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

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(assuming constant E ), and

¼ p þ E

ð7:3Þ

where p ¼ @P

=@T is the true pyroelectric coeﬃcient and p

is sometimes referred

to as a generalized pyroelectric coeﬃcient. Since a temperature change DT

produces a change in the polarization vector, the pyroelectric coeﬃcient has

three components deﬁned by

¼ p

DTi¼ 1, 2, 3 ð7:4Þ

Therefore the pyroelectric coeﬃcient is a vector but, because in practical

applications the electrodes that collect the pyrocharges are positioned normal to

the polar axis, the quantities are usually treated as scalars, and this is done in the

following discussion.

The contribution Eð@e=@TÞ (Eq. (7.3)) can be made by all dielectrics, whether

polar or not, but since the temperature coeﬃcients of permittivity of ferroelectric

materials are high, in their case the eﬀect can be comparable in magnitude with

the true pyroelectric eﬀect. This is also the case above the Curie point and where,

because of the absence of domains, the dielectric losses of ferroelectrics are

reduced, which is important in some applications. However, the provision of a

very stable biasing ﬁeld is not always convenient.

Since pyroelectric materials are polar, they are also piezoelectric, and the strain

resulting from thermal expansion will result in the development of a surface

charge. However, this is a small eﬀect that seldom exceeds 10% of the primary

pyroelectric eﬀect.

Because P

falls to zero at the Curie point, ferroelectric materials are likely to

exhibit high pyroelectric coeﬃcients just below their transition temperatures. The

various ways in which P

falls as the Curie point is approached from below are

shown in Fig. 7.1. High pyroelectric coeﬃcients are observed for ferroelectrics

that exhibit second-order transitions, such as triglycine sulphate with a transition

temperature of 49 8C and a pyroelectric coeﬃcient of at least 280 mCm

2

1

20 8C. There are diﬃculties in exploiting materials which exhibit ﬁrst-order

transitions, ﬁrst because they exhibit hysteresis – the transition occurs at a higher

temperature when the temperature is rising than when it is falling – and second

because it would be diﬃcult in most applications to keep the pyroelectrics in a

suﬃciently constant temperature environment. A number of materials are used

at temperatures well below their Curie points where, although the pyroelectric

coeﬃcients are smaller, they vary less with the ambient temperature.

For practical purposes, the very small signals generated by pyroelectric

elements must be ampliﬁed. The most widely used ﬁrst stage consists of a ﬁeld

eﬀect transistor (FET) which responds to electric potential rather than to charge.

In this case, it is advantageous for the material to have a low permittivity to match

the low input capacitance of the FET. Therefore the compositions with high

412 PYROELECTRIC MATERIALS

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permittivities which are exploited as dielectrics and piezoelectrics are unsuitable,

and special materials have been developed for pyroelectric applications.

7.2 Infrared Detection

Pyroelectric materials are used mainly for the detection of infrared radiation.

The elements for the detectors are typically thin slices of material (e.g.

1.061.060.1 mm) coated with conductive electrodes, one of which is a good

absorber of the radiation.

Figure 7.2 illustrates a detector at a temperature T above its surroundings. If

radiation at a power density W

/A is incident on the face for a time dt, the energy

absorbed is ZW

dt. The emissivity Z is for the particular surface, wavelength and

INFRARED DETECTION 413

Fig. 7.1 Form of P

(T) for various classes of ferroelectric.

Fig. 7.2 A pyroelectric detector element.

temperature conditions and, because of Kirchhoﬀ’s law, it is also a measure of

the fraction of incident energy absorbed.

If it is assumed that all the power absorbed in time dt is rapidly distributed

through the volume of the element, its temperature will rise by dT where

dt ¼ H dT ð7:5Þ

In this equation H ¼ rcAh is the heat capacity of the element where c is the

speciﬁc heat of the pyroelectric material and, in this context, r is its density. In

what follows the product rc, the volume speciﬁc heat, is given the symbol c

If part of the absorbed power is lost to the surroundings by reradiation,

conduction or convection at a rate G per unit temperature excess of the element

over its surroundings, Eq. (7.5) is modiﬁed to

dt  GT dt ¼ HdT

TT þ GT ¼ ZW

ð7:6Þ

in which the dot notation signiﬁes a time derivative. If the incident power is shut

oﬀ at t ¼ t

TT þ GT ¼ 0 ð7:7Þ

and

T ¼ T

exp







ð7:8Þ

where T

is the temperature excess at t ¼ t

and t

¼ H=G is the thermal time

constant.

To obtain a continuous response from a pyroelectric material the incident

radiation is pulsed, and this situation is analysed by assuming that the energy

varies sinusoidally with frequency o and amplitude W

. Equation (7.6) then

becomes

TT þ GT ¼ ZW

expðjotÞ

TT þ

T ¼

expðjotÞð7:9Þ

Using the integrating factor expðt=t

Þ and integrating gives

T ¼





þ jo



1

ð7:10Þ

The pyrocurrent I

collected from the electrodes is given by

414 PYROELECTRIC MATERIALS

QQ ¼

ð7:11Þ

where Q is the total instantaneous charge. If it is assumed that the element is

operating in a polar state

dQ ¼ A dP

¼ ApdT

and

¼ pA

TT ð7:12Þ

which, after substituting

TT from Eq. (7.10), becomes

¼ jo



ðGt



þ jo



1

pAZW

ð7:13Þ

The ‘current responsivity’ r

is deﬁned as the modulus of I

, so that



jopAZ

(

þ jo

1



which, after algebraic manipulation, becomes

pAZo

ð1 þ o

1=2

ð7:14Þ

A common arrangement for a detecting system where the voltage u from the

pyroelectric element is fed to the gate of an FET with a high input impedance is

shown in Fig. 7.3. The resistor R

correctly biases the FET, and C

and R

are

respectively the input capacitance and resistance of the amplifying and associated

system. The voltage output is I

/Y where the admittance Y is given by

INFRARED DETECTION 415

Fig. 7.3 A common pyroelectric detecting system.

Y ¼

þ joðC

þ C

Þð7:15Þ

and C

is the capacitance of the element. Usually, although not always,

 R

and C

 C

, so that

Y  R

1

þ joC

and

jYj¼R

1

ð1 þ o

1=2

ð7:16Þ

where t

¼ R

is the electrical time constant of the circuit. Therefore the

voltage responsivity r

is given by



jYj

ð7:17Þ

pAoZ

Gð1 þ o

1=2

ð1 þ o

1=2

ð7:18Þ

Eq. (7.18) shows that, for maximum sensitivity at low frequency, G should be

minimized by isolating the element to reduce the loss of heat. t

can be

minimized by reducing the thickness h of the detecting element so as to reduce its

thermal capacity. r

is shown as a function of frequency in Fig. 7.4. There is a

maximum at o

¼ 1=t

with only a small variation with frequency between

1/t

and 1/t

. t

and t

usually lie in the range 0.1–10 s for high sensitivity. The

maximum value of r

416 PYROELECTRIC MATERIALS

Fig. 7.4 Variation in voltage responsivity r

with frequency. Note that t

1

etc. denote o

values.

ðmaxÞ¼

pAZR

Gðt

þ t

ð7:19Þ

At high frequencies, when o

 1, o

 1 and C

 C

, Eq. (7.18) reduces

Aeo

ð7:20Þ

in which e is the permittivity of the material.

Eq. (7.20) suggests a ﬁgure of merit,

ð7:21Þ

which describes, in terms of material properties only, the eﬀectiveness of a

pyroelectric element used under deﬁned conditions. Figures of merit only apply

under given deﬁned operational conditions and care has to be exercised in

making use of them. As shown later, the appropriate ﬁgure of merit when the

intrinsic ‘noise’ arising from dielectric loss is a dominating inﬂuence is

1=2

tan

1=2

ð7:22Þ

7.3 E¡ects of Circuit Noise

All signal detectors are required to detect the signal against a background of

‘noise’. Therefore, the signal-to-noise ratio must be optimized or, put another

way, for maximum sensitivity the noise has to be minimized. The sensitivity of

any detector is determined by the noise level in the ampliﬁed output signal. In the

case of a pyroelectric detector and its associated circuitry, the principal sources

of noise are Johnson noise, ampliﬁer noise and thermal ﬂuctuations.

The noise level can be expressed in terms of the power incident on the detector

necessary to give a signal equivalent to the noise. If the noise voltage is DV

then

the ‘noise equivalent power’ (NEP) is deﬁned by

NEP ¼

ð7:23Þ

Because it is preferable to have a quantity that increases in value as the

performance of the system is improved, the ‘detectivity’ D is deﬁned as

D ¼

NEP

ð7:24Þ

EFFECTS OF CIRCUIT NOISE 417

Johnson noise and thermal ﬂuctuations are brieﬂy discussed below, Johnson

noise because it is usually the dominant noise and thermal ﬂuctuations because

they set a lower limit on the achievable noise level.

7.3.1 Johnson noise

Johnson noise arises because the random thermal motion of electrons in an

isolated resistor produces random ﬂuctuations in voltage between its ends,

covering a broad frequency band. It can be shown that

¼ 4kTgDf ð7:25Þ

where D

is the mean square Johnson current covering a bandwidth Df, k is

Boltzmann’s constant, T is the absolute temperature and g is the conductance of the

noise generator. In the case of the pyroelectric detector system discussed above,

g ¼

þ oC

tan d ð7:26Þ

where oC

tan d is the AC conductance of the pyroelectric element.

The root mean square (r.m.s.) noise voltage DV

for unit bandwidth is DI

=jYj,

where DI

is the r.m.s. noise current for unit bandwidth and Y is the admittance.

Therefore

ð4kTgÞ

1=2

jYj

ð7:27Þ

At high frequencies, when oC

tan d  1=R



4kT

1=2

tan

1=2

d ð7:28Þ

Therefore D ¼ 1=NEP ¼ r

=DV

which, on substitution from Eqs (7.20) and

(7.28), gives

D ¼

ðAhÞ

1=2

ð4kToÞ

1=2





ðe tan dÞ

1=2

ð7:29Þ

Under the conditions deﬁned the material parameter to be maximized is p, with

, e and tan d minimized as required by F

(Eq. (7.22)).

7.3.2 Thermal £uctuations

Thermal ﬂuctuations arise even when a body is in thermal equilibrium with its

surroundings through radiation exchange only. Calculation of the mean-square

418 PYROELECTRIC MATERIALS

value of the power ﬂuctuations can be accomplished by the methods of either

classical statistical mechanics or, when the radiation is considered to be

quantized into photons, quantum mechanics.

Both approaches give

¼ 16ksZT

ADf ð7:30Þ

for the mean square power ﬂuctuations covering a bandwidth Df for a body of

surface area A and emissitivity Z at equilibrium at temperature T; s is the Stefan

constant. If the body is assumed to be ‘black’ (Z ¼ 1), for unit area and unit

bandwidth

¼ 16ksT

ð7:31Þ

The r.m.s. value at 300 K is 5.5610

71/2

W, placing an upper limit of

1.8610

mHz

1/2

on the detectivity D. The highest detectivities achieved in

practice are between one and two orders of magnitude below this.

In ferroelectrics the major contributor to tan d is domain wall movement

which diminishes as the amplitude of the applied ﬁeld diminishes; the value

applicable to pyroelectric detectors will be that for very small ﬁelds. The

permittivity is also very sensitive to bias ﬁeld strength, as is its temperature

coeﬃcient. The properties of some ferroelectrics – the ‘relaxors’ – are also

frequency dependent. It is important, therefore, to ensure that when assessing the

suitability of a ferroelectric for a particular application on the basis of measured

properties that the measurements have been made using values of the parameters

(frequency, ﬁeld strength etc.) appropriate to the application. This is not always

done.

7.4 Materials

The properties and ﬁgures of merit of a range of pyroelectric materials (at 20 8C

except where indicated) are given in Table 7.1. The table omits a number of

secondary characteristics that determine suitability in particular applications.

Triglycine sulphate (TGS) has high ﬁgures of merit but is a rather fragile water-

soluble single-crystal material. It can be modiﬁed to withstand temperatures in

excess of its Curie point without depoling, but it cannot be heated in a vacuum to

the temperatures necessary for outgassing without decomposing. It is diﬃcult to

handle and cannot be used in devices where it would be subjected to either a hard

vacuum or high humidity. In contrast, polyvinylidene ﬂuoride (PVDF) has poor

ﬁgures of merit but is readily available in large areas of thin ﬁlm. It is

considerably more stable to heat, vacuum and moisture than TGS. It is

mechanically robust and, as indicated by Eq. (7.18), can have its voltage

sensitivity enhanced by the use of a large area. It also has low heat conductivity

MATERIALS 419

420 PYROELECTRIC MATERIALS

Table 7.1

Properties of some pyroelectric materials. (Data should be regarded

as approximate)

Material and form

p/mCm

2

1

tand

/MJ m

3

1

/8CF

1

/TPa

1/2

TGS, (single crystal; 35

8C)

280

38 0.01

2.3

49 0.36

DTGS (single crystal; 40

8C)

550

43 0.02

2.6

61 0.53

LiTaO

(single crystal)

230

47 0.001

3.2

665 0.17 110

(SrBa)Nb

(single crystal)

550

400 0.001

2.3

121 0.07

modiﬁed PZ (polycrystalline**)

400

290 0.003

2.5

230 0.06

300

{

0.014

{

0.06

modiﬁed PT (polycrystalline)

350

220 0.01

2.5

250 0.07

220

{

0.03

{

0.07

PVDF (ﬁlm)

12 0.01

2.4

80 0.1

P(70VDF/30TrFE)*** (ﬁlm)

7.4 0.017

2.3

121 0.22

13.6

0.25PZ 0.75PT (sol-gel thin ﬁlm)

220

350

{

0.008

{

2.7

– 2.5

(sputtered)

450

300 0.01

2.7

– 2.6

‘BST (a) (0.67Ba 0.33Sr)TiO

(ceramic; 0.6 V

1

)

7000 8800 0.004

–

25 –

124

‘PST (b) Pb(Sc

1/2

(sputtered on Si; 10 V

1

;508C)

850

600 0.0025

–

10 –

‘PST’ (c)

(ceramic; 4 V

1

;408C)

3500 2000 0.005

2.7

25 0.06 110

is also expressed in the equivalent units, 10

6

1=2

: TGS

¼triglycine sulphate: DTGS

¼deuterated TGS: **‘PZFNTU’ see text: *** co-polymer

of vinylidene

ﬂuoride and triﬂuoroethylene.

{

Measured at 33 Hz; all other dielectric data measured at

1 kHz.

Properties measured at 25

8C, unless indicated in parentheses. Where appropriate

bias electric ﬁelds in parentheses.

(a) From [2].

(b) After P. P. Donohue, M.A. Todd

et al. (2001)

Integrated Ferroelectrics

, 41, 25–34.

et al.

(1990) Ferroelectrics

106, 387–92.

and low permittivity so that both thermal and electrical coupling between

neighbouring elements on the same piece of material are minimized. Its high

tan d is a disadvantage.

Lithium tantalate is a single-crystal material that is produced in quantity by

the Czochralski method (see Section 3.11) for piezoelectric applications and is

therefore readily available. It is stable in a hard vacuum to temperatures that

allow outgassing procedures. It is insensitive to humidity. It is widely used where

precise measurements are to be made.

Strontium barium niobate is a single-crystal material with the tungsten bronze

type of structure which is made by the Czochralski method but has yet to ﬁnd a

major use. It has relaxor characteristics of the type shown in Fig. 7.1 which give

it a high pyroelectric coeﬃcient and detectivity, but its high permittivity lowers

the ﬁgure of merit F

The ceramic based on lead zirconate (PZ) has intermediate ﬁgure of

merit values. Its ﬁnal form as a thin plate is obtained by sawing up a hot-

pressed block and lapping and polishing to the required dimensions. Similar

methods must be applied to single crystals and so the costs of manufacture are

not very diﬀerent.

The adaptability of ceramics is well illustrated by the development of PZ for

pyroelectric devices. It was found initially that the addition of about 10 mol%

lead iron niobate (PbFe

1/2

) to lead zirconate converted it from an

antiferroelectric to a ferroelectric material with a relatively low permittivity and a

high pyroelectric coeﬃcient. However, this material was found to undergo a

transition between two ferroelectric rhombohedral forms at 30–40 8C which

rendered its pyroelectric output unstable. The replacement of about 5% of the B-

site atoms by Ti shifted this transition to around 100 8C without signiﬁcantly

increasing the permittivity. For some devices a somewhat lower resistivity is

advantageous since it eliminates the need for a high-value, and expensive,

external resistor. It was found that replacement of 0.4–0.8% of the B-site atoms

by uranium controlled the resistivity in the 10

–10

O m range, as shown in

Fig. 7.5; at the same time the permittivity and loss were reduced. The ﬁnal

composition Pb

1.02

(Zr

0.58

0.20

0.02

)

0.994

0.006

(PZFNTU), although

complex, can be manufactured reproducibly.

A pyroelectric response is shown by any dielectric to which an electric

ﬁeld is applied provided there is a variation in permittivity with temperature

(see Eq. 7.3). The permittivity of ferroelectrics is strongly temperature-

dependent close to the Curie point and high pyroelectric ﬁgures of merit can

be obtained by operating them in the region of T

and with a biasing

electric ﬁeld. This is because of a combination of high p and low tan d.A

little below T

a suﬃciently strong biasing ﬁeld can sweep the domains from

the material therefore removing the contribution to losses from domain wall

movements. Table 7.1 includes data for ‘BST’ and ‘PST’ operated in this

mode.

MATERIALS 421