Brazilian Journal of Physics - Progress in High-Energy Electron and X-irradiation of Insulating Dielectrics

8/6/2019 Brazilian Journal of Physics - Progress in High-Energy Electron and X-irradiation of Insulating Dielectrics

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J p = J fas + J conduction + J diffusion . (1)

produced by the trappe d charges in the insulator altered the mo tion of lo w-energy electrons in thevacuum.

A search in the library quickly found the 1957 paper by Gross on the charging of borosilicate glass[3]. There he correctly laid out the basic ideas that are used to this day. Two-MeV electrons penetrateup to 0.4 cm into the glas s. The distribution of pe netrating electron-stopping d epths comb ined withthe divergence of thermalized carrier conduction currents were correctly identified as the sources of space charge and high electric fields in the ins ulator. The book s by Bube a nd by Ros e providedfurther insight to the electronic conduction process which Gross expanded upon [4] while analyzingthe e xact quantity and spatial distribution o f charges stoppe d in the insulator.

Large Lichtenberg discharge figures were produced in the glass, as well as in the acrylic sheet, by theMeV electrons in Gross' studies. T he formation of the d ischarge figure is accompanied by a brief pulse of current.[5] The time integral of the current pulse was found to be a significant fraction of thecharge that had be en stop ped in the p reviously irradiated ins ulator. Since that time , every highene rgy radiation labo ratory feels com pelled to m ake som e of thes e fa scinating Lichtenberg figures.

X-rays and Ga mm a rays are a bsorbed in m aterial mostly by transfe rring ene rgy and m om entum tothe electrons. A high-energy electron current is thereby produced that may also generate Lichtenbergdischarge figures. Gross gen eralized this pheno me na to develop the d ielectric Compton Diode whichgenerates a current proportional to the photon flux.[6,7] Vacuum diodes were in use [8], but currentsof low-energy electrons in the vacuum complicated the results. The dielectric had the a dvantage o f suppressing currents of low-energy electrons while the high-energy electrons would traverse oneelectron range in the dielectric.

II Improvements on the box model

The ideas in the early work of Gross were general. But the first experiments were necessarily relatedto theoretical models that were analytically tractable. The box model was a simplification that provedto be very profitable, especially with monoenergetic electron beams which partially penetrated theinsulator [9,10]. In the box m odel it is assu me d either that all electrons p ene trate to the sa mestopping dep th, or that an average stopping de pth is sufficient to mode l the problem. In the d epthpene trated b y electrons, conduction is dom inated by radiation-induced mo bile ele ctron-hole pa irs. Inthe de pth beyond electron pe netration, conduction is do mina ted by norma l dark conductivity and bycharge injected from the irradiated region. T he b ox m ode l and related e xpe rime nts showed that thedom inant processe s involved the stopping of the prima ry electrons, the ge neration of s tatic electricfield by the stoppe d e lectrons, the ge neration o f electron-hole pairs in the conduction-valence bands ,and the development of conduction currents proportional to the product of local electric field andelectron-hole concentrations.

Once the box m ode l had proven the ba sic concepts, it becam e pos sible to provide com putersimula tion for the m ore gene ral problem . Gross p roposed a se mi-ana lytic mo del which requiredcomputer solution of integrals [11]. Indep ende ntly, and nea rly simultaneo usly, several groupsproduced straightforward computer simulations of the one - dime nsional problem [12-16]. Thissimulation technique, developed by many, will henceforward be called NUMIT (for numerical iteration).In the NUMIT simulation one can calculate the full time- a nd spa ce-com plexity of stopped charge,field, and conduction currents. The sim ulation allows o ne to rapidly change ma ny parameters forcomparison with expe rimen tal results. For exam ple, one ma y include the depe ndence of conductivityon e lectric field, or on a ccumu lated radiation dose , both of which had bee n m entioned by Gross in hisea rly work. In ge neral, NUMIT a llows fo r easy inclusion of the depe ndence of a ny parame ter, such asconduction current, on any of the other parameters, such as electric field and irradiation dose. NUMITallows for time and spatial de pende nt injection, diffusion, e ffects of trapping, spatially and timevarying trap concentrations, and can include the effe cts of s teep doping p rofiles to s imulatese m iconductor junction be havior.

The problem can be described mathematically in a simple fashion. Since mathematical detail is notnecessa ry in this review, the one-dim ensiona l mode l is simples t to envision. Rad iation generates acurrent which subsequently stops in, and charges, a dielectric. Electric fields develop conductioncurrents, a nd the conduction charges are provided by any so urce including pho togeneration of electron-hole pairs, thermal generation, field-induced tunneling from traps, electrode injection, etc.The sepa ration be twee n high- e nergy particles a nd conduction p rocesses in the thick m aterialsconsidered here can be arbitrary. Usually particles above 100 eV are considered primary particles, andall below 100 eV are tracked a s e ither stopped or as conduction pa rticles. The complex rea sons forthis are left unsaid. Th e ge neral equa tions are thus: The charged particle current is the s um of threeindependent terms,


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The differential eq uation for space charge dens ity is

The electric field is found from solution of

subject to the bou ndary conditions a nd a dded to any ex ternally applied e lectric field:

where a and b are the po sitions of the electrode-insula tor interfaces, a nd V app is the applied voltage.As in Gross' box mo del, this system is quasistatic and n eglects the (sm all) effects of ma gnetic field.

III Progress at high electron energies above 10 keV

1. A nalytic and Monte Carlo Det ermination of Electron Stopping Depth Distribution.

Stopping of e lectrons is often the primary process for charging insulators or insulated ma terial.Calculation o f the distribution of stopping de pths of e lectrons is ess ential for mode ling the chargingprocess. Gross provided a n e arly me asurem ent of depth distribution for dielectrics [17], and s uchproblems were also addressed by radiation transport work in the nuclear industry [18]. Gross et alprovided further measurements for direct application in the electret field with electrons from 10 to 50keV [19].

Tabata, Andreo and Ito [20] have use d the widely available Monte Ca rlo codes [21] from the nuclearradiation field to tabulate stopping de pth for norma l incidence electrons a t many e nergies from 100keV to 100 MeV in nea rly any material. A numb er of ex periments have confirme d the Monte C arloelectron transport codes for specific cases. An analytic function is available [22] which fits thetabulation [21] within a few percent for both current transmission and stopping depth distribution atall energies from 100 keV to 100 MeV. The analytic function interpolates between the electronene rgies a nd m aterial atomic numbers tabulated by Tabata and Ito, and thereby covers a b roadrange of energies and atomic numbers.

2. Eff ect of Space-Charge Fields on the Transport of Fast Electrons.

In material, the slowing of fast electrons acts as if there were an electric field continuouslydecelerating the electron. I n so lids, the s lowing is produced by an effective de celerating field of approxima tely 2 MV/cm for electrons of e nergies from 300 k eV to 3 MeV. Yet it is pos sible to sus tainspace charge fields of 2 MV/cm for minutes to hours without breakdown of the solid dielectric. Itbecome s o bvious that the largest spa ce-charge field will at least slightly alter the m otion of thehigh-energy electrons while inside the dielectric. This had been cleverly analyzed for specific cases[23,24], but full inclusion of the details of the three-dim ensiona l mo tion o f the ele ctrons fo r anyma terial and geom etry was beyond a nalytic solution. In clusion of the effe cts o f electric field in MonteCarlo transpo rt simula tion provides the ge neral solution of the problem .

Modeling of irradiations with electrons below 50 keV can usually ignore this effect. At 10 keV, theelectron stopping field is at least 20 MV/cm in typical solids, well above the sustainable static electricfield. Nevertheless , the calculational me thod was develope d a nd tried at 20 keV where the electronmo tion could be described classically [25]. The calculations found no e ffect, less than 1% chang e indepth of pe netration in a thick sla b. For the purpose o f ma thema tical m odeling, the de nsity of thedielectric can be made arbitrarily small so that the stopping power vanishes while the space-chargefield rema ins large. But e xpe rimen tal verification be low 50 ke V awaits the developm ent of low-densitysolid insulators (which see ms impos sible). With such insulators, one might m eas ure the space chargeand internal electric field distributions by any of the methods reviewed by R. Gerhard-Multhaupt [26].

Hikita and Zahn provided the impetus to extend the calculation of fast electron trajectories withelectric fields to relativistic electron velocities. T hey m ea sured the time and depth de pende ntevolution of space-charge electric fields in thick polycarbonate with partially penetrating 2-MeVelectrons [27]. In these me asurem ents, the zero-field plane was fou nd to m ove towards theirradia ted surface a s time p rogresse d. However, if the e lectric field do es n ot act on the fas t electrontrajectories, then the zero-field plane should move away from the irradiated surface [28]. By


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combining the field-depe ndent trajectories of the fast e lectrons with the NUMIT s imulation, a nd byincluding high-field conduction e ffects, the exp eriments o f Hikita a nd Zahn were correctly mo deled[28]. Gross outlined the u tility of the concept of the zero-field plane [29] which a ssists one tointerpret exp erimental results.

Irradiation of plexiglas s an d polycarbonate produces da rkened regions where the fa st electrons h avepass ed [2]. Inspe ction of this discolored layer indicates that it is su bstantially thinner than thema ximu m p ene tration of fas t electrons in the a bsence of s pace-charge fields . Here was directevidence that internal fields were foreshortening the range, but it was not studied in the literature.[Soviet Union publications in the 1970s and 80s hinted that such work was progressing, but disclosurewas lim ited lea ving the ex act res ults unclea r.] Figure 1 , taken from [28], indicates how theex periments of Hikita and Zahn a llowed the mo del to be developed to include correct chargepene tration, dose pene tration, and conduction p hysics. Experimental m ea sureme nt of e lectric field inhigh-energy irradiations is a key ingredient to further progress.

Figure 1. Comparison of Field Dependent Monte Carlo (M.C.) Simulation with Earlier (Old)

Field- Independent Simulation. The high-energy electron current penetration after tenseconds of irradia tion: without field de pe nde nce is given b y (a) o r (b), and with fieldde pen den ce is given by (c). The total current at ten se conds including conductionprocess es is given by: (d) with field-inde pen den t fast electron transp ort, and (e ) field-de pen den t fast electron transport. At ten se conds the e lectric field s treng th was of o rderMV/cm, and other details are in [28].

3. Secondary-Electron Yield from D ielectrics as a F unction of Electric Field.

Simulation, such as NUMIT, can be u sed to mod el m any details within an ex periment, includingsecondary electron em ission. Con sider a diele ctric slab with thin me tal foils painted on both sides of the dielectric. Assume that NUMIT correctly determines the currents of high-energy electrons,radiation-induced conduction currents, space-charge distribution and electric fields in the insulatorunder bom bardme nt by high-ene rgy electrons [27,28]. One can perform the ex periment and thesimula tion b y choos ing the incident electron e nergy such that a sm all fraction o f the e lectrons pas scomp letely throug h the insu lator. The current of throug h-pe ne trating e lectrons , as well as the ir dos ein the following m aterial, can be me asured as a function of time while ele ctric fields build up in theinsulator. Usua lly, the fraction pene trating an d their dose will decreas e as time p rogresses and thedielectric accumula tes sp ace charge [27,28]. NUMIT see ms to correctly simulate all of the de tails inthis irradiation, including field dependent conductivity in the insulator near the electrodes.

Consider the arrangement of Fig. 2 where the first irradiated metal foil is separated from theinsulator by a vacuum space of any chosen distance, say 1 cm. In the planar one- dimensionalgeometry, the act of separating the foil causes the following changes (all of which are included in aNUMIT s imulation):

1) Seconda ry ele ctrons , which are cond uction b and ele ctrons e scaping the ins ulator, will accele rateaway from the nega tively charged ins ulator and e nter the first me tal foil. 2) The high-energy


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Figure 3. Simulation o f the Effects o f Seconda ry-Electron Yield, SeY, on Field Build-up a ndDose Penetration.

4. Relationship Between Pulsing and the Space-charge Electric Fields.

One can monitor currents between the electrodes for the occurrence of pulsed discharges. The NUMITsimula tion o f the conditions of the irradiation will determine the electric field a t the time of the pulseddischarges. T his has bee n reviewed [32], and two ex am ples a re indicated in Figs. 4 and 5 withelectrodes attached to both s urfaces of the planar insula tors u nder partially pene trating ele ctron

bea ms. I n clear sheet stock without obvious flaws the p ulses are infreque nt. In fiberglass-filledma terial the na rrow glass fibers appa rently induce freque nt pulses. I n a ll ma terials tested, thepulsing did not occur until the field strength was above 100 kV/cm.

Figure 4. Simulation and Experiment in Clear Polycarbonate. Simulation provides the seriesof d ots. Experime nt provide s the continuous chart recorder trace o f the current to groundfrom the rear electrode . Vertical spikes are caused by sm all partial discharges in theinsulator. The ele ctric field rea ches pulsing m agnitude at the front electrode at 400seconds, and at the rear electrode at about 900 seconds.

Figure 5. Simu lation and Exp erimen t in Fiber-filled Material. The sim ulation (dots) followsthe ex perime nt, but the p ulsing freque ntly drives the chart recorder off scale. The secondtrace is the same experiment at later times, and indicates that pulsing is less frequentdespite the fact that fields have increased. Pulsing continued several days after theele ctron bea m stoppe d. The first pulse occured when the e lectric field was 110

7V/m.


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Inside the so lid ma terial, each pulse reduces only a tiny portion of the ele ctric field in the insulator.Inside fiberglass-filled insulators, pulse s will continue fo r several da ys after the radiation is turnedoff. Although discharges do not alter much of the electric field inside the dielectric, when a vacuumspace ex ists betwee n the first electrode and the insulator surface, the current pulses across thevacuum are very large, and the electric field in the entire vacuum space is substantially reduced by asingle pulse [31,33-35]. The fact that the vacuum fields are largely reduced by a single pulse ddischarge process [35] is the origin of the pulse scaling laws [33].

5. Eff ect of F ast Electrons on Spacecraft Insulation

The flux of s pace radiation is dom inated by fast e lectrons. Typically, one to two m m o f alum inumshielding is provided to protect the electronics by reducing the intensity of the radiation. This has theeffect of stopping electrons below perhaps 700 ke V, but allows the less p opulous electrons above 1MeV to penetrate into the electronic circuits. The total dose to electronic devices is reduced to anacceptable level, but the insulating m aterials e ventually develop high spa ce-charge electric fields asstopped electrons accumu late.

Analogous to the Lichtenberg discharges investigated in g lass a nd plex iglass [1,2], the spa cecraftinsulators produce discharge pulses that can interfere with electronics by producing 100-volt pulses oncircuit-board traces [36]. Pulsing of insulators has been correlated with operational problems onspacecraft [37]. Figure 6 , take n from [38], indicates the rate at which se veral insu lating ma terialspulsed during 14 mo nths in Earth orbit. The pulse rate is proportional to a power of the high-ene rgyelectron flux [39]. Insulators with fiberglass filler pulsed [38] most frequently, probably due to theelectric field enha nceme nt at the e nds o f the fiberglass. TFE base d insulators pulsed m ost frequently

during the first m onths in orbit becaus e accumu lated radiation on TFE increases the da rk conductivitythereby reducing the electric field in later months [40]. FR4 fiberglass-filled circuit-board pulsed mostfreque ntly after several m onths, probably because outgassing for several m onths reduced the da rkconductivity. Pure sapphire never pulsed, perhaps because it has a large carrier schubweg, or highradiation-induced conductivity. Clear FEP Teflon pulsed occasionally.

Figure 6. Pulse Rate Summed Over All Insulators Monitored in Space for 14 MonthsCo mp ared to Fast Electron Flux.

It is tempting to predict that a pulse will occur when the voltage, or the electric field, achieves aparticular level during the space radiation. But this sim ple m odel, a lthough ap pea ling, does not work.Ins tead , as the ele ctric field grows, so me pulsin g occurs while the ele ctric field continues to grow.Eventually the electric field will reach a maximum, and the rate of pulsing is likely to decline while themaximum field is maintained [32]. In some samples, the pulse rate declines to nearly zero. Iremem ber discussing this with B. Gross 15 years ago when h e related it to the phe nom ena of se lf hea ling in high voltage capacitors. The space test results [38] are very similar to the ground testresults [32], and a re probab ly related to Gross idea a bout self he aling.

The pulsing data from a space e xpe rimen t can be used to help spa cecraft designe rs predict the rateof pu lsing that might occur at insulators inside a spacecraft [39]. There is little other data to h elp on epredict the rate of pulsing. The me asured pu lse rate was found to relate to a power of thehigh-ene rgy electron flux . Pulse mo nitors a re rarely flown on spacecraft, and the funda me ntalmeasurement of pulse rate is rarely available. When spacecraft have problems, and the spaceelectron radiation is simu ltaneously enha nced, it is a ppea ling to blame the radiation-induced ESD


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pulsing for causing the problems. Ye t proof o f pulsing is a lmost a lways lacking. On one spacecraft asignificant pe rcentage o f ap proximately 400 problems in several instrume nts occurred simultane ously(time reso lution in the spa cecraft data stream was 32 se conds) with a large ESD pulse obs erved by apulse detector inside a different instrument [37]. Thus, it was proven that ESD pulses were the causeof num erous problems on this spacecraft. Usually, lacking actual pulse me asurem ent, one o nly infers(not proves) that ESD pulses cause d problem s if the problems occurred when the e xpos ure tohigh-ene rgy electrons is e levated.

6. Charging of Spacecraft Relative to P lasma Potential

At the surface of the spacecraft, the space radiations can charge the entire spacecraft relative to the

am bient plasm a p otential. Spacecraft surface potentials vary from a fe w volts po sitive to 20 k Vnega tive [41,42]. The surface p otential is m ea sured using electron a nd proton spe ctrom eters whichdetect the a cceleration of the normally cold ( 1 eV) plasm a p articles. Secondary electron e mission[43] and p hotoem ission from su rfaces of the spa cecraft usua lly prevent high ne gative charging.Occasionally, spacecraft experience a high flux of electrons above 10 keV which overwhelms thesecondary electron and photoelectron currents and negatively charges the spacecraft [41]. Differentpotentials between isolated po rtions of the spacecraft can e xceed 2 kV [44] a nd produce ele ctrostaticdischarge pulses that interfere with spacecraft circuits [45]. A spacecraft design standard has been inuse for a decade to help de signers prevent problem s from the charging of o uter spacecraft surfaces[46].

7. Discharge Pulse Scaling Laws, and Pulse Shapes.

An extens ive e arly set of e xpe rime ntal data were sum ma rized as p ulse s caling laws [33]. This workwas mostly performed with electron beams at ten or twenty keV, although some work with higher

ene rgy electrons from a radioa ctive source found similar results. Subseque ntly, others foun d sim ilarresults when their tests were also performed in small conductive vacuum chambers. Still others founddifferent pulse shapes when testing in much larger chambers, or with differently structured samples.Much of the pulsing da ta has bee n recently reviewed, a nd it is proposed that nearly all pulse shap escan be related to a s ingle process [35,34].

A pulse begins with a sm all discharge internal to the insulator similar to the Lichtenberg treepheno me na. For low-energy electron bea ms , it may be a s urface Lichtenberg tree. Or, it could b eginas the ex plosion o f a dielectric needle at its surface s tresse d by high e lectric field. Each of thes epheno me na issue s a b urst of partially ionized gase ous m atter into the vacuum which evolves into agaseous discharge. The gas discharge evolves and compensates the voltages on the surfacesex pose d to the vacuum-ga s discharge m edium . The current which flows in the ga s discharge producethe me asured signa ls that form the s caling laws and the pulse s hape s reported in the literature.

The gas discharge exp ands in the vacuum at thermal gas velocities to ele ctrically short-circuit

electrodes that are biase d by power supplies, s olar cell arrays, or batteries. More than 100 am perescan be conducted with only 100 volts a pplied from ba tteries [34]. The a mo unt of gas evolved, therate at which it expands into vacuum, and the current waveforms have been investigated [34]. Sincethe gas can short electrodes differing by only 100 volts, it will certainly short together spacecraftsurfaces that have voltages differing by a kV or more, and gaps of 20 cm have been spanned [ Fig. 7in 35]. It appe ars that the pulse shap e is partly controlled by the evolution of charge currents in thegaseous discharge.


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Figure 7. Arrangement of Conductors for an Efficient Compton Diode Cell. The dashed lines( ) indicate insulator foils to block low energy electron currents.

8. A pplication to Vacuum Electron Tube Glass Envelope Breakdown

Vacuum e lectron tubes were usua lly contained in a gla ss e nvelope, and discharges of the gla ss werenot reported. Yet high-ene rgy electron be am s on glass quickly produce discharge pulses [3]. Whywas this not see n in vacuum electron tube s?

Almost always, ele ctron tubes were o perated with the cathode nea r ground potential. The glassenvelope rem ained nea r ground po tential and did not ex hibit effects of static charge (unliketelevision picture tubes and computer monitors which are obviously charged and attract dust, etc.).The anod e of the tube was a t high positive voltage. Thus, e lectrons would bom bard the glassenvelope only at thermal ene rgies, no t at high ene rgies. It was unlikely for the gla ss to charge m orethan a few volts.

But high voltage can be a pplied across the glass e nvelope by ope rating the cathode at high neg ativepotential. A metal shield m ight be placed around the o utside of the glas s envelope . Electrons fromthe cathode m ight bomba rd the glass and ultimately apply the full cathode potential across theglass. Vacuum tube glass envelope breakdown has been reported [47].

9. Failure of Insulation with High-Energy Radiation at Moderate Flux.

Irradiation produces enhanced conductivity [1,4] and Lichtenberg discharge trees [3,5] in theinsulators. In most insulators the conductivity current is small, usually no larger than the currentcarried by the radia tion itself. However, the conductivity current in pho toconductors is la rge a nd thiseffect is use d to detect radiation. Usu ally, the Lichtenberg discharge trees do n ot pen etrate theinsulator. The discharge tree weak ens the insulation on ly to the extent that a thin hole drilled in theinsulation wea ken s it. The tree forms instantly in one burst and do es no t seem to produce thetracking phe nom ena that repe ated d ischarges a re k nown to produce in high voltage power supplies.Can the radiation cause ins ulation failure?

Com plicated arrange me nts of ma terial can bring together various effects with disastrous results.Ob viously a photocond uctor, ma de s ufficiently conductive, will overhea t upon ap plication of sufficientex ternal bias. R ecent exp erience in space a nd in ground tests indicates that the radiation-inducedeffe cts can cause ins ulation fa ilure that was no t pred icted. Although n ot a photocon ductor, kap tonslowly pyrolizes under radiation, including uv, to become more conductive, especially at elevatedtempe rature in sun light in space. A radiation-induced discharge by fully insulating m aterial caninitiate a current flow in nearby electrodes under battery bias [34] to induce a continuous glow

discharge. The glow discharge can initiate local he ating of ka pton which p yrolizes to becom epermanently conductive. Even if the glow discharge is stopped, the conductive kapton will overheatunder resumed bias to eventually form a carbon electrical short [49]. Spacecraft solar arrays withka pton operating above 50 volts have failed. Rearrange me nt of materials and ele ctrodes can preventsuch problem s [50].

Im me diate failure of the insulation upo n formation of the radiation-induced discharge tree has be enreported [51]. With certain arrange me nts of irradiation a nd a pplied bia s, the radiation-induceddischarge tree can be ma de to propag ate e ntirely through the insulator to form a conducting channe lof ga seou s plasm a be twee n biase d e lectrodes. The short circuit will rem ain a s long a s the po wersupply provides eno ugh en ergy to continue evolution of gas from the electrode s and nea rbyinsulation.

Cosm ic rays impinging thin insulation in m odern m icrocircuits have be en implicated in insulationfailures. Microcircuits are typically operated at ten volts and less. The cosmic ray induces a high levelof conducting e lectron-hole pairs in a subm icron tube s urrounding its track. W hether this tube candevolve into a break down, or simply appe ars as a trans ient space-time sp ike o f conductivity is asubject of controversy. The studies reviewed in this paper are at low levels of ionization, with highvoltage , and cannot contribute to resolution of this problem .

10. Another Compton Diode and Radiation Detector.

High-energy X-rays and gam ma rays pas sing through ma terial develop a forward moving flux of fas telectrons. T he divergence o f this current deposits charge in the ma terial. The total charge d epos itedis therefore proportional to the attenuation of the p hoton current [6,7]. The ba sic Compton Diode asdiscussed by Gross, therefore, produces a current which canno t exceed the initial photo-Com ptonelectron current produced by the photons upon p assa ge through one electron range in the m aterial.

Another configuration o f m aterial produces g reater total current from the sa me photon flux [48]. Thisconfiguration was determined by consideration of the de tails of the photo-e xcited a nd Co mpton-


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generated electron transport processes in multi-layer structures. The electron current produced in lowatom ic num ber ma terial, say Be, greatly exceeds that in high atom ic num ber ma terial, say Pb. This icaused by strong nuclear scattering in the Pb which decreases the forward motion of electrons.Consider a bilayer material, Be-Pb, with photons incident on the Be first. Electrons entering orgene rated in the Be mo stly move fo rward and a re e ither stoppe d in the P b, or scattered b ack fromthe Pb to be stopped in the Be. Thu s Be-Pb a bsorbs ma ny electrons a nd em its few. Next, considerPb-Be. Electrons entering or generated in Pb a re likely to be scattered ba ck out of the P b, andelectrons e ntering or gene rated in the Be are likely to pass through and e xit the Be. Thus P b-Beabso rbs few electrons and em its ma ny. The refore, a n e lectrode consisting o f Be-Pb will accumu lateelectrons from surrounding ma terial, and an electrode consisting of Pb-Be will emit ele ctrons tosurrounding ma terial.

One can alternately stack ma ny planar Be-Pb electrode s with many plana r Pb-Be e lectrodes to form abattery by pass ing gam ma rays through the s tack. The Be-Pb electrodes can be connected toge therto form the nega tive current sou rce, and the Pb-Be can be connected together to form the positivecurrent sou rce. T he total current ge nerated can e xceed that gene rated by the elem entary ComptonDiode, provided a reasona ble choice o f Be an d Pb thickne sses are chosen [48]. Series wiring of thesecells can achieve high voltage, provided that secondary electron current between cells does notcounter the development of high voltage. One can prevent secondary electron currents by interjectingthin insulator materials be tween the e lectrodes. It is certainly unusual to improve a battery bysurrounding its electrodes with insulation! The thin insulators pass the high-energy electron currentswhich provide the ele ctromo tive fo rce for the cell, a nd p revent the lo w-ene rgy electron currents whichtend to d eple te the cell po wer.

It is instructional to think of the cell in this fas hion. The full Com pton current is de veloped in o nly onelectron range o f m aterial. But very little of the gam ma rays are attenuated in one range of m aterial.If the electron current generated in the first electron range is abstracted for use, then nearly thesam e a mou nt of current can be gene rated a nd abs tracted from the second e lectron range of ma terial, and the third, etc. The proper arrange me nt of high- an d lowatom ic number ma terial bestapproaches this idea l cell arrange me nt. Although patented [48], I do no t know if this de vice is beingused anywhere.

IV Future work enabled by past successes

1. A nalysis f or Non-Normal Incidence.

Analytic functions fit to fast electron current penetration for non-normal incidence now seem possible.Although the functions for normal incidence appe ar com plicated, they are actually base d on simpleconcepts [22]. For non-norma l incidence, o ne nee ds to m odify the no rma l incidence concepts with the

following ideas. A small fraction of off-normal electrons will be scattered by the first several atomiclayers ne ar the surface to be esse ntially normal incidence. Thus, the de epe st possible p ene tration wilbe the sam e a s for normal incidence. The fraction backscattered o ut of the surface and the fractionstopped at sha llow depth will increa se mo notonically with a ngle of incidence. The fraction s topped atdee p dep th, and the a verage depth of pene tration will decreas e m onotonically with angle of incidence. The a ctual qua ntitative de pende ncies s hould be determined by app lying the Tige r codes[21] to non -normal incidence perhaps in ten-degree intervals, with sma ller intervals from 70 to 90degrees.

Secondary electron yields are proportional to do se rate in the first 50 angstrom s for m etals, 1microm eter or mo re in insulators. Co nduction a nd e lectron-hole pair production are proportional todose rate a t every point in the insula tor. Thus , the on-g oing m odels by Taba ta and co-workers fordose rate as a function of de pth for non-norma l incidence should be ada pted to our insulators.

2. Total Insulation Failure Under High-Energy Radiation.

The conditions under which insulation fails are not well characterized. How do Lichtenberg trees orother pulsed discharge processe s pa ss e ntirely through the insulator? How much ga s is evolvedduring the pulsed discharges, and how large is the gap that can be spanned as a function of appliedelectrode bias? Ca n discharge trees be prevented? Doe s radiation induce spe cial aging p roblem s?These and other questions are important for the ultimate design of improved insulation.

Ground tests for ESD pulsing caused by 10 to 50 kV electron irradiations have been interpreted toindicate that a discharge-related stream of current ha s p asse d completely through the insulator [52].This interpretation resulted from o bservation of pulses of ne gative charge flowing to ground from therear electrode, simu ltaneous with de cay of the ne gative voltage on the floating front surface of theinsulator. It was s om etimes stated that electrons pu nched through the sam ple from n ear the frontsurface.

In pe rforming sim ilar experiments, Le vy was able to prevent this pola rity of pulse by com pletely


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covering the rear electrode with insulator [34]. I interpret this to mean that negative pulsespropagate to the rear electrode during the ga seo us discharge process b y going around the ed ge of the insulator sam ple. Th e front surface ma y not discharge by punch-through of the insulator. Byblocking the gas from accessing the rear electrode, one blocks the discharge from procee ding toground via the rear electrode. W hen so blocked, the discharge o f the front surface mu st proceed bynegative charges flowing away from the floating surface, and away from the rear electrode, andtowards the electron gun, resulting in positive (image) charge flowing from the rear electrode toground. O ur expe rimen ts [34] proved that, in our tes ts, punch-through did n ot occur.

The gene ral que stion remains: under what conditions can electron irradiation cause breakdo wn of insulators between electrodes, including punch-through breakdown.

3. Field-Dependent Conduction and Emission.

Cond uction and seconda ry emiss ion are strongly depende nt on ele ctric field. This creates a problemin ana lysis a t the surface of insu lators. The conduction current that es capes the surface to becomesecondary electrons generates significant positive charging within a depth of one schubweg below thesurface. Th is requires the NUMIT to mo del conduction with a fine depth resolution ne ar the surface.For thin insulators, less than 100 m icrometers, electron e mission and field-depe ndent m obilitybecome very important parame ters. Th ese facts a re already well kn own in radiation e ffects in silicondioxide pass ivation in m icroelectronics, but NUMIT sim ulation has not bee n pe rformed in theseapplications.

4. Nature of the D ischarge Pulses.

Are the ESD pulses in irradiated insulators similar to the pulses in DC-biased capacitor dielectrics?

Certainly, the electric field plays a dominant role as causitive agent in irradiated insulators. But if wehad applied the sam e e lectric field using b atteries, would the s tatistics of pulsing have rem ained thesame? Or does radiation modulate the processes of pulse formation so that the same E-field inirradiated insula tors m ake s m ore freque nt pulses, or a different ratio of num ber of large pulses tonum ber of sma ll pulses? Until these que stions are answered, one cannot use h igh voltage alone totest for pulsing in irradiated dielectrics, one mus t use radiation in reason able simulation of thein-service radiation.

For exa mple , it is suspe cted that the fiberglass filled ma terials pulsed freque ntly because the fieldsat the tips of the fibers became enha nced and initiated freque nt pulses [53]. Radia tion alters theconductivity of m aterials. If the fiber m aterial becomes mo re conductive while the base ma terialremains constant, the pulse rate will be increas ed. But if the fibe r material rem ains constant a nd thebase ma terial conductivity increa ses, then field e nhancem ent an d pulse rate will both decreas e.

5. Discharge-Pulse Scaling Laws.

The discharge-pulse scaling laws were em pirically determined using electron be am s of 10 kV to 20 kVwhere irradiated surfaces charge to roughly 10 kV. A single pulse discharges a significant portion of the surface voltage over most or all of the s urface area. But inside a me tal box under electronradiations a bove 100 kV a t space intensities, the discharge pulses did not continue scaling to higheramplitude. Instead, the pulse amplitudes on 50 ohm transmission lines did not exceed 100 volts,and the total charge did not a lter the surface voltage mo re than a few hundred volts [55]. At highintens ity 1 MeV irradia tion, however, the pu lses did attain s ignificantly higher am plitude tha n with the20 kV irradiations [31].

It is tempting to presume that low fluxes allow charge to leak away through dark conductivity beforehigh voltage is achieved. But this m ea ns that the electric fields would be sm all and pulsing would beunlikely. Unexpectedly, pulsing is seen in space on samples of 3 mm thickness at apparently lessthan 1 kV surface voltage . Much mo re study is nee ded for application of scaling laws on spacecraft.

6. Contact Eff ects.

High-energy irradiations are often concerned with thick sam ples a nd high space-charge voltage . Theissues of blocking contacts are diminishe d be cause e xtrem e e lectric fields can be gene rated to fo rceconduction across the contact, because radiation-generated carriers cross the contact before beingthermalized, an d be cause the voltage gene rated a t the blocking contact is sm all relative to thevoltage gene rated across the thick ins ulator. Yet the issue s rema in impo rtant, and the work be gun byGross and others for thick insu lators [1,4,9,11,43,54] shou ld be continued.

7. Radiation-Induced Point-Def ect I ntroduction Rate in Insulators.

Defects are introduced into the silicon lattice by electrons above 300 keV. The rate of atomicdisplaceme nt rises rapidly as electron ene rgy is increas ed. At these ene rgies, collision can imp artenou gh ene rgy to cause a silicon a tom to m ove at least one atomic spacing to occupy an interstitialposition. The e nergy of displacem ent is related to the binding ene rgy between neighboring atoms . By


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comparing ex periments using electrons below 100 keV with expe rimen ts using e lectrons above 1MeV, it might be possible to m eas ure the effects of displaced atoms on the conduction process es inhighly insulating dielectrics.

The fast electron ha s the a dvantage o f gene rating electron ho le pa irs in the conduction/valencebands in kno wn qua ntity for fast electron e nergies a bove 100 e V. The electron-hole excitation procesis optical a nd diffe rs o nly in rate, not in kind, a s the prima ry electron b om bardmen t energy varies.Defects introduced by electron irradiation above 1 MeV may act as conduction electron or hole traps treduce the conductivity of the insulator so that it better stores charge. Irradiations below 0.1 MeV willnot directly introduce defects as readily. Comparison between the two irradiations might indicate aneffective rate of trap introduction by MeV electron bombardment. It is conceivable that insulators inextended use in space will be so altered in their charge storage properties, or practical insulators canbe modified to useful advantage. Space measurements have indicated aging of charge storageproperties, but the cause is uncertain [38].

8. Conduction Processes.

Gross and co-workers have provided m any ex am ples o f the effe cts of various conduction processeson the charging of insulators. As new sam ples a re tested, these and o ther effects are sure to beimportant, and for real a pplications o ne m ust carefully conside r the process es of conduction. Thepapers by Gross on radiation-related conductivity provide useful guidelines for interpretation of futureinsulator irradiation e xpe rimen ts. This review em phas ized the high-energy aspe cts, not m echanismsof conductivity. But full understanding of real data requires information on the conductivity processes.In various situations I h ave ha d to a pply conduction m ode ls involving: percolation, electrodeinjection, ho le transport, H, O H a nd O radicals, polarization, mu ltiple trapping levels, diffusion, e tc.However, the level of condu ctivity in thes e ex pe rime nts usu ally is excee dingly low, high field e ffectsoften are important, and the mechanisms invoked to explain the results are easily disputed becausethe ex perimental da ta are sparse while conduction phe nom ena are certainly nume rous. Co nductionpheno me na a re best studied in a large array of literature beyond that reviewed h ere.

V Summary

This paper revews the progress in understanding of electrical current and electrostatic charging, andtheir effects, in insulators irradiated by high energy particles and x-rays. Much of the progress isbased on the works of Professor B. Gross. The wide availability of computers now allows one tosimula te the full transp ort process in order to avoid the limitations of the b ox m odel. The effects of the e lectric field inside the insulator on the high en ergy electrons is now included. T he simulationprovides a method to experimentally determine the dependence of secondary electron emission onelectric field s trength a t the surface o f insulators. The occurrence o f pa rtial discharges h as bee n

correlated with the de velopme nt of internal spacecharge fie lds. The rate o f spontane ous p artialdischarge pulses in spa cecraft insulation ha s be en correlated with the flux o f fas t electrons fromspace. Spacecraft surface voltage also correlates with fast electron flux. Partial discharges at thesurface of irradiated insulators in vacuum are associated with a burst of gas which modifies or controlthe surface discharge process. Perhaps the ga s results from the Lichtenberg figure noted by Gross.The conditions for violation of the integrity of glass envelopes by electron bom bardme nt of highvoltage electron tubes have bee n investigated. Im proved C omp ton Diodes ha ve resulted fromdetailed studies o f the currents in irradiated complex ma terial structures.

The works of Gross ha ve helped to point us towards the future. Th e a nalysis of no rmal-incidenceone-dimensional problems has been successful and encourages one to confidently attempt threedime nsional p roblem s. The conditions that allow radiation to cause full insulator break down are be ingenum erated with increa sing clarity. The nature of spo ntaneo us discharge pulses is being determined.Knowledge of radiation effects in sem iconductors is be ginning to ass ist in the understanding of insulator effects. Th e d etailed de lineation of fast e lectron transpo rt and stopping no w allows o ne to

experimentally address the issue of conduction currents with more clarity.

References

1.B. Gross , Topics in Applied Physics 33 :Electrets, 217 (19 79).[ Links ]

2.B. Gross , Charge Storage in Dielectrics, a Bibliographical Review on the Electret and Related Effects ,Elsevier, Amste rdam, 1964.[ Links ]

3.


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B. Gross, Physical Review 107 (2), 368 (1957).[ Links ]

4.B. Gross, Solid State Communications 15 , 1655 (1974).[ Links ]

5.B. Gross , J. Po lymer Science 27 , 135 (1958).[ Links ]

6.B. Gross , Z. Physik 155 , 479 (1959).[ Links ]

7.B. Gross, IEEE Trans. Nuclear Science 25 (4), 1048 (1978).[ Links ]

8.B. Hess , Z. Angew. Physik 11 , 449 (1959).[ Links ]

9.L. Nunes de Oliveira and B. Gross, J. Appl. Phys. 46 (7), 3132 (1975).[ Links ]

10.B. Gross, G. M. Sessler and J. E. West, J. Appl. Phys. 45 , 2840 (1974).[ Links ]

11.B. Gross and G. F. Lea l Ferreira, J. Appl. P hys. 50 (3), 1506 (1979).

[ Links ]12.A. R. Frederickson, Radiation-induced Electrical Current and Voltage in Dielectric Structures, AFCRL-TR-74-0582 (1974).[ Links ]

13.A. R. Frederickson, IEEE Trans. Nuc. Sci. 22 , 2556 (1975).[ Links ]

14.S. Matsuok a, H. Sunaga , R. Tanaka , H. Hag iwara and K. Araki, IEEE Trans . Nuc. Sci. 23 , 1447-52(1976).[ Links ]

15.J. Pigneret and H. Strobeck, IEEE Trans. Nuc. Sci. 23 , 1886 (1976).[ Links ]

16.D. A. Berke ley, J. Appl. Phys. 50 , 3447 (1979).[ Links ]

17.B. Gross , A. Bradle y and A. P. Pinke rton, J. App l. Phys. 31 (6), 1035 (1960).[ Links ]

18.M. J. Berger, Rad iation Re search 12 (4), 422 (1960). J. Appl. Phys. 28 (12), 1502 (1957).[ Links ]

19.B. Gross, R. Gerhard-Multhaupt, K. Labonte and A. Berraissoul, Colloid & Polymer Science 262 ,93-98 (1984).

20.T. Tabata, P. Andreo and R. Ito, Nuclear Instruments and Methods B 94 , 103 (1994).[ Links ]

21.J. A. Halble ib, R. P. Kense k, G. Valde z, S. M. Seltzer and M. J. Berge r, IEEE Trans . Nuc. Sci. 39,1025 (1992).[ Links ]

22.A. R. Frederickson, J. T. Bell and E. A. Beidl, IEEE Trans. Nuc. Sci. 42 , 1910 (1995).[ Links ]

23.B. Gross and S. V. Nablo, J. Appl. P hys. 38 (5), 2272 (1967).[ Links ]

24.B. Gross, J. Dow and S. V. Nablo, J. Appl. Phys. 44 (6), 2459 (1973).[ Links ]

25.


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A. R. Frederickson and S. Woolf, IEEE Trans. Nuc. Sci. 29 (6), 2004 (1982).[ Links ]

26.R. Gerhard-Multhaupt, Phys. Rev. B 27 , 2494 (1983).[ Links ]

27.M. Hikita, M. Zahn, K. A. Wright, C. M. C ooke and J. Brenn an, I EEE Trans . Electrical In sulation23 , 861 (1988).[ Links ]

28.A. R. Frederickson, S. Woolf and J. C. Garth, IEEE Trans. Nuc. Sci. 40 (6), 1393 (1993).[ Links ]

29.B. Gross and M. M. Perlman, J. Appl. Phys. 43 , 853-7 (1972).[ Links ]

30.W. Shockley, J. Appl. Phys. 9 , 635 (1938). This is d erived fo r slowly varying currents whereMaxwell's first equation, div D=Q , alone suffices.[ Links ]

31.A. R. Frederickson, Proceedings, 17 th International Symposium on Discharges and ElectricalInsulation in Vacuum, Berkeley, CA, 517-22, July, 1996. Sponsored by IEEE and APS.[ Links ]

32.A. R. Frederickson, IEEE Trans. Elec. Insul. 18 , 337 (1983).

[ Links ]33.K. G. Balmain and G. R. Dubois, IEEE Trans. Nuc. Sci. 26 , 5146 (1979).[ Links ]

34.A. R. Frede rickson, L. Levy and C. L. Enloe, IEEE Trans Elec. Insu l. 27 (6), 1166 (1992).[ Links ]

35.A. R. Frederickson, IEEE Trans. Nuc. Sci. 43 (2), 426 (1996).[ Links ]

36.E. P. Wenaas, M. J. Treadaway, T. M. Flanagan, C. E. Mallon and R. Denson, IEEE Trans. Nuc. Sci.26 , 5152 (1979).[ Links ]

37.

M. D. Violet and A. R. Frederickson, IEEE Trans. Nuc. Sci. 40 , 1512 (1993).[ Links ]

38.A. R. Frederickson, E. G. Holeman and E. G. Mullen, IEEE Trans. Nuc. Sci. 39 , 1773 (1992).[ Links ]

39.A. R. Frederickson, IEEE Trans. Nuc. Sci. 43 , 2778 (1996).[ Links ]

40.A. R. Frederickson, Proceedings of 1981 Conference on Electrical Insulation and Dielectric Phenomena ,45-51, (1981) IEEE Publication 81-CH1668-3.[ Links ]

41.H. B. Garrett, Rev. Geo physics Space Physics 19 , 577 (1981).[ Links ]

42.E. C. Whipple, Reports on Progress in Physics 44 , 1197 (1981).[ Links ]

43.B. Gross, H. von Seggern and A. Berraissoul, Proc. Fifth Intern. Symp. Electrets, Heidelberg, 608(1985).[ Links ]

44.E. G. Mullen, A. R. Frederickson, G. P. Murphy, K. P. Ray and E. G. Holeman, IEEE Trans. Nuc. Sci.44 (6), 2188 (1997).[ Links ]

45.G. Wrenn, J. Spacecraft Rockets 32 (3), 514 (1995).[ Links ]


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46.C. K. Purvis, H. B. Garrett, A. C. Whittlesey a nd N. J. Stevens, Design guidelines for Assessing and Controlling Spacecraft Charging Effects, NASA Technical Pap er 2361 (1984).[ Links ]

47.V. D. Bochkov, Proceedings 17 th International Symposium on Discharges and ElectricalInsulation in Vacuum, Berkeley, CA, 517-22 (July, 1996). Sponsored by IEEE and APS. Also,"Investiga tion of Dielectric Strength o f Vacuum Electronic Devices O perating Above 50 kV.....''PhD Dissertation, Ryazan Rad ioenginee ring Ins titute, Ryazan, Russia (1982).[ Links ]

48.A. R. Frederickson and A. D. Morris, U. S. Letters Patent 3,780,304 "Charge Accumulation Gam maRadiation Detector" (18 December 1973).[ Links ]

49.Private C orrespond ence, Da le Ferguso n and David Snyder, NASA Lewis Re se arch Ce nter,Cleveland, Ohio , USA, Septe mber, 1997.[ Links ]

50.A. R. Frederickson, IEEE Trans. Nuc. Sci. 36 (6), 2405 (1989).[ Links ]

51.A. R. Frederickson, P. B. McGrath and P. Leung, Proceedings, 1989 Conference on ElectricalInsulation and Dielectric Phenomena, 210-17, IEEE #89CH2773-0 (1989).[ Links ]

52. B. Gross and P. Gunther, IEEE Trans. Nuc. Sci. 40 , 83 (1993).[ Links ]

53.A. R. Frederickson, Proceedings Symposium on Spacecraft Materials in Space Environment, 221-31,ONERA-CERT, Toulouse, France (Septem be r, 1988 ).[ Links ]

54.L. Nunes de Oliveira and G. F. Lea l Ferriera, Phys. Rev. B 11 (6), 2311 (1975).[ Links ]

55.A. R. Frederickson, IEEE Trans. Nuc. Sci. 40 , 1547 (1994).

[ Links ]

The following papers by Gross and co-workers are helpful, especially for conductivity.

B. Gross and R. Hessel, IEEE Trans. Elec. Insul. 26 (1), 18 (1991). [ Links ]

B. Gross , R. Gerha rd-Multhaupt, A. Berraiss oul a nd G. M. Sess ler, J. Appl. Phys. 62 (4), 1429 (1987).[ Links ]

R. G. Filho, B. Gross and R. M. Faria, IEEE Trans. on Electrical Insulation EI- 21 (3), 431 (1986).[ Links ]

B. Gross, H. Von Seggern, R. Gerhard-Multhaupt, J. Phys. D Appl. Phys. 18 , 2497 (1985).[ Links ]

B. Gross, H. Von Seggern, and J. E. West, J. App. Phys. 58 (8), 2333 (1984). [ Links ]

R. M. Faria, B. Gross, and R. G. Filho, IEEE Conf. On Electrical Insulation and Dielectric Phenomena,Cla yton, DE, Octobe r 21-24, 1984. [ Links ]

B. Gross, H. von Seggern and D. A. Berkley, Phys. Stat. Sol. (A) 79 , 607 1983. [ Links ]

B. Gross , J. A. Gia come tti and G. F. Le al Fe rreira, IEEE Trans . on Nuclear Science 28 , (1981).[ Links ]

B. Gross, IEEE Co nf. On Electrical Insula tion and Diele ctric Phe nom ena , Pocono Ma nor, Penn sylvania,O ct.-Nov. 1978 . [ Links ]

B. Gross, J. Electrostatics 1 , 125 (1975). [ Links ]

B. Gross and L. Nunes de Oliveira, J. Appl. Phys. 45 (10), 4724 (1974). [ Links ]


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Documents

Brazilian Journal of Physics - Progress in High-Energy Electron and X-irradiation of Insulating Dielectrics