The chapter first gives a brief introduction on conduction, polarization, dissipation, and breakdown of dielectrics under electric field. Then, two of electric field-related applications, dielectrics for electrical energy storage and electrocaloric (EC) effect for refrigeration are discussed. Conclusion and perspectives are given at last.
- electrical energy storage
- electrocaloric refrigeration
Dielectrics are materials that can be polarized by an applied electric field. Polarizability is the essential property for dielectrics. The term is closely related to insulator. In electrical phenomena, insulator is commonly used especially in electronic engineering and electrical engineering, that is, in electronic packaging printed circuit board, electrical wire, high voltage system, and so on. It has a longer history than “dielectrics.” The main property of an insulator is to prevent the flow of current when it is not desired. This means that insulator must have low electrical conductivity and can resist breakdown under high electric field. Physically, insulator is a subgroup of dielectrics because of the existence of polarization. And dielectrics can include insulator, semiconductor, and other materials with polarizability. Nevertheless, poor insulation could screen the polarizability of dielectrics under electric field, which makes the polarization hard to be “seen” by electrical measurement. And in most cases, poor insulation makes dielectrics useless. Thus, insulating property is commonly expected for dielectrics. Although insulating dielectrics has been applied for long time, the study on the area is continually progressing, that is, using cold sintering processing , developing broadband dielectric spectroscopy [2, 3], optoelectrical effect [4, 5], and multiferroics .
The subgroups of insulating dielectric include piezoelectric, pyroelectric (electrocaloric), ferroelectric, and multiferroic. Electrocaloric is the reverse effect of pyroelectric. Because of interesting physics and technological importance, there are enormous books dedicated to these areas. Thus, we only introduce the fundamental phenomena of dielectric under electric field in the chapter. Then, two state-of-the-art applications for dielectrics are included, which are electrical energy storage [7, 8] and electrocaloric refrigeration [9, 10, 11]. We show that electric field plays a critical role in both applications.
2. Dielectrics under electric field
The main properties for dielectric under electric field are conduction, polarization, dissipation, and breakdown. Although normally a dielectric material is a good insulator, there are still some charge carries flowing through the whole material under electric field, which is called leakage current. Under a direct current (dc) field, the current could be a constant for a material. If the detected current is
The property can also be expressed by bulk resistivity
Both conductivity and resistivity are electrical properties for all materials, that is, conductor, semiconductor, and insulator. Because of different mechanism of conduction, there is a huge gap between conductivities of dissimilar materials, which has been well understood by energy band theory. The conductivity of a conductor could be big as 109 S/m; the conductivity of good insulating dielectrics could be small as 10−18 S/m.
The DC conductivity in dielectrics is related to the hopping transition of defect charge carries, and thus, it is strongly temperature dependent:
The conductivity of dielectrics under alternative current (ac) field is related to the imaginary part of dielectric constant, which is introduced in Section 3. Since insulating is prerequired for dielectrics, the conductivity is less considered in the study of dielectrics. However, in some cases, it is crucial for dielectric properties .
Polarization is the unique electrical properties for dielectrics, depending on which concept is defined. There are diverse types of polarization, that is, electronic polarization, ionic polarization, orientation polarization, interface polarization, spontaneous polarization, and so on.
In dielectrics, if one positive charge +
From this definition, we can see that the magnitude of polarization equals to the surface charge density, in fact depending on which the spontaneous polarization of ferroelectrics is measured by Sawyer-Tower electrical bridge.
For all dielectrics under electric field, the mutual shifts of nuclei and electrons induce electronic polarization, which occur within very short time, that is, 10−14 –10−16 s. Electronic polarization exists for all materials. In ionic crystals, the relative separation of cation and anion is induced by electric field, which is called ionic polarization. The ionic polarization also builds at a very short time, that is, 10−12 –10−13 s.
In some molecules, the center of positive charge and negative charge does not coincide, which is called polar molecule. In polar molecules, permanent dipoles exist and can somehow rotate under electric field. In thermal equilibrium state, the dipoles randomly orient, and thus, there is no net polarization. When an external electric field applied, these dipoles align to it in some extent. Thus, orientation polarization is induced. The response time of these permanent dipoles changes from material to material, that is, 10−2–10−12 s. For example, in water at 300 K, the response time is around 5 × 10−11 s.
Interface polarization, which is also called space charge polarization, builds at interface between two or more heterogeneous medium, i.e., between electrodes and dielectrics, between different dielectrics, between grain boundaries in ceramics, etc. The electrons, ions, and other defects trap at these sites, which have a slow response toward AC electric field. The response time varies from case to case, that is, 107–10−6 s.
In ferroelectrics, from high-temperature paraelectric phase to low-temperature ferroelectric phase, a permanent dipole is present because of symmetry break without electric field, which is called spontaneous polarization. The spontaneous polarization can be reversed by an external electric field, which makes ferroelectrics a smart material with lots of interesting properties.
In general, the relation between polarization
From Eq. (5), we can see that
For a capacitor, electric displacement equals to the surface charge density. Assume a planar capacitor consisting of two parallel electrodes with surface
2.3. Dielectric dissipation
Under AC electric field, there are two types of current flowing through a capacitor, the so-called polarization current
The first term is still called dielectric constant, while the second term is called the imaginary part of dielectric constant. When an AC electric field
The conduction current is normally harmful for applications. Thus, there are lots of work on how to decrease dielectric loss.
Under very high electric field, the conduction current increases significantly. Finally, a dielectric enters a high conduction nonequilibrium state, which is called breakdown. Mathematically, it can be expressed as:
If a material with thickness
Except electric field, heat also induces breakdown. Thermal breakdown occurs when a material cannot efficiently dissipate the produced heat. In many cases, a breakdown is companied by both electric and thermal breakdowns. Breakdown also has randomicity, which can be described by Weibull distribution.
3. Dielectric relaxation
One essential problem in dielectrics is the response time of a dielectric material toward to a periodic external electric field. When polarization delays with respect to an external oscillating electric field, so-called dielectric relaxation occurs. Dielectric relaxation may happen at an intrinsic time (so-called characteristic relaxation time) for a particular polarization, so it can help to identify the specific polarization mechanism. It also induces significant energy loss (or, in some case, energy conversion like oscillator, and so on), which is very important for engineering applications. Because of mutual inverse between time
For clarifying a relaxation mechanism, different electric parameters may be applied, that is, complex dielectric constant
3.1. Debye relaxation
Debye relaxation equation is the most simple and elegant mathematic equation so far used to describe relaxation phenomenon:
Here exponent parameter
3.2. Maxwell-Wagner relaxation
Maxwell-Wagner relaxation is because of electric inhomogeneous of materials, that is, interface between dielectrics and electrodes, grain boundaries, and so on. It is usually represented by a two-layer equivalent electric circuit as shown in Figure 2.
The dielectric permittivity of Maxwell-Wagner relaxation can also be expressed as Debye relaxation style:
if we set the following parameters:
The electric modulus of the circuit is as follows:
From these equations, we can find that the impedance normalization highlights big resistance relaxation, while the electric modulus normalization highlights small capacitance relaxation. It should be noted that the equivalent electric circuit changes from case to case, and more complex circuit model may be applied for treating dielectric behavior of Maxwell-Wagner relaxation . Here, we only give the simplest case in which there only exist two dielectric ingredients.
3.3. Universal dielectric relaxation
Universal dielectric relaxation is also called universal dielectric response. To have a better understanding of it, we first introduce complex conductivity
For many dielectrics, A. K. Jonscher found that the frequency-dependent AC conductivity satisfies the following exponent relation :
which is called universal dielectric relaxation. If
So far, to identify a specific relaxation is still not easy. In most cases, the characteristic relaxation time constant
4. Dielectrics for energy storage
Energy and environment protection are the challenges we are facing. Effective storing energy, reducing loss, and environment pollution are the hot topics for researchers. Electrical energy perhaps is the most convenient energy form to be applied. For applications in mobile electronic devices, stationary power systems, and hybrid electric vehicles, electric energy must be stored first.
There are many ways to storage electrical energy such as battery, supercapacitor, and dielectric capacitor. Battery has very high energy storage density (10–300 W⋅h/kg), but the power density is very low (<500 W/kg) and hazard for environment. Supercapacitor has average energy storage density (<30 W⋅h/kg) and power density (10–106 W/kg). But it has shortages such as complex configuration, low operating voltage, large leakage, and short recycling period. In comparison, dielectric capacitor has the highest power density (108 W/kg), broad operating temperature, fast charging and discharging, and long recycling period. The only disadvantage is low energy storage density (10−2–10−1 W⋅h /kg). Thus, there is a crucial need for dielectric capacitor with improved energy storage density .
The energy stored in a dielectric material under an electric field can be expressed by the shadow area in Figure 3 in which different relationships between electric field
Thus, high dielectric permittivity and high breakdown field are highly desirable for the dielectrics used in energy storage devices. For linear dielectrics, a very high electric field must be applied to obtain large
4.1. Single-phase materials for energy storage
As we have stressed, ferroelectric and antiferroelectric materials have better energy storage density. However, lots of them are inorganic materials prepared by solid reaction method. Various defects, like pores, impurities, and vacancies are produced during sintering, deteriorating the dielectric strength. For instance, the theoretical antiferroelectric-ferroelectric phase transition happens at 2.2 × 107 V/m for PbZrO3, but the breakdown field for PbZrO3 ceramic is about 1 × 107 V/m. The typical energy storage density for ferroelectric ceramic is around 1 J/cm3. If materials are prepared in thin-film forms, the energy storage density could increase 10–50 times. However, reducing thickness also means reducing weight or volume, an impractical method for large energy storage application. The configuration of multilayer ceramic capacitor may be employed in this case. On contrary to ceramics, polymers have high breakdown field (108 V/m), although the dielectric constant is very small (<10). The energy storage density of polymer is around 10 J/cm3. In addition, polymers are flexible, which can be used in flexible electronics.
It is should be noted that many already developed dielectrics may have super electric energy storage density. For instance, BiFeO3-SrTiO3 is a multiferroic system . Recently, it was shown that BiFeO3-SrTiO3 thin film can get an ultrahigh energy density of ~51 J cm−3. The breakdown field of the film is 360 MV/m, which is comparable with polymer dielectrics .
4.2. Ceramic-polymer composites for energy storage
Combining high dielectric constant ceramic with high breakdown field polymer to prepare composites has been extensively studied for energy storage, which is usually called 0–3 composites because zero-dimensional ceramic particles embedded in three-dimensional polymer matrix.
By filling ceramic particles with dielectric constant
There are enormous works of 0–3 composites. For example, in BaTiO3-polymer composites, filling 40%, 70%, 70%, 40%, and 70% of BaTiO3 in epoxy, PVDF, polystyrene, PVC, and polyamide, the corresponding dielectric constant is 44 , 152 , 100 , 18 , and 80 , respectively. It is obvious that dielectric constant limited increase although high volume of ceramic particle is filled in polymer. We propose that this is probably because polymer matrix normally has higher resistivity than ceramic filler . By filling high-resistivity ceramic fillers in polymer matrix, a great increasing of dielectric constant may be achieved. As a result, the overall energy storage density can also be improved.
5. Dielectric for refrigeration
Electrocaloric (EC) effect is defined as the isothermal entropy or adiabatic temperature change of a dielectric material when an electric field is applied or removed. It could be used for efficient refrigeration and for the conversion of heat flows into electrical power. As the reverse effect of pyroelectric, EC effect has been explored before but the conclusion was that it was too small for practical applications. Recent interest on it is partly intrigued by the findings of 12 K temperature change in PbZr0.95Ti0.05O3  and more than 12 K temperature change in P(VDF-TrFE) (55/45 mol %) . More importantly, EC refrigeration has been paid great attention for its environment-friendly and solid-state characters. Nowadays, because of highly integrated, a chip may be comprised of thousands of components, which results in large heat generation. The future of IC may rely on the development of on-chip refrigeration technology, particularly with solid-state character. EC cooler is greatly expected for on-chip refrigeration.
5.1. Characterization of electrocaloric effect
At here, we first derive the equation for evaluating EC effect. The thermodynamic Gibbs free energy
According to Maxwell relation, we have
Thus, the isothermal entropy change
It is obvious that the EC effect can also be directly measured by modified differential scanning calorimeter, which has not yet commercialized. Thus, the main method is still the indirect method.
Recently we find that in fact it is possible to evaluate EC temperature variation at paraelectric phase by a simple equation because of dielectric nonlinear behavior of ferroelectric at paraelectric phase :
In fact, it is also the biquadratic coefficient in Landau-Devonshire Gibbs free energy density. Because dielectric constant of relaxor follows power law, we also can get corresponding EC temperature variation for relaxor . Since EC effect normally gets maximum at phase transition point, our method is practical for fast evaluating EC effect for materials with available Landau-Devonshire Gibbs free energy density with biquadratic term. For materials, the free energy density is not available; measuring dielectric nonlinearity under electric field also can save time than measuring temperature-dependent dielectric displacement under different constant electric fields.
More generally, EC effect over broad temperature range can also be predicted if the complete Landau-Devonshire potential of a material is available. For example, in monodomain state, the potential of Landau-Devonshire including up to eighth-power term can be written as:
5.2. The influence of electric field for electrocaloric effect
Enormous materials have been studied for their electrocaloric effect from inorganic to organic. Most of them are ferroelectrics. Using model ferroelectric BaTiO3 as an example, we can see the influence of electric field for electrocaloric effect. In single crystal, the reported
Materials in thin film can withstand high electric field; thus, large EC
5.3. Device development
Figure 4 is a schematic diagram for EC cooling cycle. One cycle includes four steps. (1) By applied electric field under adiabatic condition, EC unit changes from state 1 (
The critical point for an EC device is to achieve the unidirectional flow of entropy from a source to a sink. Some attempts to achieve it include: (1) shifting EC unit between the source and the sink [32, 33], (2) adding thermal switcher between EC unit with the sink and the source [34, 35], and (3) using liquid for heat transferring [36, 37, 38]. It is obvious that these designs increase the complexity of cooling device, which is not suitable for minimization and for chip-scale cooling. A new scheme is realized recently in which the cooler is composed of a flexible electrocaloric polymer film and an electrostatic actuation mechanism . The device works for cooling battery of smartphone, although if it will work for chip cooling is still open. We stress here the sophisticated device development for chip-scale cooling based on EC effect is strongly expected, particularly adoptable for integrated fabrication.
6. Conclusion and perspectives
Conductivity, polarization, dissipation, and breakdown are the main electric responses of dielectrics under electric field. The weak electric field response of dielectrics is mainly studied by dielectric spectroscopy technology, particularly for dielectric relaxation. Equivalent electric circuit is the main technique to separate different relaxation mechanism by combining different normalization. The shortage of dielectric spectroscopy technology is that it is largely restricted by frequency limitation. Some relaxations may not enter the window of dielectric spectrum. Developing broadband dielectric spectroscopy is therefore strongly expected.
Dielectric for electrical energy storage is highly desired, but the energy storage density is still low. Theoretically, antiferroelectric can store more electric energy. The problem is we are shortage of practicable lead-free antiferroelectric materials. In 0–3 composite, we show that filling higher resistivity ceramics in polymer matrix has very potential to get higher energy storage density.
EC effect is very important for future cooling especially for microelectronic industry. The large EC effect normally happens around the phase transition. We have developed a practical and simple equation for predicting electrocaloric effect above the phase transition point, which can be applied for fast determining EC effect of a material. The future development in the area is to find new materials with high EC effect and practical device developments for chip-scale refrigeration.
In both applications, withstanding high electric field is essential. Both energy storage density and EC effect can be significantly improved if the breakdown field can be increased. Since breakdown field largely depends on processing, developing new preparation process for dielectric is also very important.
Lists of symbols
|εr||relative dielectric permittivity or (relative) dielectric constant|
|A||surface of capacitor|
|t||thickness of capacitor|
|Ea||thermal activation energy|
|τ||characteristic relaxation time|
|ε0||permittivity of free space|