Dielectric relaxation assessment of a heat treated metal oxide varistor

H.S.B. ElaWan and S.N. AI-Refaie

Abstract The dispersion of the dielectric constant and the electrical conductivity of a metal oxide varistor depends on the heat treatment procedure during the production process of the device. 'This dependence is investigated quantitatively using a multiple-arc approach that yields the dielectric relaxation of the material. This analysis method provides an equivalent network representation that adequately simulates the experimentally measured data for devices produced using different heat treatment temperatures. The distributed and discrete networks derived from the proposed approach can be either passive or active in nature. The latter type is used to account for the negative capacitance introduced by the arc analysis.

1 Introduction

A metal oxide varistor (MOW can be made from a zinc oxide (ZnO)-based ceramic with oxide additives such as Biz03, Mn02, COO and Sh203. The sintering technique used in the production process results in a polycrystahne structure that contains conductive ZnO grains surrounded by insulating oxides that produces highly non- linear current-voltage (I-V) characteristics. These character- istics have been successfully used in the development of improved devices for the protection of electrical and electronic circuits and equipment against transient over- voltages. Intensive research work has been conducted over many years by chemists, physicists and electrical engineers with the aim of understanding the mechanisms involved in the conduction process and the dielectric phenomenon exhibited by the material [I-51. Experimental research work has shown that the electrical characteristics of the device are dependent on many factors including: (i) the temperature; (ii) the magnitude and frequency of the applied voltage; (iii) the microstructure constituents; and (iv) the sintering process involved in the production of the device [6-9]. This may justify the on-going debate and continuing research activities worldwide devoted to this multidisciplinary subject in order to achieve a comprehen- sive understanding of the overall behaviour of the MOV action based on microscopic consideration and macroscopic observations.

Under a normal operating voltage and a low applied field, the varistor behaviour can be adequately described by linear response theory, since the I-V characteristics are almost linear, and the current flowing in the device is predominantly capacitive with a small conductive leakage current component. An improved understanding of the dielectric response of the material is vital for the manufacturing of the device, and monitoring its interaction

0 IEE, ZW3 IEE Proceed@ online no. 20030453 doi: IO. 1049/ip-smt:2W30453 Paper fin1 received ZGih September 2WZ The authors an with the Al-€ljaG Faculty for Enineenng Technology, Yarmouk University, Irbid, Jordan

IEE Proc.-Sci Me-. Techno!.. VoL 150, No. 4, July2003

with other circuit components. Experimental research work has revealed several important features conceming the dielectric behaviour of the material. Among these features are the anomolously high dielectric constant, and the dependence of this constant on both frequency and temperature. Additionally, the AC conductivity and the dissipation factor of the material are temperature and frequency dependent. The temperature dependence of the various dielectric parameters is not conlined to heat treatment during production, hut is also observed during varistor service. The dielectric behaviour of the material is also manifested by the occurrence of a relaxation phenom- enon that deviates considerably from pure Dehye relaxation behaviour. Although this phenomenon has been extensively researched for various types ofdielectric materials [IO], there is growing interest in this phenomenon for electrical characterisation of the MOV device [ I l l . In an earlier research work by the authors, a generalised relaxation time distribution methodology based on a multiple-an: approach was developed and utilised in deriving equivalent circuits that adequately described the frequency dependent proper- ties of the device operating at room temperature [12]. This methodology will now be extended in order to investigate the effects of heat treatment on the dielectric properties of the ZnO ceramic. The validity of the reported modelling approach will be examined by a comparison with published test data.

2 Multiplearc analysis

2.1 General Theory Although various approaches have been proposed to analyse the dispersion of dielectric constants, the multiple- arc method has, in principle, no limitations and is potentially applicable to various dispersion data. The method analyses the dispersion in terms of the relaxation time distribution (RTD). This is facilitated using the dielectric constant complex plane whereby the real and imaginary parts of the constant, E = E' - jd', are employed to generate multiple circular arcs over the frequency range in use. The process is based on the argument that the loss part of the constant at a particular frequency is simply the sum of the losses of the arcs at that frequency. The

141

produced arcs are then used to determine the RTD function, f (U) [13]:

where

with

J-W

c, and E,, are the low- and high-frequency constants of the nth arc respectively, while m designates the number of arcs traced over the frequency range used with a, being the Spread parameter for the nth arc and has a value between zero and one. T, is the most probable relaxation time for the nth arc, while io, represents an arbitrarily chosen low frequency reference arc.

For a relation characterised by a single arc, ( I ) reduces to the form corresponding to a Cole-Cole plot. As a matter of fact each component in ( I ) resembles that for a Cole-Cole relation for a particular arc niultiplied by the arc's weighting factor,

This would imply that (1) allows the analysis of any range of data as the terms would be adjusted in accordance with the determined parameters. Meanwhile, it is essential to emphasise that a valid arc maintains the relation In(u,/ U,)= (I-a,,)ln(or,) over its range of frequency, where U, and U, are the intervals from a point on the presumed arc to em and E,,, respectively, as shown in Fig. (I). This is implemented simply by plotting In (U&") against In (U). A near-linear relation would then validate the arc and additionally determines the T~~ value. It follows therefore that a deviation of the data from this relation means a new circular arc should be traced and specified. The procedure is then repeated over the whole range from high to low frequency, and so yielding m arcs, each defined by four parameters.

Fig. 1 Generalised multiple-arc representarion

The evaluation of the RTD function provides an effective means to investigate the various factors that influence the dispersion in dielectrics, e.g. annealing and temperature effects, particularly in composite materials, such as ceramics and polymers. By introducing the dispersion

I42

parameters [14]:

(2) dr. au

Z(u) =- aU and $(U) =- dU

the real and imaginary components of the dielectric constant can then be expressed in terms of the RTD function as [12, 141:

and

where u denotes the AC conductance and E,, corresponds to the highest frequency arc.

2.2 Overlapping arcs Equation (3) is only applicable for those relations featuring a negligible overlap of the arcs, such as in the case of pure ZnO where the weak overlapping in the E" - E' relation yielded less than a 1% error in the ~ ' ( 0 ) value 1151. On the other hand, for relations that do feature pronounced overlapping, as illustrated in Fig. 1, ~ ' ( w ) , as given by (3), may be larger than the real value particularly at the low frequency range. This can be verified by examining (3) as w + 0 where:

with E , being the static dielectric constant. This error in the &'(CO) value can be rectified by

subtracting the range of overlapping between two con- secutive arcs, e.g. the AB range shown in Fig. 1 at a very low frequency. More detailed discussion in devising an appropriate correction term, E ~ ( w ) , is given in [ I Q Accordingly, ~ ' ( w ) takes the new generalised form:

&'(U) =E,, - & ( U )

where

( 6 ) and f i ( u ) and f n ( u ) are, respectively, the distribution components of arcs I and 11, Fig. 1, given by (I). Also uI and y~ are the integral limits corresponding to the AC and CB values in Fig. 1, respectively, so that

Point C can be determined algebraically once the para- meters of the consecutive arcs are known.

2.3 Network representation Equations (3) and (4) facilitate the direct network represent- ation for dispersion in a distributed form. Subsequently, an

IEE Pror-Sci Meor TechmL. Vol. ISO, No. .I July ZW3

incremental part of the network is modelled by a parallel branch consisting of a series of connected resistance- capacitance (R-C) elements, as depicted in Fig. 2. The capacitive and conductive components are expressed in terms of the dispersion parameters E(u) and u(u) , given in (2), respectively,

where

0 I I

I 7 Fig. 2 The parsive distributed R-S equitialenr network

However, for strongly overlapping arcs for which (3) is replaced by ( 5 ) the passive network modelling is not applicable since the pure capacitive branch becomes frequency dependent. Alternatively, network components independent of frequency can be realised by introducing active elements into the network. This can be achieved using negative impedance converters (MCs) along with passive R- C elements to model the negative of each term in (6) [16], as shown in Fig. 3. Over the range -m <u<uI , the dispersion parameters corresponding to the first term of (6) are given as [17)

NlC

k m

Fig. 3 An incremental brunch in the uctive distributed network

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and over the range uI1 < U < a, for the second term: m

&II(U) = (&s"-&mn)hl(u)/2 UJa)

Bcll(U) = EoEcll(U)/T (116)

"=I

Thus, the resulting distributed network becomes that of Fig. 2 in parallel with the branches corresponding to the term-n,(w) with its four incremental elements given as:

6Em = ,aU (12a)

hum = omau (12b) where n corresponds to I and 11.

Now, with the dispersion parameters derived for both types of arcs overlapping, we can convert the network into a discrete form by simply dividing the effective u-range to a finite number of equal segments, each of Au interval. An interval is then modelled by a branch with its components being given as:

for the passive part covering the whole effective u-range, and

for the active part over the range - u l l < u c a, and

&K = 2 (em - 8") 1 fil(U)aUldu/2 (15h) "=I

or the active part over the range ~ CO i U < uI. K designates branches in the passive and active parts of

the network. The multiple-arc analysis technique outlined above is illustrated by means of a flow chart in Fig. 4. The utilisation of this approach in the analysis of the dispersion relation of a heat treated MOV will now be presented.

3 Characterisation of dispersion in heat treated MOV

Kawamura PI al. [I81 reported an experimental investigation of the effect of heat treatment on the dielectric properties of a MOV ceramic. The samples used in the investigation were prepared by sintering at 1200°C. and then heat treated at various temperatures between 450°C and 900°C. The dielectric properties of the samples were measured at 0 "C in the frequency range lOOHz-100kHz. The results of that investigation are used here in conjunction with the multiple- arc analysis in order to study the effects of heat treatment on the dispersion characteristics of the MOV. The reported experimental variation of the dielectric constant and tans were used to obtain Cole-Cole plots as shown in Fig. 5. The fitted arcs yielded the dispersion parameters given in

143

consider the high frequency part of the data

i estimate an initial circular arc

determine cs, s-, r from the arc

I calculate U,.& Yo I

/-_z

no

find r,fromthe graph U subtract the i ' f rom the data

z

<do the remaining dsts prescribe a n y yes

State narcs parameters

I 1 passive network active network active network passive netwom

Fig. 4 Nehvork evaluation procedure flow chart

4 measured at 600 'C - computed

?. 50

0 350 400 450 500 550 600 650 700

a

I 0 measured at 750 'C I

100 200 3 W 4 W 5 W 600 700 800 c' b

Fig. 5 Cole-Coleplots a The case of no heat treatment and heat treated a t 6M)"C b Heat treated at 750°C and 900°C

144

Table 1. These parameters are then used to determine the relaxation time distributions at different temperatures as shown in Fig. 6.

The validity of the computed results using the multiple- arc analysis technique is examined by a comparison of the measured data as shown in Figs. 7 and 8, for two arcs obtained for no heat treatment and heat treated MOV at 600 "C, while single a r a are traced for heat treated MOV at temperatures of 750 "C and 900 "C. Generally, satisfactory agreements are obtained within an error of 5 10% over a substantial part of the frequency range.

4 Discussion of results

The macroscopic properties of the MOV ceramic are determined by the heat treatment and also the chemical and structural properties that prevail on the microscopic level. Optimisation of the design and manufacture of the ceramic requires the ability to control the microstructure, and suitable tools to characterise the resulting behaviour under different operating conditions. Therefore, adequate theore- tical models that describe such a behaviour are welcome

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Table 1: Dielectric dispersion parameters for different heal treated MOV samples

0.8

0.7

0.6

No heat treatment 0.225 580 700 1.65 0.24 505 586 0.92

600 0.275 432 547 2 0.2 358 432 3.2

150 0.46 163 800 0.91 - -

900 0.273 115 620 0.590

- ~

- ~ - ~

-

I no heat treatment "cl 0.25 [ heat treated at 600

0 . -10 -5 0 5 10 15 "

a

0.35

- . - heat treated at 900 "C

b

Fig. 6 Relaxation time diwibutions n Thc case of no heat treatment and heat treated at 600°C b Heat treated at 750°C and 9 W T

contributions towards an improved understanding of the material.

The heat treatment of the material is associated with significant changes in the dielectric constant as shown in Fig. 5. For the no heat treatment and heat treated at 600 "C samples, the Cole-Cole plots are characterised by double arcs. The no heat treatment Cole-Cole plot also shows a small amount of overlapping of the arcs. This overlapping can he accounted for by the negative capacitance behaviour of the device. Such an anomalous behaviour, has also been detected in a GaAs FIR structure subjected to a variable frequency, temperature and applied field, and has been attributed to carrier capture and emission at the interface [19]. Heat treatment at temperatures of 750°C and 900°C

IEE Pm.-Sc;. Mea. TechnoL. VoL 180, No. 4, July 2033

+ measured (no heat treatment) A measured (heat treated at 600 "c) 0 meeured (heat treated at 750 "C)

measured (heat treated ai 900 'C) - computed

^^^

4w 500R @.

- \

n.

100t.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 lOQ(fI

Fig. 7 constants for d$/erently heat rreated MOV samples

A comparison between measured and computed dielectric

0.5 1

+ measured (no heat treatment) A measured (heat treated at 600 "C) 0 measured (heat treated at 750 "C) Q measured (heat treated at 900 ' C ) - COmDuted

E 0.4

0.3

I

0.2

0.1

0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Wf)

Fig. 8 A comparison between mewred and computed ran 6 mlues /or dij'&/y heat treated MOV samples

yields Cole-Cole plots that display single arcs with a significant increase in the imaginary component of the dielectric constant, and a real part that spreads over a wider relaxation range. The corresponding relaxation time distributions undergo significant changes in both magnitude and shape as shown in Fig. 6. The double peaks found in the cam of no heat treatment and a heat treatment of 600 "C become single peaks for the other temperatures. The modification of shape and magnitude of the relaxation time distribution spectra may indicate that microstructural changes take place as a result of the heat treatment. This is clearly manifested in the results of Figs. 7 and 8, where

145

the dielectric constant and tan6 become more frequency dependent at higher temperatures as compared with lower temperatures. This may reflect the phase transition that occurs as a result of the heat treatment. The narrow relaxation time distributions obtained at higher tempera- tures is a further indication of the microstructural changes in the material that result in it becoming less disordered as a result of the heat treatment. It has been confirmed experimentally that the heat treatment enhances the densification of the MOV ceramic by rapid rearrangement of ZnO grains, and the improvement of ZnO-ZnO direct contacts [XI. The resulting heat treated material is homo- geneous, has a uniform doping distribution and grains with a'narrow size distribution [9]. The heat treatment has the effect of inhibiting local high currents caused by single large grains, and also results in an increase in the bulk conduction in the material. Furthermore, local polarisation caused by the inter-granular (additive) oxides also diminishes because of the improved homogeneity of the ceramic as a result of the heat treatment, and the shunting effect of the ZnO grains. Based on these considerations, the transitional behaviour of the dielectric properties of the MOV, as can be seen from Fig. 5 , can be related to the microstructural changes that occur in the material. For heat treatment temperatures of up to 600°C the Cole-Cole plot is characterised by two arcs, which can be categorised as low frequency and high frequency arcs. The low frequency arc can be associated with the dielectric behaviour of the additive oxides that constitute the insulating layers between the ZnO grains. At higher frequencies, the dielectric behaviour can be associated with the 2110 grains. Above a transition temperature, which lies in the range 60G750 "C, the Cole-Cole plot is characterised by a single arc, indicating the disappearance of the multi-phase microstructure of the material. The dielectric properties of the resulting new, lossy and homogeneous microstructure is dominated by that of ZnO grains, thus tracing a single arc Cole-Cole plot.

The decrease of the polarisation with increasing tem- perature for a given operating frequency is evident from the results of Fig. 7, particularly at high frequency. This behaviour can be expected, since the randomisation induced by thermal motion reduces the average magnitude of the charge separation induced by the applied field. The frequency dependence of the dielectric constant of the material at lower temperatures exhibits different trends as compared with that at higher temperatures. This major change is seen as an indication of changes occumng in the material hulk properties as a result of the heat treatment. Similar comment e n be made regarding the variation of the tan6 with both frequency and temperature, as shown in Fig. 8 where the double broadened, and nearly smeared out, peaks observed at low temperatures become single peaks at higher temperatures. In this context, the RTD function f ( u ) leads to a markedly improved spectra resolu- tion compared to the tanS-o relation, particularly for multiple arcs. For instance, the detection of resonance peaks and their locations is significant in identifying or characterising the underlying mechanisms goveming the dielectric dispersion.

It is clear from the results of Figs. 7 and 8, that the multiple-arc analysis approach has successfully simulated all the features associated with the heat treatment of the MOV ceramic. Furthermore, this methodology is exploited in deriving an equivalent network for the dielectric. Although the differential expressions, (2H12), imply a distributed network, viable representation lies with the discrete ones. This is simply achieved by dividing the effective u-range into finite segments, AIL, each representing a series R-C branch as

146

+* +: p , * * + *

+ computed using discrele network ) k a t treated tit 750 'C - computed using distributed network

i I rZ measured

A computed using discrete network - computed using diSlribUled network

600 0 measured

400 500 p&

0' 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

W t )

Fig. 9 constants for diffmtly heat treated MOV samples

A comparison between memured and computed dielectric

0.8

0.7

0.6

0.5

-2

5 0.4

0.3

0.2

0.1

I

0 ' 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

lO9lf)

Fig. 10 values for di/fely heat treafed MOV sonpies

A comparison between meamred and computed ran6

* * 100 1

I -- I

+ * 6" 1 It n

3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

109 11')

Fig. 11 M O V s a m p b h a t frearedaf 750"CdWO"C

Computed dirrrete network parmeters ( E ortd p ) for

depicted in Fig. 2. Subsequently discrete equivalent net- works consisting of 20 R-C branches are obtained at 750 "C and 900" C with satisfactory agreements with the measured

IEE Proc-Sci Mea. TedmoL. Vol 180, No. 4, July 2003

dielectric constant and tan S as indicated in Figs. 9 and IO for distributed and discrete networks respectively. The resistivity and dielectric constant for each R-C branch are shown in Fig. 11. Such a discrete network representation is necessary when assessing the interaction of the MOV device with other electrical system components. The same procedure can also be applied to construct the network for cases with systems overlapping of arcs in the Cole-Cole plot represented by active elements, as shown in Fig. 3.

5 Conclusions

The RTD corresponding to a multiple-arc approach has been employed to investigate the effect of sintering temperature on the characteristics of a MOV ceramic. The analysis has revealed the probable existance of a phase transition in MOV at a temperature around 700°C. The separated polarisation corresponding to ZnO grains and additive oxides diminishes at higher temperatures, and merges into one category of polarisation presumably dominated bv that of the additive oxides modified bv the

6 References

I

2

3

Levinson, L.M., and Philipp, H.R.: 'The physics of metal oxide varistors', J Appl. PhyJ., 1975, 46, (3), pp. 1332-1341 Eda, K.: 'Conduction mechanism of non-ohmic zinc oxide ceramics', J. Appl. Phys., 1978, 49, (5), pp. 29662973 Mahan, G.D., Levinson. L.M., and Philipp, H.R.: 'Theory of conduction in ZnO varistors', J AppL Phyt., 1979, M, (4), pp. 2799-281 1

4 Levinsan. L.M.. and P h i l i ~ ~ . H.R.: 'AC conduction of metal-oxide varistors'; J Appl. Phys., i976, 47, (3), pp. 11 17-1122 Haddad. A., Elayyan; H.S.B., German, D.M., and Waters, R.T.: 'ZnO surge arrester elements with mined direct and alternating 50Hr voltaees'. IEE Proe. Sci Mem. TechnoL. 1991. 138. IS\. 00. 26S212

5

, ~ ~ , . . . 6 Ishikiwa, T., and Yoshikado, S.: 'The effmts of additives on electrical

degradation for ZnO varistors', J. Key Eng. Mater. 2002, 216, pp. 7740 Lin, I.N. Lee, W., Liu, K., Cheng, H., and Wu, M.: 'On the microwave sintering technology for improving the properties of semiconducting electronic ceramics', J Ew. Coum Soc., 2W1, 21, pp. 2085-2088

8 Hung , I., and Li, K.: 'The effecu of heat treatment on B,O,- contained ZnO varistor', J. Marer. Res, 1994,9, (Q, pp. 15261532

9 Duran, P.. Capel, F. Tam,, I., and Moue, C.: 'Effects of low- temperature annealing on the microstructure and electrid properties of doped-ZnO varistor', J. Key Eng. Marer., 202, %213,

10 Jonscher. A.K.: 'Dielectric rehation in solids'. J. Plvs. D. ADD[

7

pp. 138P-1392 ..

Phys., 1999, 32. pp. R57-R70 Li, H., Xu, Y., Wa?g, S., and Wang, L.: 'Studies on degradation of ZnO vanston by dielectric relaxation', J. Ph.w D. Appl. Phys., 1994,

Elayyan, H.S.B., and Ai-Re% S.N.: 'Equivalent network character- ization for dielectric malerials', J. Mater. Sci, 1996, 31,

13 Ai-Refaie, S.N.: 'A generalised formula to determine the relam- tian time distribution in dielectrics', Appl. Phys., 1991, 52, nn 7 2 L 7 ? h

I I shunting effect of ZnO grains. However, the increased dielectric loss and the decrease in dielectric constant for

randomisation of the relatively conductive zno range of relaxation for the higher temperature, and this can

higher temperatures may be ascribed to an enhanced

The higher RTD resolution has also revealed a smaller

be attributed to a higher degree of uniformity attained at

n, pp. 1 9 ~ ~ 9 6 3

pp. 11%1204

12

higher temperatures. The multiple-arc methodology has facilitated the devel-

opment of an equivalent network for dielectrics. Satisfac- tory agreements have been realised in comparing the computed dielectric constant and tan6 with those corre- sponding to experimental results. While single and multiple arcs are solely represented by a passive (R-Q-based network, dispersion relations featuring overlapping arcs

rr -_- 14 AI-Refaie, S.N.: 'Parametric characterimtion of dielectric dispersion',

Appl. Phys, 1993.9, pp. 27S281 I S Ai-Rehie, S.N., and Elapan, H.S.B.: 'The relaxation time distribu-

tian in dielectrics', J. Mrrier Sci, 1992, 11, pp. 98G9-990 16 AI-Refaie, S.N.: 'A generalised representation for dielectric dispersion',

Appl PhyJ.. 1996, 62, pp. 493-497 17 Ai-Rehie, S.N.: 'Active equivalent network for states at the AlflPO,

interface', J. Solid-Sfafe Elecrron, 1999, 43, pp. 32S334 18 Kawamura, H., Isbii, Y., and Nawata, M.: 'Studies on dielectric

properties of zinc oxide ceramic varistors'. Proc. Int. Symp. on High roltaee enineerine. Yakokama 1993. Pacer No. 22.04. PP. 135-138

are additionally represented by an active subnetwork to

analysis.'

19 Shen:W.i, and P&a, A.G.U.: 'Effect &interface states on negative capacitance characteristics in GaAs homojunction far-infrared d e w tors', J. Appl. Phys., 2W1.72, pp. 107-1 I 1 account for the negative capacitance introduced by the

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