Bartnikas.R.“ Dielectrics and Insulators” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Bartnikas, R. “Dielectrics and Insulators” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
55 Dielectrics and Insulators 55.1 Introductio 55.2 Dielectric Losses 55.3 Dielectric Breakdown 55.4 Insulation Aging R. Bartnikas 55.5 Dielectric Materials Institut de recherche Gases. Insulating Liquids. Solid Insulating Materials Solid-Liquid Insulating System 55.1 Introduction Dielectrics are materials that are used primarily to isolate components electrically from each other or ground or to act as capacitive elements in devices, circuits, and systems. Their insulating properties are directly attributable to their large energy gap between hest filled valence band and the conduction band. The number of electrons in the conduction band is extremely low, because the energy gap of a dielectric(5 to 7e is sufficiently large to maintain most of the electrons trapped in the lower band. As a consequence, a dielectric, subjected to an electric field, will evince only an extremely small conduction or loss current; this current will be caused by the finite number of free electrons available in addition to other free charge carriers(ions) associated usually with contamination by electrolytic impurities as well as dipole orientation losses arising with polar molecules under ac conditions. Often the two latter effects will tend to obscure the miniscule contribution of the relatively few free electrons available. Unlike solids and liquids, vacuum and gases(in their nonionized state)approach the conditions of a perfect insulator-ie, they exhibit virtually no detectable loss or leakage Two fundamental parameters that characterize a dielectric material are its conductivity o and the value of the real permittivity or dielectric constant E. By definition, o is equal to the ratio of the leakage current density J to the applied electric field E, (55.1) Since J is in A cm-2 and E in V cm-l, the corresponding units of o are in S cm-l or Q-I cm-l. Alternatively, when only mobile charge carriers of charge e and mobility H, in cm2V-Is-I, with a concentration of n per cm3 are involved, the conductivity may be expressed as o=eun The conductivity is usually determined in terms of the measured insulation resistance R in it is then given by g= d/RA, where d is the insulation thickness in cm and a the surface area in cm2. Most practical insulating materials have conductivities ranging from 10- to 10-20 S cm-. Often dielectrics may be classified in terms of their resistivity value p, which by definition is equal to the reciprocal of o c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 55 Dielectrics and Insulators 55.1 Introduction 55.2 Dielectric Losses 55.3 Dielectric Breakdown 55.4 Insulation Aging 55.5 Dielectric Materials Gases • Insulating Liquids • Solid Insulating Materials • Solid-Liquid Insulating Systems 55.1 Introduction Dielectrics are materials that are used primarily to isolate components electrically from each other or ground or to act as capacitive elements in devices, circuits, and systems. Their insulating properties are directly attributable to their large energy gap between the highest filled valence band and the conduction band. The number of electrons in the conduction band is extremely low, because the energy gap of a dielectric (5 to 7 eV) is sufficiently large to maintain most of the electrons trapped in the lower band. As a consequence, a dielectric, subjected to an electric field, will evince only an extremely small conduction or loss current; this current will be caused by the finite number of free electrons available in addition to other free charge carriers (ions) associated usually with contamination by electrolytic impurities as well as dipole orientation losses arising with polar molecules under ac conditions. Often the two latter effects will tend to obscure the miniscule contribution of the relatively few free electrons available. Unlike solids and liquids, vacuum and gases (in their nonionized state) approach the conditions of a perfect insulator—i.e., they exhibit virtually no detectable loss or leakage current. Two fundamental parameters that characterize a dielectric material are its conductivity s and the value of the real permittivity or dielectric constant «¢. By definition, s is equal to the ratio of the leakage current density Jl to the applied electric field E, (55.1) Since Jl is in A cm–2 and E in V cm–1, the corresponding units of s are in S cm–1 or V–1 cm–1. Alternatively, when only mobile charge carriers of charge e and mobility m, in cm2 V–1 s–1, with a concentration of n per cm3 are involved, the conductivity may be expressed as s = emn (55.2) The conductivity is usually determined in terms of the measured insulation resistance R in V; it is then given by s = d/RA, where d is the insulation thickness in cm and A the surface area in cm2 . Most practical insulating materials have conductivities ranging from 10–6 to 10–20 S cm–1. Often dielectrics may be classified in terms of their resistivity value r, which by definition is equal to the reciprocal of s. s = J E l R. Bartnikas Institut de Recherche d’Hydro-Québec
The real value of the permittivity or dielectric constant e is determined from the ratio (553) where C represents the measured capacitance in F and C is the equivalent capacitance in vacuo, which is calculated for the same specimen geometry from Co=E, Ald; here E, denotes the permittivity in vacuo and is equal to 8.854 X 10-4Fcm-(8.854 X 10-2F m-in SI units)or more conveniently to unity in the Gaussian CGS system. In practice, the value of E, in free space is essentially the same as that for a gas (e. g, for air, a 000536). The majority of liquid and solid dielectric materials, presently in use, have dielectric constants extending from approximately 2 to 10. 55.2 Dielectric losses Under ac conditions dielectric losses arise mainly from the movement of free charge carriers(electrons and ns),space charge polarization, and dipole orientation [ Bartnikas and Eichhorn, 1983]. Ionic, space charge, values of o and e. This necessitates the introduction of a complex permittivity e defined in the measured and dipole losses are temperature- and frequency-dependent, a dependency which is reflected where e"is the imaginary value of the permittivity, which is equal to o/o. Note that the conductivity o determined under ac conditions may include the contributions of the dipole orientation, space charge, and onic polarization losses in addition to that of the drift of free charge carriers(ions and electrons)which determine its dc value ohase angle difference 8 between the d and E vectors, then in complex notation d and E may be expressed as D exp [(of-8)] and E, expliot), respectively, where o is the radial frequency term, t the time, and Do and E, the respective magnitudes of the two vectors. From the relationship between D and E, it follows that E It is cu the magnitude of loss of of its dissipation factor, tan8; it is apparent from Eqs.(55.5)and (55.6), that ans Examination of Eq (55.7)suggests that the behavior of a dielectric material may also be described of an equivalent electrical circuit. It is most commonplace and expedient to use a parallel circuit repre consisting of a capacitance C in parallel with a large resistance R as delineated in Fig. 55. 1. Here C
© 2000 by CRC Press LLC The real value of the permittivity or dielectric constant e¢ is determined from the ratio (55.3) where C represents the measured capacitance in F and Co is the equivalent capacitance in vacuo, which is calculated for the same specimen geometry from Co = eo A/d; here eo denotes the permittivity in vacuo and is equal to 8.854 3 10–14 F cm–1 (8.854 3 10–12 F m–1 in SI units) or more conveniently to unity in the Gaussian CGS system. In practice, the value of eo in free space is essentially the same as that for a gas (e.g., for air, eo = 1.000536). The majority of liquid and solid dielectric materials, presently in use, have dielectric constants extending from approximately 2 to 10. 55.2 Dielectric Losses Under ac conditions dielectric losses arise mainly from the movement of free charge carriers (electrons and ions), space charge polarization, and dipole orientation [Bartnikas and Eichhorn, 1983]. Ionic, space charge, and dipole losses are temperature- and frequency-dependent, a dependency which is reflected in the measured values of s and e¢. This necessitates the introduction of a complex permittivity e defined by e = e´ – je² (55.4) where e² is the imaginary value of the permittivity, which is equal to s/w. Note that the conductivity s determined under ac conditions may include the contributions of the dipole orientation, space charge, and ionic polarization losses in addition to that of the drift of free charge carriers (ions and electrons) which determine its dc value. The complex permittivity, e, is equal to the ratio of the dielectric displacement vector D to the electric field vector E, i.e., e = D/E. Since under ac conditions the appearance of a loss or leakage current is manifest as a phase angle difference d between the D and E vectors, then in complex notation D and E may be expressed as Do exp [j (vt – d)] and Eo exp[jvt], respectively, where v is the radial frequency term, t the time, and Do and Eo the respective magnitudes of the two vectors. From the relationship between D and E, it follows that (55.5) and (55.6) It is customary under ac conditions to assess the magnitude of loss of a given material in terms of the value of its dissipation factor, tand; it is apparent from Eqs. (55.5) and (55.6), that (55.7) Examination of Eq. (55.7) suggests that the behavior of a dielectric material may also be described by means of an equivalent electrical circuit. It is most commonplace and expedient to use a parallel circuit representation, consisting of a capacitance C in parallel with a large resistance R as delineated in Fig. 55.1. Here C represents e¢ = C Co e d ¢ = D E o o cos e d ¢¢ = D E o o sin tand e e s w e = ¢¢ ¢ = ¢
he capacitance and r the resistance of the dielectric For an applied voltage Vacross the dielectric, the leakage current is I,=VIR and the displacement current is Ic= joCV; since tan8=I/Ic,then ns (558) ORC It is to be emphasized that in Eq (55.8), the quantities R and C are functions of temperature, frequency, and voltage. The equivalence between Eqs. (55.7)and(55.)becomes more palpable if I, and Ic are expressed as oe.V and joe'CoV, respectively. Every loss mechanism will exhibit its own characteristic tan& loss peak, centered at a particular absorption frequency, o, for a given test temperature. The loss behavior will be contingent upon the molecular structure of the material, its thickness, and homogeneity, and the temperature, frequency, and electric field range over which the measurements are performed [Bartnikas C and Eichhorn, 1983]. For example, dipole orientation losses will be manifested only if the material contains permanent molecular or side-link dipoles; a considerable overlap may ccur between the permanent dipole and ionic relaxation T regions. Ionic relaxation losses occur in dielectric structures where ions are able to execute short-range jumps between two or more equilibrium positions. Interfacial or space charge polarization will arise with insulations of multilayered struc- FIGURE 55.1 (a)Parallel equivalent RC circuit ne individual strata or where one dielectric phase is inter persed in the matrix of another dielectric. Space charge traps also occur at crystalline-amorphous interfaces, crystal defects, and oxidation and localized C-H dipole sites in polymers. Alternatively, space charge losses will occur with mobile charge carriers whose movement becomes limited at the electrodes. This type of mechanism takes place often in thin-film dielectrics and exhibits a pronounced thickness effect. If the various losses are considered schematically on a logarithmic frequency scale at a given temperature, then the tan8 and e values will appear as functions of frequency as delineated schematically in Fig. 55. 2. For many materials the dipole and ionic relaxation losses tend to predominate over the frequency range extending from about 0.5 to 300 MHz, depending upon the molecular structure of the dielectric and temperature. For example, the absorption peak of an oil may occur at 1 MHz, while that of a much lower viscosity fluid such as water may appear at pproximately 100 MHz. There is considerable overlap between the dipole and ionic relaxation loses, because the ionic jump distances are ordinarily of the same order of magnitude as the radii of the permanent dipoles. Space charge polarization losses manifest themselves normally over the low-frequency region extending from 10-Hz to 1 MHz and are characterized by very broad and intense peaks; this behavior is apparent from Eq (55.7), which indicates that even small conductivities may lead to very large tand values at very low frequencies The nonrelaxation-type electronic conduction losses are readily perceptible over the low-frequency spectrum nd decrease monotonically with frequency The dielectric loss behavior may be phenomenologically described by the Pellat-Debye equations, relating the imaginary and real values of the permittivity to the relaxation time, t, of the loss process(i. e, the frequency at which the e peak appears: f o= 1/2 T), the low-frequency or static value of the real permittivity, E, and the high-or optical-frequency value of the real permittivity, Ex. Thus, for a loss process characterized by a single relaxation time e=Em+1+02t (559) c 2000 by CRC Press LLC
© 2000 by CRC Press LLC the capacitance and R the resistance of the dielectric. For an applied voltage V across the dielectric, the leakage current is Il = V/R and the displacement current is I C = jvCV; since tand = Il/IC , then (55.8) It is to be emphasized that in Eq. (55.8), the quantities R and C are functions of temperature, frequency, and voltage. The equivalence between Eqs. (55.7) and (55.8) becomes more palpable if Il and IC are expressed as we²Co V and jwe¢Co V, respectively. Every loss mechanism will exhibit its own characteristic tand loss peak, centered at a particular absorption frequency, vo for a given test temperature. The loss behavior will be contingent upon the molecular structure of the material, its thickness, and homogeneity, and the temperature, frequency, and electric field range over which the measurements are performed [Bartnikas and Eichhorn, 1983]. For example, dipole orientation losses will be manifested only if the material contains permanent molecular or side-link dipoles; a considerable overlap may occur between the permanent dipole and ionic relaxation regions. Ionic relaxation losses occur in dielectric structures where ions are able to execute short-range jumps between two or more equilibrium positions. Interfacial or space charge polarization will arise with insulations of multilayered structures where the conductivity and permittivity is different for the individual strata or where one dielectric phase is interspersed in the matrix of another dielectric. Space charge traps also occur at crystalline-amorphous interfaces, crystal defects, and oxidation and localized C-H dipole sites in polymers. Alternatively, space charge losses will occur with mobile charge carriers whose movement becomes limited at the electrodes. This type of mechanism takes place often in thin-film dielectrics and exhibits a pronounced thickness effect. If the various losses are considered schematically on a logarithmic frequency scale at a given temperature, then the tand and e¢ values will appear as functions of frequency as delineated schematically in Fig. 55.2. For many materials the dipole and ionic relaxation losses tend to predominate over the frequency range extending from about 0.5 to 300 MHz, depending upon the molecular structure of the dielectric and temperature. For example, the absorption peak of an oil may occur at 1 MHz, while that of a much lower viscosity fluid such as water may appear at approximately 100 MHz. There is considerable overlap between the dipole and ionic relaxation loses, because the ionic jump distances are ordinarily of the same order of magnitude as the radii of the permanent dipoles. Space charge polarization losses manifest themselves normally over the low-frequency region extending from 10–6 Hz to 1 MHz and are characterized by very broad and intense peaks; this behavior is apparent from Eq. (55.7), which indicates that even small conductivities may lead to very large tand values at very low frequencies. The nonrelaxation-type electronic conduction losses are readily perceptible over the low-frequency spectrum and decrease monotonically with frequency. The dielectric loss behavior may be phenomenologically described by the Pellat-Debye equations, relating the imaginary and real values of the permittivity to the relaxation time, t, of the loss process (i.e., the frequency at which the e² peak appears: fo = 1/2 pt), the low-frequency or static value of the real permittivity, es, and the high- or optical-frequency value of the real permittivity, e`. Thus, for a loss process characterized by a single relaxation time (55.9) tand w = 1 RC FIGURE 55.1 (a) Parallel equivalent RC circuit and (b) corresponding phasor diagram. ¢ = + - + • • e e e e w t s 1 2 2
Atomic Electron Absorption nfrared -Visible FIGURE 55.2 Schematic representation of different absorption regions [ Bartnikas, 19871 (55.10) 1+02τ2 n practice Eqs. (55. 9)and(5510) are modified due to a distribution in the relaxation times either because several different loss processes are involved or as a result of interaction or cooperative movement between the discrete dipoles or the trapped and detrapped charge carriers in their own particular environment. Since the laxation processes are thermally activated, an increase in temperature will cause a displacement of the loss peak to higher frequencies In the case of ionic and dipole relaxation, the relaxation time may be described by the relation exp (55.11) where h is the Planck constant(6.624 x 10-4Js-), k the boltzmann constant(1.38X 10-2JK-),AH the activation energy of the relaxation process, R the universal gas constant(8.314 X 10JK-Ikmol-I), and AS the entropy of activation. For the ionic relaxation process, T may alternatively be taken as equal to 1/2r, where r denotes the ion jump probability between two equilibrium positions. Also for dipole orientation in liquids, T may be approximately equated to the Debye term m/4r T, where m represents the macroscopic viscosity of the liquid and r is the dipole radius[Bartnikas, 1994]. With interfacial or space charge polarization, which may permittivity, Eq (55.10)must be rewritten as [von Hippel,/9 us dielectrics of different conductivity and a pile-up of cha
© 2000 by CRC Press LLC and (55.10) In practice Eqs. (55.9) and (55.10) are modified due to a distribution in the relaxation times either because several different loss processes are involved or as a result of interaction or cooperative movement between the discrete dipoles or the trapped and detrapped charge carriers in their own particular environment. Since the relaxation processes are thermally activated, an increase in temperature will cause a displacement of the loss peak to higher frequencies. In the case of ionic and dipole relaxation, the relaxation time may be described by the relation (55.11) where h is the Planck constant (6.624 3 10–34 J s–1), k the Boltzmann constant (1.38 3 10–23 J K–1), DH the activation energy of the relaxation process, R the universal gas constant (8.314 3 103 J K–1 kmol–1), and DS the entropy of activation. For the ionic relaxation process, t may alternatively be taken as equal to 1/2G, where G denotes the ion jump probability between two equilibrium positions. Also for dipole orientation in liquids, t may be approximately equated to the Debye term h/4pr 3 T, where h represents the macroscopic viscosity of the liquid and r is the dipole radius [Bartnikas, 1994]. With interfacial or space charge polarization, which may arise due to a pile-up of charges at the interface of two contiguous dielectrics of different conductivity and permittivity, Eq. (55.10) must be rewritten as [von Hippel, 1956] (55.12) FIGURE 55.2 Schematic representation of different absorption regions [Bartnikas, 1987]. ¢¢ = - + • e e e wt w t ( ) s 1 2 2 t = È Î Í Í ˘ ˚ ˙ ˙ - È Î Í Í ˘ ˚ ˙ ˙ h kT H RT S R exp exp D D ¢¢ = + + Ê Ë Á ˆ ¯ • ˜ e e t wt t w t w t 1 2 2 2 1 K