PTCR characteristics of semiconducting barium titanate ceramicsproduced by high-energy ball-milling

K. Park Æ J.-G. Ha Æ C.-W. Kim Æ Jun-Gyu Kim

Received: 2 February 2007 / Accepted: 29 May 2007 / Published online: 22 August 2007

Springer Science+Business Media, LLC 2007

Abstract We studied the influence of potato-starch

content and ball-milling time on the positive temperature

coefficient of resistance (PTCR) characteristics of porous

and semiconducting barium titanate ceramics, which were

produced by high-energy ball-milling followed by solid

state reaction. The sintered samples at room temperature

crystallized in the tetragonal structure, irrespective of the

potato-starch content and ball-milling time. As the ball-

milling time increased, the porosity and pore size of the

samples decreased, while and the grain size increased.

Higher potato-starch content yielded a smaller grain size

and higher porosity. The potato-starch additive and ball-

milling time had little influence on the donor concentra-

tion of the grains. A larger PTCR jump was obtained with

the addition of potato-starch mainly as a consequence of

an increase in the porosity. A higher ball-milling time

yielded both lower electrical resistivity and a lower PTCR

jump.

1 Introduction

Pure barium titanate (BaTiO3) is an electrical insulator, because

of its large energy gap [1–3]. However, the barium titanate

becomes a semiconducting material after the partial substitution

of Ba2+ by trivalent cations, or Ti4+ by pentavalent cations [4–

7]. Semiconducting barium titanate ceramics show a positive

temperature coefficient of resistance (PTCR) characteristics [1–

26]. In 1971, Heywang [8] explained the PTCR characteristics

in terms of the double Schottky barriers at the grain boundaries.

According to this model, the barriers result from electron

trapping by acceptor states at the grain boundaries [12, 13].

Since then, the model has been extended by Jonker, considering

the influence of polarization on the resistivity below the Curie

point [9]. To date, various fabrication techniques have been

attempted to improve the PTCR characteristics [27–30].

It has been reported that porous BaTiO3 ceramics exhibit a

large PTCR effect [31]. The porous ceramics are more

favorable for forming surface acceptor states compared with

ordinary dense ones [31]. Also, the porous BaTiO3 ceramics

show better heat resistance than dense ones, and thus can be

used for PTC thermistors, which can protect against over-

current in electric circuits [14, 15]. It is generally accepted that

the composition and the processing of the thermistors signif-

icantly affect the microstructure and thus change the electrical

properties. In the present study, in order to fabricate porous

ceramics and to further improve the PTCR characteristics, the

addition of potato-starch in (Ba,Sr)TiO3 was attempted. Also,

we controlled the microstructure and electrical properties by

changing the high-energy ball-milling time.

2 Experimental

The semiconducting barium titanate samples containing

0–15 wt.% potato-starch were prepared by high-energy

K. Park

Department of Advanced Materials Engineering, Sejong

University, Seoul 143-747, South Korea

J.-G. Ha

Department of Electronic Materials Engineering, Kwangwoon

University, Seoul 139-701, South Korea

C.-W. Kim

Research Institute of Industrial Science & Technology (RIST),

Pohang 790-330, South Korea

J.-G. Kim (&)

Inorganic Chemistry Examination Team, Korean Intellectual

Property Office, Daejeon 302-701, Korea

e-mail: iamjgkim@hanmail.net

123

J Mater Sci: Mater Electron (2008) 19:357–362

DOI 10.1007/s10854-007-9343-0

ball-milling followed by solid-state reaction. The semi-

conducting barium titanate powders used were

commercially available high-purity (Ba,Sr)TiO3 powders

containing 25 mol% SrO and 0.2 mol% Y2O3 (Toho

Titanium Co. Ltd, Japan). The mean particle size and fer-

roelectric Curie temperature of the powders were 0.7 lm

and 61 C, respectively. The potato-starch powders (purity:

[99.9%, mean particle size: 25 lm, Shinyo Pure Chemi-

cals Co. Ltd, Japan) were added into the (Ba,Sr)TiO3

powders. A mixture of the (Ba,Sr)TiO3 and potato-starch

powders and ethanol was milled with a planetary mill

(Fritsch, Germany) at 500 rpm for 1–20 h using ZrO2 balls

(/ 2 mm) as a grinding media. Subsequently, the mixed

powders were dried at 100 C for 4 h. The resulting dried

powders were compacted by die-pressing at 40 MPa to

prepare the green compacts (15 · 12 · 7 mm3). The green

compacts were sintered at 1,350 C for 1 h in air and then

cooled to room temperature. The samples obtained are

given in Table 1.

A thermal analysis of the mixed powders was carried out

using a differential thermal/thermogravimetric analysis

(DT/TGA: SDT Q600) in the temperature range of 0–

1,000 C at a heating rate of 10 C min–1 in air. A scan-

ning electron microscopy (SEM: S-4200, Hitachi) was used

for the analysis of the microstructure of the sintered

ceramics. An X-ray diffractometer (XRD: PW-1710, Phi-

lips) was used in order to investigate the effects of the

potato-starch additive and ball-milling time on the crystal

structure. The grain size of the ceramics was estimated by

the line-intersecting method and the porosity and pore size

of the ceramics were measured with a mercury porosime-

ter. The electrical resistance was measured with a digital

multi-meter in air from 25 C up to 300 C. In order to

calculate the electrical potential barrier of grain boundaries

and the donor concentration of grains, the capacitance–

voltage (C–V) characteristics were measured with an

impedance analyzer at room temperature at a frequency of

10 kHz.

3 Results and discussion

We found that an increase in the ball-milling time leads to

a slight decrease in the powder size and in the narrow size

distribution. The SEM micrographs of the mixed powders

for samples P15(1H), P15(10H), and P15(20H) are shown

in Fig. 1a–c, respectively. The mean sizes of the powders

for samples P15(1H), P15(10H), and P15(20H) are 0.80,

0.71, and 0.62 lm, respectively. Moreover, the added

potato-starch did not significantly affect the thermal

behavior. The typical result of DT/TGA measurements for

Table 1 Summary of the samples prepared in this study

Sample Ball-milling time (h) Potato-starch content (wt.%)

P0(1H) 1 0

P5(1H) 1 5

P10(1H) 1 10

P15(1H) 1 15

P15(5H) 5 15

P15(10H) 10 15

P15(15H) 15 15

P15(20H) 20 15 Fig. 1 SEM micrographs of the mixed powders for the potato-starch

added samples (a) P15(1H), (b) P15(10H), and (c) P15(20H)

358 J Mater Sci: Mater Electron (2008) 19:357–362

123

the mixed powders of sample P15(1H) is shown in Fig. 2.

Two exothermic peaks, accompanied with a great weight

loss, are seen in the temperature range of 260–460 C. It

was found that the results of DT/TGA for the other samples

were basically the same as those of sample P15(1H).

The XRD patterns measured at room temperature for

samples P0(1H)–P15(1H) milled for 1 h are shown in

Fig. 3. The diffraction patterns show reflections of a sin-

gle (Ba,Sr)TiO3 phase with the tetragonal structure. No

secondary phase such as carbon was detected. Also,

because the lattice parameters of the tetragonal and cubic

phases in (Ba,Sr)TiO3 are quite similar, we analyzed the

diffraction patterns at high angles. In Fig. 3, the (103) and

(310) peaks of the tetragonal phase are detected at

2h = 75.21 and 75.75, respectively. The reflected peaks

are slightly shifted towards higher angles compared with

BaTiO3 because the added Sr is present at the Ba site of

the (Ba,Sr)TiO3 lattice. The ionic radii of Sr and Ba atoms

are 1.16 and 1.35 A, respectively [32]. It was also found

that the diffraction patterns at room temperature for the

other samples ball-milled for 5–20 h were basically

equivalent to those of Fig. 3. These results indicate that

both the potato-starch content and the high-energy ball-

milling time had no significant influence on the crystal

structure.

Figure 4 shows the dependence of the electrical resis-

tivity on temperature for samples P0(1H)–P15(1H) milled

for 1 h, showing PTCR characteristics. Higher potato-

starch content yielded a larger PTCR jump. The PTCR

jumps of samples P0(1H), P5(1H), P10(1H), and P15(1H)

are 3.01 · 105, 3.03 · 105, 3.08 · 105, and 4.97 · 105,

respectively. The highest PTCR jump was obtained for

sample P15(1H). In addition, the electrical resistivity of the

potato-starch added samples P5(1H), P10(1H), and

P15(1H) was higher than that of the potato-starch-free

sample P0(1H) over the measured temperature range. In

order to reduce the resistivity of the potato-starch con-

taining samples, we ball-milled for a longer time (5–20 h)

and controlled the microstructure.

Figure 5 shows the electrical resistivity as a function of

the temperature for samples P15(1H)–P15(20H) ball-mil-

led for 1–20 h. A higher ball-milling time yielded a lower

electrical resistivity. For example, the room-temperature

resistivities of samples P15(1H), P15(10H), and P15(20H)

are 1.40 · 102, 9.55 · 10, and 5.02 · 10 X cm, respec-

tively. In addition, a lower PTCR jump was observed with

ball-milling time. The PTCR jump of samples P15(1H),

P15(10H), and P15(20H) are 4.97 · 105, 3.19 · 105, and

1.11 · 105, respectively. Room-temperature electrical

resistivity (q25 C), maximum electrical resistivity (qmax),

and PTCR jumps (qmax/q25 C) of all the samples are given

in Table 2. In order to understand the change in electrical

0 200 400 600 800 1000

)%( thgi e

W

Temperature ( οC )

oxE odn

E

Fig. 2 Result of DTA and TGA measurements for the mixed

powders of the potato-starch added sample P15(1H)

20 30 40 50 60 70 80

73 74 75 76 77 78

73 74 75 76 77 78

) 013()301(

73 74 75 76 77 78

)013(

)301(

yti sn etnIytisnetnI

) 013()301(ytisnetnI

Degree (2θ)

Degree (2θ)

Degree (2θ)

OO

OO

OO

OO

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

O

P5 (1H)

P0 (1H)

P15(1H)

P10(1H)

O (Ba ,Sr)TiO3

(a. u

.) ytisnetnI

2θ (degree)

Fig. 3 XRD patterns measured

at room temperature for samples

P0(1H)–P15(1H) milled for 1 h

J Mater Sci: Mater Electron (2008) 19:357–362 359

123

resistivity depending on the potato-starch content and ball-

milling time, as shown in Figs. 4 and 5, we investigated the

microstructure, the donor concentration of grains and the

electrical barrier height of grain boundaries.

The SEM images from the fractured surfaces for the as-

sintered samples P15(1H), P15(10H), and P15(20H) are

shown in Fig. 6a–c, respectively. The samples were highly

porous, which are favorable to oxidize the grain boundaries

[31]. With increasing ball-milling time, the porosity and

pore size of the samples decreased and the grain size

increased due to the pore pinning effect. These results are

responsible for the increase in the time between the

scattering events of charge carriers, thus decreasing the

resistivity. Furthermore, we found that a higher potato-

starch content yielded smaller grain size and higher porosity

(not shown here). The higher porosity is caused by the pores

formed due to the burn-out of potato-starch during sintering.

The porosity, mean pore size, and mean grain size for all the

samples prepared are summarized in Table 3.

The plots of the capacitance versus the applied voltage

at room temperature for samples P0(1H) and P15(1H) are

shown in Fig. 7, showing a nearly linear dependence

between the two parameters. The donor concentrations of

the grains and the electrical potential barriers of the grain

boundaries for all the samples are calculated using the

equation proposed by Mukae et al. [33] and summarized in

Table 4. According to Table 4, the potato-starch content

and ball-milling time did not cause a noticeable change in

the donor concentration of grains. However, at a fixed ball-

milling time of 1 h, the added potato-starch leads to an

increase in the electrical barrier height of grain boundaries

mainly because of the oxidation of the grain boundaries.

The oxygen in the porous ceramics is adsorbed at the grain

boundaries during sintering in air, thus increasing the

electrical potential barrier height, which results from an

increase of surface states density [8, 12, 13, 31]. Also, at a

given potato-starch content of 15 wt.%, the electrical bar-

rier height of grain boundaries decreased as the ball-milling

time increased.

From the above electrical and microstructural proper-

ties, an increased resistivity with potato-starch content is

attributed to an increase in the electrical barrier height of

grain boundaries, porosity and the grain boundary area. In

addition, a decreased resistivity with ball-milling time is

largely due to a decrease in the electrical barrier height,

porosity, and grain boundary area. Furthermore, the PTCR

jump slightly increased with the potato-starch content as a

consequence of an increased porosity, which can be

explained by the barrier model proposed by Heywang [8,

12, 13]. We propose that the addition of potato-starch is

0 50 100 150 200 250 300101

102

103

104

105

106

107

108

P15 (1H) P15 (5H) P15 (10H) P15 (15H) P15 (20H)( ytivitsiser la cirtcel

EΩ

)mc

Temperature ( )°C

Fig. 5 Electrical resistivity as a function of temperature for samples

P15(1H)–P15(20H) ball-milled for 1–20 h

0 50 100 150 200 250 300101

102

103

104

105

106

107

108

P0 (1H)P5 (1H)P10 (1H)P15 (1H)

( ytivitsiser lacirtcelE

Ω)

mc

Temperature ( )°C

Fig. 4 Dependence of the electrical resistivity on temperature for

samples P0(1H)–P15(1H) milled for 1 h

Table 2 Room-temperature electrical resistivity (q25 C), maximum

electrical resistivity (qmax), and PTCR jumps (qmax/q25 C) for the

samples

Sample q25 C (X cm) qmax (X cm) PTCR jump

(qmax/q25 C)

P0(1H) 3.18 · 10 9.57 · 106 3.01 · 105

P5(1H) 5.05 · 10 1.53 · 107 3.03 · 105

P10(1H) 9.09 · 10 2.80 · 107 3.08 · 105

P15(1H) 1.40 · 102 6.96 · 107 4.97 · 105

P15(5H) 1.16 · 102 3.06 · 107 2.64 · 105

P15(10H) 9.55 · 10 3.05 · 107 3.19 · 105

P15(15H) 7.80 · 10 1.50 · 107 1.92 · 105

P15(20H) 5.02 · 10 5.57 · 106 1.11 · 105

360 J Mater Sci: Mater Electron (2008) 19:357–362

123

desirable for an increase in the PTCR jump and an increase

in milling time leads to a decrease in the resistivity over the

measured temperature range.

4 Conclusions

The crystal structure, microstructure, and electrical prop-

erties of the porous and semiconducting barium titanate

ceramics, which were produced by high-energy ball-mill-

ing followed by solid state reaction, were studied. The

results obtained are as follows:

(1) The XRD patterns show reflections of a single

(Ba,Sr)TiO3 phase with the tetragonal structure. Both

the potato-starch content and high-energy ball-milling

had no significant influence on the crystal structure.

(2) With increasing ball-milling time, the porosity and

pore size of the samples decreased and the grain size

increased due to the pore pinning effect. Higher

potato-starch content yielded a smaller grain size and

higher porosity.

Fig. 6 SEM images from the fractured surfaces for the as-sintered

samples (a) P15(1H), (b) P15(10H), and (c) P15(20H)

0.0 0.5 1.0 1.5 2.0

1

2

3

4

5

6

7

8

Applied voltage per grain boundary (10 -3 V)

C2(/1-C/1

0)2

01( 6

mc 4

F/2)

P15(1H) P0 (1H)

Fig. 7 Plots of the capacitance versus the applied voltage at room

temperature for samples P0(1H) and P15(1H)

Table 3 Porosity, mean pore size and mean grain size of the samples

Sample Porosity

(%)

Mean

pore

size (lm)

Mean

grain

size (lm)

P0(1H) 7.18 0.28 6.71

P5(1H) 15.86 0.92 5.76

P10(1H) 20.95 1.45 5.01

P15(1H) 25.87 2.47 4.68

P15(5H) 24.71 1.93 5.52

P15(10H) 22.83 1.55 6.45

P15(15H) 17.75 0.98 7.43

P15(20H) 15.53 0.42 7.91

Table 4 Donor concentrations of grains and electrical potential

barriers of grain boundaries at 25 C for the samples

Sample Donor concentration

of grains (#/cm3)

Electrical potential barrier

of grain boundaries (eV)

P0(1H) 5.12 · 1018 0.005

P5(1H) 4.67 · 1018 0.008

P10(1H) 4.52 · 1018 0.014

P15(1H) 4.38 · 1018 0.022

P15(5H) 4.45 · 1018 0.018

P15(10H) 4.51 · 1018 0.015

P15(15H) 4.59 · 1018 0.012

P15(20H) 4.78 · 1018 0.008

J Mater Sci: Mater Electron (2008) 19:357–362 361

123

(3) The potato-starch additive and ball-milling time did

not cause a noticeable change in the donor concen-

tration of grains.

(4) As the potato-starch content increased, the resistivity

also increased due to an increase in the electrical

barrier height of grain boundaries, porosity and grain

boundary area and the PTCR jump increased as a

consequence of an increased porosity.

(5) A higher ball-milling time yielded a lower electrical

resistivity and a lower PTCR jump. The lower

electrical resistivity was attributed to an increase in

the electrical barrier height of the grain boundaries,

the porosity and the grain boundary area.

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