Contact resistance of the electrodes on semiconducting ceramics

0038-1098/87 $3.00 + .00 © 1987 Pergamon Journals Ltd.

Solid State Communications, Vol. 64, No. 4, pp. 617-619, 1987. Printed in Great Britain.

C O N T A C T RESISTANCE O F T H E E L E C T R O D E S ON S E M I C O N D U C T I N G CERAMICS Sang-Ok Yoon and Hyung-Jin Jung Inorganic Materials Laboratory, KAIST, Seoul, Korea and Ki-Hyun Yoon Department of Ceramic Engineering, Yonsei University, Seoul, Korea

(Received 14 May 1987 by H. Kamimura) The electrical contact resistances of several different kinds of electrode on a semiconducting BaTiO3 ceramic body were measured both by 2-probes method using the thickness varying and the complex impedance method. These two methods are easily available and agreed well with each other in the case of lower ohmic contact electrode, but for the higher ohmic contact resistances the contact resistances could be obtained by the complex impedance method only. 1. I N T R O D U C T I O N T H E ROLE OF E L E C T R O D E S is very important for the measurement of the electrical properties on semiconducting ceramics. In the selection of electrodes, we must consider that which is ohmic or nonohmic and low resistance ohmic or high resistance ohmic contact. Generally, I n - G a alloy and electrolysis Ni electrode are applied at low resistance ohmic contact in character and Ag, Au, Pt and etc. are high resistance [1, 2]. The measuring methods of the resistivity concerned with a semiconductor are 2-probe, 3-probe, 4-probe and multi-probe methods [3], and in these methods, the bulk resistance can be simply measured by 2-probe method with an electrode. But the measured resistance (Rm) contains not only a bulk resistance (Rb) of the specimen but also a contact resistance (Rc) of the electrode, that is, R m must be corrected by the term of the contact resistance of the electrode. If the R, has a much higher value compared with the Rb, Rm cannot be used in calculating the bulk resistivity in case of the semiconducting ceramics. Therefore, in this study the contact resistance of several electrodes were calculated by using the thickness varying method and complex impedance method on the semiconductive barium titanate ceramics.

Nb205 and small amounts of sintering additives such as AI2 03, SiOz were mixed and grinded in zirconia ball mill with distilled water for 10 h, and completely dried at 120°C. The mixed powders were pressed into rectangular rods (7.7 x 8 × 35ram) under pressure of 500kgcm 2 and then sintered at 1350°C for 2 h in air on Pt plate in an electrical furnace. The sintered matters were then sliced into various thickness of about 0.5, 1, 1.5, 2 and 2.5 mm, in order to give a uniform area (6.6 × 6.8ram) and also prevent the possible effect of surface oxidation. After polishing the surfaces slightly, electrodes were coated on both surfaces by various methods such as electrolysis plating [4, 5] rubbing, evaporating and brushing. D.c. resistance of specimens was measured using d.c. powder supply (GPO 16-10, Takasago Co., Japan) and digital multimeter (175, Keithley Co., USA) from current-voltage characteristics. And the complex impedance measurement with changing frequency was carried out in the range of 5 Hz to 13 M H z by LF impedance analyzer (4192A, Hewlett Packard Co., USA).

2. E X P E R I M E N T S The specimens were parepared by the conventional ceramic process. BaTiO 3 powder ( > 9 9 % . Ferro Corp., Transelco Div., U.S.A.), 0.2mo1% 617

3. RESULTS A N D DISCUSSION Figure 1 shows the relationship between measured resistance and thickness of the specimens. Actually, the measured resistance (Rm) of the specimen consists of the bulk resistance (Rb) which is proportional to the specimen thickness and the contact resistance (Re) of the electrode which is not concerned with the specimen thickness and constant value. Thus the relationship between the measured

618

ELECTRODES ON SEMICONDUCTING CERAMICS

Vol. 64, No. 4

" Ni 1.75mm • In-Ga 1,8 rnm

~3 o

eln-Ga

/

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6C

100K

°

%,

E

2M i ,

er

1

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(a )

,, AI t 0 m m 2

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mm

o

x N

o'.s

;.o

~.'s

d [ram ]

5O/~ i

.

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Fig. 1. Relationship between measured resistance and specimen thickness for In-Ga and Ni electrode.

(1)

Therefore, the contact resistance (R,.) can be separated from the measured resistance (R,,) with changing thickness of the specimen by the above equation. In this figure the measured values are clearly proportional to the increase of the specimen thickness, and agreed well with equation (1). The constant term is approximately below 1 D and means the contact resistance of these electrodes. And also, the slope (Q/A) of Ni and In-Ga electrode appear at 1.455 and 1.636, respectively. This difference can be understood by influence of the immersed Ni plating solution through the pores and defects within the body in electroding process. When the Rc is much higher than the Rb, it is very difficult to find the tendency corresponding with the specimen thickness by the equation (1). Figure 2 shows the complex impedance diagrams of the In-Ga and Ni electrodes (a), A1 and Au electrodes (b) and Pt electrode (c). A semiconducting ceramic contains free electrons generated within grains and electrons trapped at grain boundaries. Thus a depletion layer is formed within

bt~z 4

3

Z IX 102ohm]

(b)

resistance (Rm) and the specimen thickness (d) can be represented as follows; R,, = ~ d + R,.

2

~

Pt 1,5ram 3

'O 2

x N

p,°'5 g

~IK

\ 5

Z [X10"3 ohrn]

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Fig. 2. Complex impedance diagrams of In Ga and Ni electroding (a), A1 and Au electroding (b) and Pt electroding specimens (c). the grain on either side of the grain boundary. And also, another depletion layer is formed between electrodes and both surfaces of specimen due to the junction of the semiconductor and metal. This semiconducting ceramic with the electrodes can be expressed an equivalent circuit as shown in Fig. 3. The complex impedance method for the equivalent circuit was introduced by Bauerle on zirconia solid electrolytes [6]. A measured complex impedance (Z) is separated a real part (Z') and a imaginary part (Z") of the impedance by changing frequency as the following equations;

Rgb

Rel

Table 1. The contact resistance o f different kinds o f electrode on a same bod o f BaTiO Electrode

Cgb

Ni

Gel

Fig. 3. Equivalent circuit of a semiconducting ceramic with electrode. Rg. b Z

= Rg+ 1 +

_

v~,2~2 Kg.b([72.b

Rel + 1 + w 2RelC 2 2

(

\

619

E L E C T R O D E S ON S E M I C O N D U C T I N G CERAMICS

Vol. 64, No. 4

+

J 1 + w *xg.btg. b .

2 n2

,,'~2

_Ro, Ce,

Method Electroless

Heat Trea tm,er,t Plating

In-Ga

Rubbing

~0

AI

Evapilrating

NO

Au

Evaporating

Pt +

Brushing

C o n t a ( t Resistance(i~hm)

o50°C, ?0 min

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1200°C, 10 min

4.5

-

5

x 102

- 6.5 × 103

+ 4052C Ferro Co., U.S.A.

)

1 + w2R~IC~2/

(2)

where, w is a frequency. Rg, Rg.b and Rel are the resistance of grains, grain boundaries and electrodes respectively. And Cg.h and C~l are the capacitance of grain boundaries and electrodes. According to the equation (2), it is expected to become Z ~ R e in a high frequency region, and the Z agrees with R~ -'k Rg.~ + R d in a very low frequency region. The contact resistance of electrodes can be separated from the measured impedance of the specimen in a low frequency region. As shown in Fig. 2(a), the contact resistances of both electrodes are very low in comparison with the bulk resistances on the specimens. The value of the contact resistance of both faces is about 0.7 f~ for the heated Ni electrode and about l f2 for the In Ga electrode. Thus the contact resistance of electrode is to be negligible for the electrodes having such a low ohmic contact. In Fig. 2(b), bulk resistance and electrode resistance are clearly separated from the measured resistance, and this phenomena agree very well with the suggested equivalent circuit on semiconducting ceramics as represented in Fig. 3. The bulk resistance increases with increase in the specimen thickness and the contact resistances of the electrodes are approximately in the range of 300 to 500 f~ for Au and 250 to 350f~ for AI. For electrode having high contact resistance, the complex impedance diagram is appeared like Fig. 2(c). Where the most of measured resistances seems to be due to the portion of electrode contact, and on the

other hand the bulk resistance is nearly neglected. The contact resistance of the Pt electrode is approximately sited in the range of 4.5 to 6.5 Kf~. Therefore, in the case of semiconducting ceramics with high ohmic contact of electrode, the measured resistance is mostly due to the contact resistance of the electrode. 4. C O N C L U S I O N The contact resistance of several different kinds of electrodes on the both faces of a semiconducting ceramic body were experimentally obtained as given in Table 1. The contact resistance of the electrode can be measured either by the 2-probes method with the thickness varying and the complex impedance method. Both methods are easily available and agreed very well with each other for the electrodes having lower ohmic contacts. But the electrodes for higher ohmic contacts, the contact resistance can be obtained only by the complex impedance method.

REFERENCES 1. 2. 3. 4. 5. 6.

H.A. Sauer & S.S. Flaschen, Proc. Electronics Comp. Symp. p. 41, Publishers, New York (1956). H.M. Landis, J. Appl. Phys. 36, 2000 (1965). N.M. Tallan, Electrical Conductivity in Ceramics and Glass, Part A, p. 93, Marcel Dekker Inc., New York (1983). T. Nitta, K. Nagase & S. Hayakawa, J. Am. Ceram. Soc. 49, 457 (1966). D.R. Turner & H.A. Sauer, J. Electrochem. Soc. 107, 250 (1960). J.E. Bauerle, J. Phys. Chem. Solids 30, 2657 (1969).