Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

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If the temperature changes, then the resonance frequency f

will also change

because of changes in e

and D. Diﬀerentiating Eq. (5.35) with respect to

temperature gives

¼



ð5:36Þ

is the temperature coeﬃcient of resonance frequency TC

is the

temperature coeﬃcient of linear expansion a

and

is the temperature

coeﬃcient of permittivity TC

. Substitution into Eq. (5.36) gives

¼ð

þ a

Þð5:37Þ

In the microwave dielectrics context TC

is usually written t

. It follows from Eq.

(5.37) that achievement of a temperature-independent resonance frequency, i.e.

¼ 0, requires balanced control over TC

and a

The frequency response of a DR coupled to a microwave circuit is shown in

Fig. 5.34. The selectivity Q of the resonator is given by f

=Df and, under

conditions where the energy losses are conﬁned to the dielectric and not to eﬀects

such as radiation loss or surface conduction Q ðtan dÞ

1

where tan d is the loss

factor for the dielectric.

The requirements for DR ceramics are now clear.

1. In order to miniaturize the resonator and to ensure that the electromagnetic

energy is adequately conﬁned to the resonator, e

must be large and is usually

in the range 30 5 e

5 100.

2. To ensure stability against frequency drift with temperature, the temperature

coeﬃcient t

must be close to zero, which implies control over TC

and a

3. To optimize frequency selectivity, Q ¼ðtan dÞ

1

must be maximized and is

usually greater than 1000.

302 DIELECTRICS AND INSULATORS

Fig. 5.34 Frequency response of a microwave resonator.

TEAMFLY

Team-Fly

Microwave engineers ﬁnd it helpful to characterize a microwave dielectric by

the product Qf ( f measured in GHz) which, as a rough ‘rule of thumb’, is

assumed to be constant. The theoretical justiﬁcation for this is as follows.

Figure 2.38 illustrates that in the case of an ionic solid the optical mode of the

lattice vibration resonates at an angular frequency, o

, in the region of 10

Hz.

In the frequency range from approximately 10

–10

Hz dielectric dispersion

theory shows the contribution to permittivity from the ionic displacement to be

nearly constant and the losses to rise with frequency according to

tan d ¼ðgo

f or Qf ¼ðgo

2

 constant (5:38Þ

in which g is a damping factor (see Eq. (2.105)).

It has to be stressed that the relationship is at best a rough guide. There will

almost certainly be contributions to dielectric loss occurring at frequencies

between the microwave region and the ionic lattice resonance frequency that

complicate the Q( f ) relationship. For example, such contributions may arise

through polarization processes associated with dislocations and microstructural

features. There is no alternative to making the measurement if reliable loss data

at a particular frequency are required.

Ceramic compositions

The following discussion outlines the historical path taken in the development of

microwave ceramics combining high permittivity, high Q and zero t

with long

term stability and at an economic cost. Key references are given in the overview

by R. Freer [10].

Titania (TiO

) ﬁrst attracted attention because of its high relative permittivity

 100) and low loss (tan d  3 10

4

). However, a very high t

 400 MK

1

renders it totally unsuited.

MEDIUM-PERMITTIVITY CERAMICS 303

Fig. 5.35 TC

of zirconate compositions with varying titanium contents (CZT; CaZrO

3

–

CaTiO

:SZT; SrZrO

–SrTiO

(measured at 4 GHz).

Interest turned to compositions of high permittivity titanates and zirconates in

which one member exhibited a negative and the other a positive TC

, the

objective being to achieve t

¼ 0. The eﬀect of composition on TC

for two such

systems is shown in Fig. 5.35. Another system which attracted interest is

MgTiO

–CaTiO

in which the end members have the dielectric properties shown

in Table 5.7. The composition Mg

0.95

0.05

TiO

yields t

 0, e

¼ 21 and

Q ¼ 8000 at 7 GHz.

As early as 1952 the ZrO

–TiO

–SnO

(ZTS) system was being investigated for

possible exploitation in capacitors with low TCCs and in the 1970s [11] it

attracted interest for microwave applications. Figure 5.36 shows the region

established as single phase ZTS having the orthorhombic ZrTiO

structure after

ﬁring and annealing mixtures of ZrO

, TiO

and SnO

powders at 1400 8C. The

locus of compositions for which t

¼ 0 is shown.

304 DIELECTRICS AND INSULATORS

Table 5.7 Dielectric properties measured at 7 GHz (after [10])

Q t

=MK

1

MgTiO

17 22 000 45

CaTiO

170 1800 800

Fig. 5.36 The Zr

(ZTS) system: the shaded area indicates the single-phase

microwave ceramic ﬁeld (after [11]).

In the 1970s barium nonatitanate (Ba

or ‘B

’) was identiﬁed as a

candidate. Although not easy to process to a reproducible product because of the

existence of many BaO-TiO

phases (see Fig. 5.41) it is manufactured on a

commercial basis.

The modiﬁed perovskite, barium zinc tantalate (Ba(Zn

1/3

2/3

) (‘BZT’),

was reported in the 1980s to oﬀer a combination of high permittivity coupled

with exceptionally high Q. It was established that the high Q resulted from long

anneals at high temperatures (41400 8C, 100 h) and that this was accompanied

by increased ordering of ions on the B-sites. Unfortunately zinc evaporation and

grain-growth also occurred, well illustrating the diﬃculties encountered in

attempting to unambiguously establish correlations between losses and

compositional, structural and microstructural changes in electroceramics.

Subsequent research established a ﬁrm correlation between Q-value and B-site

order although the underlying reasons for the correlation remained unclear. A

signiﬁcant advance made in the mid-1980s, especially from the commercial

standpoint, was the discovery that small (55 mol.%) additions of BaZrO

led to

very high Q-values being achieved with relatively short annealing times

(1500 8C, 4 h). There is experimental evidence that the structure consists of

B-site ordered domains at the nanometre size scale [12] similar to that occurring

in the case of the relaxor ferroelectrics (see Section 5.7.2). The role of the Zr ion

in inﬂuencing the ordering kinetics is not understood but it is suggested that the

increase in Q is, at least in part, a consequence of its segregation to the domain

boundaries where it has a stabilizing eﬀect; ‘mobile’ domain boundaries would be

expected to contribute to losses.

The t

value for BZT can be tailored to be near zero by the substitution of Ni

for some of the Zn so that there are commercial compositions based on

(1  x)Ba[(Zn,Ni)

1=3

2=3

–xBaZrO

system with the Ni: Zn atom ratio

approximately 1:7 and x ¼0:03.

Other microwave dielectrics have been identiﬁed and developed into

commerical products and those currently exploited are listed in Table 5.8. The

modiﬁed neodymium titanates are particularly important because of their high

permittivity values and the reduction in resonator size this oﬀers.

Broadly speaking microwave dielectrics are all processed in conventional ways,

that is by mixing starting materials, calcining, comminution, pressing and ﬁring.

Somtimes hot-pressing is used. DRs have to be made to close dimensional

tolerances and this requires diamond machining as a ﬁnal step.

There are many factors which contribute to dielectric loss and in the case of

the complex ceramic compounds discussed above, to achieve a satisfying

understanding of the relative magnitudes of the various loss mechanisms is

challenging. There will be contributions to loss intrinsic to the idealized structural

chemistry of the material and it is now clear that this is complicated by a domain

structure. There will also be contributions of an extrinsic nature, particularly

those associated with departures from the ideal structure, point defects and

MEDIUM-PERMITTIVITY CERAMICS 305

‘dislocations’ and of course, various microstructural features, grain size, grain

boundaries and second phases. Even though second phases may in toto be

present in extremely small amounts, the manner in which they are distributed can

have an eﬀect on properties disproportionate to the amounts (see Chapter 3,

Question 19). A clear and unambiguous understanding of dielectric loss

mechanisms will only result from research in which impurities are controlled

to the p.p.m. level, or lower. All the above variables, particularly the

introduction of impurities, depend strongly on all aspects of ‘processing’,

especially those involving high temperatures.

In contrast to dielectric losses permittivity is not, in general, sensitive to small

amounts of impurities and for homogeneous dielectrics values can be calculated

as described in Section 2.7.1, and the various ‘mixture’ rules allow good estimates

to be made for multiphase dielectrics. For Ba- and Sr-based dielectrics having the

perovskite structure the variation of permittivity with temperature, which

determines t

(see Eq. (5.37)), can be correlated with the ‘tolerance factor’ t (see

Section 2.7.3) [13] providing guidance for tailoring ceramics to have t

¼ 0.

Measurement of dielectric properties

The development of improved microwave ceramics, and especially research into

loss mechanisms, necessitates reliable methods for characterizing properties,

particularly Q. A popular method is that described by Hakki and Coleman [14]

306 DIELECTRICS AND INSULATORS

Table 5.8 Commercial microwave ceramics

Ceramic e

Q(2 GHz)Q(f/GHz)

0.95

0.05

TiO

20 – 8000 (7)

Ba[Sn

(Mg

1/3

2/3

)

1x

25 – 43 000 (10)

Ba(Zn

1/3

2/3

‘BZT’ 30 45 000 14 000 (12)

Zr-modiﬁed ‘BZT’ 30 – 10 000 (10)

(Zr

1x

)TiO

‘ZTS’ 35–38 18 500 10 000 (5)

‘B

’ 39 20 000 10 500 (5)

Ca titanate–Nd aluminate ‘CTNA’ 45 21 000 11 000 (5)

Zr-titanate–Zn-niobate ‘ZTZN’ 45 21 000 11 000 (5)

BaNd

77 3800 4000 (1.8)

(Ba,Pb) Nd

90 2000 2000 (1.8)

Ceramic e

Q(f/GHz) t

=MK

1

TiO

100 17 000 (3) 400

10 33 000 (10) 50

In all cases, through minor compositional changes, the t

can be adjusted to + a few MK

1

. Data for

titania and alumina are included for comparison.

and Courtney [15]. A dielectric cylinder, typically 15 mm in diameter and

5–10 mm long, is placed between two parallel conducting planes forming, in

eﬀect, a shorted waveguide (Fig. 5.37). Two antennas, which are loosely

electromagnetically coupled to the system, radiate power into and extract power

from the cavity. Essentially, e

is determined from the resonance frequency f

and Q from f

=Df, where Df is the 3 dB bandwidth. Such measurements are by no

means straightforward to make, but are capable of yielding e

and Q values with

an accuracy to about 1% and about 10%, respectively.

Sometimes the DR carries a ﬁred-on silver coating. This is so with coaxial DRs

when the outer and inner surfaces of a hollow cylinder are silvered. The Q of the

DR can be written

1=Q ¼ 1=Q

þ 1=Q

rad

(5:39Þ

where 1=Q

,1=Q

and 1=Q

rad

are respectively the contributions to total loss from

the dielectric, from the conducting surface and from radiated power. Usually

1=Q

rad

can be neglected, and it can be shown that even for a coating of pure silver

is not greater than approximately 1000 at 900 MHz. For such an application

there is little point in striving to obtain Q

values greater than approximately

5000 since they would have a relatively insigniﬁcant eﬀect on Q. What may be

beneﬁcial is giving the dielectric surface a high polish before being silver coated.

Dielectric resonators are extensively used in mobile communications

technology. As far as selectivity and temperature drift are concerned the

requirements for hand-held units are far less demanding than for those used in

the base stations, and for the more general ﬁlter applications. For example, for

MEDIUM-PERMITTIVITY CERAMICS 307

Fig. 5.37 Apparatus for measuring the microwave characteristics of dielectrics. Inset, detail

showing specimen between conducting planes, and antennas.

hand-held units the resonators are silver plated whereas for base station ﬁlters

much higher Q-values (e.g. 420 000 at 2 GHz) are essential.

Figure 5.38 shows a microwave oscillator built on to a ceramic substrate and

incorporating a dielectric resonator.

LTCC and microwave technology

LTCC technology is extensively exploited in microwave technology and the

following discussion should be read in conjunction with Section 5.5.5.

Microwave LTCC materials are essentially established microwave ceramic

compositions ﬂuxed to allow processing to a glass-ceramic at temperatures lower

than 900 8C. For example, the microwave dielectric BaNd

(see

Table 5.8) mixed with a glass (B

27 mol.%, Bi

35 mol.%, SiO

6 mol.%

ZnO 32%), both in ﬁnely powdered form, compacted and processed at 900 8C for

3 h produced a glass-ceramic with values for e

, t

and Q of approximately 67,

4MK

1

and 41000 (at 6 GHz), respectively [16].

308 DIELECTRICS AND INSULATORS

Fig. 5.38 Microwave ceramic components: (a) metallized ceramic ‘engine block’ for 40 MHz

pass band ﬁlter at 1.4 GHz; (b) 11.75 GHz oscillator incorporating ceramic dielectric resonator

together with various resonator pucks.

MEDIUM-PERMITTIVITY CERAMICS 309

Table 5.9 Dielectric properties of microwave LTCCs [17]

Ceramic e

Q(6–7 GHz)

Commercial MgTiO

–CaTiO

* 21.4 3700

Commercial LTCC 7.4 320

LTCC** 8.5 41000

*Composition approximately that given in Table 5.8.

**No prior glass melting – see text.

Fig. 5.39 (a) Schematic of a l=4 strip line resonator ‘pass-band’ ﬁlter exploiting LTCC

technology; the approximate overall dimensions are: 1561061 mm. (b) Equivalent circuit: C

is the ‘pad-to-strip-line’ capacitance and L and C the inductance and capacitance of the strip-

line.

In a similar study [17] a commercial microwave dielectric, MgTiO

–CaTiO

,was

ﬂuxed with SiO

and ZnO powders avoiding the prior glass-melting step.

After ﬁring at 900 8C the ﬁnal product was a crystalline glass ceramic with no

detectable amorphous phase and oﬀering useful dielectric properties (Table 5.9).

Oscillators and ﬁlters do not always take the form of the ‘puck’ as illustrated in

Fig. 5.38 but also as ‘strip-lines’. Figure 5.39 illustrates a structure for a l=4 strip

line resonator exploiting LTCC technology.

The principle of the resonator is the same as that of a vibrating string and in

the illustrated example one end of the line is maintained at ‘ground’ potential

(the node) and the other is the antinode. The permittivity of the surroundings

determine the length of the line for a particular resonance frequency and, in this

case, also serves to capacitively couple energy into and out of the resonator.

To tailor the stop- or pass-band to requirements more than one line will be

involved (coupled resonators), and the geometries will depart from the simple

form illustrated.

The constant drive to miniaturize components for communications devices is

stimulating eﬀorts to develop LTCC technology into three dimensional circuitry

in which passive components (resistors, capacitors and inductors) are packaged

into the structure with the active, integrated circuits, bonded to the outer surface.

The technology is reviewed by W. Wersing et al. [18].

5.7 High-permittivity Ceramics

Dielectrics with relative permittivities exceeding 1000 are based on ferroelectric

materials and are more sensitive to temperature, ﬁeld strength and frequency

than lower-permittivity dielectrics. Development in the past 50 years has resulted

in improvements in stability whilst retaining the desirable high-permittivity

310 DIELECTRICS AND INSULATORS

Table 5.10 Coding for temperature range and capacitance variation for Class II/III

capacitors

EIA Code Temperature range/8C EIA Code Capacitance change/%

X5 755 to +85 D +3.3

X7 755 to +125 E +4.7

X8 755 to +150 F +7.5

Y5 730 to +85 P +10

Z5 +10 to +85 R +15

S +22

T +22 to 733

U +22 to 756

V +22 to 782

Example: a capacitor is required for which the capacitance value at 25 8C changes by no more than +7.5%

in the temperature range 730 8C to +85 8C; the EIA Code will be Y5F. EIA codes D–R; Class II: Codes

S–V; Class III.

feature. The Electronics Industries Alliance (EIA) of the United States has

devised a scheme for specifying the variability of capacitance with temperature in

the ranges of practical interest. The coding is deﬁned in Table 5.10, and Fig. 5.40

shows typical characteristics compared with those of Class I controlled

temperature coeﬃcient dielectrics.

5.7.1 Modi¢ed barium titanate dielectrics

The dielectric characteristics of barium titanate ceramics with respect to

temperature, electric ﬁeld strength, frequency and time (ageing) are very

dependent on the substitution of minor amounts of other ions for Ba or Ti.

HIGH-PERMITTIVITY CERAMICS 311

Fig. 5.40 Variation of capacitance with temperature for (a) Class I C0G, (b) Class II X7R

and (c) Class III Z5U dielectrics.

(a)

(b)

(c)