performance characteristics of dielectrics in the presence of space charge

544 IEEE Transactions on Dielectrics and Electrical Insulafion Vol, 4 No. 5, Ocfober 1997

Performance Characteristics of Dielectrics in the Presence of Space Charge

R. Bartnikas Institut de Recherche $Hydro-Quebec, Varennes, Quebec, Canada

ABSTRACT The short and long-term dielectric behavior of a number of representative electrical insulating systems is compared in the presence of space charge. Dielectric materials, used both in the com- munications and power application areas, are considered. In this overview, particular attention is given to thin inorganic films, organic solid-liquid and solid polymer systems as regards to the manner in which space charge affects their dielectric loss, voltage breakdown, treeing and electrical aging characteristics.

1. INTRODUCTION HE relatively recent increase of interest in space charge mecha- T nisms may impel one to construe that the study of space charge

behavior and its associated effects represents a new field of endeavor, However, space charge effects in dielectrics have been recognized and studied for more than a century, beginning with the time when absorption phenomena were first observed [l-61. The early approach was necessarily macroscopic or Wagner type [7] in the sense that the dielectric material was considered as a continuum of constant permittivity and conductivity, a concept which readily accounted for charge carrier accumulation at interfaces of dissimilar dielectric layers or interfaces within inhomogeneous dielectrics and at dielectric-metallic electrode boundaries. Charge carrier pile-up or trapping at these boundaries, which led to macroscopic field distortions, was and still is commonly referred to as either interfacial polarization or space charge polarization. The evidence that charge carriers penetrate or become absorbed within a thin layer adjacent to the electrodes when the solid dielectric is subjected to an electric field and then are gradually released when the dielectric is short circuited, was already established in the 1920's and 1930's [8]. The concept of actual charge traps on a microscopic scale took some more time to be accepted. A case in point concerns Boning's detailed treatise in 1938 [9] to explain the tan 6 maxima of solid-liquid insulating systems observed as a function of applied voltage under ac conditions in terms of mobile and adsorbed charge carriers; his approach was rejected in favor of a mechanism propounded by Garton [lo] to account for the same effect, but without invoking the necessity of absorbed or trapped ions. To this very day, the foregoing tan 6 behavior with voltage is referred to as the Garton effect, even in cases of solid dielectrics where it is palpably inapplicable.

Reticence towards the concept of electronic and ionic charge traps became increasingly less salient as more detailed information became available on the molecular structure of dielectrics; thus the approach to dielectrics gradually shifted from the macroscopic to the microscopic point of view. The procedures developed in solid state physics, applied

principally for semiconductors [ll], were extended to dielectrics. By the mid 1950's, the space charge behavior arising with electron conduction mechanisms in single crystal dielectrics was reasonably well formulat- ed as regards to charge carrier mobility, shallow and deep trap distribution energies, trapping time and cross section [12]. The same ideas were extended to polymer single crystals; in these materials, the folding layers of the polymer have different energy levels compared to the interior of localized sites for electron trapping [13]. However, the substantially more intricate character of the charge carrier trapping process in polycrystalline and amorphous polymers presented far more formidable dif- ficulties, partly as a result of a lack of detailed structural knowledge on the polymers and partly due to a paucity in data on rigorously controlled fundamental experiments on well defined complex polymer dielectrics. Although in crystalline-amorphous polymers, some ionic conduction losses may occur at the crystalline-amorphous interfaces and the free volume portion of the polymer, the magnitude of the ionic conduction current would be expected to be relatively small when compared to the ionic charge carrier currents that are observed commonly in some glasses where an openmolecular structure of the glass matrix provides ample latitude for ionic migration.

The performance of dielectrics may be influenced appreciably in the presence of space charge. Although solid polymer dielectrics perform satisfactorily under low dc stresses, their use at high dc stress can lead to catastrophic failure where polarity reversal is an operational constraint as in dc power transmission cables. In such circumstances, the electrical field due to the space charge would add to the reversed dc field and the resultant field may exceed the breakdown value of the solid insulation. Another example of a weakness of solid insulation as compared to solid-liquid insulating systems is that of long term deterioration due to treeing, where space charge mechanisms again are implicated. In this paper we shall examine in terms of the space charge process the com- parative short and long term performance of a number of representative solid and solid-liquid dielectric systems employed in electron devices and HV power apparatus and cables. Particular attention will be given _ _

1670-98?8/97/$3.00 @ 1997 IEEE "

IEEE Transactions on Dielectrics and Electrical Insulation Vol, 4 No. 5, October 1997 545

to the effects of space charge upon dielectric losses, breakdown strength and insulation aging as a result of electrical and water trees.

2. PRELIMINARY CONSIDERATIONS

Although it is well agreed that there are three types of charge carrier traps, namely the dipole, polaron (polarized region) and Coulomb traps, the exact nature of these traps is generally not well defined for materials of different molecular structure and morphology. Charge trapping may occur at atomic impurity sites, physical defects, various chemical groups, amorphous-crystalline interfaces and within the free volume between the molecular chains of polymers. Oxidation of a polymer dielectric results in the formation of carbonyl groups and other double carbon bonds that may act as trapping sites. Molecular oxygen traps are usual- ly hydrogen bonded to the hydrocarbon structure of the polymer. The depth or the potential well of the traps is a function of the thermal agitation of ions about their mean position, random orientation of dipoles and molecular structure irregularities. This leads to a distribution of trap depths and, therefore, to a distribution in the life times of the charge carriers. Charges residing in shallow traps have sufficient thermal energy at room temperature to contribute to the measured steady state leakage current density by means of the hopping process that takes place between the defect sites. Molecular movement resulting from thermal agitation also contributes to the release of charge carriers from their traps. Thus, the measured leakage or steady state current density of a dielectric material is determined by the drift of the free charge carriers and the hopping of charge carriers between shallow trap sites.

The trapping mechanism has been succinctly examined by Wintle [14]; the trapping or condensation rate of electronic charge carriers may be expressed as

where nt is the concentration of filled traps, Nt is the total trap concentration, n is the free electron concentration and A1 is the trapping rate constant. The detrapping of the electrons is governed by the detrapping rate constant A2 such that

[ 21 = -A2nt(NC - n)

where N, is the density of states at the conduction band. In terms of Fermi statistics, the relationship between the rate constants AI and A2 is given by 1151

A2 = Alexp -~ [ (3)

where E, is the energy level of the conduction band edge and Et is the energy level of the trap; thus by definition (E, -Et) is the depth of the trap or the binding energy of the charge at the trap center. For shallow traps, the value of (E, - Et) or the trap depth is << 0.8 eV so that at room temperature a number of the condensed charge carriers in such traps may gain sufficient energy to surmount their potential barrier and contribute to the steady state leakage current in the field direction. At the crystalline-amorphous interfaces in polymers and oxidized regions where the charge carriers are bound by stronger Coulomb forces, deeper

traps result, having levels in the range of 1.1 to 1.5 eV. At the sites of the deeper wells, the charge carrier detrapping probabilities are greatly reduced.

In the area of dielectrics, the fundamental concepts on trapping processes were first tested on single crystal dielectrics with well defined structure and then extended with only minor modifications to the more complex polycrystalline and amorphous dielectric systems. With single crystal dielectrics free of imperfections, the electronic charge carriers at the ohmic contacting electrodes would be expected to be injected into the conduction band so that the idealized conduction current density J would vary as the square of the applied voltage V given by the Mott- Gurney relation [16-18]

J = Ap&'V2d-' (4)

where A is the area of the electrodes, p is the mobility of the charge carriers, d is the thickness of the dielectric and E' is the real value of the permittivity. In a physically real single crystal dielectric, most of the injected charge carriers condense from the conduction band into traps created by the imperfections. The effect of the imperfections is thus to decrease the mobility ,u of the charge carriers, which essentially becomes a function of the distribution, density and depth of the traps while the trapping rate itself is determined by the capture cross-section of the traps [12]. Thus, space charge has a direct influence on the form of the current density vs. voltage characteristic, which has been used extensively in fundamental studies to gain insight into the space charge mechanism as function of the molecular structure and composition of different dielectric materials. Since the electrons in shallow traps are sufficiently close to the conduction band to be in thermal equilibrium with the electrons in the conduction band, it has been demonstrated by Rose [12] that the conduction process is controlled by the shallow traps and can be approximated by a modified form of the Mott-Gurney equation given by

J' = A ~ e d V ~ d - ~ (5)

where p is the mobility of the free charge carriers and 8 is defined by

where Nt now represents the concentration of shallow traps having a depth equal to (E, -Et). Since the vast majority of the injected charge carriers at the ohmic contact electrode become condensed in the traps and only a relatively small number of electrons remainmobile, the quan- tity 8 is necessarily small i.e.

(7)

Consequently the hypothetical current density J , where all injected carriers would remain mobile, is substantially larger than J', where most of the injected carriers become settled in the shallow traps.

The presence of deep traps may have a very pronounced effect on the shape of the current density vs. applied voltage characteristic. For the case of the single crystal dielectric containing deep traps, the assump- tion of an exponential distribution of the deep traps leads to a current

546 Barfnikas: Performance of Dielectrics in fhe Presence of Space Charge

density of the form [19]

where B is the pre-exponential factor in the distribution of the deep traps and T, is a characteristic temperature which approximates the rate of the deep trap density changes with energy, Equation (8) indicates that above the ambient temperature T, a greater dependence of the current density upon voltage will result. In practice, it has been a well recognized fact for a number of decades that charge density is highest adjacent to the electrodes or sharp protrusion points where charge injection occurs. Thus, the form of Equation (8) would be appreciably modified for different forms of deep trap distribution. Moreover, in high molecular weight crystalline-amorphous polymers, the current density dependence upon voltage will differ substantially from that observed on single crystal dielectrics primarily because of the large number and different types of defects and the electronic as well as ionic charge carriers involved. However, the idealized single crystal model of Rose [19] serves as a good basis and effective means to compare and interpret the more intricate trapping behavior in complex structured dielectrics.

Dielectric loss measurements carried out under ac conditions are particularly effective in the investigation of space charge phenomena where ionic conductivity is involved, because of the substantially lower ionic mobilities as compared to those characterizing electrons. The ionic dc and ac conduction and trapping models are essentially based on the classical two potential well model in which the two-well minima are sep- arated by a barrier of height AH, and distance 2a [14,20]. Under the application of an electrical field E, in the direction from the ion well or trap at site A to that at site B, the ion located at site A will require (AH - eaE,) of energy to surmount the barrier in moving from A to B. While the ion at site B in its attempt to move to site A, would face an energy barrier of (AH + eaE,). Thus the probability r(AB of an ion moving from A to B, would be exp[eaE,/kT] as opposed to the probability r B A = r exp(-eaE,/kT) in moving from B to A; evi- dently, > r B A . At zero external field, the probability r in moving from A to B or vice versa is equal to v exp[-AHlk t] , where v is the vibration frequency of the ions within the wells i.e., number of at- tempted ion jumps per unit time (ca. 1011 to jumps per second). The imaginary permittivity component E”, or loss factor characterizing this process is

(9)

where E, is the static value of the real permittivity, E, its optical value and o the radial frequency term. The relaxation time of the process is T = 1/2I’; thus the peak magnitude of E / / and its position on the o scale as well as the broadening of the E” vs. o curve would be expected to be a function of the ion trap depth and distribution. The esti- mates of the average trap depth can be determined in terms of activation energy obtained from a plot of the E” maxima as a function of the in- verse absolute temperature T. It is to be noted that the ac conductivity o,,, by definition equal to WE”, is generally not the same as the dc conductivity Ode. The ac value of the conductivity involves jumps of the

ions between defect sites in their own vicinity, wlule dc conduction results from long range ionic migration whereby each ion must surmount a large number of different potential barriers along its path in the direction of the external field towards the electrodes.

It must be observed that a variety of ionic models based on the two potential well model have been employed to approximate more closely particular experimental data. However, though the models vary in the extent of their detailed complexity, they do not deviate greatly in princi- ple from the idealized two potential well model. The two potential well model has been employed extensively in the studies of conduction, dielectric loss and space charge mechanisms in glasses, thin film inorganic dielectrics and solid-liquid insulating systems. It has less application to polymers that possess a more closed molecular structure where only restricted latitude exists for ionic motion, i.e., confined to the amorphous phase, along interfaces of the crystalline and amorphous regions and within the free volume. Even in an open structure, the collisions between the relatively large ions and the lattice take place very frequently so that under dc conditions the ions become readily captured by the adjacent well sites along their path and must again surmount the energy barrier before re-commencing their migration in the direction of the field. At fields of - 10 kV/cm, the potential wells may become distort- ed and deviations from ohmic behavior are manifest [14].

3. THIN FILM INORGANIC DIELECTRICS

Thin film dielectric materials are primarily employed in integrated circuits for capacitors and the passivation of electron devices. In the latter case, low loss dielectric films are required to control surface state phenomena in the electron devices. Since silicon is at the base of the current integrated circuit technology, we shall confine our discussion for illustrative purposes to silicon dioxide, SiOz, films that constitute an in- tegral part of the thermally oxidized-passivated silicon semiconductor surfaces. It is now well established that losses in Si02 films are of an ionic nature and that sodium ions comprise the principal charge carriers [20]. As very thin dielectric films are involved, the relaxation time is directly dependent upon the ion transit time across the film and the electrodes become blocking thereby leading to an interfacial polarization effect. Were the ions to drift unhmdered over the potential barriers between the two electrodes, then in the absence of a space charge field at the electrodes the relaxation tim T would be given by [21]

(10) d

2PEO T z z -

where p is the mobility and E, the electrical field. But as the charge pile- up at the blocking electrodes causes the current to become space charge limited, then for singly charged carriers of the same sign whose charge is compensated by quasi-stationary charge centers in the dielectric bulk, the relaxation time assumes the form [21]

where n is the concentration of the free charge carriers and the relaxation time T, characterizing the long range excursions of the charge carriers limited at the electrodes, is much longer than that due to the ionic

IEEE Transactions on Dielecfrics and Electrical Insulation Vol. 4 No. 5, October 1997 547

jumps between the respective wells, which is equal to ir as defined by Equation (9).

In a MOS (metal-oxide silicon) structure, a built-in potential arises as a result of the semiconductor-metal work function difference [22]. Fig- ure 1 depicts a representative relaxation spectrum of a Si-SiOz-Cr thin film capacitor, with time as a parameter [23]. Since the losses in Si02 films have been demonstrated to arise from the migration of sodium ions, the decrease of the dielectric losses (E" maxima) with time must be taken as indicative of the removal of the positive sodium ions from the volume of the dielectric because of the built-in voltage bias resulting from the work function difference between the chromium and silicon electrodes [23,24]. A still further reduction in the charge carrier concentration may take place possibly because of the Coulomb repulsion of the sodium ions in the absence of any compensating negative charges within the silicon dioxide. The losses in the dielectric diminish to very small values as the sodium ions upon reaching the chromium electrode, become immobilized or trapped in either shallow or deep traps. The sodium ions easily may be ejected from the shallow traps by the application of a positive counter bias to the chromium electrode as is apparent from Figure 2. It is evident that the migration of the sodium ions in the bulk of the Si02 films controls the loss current only during one half of the ac wave, since during the other half cycle the current is space charge limited by the release mechanisms of the ions from the more shallow traps. The determined activation energies, which reflect the combined influence of the two conduction mechanisms range from N 0.91 to 1.21 eV [24]. The long range excursions executed by the sodium ions lead to a thickness effect in the observed dielectric losses as portrayed in Figure 3; this behavior is in qualitative agreement with the form of Equation (11).

The presence of mobile and trapped ions in the MOS structure leads to instabilities in the performance of oxide-passivated semiconductor devices. Their effects are evaluated in terms of the flat-band voltage shifts and the hysteresis of the capacitance C lis. voltage V plots. The flat-band voltage shift constitutes a measure of the mobile ion concentration. Figure 4 illustrates the effect of trapped charge on the flat-band voltage shift at 1 MHz obtained on a highly sodium ion contaminated MOS structure of Si-SiO2-Cr. [23] The C - V curves in the direction of the horizontal arrow commencing with trace (a) are obtained after the specimen is cooled to room temperature whilst under positive bias after being subject to a bias temperature stress of 5 x lo5 V/cm at 250°C for 3 min. Each successive hysteresis curve represents an elapse of 33 s. The rapid displacement of the C - V hysteresis characteristics in the direction of the arrow indicates a continuing depletion of ions from the vicinity of the semiconductor electrode; after several sweeps, the limit of the shift (indicated by the tip of the horizontal arrow) is reached. The application of a negative bias Of 5 x lo5 V/cm at room temperature for 5 min, reduces further the flat-band potential to (b). Finally trace (c) is obtained at room temperature, following the subjection of the specimen to a negative bias of 5 x lo5 V/cm at 250°C for 5 min and cooling it subsequently to room temperature i.e., the majority of the ions are thereby driven to the metal-oxide interface. The difference in the flat-band po- sitions of (b) and (c) yields thus the ion concentration remaining at the semiconductor-oxide interface, corresponding to the situation of (b), as 3 . 1 ~ 1 0 ~ ' ions/cm3. [23]

= 2 w

1

0 1 10 ld ld

Fteclucncy f (Hz) Figure 1. Time dependence of relaxation spectrum in a 240 nm thick Si-

SiOz-Cr capacitor at 400°C, (a) t = 0, (b) t = 12 h, (c) t = 6 days (after Kriegler and Bartnikas [23]).

I I I I I

T = 430'C 215 nm specimen

2o t

1 1 I I I 10.2 -10 1 10 I@

Frequency f (Hz) Figure 2. Bias dependence of the loss factor for a Si-SiOz-Cr specimen

having a sodium surface contaminationof 7 . 5 ~ 10" ions/cm2, with positive bias on the chromium electrode as a parameter (after Kriegler and Bart- nikas [24]).

4. SOLID-LIQUID SYSTEMS In much of the HV electrical power apparatus such as transformers

and capacitors as well as cables, solid dielectrics are frequently used in conjunction with dielectric liquids in order to prevent the formation of gas cavities. The solids in sheet or tape form are dried under heat and vacuum in order to remove the air and free moisture prior to impreg- nation with the liquid. In such systems clearly defined solid-liquid interfaces arise and which, if not properly matched in their conductivities

548 Baufnikas: Performance of Dielectrics in the Presence of Space Charge

I I I 1

VB = 0.4 V

0' 1 l I 10-1 1 10 162

Frequency f (Hz) Figure 3. Thickness dependence of dielectric loss measured on a Si-

SiOZ-Cr2 specimen with a sodium surface contamination of 7 . 5 ~ 10" ions/cm2 (after Kriegler and Bartnikas [24]).

I 1 I I I

0 ' t I I I I J

-20 -15 -10 -5 0 5 Voltage bias (V)

Figure 4. Room-temperature C- V characteristics of a highlycontami- nated MOS specimen at 1 MHz: (a) traces of subsequent voltage sweeps after an elevated temperature positive bias stress; @) trace following a room- temperature negative bias stress; (c) trace following an elevated temperature negative bias stress (after Kriegler and Bartnikas [23]).

and permittivities, can lead to significant interfacial space charge losses under ac conditions. If for simplicity one considers the classical two layer dielectric Wagner system, then the dissipation factor due to the mobile charge carriers and the interfacial space charge contributions may be expressed as [25]

T* KWT*

(12) + (1+WZT*' )

K tan6 = I +

where K is the Wagner absorption factor; it is a function of the respective time constants of the solid layer 71, the liquid layer, 7 2 , and the solid-liquid layers combined T*. Obviously, if the two respective dielectric layers are perfectly matched at all temperatures and voltage stresses, then K = 0 and tan 6 is solely determined by the free charge carrier and shallows trap conduction losses in the individual solid and liquid strata.

Figure 5 depicts a typical frequency response spectrum of a 0.165 mm

thick oil-kraft paper combination, comprising a 0.127 mm thick oil- impregnated kraft paper sheet situated between two oil films having an approximate thickness of 0.019 mm [26]. The oil impregnant utilized is a medium-viscosity pipe cable oil. The most likely charge carriers, re- sponsible for the dielectric loss in the oil films, are believed to be protons [26]. There are several preponderant ionic loss mechanisms active in the oil-paper systems: long range ionic migration, interfacial space charge polarization at the oil-paper and electrode boundaries and short range ionic jump trapping-detrapping processes within the solid paper structure. At lower test temperatures in the range of frequencies extending upwards from the power frequency, some residual dipole contribution to the overall dielectric loss may occur as a result of the remnant dipole loss due to the dipole orientation of the larger molecules in the oil and paper structure.

Figure 6 illustrates the relative contributions to the value of tan 6 of the interhcial or space charge polarization process as compared to that of the mobile charge carrier movement under dc conditions (i.e./ steady state leakage current). It can be observed that the interfacial space charge losses exceed appreciably those due to the free charge carrier movement. The activation energy characterizing the free charge carrier conductivity is in the range of 0.40 to 0.47 eV, whilst that under ac conditions comprising both free charge carrier movement and space charge limited conduction ranges from 0.37 to 0.48 eV. These values suggest the involvement of very shallow traps at both the solid-liquid boundaries as well as at the blocking electrodes. The shallowness of the traps of the oil- paper system may account for its excellent performance under dc polarity reversal conditions as opposed to the catastrophic behavior of some solid insulations, e.g., PE which are characterized by deep traps from which the charge carriers are not readily emitted. The low activation energies, furthermore, imply that protons are most probably the principal species of charge carriers in oil-paper systems. The experimentally determined values of activation energy compare well with those reported for hydrogen ion migration in glasses [27].

I I I I I I

FTUenCY f W) Figure 5. Figure 5 Frequency-response characteristics of a 0.165 mm

thick oil/oil-paper/oil film (after Bartnikas 1261).

In Figure 7, it is evident from the tan 6 behavior with voltage that the space charge processes centered primarily over the lower frequencies, exert very little effect on the loss magnitude at the fixed frequency of 60 Hz under HV conditions. Only a minor space charge effect is evinced over the lower field strengths at 85°C. However, if the paper is poorly dried, space charge losses may attain prodigious values over the lower fields as is apparent from Figure 8, which reveals a typical Boning-Garton effect (ie,, a peak in loss and a subsequent diminution with voltage) [28]. The peak value in the loss at lower field strength is

IEEE Transactions on Dielectrics and Electrical Insulation bl. 4 No. 5, October 1997 549

Experimental curve

10-8 I l l 10-2 10'' 1 10 floz Id la4 Id

6 o H z Frequency f (Hz)

Figure 6. dc conductivity contribution and the overall tan8 value as a function of frequency at 85°C for a 0.165 mm thick oil/oil-paper/oil film (after Bartnikas [26]).

associated with increased conduction losses in the paper portion resulting from the dissociation of electrolytic impurities in the moist paper matrix due to the high permittivity of water, ca. 80. The high dielectric losses associated with the space charges in the poorly dried papers can lead to hot spots and, hence thermal instability and eventual breakdown of the insulating system. The criteria for thermal instability is defined by

= oe'E2 tan 6 KAAT

1 (13)

where the left hand side represents the heat transfer (J/s), along a path I (cm) of cross-sectional area A (cm2) of the dielectric with a thermal conductivity constant of K (J/C cm s), in the direction of the temperature gradient created by the temperature difference AT in "C. The right hand side of the equation represents the dielectric loss in J/s, where E, denotes the electrical field.

In the oil-paper structure, a portion of the space charge loss takes place at the solid-liquid boundary itself. If the paper dielectric is re- placed by a solid plastic dielectric, then the interfacial polarization loss arises primarily from a charge carrier pile-up at the interface of the plastic sheet and the contiguous oil film layer. Figure 9 portrays a typical frequency response characteristic obtained on a polycarbonate oil- impregnated cable model constructed with six layers of tapes having an overall cable model insulation thickness of 0.90 mm. The same hollow core cable mineral oil, used for the oil-paper specimens, is also employed on these models. Figure 9 must be interpreted in conjunction with the calculated data (using Equation (12) presented in Figures 10 and 11, which demonstrate that at the power frequency of 60 Hz, the interfacial space charge losses exceed the charge carrier losses at room

0 30 60 90 120 150 180 Average voltage stress (kV/cm)

Figure 7. tan 6 vs. average voltage stress characteristics at room temperature and 85°C obtained on cable model impregnated with a hollow core cable oil (after Bartnikas [26]).

I I I I I I I 0 30 60 90 120 150 180 210

Average voltage stress (lcV/cm) Figure 8. Typical space-charge effect observed on an insufficiently dried oil-paper cable model impregnated with an hollow core cable oil (after Bartnikas [28]).

temperature but that the converse is true at 85°C. While the charge carriers in the oil films are likely to be mainly protons, those in the polycarbonate film may be both electrons and impurity ions. The existence of the latter is probable because of remnant solvent residues in the polycarbonate; in addition, the glassy non-crystalline structure [29,30] of the polycarbonate is sufficiently open to provide some latitude for ionic migration. Since the respective conductivities of the plastic and liquid films are hnctions of the electrical field, the relative contributions of the charge carrier and interfacial space charge generated losses at 60 Hz will differ somewhat from the behavior evinced as a function of frequency at low electrical fields. Figure 12 delineates this behavior of tan 6 as a function of the electrical field, with temperature as a parameter. Com- parison with Figure 7 shows that at a cable operating temperature of 85"C, the overall dielectric losses in the polycarbonate-oil insulating system are higher than those in the oil-paper insulating system; however, the situation is markedly reversed over the higher field region.

5. SOLID INSULATING SYSTEMS The manner in which electronic conduction may contribute to the

space charge loss mechanism, occurring in solid polymeric type insulating systems under normal operation of electrical power apparatus and

550 Bartnikas: Performance of Dielectrics in the Presence of Space Charge

Frequency f (Hz) Figure 9. Relaxation spectra obtained at room temperature and 70°C on

a polycarbonate cable model impregnated with a hollow core cable oil (after Bartnikas [28]).

I I I I I I I

10-5 I I I 1 I I I

io4 10-2 10-1 1 10' f ld ld Frequency f (Hz) 60 H z

Figure 10. Relative effects of dc conductivity and interfacial space charge polarization upon the tan 6 value of a two-layer oil-polycarbonate combination at room temperature (after Bartnikas [28]).

I I I I I I Conductivity contribution

- - -

.- 0 IO" -

10-5 I I I I I I I

10-4 10-3 10-2 1 ~ 1 1 101 +lo2 ld 60 HZ

Fresuencr f (Hz) Figure 1 1. Relative effects of dc conductivity and interfacial space

charge polarization upon the tan 6 value of a two-layer oil-polycarbonate combination at 85°C (after Bartnikas [28]).

cables under ac conditions is not fully understood. Although electronic conduction is field dependent, the relatively high mobility of the electrons results generally in a frequency independent loss, which makes it difficult to establish exactly its contribution to the overall dielectric losses that take place over the power frequency range.

In analogy with the electronic conduction behavior of single crystal solid dielectrics, Watson [ 31,321 suggested that in amorphous dielectrics (which should also be applicable to amorphous regions in crystalline- amorphous dielectrics), the motion of charge carriers is repeatedly in- terrupted by trapping of the electrons in the localized states until they are re-emitted into their extended states. He gives the release time as

1 I I I I I Lo 3 .0030

I I I I I 1 0 30 60 90 120 150 180

Average voltage stress (kVlcm) Figure 12. tan 6 vs. average voltage stress characteristics obtained at

room temperature and 85°C on a polycarbonate cable model impregnated with a hollow core cable oil (after Bartnikas [28]).

where Em is a time-dependent thermalization energy, E, is the position of the mobility or extended states edge and vo is the jump frequency of the electrons (w lo-'' s-'). Depending on the trap release time, the drift mobility assumes values appreciably smaller than that characterizing the movement of free electrons, because of the proportionately longer times that the electrons reside trapped in the localized states. If the trapping time would reach lengths such that the effective average electron mobility would approach that of the much slower ionic charge carriers, then presumably it would be difficult to discriminate under some circumstances between the two mechanisms. In order to gain a better insight in the complex electronic conduction process in films of solid organic polymers involving traps, Watson [33] has propounded a very useful simplified electronic conduction model. In neglecting the retrapping of electrons, he arrives at a rather remarkable result, that indicates that the dc conduction current due to detrapped electrons varies inversely with time ie., precisely what is observed in practice when the leakage current is measured as a function of time in a solid polymer type insulation subjected to an external electrical field gradient. The decay current i( t) arising from the migration of detrapped electrons is of the form

k T v t

i( t) = --n(E)

where n ( E ) denotes the trap distribution density, such that a plot of i(t)t vs. kT ln (v t ) yields to a first approximation the distribution of the electron trap depths. Admittedly, as Watson is careful to point out, Equation (15) tends to underestimate the current associated with the shallow traps, from which the detrapping probability is high, and overestimates the effectiveness of the deep traps. Nevertheless, Equa- tion (15) constitutes a most useful approximation.

In crystalline-amorphous polymers such as the various commercial grades of PE, in addition to the electronic losses in both the crystalline and amorphous phases, ionic losses may occur due to remanent traces of catalysts or other ionic impurities. Ionic losses differ in their ac dielectric loss behavior from the electrons in that as well as being voltage dependent they are also influenced by the frequency of the field. This

IEEE Transacfions on Dielectrics and Electrical Insulation Vol. 4 No. 5, October 1997 551

behavior may be approximated by a conductivity of the form [34-361

where for an ionic jump distance taken to be equal to 2a and a correlation factor A having values between 0 and 1, the pre-exponential term cia is given by

4N,qvAa sinh . [g] Go =

Eo

where No is the ion concentration, q the ionic charge, v the jump frequency of the ions, E, the external electrical field, U, is the free volume of the polymer, U the free volume which is sufficiently large to accom- modate the jumping ion, and W is the ionic dissociation energy and A H is the depth of the ion traps.

Ionic conduction in polymers may lead to space charge losses at the crystalline-amorphous boundaries or within the amorphous regions themselves, should the latter contain several phases such as those that may arise with fillers. However, in low loss solid polymers, the space charge losses at and in the vicinity of the power frequency tend to be of a low magnitude, because the charge carriers that are condensed in deep traps are held immobile. Figure 13 presents a comparison of the real value of the permittivity of typical commercial grade unfilled cross-linked polyethylene (XLPE), filled XLPE and EPR (ethylene propylene rubber) as a function of temperature at a frequency of 60 Hz [37]. It can be perceived that the unfilled XLPE has a smaller permittivity than the filled XLPE and EPR; the latter, represents a material with a proportionately high filler content. The inclusion of fillers creates additional phases in the polymeric material, resulting in augmented interfacial polarization losses as well as dipole losses, should some of these fillers contain polar molecules. The gradual diminution of the permittivity with temperature in Figure 13 for all three materials must be ascribed to a reduction in their density at the elevated temperatures. For the filled and unfilled XLPE, the abrupt fall in the E' value in the proximity of 110°C is a direct consequence of the softening of the dielectric solid at the transition temperature. The corresponding tan 6 behavior for the three materials is shown in Figure 14, from which it is apparent that the losses commence to increase appreciably as the transition temperature is approached. The observed increase must be attributed to a rise in ionic losses due to increased ionic mobility as well as interfacial and space charge losses. The background loss or the base tan 6 magnitude, upon which the observed variations are superimposed, is most likely due to electronic conduction and dipole losses. The latter may arise from the relaxation of CH2 units in the case of XLPE within the crystalline regions and oxidation by- products such as the carbonyl groups, though in this particular case in- frared analysis does not reveal any presence of the carbonyl groups [37]. The peak in the tan 6 value for the unfilled XLPE within the temperature range from 110 to 150°C most probably denotes a space charge loss peak and the rapid rise of tan 6 with temperature for the EPR and filled XLPE materials would infer a peak at some temperature above 150°C. The peak in this temperature region for PE, when obtained at a higher frequency (w 1 kHz), is the so-called a-peak and is generally ascribed to dipole phenomena as a result of the vibrational and reorientational molecular motions within the crystalline regions. These effects would

be expected to affect the tan 6 peak observed here for the filled XLPE obtained at 60 Hz, though their overall contribution may be substantially less than that associated with space charge losses. It should be empha- sized that the behavior evinced in the temperature range of 110 to 150°C is of particular practical importance because it covers the emergency operating temperatures for these three materials when used as insulants in power cables.

The frequency response characteristics, obtained on XLPE with temperature as a parameter, are presented in Figure 15. As the temperature is raised to > 23"C, the portion of an absorption peak in tan 6 becomes discernible at the emergency operating temperature of 130°C. The wide- ly dispersed peak encompasses the ionic conduction, space charge as well as some molecular orientation processes. The dispersed relaxation process suggests that, particularly in the latter case, cooperative molecular reorientation may be involved. From Figures 13 to 15 it is apparent that for temperatures considerably below the transition temperature, the losses in the filled and unfilled XLPE materials are relatively small when compared to the solid-liquid systems described in the previ- ous Section for which the interfacial space charge polarization losses are much higher. Thus, from the point of view of dielectric losses, unfilled XLPE constitutes a low dielectric loss insulating system when applied in extra HV power transmission cables.

2.9 I I I I I I I I i

- 2.7 W I

I 2-5 # 2.3 3 4 8 2.1 U

1.7 I I I I 1 1 I I I 10 30 50 70 90 110 130 150 170

Temperature ("C) Figure 13. Permittivity as a function of temperature obtained at 60 Hz

for typical XLPE, filled XLPE, and EPR formulations (after St-Onge et al. [W). In the past it has been well recognized that charge trapping in di-

electrics tends to occur in the vicinity of the electrodes. Beginning with the early 1970's there have been a number of methods developed to determine the spatial distribution of the trapped charge in solid dielectrics [38] and the results thus obtained also indicate higher charge densities in the proximity of the electrodes. No results are reported to suggest any definite relationship between a given form of charge distribution and the short or long time performance of the solid insulating materials evaluated, though intuitively some relationship should perhaps ex- ist between the space charge distribution and the configuration of any subsequent tree formations. The existence of such a relationship would depend greatly upon the accuracy with which the space distribution can be determined. Nevertheless, the space charge distributions measured on solid polymeric insulation appear to exhibit some dependence

I I I I I I

I I I I I I I

10 30 50 70 90 110 130 150 Temperatun: ("C)

Figure 14. tan 6 vs. temperature characteristics of XLPE, filled XLPE, and EPR at 60 Hz (after St-Onge etal. [37]).

10-3

I -

1 0-5 10 102 Id 104

Frequency f (Hz) Figure 15. Frequency spectra of commercial XLPE (after St-Onge et al.

on residual cross-linking products and polymer oxidation, which have been demonstrated by other methods to act as charge traps. Since the charge distribution methods are not capable of identifying directly the type of the charge carriers involved, usage of the less specific terminol- ogy of homocharges and heterocharges is frequently made when dis- cussing such distributions. There are a number of non-destructive space charge distribution measurement techniques presently available, namely the thermal pulse, pressure wave propagation, laser intensity modu- lation and pulse electro-acoustic methods. Though there is some qualitative agreement between the different measuring methods involving the types of polymers evaluated, the numerical reproducibility and accuracy appears to be poor. The accuracy with which the space charge distribution itself is determined is contingent upon the degree to which the space charge profile measurement is influenced by permanent dipole

W1).

Bartnikas: Performance of Dielectrics in the Presence of Space Charge

polarization effects within the dielectric and the surface charges present on the electrodes. It has been recently demonstrated that the effect of surface charges situated at the electrodes may be minimized by means of a software type simulation model [39,40] when employed in conjunction with the pulse electro-acoustic method [41]. In the latter method, a short duration electrical pulse applied to the specimen causes charge displacements, whereby a pressure wave is generated; this wave is in turn detected by means of a transducer whose resulting output voltage signal is processed to derive the space charge distribution. The inher- ently low resolution characteristics render this particular method and the associated simulation model more suitable for space charge distribution measurements on thick insulation structures used in large power apparatus and cables.

6. DIELECTRIC BREAKDOWN OF SOLIDS

Electrical breakdown of solids may involve thermal, mechanical and electrical mechanisms. From the electrical point of view, irrespective of whether one subscribes to the tenet that the electrical breakdown is initiated by collision ionization of conduction electrons or field emission from the cathode, space charge effects appear to play a dominant role under dc conditions 1421. In the case of collision ionization, it may be argued that positive ions are created and that these then drift to the cathode where they accumulate forming a positive space charge that aug- ments the field adjacent to the cathode thereby further increasing the electron emission until instability develops and breakdown ensues [43]. In Si02 films, it has been suggested that field emission from the cathode is enhanced by the formation of an adjacent space charge cloud of mobile sodium ions that are present due to contamination. When a sufficiently large sodium ion concentration is formed, the critical electrical field necessary for breakdown is exceeded [44,45].

As pointed out in Section 1, the formation of deep charge traps in PE renders it unsuitable for HV dc power transmission applications where polarity reversal is a requirement. This observation has been well doc- umented by Bradwell et al. [46], who demonstrated that de prestressing of opposite polarity leads to a positive charge build-up adjacent to the cathode whose created field is additive to the applied direct or impulse field. Furth'er support for the involvement of space charges in the dc and impulse breakdown processes is provided by the results obtained by Artbauer and Griac 1471 on PE, which demonstrate the dc breakdown strength to be lower than the impulse breakdown strength at temperatures below 30°C; above 30°C the converse situation is found to prevail. This behavior infers that at low temperatures the dc breakdown process is space charge controlled as there is sufficient time available for space charge to be created witha slowly rising direct voltage field. Whereas at high temperatures, space charge build-up is hindered due to increased thermal agitation and mobility of the charge carriers.

Figures 16 and 17 depict the respective mean 60 Hz and impulse breakdown vs. temperature characteristics obtained on filled and unfilled XLPE and EPR, using epoxy enclosed HV electrodes of the type described by de Tourreil and Mailhot [48]. Although these electrodes do not provide intrinsic breakdown values, they represent a considerable improvement over the ASTM and IEC type electrodes. Over the lower temperature regime, the 60 Hz and impulse breakdown strengths are

IEEE Transactions on Dielectrics and Electrical Insulation b l . 4 No. 5, October 1997 553

seen to be highest for the more crystalline material (unfilled XLPE) and least for the completely amorphous EPR. The latter highly filled material appears to be relatively unaffected by temperature as the 60 Hz and impulse breakdown strengths of both the unfilled and filled XLPE are found to decrease with temperature, though at a different rate such that over the higher temperature region, the breakdown strengths of the filled XLPE exceed those of the unfilled XLPE. It can be seen that the impulse breakdown vs. temperature characteristics for both the filled and unfilled XLPE, after exhibiting initially a rapid fall in breakdown strength up to the melting transition temperature, display very little variation with temperature thereafter. Under impulse conditions, the effects of space charge are negligible and the variation of the impulse strength with temperature must be attributed to other influences than space charges.

0 50 100 150 m Temperature ("C)

Figure 1 6. ac breakdown field as a function of temperature for filled and unfilled XLPE and EPR (after St-Onge et al. [37]).

Over the investigated range of temperatures, the materials containing fillers tend to display a weaker temperature dependence as is evinced in both Figures 16 and 17. At the lower temperatures, the initially high dielectric strength of the unfilled XLPE is significantly depressed with the addition of a filler. But, as can be perceived from both the 60 Hz and impulse breakdown characteristics, the addition of fillers imparts a ben- eficial property to the polymer over the higher temperature regime. It is to be noted that at the normal cable operating temperature of 90°C, all three investigated dielectric materials (filled and unfilled XLPE as well as the high filler content EPR) exhibit less difference in their breakdown strengths. With rising temperature, the ac breakdown mechanism would be expected to assume an increasingly thermal character; in addition, the mobility of the injected charge carriers would tend to de- press further the breakdown strength. Both effects would be more pronounced in materials containing less inorganic filler.

7. LONG TERM BREAKDOWN PROCESSES

When a solid dielectric sheet is subjected to an electrical field, a charge Qs will accumulate on the surface of the layer adjacent to the electrode and an additional charge will be injected into the bulk of the

I I I

0 50 100 150 U10 Tcmp~aturc ("0

Figure 17. Impulse breakdown field as a function of temperature for

dielectric. The penetration depth of the charge carriers and the number of deep traps filled will increase with the time of the application of the electrical field and its magnitude. If N, is taken to denote the volume density of deep traps with large charge trapping cross section and long release time, then the total charge per unit area may be expressed as [49-511

Q = Qs + eN,z

where z represents the maximum penetration distance of charge into the dielectric bulk. From this it can be demonstrated that

filled and unfilled XLPE and EPR (after St-Onge et al. [37]).

(18)

where z' denotes the mean penetration distance. The above expres- sion may be employed to estimate the deep trap concentration N,, in terms of the slope of the plot of vs. Q. Using the data obtained on My- larTM films, Seiwatz etal. [49-511 find a trap concentration of cm-3 for an injection field of 2x lo5 V cm-l with a corresponding charge mean penetration distance of - 1 pm for a total film thickness of 5 pm. The value of the critical injection field is somewhat lower than that of 1 . 2 ~ lo6 V/cm found for PE [52]. However, with increasing electric field, charge penetration attains larger depths [53]. It is often argued that under direct fields, charge injection eventually ceases, because of the counter electric field created by the injected charge. Superficially this hypothesis may appear plausible except that if indeed such is the case, one is at a loss to account for the electrical tree propagation mechanism that is sometimes observed to occur under dc conditions.

Under alternating electrical fields, electrons and holes will be alter- natively injected into a solid dielectric from either a metallic surface or

554 Bartnikas: Perfonnance of Dielectrics in the Presence of Space Charge

semiconducting polymer shield electrode (as in the case of solid dielectric extruded cables) with each half cycle. The density of the negative and positive injected carriers will increase with time and at higher Val- ues of voltage gradient increasingly deeper traps will become filled. The nearly simultaneous injection of oppositely charged carriers would be expected to lead subsequently to their recombination resulting in photon emission. The detected electroluminescence in the ultra-violet (W) range in the case of PE (cable insulation) [54,55] is believed to be caused by such process and the associated electrical tree growth is likely to arise from the photo-chemical degradation induced by the uv radia- tion. A similar mechanisms would be anticipated to lead also to tree growth in EPR insulation, even though its opaqueness prevents the de- tection of electroluminescence. Although with smooth electrode and semiconducting shield surfaces, the required values of stress (w lo5 to I O 6 V/cm) for electron injection under normal operation voltages would not be attainable, the occurrence of any protrusion or asperity on their surface would readily create the field enhancement required for charge injection and subsequent electrical tree initiation [56]. Failures of rotating machine insulation occur often under service in environments where the HV motors are exposed to switching surges of both polarity created by the operation of vacuum switchgear, with each switch-on event comprising several hundred voltage surges. Experimental work has demonstrably shown that subjection of epoxy insulation to voltage surges results in electroluminescence prior to the onset of electrical treeing and partial discharge, which are the precursor stages leading to eventual voltage breakdown of the epoxy insulating system [57-591. The absence of any dependence of the electroluminescence spectra upon the magnitude of the applied voltage implies that the principal source of photon generation is associated with the electron-hole recombination process, namely the creation and depletion of the trapped space charges.

Charge injectionmay arise also from sharp stress concentration points of impurity inclusions within the volume of the solid dielectric, culmi- nating in electrical tree growth at these sites. Also frequently electrical trees are observed to propagate from cavity occlusions in the solid dielectric, though the process of electrical tree initiation from such cavities is not well understood. However, recent evidence indicates that even in relatively small gas filled cavities, extremely intense electrical fields in the order of 400 kV/cm to 1.5 MV/cm may develop adjacent to the cathode as a consequence of a positive ion space charge in the gas within the cavity [60,61]. In such circumstances, the development of very intense rapid discharges within the gas will subject the solid dielectric adjacent to the cavity to an intense bombardment of charged particles, leading to charge injection into the dielectric in accordance with Equations (18) and (19). Figures 18 and 19 delineate the electrical field across a 0.5 mm gap for the cases of a voltage only slightly above, and another considerably above the breakdown voltage. The amount by which the applied voltage exceeds the nominal value of the breakdown voltage of the gas cavity is influenced by the statistical time lag for the appearance of a free electron necessary to initiate the electron avalanche to precipitate breakdown.

Electrical trees consist of conductive hollow channels and once initiated will proceed to propagate until the entire insulation thickness is tra- versed and breakdown ensues. In contradistinction, water trees consist

of disconnected branches containing water. Water trees require the presence of moisture and generally are initiated also at field enhancement points, though the amplitude of these fields is more than an order of magnitude less than that required for electrical trees [62]. Since charge injection is involved in water tree growth, a space charge mechanism is implicated. The involvement of space charge is further substantiated by the observation that the incidence of water tree occurrence increases with the electrical field [66]. With water trees an aqueous phase is involved and, consequently, electrolytic ions due to various impurities in the cable dielectric (PE or EPR) will interact in a complex manner with the injected electrons and holes under ac conditions. Although water trees may bridge completely the electrodes across a PE specimen, breakdown may not necessarily take place, thereby indicating that notwithstanding the activity of electronic and ionic charge carriers under an externally applied field, the electrical conductivity of the water tree region is negli- gibly small. Frequently, electrical failure may be observed to occur when an electrical tree forms within the structure of the water tree and bridges the water tre'e to either one of the electrodes. Water trees are well known to cause definite long term deterioration of the solid dielectric medium and have been linked to failures of both EPR and PE cables operating under ac conditions in a wet environment. Removal of moisture from the cables in service results in a complete disappearance of the water trees and cable life is found to be correspondingly prolonged. This behavior indicates that the small amount of electron and hole injection at relatively low electrical fields, which takes place at various asperities, is not sufficient per se to lead to long term deleterious space charge effects provided the water medium is eliminated.

There is considerable experimental evidence to suggest that the long term deterioration of solid polymer dielectrics in a wet environment may arise due to chemical and mechanical effects induced by the electrical stress acting on the solid dielectric [56]. The electrical field may influence the oxidation mechanism in the polymer [63] or create mechanical forces that may lead to cracking of the insulation [64]. However, it is more probable that both chemical and mechanical effects may act simul- taneously as inferred in [65], where a direct correlation between water tree growth and fracture toughness of the polymer could not be found and the water tree length, and not its structure, was determined to be a controlling feature of the long term failure. It is rather astounding that notwithstanding the enormous amount of effort expended in the investigations on the phenomenon of water treeing, relatively little serious thought has been given to ascertain the influence of space charges.

8. CONCLUSION HE space charge trapping and detrapping behavior was examined T in a number of practical solid dielectric materials and solid-liquid

composites with the purpose of emphasizing the underlying signifi- cance of space charge effects on the short and long term performance of some electrical insulating systems employed in electron devices, HV power apparatus and cables. Particular attention was given to the manner in which electrons and ions become trapped in crystalline and amorphous dielectrics and how the resulting space charge may influence electrical conductivity, dielectric loss, breakdown strength, treeing and aging characteristics of these materials in the presence of contaminants, field enhancing asperities and discharging cavities. It was shown that

IEEE Transactions on Dielectrics and Electrical Insulation hl. 4 No. 5, October 1997

I I I I I I

I I I I I I

10 lo I I I I I I 0.05 0.1 0.2 0.3 0.4 0.5

Axial distance ( mm )

555

5

Figure 19. Calculated electrical field vs. distance from cathode of a 0.50 mm gap in air-like mixture at atmosphere pressure at high overvolt- age, with discharge development time as a parameter (after Bartnikas and

Axial distance ( mm) Figure 18. Calculated electrical field vs. distance from cathode of a

0.50 mm gap in air-like mixture at atmospheric pressure at low overvolt- age, with discharge development time as a parameter (after Bartnikas and Novak [61]).

space charges may play a predominant role in determining the overall dielectric behavior of electrical insulating systems and that space charge studies have rendered important contributions in elucidating some of the more complex dielectric phenomena observed.

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Manuscript was received on 1 February 1997, in revised form 17May 199%

performance characteristics of dielectrics in the presence of space charge

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