Applications of inhomogeneous materials: Optical and electrical properties

Physica A 157 (1989) 482-488 North-Holland. Amsterdam

APPLICATIONS OPTICAL G.A.

OF INHOMOGENEOUS

AND ELECTRICAL

MATERIALS:

PROPERTIES

NIKLASSON

Physics Department,

Chalmers

University of Technology,

S-412 96 Gteborg,

Sweden

Invited paper The electrical and optical properties of inhomogeneous materials are of importance in many applications. In this paper we consider particulate composites. Important applications of the electrical properties of such materials are found in cermet resistors and ZnO based varistor materials. The optical properties of composite media are of importance for selective absorption of solar energy, radiative cooling and energy-efficient windows. Recent progress in materials for these applications is discussed.

1. Introduction In this paper we review some current important applications of inhomogeneous materials. The scope of the paper is limited to materials consisting of a mixture of two or more well-defined constituents. Some examples are particles dispersed in a continuous matrix and mixtures als. Such composites are of interest because optical

properties.

Often

the properties

of particles of different materiof their unique electrical and

can be tailored

by varying

parameters

such as composition, particle size, constituent materials etc. Important applications are found in the areas of energy conservation, high voltage engineering, microelectronics and others. A full coverage

of the field of inhomogeneous

materials

is not possible

in a

brief review, so we limit ourselves to some important applications. In section 2 below we describe the desirable electrical properties of materials used in resistors and in overvoltage protection devices. As examples we consider “thick film” cermet resistors and ZnO-based varistor materials. Subsequently, in section 3, we review the possibility to use dielectric spectroscopy as a means for characterizing inhomogeneous insulating and semiconducting materials. Section 4 is devoted to the optical properties of inhomogeneous materials. We consider applications related to spectral selectivity, such as selective solar absorbers, radiative cooling foils and energy-efficient window coatings. Our 0378-4371/89/$03.50 0 /M~,r+h Ur.ll,,A Dh..o:,v.

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G. A. Niklasson

I Applications of inhomogeneous

current understanding of the physical properties review is also briefly described.

materials

483

of the materials treated in this

2. Applications of electrical properties The electrical properties of inhomogeneous materials have attracted considerable interest in the last decades. The mechanism of electrical conductivity in coevaporated and cosputtered metal-insulator composites has been established. The temperature and field dependence of the conductivity can be described by models of tunneling between metal particles [l]. For a detailed understanding percolation arguments appear to be necessary [2-41. Thin films of metal-insulator composites have been applied as coatings to vidicon targets [5]. Related Si-SiO, composites have important applications in solid state devices [6]. The above mentioned composites consist of metal or semiconductor particles dispersed essentially randomly in an insulator. In this section we concentrate on a few considerably more complicated composite structures of technological importance. 2.1.

Thick film resistors

Resistive films, used for example in microelectronic circuits, should have a well defined resistance with a low temperature dependence. So called thick film cermet resistors [7] are very interesting for this application. The materials are supplied as a suspension of glass and conducting metal oxide particles in an organic fluid. The most common conducting materials are oxides of ruthenium (RuO,, Pb,Ru,O,, Bi,Ru,O,). The resistors are applied by screen printing, in a desired pattern, drying and firing (heating to high temperature). The thickness of the resulting films is usually lo-20 pm. The resistivity of the films can be varied over several orders of magnitude by varying the metal oxide volume fraction. The resistivity also displays a shallow minimum near room temperature, which leads to a low temperature coefficient of resistance (TCR) 17, 81. The electrical properties of these cermet resistors are not completely understood but significant progress has been made. The composite becomes conducting for metal oxide volume fractions, f, above the percolation threshold, f,, which can be as low as f, = 0.02 [9]. The percolation threshold decreases as the ratio of glass to metal oxide particle size becomes higher [lo, 111. When the glass particles are much larger than the conducting ones, the latter will occupy positions at the surfaces of the larger particles. It has been established that percolation in shells at the surfaces of large particles leads to lower critical

G. A. Niklasson I Applications of inhomogeneous

484

volume

fractions

threshold values are

the

than

in the range

presently

generally

not

explained

sign of the TCR conducting

random

conductivity 1.7-7

percolation

varies

of u -

for different

understood. as being

The

samples small

can be connected

Above

(f-f,)‘.

The [9-11,

TCR

due to two competing

[8, 16, 171. A recent

particles

[ll-151.

materials

percolation

near

151. These room

mechanisms model

the

percolation t displays

exponent

differences

temperature

is

with different

[18] assumes

that the

in two ways. They may be connected

by

a small conducting neck or via a thin tunneling barrier of glass. A threecomponent percolation model [18] based on these concepts gives good fits to the experimental temperature dependence of the conductivity. The formulation of nonstandard percolation models appears to be a viable way to investigate the relation between the structure and the electrical properties of thick film cermet

2.2.

resistors.

Varistor materials

Varistors based on ZnO [19] are materials with highly nonlinear current voltage relationship. The coefficient of nonlinearity, p, defined by the relationship between the current I and voltage V, I - V”, can be as high as p = 100 [19]. This makes ZnO varistors highly effective devices for protection against transient overvoltages. The ceramic varistors are produced by sintering of pressed oxide powders. The ZnO varistor materials consist mainly of doped ZnO grains and intergranular phases, which often contain Bi-oxide [20]. The current-voltage curve can be divided into three regions. At low voltages the resistivity

is high and the material

is insulating.

However

a small leakage

current is apparent. It is probably due to conduction through a continuous skeleton of Bi-rich phases, primarily located at the triple grain junctions [21]. At higher voltages the current increases very rapidly with increasing voltage. The

electrical

properties

in the region

of nonlinearity

are controlled

by the

potential barriers at the interfaces between ZnO grains [19, 22-241. The details of the barriers and the conduction mechanism needs further clarification. The nonlinear Z-V curves may be due to excitation of charge carriers above the barrier [22, 231 or to tunneling processes [19, 241. Finally, at very high voltages the barriers do not influence the electrical properties any more, and the I-V curve shows the resistivity of the ZnO grains. Recently a thin film varistor with high p has been produced [25]. It consists of a B&O, on ZnO two-layer thin film deposited by rf sputtering. Varistor action is controlled by negative charges and a potential barrier at the ZnOB&O, interface [25]. It is likely that the properties of varistor materials will be an active research area for some time to come.

G. A. Niklasson I Applications of inhomogeneous

materials

485

3. Dielectric spectroscopy

By dielectric spectroscopy one can measure the complex dielectric permittivity or the complex conductivity, (T(W), in a wide frequency range; typically 10m4Hz < w < 10’ Hz. These quantities contain much information on the electrical properties of inhomogeneous materials. There is a possibility to deduce from U(W), the geometry of the clusters of conducting particles or localized states in the insulator, which are responsible for the ac conductivity [26]. There are however other factors that may influence the dielectric properties, namely a distribution of transition rates [27] and effects of interactions between the charge carriers [28, 291. A better understanding of these various processes is necessary in order to develop dielectric spectroscopy into a useful tool for materials characterisation. At present it is only in special cases that one can make a clearcut interpretation of dielectric spectra. As examples we describe the dielectric properties of the materials we considered in section 2. Kubovy and Stefan [30] studied a Pb,Ru,O,-based thick film resistor and found the relationship a(o) - o(O) - w”.78 over two decades of frequency. This is fairly close to what is expected from percolation theory, which predicts an exponent of about 0.7 [26]. Hence these measurements support a percolation picture of the films. A varistor based on ZnO showed [31] a dc conductivity at low frequencies crossing over to a dependence a(w) - o”.5 at w > 0.01 Hz. This behaviour is probably due to conduction on a regular (non-fractal) network [31]. We think that the low field conduction takes place on a regular network of intergranular Bi-rich phases, as mentioned above.

4. Applications

of optical properties

In this section we consider the optical properties of inhomogeneous materials and consider some interesting applications which depend on the spectral selectivity [32] of coatings composed of small particles in a matrix. 4.1. Selective solar absorbers Spectrally selective coatings, which have a high absorption of solar energy and a low thermal emittance [33], are necessary for efficient collection of solar energy. Inhomogeneous metal-insulator composites have been found to be very suitable for this purpose. Co-evaporated composites such as Ni-Al,O,, Pt-Al,O, [34] and Co-Al,O, [35] can be produced with a solar absorptance, (Y, around 0.9 and a thermal emittance, E, in the range 0.1-0.2. The perform-

G. A. Niklasson I Applications of inhomogeneous

486

ante

of the coatings

taking

advantage

by chemical selectivity. composites.

can be further

of surface

vapour

roughness

deposition

The most widely Black chrome

improved

materials

by composition

grading

[34] or by

[36]. A MO-MOO, composite

1371 (black used selective

[38, 391 produced

molybdenum) solar absorbers

produced

also displays

a good

are metal-insulator

by electro-deposition

is a complex

Cr-CrzO, composite with a graded composition profile. Another commercial coating is nickel pigmented anodic aluminium oxide produced by anodization and electrolytic metal particles

coloration is often

[40]. In these coatings the selective absorption boosted by other effects such as interference

of the and

surface texture. The selective optical properties of metal-insulator composites can to a high degree be understood within the framework of effective medium theories [34, 3.5, 38, 401. The optical effects of surface roughness have been treated by diffraction theory [39]. Further studies are necessary in order to obtain a quantitative understanding of the optical properties of metal-insulator composA hitherto unsolved problem is the ites over a wide composition range. description of the optical properties close to the metal-insulator transition. Selective absorbing paints are interesting because of fairly good selectivity and very low cost [41]. These coatings are composed of absorbing particles (Fe,O,, FeMnCuO,) dispersed in a binder; often a silicone. Particle sizes are often above 0.1 pm, which means adequate. Instead multiple scattering comparison of theory and experiment

4.2.

Foils for radiative

that effective medium theory should be used has so far been carried

theory is not [42]. Very little out.

cooling

Selective foils having a low solar transmittance and a high transmittance in the atmospheric window region between wavelengths of 8 and 13 pm can be used to cool an underlying emissive material. The energy emitted in the 8-13 pm interval balances and can even be greater than the absorbed solar radiation. Initial work on polyethylene foils pigmented by TiO, showed that radiative scattering achieved.

4.3.

cooling

by this concept

calculations

[44] indicate

Coatings for energy

efficient

is indeed

possible

that optimal

[43]. Preliminary

properties

multiple

have so far not been

windows

Several coatings and materials considered for use in energy efficient windows are particulate composites. A few examples are given below. The solar transmittance of noble-metal based transparent heat mirrors can be significantly increased by using network metal films close to the metal-insulator

G. A. Niklasson I Applications of inhomogeneous

materials

487

transition instead of continuous films [45]. The darkening of photochromic glasses is due to the formation of small Ag particles [46] under ultraviolet irradiation. Liquid-crystal-polymer composites can be used to obtain voltage induced switching between clear and diffusely scattering states in windows [47]. Finally, we mention that silica aerogels, which consist of a very porous network of SiO, particles [48] are very interesting as transparent thermal insulation materials.

Acknowledgements

This work was financially supported by grants from the Swedish Natural Science Research Council, The National Swedish Board of Technical Development and ABB Research and Development, Vaster&s, Sweden. I wish to thank my collaborators C.G. Granqvist, K. Brantervik, E. Olsson, T.S. Eriksson and G.B. Smith.

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