# Electrical Properties of Polymers, Ceramics, Dielectrics, and Amorphous Materials Part 3

## Dielectric Properties

Insulators (also often called dielectric materials) possess a number of additional important electrical properties that make them useful in the electronics industry. They will be explained in this section.

When a voltage is momentarily applied to two parallel metal plates which are separated by a distance, L, as shown in Fig. 9.16, then the resulting electric charge essentially remains on these plates even after the voltage has been removed (at least as long as the air is dry). This ability to store an electric charge is called capacitance, C, which is defined to be the charge, q, per unit applied voltage, V, that is:

where C is given in coulombs per volt, or farad (see topic 4). Understandably, the capacitance is higher the larger the area, A, of the plates and the smaller the distance, L, between them. Further, the capacitance depends on the material that may have been inserted between the plates.

Figure 9.16. Two metal plates, separated by a distance, L, can store electric energy after having been charged momentarily by a battery.

The experimental observations lead to determines the magnitude of the added storage capability.

where

It is called the (unitless) dielectric constant (or occasionally the relative permittivity, er). e0 is a universal constant having the value of 8.85 x 10-12 farad per meter (F/m), or As/Vm, and is known by the name permittivity of empty space (or of vacuum). Some values for the dielectric constant are given in Table 9.1. The dielectric constant of empty space is set to be 1, whereas e of air and many other gases is nearly 1. The dielectric constant is frequency dependent.

We now need to explain why the capacitance increases when a piece of a dielectric material is inserted between two conductors [see Eq. (9.10)]. For this, one has to realize that, under the influence of an external electric field, the negatively charged electron cloud of an atom becomes displaced with respect to its positively charged core; compare Fig. 9.17(a) with (b).

Table 9.1. DC Dielectric Constants of Some Materials

 Potassium tantalate niobate 6,000 4,000 Ferroelectric 700 170 Water 81.1 Acetone 20 Silicon 11.8 GaAs 10.9 Marble 8.5 Soda-lime-glass 6.9 Porcelain 6.0 Epoxy 4.0 Fused silica 4.0 Dielectric Nylon 6,6 4.0 PVC 3.5 Ice 3.0 Amber 2.8 Polyethylene 2.3 Paraffin 2.0 Air 1.000576

Figure 9.17. An atom is represented by a positively charged core and a surrounding, negatively charged, electron cloud (a) in equilibrium and (b) in an external electric field. (c) Schematic representation of an electric dipole as, for example, created by separation of the negative and positive charges by an electric field, as seen in (b).

As a result, a dipole is created, which has an electric dipole moment

where x is the separation between the positive and the negative charge as depicted in Fig. 9.17(c). (The dipole moment is generally a vector pointing from the negative to the positive charge.) The process of dipole formation (or alignment of already existing dipoles) under the influence of an external electric field that has an electric field strength, E, is called polarization. Dipole formation of all involved atoms within a dielectric material causes a charge redistribution so that the surface nearest to the positive capacitor plate is negatively charged (and vice versa), see Fig. 9.18(a). As a consequence, electric field lines within a dielectric are created which are opposite in direction to the external field lines. Effectively, the electric field lines within a dielectric material are weakened due to polarization, as depicted in Fig. 9.18(b). In other words, the electric field strength in a material,

is reduced by inserting a dielectric between two capacitor plates.

Within a dielectric material the electric field strength, E, is replaced by the dielectric displacement, D (also called the surface charge density), that is,

The dielectric displacement is the superposition of two terms:

where P is called the dielectric polarization, that is, the induced electric dipole moment per unit volume [Fig. 9.18 (c and d)].

Figure 9.18. Schematic representation of two capacitor plates between which a dielectric material is inserted. (a) Induction of electric dipoles of opposite charge. (b) Weakening of the electric field within the dielectric material [Eq. (9.13)].(c) The direction of the polarization vector is from the negative induced charge to the positive induced charge see Fig. 9.17(b). (d) The dielectric displacement, D, within the dielectric material is the sum of e0E and P [Eq. (9.15)].

The units for D and P are C m"2; see Eq. (9.14). (D, E, and P are generally vectors.) In summary, the polarization is responsible for the increase in charge density (q/A) above that for vacuum.

The mechanism just described is known by the name electronic polarization. It occurs in all dielectric materials that are subjected to an electric field. In ionic materials, such as the alkali halides, an additional process may occur, which is called ionic polarization. In short, cations and anions are somewhat displaced from their equilibrium positions under the influence of an external field and thus give rise to a net dipole moment. Finally, many materials already possess permanent dipoles that can be aligned in an external electric field. Among them are water, oils, organic liquids, waxes, amorphous polymers, polyvinylchloride, and certain ceramics, such as barium titanate (BaTiO3). This mechanism is termed orientation polarization, or molecular polarization. All three polarization processes are additive if applicable; see below and Fig. 9.19.

Most capacitors are used in alternating electric circuits. This requires the dipoles to reorient quickly under a rapidly changing electric field. Not all polarization mechanisms respond equally quick to an alternating electric field. For example, many molecules are relatively sluggish in reorientation.

Figure 9.19. Schematic representation of the polarization as a function of excitation frequency for different polarization mechanisms. (A further mechanism, called "space charge polarization" which occurs at interphases between impurities and the matrix, and at grain boundaries withstands frequencies up to only 0.1 to 1 Hz. This is not shown here because of its relative unimportance for capacitors).

Thus, molecular polarization breaks down already at relatively low frequencies; see Fig. 9.19. In contrast, electronic polarization responds quite rapidly to an alternating electric field even at frequencies up to about 1016 Hz.

At certain frequencies a substantial amount of the excitation energy is absorbed and transferred into heat. This process is called dielectric loss. It is imperative to know the frequency for dielectric losses for a given material so that the respective device is not operated in this range.

## Ferroelectricity, Piezoelectricity, Electrostriction, and Pyroelectricity

Certain materials, such as barium titanate, exhibit spontaneous polarization without the presence of an external electric field. Because these materials have electrical dipoles, their dielectric constants may be orders of magnitude larger than those of non-polar dielectrics (see Table 9.1). Thus, they are quite suitable for the manufacturing of small-sized, highly efficient capacitors. A ferroelectric material is a material in which these dipoles can be reoriented using an external electrical field. Specifically, if a ferroelectric material is exposed to a strong electric field, E, its permanent dipoles become increasingly aligned with the external field direction until eventually all dipoles are as close to parallel to the field as possible and saturation of the polarization, Ps, is achieved, as depicted in Fig. 9.20.

Figure 9.20. Schematic representation of a hysteresis loop for a ferroelectric material in an electric field. Compare to Fig. 15.6.

Once the external field has been withdrawn, a remanent polarization, Pr, remains which can only be removed by inverting the electric field until a coercive field, Ec, is reached (Fig. 9.20). By further increasing the reverse electric field, orientation of the dipoles in the opposite direction is achieved. Finally, when reversing the field once more, a complete hysteresis loop is obtained, as depicted in Fig. 9.20. Therefore, ferroelectrics can be utilized for memory devices in computers, etc. The area within a hysteresis loop is proportional to the energy per unit volume that is dissipated once a full field cycle has been completed.

It should be emphasized at this point that ferroelectrics do not necessarily contain iron, as the name might suggest. Instead, the name is derived from the similarity of some properties of ferroelectric substances to those of ferromagnetic materials such as iron. In other words, ferroelectricity is the electric analogue to ferromagnetism, which will be discussed in Section 15.1.3.

A critical temperature, called the Curie temperature, exists, above which the ferroelectric effects are destroyed and the material becomes paraelectric. Typical Curie temperatures range from "200° C for strontium titanate to at least 640°C for NaNbO3.

The question that remains to be answered is, how do certain materials such as BaTiO3 possess spontaneous polarization? This can be explained by recognizing that in the tetragonal crystal structure of BaTiO3, the negatively charged oxygen ions and the positively charged Ti4+ ion are slightly displaced from their symmetrical positions, as depicted in Fig. 9.21. This results in a permanent ionic dipole moment along the c-axis within the unit cell.

Figure 9.21. Tetragonal crystal structure of barium titanate at room temperature. Note the upward displacement of the Ti4+ ion in the center compared to the downward displacement of all surrounding O2" ions. a = 0.398 nm; c = 0.403 nm.

Figure 9.22. Schematic representation of spontaneous alignments of electric dipoles within a domain and random alignment of the dipole moments of several domains in a ferroelectric material such as BaTiO3.

A large number of such dipoles line up in clusters (also called domains); see Fig. 9.22. In the virgin state, the polarization directions of the individual domains are, on average, randomly oriented, so that the material has no net polarization. An external field eventually orients the dipoles of the favorably oriented domains parallel to E. Specifically, those domains in which the dipoles are already nearly parallel to E grow at the expense of unfavorably oriented domains.

By heating BaTiO3 above its Curie temperature (120°C), the tetragonal unit cell transforms into a cubic cell whereby the ions now assume symmetric positions. Thus, no spontaneous alignment of dipoles remains, and BaTiO3 is no longer ferroelectric.

If pressure is applied to a ferroelectric material, such as BaTiO3, a change in the magnitude of the just-mentioned polarization may occur, which results in a small voltage across the sample. This effect is called piezoelectricity.20 It is found in a number of materials, such as quartz (though much weaker than in BaTiO3), ZnO, and complex ceramic compounds such as Pb(Zr,Ti)O3 (called PZT) and lead-free Bi0.5Na0.5TiO3 and K0.5Na0 5NbO3. Piezoelectricity is utilized in devices that are designed to convert mechanical strain into electricity. Those devices are called transducers. Applications include strain gages, microphones, sonar detectors, and phonograph pickups, to mention a few.

The piezoelectric effect in which stress is used to generate voltage is referred to as the direct piezoelectric effect. The converse mechanism, in which an applied electric field produces a change in dimensions in a ferroelectric material, is called the converse piezoelectric effect. The magnitude of such an effect may be up to 6 x 10-10 m/V for some of the Pb(Zr,Ti)O3 materials. Examples of devices utilizing this effect include earphones, ink jet printer heads, and diesel fuel injectors. Probably the most important application, however, is the quartz crystal resonator, which is used in electronic devices as a frequency selective element. Specifically, a periodic strain is applied to a quartz crystal by an alternating electric field, which excites this crystal to vibrations. These vibrations are monitored, in turn, by piezoelectricity. If the applied frequency coincides with the natural resonance frequency of the molecules, then amplification occurs. This way, very distinct frequencies are produced, which are utilized for clocks or radio frequency signals.

Another phenomenon through which an electric field generates a change in dimensions is electrostriction. Electrostriction is a quadratic effect between electric field and mechanical strain, whereas piezoelectricity obeys a linear relationship. Electrostriction can be observed in all dielectric materials.

A related effect is pyroelectricity21 which is observed in certain materials such as GaN, CsNO3, polyvinyl fluorides, LiTaO3, tendons, bones, and tourmaline (a silicate containing Al, Fe, Mg, Na, Li, or K). It describes a temporary voltage across the ends of these materials when the entire substance is heated or cooled. The change in temperature causes a variation of the polarization. The voltage, however, disappears after some time, due to current leakage. Pyroelectric materials are also piezoelectric. The reverse is not always true. Pyroelectricity was first described by Theophrastus in 314 BC who observed that tourmaline attracted small pieces of ash and straw when heated. In closing it is emphasized that pyroelectricity is not the same as thermoelectricity which we discussed in Section 7.7 where only one end is heated.