Space Charge in Solid Dielectrics

11

SPACE CHARGE IN SOLID DIELECTRICS

This chapter is devoted to the study of space charge build up and measurement ofcharge density within the dielectric in the condensed phase. When an electric fieldis applied to the dielectric polarization occurs, and so far we have treated the

polarization mechanisms as uniform within the volume. However, in the presence ofspace charge the local internal field is both a function of time and space introducing non-linearities that influence the behavior of the dielectrics. This chapter is devoted to therecent advances in experimental techniques of measuring space charge, methods ofcalculation and the role of space charge in enhancing breakdown probability. A preciseknowledge of the mechanism of space charge formation is invaluable in the analysis ofthe polarization processes and transport phenomena.

11.1 THE MEANING OF SPACE CHARGE

Space charge occurs whenever the rate of charge accumulation is different from the rateof removal. The charge accumulation may be due to generation, trapping of charges, driftor diffusion into the volume. The space charge may be due to electrons or ionsdepending upon the mechanism of charge transfer. Space charge arises both due tomoving charges and trapped charges.

Fig. 11.1 shows the formation of space charge due to three processes in a dielectric thatis subjected to an electric field1.

(a) The electric field orients the dipoles in the case of a homogenous material and theassociated space charge is a sharp step function with two peaks at the electrodes.(b) Ion migration occurs under the influence of the electric field, with negative chargesmigrating to the positive electrode and vice-versa. The mobility of the various carriers

515

are not equal and therefore the accumulation of negative charges in the top half israndom. Similarly the accumulation space charge due to positive charges in the bottomportion is also random and the voltage due to this space charge is also arbitrary. Thespace charge is called "heterocharges".(c) Charges injected at the electrodes generate a space charge when the mobility is low.The charges have the same polarity as the electrode and are called "homocharges."

V o

Fig. 11.1 Development of charge distribution p (z) in a dielectric material subjected to anelectric field, (a) dipole orientation, (b) ion migration, (c) charge transfer at the interfaces(Lewiner, 1986, © IEEE).

A modern treatment of space charge phenomenon has been presented by Blaise andSarjeant2 who compare the space charge densities in metal oxide conductors (MOS) andhigh voltage capacitors (Table 11.1). The effect of moving charges is far less in chargingof the dielectric and only the trapped charges influence the internal field.

11.2 POLARONS AND TRAPS

The classical picture of a solid having trapping sites for both polarities of charge carriersis shown earlier in Fig. 1.11. The concept of a polaron is useful in understanding thechange in polarization that occurs due to a moving charge.

Table 11.1Electronic space charge densities in MOS and HV capacitors (Blaise and Sargent, 1998)

(with permission of IEEE)

MOSParameter

mobilityCurrent densityApplied field

Charge densityCharge cone.

unit

m2/VsA/m2

MV/mC/m3

/m3

Mobile

~20xl O'4

10-104

100-120020u-0.0210'8-10'5

Trapped

100-1200300-30,000

0.1-0.01

HVMobilecharges10'7-10-4

10'2-0.110-100

200u-0.02

capacitorsTrappedcharges

10-100-

2xlO'8-2xlO-6 10'3-10

An electron moving through a solid causes the nearby positive charges to shift towards itand the negative charges to shift away. This distortion of the otherwise regular array ofatoms causes a region of polarization that moves with the electron. As the electronmoves away, polarization vanishes in the previous location, and that region returns tonormal. The polarized region acts as a negatively charged particle, called polaron, and itsmass is higher than that of the isolated charge. The polarization in the region due to thecharge is a function of the distance from the charge. Very close to the charge, (r < re ),where r is the distance from the charge and re is the radius of the sphere that separates thepolarized region from the unpolarized region. When r > re electronic polarizationbecomes effective and when r > r^ ion polarization occurs.

Let us consider a polaron of radius rp in a dielectric medium in which a fixed charge qexists. The distance from the charge is designated as r and the dielectric constant of themedium varies radially from zpolaron is, according to Landau

at 1*1 < rp to ss

1 1

at r2 > rp. The binding energy of the

(11.1)

where rp is the radius of the polaron, So, and ss are the dielectric constants which showsthat smaller values of rp increase the binding energy. This is interpreted as a morelocalized charge. The localization of the electron may therefore be viewed as a couplingbetween the charge and the polarization fields. This coupling causes lowering of thepotential energy of the electron.

The kinetic energy determines the velocity of the electron which in turn determines thetime required to cross the distance of a unit cell. If this time is greater than thecharacteristic relaxation time of electron in the ultraviolet region, then the polarizationinduced by the electron will follow the electron almost instantaneously. The oscillationfrequencies of electron polarons is in the range of 1015-1016 Hz. If we now consider theatomic polarization which has resonance in infrared frequencies, a lower energy electronwill couple with the polarization fields and a lattice polaron is formed. The infrared

1 0 1 1

frequency domain is 10 -10 Hz and therefore the energy of the electron for theformation of a lattice polaron is lower, on the order of lattice vibration energy. Thelattice polaron has a radius, which, for example in metal oxides, is less than theinteratomic distance.

Having considered the formation of polarons we devote some attention to the role of thepolarons in the crystal structure. Fig. 11.2(a) shows the band structure in which the bandcorresponding to the polaron energy level is shown as 2JP [ Blaise and Sargent, 1998]. Ata specific site i (11.2b) due to the lattice deformation the trap depth is increased andtherefore the binding energy is increased. This is equivalent to reducing the radius of thepolaron, according to equation (11.1), and therefore a more localization of the electron.This variation of local electronic polarizability is the initiation of the trappingmechanism.

Trapping centers in the condensed phase may be classified into passive and activecenters. Passive centers are those associated with anion vacancies, that can be identifiedoptically by absorption and emission lines. Active trapping centers are those associatedwith substituted cations. These are generally of low energy (~leV) and are difficult toobserve optically. These traps are the focus of our attention.

11.3 A CONCEPTUAL APPROACH

Focusing our attention on solids, a simple experimental setup to study space charge isshown in fig. 11.34. The dielectric has a metallic electrode at one end and is covered by aconducting layer which acts as a shield. The current is measured through the metallicend. The charges may be injected into the solid by irradiation from a beam of photons,X-rays or gamma rays. Photons in the energy range up to about 300 keV interact with a

solid, preferentially by the photoelectric effect. Photons above this energy interact byCompton effect; an increase of wavelength of electromagnetic radiation due to scatteringby free or loosely bound electrons, resulting in absorption of energy (Gross, 1978). Thesecondary electrons are scattered mainly in the forward direction. The electrons move acertain distance within the dielectric, building up a space charge density and an internalelectric field which may be quite intense to cause breakdown.

w(a)

0

W J

(b)

c.b./ \

\\v\\ u \ \vuu \ \ \ \ \ \ \vvx \ \vvvvv (a)

polaron sites

I trapion

(b)

Fig. 11.2 (a) Potential wells associated with polaron sites in a medium of uniformpolarizability, forming a polaron band of width 2Jp. (b) Trapping effect due to a slightdecrease of electronic polarizability on a specific site i, (adi < ad). The charge is stabilized atthe site due to lattice deformation. This leads to the increase of trap depth by an amountdWion- The total binding energy is Wb= 8Wir + 5WiOn (Blaise and Sargent, 1998, © IEEE).

The space charge build up due to irradiation with an electron beam is accomplished by asimple technique known as the 'Faraday cup'. This method is described to expose theprinciple of space charge measurements. Fig. 11.4 shows the experimental arrangementused by Gross, et al5. A dielectric is provided with vacuum deposited electrodes andirradiated with an electron beam. The metallic coating on the dielectric should be thinenough to prevent absorption of the incident electrons. The electrode on which theirradiation falls is called the "front" electrode and the other electrode, "back electrode".Both electrodes are insulated from ground and connected to ground through separate

current measuring instruments. The measurements are carried out in either current modeor voltage mode and the method of analysis is given by Gross, et al.

Dielectric

a —

Build-upregion scatter

Region

Radiant Energy FluxDensity

Compton Current Density

Space Charge Density

Electric Field Strength

Fig. 11.3 (a) Technique for measurement of current due to charge injection, (b) Schematic forvariation of space charge density and electric field strength (Gross, 1978, ©IEEE).

Electrical field, particularly at high temperatures, also augments injection of charges intothe bulk creating space charge. The charge responsible for this space charge may bedetermined by the TSD current measurements described in the previous chapter. Inamorphous and semicrystalline polymers space charge has a polarity opposite to that ofthe electrode polarity; positive polarity charges in the case of negative poling voltageand vice-versa. The space charge of opposite polarity is termed heterocharge whereasspace charge of the same polarity is termed homocharge. In the case of the heterocharges the local space charge field will intensify the applied field, whereas in the case

of homo charges there will be a reduction of the net field. In the former case ofheterocharges, polarization that occurs in crystalline regions will also be intensified.

•1

Fig. 11.4 Split Faraday cup arrangement for measurement of charge build up and decay. A-Front electrode, B-back electrode, s-thickness of dielectric, r -center of gravity of spacecharge layer. The currents are: Ii-injection current, H -front electrode current, I2=rear current,I=dielectric current (Gross et. al. 1973, with permission of A. Inst. Phys.).

The increase in internal electric field leads to an increase of the dielectric constant s' athigh temperatures and low frequencies, as has been noted in PVDF and PVF . It isimportant to note that the space charge build up at the electrode-dielectric interface alsoleads to an increase of both &' and s" due to interfacial polarization as shown in section4.4. It is quite difficult to determine the precise mechanism for the increase of dielectricconstant; whether the space charge build up occurs at the electrodes or in the bulk.Obviously techniques capable of measuring the depth of the space charge layer shed lightinto these complexities.

The objectives of space charge measurement may be stated as follows:

(1) To measure the charge intensities and their polarities, with a view to understandingthe variation of the electric field within the dielectric due to the applied field.(2) To determine the depth of the charge layer and the distribution of the charge withinthat layer.(3) To determine the mechanism of polarization and its role in charge accumulation.

(4) To interpret the space charge build up in terms of the morphology and chemicalstructure of the polymer

In the sections that follow, the experimental techniques and the methods employed too

analyze the results are dealt with. Ahmed and Srinivas have published a comprehensivereview of space charge measurements, and we follow their treatment to describe theexperimental techniques and a sample of results obtained using these techniques. Table11.2 presents an overview of the methods and capabilities.

11.4 THE THERMAL PULSE METHOD OF COLLINS

The thermal pulse method was first proposed by Collins9 and has been applied, withimprovements, by several authors. The principle of the method is that a thermal pulse isapplied to one end of the electret by means of a light flash. The flash used by Collins hada duration of 8us. The thermal pulse travels through the thickness of the polymer,diffusing along its path. The current, measured as a function of time, is analyzed todetermine the charge distribution within the volume of the dielectric. The experimentalarrangement is shown in Fig. 1 1.5.

The electret is metallized on both sides (40 nm thick) or on one side only (lower fig.11.5), with an air gap between the electret, and a measuring electrode on the other. Bythis method voltage changes across the sample are capacitively coupled to the electrode.The gap between the electrode and the electret should be small to increase the coupling.The heat diffuses through the sample and changes in the voltage across the dielectric,AV(t), due to non-uniform thermal expansion and the local change in the permittivity, aremeasured as a function of time. The external voltage source required is used to obtain thezero field condition which is required for equations (1 1 .3) and (1 1 .4) (see below).

Immediately after the heat pulse is applied, temperature changes in the electret areconfined to a region close to the heated surface. The extent of the heated zone can bemade small by applying a shorter duration pulse. The process of metallizing retains heatand the proportion of the retained heat can be made small by reducing the thickness ofthe metallizing. In the ideal case of a short pulse and thin metallized layer, the voltagechange after a heat pulse applied is given by

(11.2)

where pT is the total charge density (C/m2). Determination of the total charge in theelectret does not require a deconvolution process.

Table 11.2Overview of space charge measuring techniques and comments (Ahmed and Srinivas,

1997). R is the spatial resolution and t the sample thickness.(with permission of IEEE)

MethodThermal pulse method

laser intensitymodulation method

Laser induced pressurepulse method

Thermoelasncallygenerated UPP

Pressure wavepropagation method

Non-structured acousticpulse method

Laser generated acousbcpulse method

Acoustic probe method

Piezoelectncally-generated pressure stepmethodThermal step method

Electro-acoustic stresspulse method

PhotoconductivitymethodSpace charge mapping

Spectroscopy

Field probe

DisturbanceAbsorption ofshort-tight pulse in frontelectrodeAbsorption ofmodulated light in frontelectrodeAbsorption of shortlaser light pulse in frontelectrodeAbsorption of shortlaser light pulse in thinburied layerAbsorption of shortUser light pulse in metaltarget

HV spark betweenconductor and metaldiaphragm

Absorption of shortlaser light pulse in thinpaper target

Absorption of laser lightpulse in front electrode

Electrical excitation ofpiezoelectric quartzplateApplying twoisothermal sourcesacross sampleForce of modulatedelectric held on chargesin sample

Absorption of narrowlight beam in sampleInteraction of polarizedlight with field

Absorption of excitingradiation in sample

None

Scan mechanismDiffusion according toheat-conductionequationsFrequency-dependentsteady-state heat profile

Propagation withlongitudinal soundvelocit)Propagation withlongitudinal soundvelocityPropagation withlongitudinal soundvelocity

Propagation withlongitudinal soundvelocity


Propagation withlongitudinal soundvelocityPropagation withlongitudinal soundvelocityThermal expansion ofthe sample


External movement oflight beamparallel illumination ofsample volume ormovement of light beamor sampleExternal movement ofradiation source orsampleCapacinve coupling tothe field

Detection process\foltagechangeacrosssample

Current between sampleelectrodes


Current or voltagebetween sampleelectrodes\foltageorcurrentbetween sampleelectrode

\foltage between sampleelectrode

\Wtage between sampleelectrodes

\foltage between sampleelectrodes



Piezoelectric transducerat sample electrode

Current between sampleelectrodesPhotographic record

Relative change in theobserved spectrum

Current

r(nm)3*2

>2

1

I

10

1000

50

200

1

150

100

^1.5

200

5*50

1000

*(M"0~200

~25

100 - 1000

50-70

5-200

< 10000

<3000

2000 - 6000

25

2000 - 20000

< 10000

—-

-

< 20000

CommentsHigh resolution requiresdeconvolution

Numericaldeconvolution isrequiredNo deconvolution isrequired

Deconvolution isrequired

Resolution improvedwith deconvolutionAlso used for surfacecharge measurementsUsed for solid andliquid dielectric Higherresolution withdeconvoluhonDeconvolution isrequired Target andsample immersed indielectric liquid



Deconvoluhon isrequired Also used forsurface chargemeasurementsNondestructive forshort illumination timeMostly used ontransparent dielectricliquids

Few applications

Destructive

Incident light

Metallizing

Etectret

To preamplifier

Incident light

^ Air gap

f Electret /•/>\ ' \1

P

' l\ \>\

/////.//A\ ^^ Sens

!x

V C

Sueng

To preamplifi

Fig. 11.5 Schematic diagram of the apparatus for the thermal pulsing experiment in the doublemetallizing and single metallizing configurations. (Collins, 1980, Am. Inst. Phys.)

The observed properties of the electret are in general related to the internal distributionof charge p (x) and polarization P(x) through an integral over the thickness of the sample.The potential difference V0 across the electret under open circuit conditions (zeroexternal field) is given by

*;=•^00

(11.3)

where p(x) is the charge density in C/m3 and d the thickness of the sample.

Collins (1980) derived the expression

*S*00J A f \ DAp(x)-B—

axJ

(11.4)

where A = ax - ae and B = ap - a^- ae, x is the spatial coordinate with x = 0 at the pulsedelectrode. p(;x;) and P(JC) are the spatial distributions of charge and polarization. Thesymbols a mean the following:

ax = Thermal coefficient of expansiona£= Temperature coefficient of the dielectric constantap= Temperature coefficient of the polarization

There are two integrals, one a function of charge and the other a function of temperature.Two special cases are of interest. For a non-polar dielectric with only inducedpolarization P = 0, equation (1 1 .4) reduces to

(11.5)

For an electret with zero internal field

/>(*) = +fr (1L6)ax

.7)

Collins used a summation procedure to evaluate the integral in equation (11.5). Thecontinuous charge distribution, p(x) is replaced by a set of N discrete charge layers pn

with center of gravity of each layer at mid point of the layer and having coordinate x-} = (j- V^d/N with j = 1, 2, ...N. The integral with the upper limit x in equation (11.5) isreplaced with the summation up to the corresponding layer Xj. Equation (11.5) thensimplifies to

(11.8)

Assuming a discrete charge distribution the shape of the voltage pulse is calculated usingequation (1 1.8) and compared with the measured pulse shape. The procedure is repeatedtill satisfactory agreement is obtained. Collins' procedure does not yield a uniquedistribution of charge as a deconvolution process is involved.

The technique was applied to fluoroethylenepropylene (FEP, Teflon™) electrets and thedepth of charge layer obtained was found to be satisfactory. Polyvinylidene fluoride(PVDF) shows piezo/pyroelectric effects, which are dependent on the poling conditions.A copolymer of vinylidene fluoride and tetrafluoroethylene (VF2-TFE) also has verylarge piezoelectric and pyroelectric coefficients. The thermal poling method has revealedthe poling conditions that determine these properties of the polymers. For example, inPVDF, a sample poled at lower temperatures has a large spatial non-uniformity in thepolarization across its thickness. Even at the highest poling temperature some non-uniformity exists in the spatial distribution of polarization. Significant differences areobserved in the polarization distribution, even though the samples were prepared fromthe same sheet.

Seggern10 has examined the thermal pulse technique and discussed the accuracy of themethod. It is claimed that the computer simulations show that the only accurateinformation available from this method is the charge distribution and the first fewFourier coefficients.

11.5 DEREGGI'S ANALYSIS

DeReggi et al.11 improved the analysis of Collins (1980) by demonstrating that thevoltage response could be expressed as a Fourier series. Expressions for the open circuitconditions and short circuit conditions are slightly different, and in what follows, weconsider the former12.

The initial temperature at (x,0) after application of thermal pulse at ;t=0, t=0 may beexpressed as

ro,o) = +Aro,o) (11.9)

where TI is the uniform temperature of the sample before the thermal pulse is applied,and AT(x,0) is the change due to the pulse. AT(jc,0) is a sharp pulse extending from x = 0with a width s«d. From equation (11.9) it follows that the temperature at x after theapplication of the pulse is

T(x,t) = Tl+AT(x,t) (11.10)

where

cosn=1

exp-n2t

(11.11)

= \imAT(x,t)

a" ~ 7a

The temperature at the surface is given by

(11.12)

(11.13)

n=l

(11.14)

(11.15)

0 o

where T = d /TI K and k is called thermal diffusivity. The dimensionless quantitiesAT(0,t)/ao and AT(d, t)/ao can be obtained by measuring the transient resistance of one orboth the electrodes. Then the ratios an/ao and TI can be determined without knowing thedetailed shape of the light pulse.

Substituting equation (11.15) into (11.5) the voltage at time t is given as

n(11.16)

where the following relationships hold.

A0 = (11.17)

r , , . ,n7rx= jp(x)sm(— -)dx (11.18)

The terms an and An are the coefficients of Fourier series expansions for AT(x,0) and p(jc)respectively, if these are expanded as cosine and sine terms, respectively.

For the short circuit conditions, equations for the charge distribution and the polarizationdistribution are given by Mopsik and DeReggi (1982, 1984). About 10-15 coefficientscould be obtained for real samples, based on the width of the light pulse. Thepolarization distribution determined will be unique as a deconvolution procedure is notresorted to. Fig. 11.6 shows the results for a nearly uniformly poled polyvinylidenefluoride (PVF2) which was pulsed alternately on both sides. An interesting observation inthis study is that there is a small peak just before the polarization falls off.

A further improvement of the thermal pulse technique is due to Suzuoki et. al.13 whotreat the heat flow in a slab in the same way as electrical current in an R-C circuit withdistributed capacitance. The electrical resistance, capacitance, current and voltage arereplaced by the thermal resistance Rt, thermal capacitance Q, heat flow q (jc, t) andtemperature T(;c, t), respectively.

The basic equations are:

1 /•> V /-N 1 /•>

OX Ot

= rZv-v (H20)dx dt

The heat flux is given by

^ /( — CO 1 / / 2 2 > \ / /rx^-v \

'" 01.21)

2.0

1.0

0.0

_ 4 i i

0.2 0.4 0.6 0.8X

1.0

Fig. 11.6 Polarization in PVF2 sample. The solid line is experimental distribution. The dashedline is the resolution expected for a step function, at x = 0.5 (DeReggi, et al., 1982, withpermission of J. Appl. Phys.).

The total current in the external circuit at t = 0, when the specimen is illuminated at x = 0is given by

(11.22)

Similarly, the current, when the specimen is illuminated at x = d, is

(11.23)

The total amount of space charge is

a=- (11.24)

The mean position of the space charge is

*- 72(0) (11.25)

The thermal pulse was applied using a xenon lamp and the pulse had a rise time of 1 00îs, width SOOus. Since the calculated thermal time constant was about 5ms, the lightpulse is an approximation for a rectangular pulse. The materials investigated were HDPEand HDPE doped with an antistatic agent. Fig. 11.7 shows the measured currents indoped HDPE. Homocharges were identified at the anode and in doped HDPE a strongheterocharge, not seen in undoped HDPE, was formed near the cathode.

11.6 LASER INTENSITY MODULATION METHOD (LIMM)

Lang and Das Gupta14 have developed this method which is robust in terms of dataaccuracy and requires only conventional equipment, as opposed to a high speed transientrecorder, which is essential for the thermal pulse method. A thin polymer film coatedwith evaporated opaque electrodes at both surfaces is freely suspended in an evacuatedchamber containing a window through which radiant energy is admitted. Each surface ofthe sample, in turn, is exposed to a periodically modulated radiant energy source such asa laser. The absorbed energy produces temperature waves which are attenuated andretarded in phase as they propagate through the thickness of the specimen. Because ofthe attenuation, the dipoles or space charges are subjected to a non uniform thermal forceto generate a pyro-electric current which is a unique function of the modulationfrequency and the polarization distribution.

Let CD rad s"1 be the frequency of the sinusoidally modulated laser beam and the specimenilluminated at x = d. The surface at x = 0 is thermally insulated. The heat flux absorbedby the electrode is q (d. t) which is a function of the temperature gradient along thethickness. The one dimensional heat flow equations are solved to obtain the current as

J>(*)coshD(y + l)xdx (1 1 .26)*r. iwDsmhD(j + \}d *

1 /O

where D= (o/2K) , j is the complex number operator and C contains all the positionand frequency-dependent parameters. The current generated lags the heat flux because ofthe phase retardation of the thermal wave as it progresses through the film. The currenttherefore has a component in phase and in quadrature to the heat flux.

The mathematical treatment of measured currents at a number of frequencies fordetermining P(;c) involves the following steps: The integral sign in equation (11.26) maybe replaced by a summation by dividing the film into n incremental thickness, each layerhaving its polarization, Pj, where j=1,2,....n. The matrix equation [I] = [G] [P] where

(11.27)[CVo(/ + l) cosh £>(/•

[DsmhD(i-

is solved. The in-phase component of measured current is used with the real part of Gand the quadrature component is used with the imaginary part. It is advantageous tomeasure I(o) at more than n frequencies and apply the least square method to solve for P.

—v 500 US

-50

(J

-100

-150L

250 V500 V

1500 V

Fig. 11.7 Experimental thermal pulse currents in doped HDPE for (a) cathode illumination(b) anode illumination. Negative currents show the existence of a positive space charge in thesample (Suzuoki et al, 1985; with permission of Jap. J. Appl. Phys.)

Fig. 11.8 shows the polarization distributions and pyroelectric currents versus frequency.Because of the impossibility of producing an experimentally precise type of polarization,a triangular distribution was assumed and the currents were synthesized. Using the in-phase and quadrature components of these currents, the polarization distribution wascalculated as shown by points. The parameters used for these calculations are d = 25.4um, K = 0.1 x 10"7 mY1, 102 < f < 105 Hz (101 values), obtaining 51 values of Pk. Lang

and Das Gupta (1981) have used the LIMM technique to study spatial distribution ofpolarization in PVDF and thermally poled polyethylene.

11.7 THE PRESSURE PULSE METHOD

The principle of the pressure pulse method was originally proposed by Laurenceau, etal.15 and will be described first. There have been several improvements in techniques thatwill be dealt with later. The pressure probe within a dielectric causes a measurableelectrical signal, due to the fact that the capacitance of a layer is altered in the presenceof a stress wave. The pressure pulse contributes in two ways towards the increase ofcapacitance of a dielectric layer. First, the layer is thinner than the unperturbed thicknessdue to the mechanical displacement carried by the wave. Second, the dielectric constantof the compressed layer is increased due to electrostriction caused by the pulse .

A IN-PHASE

• QUADRATURE

0.2 0.4 0.6 0.8

POSITION (X/L)

Fig. 11.8 (a) Pyroelectric current versus frequency (x = 0 and x = d refers to heating from x= 0 and x = d side of the film, fy = 0 and § = 7i/2 refers to in phase or in quadrature with heatflux respectively, (b) Polarization distributions (solid line) and calculated distributions(points). Selected data from (Lang and Das Gupta, 1981, with permission of Ferroelectrics).

A dielectric slab of thickness d, area A, and infinite-frequency dielectric constant 8*. withelectrodes a and b in contact with the sample, is considered. The sample has acquired,due to charging, a charge density p (x) and the potential distribution within the dielectricis V (x). All variables are considered to be constant at constant x; the electrode a isgrounded, electrode b is at potential V. The charge densities a a and (Jb are given by

d_-(AQV_<% 7 A °° 7d A d

(11.29)v ^" d A d

where

a

\xp(x)dxn d

and ^= \p(x)dx (11.30)

Expressions (1 1.28) and (1 1.29) show that if V = 0 and if the sample is not piezoelectric,a uniform deformation along the x axis does not alter the charges on the electrodes since(d-(x))/d remains constant. This implies that in order to obtain the potential or chargeprofiles, a non-homogeneous deformation must be used. A step function compressionalwave propagating through the sample with a velocity v, from electrode a towards b,provides such a deformation. As long as the wave front has not reached the oppositeelectrode, the right side of the sample is compressed while the left part remainsunaffected (Fig. 1 1 .9). The charge induced on electrode b is a function of the chargeprofile, of the position of the wave front in the sample, but also of the boundaryconditions at the electrodes: Open circuit or short circuit conditions. In the first case theobservable parameter is the voltage, in the second case, the external current.

Let the unperturbed thickness of the sample be d0, and A p the magnitude of pressureexcess in the compressed region, (3 the compressibility of the dielectric defined as thefractional change in volume per unit excess pressure, (3 = -AV/(VAp). The compressedpart of the dielectric has a permittivity of s' and ;cf is the position of the wave front attime t, which can be expressed as Xf = d-v0 t. In the compressed region charges, whichare supposed to be bound to the lattice, are shifted towards the left by a quantity u (x,t) =-(3 Ap (x-Xf). In the uncompressed part the charges remain in the original position.

The electric field in the uncompressed part is E(;c,t) and E' (jc,t) in the compressed part.At the interface between these regions the boundary condition that applies is

f,f) = e'E'(xf,i) (11.31)

The boundary condition for the voltage is

(11.32)

-> z

at'

Fig. 11.9 Charge in a dielectric between two electrodes, divided into a compressed region ofpermittivity s' and an uncompressed region of permittivity s; the step function compression travelsfrom right to left at the velocity of sound. The position of the wave front is Xf. The undisturbedpart has a thickness do (Laurenceau, 1977, with permission of A. Inst. of Phy.).

Laurenceau, et al. (1977) provide the solution for the voltage under open circuitconditions as

(11.33)

The current under short circuit conditions is

A x f + ( e / £ ' ) ( d - x f )(11.34)

Equations (11.33) and (11.34) show that the time variation of both the voltage andcurrent is an image of the spatial distributions of voltage and current inside the sample

prior to perturbation. The front of the pressure wave acts as a virtual moving probesweeping across the thickness at the velocity of sound.

Laurenceau, et al. (1977) proved that the pressure pulse method gives satisfactoryresults: a compressional step wave was generated by shock waves and a previouslycharged polyethylene plate of 1 mm thickness was exposed to the wave. The short circuitcurrent measured had the shape expected for a corona injected charge, reversed polarity,when charges of opposite sign were injected. Further, the charges were releasedthermally and the current was reduced considerably, as expected.

Lewiner (1986) has extended the pressure pulse method to include charges due topolarization P resulting in a total charge density

dPp(x) = ps(x)- — (11.35)

ax

where ps is the charge density due to the space charge. The open circuit voltage betweenthe two electrodes is given by

xrV(t) = j3G(sr) $E(x,0)p(x,t)dx (1 1.36)

o

where Xf =vt is the wave front which is moving towards the opposite with a velocity v,G(sr) is a function of the relative permittivity which in turn is a function of pressure. Inshort circuit conditions the current I(t) in the external circuit is related to the electric fielddistribution by

(1L37)

where C0 is the uncompressed geometric capacitance, C0 = S0sr A/d. Equations (11.36)and (11.37) show that if p(jc, t) is known, the electric field distribution may be obtainedfrom the measurement of V(t) or I(t). If the pressure wave is a step like function ofamplitude Ap (fig. 1 1-9) then V(t) will be a mirror image of the spatial distribution of thepotential in the sample as discovered by Laurenceau, et al. (1977), whereas I(t) is directlyrelated to the electric field. If the pressure wave is a short duration pulse, then V(t) andI(t) give directly the spatial distributions of the electric field and charge density. If thepressure wave profiles change during its propagation through the sample, this effect canbe taken into account by a proper description of p(x, t). The techniques used to generate ashort rise time pressure waves are shock wave tubes, discharge of capacitors in fluids,

piezoelectric transducers and short rise time laser pulses. Fig. 11.10 shows a typicalexperimental set up for the laser pulse pressure pulse method.

electrodee • ample

fast recorder

X-Yrecorder

computer oecilloecope

Fig. 11.10 Experimental set up for the measurement of space charge (Lewiner, 1986, © IEEE)

The choice of the laser is governed by two conditions. First, the homogeneity of thebeam must be as good as possible to give a uniform pressure pulse over the entireirradiated area. Second, the duration of the laser pulse is determined by the thickness ofthe sample to be studied. For thin samples, < 100 jam, short duration pulses of 0.1-10 nsduration are appropriate. For thicker samples broader pulses are preferred since there isless deformation of the associated pressure pulse as it propagates through the thickness.The power density of the laser beam between 106-108 W/cm2 yields good results.

The measured voltage and current in 50 um thick Teflon (FEP) film charged withnegative corona up to a surface potential is of 1250 V is shown in Fig. 11.11. The chargedecay as the temperature of the charged sample is raised, is shown in Fig. 11.12. Thecharged surface retains the charge longer than the opposite surface, and highertemperature is required to remove the charge entirely. The LIPP technique is appliedwith several variations depending upon the method of generating the pressure pulse. Themethods are briefly described below.

6 10 -

« tlm. (n.) 40

Fig. 11.11 Current and voltage wave forms measured during the propagation of a pressure pulsethrough a negative corona charged FEP film of 50 jam thickness. T is the time for the pulse toreach the charged surface (Lewiner, 1986, © IEEE).

120:140s

160'

180V

200s

220*

240*

260

20 40tlm* (n«)

60

Fig. 11.12 Charge decay with temperature in negative corona charged FEP film. Charged sideretains charges longer (LEWINER, 1986, © IEEE)

11.7.1 LASER INDUCED PRESSURE PULSE METHOD (LIPP)

A metal layer on one side of a dielectric absorbs energy when laser light falls upon it.This causes stress effects and a pressure pulse, < 500 ps duration, is launched, whichpropagates through the sample with the velocity of sound. Fig. 11.13 shows theexperimental arrangement used by Sessler, et al.17. The method uses one sided metallizedsamples and it is charged at the unmetallized end by a corona discharge. The laser lightpulses, focused on the metallized surface, having a duration of 30-70 ps and 1-10 mJenergy, are generated by a Nd:YAG laser.

PULSEDLASER

\

FRONTELECTRODE

SAMPLE

N,ABSORBING

, LAYERX

\

rPRESSURE!

PULSE

-SURFACE CHARGE

SAMPLE-HOLDER'ELECTRODE

AIRGAP

/ELECTRODE

I—n>i—i®I L -J U-JAMPLIFIER

OSCILLO'SCOPE

Fig. 11.13 Experimental setup for the laser-induced pressure-pulse (LIPP) method for one sidedmetallized samples (Sessler, et al., 1986, © IEEE).

The pressure pulse generates, under short circuit conditions, the current signal

7(0 =Apr

3*. dx(11.38)

x=vt

where A is the sample area, p the amplitude of the pressure, i the duration of the pressurepulse, PO the density of the material, s the sample thickness, g the air gap thickness, e (x)the piezoelectric constant of the material, ss the static (dc) dielectric constant and £*, theinfinity frequency dielectric constant.

11.7.2 THERMOELASTIC STRESS WAVES

This method has been adopted by Anderson and Kurtz (1984). When some portion of anelastic medium is suddenly heated thermoelastic stress waves are generated. A laserpulse of negligible duration enters a transparent solid and encounters a buried, opticallyabsorbing layer, causing a sudden appearance of a spatially dependent temperature risewhich is proportional to the absorbed energy.

optical absorber

laserpulse .^

\

sapphirewindow

/

Mylay

larers

-A

brass

AA,— r»

fi~~¥•—^ 50 Q

coax

V

i io6Q

Fig. 11-14 (a) Pressure pulse in a slab of dielectric containing a plane of charge Q. The pulsetravels to the right. Electrode 2 is connected to ground through a co-axial cable and measuringinstrument, (b) Experimental arrangement for measuring injected space charge. The Mylar filmadjacent to the sapphire window acquires internal charge as a result of being subjected to high-field stress prior to installation in the measurement cell. Thicknesses shown are not to scale.(Anderson and Kurtz, 1984 © Am. Inst. Phys.)

The thickness of the sample in the x direction is assumed to be small compared to thedimensions along the y and z directions so that we have a one dimensional situation. Atthe instant of energy absorption the solid has inertia for thermal expansion and hencecompressive stress appears in the solid. The stress is then relaxed by propagation, in theopposite direction, of a pair of planar, longitudinal acoustic pulses which replicate theinitial stress distribution. Each of these pressure pulses carries away half of themechanical displacement needed to relax the heated region. The measured signal is thevoltage as a function of time and a deconvolution procedure is required to determine thecharge density (Anderson and Kurtz, 1984).

11.7.3 PRESSURE WAVE PROPAGATION (PWP) METHOD

i ftIn this method the pressure wave is generated by focusing a laser beam to a metal targetbonded to the dielectric sheet under investigation. Earlier, Laurenceau, et al. (1977) hadused a step pressure wave to create non-homogeniety as described in section 12.7 above.Though the step function has the advantage that the observed signal is the replica of thepotential distribution within the volume before the pressure wave arrived, the difficultyof producing an exact step function limited the usefulness of the method. When a highspatial resolution is required the pulse shape should be small, which is difficult toachieve with a shock tube for two reasons.

First, the shock wave travels in the shock tube with a velocity of a few hundred metersper second; a small angle between the wave front and the sample results in a strongdecrease of the spatial resolution. Second, the reproducibility of the wave shape is poor.In the PWP method Alquie, et al. (1981) generalize the calculation to an arbitrary shapeof the pressure pulse. The time dependence of the voltage across the sample has a uniquesolution for the electric field distribution within the sample. Fig. 11.15 shows the samplewhich has a floating electrode in the middle and two identical samples of FEP on eitherside. The solution for the electric field shows a sharp discontinuity at the point wherethere is a charge reversal as expected.

aluminum target

laser beam - — V(0,t)

bonding layer

Fig. 11.15 Sample preparation for field distribution study in FEP. Two discs metallized on bothsides are joined in the middle creating a floating electrode through which the sample was charged(Alquie, 1981, © IEEE).

11.7.4 NONSTRUCTURED ACOUSTIC PROBE METHOD

The measurement of electric field within a charged foil of relatively small thickness, -25um-lmm, offers more flexibility in the choice of methods because the pulses are notattenuated as much as in thicker samples. For larger systems or thicker samples adifferent approach, in which the electric field is measured by using a nonstructuredacoustic pulse to compress locally the dielectric of interest, has been developed byMigliori and Thompson19. In this technique the pulse shape is unimportant, andattenuation effects are easily accounted for, thereby increasing the effective range of theprobe to several tens of centimeters in polymers. Because the probe is sensitive toelectric fields, small variations in electric fields and space charge are detectable. Fig.11.16 shows the experimental arrangement. An acoustic pulse is generated using a sparkgap which is located in a tube and situated at about 0.1 mm from a replaceable metaldiaphragm. An energy storage capacitor, also located in the same tube (fig. 11.16a)provides the energy for a spark.

OILEXHAUST

CHARGINGINPUT I ENERGY

STORAGECAPACITOR

a

b

Fig. 11.16. (a) Diaphragm-type acoustic pulse generator used to generate non-structured acousticpulses for electric field measurements in oil and polymers, (b) Block diagram of theinstrumentation used to acquire and process the acoustic and electrical signals required for anacoustic electric field measurement. The box labeled CLART represents the capacitance- likeacoustic receiving transducer, and the two pre-amplifiers are described in the text (Migliori andThompson, 1980, with permission of J. Appl. Phys.).

The other end of the tube is closed with a thick brass plate and the tube is filled withtransformer oil. The capacitor is charged until breakdown occurs between the conductorand the metal foil. The spark current ( -100A) has a rise time of a fraction of a us andlaunches an acoustic wave having a peak amplitude of ~103 Pa.

The acoustic signal is measured by a capacitance-like acoustic transducer, preamplifierand bias supply immersed in oil in its own tank, which is shielded. This tank is shown asCLART in fig. (1 1-1 6b). The measured voltage due to the acoustic pulse is given by

(11.39)

where i is the time required to pass a particular point. The technique was employed tomeasure space charge in an oil filled parallel plate capacitor, and 16mm thickpoly(methyl methacrylate) (PMMA).

11.7.5 LASER GENERATED ACOUSTIC PULSE METHOD

The non-structured acoustic pulse method described in the previous section has thedisadvantage that the generated pulse is not reproducible. It also suffers from insufficientbandwidth and the ratio of low frequency energy to high frequency energy is too high.An improved technique is adopted by Migliori and Hofler20 using a laser to generate theacoustic pulses (Fig. 11.17). Light from a ruby laser which generates pulses of 1.5 J and15 ns half width is directed through a plate glass window into an aluminum tank filledwith liquid freon. The tank contains a laser beam absorber to convert radiation topressure, a pressure transducer and pre-amplifier, the sample under test and itspreamplifier.

The beam strikes an absorber which consists of a carbon paper stretched flat and with thecarbon side towards the film. Alignment of the laser perpendicular to the beam is notcritical. The paper absorbs radiation and the freon entrained between the paper fibres isheated. The pressure wave has a rise time of about 15 ns and a peak of 0.5 Mpa. Themethod is sensitive enough to determine the electric fields in the range of 50 kV/m, witha spatial resolution of 50 um in samples 3 mm thick.

11.7.6 ACOUSTIC PULSE GENERATED BY MECHANICAL EXCITATION

Mechanical excitation may also be used to generate acoustic pulses for probing theelectric field within a charged dielectric and this method has been adopted by Roznovand Gromov21. A Q-switched ruby laser is used to illuminate a graphite disk with 30 nspulses and an energy density of 0.5 J/cm2.

oil coupling film acoustic step\ / signal

50ftelectrode

Fig. 11.17 Laser generated acoustic pulse method to measure the electric fieldinside a solid dielectric (Migliori and Hofler, 1982, with permission of Rev. Sci.Instr.).

11. 7. 7 PIEZOELECTRIC PRESSURE STEP METHOD (PPS)

The pressure pulse step method used by Gerhardt-Multhaupt, et al.22 is shown in fig.11.18. Charging a cable and discharging through a relay-trigger, generates a square pulseof 400-600 V and 100 ns duration. The sequence of the positive and negative pulse isapplied to a 3 mm thick piezoelectric quartz pulse. A thin (-100-200 nm) layer ofsilicone oil couples the generated pressure pulse with the metallized surface of thesample. This sandwich of quartz-oil-sample ensures good acoustic contact. Theunmetallized surface is in contact with a conducting rubber disc which is connected to apreamplifier and an oscilloscope. The sample is charged by electron beam of varyingenergy. This method of charging has the advantage that increasing the energy of thebeam can vary the depth of penetration of charges.

FRONTCHARGE

-HOLDER

23Fig. 11.18 Principle of Piezoelectric pressure step method (PPS) (Sessler , 1997, © IEEE).

11.7.8 PULSED ELECTRO-ACOUSTIC STRESS METHOD

The method adopted by Takada and Sakai24 is based on the principle that an electricalpulse applied to a dielectric with a stored charge launches an acoustic pulse thatoriginates from the bulk charge. A dc electric field is applied to deposit charges in thebulk and an ac field of a much smaller magnitude, having 1 MHz frequency, is appliedto launch the acoustic wave. The dc supply and ac oscillators are isolated appropriatelyby a combination of resistance and capacitance.

A piezoelectric transducer is attached to each electrode and the acoustic field excited bythe alternating field propagates through the electrodes to the transducer. The electricalsignal detected by the transducer is amplified and rectified. The method measures theelectric fields in the interface of a dielectric, and utilizes a transducer and associatedequipment at each electrode. Further, the signal from the grounded electrode may bemeasured by directly connecting to a recorder, but the signal from the high voltageelectrode needs to be isolated by an optical guide and appropriate data transfer modules.

The technique was improved subsequently by Takada, et al25 whose experimentalarrangement is shown in fig. 11.19. The oscillator of the previous method is replacedwith a high voltage pulser and the signal from the piezoelectric transducer is recorded ona dual beam oscilloscope for further analysis.

Xi

d -

Piezodevice

Dual-beamoscilloscope

Upperelectrode

Oil

*"

Al-metallized

Acousticabsorber

Fig. 11.19 Pulsed Electro-Acoustic Method [Takada et. al., 1987, © IEEE)

11.7.9 ELECTRON BEAM METHOD

This method was used by Sessler, et al. prior to the methods described above26. A mono-energetic electron beam is incident through the front electrode under short circuitconditions (both electrodes connected to ground through small impedance). A brief

97comment about the method of charging is appropriate here. Arkhipov, et al. haveshown, by theoretical analysis, that if the rear electrode is grounded and the front(radiated) electrode is open circuited, the space charge build up takes place mostly in theun-irradiated region. For a grounded front electrode, with the rear open circuited, there isonly weak charging in the irradiated region. Consequently, a dielectric is much lesscharged for the second mode than the first.

The beam generates a radiation induced conductivity to a depth determined by its energy.At the plane of the maximum penetration maximum conductivity occurs and the plane istreated as a virtual electrode (thickness ~5um). Since the depth of the plane depends onthe energy, the virtual electrode may be swept through the dielectric by increasing theenergy of the electrons. The currents are measured at each electrode from which thespatial distribution of charges are determined. The method is destructive in the sense thatthe charge is removed after experimentation.

11.7.10 SPECIAL TECHNIQUES

Techniques dependent on special effects or restricted to selected dielectric materials aredescribed below.

1. Kerr Effect: The Kerr effect, generally applied to birefringent liquids such asnitrobenzene, consists of passing plane polarized light (called a polarizer) through a cellcontaining the dielectric. The electric field in the dielectric splits the plane polarized lightinto two components, one component traveling faster than the other. The phasedifference between the two components makes the emerging light circularly polarized.This effect is known as the Kerr effect and the intensity of the output light measured by aphotomultiplier is dependent on the square of the electric field. The Kerr effect, when itoccurs in solids is usually referred to as Pockels effect. This method has been employedby Zahn, et al.28 to study electron beam charged PMMA, having a self field of 1-2.5MV/m.

2. Spectroscopic Method: In an electric field the spectral lines shift or split and thisphenomenon is known as the Stark effect. By observing the spectrum in a spectroscopethe field strength may be determined .

A variation of the Stark effect is to make use of the principle that very weakly absorbedvisible monochromatic light liberates carriers that move under the field of trappedcharges. By detection of the photocurrent produced one could infer the chargedistribution30.

3. Field Probe and Scanning Microscopic Methods: Measurements of an electric fieldby probes have been used to compute the charge distribution (Tavares, 1973). A scanningmicroscope has also been used to determine the charging behavior of PMMA underelectron beam irradiation31.

4. Vapor Induced Depolarization Currents (VIDC): This method is based on theprinciple that, when a charged dielectric is exposed on one of its faces to a saturatedvapor of a solvent, diffusion occurs and the trapped charges are released. A current isdetected in the external circuit from which the magnitude of the trapped charge may beevaluated32.

11.8 EXPERIMENTAL RESULTS

The experimental results in fluoropolymers have been succinctly summarized by Sessler(1997), considering different methods of charging and different techniques ofmeasurement. Table 11.3 provides references to selected data. In the following webriefly discuss some polymers of general interest.

Poly(ethylene) (PE); (a) unirradiated

The PEA method has been applied by Mizutani, et al.33 to study space charge in threedifferent grades of PE at electric field strengths up to 90 MV/m. Homocharges wereobserved and the space charge was dependent on the electrode material suggestingcarrier injection from both electrodes. These results confirm the results of the earlierfield probe method adopted by Khalil and Hansen34. To separate injected charges fromthe ionized impurities, Tanaka, et al. have adopted a technique of charge injectionsuppression layers35. The pulsed acoustic technique was employed to measure spa chargedensity. In LDPE with suppression layers on both electrodes heterocharges are observed.However, by removing charge suppression homo charges were observed. This techniqueyields the true charge injected by the electrodes into PE.

In HDPE homocharges are identified at the anode, and in doped HDPE a strongheterocharge, not seen in undoped HDPE, is formed near the cathode (Suzuoki et. al.(1995).

Poly(ethylene) (PE); (b) irradiated

Chen, et al.36 have observed, by LIPP technique, that the energetic ionizing radiationssuch as a y-source can alter the chemical structure and may also give rise to the presenceof trapped charges. Low radiation doses (< 10 kGy) were observed to affect the lowdensity polyethylene differently when compared with high doses (> 50 kGy).

A. CROSS LINKED POLYETHYLENE (XLPE)

XLPE is being used increasingly in the power cable industry and two main chemicalmethods are employed to produce it from low density polyethylene. One method is to usea peroxide (dicumyl peroxide, DCP) which decomposes to form free radicals or a silanebased grafting process. The space charge accumulation has been measured by the LIPPtechnique and the observations are:

1. The cross linking method appears to determine the polarity of the space chargeadjacent to the electrodes. The DCP cross linking favors heterocharge, and silane crosslinking favors homocharge. The charge densities do not vary appreciably.

2. Reversing the applied voltage polarity results in a near-perfect inversion of the spacecharge across insulator/polymer interface. This is interpreted as evidence for electrontransfer by tunneling from donor to acceptor states centered on the Fermi level.

B. FLUOROETHYLENE PROPYLENE (FEP)

The LIPP technique of Sessler et. al. (1977) is applied to FEP, which is charged withelectron beams, energy ranging from 10 to 50 keV, as permanent polarization does notoccur. Surface charges are observed and very little trapping occurs within the samplevolume, in agreement with the results of laser induced acoustic pulse method. DasGupta, et al'38 have measured the spatial distribution of charges injected bymonoenergetic electrons by both LIPP and LIMM techniques and good agreement isobtained between the two methods (Fig. 11.20).

400

•ea

TEFLON-FEP:Sample C

25 keV from free surface

-3000.4 0.6

Thickness

Fig. 11.20 LIPP and LIMM techniques applied to 25 j-im FEP with 40 keV electrons from non-metallized side (Das Gupta, et al. 1996, with permission of Inst. Phys., England).

Fig. 11.21 shows the evolution of charge characteristic in FEP charged by electron beamat 120° C. As the annealing duration is increased the charge peak broadens with thecharge depth increasing from about 10 um with no annealing, to about 22 jam withannealing at 120°C. This broadening is caused by charge release at the higher

temperature, charge drift in the self-field extending towards the rear electrode and fast^22 -3retrapping. The calculated available trap density is 2.5 x 10 m" but the highest filled-

trap density in electron beam experiments is 6 x 1021m-3(Sessler, 1977).

In a recent study Bloss, et al.39 have studied electron beam irradiated FEP by using boththe thermal pulse (TP) and LIPP method. The TP method has high near-surfaceresolution, better than 100 nm. The Lipp method has nearly constant resolution withdepth. The electron beam deposits a negative charge and in addition, a negative chargelayer was formed close to the electrode-polymer interface if the electron beam enteredthe dielectric through the interface. This effect is attributed to the fact that the metalelectrode scatters the electron beam, producing secondary electrons. The secondaryelectrons have much less energy than the primary ones and do not penetrate deep in tothe volume. Since there is no scattering at the unmetallized surface, there are nosecondary electrons and only the primary electrons enter the sample.

Teflon charged with 30 keV e-beam

annealing at 120%

rear •(•eirod*

Depth ((im)

Fig. 11.21 Evolution of charge distribution in 30 keV electron-beam charged Teflon FEP withannealing time at 120°C, as obtained by LIPP method, (Sesslerl997, © IEEE).

C. POLY(VINYLIDENEFLUORIDE) PVDF

The LIPP technique of Sessler, et al. (1986) has shown that the piezoelectric materialdoes not form permanent polarization till a threshold electrical field of 100 MV/m isattained. The permanent component of the polarization increases more thanproportionally to the voltage, which is characteristic of ferroelectric material. The

permanent polarization is reasonably uniform in the volume, which is typical for highfield room temperature poling of PVDF. The same result has also been obtained by thethermal pulse method of De Reggi (1984). The polarization is due to combined effects ofinstantaneous polarization, electrode charges and space charges accumulated near theelectrodes.

D. POLY(TETRAFLUOROETHYLENE)

Corona charged PTFE shows that the trapped charge does not spread as measured by thethermal pulse method. However, PPS measurements of positively and negatively coronacharged laminates of the dielectric show that there is some minor spreading towards theelectrodes. At high humidity the centroid of the charge has even been observed beneaththe sample surface. Positive and negative corona charging at temperatures of 260°Cshows a larger and definite bulk charge which is non-uniformly distributed.

11.9 CLOSING REMARKS

As discussed above, a number of methods have been developed for the measurement ofspace charge in both thin and relatively thick samples (Table 11.3). The method ofanalyses of the signals have also increased the accuracy of determination of the chargedistribution and charge depth. The thermal methods require a deconvolution technique toderive the spatial distribution of charges, p(x), from the measured current as a function oftime, I(t). The deconvolution may be achieved by the Fourier coefficients of p(x). Theaccuracy of the current measurement limits the number of coefficients to -10, if thesample is pulsed from both sides (Sessler, et al., 1986).

Table 11.3Selected Space Charge Measurement in Polymers

The number within square brackets refers to references at the end of the section.Method

Thermal Pulse Method

DeReggi's Method

LIMM

Pressure Pulse Method

PolymerPolyethylene

Fluoroethylenepropylene (FEP)

PVDF

PolyethyleneFluoroethylenepropylene (FEP)

PVDF

Poly(ethylene)

PET

Laser Induced Pressure Pulse Method (LIPP) Fluoroethylenepropylene

Thermoelastic Stress WavesPressure Wave Propagation (PWP) MethodNonstructured Acoustic Probe method

Mechanically generated acoustic ProbeMethod

PVDFPolyimide (Kapton)PET (Mylar)Cross linked polyethylene(XLPE)

Polyethylene

PETFluoroethylenepropylenePMMA

PMMA

Polyethylene

ReferenceSuzuoki et. al.,(1985),|40]

Collins (1980),Bloss et. al.(2000)DeReggi et. al.(1982,1984)[41]

Das Gupta et.al. (1996)Lang and DasGupta (1981)Laurenceau(1977)Anderson andKurtz (1984).Alquie et. al.(1981),Lewiner(1986), DasGupta et. al.(1996)Sessler(1997)Sessler(1997)Sessler(1997)Bambery andFleming(1998)Lewiner(1986),[42]Sessler (1997)

Migliori andThompson(1980)Rozno andGromov(1986)Rozno andGromov(1986)

TableMethod

Piezoelectric Pulse Step (PPS)

Pulsed Electro-acoustic Stress Method

Electron beam sweeping

Kerr Effect

Field Probe

11.3 ContinuedPolymerFluoroethylenepropylene

Mylar

P(VDF-TFE)PE, PET, PS, PVDF, XLPE,

LDPE

PMMAFEP

PMMA

LDPE

ReferenceGerhard-Multhauptal. (1983)Gerhard-Multhauptal. (1983)[43]

(Takada et1983), l44],Tanaka et.(1995)[46]

Sessler et.(1977)Zahn et.(1987)Khalil et.(1988)

et.

et.

al.[45]

al.

al.

al.

al

The thermal methods have the advantage of a high depth resolution for thickness lessthan ~ 100|um. The acoustic methods have the advantages of a good resolutionthroughout the bulk (~l-2 um). The Thermal Pulse method, LIMM, LIPP and PEA arebeing increasingly used in preference to other methods. It is now possible to measure thespace charge by more than one technique and these complementary measurements havebeen carried out in FEP, using the LIMM and LIPP techniques (Das Gupta et. al., 1996),and LIPP and TP methods (Bloss, et al. 2000). Such techniques help to isolateexperimental artifacts from the characteristics of the dielectric under study.

Damamme, et al.47 have discussed the points to which attention should be paid incalibrating the experimental setup. Calibration generally falls into two broad categories:one, the parameters that are associated with the charging method, charge, potential,temperature, energy of injected electrons and their total charge, etc. The latter may bemeasured to an accuracy of ± 1 pc. The charge response resolution is ~ 2 f C but it maybe particularly difficult to achieve this accuracy in case of short laser pulses. The secondis connected with the measurement technique used. The analyses of measurementsrequire several physical properties of the polymer, such as the speed of sound, thethermal diffusivity, the permittivity, the high frequency dielectric constant, etc. Theseproperties should be measured in situ, preferably, to remove ambiguity in their values.Since a host of experimental techniques are required it may not always be possible toaccomplish this. In such situations the properties obtained for the same sample withparticular reference to humidity, previous history, etc. should be used.

The role of the space charge in the performance characteristics of dielectrics has beenA ft

discussed by Bartnikas in both communication and power application areas. Futurework should be concentrated on establishing a clear connection between chargingcharacteristic and operational performance in the technological applications.

11. 10 REFERENCES

1 J. Lewiner, IEEE Trans, on El, 12 (1986) 351.2 G. Blaise and W. J. Sarjeant, "IEEE Trans, on Diel. EL, 5 (1998) 779.3 H. Frolich, "Introduction to the theory of the polaron", in "Polarons and Excitons", Eds

: C. G. Kwyer and G. D.Whitefield,: Oliver & Boyd, London, 1963.4 B. Gross, IEEE Trans, on Nucl. Sci., NS-25 (1978) 1048.5 B. Gross, J. Dow, S. V. Nablo, J. Appl. Phys., 44 (1973) 2459.6 B. Gross, G. M. Sessler, J. E. West, Appl. Phys. Lett., 22 (1973) 315.7 S. Osaki, S. Uemura, Y. Ishida, J. Poly. Sci. A-2, 9 (1971) 585.8 N. H. Ahmed and N. N. Srinivas , IEEE Trans. Diel. EL, 4 (1997) 644.9R. E. Collins, J. Appl. Phys., 51 (1980) 2973.10 H. Von Seggern, Appl. Phys. Lett., 33 (1978) 134.! ' A. S. DeReggi, C. M. Guttmann, F. I. Mopsik, G. T. Davis and M. G. Broadhurst,Phys. Rev. Lett, 40 (1978) 413.

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23 G. M. Sessler, IEEE Trans. Diel. Elec. Insu. 4 (1997) 614.24 (a) T. Takada and T. Sakai, IEEE Trans. Elec. Insu., EI-18, (1983) 619.

(b) T. Takada, IEEE Trans. Diel. Elec. Insul., 6 (1999) 519.25 T. Takada, T. Maeno and Kushibe, IEEE Trans. Elec. Insul., 22 (1987) 497.26 G. M. Sessler, J. E. West, D. A. Berkeley and G. Morgenstern, Phys. Rev. Lett., 38

(1977)368.27 V. I. Arkhipov, A. I. Rudenko and G. M. Sessler, J. Phys. D: Appl. Phys., 24 (1991)

731.

28 M. Zahn, M. Hikita, K. A. Wright, C. M. Cooke and J. Brennan, IEEE Trans. Elec.Insu.,22(1987)181.

29 S. J. Sheng and D. M. Hanson, J. Appl. Phys., 45 (1974) 4954.30 A. D. Tavares, J. Chem. Phys., 59 (1973) 2154.31 Z. G. Song, H. Gong and C. K. Ong, J. Appl. Phys., 30 (1997) 1561.32 M. Falck, G. Dreyfus, and J. Lewiner, Phys. Rev., 25 (1982) 550.33 T. Mizutani, H. Semi and K. Kaneko, IEEE Trans. Diel. Elec. Insul., 7 (2000) 503.34 M. S. Khalil, B. S. Hansen, IEEE Trans. Elec. Insu., 23 (1988) 441.35 Y. Tanaka, Y. Li, T. Takada and M. Ikeda, J. Phys. D: Appl. Phys., 28 (1995).36 G. Chen, H. M. Banford, A. E. Davies, IEEE Trans. Diel. Elec. Insul., 5 (1998) 51.37 K. R. Bambery and R. J. Fleming, IEEE Trans. Diel. Elec. Insul., 5 (1998) 103.38 D. K. Das Gupta, J. S. Hornsby, G. M. Yang and G. M. Sessler, J. Phys. D: Appl.Phys., 29 (1996) 3113.

39 P. Bloss, A. S. DeReggi, G. M. Yand, G. M. Sessler and H. Schafer, J. Phys. D: Appl.Phys., 33 (2000) 430.

40 A. Cherfi, M. Abou Dakka, A. Toureille, IEEE Trans. Elec. Insu. 27 (1992) 1152.41 M. Wiibbenhorst, J. Homsby, M. Stachen, D. K. Das Gupta, A. Bulinski, S. Bamji,

IEEE Trans. Diel. Elec. Insul., 5 (1998) 9.42 T. Mizutani, IEEE Trans. Diel. Elec. Insul., 1 (1994) 923.43 S. N. Fedonov, A. E. Sergeeva, G. Eberle and W. Eisenmenger, J. Phys. D: Appl.

Phys., 29 (1996)3122.44 Y. Li, M. Yasuda, T. Takada, IEEE Trans. Diel. Elec. Insul., 1 (1994) 188.45 X. Wang, N. Yoshimura, Y. Tanaka, K. Murata and T. Takada, J. Phys D: Appl. Phys.,

31(1998)2057.46 T. Maeno, T. Futami, H. Kushibe, T. Takada and C. M. Cooke and J. Brennan, IEEE

Trans. Elec. Insul., 23(1988)433.47 G. Damamme, C. Le Gressus and A. S. De Reggi, IEEE Trans. Diel. Elec. Insu., 4

(1997)558.48 R. Bartnikas, Trans. Diel. Elec. Insul. 4, (1997) 544.

APPENDIX 1TRADE NAMES OF POLYMERS

Chemical namePoly(tetrafluoroethylene)

Poly(fluoroethylene-propylene)

Poly(3-perfluoropropoxy-perfluorohexamethylene)Poly(ethyleneterephthalate) (PET)Aromatic polyamide

Polyimide (PI)

Polyetherimide (PEI) Ultem

Trade nameTeflon PTFEHalonfluonTeflon FEP

Formula

(CF2-CF2), (C3F6)y

Teflon PFA (C2F4), (C2F3OX C3F4

Mylar

Remarksrods, sheets,Film,extrusionFilm,molding andextrusionFilm,extrusion

(CO2 C6H6 CO2 C2H4X Film, tubing

Nomex,Kevlar (NH C6H6 NH CO C6H6 Paper,CO)* laminates

Kapton [(C6H6)3 O (C2NO2)2L Film,Upilex enamel,Pyre-ML resin

[(C2 N02)2 (C6H6)5 O Film,C3H6]X

Poly(methylmemacrylate) (PMMA)

PerspexAcrylicLuciteAcrylitePlexiglas

(C5 H8 O,),

moldingresinmoldingresin, sheets

557

Chemical name Trade name Formulaethylene Tefzeltetrafluoroethylene (ETF) HostaflonPolyetherketone PEEK

Polyvinylidene fluoride(PVDF)Polychlorotrifluoro-ethylene(PCTFE)Polystyrene-butadiene

Polycarbonate (PC)

PolybutyleneTerephthalate (PBT) orPolytetramethyleneterephthalate (PTMT)Nylon

Polysulfone

Phenol formaldehyde

Polyester-imide (PEI)

(C4H4F4)X

[(C6H6)3 C

(C2 H2 N)n

(C2 F3 Cl)n

Kynar

Kel-F

K-resin

Lexan, Calibre, H [(C6H6)2C4H6O3]n OHMakrolonUltradur [(C6H6) C6 O4 H8)]n

ValoxCelanex

Capron, Rilsan, [Ci2H22O2N2]n

Ultramid,Celanese, Zyteland VydyneUdel, [(C6H6)4 C3H6 O S02]n

Ultrason SBakelite [(C6H6)4 C3 O3 H8]n

TeramidIsomid

[(C6H6)4C18H8018N8]

RemarksFilm,extrusionmoldingresinFilm,

Film,extrusion

moldingresinMoldingcompoundMoldingResin

MoldingResin,extrusion,enamelMoldingresinResin,Laminateenamel

APPENDIX 2General Classification of Polymer Dielectrics

ThermoplasticRESINS FilmsAcetal Cellulose

Acetate(CA)

Acrylic

Amide (Nylon)

PolyetherimidePolyarylate

PolybutyleneTerephthalatePolycarbonate ETFE

Polyetheretherketone ECTFE

Polyethylene ether PVDFPolyphenylene PCTFEPolypropylene PC

Polystyrene PETStyrene-Butadiene PE

Elastomers

Natural rubber(polyisoprene)

Butyl rubber

Cellulosetriacetate

PTFEPFAFEP

StyreneButadiene

RubberNeoprene

EPDMEPR

chlorosulfonatedpolyethylene

(CSM)Chlorinated

polyethylene(CP)

Thermosetting Ceramic/glass

Alkyds orthermosetting

polyesterAllyls

Aminos

EpoxyPhenolics

Alumina

Aluminumnitride

Aluminumsilicate

BerylliaBoron nitride

Cordierite

Diamond

Magnesia

PorcelainSapphire

SilicaSteatiteZircon

559

Thermoplastic Elastomers Thermosetting Ceramic/glass ThermoplasticStyrene acrylonitrile PI

Acrylonitride PPAbutadiene styrene

Polysulfone PPPolyether sulfone P&

PVCPS

PESPEI

APPENDIX 3Selected Properties of Insulating Materials

OoofiIo

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APPENDIX 4Relative Ranking of Thermoplastic Polymers

1= Most desirable, 18= Least desirable

567

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m

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<N=O^

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in0-

oT—

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1— 1

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r^^00CD

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J3O03fl(U

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wtt-loyoo

APPENDIX 5SELECTED PROPERTIES OF POLYMER INSULATING MATERIALS

POLYMER

Acetal homo-polymer

Acetal copolymer

AcrylicAcrylonitrile butadiene -styreneEpoxy, Bisphenol A

Modified polyphenylene -oxide

Nylon 6/6

Nylon II1

Polyamide-imide

Polybutylene terephthalate

Polycarbonate

Polyetherimide

PolyethersulfonePolyethylene, LD

RecommendedTemp(°C)90

105

95

95

105

130

65

260

150

115

170

180

80

Volumeresistivity

(Qm)IxlO13

IxlO14

IxlO16

2xl014

IxlO14

IxlO1 3

IxlO 1 4

8xl014

4xl014

8xl014

7xl015

>lx!015

IxlO1 4

Arcresistance

(s)220

240 (burns)

no tracking

100

1003

75

130

123

230

184

120

128

70

1602

569

Polyethylene, HDPolyimide, unreinforced

Polyphenylene sulfide

Polypropylene

Polystyrene

PolysulfonePoly(tetrafluoroethylene)

Poly(trifluorochloroethylene)

PVC

Poly(vinylidene fluoride)

Styrene acrylonitrile

Styrene butadiene

90240

205

105

70

150

260

200

80

135

80

65

IxlO1 4

IxlO16

IxlO1 4

>lx!014

IxlO1 4

5xl014

>lx!016

>lx!016

IxlO1 2

2xl012

>lx!014

IxlO1 4

235

152-2303

34

150

65

122

>2003

>3603

60-802

50-603

115

50

1. W. T. Shugg, Handbook of Electrical and Electronic Insulating Materials, IEEE, 19952. J. Brandrup and E. H. Immergut, Eds., Polymer Handbook, Wiley-Interscience, NewYork (1977).3. Vishn Shah, Handbook of Plastics Testing Technology, Wiley-Interscience, New York(1984).

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Space Charge in Solid Dielectrics