 – The ln(ρ/T1/4)  f(T–1/4) dependence for the bulk 
nanograined Bi2Te3 material 
 
 HOPPING CONDUCTIVITY AND NEGATIVE MAGNETORESISTANCE… J. NANO- ELECTRON. PHYS. 7, 04073 (2015) 
 
 
04073-3 
So, within the temperature ΔT  T1 – T2 interval 
the variable-range hopping conductivity can takes 
place in the bulk nanograined Bi2Te3 material. 
As was mentioned above, negative magnetore-
sistance can take place within the the temperature 
interval of the variable-range hopping conductivity. 
Negative magnetoresistance was really observed for 
the sample under study as is shown in Figure 5 as an 
instance. This Figure demonstrates the change in the 
specific electrical resistivity, Δ(B)/(0)  [(B) –
(0)]/(0) under external magnetic field, B, for the tem-
perature of 60 K. 
 
0 2 4
-0,0002
0,0000
0,0002
0,0004
 B, T



(0
)
 
 
Fig. 5 – The Δ/(0) vs. B for the bulk nanograined Bi2Te3 
material at 60 K 
 
One can see that the Δ(B)/(0) value first decreases 
as B increases up to ~ 1.7 T. This behaviour is corre-
sponding to the negative magnetoresistivity.  
Under higher magnetic field Δ(B)/(0) vs. B de-
pendence shows usual positive behaviour of the magne-
toresistivity. 
 Further experiments should be done to examine 
negative magnetoresistivity in material under study 
phenomenon in detail.  
 
4. CONCLUSIONS 
 
The bulk nanograined Bi2Te3 material was pre-
pared by the microwave assisted solvothermal method 
and cold isostatic pressure method. It was found that 
the temperature dependence of the specific electrical 
resistivity can be divided into metallic conductivity 
interval and semiconductor conductivity interval. With-
in the temperature ΔT  90 K-35 K interval the varia-
ble-range hopping conductivity takes place in material 
under study. Negative magnetoresistance was observed 
at the same temperature interval.  
 
AKNOWLEDGEMENTS 
 
All the studies were carried out by the scientific 
equipment of the joint research center "Diagnostics of 
structure and properties of nanomaterials" of Belgorod 
National State University which financially supported 
with Ministry of Science and Education of RF under 
project No 14.594.21.0010, unique code 
RFMEFI59414X0010. This work was also financially 
supported by the Ministry of Education and Science of 
the Russian Federation under projects No 2014/420-1 
and 3.308.2014/K. 
 
 
REFERENCES 
 
1. Q.G. Zhang, X. Zhang, B.Y. Cao, Appl. Phys. Lett. 89, 
114102 (2006). 
2. W. Liu, X. Yan, G. Chen, Z. Ren, Nano Energ. 1, 42 (2012). 
3. P. Pichanusakorn, P. Bandaru, Mater. Sci. Eng. R 67, 19 
(2010). 
4. O. Ivanov, O. Maradudina, R. Lyubushkin, J. Alloy. 
Compd. 586, 679 (2013). 
5. O. Ivanov, O. Maradudina, R. Lyubushkin, Mater. Char. 
99, 175 (2015). 
6. J. Han, M. Shen, W. Cao, A.M.R. Senos, P.Q. Mantas, 
Appl. Phys. Lett. 82, 67 (2003). 
7. V. Ambegaokar. B.I. Halperin, J.S. Langer, Phys. Rev. B 4, 
2612 (1971). 
8. B.I. Belevtsev, N.V. Dalakova, A.S. Panfilov, I.S. Braude, 
A.V. Bondarenko, Low Temp. Phys. 29, 300 (2003). 
9. Deng, X.S. Zhou, G.D. Wei, J. Liu, C.W. Nan, S.J. Zhao,  
J. Phys. Chem. Solids 63, 2119 (2002). 
10. R. Laiho, A.V. Lashkul, K.G. Lisunov, E. Lahderanta, 
M.A. Shakhov, V.S. Zakhvalinskii, J. Phys.: Condens. Mat. 
20, 295204 (2008). 
11. N.F. Mott, E.A. Davies, Electron Processes in Non-
Crystalline Materials (Oxford: Clarendon: 1979). 
12. B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped 
Semiconductors (Berlin: Springer: 1984). 
 


Hopping Conductivity and Negative Magnetoresistance of the Bulk Nanograined Bi2Te3 Material

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 7 No 4, 04073(3pp) (2015) Том 7 № 4, 04073(3cc) (2015)   2077-6772/2015/7(4)04073(3) 04073-1  2015 Sumy State University Hopping Conductivity and Negative Magnetoresistance of the Bulk  Nanograined Bi2Te3 Material  O.N. Ivanov, R.A. Lyubushkin, M.N. Yaprintsev, I.V. Sudzhanskaya  Belgorod State University, 85, Pobedy St., 308015 Belgorod, Russia  (Received 01 October 2015; published online 24 December 2015)  The bulk nanograined Bi2Te3 material was prepared by the microwave assisted solvothermal method and cold isostatic pressure method. It was found that above T* ≈ 190 K the temperature dependence of the specific electrical resistivity of material is of metallic type, while below this temperature a semiconductor conductivity takes place. Within the temperature ΔT ≈ 90 K-35 K interval the electrical conductivity of ma-terial can be described by the variable-range hopping conductivity mechanism. Negative magnetore-sistance was observed at the same temperature interval.   Keywords: Bulk nanograined materials, Hopping conductivity, Magnetoresistance.   PACS numbers: 72.10.Fk, 72.15. – v   1. INTRODUCTION  It is known that the nanograined materials are dis-ordered and inhomogeneous materials [1-3]. As a rule, such kind of materials consists of numerous conducting or semiconducting grains separating by insulating inter-faces [4, 5]. Specific mechanisms of the electrical conduc-tivity can take place in electrically inhomogeneous solid. In particular, hopping conductivity of various types is predicted for disordered and inhomogeneous semicon-ductors at low temperatures [6, 7]. It is important to note that unusual physical properties including negative magnetoresistance can also observed the hopping con-ductivity phenomenon [8]. The aim of this paper is to find out and analyze the features of the specific electrical conductivity of the bulk nanograined Bi2Te3 material.  2. EXPERIMENTAL PROCEDURE  Microwave-solvothermal synthesis (closed reactor ERTEC model 02-02) was applied to prepare the na-nosized Bi2Te3 powder. As is known, compared with the conventional methods, the microwave-assisted heating technique has the advantages of very short time of syn-thesis, simplicity and energy efficiency, small particle size of the products, narrow particle size distribution and high purity [9]. Analytically pure chemicals were used for the syn-thesis from LANHIT-LTD (bismuth oxide Bi2O3 with 99.9 % purity, tellurium oxide TeO2 with 99.9 % purity and L-cysteine (cys ≥ 97 %). Ethylene glycol (EG 99,8 % purity), nitric acid (HNO3 70 % with purity) and N,N-dimethylformamide (DMF anhydrous 99.8 % purity), were purchased from Sigma-aldrich. Oxides of bismuth and tellurium taken in a stoichio-metric ratio was dissolving in concentrated nitric acid, resulting solution was mixed in a ratio of 1 : 1 of eth-ylene glycol and cosolvent (DMF or DMSO or CAN). Then 4.2 mmol of L-cysteine was added to resulting solution with stirring for 30 min.  The microwave-assisted reaction was carried out in an ERTEC 02-02 microwave reactor, with a power of 300 W at 2.45 GHz working frequency. Synthesis was carried out for 20 min at temperature of 453 K and pres-sure of 40 bar. The powder after synthesis was cold isostatically pressed uder pressure 2800 bar. Then, the pressured powder was calcined at 623 K for 2 h in Ar atmosphere. X-ray diffraction (XRD) analysis was performed for the phase and crystal structure determination by using a Rigaku Ultima IV diffractometer with CuKα - radiation (a step width of 0.03 and a counting time of 1.6 s/step). Transmission electron microscope (TEM), JEM-2100, was applied to study morphology of the powders (for an accelerating voltage of 200 kV). Scanning electron micro-scope (SEM), Nova NanoSEM, was used to examine the grain structure of the bulk material (for an accelerating voltage of 2 kV). The specific electrical resistivity, , was measured by four-probed method at 0.1 mA dc current using the sin-tered samples with Ag electrodes. Magnetic field up to 5 T directed perpendicular to the electrical current can be applied to the sample during the  measurements.   3. RESULTS AND DISCUSSION  XRD-analysis confirmed that the synthesized powder is the single-phase Bi2Te3 compound (space symmetry group is   ̅ ). TEM-image in Fig. 1 shows a typical morphology of the powder. It is seen that the powder mainly consists of irregularly shaped nanoparticles of 20-50 nm in size. The bulk Bi2Te3 material has dense, homogeneous and porousless structure (Fig. 2). Nano- and microsized grains having a crystal faceting can be taken as evidence of intense sintering of the nanopowder. The temperature dependence of the specific electrical resistivity for the sample under study taken for the 2÷300 K interval is shown in Fig. 3. One can see that this dependence is rather complicated and can be divided into two temperature fields. Above the temperature T*  190 K, the resistivity decreases at cooling. Such kind of behavior is typical for metals or degenerate semiconductors having T-independent concentration of charge carriers. Below T* the resistivity increases as temperature decreases. This (T) dependence is characteristic for semiconductors.   O.N. IVANOV, R.A. LYUBUSHKIN, ET AL. J. NANO- ELECTRON. PHYS. 7, 04073 (2015)   04073-2   Fig. 1 – TEM-image of Bi2Te3 nanoparticles    Fig. 2 – SEM-image of the bulk nanograined Bi2Te3 material  A few mechanisms of the electrical conductivity could lead to the (T) dependence like the dependence presented in Fig. 3 below T*. One can see that this dependence is rather complicated and can be divided into two temperature fields. Above the temperature T*  190 K, the resistivity decreases at cooling. Such kind of behavior is typical for metals or degenerate semiconductors having T-independent concentration of charge carriers. Below T* the resistivity increases as temperature decreases. This (T) dependence is characteristic for semiconductors. A few mechanisms of the electrical conductivity could lead to the (T) dependence like the dependence presented in Fig. 3 below T*. First of all, it should be noted that temperature T* is low enough to generate of charge carries via transitions of electrons from valence band into conduction band. Typical mechanism of the electrical conductivity of semiconductors is the thermal activation of the charge carriers from shallow impurity levels to the conduction or valence band. In this case, the (T) dependence will satisfy the law      0 exp /aТ E kT  , (1)  the 0 is the prefactor, k is the Boltzmann constant and Ea is the activation energy.  0 75 150 225 3004,04,55,0T*T, K, 10-3, ohm. m  Fig. 3 – The (T) dependence for the bulk nanograined Bi2Te3 material  It was found that the experimental (T) dependence cannot be described by the expression (1). So, another mechanism of the electrical conductivity explaining the experimental data should be applied. As was mentioned above the hopping conductivity can take place in the bulk nanograiened materials.  The hopping conductivity can be realized via differ-ent mechanisms given by a universal equation [10]      0exp /ppТ DT T T     , (2)  where D is a constant, T0 is a characteristic tempera-ture and p is an exponent depending on regime of the localized electrons hopping. The case of p  1 corresponds to the regime of near-est-neighbor hopping (NNH) conductivity and p  1/4 and 1/2 to the Mott [11] and the Shklovskii-Efros [12] types of variable-range hopping conductivity, respec-tively. It was established that the best fitting by the ex-pression (2) can be achieved at p  1/4 for the tempera-ture interval from T1  90 K down to T2  35 K (Fig. 4).  0,32 0,40 0,48 0,56-6,6-6,3-6,0T2ln(/T1/4)T-1/4, K-1/4T1  Fig. 4 – The ln(ρ/T1/4)  f(T–1/4) dependence for the bulk nanograined Bi2Te3 material   HOPPING CONDUCTIVITY AND NEGATIVE MAGNETORESISTANCE… J. NANO- ELECTRON. PHYS. 7, 04073 (2015)   04073-3 So, within the temperature ΔT  T1 – T2 interval the variable-range hopping conductivity can takes place in the bulk nanograined Bi2Te3 material. As was mentioned above, negative magnetore-sistance can take place within the the temperature interval of the variable-range hopping conductivity. Negative magnetoresistance was really observed for the sample under study as is shown in Figure 5 as an instance. This Figure demonstrates the change in the specific electrical resistivity, Δ(B)/(0)  [(B) –(0)]/(0) under external magnetic field, B, for the tem-perature of 60 K.  0 2 4-0,00020,00000,00020,0004 B, T(0)  Fig. 5 – The Δ/(0) vs. B for the bulk nanograined Bi2Te3 material at 60 K  One can see that the Δ(B)/(0) value first decreases as B increases up to ~ 1.7 T. This behaviour is corre-sponding to the negative magnetoresistivity.  Under higher magnetic field Δ(B)/(0) vs. B de-pendence shows usual positive behaviour of the magne-toresistivity.  Further experiments should be done to examine negative magnetoresistivity in material under study phenomenon in detail.   4. CONCLUSIONS  The bulk nanograined Bi2Te3 material was pre-pared by the microwave assisted solvothermal method and cold isostatic pressure method. It was found that the temperature dependence of the specific electrical resistivity can be divided into metallic conductivity interval and semiconductor conductivity interval. With-in the temperature ΔT  90 K-35 K interval the varia-ble-range hopping conductivity takes place in material under study. Negative magnetoresistance was observed at the same temperature interval.   AKNOWLEDGEMENTS  All the studies were carried out by the scientific equipment of the joint research center "Diagnostics of structure and properties of nanomaterials" of Belgorod National State University which financially supported with Ministry of Science and Education of RF under project No 14.594.21.0010, unique code RFMEFI59414X0010. This work was also financially supported by the Ministry of Education and Science of the Russian Federation under projects No 2014/420-1 and 3.308.2014/K.   REFERENCES  1. Q.G. Zhang, X. Zhang, B.Y. Cao, Appl. Phys. Lett. 89, 114102 (2006). 2. W. Liu, X. Yan, G. Chen, Z. Ren, Nano Energ. 1, 42 (2012). 3. P. Pichanusakorn, P. Bandaru, Mater. Sci. Eng. R 67, 19 (2010). 4. O. Ivanov, O. Maradudina, R. Lyubushkin, J. Alloy. Compd. 586, 679 (2013). 5. O. Ivanov, O. Maradudina, R. Lyubushkin, Mater. Char. 99, 175 (2015). 6. J. Han, M. Shen, W. Cao, A.M.R. Senos, P.Q. Mantas, Appl. Phys. Lett. 82, 67 (2003). 7. V. Ambegaokar. B.I. Halperin, J.S. Langer, Phys. Rev. B 4, 2612 (1971). 8. B.I. Belevtsev, N.V. Dalakova, A.S. Panfilov, I.S. Braude, A.V. Bondarenko, Low Temp. Phys. 29, 300 (2003). 9. Deng, X.S. Zhou, G.D. Wei, J. Liu, C.W. Nan, S.J. Zhao,  J. Phys. Chem. Solids 63, 2119 (2002). 10. R. Laiho, A.V. Lashkul, K.G. Lisunov, E. Lahderanta, M.A. Shakhov, V.S. Zakhvalinskii, J. Phys.: Condens. Mat. 20, 295204 (2008). 11. N.F. Mott, E.A. Davies, Electron Processes in Non-Crystalline Materials (Oxford: Clarendon: 1979). 12. B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped Semiconductors (Berlin: Springer: 1984).  

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Hopping Conductivity and Negative Magnetoresistance of the Bulk Nanograined Bi2Te3 Material

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