Non-ohmic conduction in tin dioxide based ceramics with copper addition
The current-voltage characteristics and temperature dependences of electrical conductivity in SnO₂-Co₃O₄-Nb₂O₅-Cr₂O₃-CuO semiconductor ceramics are studied, and possible mechanism of non-ohmic conduction in these materials is discussed. Due to addition of CuO up to 0.5 mol.%, the nonlinearity...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| Cite this: | Non-ohmic conduction in tin dioxide based ceramics with copper addition / A.V. Gaponov, A.B. Glot // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 71-76. — Бібліогр.: 24 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1176252025-06-03T16:28:46Z Non-ohmic conduction in tin dioxide based ceramics with copper addition Gaponov, A.V. Glot, A.B. The current-voltage characteristics and temperature dependences of electrical conductivity in SnO₂-Co₃O₄-Nb₂O₅-Cr₂O₃-CuO semiconductor ceramics are studied, and possible mechanism of non-ohmic conduction in these materials is discussed. Due to addition of CuO up to 0.5 mol.%, the nonlinearity coefficient is increased up to 75, and the electric field is decreased down to 3900 V∙cm¹ (at 1 mA∙cm⁻²). It makes CuO addition useful for the preparation of SnO₂-based varistors. It is concluded that the electrical conduction is controlled by grain-boundary barriers. The activation energy of electrical conduction (the barrier height φ) is decreased with an increase in the electric field E. The higher slope of the dependence at high fields can be related to a participation of minority carriers (holes). The addition of more than 0.5 mol.% CuO leads to degradation of the varistor effect due to percolation via quite conductive CuO-based intergranular phase. 2011 Article Non-ohmic conduction in tin dioxide based ceramics with copper addition / A.V. Gaponov, A.B. Glot // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 71-76. — Бібліогр.: 24 назв. — англ. 1560-8034 PACS 73.30.+y, 73.40.-c, 73.50.Fq https://nasplib.isofts.kiev.ua/handle/123456789/117625 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The current-voltage characteristics and temperature dependences of electrical
conductivity in SnO₂-Co₃O₄-Nb₂O₅-Cr₂O₃-CuO semiconductor ceramics are studied, and
possible mechanism of non-ohmic conduction in these materials is discussed. Due to
addition of CuO up to 0.5 mol.%, the nonlinearity coefficient is increased up to 75, and
the electric field is decreased down to 3900 V∙cm¹ (at 1 mA∙cm⁻²). It makes CuO addition useful for the preparation of SnO₂-based varistors. It is concluded that the electrical conduction is controlled by grain-boundary barriers. The activation energy of
electrical conduction (the barrier height φ) is decreased with an increase in the electric field E. The higher slope of the dependence at high fields can be related to a participation of minority carriers (holes). The addition of more than 0.5 mol.% CuO leads to degradation of the varistor effect due to percolation via quite conductive CuO-based intergranular phase. |
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Gaponov, A.V. Glot, A.B. |
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Gaponov, A.V. Glot, A.B. Non-ohmic conduction in tin dioxide based ceramics with copper addition Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Gaponov, A.V. Glot, A.B. |
| author_sort |
Gaponov, A.V. |
| title |
Non-ohmic conduction in tin dioxide based ceramics with copper addition |
| title_short |
Non-ohmic conduction in tin dioxide based ceramics with copper addition |
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Non-ohmic conduction in tin dioxide based ceramics with copper addition |
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Non-ohmic conduction in tin dioxide based ceramics with copper addition |
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Non-ohmic conduction in tin dioxide based ceramics with copper addition |
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non-ohmic conduction in tin dioxide based ceramics with copper addition |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2011 |
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https://nasplib.isofts.kiev.ua/handle/123456789/117625 |
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Non-ohmic conduction in tin dioxide based ceramics with copper addition / A.V. Gaponov, A.B. Glot // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 71-76. — Бібліогр.: 24 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT gaponovav nonohmicconductionintindioxidebasedceramicswithcopperaddition AT glotab nonohmicconductionintindioxidebasedceramicswithcopperaddition |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 71-76.
PACS 73.30.+y, 73.40.-c, 73.50.Fq
Non-ohmic conduction in tin dioxide based ceramics
with copper addition
A.V. Gaponov1, A.B. Glot2
1Dnipropetrovsk National University, 72, Gagarin Ave., 49010 Dnipropetrovsk, Ukraine
E-mail: alexei_gaponov@ukr.net
2Universidad Tecnológica de la Mixteca, Carretera a Acatlima km.
2.5, Huajuapan de León, Oaxaca, 69000, México
E-mail: alexglot@mixteco.utm.mx
Abstract. The current-voltage characteristics and temperature dependences of electrical
conductivity in SnO2-Co3O4-Nb2O5-Cr2O3-CuO semiconductor ceramics are studied, and
possible mechanism of non-ohmic conduction in these materials is discussed. Due to
addition of CuO up to 0.5 mol.%, the nonlinearity coefficient is increased up to 75, and
the electric field is decreased down to (at ). It makes CuO
addition useful for the preparation of SnO
1cmV3900 −⋅ 2cmmA1 −⋅
2-based varistors. It is concluded that the
electrical conduction is controlled by grain-boundary barriers. The activation energy of
electrical conduction (the barrier height φ) is decreased with an increase in the
electric field E. The higher slope of the dependence at high fields can be related
to a participation of minority carriers (holes). The addition of more than 0.5 mol.% CuO
leads to degradation of the varistor effect due to percolation via quite conductive CuO-
based intergranular phase.
σE
)(EEσ
Keywords: non-ohmic conduction, grain boundary, varistor, barrier height, tin dioxide
ceramics.
Manuscript received 25.01.10; accepted for publication 02.12.10; published online 28.02.11.
1. Introduction
Zinc oxide (ZnO) ceramics with certain additives
exhibits strong non-ohmic conduction and, therefore,
these materials are used for fabrication of varistors –
transient voltage suppression devices [1, 2]. Quite high
non-ohmic conduction was also observed in tin dioxide
(SnO2) based ceramics [3, 4]. This observation means
that ZnO ceramics are not unique materials with highly
nonlinear current-voltage characteristics. ZnO varistors
exhibit some disadvantages (for example, electrical and
thermal degradation) [2, 5, 6]. Therefore, there is a hope
that varistors based on tin dioxide could possess better
properties [5, 6]. It was realized that basic electrical
behaviour of SnO2 and ZnO varistors are quite similar,
because electrical conduction in these ceramics is
controlled by the grain-boundary barriers [3-6].
In recent years, SnO2 ceramics with the varistor
effect were rather intensively studied [7-10] mainly from
the materials science view-point. However, the
mechanism of non-ohmic conduction in SnO2 varistor
ceramics is still unclear. It was shown that addition of
oxides with a low melting point (Bi2O3, V2O5, CuO)
gives certain improvements in the density and electrical
parameters of SnO2 varistor ceramics [11-15]. Probably,
addition of copper oxide to SnO2-CoO-Nb2O5-Cr2O3
looks quite useful for the achievement of desired
parameters of SnO2 varistors [14, 15]. Thus, in this paper
we have studied SnO2-CoO-Nb2O5-Cr2O3 ceramics with
various amounts of CuO addition. But there is no
information about the conduction mechanism in these
materials. Therefore, it would be interesting to study the
high-field conduction at various temperatures in recently
developed SnO2-CoO-Nb2O5-Cr2O3-CuO varistor
ceramics.
Usually, the current-voltage characteristics of oxide
varistors are approximated within the narrow range of
current densities by the empiric expression j = BEβ,
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
71
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 71-76.
where j is the current density and E is the electric field, β
is a dimensionless constant (nonlinearity coefficient) and
B is a constant with dimension giving the current density
j in , if the electric field E is expressed in
. The nonlinearity coefficient is defined by the
expression β = (E
2cmA −⋅
1cmV −⋅
/ j) (dj / dE). Usually the nonlinearity
coefficient is estimated at a fixed current density (for
example, at ). In this case, it can be denoted
as β
2cmmA1 −⋅
1. For the indication of the electric field range where
the nonlinearity of j (E) characteristic takes place, the
value of the electric field at (E2cmmA1 −⋅ 1) is
introduced. The values β1 and E1 are used frequently as
the main empiric parameters of a varistor.
However, the empiric j (E) expression and empiric
parameter β1 cannot enable in understanding the
mechanism of non-ohmic conduction. Therefore, starting
from the assumption that non-ohmic conduction in ZnO
and SnO2 varistor ceramics is attributed to the decrease
of the barrier height with electric field, the expression
for the current-voltage characteristic was obtained
[12, 16, 17]:
)exp()( 0 EEEj ασ= , (1)
where σ0 is the conductivity of material at low electric
fields, α is the nonlinearity factor. In the case of
thermionic emission across the barrier, the parameter α
is proportional to the rate of change in the barrier height
φ with the electric field E [12, 16, 17]:
⎟
⎠
⎞
⎜
⎝
⎛ ϕ
−=α
dE
d
kT
1 , (2)
where k is the Boltzmann constant, T is the absolute
temperature.
Therefore, in this paper electrical properties of
SnO2-CoO-Nb2O5-Cr2O3 ceramics with various amounts
of CuO addition were studied, then current-voltage
characteristics of some SnO2-CoO-Nb2O5-Cr2O3-CuO
ceramics at different temperatures were obtained, and
the dependences of the activation energy of electrical
conduction on the electric field were found from them.
2. Experimental details
Ceramics were prepared by the conventional oxide
mixture method using distilled water. The compositions
were (mol.%) (99.4 – x) SnO2, 0.5 Co3O4, 0.05 Nb2O5,
0.05 Cr2O3, x CuO, x = 0; 0.1; 0.5; 2; 8 (Table). After
wet milling and drying, obtained powder was pressed in
tablets 12 mm in diameter and about 0.7 mm in
thickness under the axial pressure 45 MPa. Pressed disks
were sintered at 1520 K in air. The details of preparation
are described in [14, 15]. To determine the grain size,
scanning electron microscopy (SEM) was used. The
shrinkage γ was calculated according to the expression
, where D1
00 )( −−=γ DDD 0 and D are diameters of a
sample before and after sintering, respectively.
Electrical measurements were performed using In-
Ga eutectic electrodes prepared at room temperature (for
the study of current-voltage characteristics of the
samples with various CuO amounts at 300 K) and Ag-
electrodes obtained at 1070 K (for the measurements at
different temperatures). It was found that such a heat
treatment at 1070 K leads to a decrease in nonlinearity of
current-voltage characteristics.
Current-voltage characteristics were recorded in air
within the temperature range 300–423 K. The relative
humidity of ambient air was about 50 % at 300 K. The
results were obtained avoiding a self-heating of the
samples. The nonlinearity coefficient β1 and electric field
E1 were estimated at the current density 10–3 A⋅cm–2.
Temperature dependence of dc electrical
conductivity σ(T) was obtained in the range 300–473 K
at heating and cooling the samples in air with a rate
close to 1 K/min. Below about 350 K, conductivity was
decreased at heating due to desorption of water
molecules [11, 18]. The activation energy of electrical
conduction Eσ(0) at low electric fields (in ohmic region)
was estimated from the high-temperature (350–473 K)
part of σ0(T) dependence using the equation:
)/)0(exp(000 kTEσ−σ=σ , (3)
where σ00 is a constant.
Table. Some parameters of SnO2-Co3O4-Nb2O5-Cr2O3-CuO ceramics (electrical parameters were obtained for the
samples with In-Ga electrodes).
CuO (mol.%) 0 0.1 0.5 2 8
Linear shrinkage γ (%) 9.0 9.2 11.7 11.4 9.3
Average grain size lg (μm) 4 5 8 8 8
Electrical conductivity σ
(Ohm–1⋅ cm–1)
1.2⋅10–12
3.2⋅10–12
4.8⋅10–12
1.4⋅10–10
5.7⋅10–9
Activation energy of electrical
conduction Eσ(eV)
1.2 1.0 0.94 0.65 0.34
Nonlinearity coefficient β1 54 61 75 7.6 3.1
Electric field E1 (V⋅ cm–1) 6280 4870 3900 8540 14740
Normalized nonlinearity coefficient
βE = β1/E1 (cm⋅ V –1)
8.6⋅10–3
1.25⋅10–3
1.9⋅10–3
8.9⋅10–4
2.1⋅10–4
Relative dielectric permittivity ε(1 kHz) 114 397 865 130 60
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
72
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 71-76.
The capacitance was measured at the frequency
1 kHz using LCRG meter Tesla BM 591.
3. Results and discussion
The current-voltage characteristics of SnO2-Co3O4-
Nb2O5-Cr2O3-CuO ceramics with various CuO amounts
are shown in Fig. 1. Rather strong variation in the low-
field conductivity σ, nonlinearity coefficient β1 and
electric field E1 for the samples with different CuO
additions have been found (Table).
The addition of CuO in the range 0–0.5 mol.%
gives some increase in the nonlinearity coefficient
(Fig. 1, curves 1 to 3). The highest value β = 75 was
found for the sample with 0.5 mol.% CuO (Table). This
value is higher than that observed by us earlier [14] due
to the absence of heat treatment at 1070 K (due to use of
In-Ga eutectic electrodes). Higher amounts of CuO
addition (more than 0.5 mol.%) cause a strong decrease
in the nonlinearity and a rise of the low-field
conductivity (Fig. 1, curves 4 to 5).
The reason for an increase in the nonlinearity
coefficient on CuO addition in the range 0–0.5 mol.%
(Fig. 1 and Table) can be due to the formation of higher
amount of liquid CuO-phase and related more
homogeneous distribution of Co3O4 and Cr2O3
impurities throughout a sample. These additives play an
important role in the obtaining of SnO2 ceramics with
highly nonlinear current-voltage characteristics [3, 6].
Within the range 0 to 0.5 mol.% CuO, the electric
field E1 (at current density 10–3 A⋅cm–2) is decreased
(Fig. 1, curves 1 to 3). It is explained by the grain size
growth with the copper oxide content (Table). Observed
slight increase in the low-field conductivity in the range
0–0.5 mol.% CuO (Fig. 1, curves 1 to 3) is rather due to
the grain growth. Such a change is typical for a
transition from high-voltage to low-voltage ZnO
varistors.
Fig. 1. Current density vs. electric field in SnO2-Co3O4-Nb2O5-
Cr2O3 varistor ceramics with various amounts of CuO addition,
mol.%: 0 (1), 0.1 (2), 0.5 (3), 2 (4), 8 (5).
Subsequent decrease in the nonlinearity coefficient
with CuO addition in the range 2–8 mol.% (Fig. 1 and
Table) can be due to percolation across the fairly
conductive intergranular CuO phase covering SnO2
grains and acting as an electrical shunt to the grain
boundaries. Similar situation was recently observed in
SnO2-Co3O4-Nb2O5-Cr2O3-V2O5 varistor ceramics with
variation in V2O5 addition [13].
Temperature dependences of dc electrical
conductivity σ(T) for the samples with different CuO
amount have been shown in Fig. 2. With a rise in CuO
addition, the electrical conductivity at a fixed
temperature is increased, and the activation energy of
electrical conduction Eσ becomes lower (Table). Below
about 350 K, conductivity of ceramics with CuO
addition in the range 0–0.5 mol.% (curves 1-3 in Fig. 2)
was affected by humid air (see [11, 13, 18]). In the case
of low CuO amounts, humid air can penetrate inside the
sample and reach grain-boundary areas. Though at
higher values of CuO additives, σ(T) curves are not
distorted in the low-temperature part (curves 4 and 5 in
Fig. 2) probably because CuO-phase covers SnO2 grains
[14] and prevents penetration of humid air to the grain-
boundary regions.
Electrical conduction in SnO2 ceramics is
controlled by the grain-boundary potential barriers [3-
16]. The activation energy of electrical conduction Eσ is
a measure of the barrier height φ (φ ≅ Eσ), because using
the literature data for single crystals [19] it can be
assumed that the Fermi level in the doped SnO2 grain
bulk is situated quite close to the conduction band edge.
Oxygen vacancies and Nb impurities can serve as
shallow donors in SnO2 [19]. The observed decrease in
the low-field barrier height with CuO addition can be
explained by the presence of CuO-phase in the
samples [15].
The relative dielectric permittivity ε = 114 of SnO2-
Co3O4-Nb2O5-Cr2O3 ceramics (Table) is quite high due
to the existence of thin depletion grain-boundary
regions. In the range 0–0.5 mol.% CuO, the grain size lg
is increased, and therefore, ε of ceramics becomes higher
(Table). However, SnO2-Co3O4-Nb2O5-Cr2O3-CuO
ceramics with 2–8 mol. % CuO exhibits lower ε values
(Table) due to the influence of copper oxide phase with
not high relative dielectric permittivity about 10.
As far as the electrical conduction in SnO2
ceramics near room temperature is thermally-activated
process with a rather high activation energy [11-14], the
thermionic emission across the barrier is the most
probable conduction mechanism near 300 K. In this
case, the temperature dependence of conductivity
σ (T, E) = j (T, E) / E in electric field can be written in the
form similar to Eq. (3) where Eσ(0) should be replaced
for the activation energy at any electric field Eσ(E).
Then, using Eqs (1) and (2) we have:
E
dE
dEEE ⎟
⎠
⎞
⎜
⎝
⎛ ϕ
−−= σσ )0()( . (4)
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
73
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 71-76.
Fig. 2. Temperature dependence of dc low-field electrical
conductivity in air (heating) for SnO2-Co3O4-Nb2O5-Cr2O3-
CuO varistor ceramics with various amounts of CuO addition,
mol.%: 0 (1), 0.1 (2), 0.5 (3), 2 (4), 8 (5).
The activation energy is linearly decreased with
electric field, if the rate of change of the barrier height
with electric field is constant. This can be
experimentally verified.
In Fig. 3, current-voltage characteristics of studied
ceramic material have been presented in the scale
. Two regions with different non-zero
slopes are seen. They are related to the nonlinearity
factors α = α
EEj −)/log(
1 (for mean fields) and α = α2 > α1 (for the
high ones), respectively. The ohmic region with α = 0 at
lowest fields is not revealed. The value α1 is related to
the increase in conductivity at electric fields that are
lower than in the highly nonlinear region. The value α2
is related to the highly nonlinear region of current-
voltage characteristic which is empirically described by
the nonlinearity coefficient β1 estimated at . 2cmmA1 −⋅
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 4. Field dependence of the activation energy of electrical
conduction in SnO2-Co3O4-Nb2O5-Cr2O3 ceramics (curve 1;
nonlinearity coefficient β1 = 54), in SnO2-Co3O4-Nb2O5-Cr2O3
ceramics with 0.1 mol. % CuO (curves 2 and 2′; nonlinearity
coefficient β1 = 61) and with 0.5 mol.% CuO (curve 3;
nonlinearity coefficient β1 = 21). The activation energy was
estimated at temperatures near 400 K (curves 1-3) and near
320 K (curve 2′).
Fig. 3. Dependence of electrical conductivity on electric field
for SnO2-Co3O4-Nb2O5-Cr2O3-CuO varistor ceramics (with
0.1 mol.% CuO addition) at various temperatures: 304 (1),
343 (2), 383 (3) and 423 K (4).
From the family of current-voltage characteristics
at various temperatures, the dependences of conductivity
σ (T, E) = j (T, E) / E at fixed electric fields on
temperature were plotted. The activation energy of
electrical conduction Eσ(E) was estimated from the high-
temperature part of σ(T) dependence (at about 400 K)
because at this region thermionic conduction mechanism
is more probable. The obtained dependence of the
activation energy on electric field is presented in Fig. 4
(curve 2). Rather high values of Eσ in Fig. 4 are in
accordance with assumed thermally activated transition
of electrons. The slight decrease of the slope inherent to
the experimental dependence in the scale at
lower temperatures (in the vicinity of 320 K) gives
respective displacement of the E
1log −−σ T
σ(E) curve to lower
values (curve 2′ in Fig. 4). Lower values of the
activation energy can be related to the gradual
changeover from thermionic emission to thermally-
assisted tunnelling. At thermally-assisted tunnelling,
electrons cross the barrier at different energies with a
maximum at certain energy. This energy probably
reflects the activation energy at thermally-assisted
tunnelling. Such situation also takes place in ZnO
varistors below about 300 K [5].
The j (E) characteristics at various temperatures
were also obtained for the samples with different
amounts of CuO additives, and the same treatment of
experimental data was performed. It is seen that for all
the studied samples of SnO2 varistors the barrier height
is decreased with electric field (Fig. 4). Earlier, similar
behaviour was found for SnO2-Co3O4-Nb2O5-Cr2O3-
Bi2O3 varistor [12].
It is clearly seen that for the sample with the high
nonlinearity coefficient (β1 = 61), Eσ(E) dependence
exhibits a low-field part with low slope and a high-field
part with higher slope (Fig. 4, curve 2). Relatively weak
decrease of Eσ at low electric fields in comparison with
74
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 71-76.
the model of grain boundary with fixed interface charge
[20] is due to the capture of electrons at the interface.
The experimental confirmation of this effect was
obtained recently from the isothermal capacitance decay
at a voltage bias and subsequent increment of
capacitance at zero bias [14].
At high electric fields where high nonlinearity is
observed, the activation energy of electrical conduction
and the barrier height in SnO2 varistors (0.3–0.5 eV) are
still quite high (Fig. 4). This fact means that the
conduction process is thermally activated not only at low
but also at high electric fields. This makes possible fairly
simple explanation of conduction in SnO2 varistors as
thermionic emission across the barrier with the barrier
height dependent on electric field.
The experimental dependence of the barrier height
on the electric field φ(E) in SnO2 based varistors consists
of two parts: the first one gives a slight decrease in the
barrier height at low electric fields, and the second gives
a stronger decrease at higher fields. It is necessary to
mention that according to the developed approach [12,
16, 17], the obtained dependence φ(E) (Fig. 4, curve 2)
reflects a shape of the dependence on the electric
field (Fig. 3, curve 1).
σlog
It is interesting to note that α-values in Fig. 3 are
temperature-dependent, because the slopes of curves are
gradually decreased with temperature. This fact is
related to the thermionic emission of electrons across the
grain-boundary barrier (see Eq. (2)).
Probably, a higher slope of the φ(E) dependence at
high fields in SnO2 varistors is related to a decrease of
the negative interface charge on absolute value as a
result of impact ionization in reverse biased depletion
region or Zener tunnelling from valence to conduction
band. It can lead to appearance of minority carriers
(holes) in n-SnO2. As a possible confirmation of hole
generation at high fields in ZnO varistors, the
observation of electroluminescence [21, 22] and
negative capacitance [23] are considered. Earlier the
negative capacitance was observed in SnO2 varistors
with low nonlinearity [4], and recently we have observed
the negative capacitance in SnO2-Co3O4-Nb2O5-Cr2O3-
CuO ceramics with high nonlinearity [24].
4. Conclusions
Electrical properties of tin dioxide based SnO2-Co3O4-
Nb2O5-Cr2O3 ceramics with CuO addition in the range
0–8 mol.% are studied. The nonlinearity coefficient is
increased from 54 to 75 in the range 0–0.5 mol.% CuO,
and further it is decreased to 3–7 in the range 2–8 mol.%
CuO. The conduction mechanism in ceramics with 0–
0.5 mol.% CuO is grain-boundary controlled. The
decrease in the barrier height with the voltage is
responsible for non-ohmic behaviour. The activation
energy of electrical conduction Eσ in SnO2 varistors as a
function of electric field E is obtained experimentally.
For the samples with a high nonlinearity coefficient,
Eσ(E) dependence exhibits the low-field part with low
slope and high-field part with higher slope. The highly
nonlinear rise of the current density with electric field
(the varistor effect) is related to the strong decrease in
the activation energy Eσ(E) (the barrier height). As far as
the activation energy is quite high (about 0.3–0.5 eV) at
high electric fields, the conduction process is thermally
activated not only at low but also at high electric fields.
The higher slope of Eσ(E) dependence at high fields can
be related to a contribution of minority carriers (holes).
References
1. M. Matsuoka, Nonohmic properties of zinc oxide
ceramics // Jpn. J. Appl. Phys. 10(6), p. 736-746
(1971).
2. T.K. Gupta, Application of zinc oxide varistors // J.
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2. Experimental details
3. Results and discussion
4. Conclusions
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