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Electrical Conductivity and Dielectric Properties of Bi4Ti3O12
A. Agasiev, M. Mamedov, M. Muradov
To cite this version:
A. Agasiev, M. Mamedov, M. Muradov. Electrical Conductivity and Dielectric Properties of Bi4Ti3O12. Journal de Physique III, EDP Sciences, 1996, 6 (7), pp.853-861. �10.1051/jp3:1996159�.
�jpa-00249496�
Electrical Conductivity and Dielectric Properties of B14T1301~
Films
A-A- Agasiev, M-Z- Mamedov and M-B- Muradov
Baku State University, Baku 370145, Azerbaijan
(Received 19 June 1995, revised 15 January and 15 April 1996, accepted 17 April 1996)
PACS.72.40.w Photoconduction and photovoltaic effects; photodielectric effects
Abstract. The present paper deals with the investigation of electrical and dielectric proper- ties of structures based
on B14T13012 films. It has been found that the nonlinearity of the I U characteristics in Me-B14T13012-Me structures is attributed to intercrystalline potential barri-
ers. The height of the intercrystalline barrier (4lo # 0.12 eV) and the mean size of crystallise (L = 0.3 pm) have been determined. At rather low temperatures, the hopping conductivity
with a mean length of hopping, r~ 2.6 x 10~~ cm~~ev~~, is shown to be a dominant process at the charge transfer. It has been found that the electrical conductivity (a) in the direction par- allel to the C-axis ("sandwich" configuration) shows an anomaly in the phase transition region (r~ 950 K), while in the direction perpendicular to the C-axis, a simple bending of a us. T is observed. The latter is explained by the change of spontaneous polarization in B14T13012 films.
The temperature dependence of the dielectric constant and the dielectric loss tangent have the maxima in the range of the phase transition temperature. The dielectric constant values are
r~ 650
r~ 120 for the structures of "sandwich" and planar configurations, respectively. This fact indicates the presence of a polarization component in the given direction. The diffusion of the
phase transition is explained by the imperfection of the film structure.
1. Introduction
Among the ferroelectrics known at present, the ferroelectric compounds of complex oxides are of great interest and importance. The ferroelectrics with perovskite structure are the most
important among the compounds of this class. B14T13012 belongs to this class of compounds.
The structure consists of perovskite-like layers obtained on section of cubic perovskite lattice
parallel to (001) plane alternating with bismuth-oxygen layers [ii.
The interest to film structures based on bismuth titanate is due to perspective of their appli-
cation in microelectronics, integral optics and also in producing the optical reverse media. The investigation of non-ohmic phenomena and dielectric properties of oxygen-octahedral ferroelec- tric B14T13012 is of great interest due to application in technics producing oxidic varistors [2],
radiation transformer [3]. The investigation results are also of great importance for understand- ing the mechanism of conductivity and contact phenomena in Me-B14T13012-Me structure and
as a whole, on the metal-high ohmic semiconductor contact and also to understand the mech- anism of ferroelectric phenomena in such films. In this connection, a detailed investigation
of current-voltage II U) characteristics, electroconductivity and dielectric constant of struc- tures on the base of bismuth titanate at different temperatures versus the configuration and the material of electrodes has been carried out in the present paper.
@ Les #ditions de Physique 1996
854 JOURNAL DE PHYSIQUE III N°7
2. Experimental
The B14T13012 (BTO) thin fi1nls obtained by dc magnetron sputtering [4] were used for in-
vestigation. The fi1nl composition was studied using microanalyzer Camebax-56, while the
structure and the morphology were investigated on the electron microscopes EM-14 and REM-
loo M. Al, Pt, Ag deposited by vacuum evaporation were used as the contacts. Electrical and dielectric nleasurements were carried out in vacuum at r~J 10~~ Torr in the temperature range
of 77 1000 K.
The dielectric constant and the dielectric loss tangent were measured with the use of stan- dard bridge E8~2 at the fixed frequency of i kHz. Despite of a number of papers [2,5] dealing
with investigation of I U characteristics of the structures based on bismuth titanate, the
nature of the I U characteristic non-linearity in the above structures is substantiated insuf-
ficiently. For this purpose, a detailed investigation of I U characteristics of structures based
on bismuth titanate at different temperatures versus the sample thickness, the configuration
and the material of electrodes has been carried out in the present paper.
3. Results and Discussion
The typical I- U characteristics for planar samples is shown in Figure i. The distance between electrodes d was
r~J 2 mm. As seen in Figure i, at U
= 0 400 V (E
r~J o 4 x io~ V m~~)
the I U characteristic is linear indicating a lack of the injection currents. Such a behaviour of the I U characteristic is probably due to a high resistivity of the films. The BTO film
resistivity exceeds the value 10~~ fl cm at 293 K, and at 923 K (the Curie point) it is of the order of 10~ fl cnl.
The investigation of the I U characteristics of the "sandwich" type structure based on poly- crystalline bismuth titanate at different temperatures showed that three regions are distinctly
revealed in the above characteristic. The ohmic region I
+~ U (low U, U < Ui), a superlinear
1(10~~~) A
3
200 300 400 u(vj
Fig. 1. The dark current-voltage characteristic of B14T13012 film in planar configuration of
Al-B14T13012-Al, T
= 293 K.
log(U(V))
1
/&
>
m -6 -
~ i $~
~ ~i (I) tS
-7 ff
~ -
~/
%~ ~
_
-9
1 3 5
U; U aU~, (V)
Fig. 2. The dark current-voltage characteristic of B14T13012 film at T
= 293 K in "sandwich"
configuration of Sn02 -B14T13 O12-Al inlogI log U (1), logI U(2) and log ~
~~~ (U -a U~
1- 4a
(3) (a
= o.04 V~~).
region I
r~
U">I (Ui < U < U2), and the second superlinear region I r~ U">~ (U > U3).
The analysis has shown that the curves of the I U characteristic in the superlinear region
are normalized in the coordinates log(1/(1- 4a~U~)) (U au~) (Fig. 2) where a is a
parameter obtained from the experimental I U characteristic by iteration method described in reference [6] in detail. Such a dependence is typical for electron transfer in semiconductors
with intergranular barriers [7].
The mechanism of a semiconductor conductivity with intergranular barriers is considered in [7] taking into account the real nature of the barriers. Using a diffusion theory and with a full occupancy of boundary acceptor states in the case of depletion of the Schottky layers, the I U characteristic of a semiconductor with a single intergranular boundary normal to the
direction of the current has the form:
~L2
~
164l(
~
~~~
T)~
~~~ kT 2kT ~
6kT4lo~
~~~
where ~1is the electron mobility in the volume, k is the Boltzmann constant, T is the tem-
perature, e is the electron charge, Ns is the density of boundary states on the intergranular wall, V is the voltage, 4lo is the height of intergranular barrier at V
= 0, e is the dielectric constant, L~
= ekT/4ire~ND, ND is a donor concentration in the volume. The voltage at a
single intergranular boundary is V
= U/~ for the structures with the intergranular boundaries
number in the interelectrode gap ~ and at the applied voltage U. The given model explains the linear and the exponential regions of the I U characteristic. According to equation (1)
856 JOURNAL DE PHYSIQUE III N°7
at U < Ui " ~kTle we have
j =
fUexp (-~)
(2)at U » Ui the exponential I U characteristic takes place:
j = ~~j(fi(1 4a~U~)e~°/~~ exp
)
(UaU~)j (3)
~~~~~ ~
8i~~
The value of ~ is determined independently of the slope of a linear region of the I U characteristic log I
r~
U. The values of the height of intergranular barrier, ~o, and the number of intergranular barriers, ~, for "sandwich" structures determined in such a manner from the
exponential I U characteristics were respectively 4lo = 0.12 eV and 7i
= 29. At high electrical fields the voltage at the intercrystalline boundary is of the order and larger than the height of the barrier, U > U2 = ~4lo, the barriers are removed by the field and the ohmic dependence (in the lack of any strong field effects) should be observed again. The critical voltages Ui and U2 allow to determine ~ and 4lo independently. The obtained values of ~ and 4lo, ~
= 31
and 4lo " o-lo eV, respectively, are rather close to the previous values. The average grain
size, h
= d/~
= 0.24 0.38 ~lm, determined from the experimental data are close to those
lo.18 o.39 ~lm) obtained from the electron microphotography of the surface. This fact favours the model considered.
As seen from the experimental I- U characteristic, at high voltages, U > U2, the transition to the dependence close to ohmic dependence is observed. However, this small region transfornls to a superlinear one with the exponent i < n < 4 again. With the change of the voltage in the ohmicity region of the I U characteristic both the activation energy and the behaviour of conductivity in the low-temperature region remain unchanged. With increase of the voltage
in the nonlinear region, the activation energy decreases. The decrease of the activation energy
(AE~ = 0.17 eV) at voltages U > U2 is more than the mean height of intergranular potential barriers (4lo = o-lo eV) estimated from the nonlinear I U characteristics. The decrease of activation energy as well as the superlinear region of the I U characteristic are most
likely attributed to the conductivity in crystals in model of bended bands la highly doped compensated semiconductor model) at strong fields. The prediction for the given model is a
high concentration of impurity centers and a wide band (Eg r~ 3.71 eV) of B14T13012.
The following typical regions can be separated in the temperature dependence of dark elec- trical conductivity aT (Fig. 3, curve i), I-e- a high-temperature region (T > 250 K) and
a low-temperature region (T < 250 K). The exponential temperature dependence of dark
conductivity with a constant activation energy E; is observed in the high-temperature region:
aTjT)
r~ exp(-E; /kT). j4)
In the low-temperature region the activation energy continuously decreases with decreasing
temperature. The temperature dependence of conductivity in log(a) T~~R coordinates is shown in Figure 3, curve 2. In the low-temperature range the above dependence is linear and the slope of the straight line is 45 dg~~H in this case. The given peculiarities are typical
of cases when the charge transfer by hopping is dominant. The fact that the temperature
dependence of bismuth titanate electric conductivity at low temperatures is linear in log(a) T~~H coordinates and the charge carrier mobility is observed in the range of 0 is cm~/V s [8]
allows to conclude that at low temperatures with dc a hopping conductivity with a variable
T-lH (K~~H) -
' ' ,,
' (2)
i =
E i
/ , fl
) '~ (l) jZ
~i
2 5
io3
y (K~~) -
Fig. 3. The temperature dependence of the electrical conductivity with dc of B14T13012 film in
coordinates a -10~ IT (1) and a T~~/~ (2).
length of hopping over the states near the Fermi level is the dominant process at the charge carrier transfer.
In this case, a is determined by the Mott low [9]:
a = ao exp(-BT~~R)
where B
= 2[03/kN(EF))~/~, a~~ is the radius of the localized state, N(EF) is the density
of states near the Fermi level. Using the obtained parameter B
= 45 dg~~R which is a characteristic of a hopping conductivity, the values of N(EF) at o~~
= 8 1
were estimated. It has been found that N(EF)
" 8.04 x 10~~ cm~~ eV~~ that corresponds to the value of N(EF)
for another disordered structures [9]. With increasing temperature a mean length of the charge
carrier hopping decreases in accordance with the expression
y ~-l j~jn-1/4
2.73
When a~~
= 8 1, the hopping values
are f = 37.69 1 and f
=
33.181 at 150 K and 250 K, respectively.
In BTO the phase transition is observed at r~ 950 K [lo]. Therefore one can assume the effect of ferroelectric phenomena on the electrical conductivity mechanism in the range of phase
transition temperature.
The crystallographic polar axis Z is known to coincide with a tetragonal axis C of a high- temperature phase of bismuth titanate, and in the case of thin layers the C-axis is perpendic-
ular to the plane of a substrate [IIi. The strong covalent bonds take place along the C-axis, while in the direction perpendicular to the C-axis the weak van der Waals forces act [12].
This fact indicates the possibility of anisotropy of physical properties of BTO layers. There-
fore, to study the anisotropy of electrical conductivity, the structures based on BTO films in
858 JOURNAL DE PHYSIQUE III N°7
-5
I
~ -6
[
~
~ ~
~ '
_~
-9
-io
i
1
~~~ (K~~)
Fig. 4. The temperature dependence of the electrical conductivity of B14T13012 film in a "sandwich"
configuration.
planar and sandwich configurations, I-e- in the direction perpendicular and parallel to the C-axis, were used. The measurements have shown that in the range of the phase transition
temperature in the direction of the C-axis ("sandwich" structure) the electrical conductivity anomaly is observed (Fig. 4). In this case a decrease of electrical conductivity and an increase in activation energy are observed. The anomalies of electrical conductivity in the direction
perpendicular to the C-axis (the planar structure) are not revealed. In such structures the
bending of the temperature dependence of electrical conductivity is only observed (Fig. 5).
The anomaly of electrical conductivity is probably due to the spontaneous polarization in BTO films. The ferroelectric phase transition effect on the temperature dependence of conductivity of ferroelectrics-semiconductors is determined by the following factors: i) the dependence of
the conductivity parameters on the square of polarization (l~~ r~v jT Tcj) (the bending at the
point of the phase transition shown in Fig. 5 can be considered as an example); 2) the screening
of a spontaneous polarization. With the change ofspontaneous polarisation both the charges screening the above polarization and those attributed to the free charge carriers also alter. It is clear that if the first factor is typical both of the bulk samples and the films, the second
factor is characteristic only for films with the thickness comparable to the screening length L.
In a planar geometry the screening charges are located at distance of the order of L, while in
"sandwich" configuration they occupy the whole volume. Therefore, the essential difference in peculiarities of the temperature dependence of conductivity in the phase transition region
should be observed for planar and "sandwich" configurations.
To clarify the nature of electrical ordering in BTO layers, the investigation of the temper-
ature dependence of the dielectric constant in different directions indicating the presence of
spontaneous polarization is of great interest. The typical temperature dependence of the di- electric constant of "sandwich" structure based on BTO when heated and on cooling is shown in Figure 6. The maxima of the dielectric constant at
+~ 950 K of approximately equal value
= -5
'
[
(
bo
1~
1
9
1
1
io3 y jI(~~j
Fig. 5. The temperature dependence of the electrical conductivity of B14T13012 in planar configu-
ration.
e
(2j
400 500 600 700 800 900 1000
~~~~
Fig. 6. The temperature dependence of e of B14T13012 film in "sandwich" configuration of Pt-B14T13012-Pt; 1) heating; 2) cooling.
(+~ 560) are observed in the both directions. The maxima at
+~ 950 K correspond to the phase
transition to the paraelectric phase. This fact agrees with the data obtained for crystals [12].
The temperature dependence of the dielectric constant for Pt-B14T13012-Pt structures in
planar configuration (in the direction perpendicular to the C-axis) is shown in Figure 7. As
seen in Figure 7, a snlall maximum of the dielectric constant is observed in the phase transition
region (r~ 950 K) on heating and on cooling. A small value ofe(r~ 120) points to the presence of
860 JOURNAL DE PHYSIQUE III N°7
e
200
(2) o
loo
Iii
0
400 500 600 700 800 900 1000
~nj~j
Fig. 7. The temperature dependence of e of B14T13012 film in
a planar configuration; ii heating;
2) cooling.
tan&
1
0.9 0.8
0.6 (~)
0.4
o ~ (2)
0.2 o-1 0
~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~
T (K)
Fig. 8. The temperature dependence of tan of B14T13012 film; 1) "sandwich" configuration; 2)
a
planar configuration.
polarization component in the given direction. The diffusion of the phase transition is probably explained by imperfection of the film structure.
The temperature dependence of the dielectric loss tangent (tan b) for such structures also has
a particular maximum in the phase transition region (Fig. 8). A characteristic temperature dependence of e and tanb indicates the presence of a spontaneous polarization in BTO layers leading to anomaly of electrical conductivity in structures based on the bismuth titanate.
4. Conclusion
Based on the studies carried out, one can conclude that the observed nonlinearity of the I U characteristics in Me-B14T13012-Me structures is attributed to intercrystalline potential barriers with a mean value of the barrier, 4lo r~ 0.12 eV, and a mean size of crystallites,
L
r~ 0.3 ~lm. The exponential dependence of conductivity in a high-temperature region,
T > 250 K, with a constant activation energy, E;
= 0.15 eV, and a decrease of activation
energy with decreasing temperature, as well as a linear dependence log(a) T~~R in the
low-temperature region and a low charge carrier mobility in bismuth titanate allow to assume
that, at low temperatures, a hopping conductivity is a dominant process of charge transfer.
The anomaly of electrical conductivity in the ferroelectric phase transition region for the struc-
tures with the different geometry is probably due to a spontaneous polarization in BTO layers.
The maxima of e and tan b in the phase transition region the diffusion of which is probably
attributed to a structural disordering of the film also point to the presence of a spontaneous polarization.
References
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[2] Krainik N-N-, MyInikova E-I-, Pometichenko S-F-, On the dielectric properties of B14T13012 crystals, Fiz. Tuerd. Teta 9 (1968) 260-263.
[3] Sugibuchi K., Kurogi Y. and Endo N., Ferroelectric field effect memory device using B14T13012 film, J. Appt. Phys. 46 (1975) 2871-2877.
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The proofs have not been corrected by the authors.
