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242 CERAMIC CONDUCTORS

TEAMFLY

Team-Fly

DIELECTRICS AND

INSULATORS

‘Ceramic dialectrics and insulators’ is a wide-ranging and complex topic

embracing many types of ceramic, physical and chemical processes and

applications. Broadly speaking over the past century there have been clearly

discernible trends; for example, in the case of electric power transmission to

higher line voltages for greater transmission eﬃciency. Radio broadcasting and

radar technologies made their appearance and as they developed to operate at

steadily increasing frequencies and power levels, so too did the demand for

ceramics tailor-made for a variety of essential components. But it is the

‘computer’ and ‘communications’ technologies which have had the most

signiﬁcant impact on ceramic insulators and dielectrics. Here, because of the

development of silicon and GaAs semiconductor integrated circuits, the trend

has been to lower operating voltages and to frequencies in the 1–10 GHz range.

The need for ‘miniaturization’ has accompanied the demand for increased

computing power and the advent of satellite and mobile communications.

With the increase in complexity of equipment, for example a mobile phone of

the next generation and suited to ‘Bluetooth’ technology may well contain a few

hundred capacitors, about half that number of resistors and perhaps a few tens

of inductors. This dramatic increase in passive component packing density is

placing a strain on surface mount technology, and on reliability because of the

large number of solder joins. The problem is being addressed through eﬀorts to

develop fully integrated three dimensional ceramic packages with the active,

semiconductor circuits and components which cannot be integrated because of

their size, mounted on the surface. This technology is based on low temperature

co-ﬁred ceramics (LTCC).

To structure a discussion around all these developments is not an easy task

and we have attempted to assist in intelligibility by presenting it in two parts.

Electroceramics: Materials, Properties, Applications. 2nd Edition. Edited by A. J. Moulson and J. M. Herbert.

& 2003 John Wiley & Sons, Ltd: ISBN 0 471 49747 9 (hardback) 0 471 49748 7 (paperback)

Part I is focused on capacitors, providing the oportunity to introduce the many

important ideas relating to their performance and, indeed, to the wider

application of dielectrics and insulators. Part II is concerned with the important

ceramic types and their applications.

The monographs [1] and [2] are recommended for supplementing the

discussions.

PART I CAPACITATIVE APPLICATIONS

5.1 Background

Dielectrics and insulators can be deﬁned as materials with high electrical

resistivities. Dielectrics fulﬁl circuit functions for which their permittivities e and

dissipation factors tan d are also of primary importance. Insulators are used

principally to hold conductive elements in position and to prevent them from

coming in contact with one another. A good dielectric is, of course, necessarily a

good insulator, but the converse is by no means true.

Just as there is no perfect insulator, neither is there a perfect dielectric, and in

the various usage contexts some parameters are more suitable than others for

describing the departure from perfection. For example, a power engineer would

focus attention on the loss factor e@ ¼ e

tan d (Eq. (2.102)) because it is

dissipation of energy and the attendant heating and wastage which are the chief

concerns. An electronics engineer would be more concerned with tan d, and

certainly so when dealing with oscillator and ﬁlter circuits which exploit the

electrical resonance phenomenon. The sharpness of tuning at resonance depends

on the ‘quality factor’ or Q of the circuit: the higher is Q the lower is the damping

and the sharper is the resonance. Q is determined by the components comprising

the circuit and, in particular, by the dielectric properties of the materials used;

tan d is a material property and its reciprocal is Q. In dealing with dielectric

heating a signiﬁcant parameter is the dielectric conductivity s

a:c:

¼ oe@ ¼ oe

tan d

(Eq. (2.98)). These various parameters are a measure of essentially the same

thing, i.e. the dissipation of energy in the dielectric in an alternating electric ﬁeld.

In some applications of ceramics in electronics their insulating rather than

dielectric properties are signiﬁcant. Examples of such applications are substrates

on which circuits are constructed, parts of variable air capacitors and coil

formers. These are essential constructional parts whose function is simply to

support circuits, capacitor vanes or coils respectively, and the ideal material

244 DIELECTRICS AND INSULATORS

would have e

¼ 1 and tan d ¼ 0 ðQ ¼1Þ across the desired frequency and

temperature ranges – in fact a solid vacuum would be ideal!

The uses to which insulating ceramics are put are many and varied; although a

very large number of types have been developed to meet particular demands it is

possible to discern certain trends, and it is around these that the following

discussion is developed. One such trend has been meeting the demands set by the

increase in line voltages as power transmission networks have developed; another

is the move towards higher frequencies as telecommunications systems have

advanced. With regard to the latter trend, it is shown in Section 2.7.2, that the

power dissipated in an insulator or a dielectric is proportional to frequency. This

explains the demand for low-loss dielectrics for high-frequency applications.

High-loss-factor dielectrics for high frequencies cannot be tolerated, partly

because excessive power dissipation can lead to unacceptable rises in

temperature, and even breakdown in high-power devices, and partly, and more

importantly, because the resonances in tuned circuits become less sharp so that

the precise selection of well-deﬁned frequency bands is not possible.

Before embarking on a detailed consideration of the application of dielectrics

and insulators, it is opportune to focus attention brieﬂy on ‘dielectric strength’

and ‘thermal shock resistance’. Both properties demand careful consideration in

certain applications of dielectrics and insulators. They are by no means simple to

deﬁne and, generally speaking, it is necessary only to develop some appreciation

of how component and operational parameters determine them.

5.2 Dielectric Strength

Dielectric strength is deﬁned as the electric ﬁeld just suﬃcient to initiate

breakdown of the dielectric. The failure of dielectrics under electrical stress is a

complex phenomenon of very considerable practical importance. Theories have

been developed to explain what is termed the intrinsic strength of a material.

Single crystals have usually been used to measure this, with the specimen

geometry and electrode arrangement carefully designed and the ambient

conditions closely controlled. Under such conditions reasonably reproducible

data and satisfactory agreement with theory are obtained. Unfortunately electric

strength depends markedly on material homogeneity, specimen geometry,

electrode shape and disposition, stress mode (d.c., a.c. or pulsed) and ambient

conditions, and in practice inadequate control is often exercised over these

variables.

In the industrial situation thermal breakdown is the most signiﬁcant mode of

failure and is avoided through experience rather than by application of theory.

Nevertheless it is important to appreciate the mechanisms leading to thermal

breakdown. A third mode of failure, referred to as discharge breakdown,isof

importance in ceramics because it has its origins in porosity.

DIELECTRIC STRENGTH 245

5.2.1 Test conditions

Electric strength data are meaningful only if the test conditions are adequately

deﬁned: for example, if d.c. loading is employed the rate of voltage increase

should be speciﬁed, if pulsed voltages are used the rise time should be speciﬁed

and if a.c. loading is adopted the frequency and waveform should be speciﬁed.

The importance of sample geometry can be appreciated from Fig. 5.1. With the

geometry (a), although a large volume of the specimen is stressed, failure is likely

to be initiated from the electrode edges where the average electrical stress is

magniﬁed by a signiﬁcant but uncertain factor. With the geometry (b) failure

would probably occur at the centre where the stress is a maximum and known.

Therefore more meaningful data are likely to be obtained using geometry (b).

When testing electric strength there is the risk of ‘ﬂash-over’ across the

specimen surface between the electrodes. This is avoided by making the

measurement with the specimen immersed in an insulating liquid, such as

transformer oil, which displaces air from the ceramic surface.

5.2.2 Breakdown mechanisms

Intrinsic breakdown

When a homogeneous specimen is subjected to a steadily increasing voltage

under well-controlled laboratory conditions, a small current begins to ﬂow which

increases to a saturation value. As the voltage is further increased a stage is

reached when the current suddenly rises steeply from the saturation value in a

time as short as 10

s and breakdown occurs. The very short rise time suggests

that the breakdown process is electronic in character.

Intrinsic breakdown is explained as follows. When the ﬁeld is applied the small

number of electrons in thermal equilibrium in the conduction band gain kinetic

energy. This energy may be suﬃcient to ionize constituent ions, thus increasing

the number of electrons participating in the process. The result may be an

electron avalanche and complete failure. Intrinsic breakdown strengths are

typically of the order of 100 MV m

246 DIELECTRICS AND INSULATORS

(a) (b)

Fig. 5.1 Cross-sections of disc specimens for measurement of electric strength: (a) standard

ﬂat disc; (b) recessed disc.

Thermal breakdown

The term ‘thermal breakdown’ is restricted to those cases in which the

breakdown process can be described in terms of the thermal properties of the

dielectric.

The ﬁnite d.c. conductivity of a good dielectric results in Joule heating; under

a.c. ﬁelds there is additional energy dissipation. If heat is generated in the

dielectric faster than it can be dissipated to its surroundings, the resulting rise in

temperature leads to an increase in conductivity and to dielectric loss. These are

the conditions leading eventually to ‘runaway’, culminating in breakdown. The

situation is identical with that already discussed in detail in Section 4.4.1, in the

context of the negative temperature coeﬃcient (NTC) thermistor.

Attempts have been made to develop a comprehensive theory of thermal

breakdown, but solutions to the governing diﬀerential equation can be found

only for the simplest of geometries. Another serious obstacle to achieving a

realistic theoretical description is that the functional relationships connecting

charge movement with ﬁeld and temperature, and thermal diﬀusivity with

temperature, are invariably very poorly deﬁned. The expression

tan d

1=2

’ ð5:1Þ

for the breakdown voltage U

of a ﬂat disc with a.c. applied across its thickness

identiﬁes the important parameters which include the temperature coeﬃcient of

loss factor a

and ’ which is a function of specimen thickness and heat transfer

to the environment. It is evident that the variables determining thermal

breakdown fall into one of two categories. One is concerned with material

properties, i.e. thermal conductivity l and loss factor, and the other with

operational conditions, i.e. frequency, specimen dimensions and heat transfer to

the surroundings. In practice, lack of suﬃciently precise information regarding

the various parameters precludes the possibility of developing an equation

corresponding to (5.1).

The eﬀect of temperature on electrical breakdown for an aluminous porcelain

shown in Fig. 5.2 illustrates the expected marked decrease in strength arising

through thermal breakdown of the glassy phase initiated above a critical ambient

temperature (see Section 2.6.3).

Discharge breakdown

A ceramic is rarely homogeneous, a common inhomogeneity being porosity.

There is strong evidence to show that breakdown can be initiated at pores and

that the occurrence of gas discharges within pores is an important factor. There

DIELECTRIC STRENGTH 247

is a close apparent analogy with the mechanical strength of ceramics, where

probability of failure depends upon the occurrence of defects, one of which is

critical under the imposed conditions. Just as with the mechanical analogue,

electric strength depends upon specimen size, because a decrease in size reduces

the probability of occurrence of a critical defect at the given stress. A typical plot

of electric strength against specimen thickness is shown in Fig. 5.3.

The mechanism of breakdown originating from discharges in a pore is by no

means self-evident, but the starting point is that the electric ﬁeld in a pore is

greater than that in the surrounding dielectric. For a disc-shaped cavity with its

plane normal to the applied ﬁeld E, the ﬁeld E

within the cavity is given by

E ð5:2Þ

248 DIELECTRICS AND INSULATORS

Fig. 5.2 Dependence of electric strength on ambient temperature for an aluminous porcelain.

Fig. 5.3 Dependence of the electric strength of alumina ceramic on specimen thickness.

where e

is the relative permittivity of the cavity gas and has a value close to

unity, and e

is the relative permittivity of the dielectric. For a spherical pore

E ð5:3Þ

provided that e

 e

When the voltage applied to a porous dielectric is steadily increased a value is

reached when a discharge occurs in a particular pore. Under d.c. conditions the

discharge is quickly extinguished as the ﬁeld falls in the cavity. Then, following

charge leakage through the material, the sites will recharge until discharge occurs

again. The interval between discharges will depend upon the charge leakage time

re (see Eq. (5.10)), which can have minimum values of approximately 10

s for

ceramics at room temperature.

How discharges within pores lead to total breakdown of the dielectric is a

matter for debate. It may result from the propagation of a discharge ‘streamer’

through the ceramic, possibly progressing from pore to pore and encouraged by

the increased electric stress to which the material between discharging pores is

subjected and perhaps also by enhanced stress in the material close to a

discharging pore. Alternatively, failure might be a direct consequence of the

generation of heat by the discharge. Estimates of the rise in temperature in the

material immediately adjacent to a discharging pore range from a few degrees

Celsius for a low-permittivity ceramic such as alumina to about 10

3 8

C for high-

permittivity ferroelectric ceramics. Clearly the larger the pore is the more likely it

is to lead to breakdown.

DIELECTRIC STRENGTH 249

Fig. 5.4 Dependence of electric strength on specimen density (high-purity alumina).

Because discharges occur every half-cycle under a.c. conditions, breakdown is

more likely than in the case of applied d.c., when the leakage time determines the

discharge rate. Accordingly, a.c. breakdown voltages are lower than those for

d.c.

Although there may be doubt concerning the mechanisms by which discharges

lead to failure there is none regarding the fact that high electric strength is

favoured by low porosity. A typical plot of density against electric breakdown

strength is shown in Fig. 5.4.

Long-term effects

In some materials the prolonged application of electric stress at a level well below

that causing breakdown in the normal rapid tests results in a deterioration in

resistivity that may lead to breakdown. There are a large number of possible

causes, and the eﬀects may not show up in the brief tests carried out during

development and production operations.

Among the possibilities are the eﬀect of the weather and atmospheric pollution

on the properties of the exposed surfaces of components. They will become

roughened and will adsorb increasing amounts of moisture and conductive

impurities. Surface discharges may occur which will result in further deteriora-

tion due to local high temperatures and the sputtering of metallic impurities from

attached conductors.

Electrochemical action takes place under d.c. stress both on the surface and in

the bulk of materials. It may cause silver to migrate over surfaces and along grain

boundaries, thus lowering resistance. Sodium ions in glassy phases migrate in a

d.c. ﬁeld and vacant oxygen sites migrate in crystalline phases. Such changes

result in local variations in electrical stress that contribute to breakdown.

The eﬀects of diﬀering geometries, materials and operating conditions provide

a large number of possibilities for eventual failure which can only be mitigated by

good design based on experience. Prolonged tests under practical running

conditions are necessary before a new material becomes generally acceptable.

Gradual processes that may lead to failure are discussed in the sections

concerned with particular materials (see Sections 5.4.1 and 5.6.2).

5.3 Thermal Shock Resistance

Thermal shock resistance (TSR) is of importance in both the fabrication and

applications of many electronic ceramics.

Precise evaluation of TSR is diﬃcult for many reasons, one being that a failure

criterion which depends on the application has to be adopted. For example, a

refractory lining to a furnace may repeatedly crack during thermal cycling but,

250 DIELECTRICS AND INSULATORS

because its structure retains its overall integrity, it has not ‘failed’. However, a

glass beaker is usually regarded as having failed when it cracks. A criterion for

failure therefore has to be deﬁned for every usage situation, and the same applies

to TSR testing. A small crack developed in a porous specimen need not constitute

‘failure’, but in a dense ceramic intended for advanced engineering applications it

probably would. TSR is very dependent upon component shape and this, together

with the precise mode of testing, is an important variable. Despite these real

diﬃculties a useful guide to TSR is the quantity ls

Y,wherel is the thermal

conductivity, s

is the strength, Y is the Young modulus and a

is the coeﬃcient

of linear expansion. Therefore materials with high l and s

and low Y and a

are

favoured for high-thermal-shock applications. Because s

=Y is approximately

constant (about 10

) for many ceramics, the signiﬁcant parameters determining

TSR are l and a

. However, it must be emphasized that this is only a rough guide

and the matter of TSR, like electric strength, is extremely complex.

5.4 Capacitors

Capacitors can fulﬁl various functions in electrical circuits including blocking,

coupling and decoupling, a.c.–d.c. separation, ﬁltering and energy storage. They

block direct currents but pass alternating currents, and therefore can couple

alternating currents from one part of a circuit to another while decoupling d.c.

voltages. A capacitor can separate direct from alternating currents when the

capacitance value is chosen such that the reactance 1/oC is low at the frequency

of interest; similarly it can discriminate between diﬀerent frequencies. The charge

storage capability is exploited in, for example, the photoﬂash unit of a camera.

The operational capabilities of the various capacitor types are compared with

the help of the characteristics described below.

5.4.1 Capacitor characteristics

Volumetric e⁄ciency

Volumetric eﬃciency, as the name implies, is a measure of the capacitance that

can be accommodated in a given size of capacitor. In the case of a parallel-plate

capacitor of area A and electrode separation h,

C ¼ e

ð5:4Þ

and the volumetric eﬃciency C/V is given by

ð5:5Þ

CAPACITORS 251