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

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10 000 h. LaCrO

was considered a prime candidate for this application since it

combines a melting point of 2500 8C with high electronic conductivity (about

100 S m

1

at 1400 8C) and resistance to corrosion. There is now little interest in

MHD systems but LaCrO

is established as a specialized heating element.

LaCrO

is one of the family of lanthanide perovskites RTO

, where R is a

lanthanide and T is a period 4 transition element. In the cubic unit cell R

occupies the cube corners, T the cube centre and O the face-centre positions. The

coordination numbers of T and R are 6 and 8 respectively. LaCrO

loses

chromium at high temperatures, leaving an excess of O

2

ions. The excess charge

is neutralized by the formation of Cr

4þ

which results in p-type semiconductivity

with ‘hole hopping’ via the localized 3d states of the Cr

3þ

and Cr

4þ

ions. The

concentration of Cr

4þ

can be enhanced by the substitution of strontium for

lanthanum. A 1 mol.% addition of SrO causes the conductivity to increase by a

factor of approximately 10 (see Section 2.6.2).

Heating elements are formed by normal ceramic processing. Strontium acts as

a sintering aid as well as promoting conductivity, and cobalt can be added to

limit grain growth. Sintering takes place in a reducing atmosphere

 10

12

atm or 10

7

Pa) at temperatures close to 1700 8C and is followed

by an anneal in oxygen that establishes the high conductivity.

Satisfactory conductivity is maintained up to 1800 8C in air but falls oﬀ at low

oxygen pressures so that the upper temperature limit is reduced to 1400 8C when

the pressure is reduced to 0.1 Pa. A further limitation arises from the volatility of

which may contaminate the furnace charge. The combination of high

melting point, high electronic conductivity and resistance to corrosion has led to

the adoption of lanthanum chromite for the interconnect in high temperature

solid oxide fuel cells (see Section 4.5.3).

4.1.4 Tin oxide

Tin oxide (SnO

) has found applications in high-temperature conductors, ohmic

resistors, transparent thin-ﬁlm electrodes and gas sensors.

It crystallizes in the tetragonal rutile structure (see Fig. 5.27) with cell

dimensions a ¼ 474 pm and c ¼ 319 pm; in the single-crystal form it is known by

its mineralogical name, cassiterite. It is a wide band gap semiconductor, with the

full valence band derived from the O 2p level and the empty conduction band

from the Sn 5s level. The band gap at 0 K is approximately 3.7 eV, and therefore

pure stoichiometric SnO

is a good insulator at room temperature when its

resistivity is probably of the order of 10

O m.

In practice both natural and synthetic crystals are oxygen deﬁcient, leading to

donor levels approximately 0.1 eV below the bottom of the conduction band and

consequently to n-type semiconductivity. Doping the crystal with group V

elements also induces n-type semiconductivity; the usual dopant is antimony.

The ground state electronic conﬁguration of the Sb atom is 5s

, and when it

142 CERAMIC CONDUCTORS

TEAMFLY

Team-Fly

replaces Sn

4þ

¼ 69 pm) in the SnO

lattice it does so as Sb

5þ

¼ 61 pm). The

n-type conductivity is due to electrons ionized from the 5s

state.

Antimony-doped SnO

is a complex system and is far from completely

understood. The interpretation of data is complicated by the fact that both the

stoichiometry of the host lattice and the oxidation state of the dopant are

dependent upon ambient oxygen partial pressure and temperature. The

successful exploitation of semiconducting SnO

has been achieved largely

through development work guided by a general understanding of underlying

principles, as indeed is the case for much of electroceramics technology.

An important application of SnO

in ceramic form is in conducting electrodes

for melting special glasses, such as those used for optical components and lead

‘crystal’ tableware. The ideal glass-melting electrode should have a high electrical

conductivity at room temperature and, of course, at glass-melting temperatures

and a high resistance to corrosion by the glass. In addition, it must not discolour

the glass. SnO

is the only material, apart from platinum, which fulﬁls these

requirements for glasses containing lead oxide.

SnO

itself does not readily sinter to a dense ceramic and so sintering aids such

as ZnO (r

(Zn

2þ

) ¼ 75 pm) and CuO (r

(Cu

2þ

) ¼ 73 pm) are added, together with

group V elements such as antimony and arsenic to induce semiconductivity. Some

of the sintering aids enter the lattice, tending to negate the eﬀect of the dopants

added to induce semiconductivity, and successful compositions, typically

containing more than 98 wt% SnO

, have been arrived at by trial and error.

The oxide powder, together with binders, is commonly isostatically pressed

into the forms shown in Fig. 4.3 and ﬁred in oxidizing conditions at

approximately 1400 8C. Under these conditions sintered densities in the range

6500–6700 kg m

3

(theoretical density for SnO

is 7002 kg m

3

) are achieved. The

largest electrodes made in this way are in the form of cylinders about 600 mm

long and 150 mm in diameter weighing approximately 60 kg. Cooling from the

sintering temperature is carried out, in part, in a nitrogen atmosphere with the

object of creating electron-compensated oxygen vacancies and so enhancing

room temperature conductivity which is typically of the order of 10

1

. The

high conductivity minimizes Joule heating in the electrode region outside the

molten glass.

The form of the glass-melting furnace is shown in Fig. 4.4 although in practice

the electrodes may well be a substantial part of the furnace walls. The charge

(‘cullet’) is preheated, using gas or oil, to about 1000 8C when it has suﬃcient

conductivity to be directly heated to the required temperature (1300–1600 8C) by

power dissipated internally. By supplying the heat from within the body of the

glass melt rather than from the outside, the free surface temperature is kept

relatively low and thus the excessive loss of volatile elements, particularly lead, is

avoided. The process is economic since the heat is generated in the glass, where it

is required. The elements are resistant to attack by glass and so have long service

lives, typically 2 years.

HIGH-TEMPERATURE HEATING ELEMENTS AND ELECTRODES 143

144 CERAMIC CONDUCTORS

Fig. 4.3 Isostatically pressed tin oxide electrodes for producing high quality glasses; the

length of the longest electrode in the illustration is approximately 500 mm. (The contacting

stubs may be wrapped with silver foil to reduce resistance.) (Courtesy of Dyson Technical

Ceramics.)

Fig. 4.4 Heating a glass melt: the power (I

R) is introduced directly into the melt via tin

oxide electrodes.

4.1.5 Zirconia

The ‘Nernst ﬁlament’, once used as a light source, consisted of zirconia (ZrO

)

doped with thoria and ceria. Preheating the ﬁlament to about 600 8C using an

external source reduces its resistance to a value which permits direct Joule

heating to be eﬀective when temperatures of up to 1800 8C can be attained. More

recently the development of stabilized ZrO

(see Section 4.5.3) has made it

possible to use ZrO

-based ceramics as furnace elements, although they also

always require preheating to reduce the resistance to a level at which Joule

heating is eﬀective. Its high negative temperature coeﬃcient of resistance makes

it necessary to have a resistor, preferably with a high positive temperature

coeﬃcient, in series with it to limit current.

Once the element has reached temperatures exceeding about 700 8C it can also

be used as a susceptor and heated by eddy currents generated by an induction

coil and a high frequency (0.1–10 MHz) power source.

ZrO

was one of the earliest ceramics in which conduction by oxygen ions was

observed and now this characteristic is exploited in fuel cell and sensor

technologies (see Sections 4.5.3 and 4.6.1).

4.2 Ohmic Resistors

Most resistors for electrical and electronic applications are required to be ohmic

and to have small temperature coeﬃcients of resistance. The major requirement in

electronics is for resistors in the range 10

–10

O, while materials with suitable

electrical properties usually have resistivities less than 10

6

O m. Fabrication of a

O resistor of length 110 mm from a material with a resistivity of 10

6

O m

requires a cross-sectional area of 10

12

, i.e. a strip 1 mm thick and 1 mm wide, for

example. This is not a technical impossibility, but other more economic routes to

resistor manufacture have been established based on the following two principles.

1. Very thin conductive layers are deposited on an insulating substrate and large

length-to-width ratios are obtained by etching a suitable pattern.

2. The conductive material is diluted with an insulating phase.

These methods are often combined.

4.2.1 Thin ¢lms

Thin ﬁlms of thickness typically 10 nm are readily formed in a vacuum chamber

by evaporation, ‘sputtering’, or chemical vapour deposition (CVD). Many

metals and metal alloys, e.g. aluminium, silver, gold and Ni–Cr, can be

OHMIC RESISTORS 145

evaporated from the molten state and condensed onto suitable substrates. Ni–Cr

alloys with resistivity values of about 10

6

O m are deposited in thin-ﬁlm form

and provide a basis for the manufacturer of high-value resistors.

Thin-ﬁlm oxides are usually formed by ‘sputtering’. The chamber is ﬁlled with

argon at a pressure of typically about 1 Pa to which a small amount of oxygen is

added. The target is usually a disc of the oxide to be sputtered ﬁxed to a metal

plate. The substrate on which the ﬁlm is to be deposited rests on a metal plate. A

high-frequency (about 1 MHz) high-voltage (about 5 kV) is applied between the

two plates and a plasma is developed. Gaseous ions bombard the source and

detach clusters of ions or molecules from its surface which pass through the

plasma and are deposited on the substrate. SnO

,In

and mixtures of these

oxides, e.g. 90In

–10SnO

, are deposited as transparent conductive ﬁlms by

this method. They are essential to the functioning of many electro-optical devices.

Indium tin oxide (ITO) ﬁlms are also commonly deposited by CVD in the

manufacture of ﬁlm resistors. Glass, or sometimes steatite, rods are heated to

about 700 8C in air of controlled humidity and a mixture of tin tetrachloride and

antimony pentachloride is then introduced for a few seconds. Reaction with water

occurs on the surface of the rods, resulting in the formation of a thin ﬁlm of mixed

oxides which is ﬁrmly attached to the substrate. The antimony lowers the

resistivity of the SnO

and also enables the temperature coeﬃcient of resistance to

be controlled near to zero; the SnO

alone gives a high negative coeﬃcient. A

small fraction of the O

2

ions in the deposit are replaced by Cl



ions, and these

also lower the resistivity because the lower negative charge of Cl



compared with

2

is compensated by an electron in the conduction band. The resulting units

require a protective layer of impervious lacquer to inhibit the eﬀects of moisture

but are very stable and reliable in use; because of the strong adhesion of the ﬁlm

open circuits do not occur through detachment of small pieces, which

occasionally happens with sputtered carbon ﬁlms. The presence of moisture

and soluble ionic material on the ﬁlm can set up electrolytic action which results in

a portion of the ﬁlm being converted to metallic tin with a resultant diminution in

resistance, but care in production makes this a very rare occurrence.

Enhanced length-to-width ratios can be achieved by cutting a spiral groove

through the resistive ﬁlm and into the cylindrical rod substrate. Resistance values

can be kept within close tolerances by stopping the groove cutting automatically

when a preset value is reached. Patterned deposits on ﬂat surfaces can be formed

by a number of processes, e.g. by an air jet carrying abrasive particles or by

volatilization by an infrared laser beam or an electron beam. Frequently

photolithography is used when a layer of photosensitive material, called a ‘resist’,

is formed on the deposited ﬁlm. The resist is exposed to a pattern of light that

renders it insoluble and the unexposed regions are then removed with a solvent.

The deposit is then immersed in a reagent that dissolves the sputtered material

and not the resist. Finally, the remaining resist is removed. Examples of thin-ﬁlm

resistors are shown in Fig. 4.5.

146 CERAMIC CONDUCTORS

4.2.2 Thick ¢lms

Rather thicker ﬁlms with thicknesses typically in the range 10–15 mm are made by

what is termed the ‘thick-ﬁlm’ or ‘silk-screen’ technique. Silk screening is a well-

established method for printing artwork. The screens were formerly silk but are

now meshes of either nylon or stainless steel. Patterns are formed by coating

them with a resist, exposing them to a pattern of light and washing out the

unexposed parts. The screen is held taut in a frame that is ﬁxed 1–3 mm above

the surface to be printed. A paint of a stiﬀ creamy consistency is swept across the

screen by a hard rubber squeegee with suﬃcient pressure to force the screen, now

loaded with paint, into contact with the underlying surface. The consistency of

the paint is such that, as the screen rises from the surface, it ﬂows over the spaces

left by the threads or wires of the screen so that there is only a small variation in

the thickness of the deposit.

Resistors are formed by taking a conductive powder and mixing it with

powdered glazes and an organic vehicle that imparts the necessary rheological

properties. Mixing is carried out on a set of rollers running at diﬀerent speeds as

described under calendering (see Section 3.6.7), and this ensures a very high

degree of dispersion of the components. A required resistor pattern is silk

screened onto a substrate, usually a 96% alumina. A carefully controlled ﬁring

schedule ensures that the organic solvents evaporate (100–150 8C), the remaining

organic compounds evaporate or are burned out (200–450 8C) and, ﬁnally, the

inorganic glass and active resistive components mature and bond to the substrate

(850 8C for about 10 min). The complete ﬁring takes about 1 h. Metal conductors

and contact pads can be made using the same technique. Examples of thick-ﬁlm

devices and circuits are shown in Fig. 4.5.

Although it is simple to prepare pastes and use them to make resistors, the

structure of the resulting components is complex and the conduction

mechanisms remain a matter for debate.

The active components are usually highly conductive oxides (10

–10

1

)

such as PdO, RuO

,Bi

and Bi

. Electrically they behave as metals

and have low positive temperature coeﬃcients of resistivity (TCR). The glaze is

usually a lead borosilicate, of composition typically (in wt%) 52PbO–35SiO

–

10B

–3Al

. The resistors normally give high resistivities and negative

temperature coeﬃcients for low concentrations of the conductive component,

and low resistivities and positive temperature coeﬃcients for high concentra-

tions, as shown in Fig. 4.6

{

. This behaviour diﬀers markedly from that to be

expected from a random distribution of conductive particles in an insulating

matrix. The conductivity of dispersions of metal particles of mean size around

OHMIC RESISTORS 147

{

In characterizing the resistance of the printed ﬁlms used in microelectronics it is the practice to deﬁne a

‘surface resistivity’, r

¼ r=h, in which h is the ﬁlm thickness. It is also common practice to express r

‘units’ of ‘ohms per square’ or simply O=

; r

is equivalent to the resistance measured between opposite

edges of a printed square.

148 CERAMIC CONDUCTORS

Fig. 4.5 Film devices and circuits: (a) thin-ﬁlm resistors on glass and steatite substrates; (b)

thick-ﬁlm resistor networks on ‘snapstrate’ alumina substrate; (c) various thick-ﬁlm resistors;

(d) hybrid microcircuits. (Components kindly supplied by General Hybrid, C-MAC and

Welwyn Components Ltd.)

100 mm in an insulating matrix is very low when the metal concentration is small

and then increases by several orders of magnitude over a concentration range of

a few per cent around 10 vol.% (see Fig. 2.49), with only a small increase for

higher concentrations. This is understandable as a consequence of the

establishment of continuous contact between particles from electrode to

electrode at a well-deﬁned concentration.

Transmission electron micrographs show that the dispersed conductive

particles form convoluted chains with the particles either close together or in

contact. According to this model there will be chains of conductive particles

joining the electrodes even at high dilutions. The resistance is provided by two

components, that due to the interior of the conductive particles and that due to

the areas of near contact between them. The former will provide a positive

temperature coeﬃcient of resistance whilst the latter, if it depends on some form

of thermally activated semiconductive behaviour, will provide a negative

coeﬃcient. So far it has not been possible to determine the properties of the

material between the surfaces of the particles. The solubility of the conductive

oxides in the glaze has been shown to be very small but, as the intergranular layer

is very thin, it may be enough to endow the glaze with a suﬃcient level of

conductivity.

The glaze component is resistant to moisture so that units are stable in normal

ambients. Their mode of fabrication allows whole patterns of resistors to be

made at once, although strict control of production conditions is necessary to

OHMIC RESISTORS 149

Fig. 4.6 Electrical characteristics of RuO

thick-ﬁlm resistors.

ensure reproducibility. Generally several batches of paste are made and the

values they yield on processing are determined. The required value can then be

obtained by blending two batches whose values span that required, using

Lichtenecker’s relation (Eq. (2.131)) to determine the ratio in which the two end-

members must be combined. Values can ﬁnally be trimmed into tolerance by

volatilization using a laser beam or by jet abrasion.

4.3 Voltage-dependent Resistors (Varistors)

4.3.1 Electrical characteristics and applications

There are a number of situations in which it is valuable to have a resistor which

oﬀers a high resistance at low voltages and a low resistance at high voltages as is

the case in the current–voltage characteristic shown in Fig. 4.7.

Such a device can be used as shown in Fig. 4.8 to protect a circuit from high-

voltage transients by providing a path across the power supply that takes only a

small current under normal conditions but takes a large current if the voltage

rises abnormally, thus preventing high-voltage pulses from reaching the circuit.

High-voltage transients are of suﬃciently frequent occurrence in most power

supplies to make the protection of sensitive circuits essential. Transistors and

integrated circuits are particularly susceptible to damage by transients.

Ceramics based on SiC and ZnO are two materials in everyday use that have

the characteristic shown in Fig. 4.7. In both cases it has been established that the

resistance is controlled by the region in which the ceramic grains contact one

another.

The microstructure of a ceramic for a voltage-dependent resistor (VDR) can

be visualized as shown in Fig. 4.9(a) with IGLs of varying thickness between

grains that diﬀer in size by about a factor of 10. An idealized structure which is

150 CERAMIC CONDUCTORS

Fig. 4.7 Typical current–voltage relation for a voltage-dependent resistor.

useful for calculating average properties is shown in Fig. 4.9(b), but it must be

appreciated that in practice the high-current paths are likely to be via those

particles separated only by the thinnest IGLs, so that regions of high current

density will form tortuous routes between the electrodes.

The VDR behaviour in ZnO varistors is governed by electron states that are

formed on the surfaces of crystals as a consequence of the discontinuity. These

surface states act as acceptors for electrons from the n-type semiconductor.

Electrons will be withdrawn from the region near the surface and replaced by a

positive space charge. In this way oppositely oriented Schottky barriers will be

created at the surfaces of neighbouring crystals so that a high resistance will be

oﬀered to electron ﬂow in either direction (Fig. 4.10(a)). The situation with an

applied ﬁeld is shown in Fig. 4.10(b). With low applied ﬁelds small thermally

VOLTAGE-DEPENDENT RESISTORS (VARISTORS) 151

Fig. 4.8 Use of a voltage-dependent resistor (VDR) to protect a circuit against transients.

Fig. 4.9 Illustrations of (a) actual and (b) idealized microstructure of a varistor.