Methods For High Resistivity Measurements Related To Spacecraft Charging

Transcription

1 Utah State Univesity Junal Aticles Mateials hysics Methds F High Resistivity Measuements Related T Spacecaft Chaging JR Dennisn Utah State Univesity Jeilyn Bunsn Utah State Univesity asanna Swaminathan Utah State Univesity Nelsn Geen Califnia Institute f Technlgy A Rbb Fedeicksn Califnia Institute f Technlgy Fllw this and additinal wks at: at f the Cndensed Matte hysics Cmmns Recmmended Citatin Dennisn, JR; Bunsn, Jeilyn; Swaminathan, asanna; Geen, Nelsn; and Fedeicksn, A Rbb, "Methds F High Resistivity Measuements Related T Spacecaft Chaging" (2006). Junal Aticles. ape This Aticle is bught t yu f fee and pen access by the Mateials hysics at DigitalCmmns@USU. It has been accepted f inclusin in Junal Aticles by an authized administat f DigitalCmmns@USU. F me infmatin, please cntact dylan.buns@usu.edu.

2 2191 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS Methds F High Resistivity Measuements Related T Spacecaft Chaging J.R. Dennisn, Jeilyn Bunsn, asanna Swaminathan, Nelsn W. Geen and A. Rbb Fedeicksn Abstact A key paamete in mdeling diffeential spacecaft chaging is the esistivity f insulating mateials. This paamete detemines hw chage will accumulate and edistibute acss the spacecaft, as well as the time scale f chage tanspt and dissipatin. ASTM cnstant vltage methds ae shwn t pvide inaccuate esistivity measuements f mateials with esistivities geate than ~10 17 Ω-cm with lng plaizatin decay times such as ae fund in many plymes. These data have been shwn t ften be inapppiate f spacecaft chaging applicatins, and have been fund t undeestimate chaging effects by ne t fu des f magnitude f many mateials. The chage stage decay methd is shwn t be the pefeed methd t detemine the esistivities f such highly insulating mateials. A eview is pesented f methds t measue the esistivity f highly insulating mateials including the electmeteesistance methd, the electmete-cnstant vltage methd, and the chage stage methd. The diffeent methds ae fund t be apppiate f diffeent esistivity anges and f diffeent chaging cicumstances. A simple, macscpic, physics-based mdel f these methds allws sepaatin f the plaizatin cuent and dak cuent cmpnents fm lng duatin measuements f esistivity ve day- t mnth-lng time scales. Mdel paametes ae diectly elated t the magnitude f chage tansfe and stage and the ate f chage tanspt. The mdel lagely explains the bseved diffeences in esistivity fund using the diffeent methds and pvides a famewk f ecmmendatins f the apppiate test methd f spacecaft mateials with diffeent esistivities and applicatins.. Index Tems Mateials Testing, Resistivity, Spacecaft Chaging, Space Envinment Effects. T I. INTRODUCTION he cental theme f spacecaft chaging is hw spacecaft inteact with the plasma envinment t cause chaging. Manuscipt eceived Decembe 15, Suppt f the pjectwas pvided fm the NASA Space and Envinments Effects gam, the USU Space Dynamics Labaty Enabling Technlgies gam, and the NASA Rcky Muntain Space Gant Cnstium. J. R. Dennisn, Jeilyn Bunsn and asanna Swaminathan ae with the hysics Depatment, Utah State Univesity, Lgan, UT USA, (phne: ; fax: ; JR.Dennisn@usu.edu ). N. W. Geen is an Assciate Enginee with the Reliability Engineeing Office f the Jet pulsin Labaty, Califnia Institute f Technlgy, asadena CA , (phne: , fax: , Nelsn.W.Geen@jpl.nasa.gv ). A. R. Fedeicksn was a inciple Reseach Scientist with the Reliability Engineeing Office f the Jet pulsin Labaty, Califnia Institute f Technlgy, asadena CA , ( Athu.R. Fedeicksn@jpl.nasa.gv ). This pape fcuses n esistivity f insulats and its elatin t spacecaft chaging. Resistivity is a key mateial paamete input f analytic spacecaft chaging mdels such as NASCA and SENVIS. Specifically, we will fcus n undestanding what mateials ppeties t measue, hw best t measue them, and hw t undestand these ppeties in the cntext f spacecaft chaging [1]. We als pesent suggested mdificatins t make t new spacecaft chaging guidelines as elated t esistivity measuements f gd insulats [2]. Spacecaft accumulate chage and adpt ptentials in espnse t inteactins with the plasma envinment. A key paamete in mdeling diffeential spacecaft chaging is the esistivity f insulating mateials. This detemines hw chage will accumulate and edistibute acss the spacecaft, as well as the time scale f chage tanspt and dissipatin. Existing spacecaft chaging guidelines [3,4] ecmmend use f standad esistivity tests and impted esistivity data fm handbks that ae based pincipally upn ASTM methds [5,6] that ae me applicable t classical gund cnditins and designed f pblems assciated with pwe lss thugh the dielectic, than f hw lng chage can be sted n an insulat. These data have been fund t undeestimate chaging effects by ne t fu des f magnitude f spacecaft chaging applicatins [7-10]. Classical methds t measue thin film insulat esistivity use a paallel plate capacit methd t detemine the cnductivity f insulats by applying a cnstant E-field (vltage). The pesence f tw cnducting sufaces, the chage and E-field pfile, and the chage injectin methd diffe fm typical spacecaft scenais. Als, the classical methds fail t fully take int cnsideatin the fact that esistivity cntinues t change ve lng time peids as the mateial espnds t the applied electic field and the accumulated chage distibutin. Cnstant vltage and simila standad methds ely n electmete measuements f cuent, vltage esistance. They have been fund t ften be instumentatin eslutin limited t accuate measuements f esistivities f less than t Ω-cm [1,5,11]. Incnsistencies in sample humidity, sample tempeatue, initial vltages and the facts fm such tests cause significant vaiability in esults [5]. Measuements epted hee wee all dne at m tempeatues and vaiatins in tempeatue ae nt expected t affect measued esistivity values within expeimental uncetainties. Limited electic field dependence f esistivity was bseved and is epted elsewhee [10]. Radiatin induced cnductivity unde simultaneus high adiatin flux and mateial mdificatin due t adiatin damage fm high fluences ae

3 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING 2192 (a) (b) Figue 1. (a) Schematic f cicuit defining the esistance R x f a device X in tems f a suce vltage V s and a cuent I thugh Ohm s Law, R xv s/i. (b) Sample dimensins used t define the esistivity ρ xr x A/l, in tems f the length l and the css sectinal aea Ah w. knwn t affect esistivity values, but ae nt significant effects f the lw adiatin expsues f expeiments such as thse epted hee. Futhe, the duatin f standad tests ae sht enugh that the pimay cuents used t detemine esistivity ae ften caused by the plaizatin f mlecules by the applied electic field athe than by chage tanspt thugh the bulk f the dielectic [1,7,8]. Testing ve much lnge peids f time in a well-cntlled vacuum envinment is equied t allw this plaizatin cuent t becme small s that accuate bsevatin f the me elevant chaged paticle tanspt thugh a dielectic mateial is pssible. We cncluded then that the classical esistivity methd may nt be mst apppiate test methd f spacecaft chaging pblem [1,12]. The chage stage methd was develped by Fedeicksn et al. [7,8,13-16], Levy et al. [17-19] and thes [20,21] t measue the esistivity in a me applicable cnfiguatin. In this methd, chage is depsited nea the suface f an insulat and allwed t migate thugh the dielectic t a gunded cnduct. Chage stage esistivity tests have nw been dne f lyimides, Myla, Tefln, Glass, Cicuit Bads, and the cmmn spacecaft mateials [7-9]. The study by Geen et al. [9] in these pceedings descibes a chage stage study f selected samples emaining fm the Intenal Dischage Mnit (IDM) expeiment n the CRRES satellite [13,15,22,23]. The sample set n CRRES was chsen t cve a ange f dak cuent esistivity values and plaizatin magnitudes and ates. Hence, the set pvides an excellent test bed f bth the chage stage methd f esistivity measuements and the behavi f dielectics in the space envinment. In this pape, we pesent a simple, macscpic, physicsbased mdel t descibe the diffeent test methds used t measue esistivity f highly insulating mateials. The mdel allws sepaatin f the plaizatin cuent and dak cuent cmpnents fm lng duatin measuements f esistivity ve day- t mnth-lng time scales. Mdel paametes ae diectly elated t the magnitude f chage tansfe and chage stage and t the ate f chage tanspt. The mdel lagely explains the bseved diffeences in measued esistivity fund using the diffeent methds and pvides a famewk f ecmmendatins f the mst apppiate test methds f spacecaft mateials f a wide ange f esistivities and applicatins. II. MODEL OF CAACITOR CHARGING AND DISCHARGING The ppsed mdel is develped fm vey basic pinciples Gauss Law and the cnstitutive elatin f macscpic electic fields, the definitins f basic mateials ppeties including esistivity and dielectic cnstant, and a few assumptins abut sample gemeties and cnditins. Reades ae familia with cncept f esistance as the pptinality cnstant in Ohm s Law: R V / I. R is an extinsic ppety that measues the esistance t flw f electic cuent, I, f an electmtive diving fce (vltage), V, f a paticula electical cmpnent (see Figue 1a). Resistivity, ρ, is the pptinality cnstant in anthe fm f Ohm s Law, ρ E / J, whee E is the electic field and J is the electic cuent density. Fm these tw fms f Ohm s Law, it is evident that ρ R A/l 1 /, whee A is the csssectinal aea f the esist, l is the length f the esist and is the cnductivity (efe t Figue 1b). A key advantage t the use f esistivity is that ρ is an intinsic mateial ppety that des nt depend n the amunt f mateial in a specific sample n its gemety. F mst esistivity test methds, the highly insulating samples can be teated as simple paallel plate capacits. This simple mdel is als applicable t mst spacecaft chaging situatins encunteed in bth suface chaging f extei insulating catings and chaging f insulats in the intei f spacecaft. Almst all chage esulting fm space envinment inteactins is depsited within micns f the suface (except f elatively ae vey high enegy incident paticles) and can tavel nly sht distances in highly insulating mateials that pesent the maj pblems in spacecaft chaging. These spacecaft elements typically have lateal dimensins n the de f mm t metes. Thus, mst dielectics f cncen can be cnsideed thin-film dielectics. Even f intei deep dielectic chaging esulting fm high enegy incident paticles that can penetate futhe int the spacecaft and inteact with imppely shielded dielectics (e.g., cable insulatin, pinted cicuit bad insulatin, insulating stand-ffs), the chage is typically depsited ve a faily naw depth ange and des nt migate lage distances; thus, this t can be easnably appximated in mst cases as a thin film-dielectic.

4 2193 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS (a) (b) (c) (d) (e) Figue 2. Resistivity can be measued using the simple RC time cnstant methd. (a) Simple thin film capacit sample gemety with thickness d, suface aea A, pemittivity, and esistivity ρr A/d, whee R is the sample esistance. (b) Schematic f a simple RC test cicuit with sample capacitance C and esistance R f a sample with suface vltage V(t)V e -t/τ as a esult f sted chage (t) e -t/τ. (c) A typical decay cuve f sample vltage as a functin f time, t, with time cnstant τr C ρ. (d) Schematic f Capacit (Cnstant Vltage) Resistivity Test Cicuit. (e) Schematic f Chage Stage Resistivity Test Cicuit. Chage depsited in the thin-film insulats typically dissipates thugh the insulat t a cnducting substate. Theefe, thin-film paallel plate capacits ae usually gd mdels f bth dielectics measued with standad esistivity test methds and f thse f cncen in spacecaft chaging. The behavi f chage accumulatin and dissipatin n a paallel-plate capacit is well knwn. Vltage ( chage) decay depends expnentially n time, t, with decay cnstant, τ, thugh a elatin f suface vltage chage density V(t)V e -t/τ (t) e -t/τ, with τr C ρ, (1) whee V and ae the initial vltage chage density, espectively. A typical decay cuve f sample vltage as a functin f time t with time cnstant τr C ρ is shwn in Figue 2c [3]. The decay cnstant f a specific sample can be expessed in tems f the tw extinsic ppeties R and C, whee R is the esistance f the dielectic acss the capacit and the capacitance f the thin-film paallel plate capacit, C A/d, whee F/m is the pemittivity f fee space, is the pemittivity in a dielectic medium, and / is the elative pemittivity. Altenately, the decay cnstant f a given mateial can be expessed as the pduct f the esistivity and the dielectic cnstant. Resistivity is a measue f hw fast fee chage applied t the capacit will dissipate by migating thugh the dielectic. The dielectic cnstant descibes the espnse f the mateial t the electic field inside the capacit; that is, the change in elative dielectic cnstant is the ati f the bund chage n the capacit plates (equal t the plaizatin field f the diples within the dielectic geneated in espnse t the electic field pduced by the fee chage) t the fee chage. In tems f chage density n the capacit plates, Ttal ttal chage density (2) feechage density Fee bund chage density Bund ( 1) feechage density Fee

5 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING 2194 Figue 3. Chage distibutin f a paallel plate capacit cnnected t a cnstant vltage suce, V (a) with vacuum unplaized mateial ( 1) between the plates and (b) with a dielectic mateial ( >1) between the plates. The dielectic cnstant and the electic flux density, D, ae defined thugh the cnstitutive elatin f the macscpic electic field as D E E E + (3) Figue 3 illustates tw situatins, when the mateial between the capacit plates is unplaized ( 1) and when it is plaized ( >1). The plaizatin ( -1) E is a field that esults fm the espnse f the medium t an applied electic field, E, and can be thught f as due t the alignment f the diples within the dielectic mateial t the electic field E. The cnstitutive elatin, Eq. 3, tgethe with a statement f chage cnsevatin, Ttal Fee + Bund, leads t expessins f the chages defined nly in tems f the E- field and the fee chage dependant macscpic mateial paamete : Ttal E D Fee E Bund ( 1) E whee f the actual ttal chage density n the capacit plates Ttal, nly a factin f the chage density Fee cntibutes t the neutalizatin f the vltage n the plates and the emainde f the chage density Bund is bund chage neutalized by the plaizatin f the dielectic mateial. Thus, any time dependence in chage must fllw fm time dependence in eithe Fee (t) E(t) fm (t). Nw we cnside caefully tw simple scenais f the chage density f a paallel plate capacit t change with time: (i) via changes in Fee (t) with vacuum unplaized mateial ( 1) between the plates and (ii) via changes in (t) with a dielectic mateial ( >1) between the plates. Fist, we cnside a capacit filled with a nn-dielectic mateial, ne with 1, as shwn in Figue 3a. With a vltage suce cnnected, the capacit has an equilibium (timeindependent) chage n the plates given by (4) Fee E with E V / d (5) whee the unifm electic field, E, is equal t the applied vltage divided by the plate sepaatin, d. If the vltage suce is discnnected, the capacit dischages as the fee chage leaks thugh the dielectic in Ohmic fashin. All f the time dependence f Eq. 5 is cntained in the applied electic field and thee is n mateial time dependence. The decaying fee suface chage density as a functin f time, can then be mdeled using Eqs. 1 and 5 as Fee τ DC Fee τ DC E( t) V Ve e, d d with τ DC ρdc and (6) whee Fee is the initial sample suface chage, and Fee (t) is the decayed suface chage afte a time inteval, t. In this appximatin, the RC-time cnstant elaxatin time, τ DC, f dischaging capacit can be witten as the fee chage elaxatin time equivalently the chage stage decay time, the time it takes f the fee suface chage t dp t 1/e ( 37%) f its initial value. The dak cuent esistivity ρ DC is diectly pptinal t the dak cuent elaxatin time. Nte that in this simple mdel, decay time is an intinsic mateial ppety, independent f suface aea thickness. A smewhat me geneal mdel allws f sme f the fee chages t be tapped within the dielectic as it is tanspted thugh the mateial, esulting in a esidual ptential, V. In the mdified mdel Fee τ DC Fee Fee [( V V ) e + V ] ( ) d with / τ DC Fee +, τ DC ρ DC and whee the asympttic limit f ttal amunt f chage tapped in the mateial is Fee. Nte that when >1, (t), as discussed belw, τ DC in Eqs. 6 and 7 is eplaced by ρ DC (t), with (t), given by Eq The secnd way that the chage densities change with time is f the mateial t change with time thugh the macscpic mateial paamete (t). The initial pemittivity is 1, if thee is assumed t be n initial chage distibutin in the mateial and the mateial is initially unplaized. As the mateial becmes plaized, (t ). Equivalently, this cnditin assumes that thee ae n initial bund chages Bund Ttal - Fee 0, and the numbe f bund chages gws t an asympttic limit Bund : ( 1 ) Bund Fee e / τ e / τ + ; Bund Fee Bund Fee e / τ ( 1 e ) + 1 (7)

6 2195 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS (8) In this mdel, the plaizatin time, τ, is the ate f the espnse f the medium t an applied electic field, and can be thught f as the ate at which the diples within the mateial espnd t the extenally applied electic field E. It is the time it takes f the bund suface chage t incease t (1-1 /e) ( 63%) f its final value. Nte that in this simple mdel, the plaizatin time is als an intinsic mateial ppety, independent f suface aea thickness. Me geneally, if the mateial had a esidual plaizatin initial chage distibutin pi t chage depsitin (f example fm bmbading the sample with high enegy paticles and ceating tapped chage if the mateial became patially plaized duing the bief cnnectin t a vltage suce duing the time it tk t depsit chage), then Bund 0 equivalently >1, and ( ) Fee Bund III. MODEL OF RESISTIVITY TEST METHODS We ae nw eady t develp mdels f tw methds f measuing the esistivity cnsideed belw, the Electmete Cnstant Vltage Methd and the Chage Stage Decay Methd. Me detailed discussins f these and additinal esistivity test methds ae fund in [1], [5], and [11]. A. Cnstant Vltage Resistivity Test Methds In the Cnstant Vltage methd, a cnstant vltage is applied t tw paallel plate capacits with the dielectic test sample between the plates, and the cuent fm the supply is mnited with and electmete (see Figue 2d). They in this sectin is als applicable t digital multimete, electmete in esistance mde, and electmete in Cnstant Vltage Mde esistivity test methds. If the capacit plate vltage is held cnstant at V, the electic field, E V /d, is als cnstant. The capacit will be chaged such that the fee chages n each plate pduce a ptential diffeence equal and Fee ppsite t the fixed vltage, V d, as illustated in Figue 3a The time-dependant ttal chage, fm Eq. 4a is then Ttal V / τ E [( ) e + ] (10) d Bund Bund / τ Fee Bund ( ) e + ( + ) The plaizatin cuent is then given by Ttal d A I( t) A dt τ / τ V C e τ e / τ Bund Fee + ; e / τ Bund Bund ( ) Bund Fee e / τ (9) (11a) whee A is the aea f the sample and the fee ai capacitance f the sample is C A/d. The cuent t the plates fm the vltage suce is the sum f tw cmpnents, the plaizatin cuent and the leakage cuent, whee I V A 1 V C Leak d ρdc (11b) ρdc Hee, the dak cuent cnductivity, ρ DC, is assumed t be a cnstant, independent f time and E ( equivalently V ). Cmbining Eqs. 11a and 11b, the ttal cuent as a functin f time is I ( t;,, τ, ρ DC ) I + I Leak V 1 C e τ + / τ 1 (12) ρ DC In the limit f sht time, with ρ DC»τ and 1, the cuent exhibit expnential decay with I ( t;,, τ ) I V C, e τ / τ (13) In the limit f lng time, with t»τ, the cuent appaches an asympttic limit equal t nly the leakage cuent I ( t;, ρ ) I DC Leak V C ρ DC (14) B. Chage Stage Decay Resistivity Test Methd Ttal In this methd, an initial chage is depsited n the sample suface. This can esult fm the diect depsitin f chage as is the case f the chage stage decay methd fm the cnnectin f a vltage suce which is subsequently emved as is the case f the vltage ate-f-change methd. The suface chage is then mnited using a nn-cntact electic field pbe, as Bund (t) develps in espnse t the electic field geneated by Fee (t) and Ttal (t) is allwed t dischage thugh the thin-film dielectic t an undelying gunded cnduct. With the chage suce (vltage supply) discnnected fm the plate, Ttal (t) and nt just Ttal (t) must dischage thugh the dielectic. The capacit plate vltage as a functin f time that esults fm a depsited suface chage density Ttal (t), using Eqs. 4 and 5 is V CS Ttal Fee d d (15) Nte that the time evlutin f the chage stage vltage depends n bth the chage dissipatin Fee (t) via the dak cuent esistivity and the evlving plaizatin f the dielectic thugh (t). Inseting the esults f Eqs. 7 and 9, we find Fee Fee / ρdc Fee Fee Fee Bund Bund d ( ) e + V ( t; CS,,,, ρ DC, τ ) Bund Fee Bund Fee e / τ /τ, with ( ) e + (16) Bund Fee

7 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING 2196 in tems f the initial and final vltages and pemittivities, V CS ( t; V, V with,, τ, τ ), DC ( V V ) / τ ( ) e + e ρdc + V, (17) If thee is n initial plaizatin, 1. If thee ae fee chages tapped within the dielectic as they ae tanspted thugh the mateial, then as t this esults in a esidual ptential, V >0. In the limit f sht time, with τ DC»τ, V CS / τ [ + ( ) ] 1 e ( t; V,,, τ ) V (18) In the limit f lng time, with τ DC»τ, V CS ρ [( V V ) e + V ] DC ( t; V, V,,, ρ DC) (19) IV. COMARISON OF RESISTIVITY TEST METHOD RESOLUTIONS Deteminatin f esistivity f mateials can be a difficult pcess, cmplicated by bth instumentatin and pcedual methds and by extenal cnditins that ae difficult t cntl but that can have vey lage effects n the test esults. This sectin pvides a discussin f fu cmmnly accepted esistivity test pcedues, with an emphasis n thei eslutin and valid ange f applicability (efe t Table I f a summay), as they elate t the simple physics-based they pesented abve. We assume in this sectin that the test appaatus and methds ae well designed t minimize pblems fm sample cntaminatin, tempeatue, humidity, vibatin, electmagnetic intefeence, dielectic beakdwn and the cnfunding vaiables. Futhe details can be fund in Test tcl f Chage Stage Methds [1], that descibes in detail test appaatus, measuement methds and analysis techniques f these and the esistivity test methds apppiate f high esistivity insulats used in space applicatins. Recmmended test pcedues and instumentatin f multimete and electmete test methds ae descibed in test pcedues standads [5,6] and als in standad efeences such as [11] and [24]. A thugh discussin f envinmental cnditins and thei effects n the pecisin and accuacy f esistivity measuements using electmete methds is given in Appendix X1 f ASTM D [5] and als in standad efeences such as [11] and [12]. ASTM Standad 618 [25] pvides ecmmendatins f sample cnditining pi t the measuements. A. Digital Multimete Methd Standad digital multimetes (DMM) use an intenal vltage suce t detemine esistance. DMMs use a lwe accuacy shunt type ammete. The methd is usually limited by the intenal esistance f the mete, which typically des nt exceed ~10 10 Ω f a vey gd multimete [11]. Multimetes ae typically useful in measuing esistivity n highe than ~10 12 Ω cm. Such esistivities cespnd t a lngest measuable decay time f ~0.1 sec. As such, esistivity measuements with multimete ae nt useful f measuing esistivity f mateials likely t cause chaging pblems in spacecaft applicatins. B. Electmete in Resistance Mde Methd Standad digital electmetes peating in a stand alne esistance mde als use an intenal vltage cuent suce t detemine esistance, but have highe eslutin feedback style ammetes than digital multimetes. Measuements f cuent with a cnstant-vltage suce ae the pefeed methd [11]. Measuements at this level equie vey gd electmetes and caeful attentin t the test cicuit and sample pepaatin. The methd is limited by the sensitivity f the esistance mete, which typically des nt exceed ~10 16 Ω f a vey gd electmete [11]. Electmetes in a esistance mde with ideal test fixtues ae useful in measuing esistivity n highe than ~10 16 Ω cm. Such esistivities cespnd t a lngest measuable decay time f ~45 min. Limitatins f the test facilities electmetes typically limit measuements with digital electmetes peating in a stand alne esistance mde t ne tw des f magnitude less esistivity decay times, n the de f <10 15 Ω cm ~5 min, espectively. Nte that this decay time is cmpaable t the 1 min settling time suggested f esistivity measuements using the ASTM 257 test methd [5]. As such, esistivity measuements with electmetes peating in a esistance mde unde the mst favable test cnditins ae able t measue esistivity f mateials at the theshld f thse mateials likely t cause chaging pblems in spacecaft applicatins. C. Electmete in Cnstant Vltage Mde Methd Standad digital electmetes peating in a cnstantvltage mde ffe a mdest but imptant impvement ve stand alne electmetes peating in the esistance mde. This is the methd used mst ften f deteminatin f esistivity values fund in standad engineeing handbks [24,27]. Measuements t detemine esistance with this methd equie use an extenal cnstant-vltage suce and a vey gd electmete peating as an ammete with vey high cuent sensitivity.

8 2197 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS Table I. COMARISON OF THE AROXIMATE MAXIMUM RESISTIVITY MEASURABLE WITH VARIOUS TEST METHODS a,e Methd Digital Multimete Electmete Resistance Electmete Cnstant V Chage Stage Decay Maximum Detectable Resistance Values and Decay Time Cnstant c Typical Maximum Measuable Values (±6%) Resistance Cuent Resistivity Decay Time Cnstant d ~ Ω / ~5 sec b,d ~10 10 Ω ~ A ~ Ω cm 0.1 sec ~10 16 Ω / ~10 14 Ω e ~ A ~ Ω cm <45 min ~3 days b,d ~ Ω / ~ Ω ~ A b,d ~ Ω cm <1.5 day ~150 days e ~ Ω / <70 y ~ Ω ~ A ~ Ω cm <15 y (R max C Ω F) g (R max C Ω F) (I min ΔV/R max ) bf Ntes: a. Assumes a typical sample with suface aea A10 cm 2, sample thickness d1 mm, and elative dielectic cnstant 3, with an initial vltage V 500 V. Such a sample has a capacitance f 26 pf and an electic field f V/m, well unde typical dielectic stengths f ~10 7 V/m. d must be geate than 50 μm t avid beakdwn at V 500 V. F thinne mateials, lwe vltages must be used. b. Dentes the limiting pcess f the test methd. Refe t the text f details. c. Calculatin f the decay cnstant is based n Eq. (1) that teats a thin-film insulat as a simple plana capacit with decay time pptinal t esistivity. d. Based n well designed test cnfiguatins and typical instument eslutins listed in Table 5.1a f [11]. e. Based n well designed test cnfiguatins, typical instument eslutins and values listed in Table 2 f ASTM D [5]. f. Limits based n a vltage eslutin f ΔV±1 V f the TReK electstatic field pbe [26] made ve a time peid f ~10 days [12]. g. Limit is set by csmic ay/backgund adiatin and spacing pblems. This cespnds t ~20 electns sec -1 cm -2. The methd is limited by the sensitivity f the ammete, which typically des nt exceed ~ A f a vey gd electmete [11]. Such electmetes in a cnstant-vltage mde unde ideal test cnditins ae useful in measuing esistivity up t ~10 17 Ω cm. Such esistivities cespnd t a lngest measuable decay time f ~1.5 days. It is imptant t ecgnize that this limiting sensitivity f ~500 femtamps is exceedingly small and equies the utmst cae t achieve. This sensitivity is clse t the fundamental limit f detectable cuent set by Jhnsn nise, at a pint whee effects fm the 1/f nise levels and white nise levels ae f cmpaable magnitude [11]. The limiting sensitivity is als cmpaable t the input ffset cuent, which f high end electmetes anges fm 5 fa t as lw as 50 aa [11]. Limitatins f the test facilities electmetes typically limit measuements with digital electmetes peating in a cnstant-vltage mde t ne tw des f magnitude less esistivity decay times, n the de f <10 16 Ω cm a few h, espectively. It is pssible t incease the uppe limit f measuable esistivity by using highe test vltages than the 500 V at a sample thickness f 1 mm assumed f the calculatins in Table I. Hweve, cae must be taken nt t exceed an electic field stength in excess f the typical beakdwn field stength f ~10 7 V/cm, pssible significant field dependence f the esistivity f fields abve ~10 5 V/cm. Electic field enhancement using highe test vltages can be educed by using thicke samples; hweve samples much beynd the assumed 1 mm thickness ae nt applicable t spacecaft cnditins. Sample thicknesses must be geate than 50 μm t avid beakdwn at a typical dielectic stength f ~10 7 V/cm f initial vltages f V 500 V; f thinne mateials, lwe vltages must be used. Since many high esistance mateials cmmnly used in the space envinment ae highly plaizable and time is equied f a sample t adjust t an applied electic field, esistivity measuements will ften cntinue t change f times well in excess f the standad 1 min settling time peid ecmmended in ASTM D [5]. The time f the sample t becme fully plaized and the s-called absptin cuent plaizatin cuent t damp twad ze is ften tens f minutes, but can exceed hus even days. It is theefe ecmmended that cuent measuements shuld be taken as a functin f time and be extended beynd the ASTM ecmmended settling time f 1 min, until the cuent is seen t appach a cnstant value epesentative f the tue leakage ( dak) cuent f the mateial. Because handbk values measued using ASTM 257 ae taken afte nly 1 min, they will unde estimate the esistivity. The me plaizable the mateial and the lnge the decay time cnstant f the plaizatin cuent, the futhe ff ASTM 257 measuements at 1 min will be fm the lng-tem dak cuent limit [1]. An expessin f the ati f the cnstant-vltage mde cuent measued at sme time Τ fm Eq. 12 t the asympttic limit at lng times, I Leak fm Eq. 11, is given by: I ( t Τ) τ DC Τ / τ e + 1 I ( t ) τ 1 ρ ( t Τ) τ DC Τ / τ e + 1 (20) ρ ( t ) τ The discepancy is me pnunced f mateials that have lage plaizatin have plaizatin decay cnstants much lnge than the wait time.

9 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING Cuent (pa) 6 4 Cuent (pa) Time (s) Time (s) (a). (c) Cuent (pa) Cuent (pa) Time (s) Figue 4. Cuent vesus elapsed time measued using the Cnstant Vltage Methd, unde vacuum cnditins f ~1 h with a cnstant applied vltage f 200 V. Only the fist 5 min f data ae shwn in the gaphs. Fits (slid lines) ae based n Eq. 12 Full amplitude data f (a) 25 μm thick lw density plyethylene film and (c) 25 μm thick Myla TM film with an evapated aluminum cating n ne side. The estimated plaizatin decay times ae ~13 sec and ~3 sec, espectively. (b) and (d) Expanded vetical scale shwing cuve fit details nea the plaizatin decay time and asympttic cuent at lng time. (b) The dashed line indicates the aveage value f the last ~53 min; the dtted lines shw the standad deviatin f these pints. The asympttic cuent is (0.3±0.1) pa, cespnding t a dak cuent esistivity f ~ Ω cm. (d). The dashed line indicates the aveage value f the last ~43 min; the dtted lines shw the standad deviatin f these pints. The asympttic cuent is (0.005±0.15) pa, indicating that the dak cuent esistivity is belw the instumental eslutin f the appaatus. As such, esistivity measuements with electmetes peating in a cnstant-vltage mde unde the mst favable test cnditins, taken f peids f time lng cmpaed with the plaizatin decay time, ae able t measue esistivity f mateials at the theshld f thse mateials likely t cause maginal chaging pblems in spacecaft applicatins. Resistivity measuements with electmetes peating in a cnstant-vltage mde unde the me ealistic test cnditins f acquisitin times f lnge than τ, ae able t measue esistivity f mateials at the theshld f thse mateials likely t cause sevee chaging pblems in spacecaft applicatins. Refe t Table II f cmpaisn f sme typical data. Chage Stage Decay Methd Resistivity methds descibed abve measue thin film insulat esistivity by applying a cnstant vltage t tw electdes suunding the sample and measuing the esulting cuent f a peid f time. These methds use classical gund cnditins and ae basically designed f the pblems (b) Time (s) (d) assciated with pwe lss thugh the dielectic and nt hw lng chage can be sted n an insulat suface in the insulat intei [28]. Hweve, esistivity is me apppiately measued f spacecaft chaging applicatins as the "decay" f chage depsited n the suface f an insulat. Chage decay methds expse ne side f the insulat in vacuum t a chage suce, with a metal electde attached t the the side f the insulat; this depsits a chage n the suface f the insulat (efe t Figue 2e). Data ae btained by capacitive cupling t measue the esulting vltage ( me cectly, electic field) due t chage n the pen suface. Measuements t detemine esistance with this methd equie use an extenal chage depsitin suce and a vey gd electstatic field pbe. A nn-cntact capacitive cupling methd, mst cmmnly based n the Kelvin pbe methd [29], is used t measue the electstatic field abve the sample suface [30]. Since thee is n electical cntact made between the pbe and the adjacent chaged suface, the pbe acts as an infinite esistance vlt mete. The chage stage decay methd eslutin is detemined by the limits f the TReK pbe and

10 2199 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS the sample/pbe gemety [1,30,31]. It is difficult t place accuacy limits n the chage stage decay methd, since they ae detemined nt nly by the accuacy f the vltage measuement but als the ate f change f the electstatic vltage eading. The eslutin f a chage stage methd test appaatus can be estimated by detemining an effective minimum measuable cuent, I min C (dv/dt). Cnside a typical sample with C 26 pf, with suface aea A10 cm 2, sample thickness d1 mm, a elative dielectic cnstant 3, and an initial vltage V 500 V (see Table I). F typical instumentatin at JL and USU, the minimum vltage change measuable is ~1 V ve a time span f abut 10 days [28]. This cespnds t an effective minimum measuable cuent, I min ~ A, <200 electns sec -1 a flux f <20 electns sec -1 cm -2. Such chage stage methd measuements unde ealizable test cnditins [1,12] ae useful in measuing esistivity up t ~ Ω cm, which cespnd t a lngest measuable decay time f >15 y. F a well designed appaatus, which limits sample leakage cuents, stay capacitance, and dischage due t inized gas and phtemissin, the esistivity detectin limit is set by csmic ays and Eath backgund adiatin that can diectly impact the sample t emve chage fm it. The backgund adiatin effect can be lagely measued and its cntibuted e estimated; it cntibutes ~10 electns sec -1 a flux f ~1 electns sec -1 cm -2 and begins t be a pblem at a esistivity f >10 22 Ω cm equivalently a decay time f almst a centuy. Despite these exteme values, the eslutin f the chage stage decay methd has aleady been shwn t within appximately ne t tw de f magnitude f the csmic ay/backgund limit [1,11]. As such, esistivity measuements with the chage stage methd unde ealistic test cnditins ae able t accuately measue esistivity f mateials f the full ange f thse mateials likely t cause maginal and sevee chaging pblems in spacecaft applicatins. Such high pecisin measuements cme at the expense f mnth-lng measuements and cmplex appaatus. V. RESISTIVITY TEST RESULTS This sectin descibes epesentative measuements f the esistivities f cmmn spacecaft insulats made using the Cnstant Vltage and Chage Stage Methds. These data sets ae mdeled using the simple physics-based appach develped abve. We give a bief discussin cmpaing the esults f the fitting paametes t tabulated mateials ppeties and the electnic stuctue f the mateials. The cmpaisn validates the they and u cnclusins as t instumental eslutin f the diffeent test methds as discussed abve. A. Electmete in Cnstant Vltage Mde Test Results Tw pttypical dielectic mateials wee tested using the cnstant vltage methd. The USU appaatus used fllws the ASTM 257 guidelines [5] using a guaded electde cnfiguatin, lw nise shielded cabling, and a sensitive electmete (Keithley, Mdel 6485) with a cuent eslutin f ~0.1 pa. It has a vacuum chambe with a base pessue f ~10-4 T. Cuent vesus elapsed time was measued f ~1 h with a cnstant applied vltage f 200.0±0.1 V. Results f the samples tested ae shwn in Figue 4, alng with fits based n the theetical mdel descibed abve using Eq. 12. Details f the appaatus, test methds and data analysis ae fund elsewhee [1,28,32]. Figue 4a shws the data set f a 25 μm thick lw density plyethylene (LDE) film. The tabulated values f dielectic cnstant and esistivity ae 2.28 and Ω-cm, espectively [27]. A plaizatin decay time f ~13 sec is estimated fm a fit based n Eq. 12. Figue 4b shws the expanded vetical scale shwing cuve fit details nea the plaizatin decay time and the asympttic cuent behavi at lng elapsed time. The dashed line indicates the aveage cuent value f the last ~53 min (22 data pints); the dtted lines shw the standad deviatin f these last pints. The asympttic cuent is I Leak ~(0.3±0.1) pa, clealy just abve the eslutin limit f the electmete. This esidual cuent cespnds t a dak cuent esistivity f ~ Ω-cm, using Eq. 11. Nte this measued esistivity is just abve the esistivity detectin limit f the Cnstant Vltage Methd estimated in Table I. Based n the cuent measued at an elapsed time f 60 sec as specified in ASTM , ρ ASTM ~ Ω-cm which is a fact f tw less than the asympttic limit ρ DC. Using this fact f tw in Eq. 20 pedicts a value f τ ~6 sec, which is in easnably g ageement with τ ~13 sec btained by fitting the full data set with Eq. 12. Figue 4c shws the data set f a 25 μm thick plyethylene teephthalate (ET plyeste) Du nt Myla TM film with an evapated aluminum cating n ne side. The tabulated values f dielectic cnstant and esistivity ae 3.2 and Ω- cm, espectively [27]. A plaizatin decay time f ~3 s is estimated fm the fit. Figue 4d shws the expanded vetical scale shwing cuve fit details nea the plaizatin decay time the asympttic cuent at lng elapsed time. The dashed line indicates the aveage cuent value f the last 43 min (24 data pints); the dtted lines shw the standad deviatin f these pints. The asympttic cuent is 0.005±1.5 pa, indicating that the dak cuent esistivity is belw the instumental eslutin f the appaatus. This esult is cnsistent with the fact that the ASTM esistivity f Myla TM was ~100 times that f LDE and that the measued dak cuent esistivity f LDE was vey nea the eslutin f the appaatus. Based n the cuent f ~2 pa measued at an elapsed time f 60 sec as specified in ASTM , ρ ASTM ~ Ω-cm which is a fact f 5 less than the detectin limit f the USU Cnstant Vltage appaatus and a fact f 10 less than the tabulated value. B. Chage Stage Methd Test Results Thee pttypical dielectic mateials wee tested using the chage stage methd and the geneal esults wee pesented in a cmpanin pape in these pceedings [9]. This study illustates well hw the mdel develped hee captues the physical ppeties f a wide ange f mateials. F the analysis in this study (and shwn in Figue 5), the suface vltage measuements wee fit using a least-squaes fit methd f: (i) the full data set using Eq. 17 with five fitting paametes,, V,,, τ DC, and τ,

11 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING Vltage (V) 100 Fee Chage (pc/m^2) Fee Fee_inf_ Elapsed time (h) (a) Elapsed time (h) (b) Figue 5. (a) Lg-lg plt suface vltage as a functin f time ve ~20 days f a 317 μm thick FR4 pinted cicuit bad mateial at an initial vltage f V 498 V, as measued with the chage stage decay methd [9]. Cuves shws fits with a thee paamete fit using Eq. (17) (dashdt) [with 5.3, τ 5 h, and τ DC10 days with V 0 V and 1]; a five paamete fit using Equatin (17) (slid) [with 1.03, 4.68, V 107 V, τ 25.1 h, and τ DC5.0 days ]; an ealy time limit mdel using Eq. (18) (dashed); and the late time limit mdel with Equatin (19) (dtted). (b) edicted bund (slid) and fee (dashed) chage as a functin f elapsed time f FR4. lts ae based n a thee paamete fit using Equatin (17). The initial and final values f the fee chage fm the fit ae als shwn as sht dashed lines (ii) (iii) (iv) the full data set using Eq. 17 with thee fitting paametes, τ DC, and τ, plus 1 and V 0, the initial six data pints using Eq. 18 with and τ as fitting paametes, and the last six data pints using Eq. 19 with τ DC as a fitting paamete. In each case, V was set t the measued initial vltage. Results f the FR4 sample tested ae shwn in Figue 5a, alng with fits based n the theetical mdel descibed abve. Figue 5b shws the pedicted evlutin f the ttal, fee and bund chage densities as a functin f time, based n the esults f the fits and Eqs. 4, 7 and 9. Simila esults f TFE and alumina samples ae shwn in Geen [9]. (i) The FR4 samples tested wee a themset epxy esin, fibeglass einfced, Cu-clad laminate made by Micaply C. [9]. FR4 is a cmpsite mateials typically used f pinted cicuit bads [33,34]. FR4 shwed a faily apid initial dp in ptential immediately afte chaging due t plaizatin. Respnse f the lng chain plymes and mdificatins f defects f the FR4 cmpsite wee simila t thse f TFE, as evidenced by a simila lng plaizatin decay time τ ~25 h and the slw ise f the bund chage pedicted in Figue 5b. The highe ati f ttal chage t fee chage in Figue 5b is indicative f highe plaizatin than in TFE and a elative dielectic cnstant f >5. The plyme and glass in FR4 have pemanent diples unlike TFE and the defect density is high due t the cmpsite natue f the mateial. The unusually lage (~20%) esidual vltage, V, suggests that thee is substantial esidual chage in the FR4 sample. The FR4 has a dak cuent esistivity f ~ Ω-cm, between that f the the tw samples; this is evident in the intemediate dak cuent decay cnstant τ DC ~5 days and in the mdest decay f fee chage pedicted in Figue 5b. Measuements with a diffeent technique n a simila FR4 spacecaft mateial fund a dak cuent esistivity f ~ Ω-cm [35], a fact f ~5 less than u measued ρ DC. (ii) Fibe filled TFE samples exhibited little plaizatin cuent and had a vey high dak cuent esistivity f ~ Ω-cm, with a dak cuent decay cnstant τ DC ~1 y. Nte this is nly abut a fact f 15 less than the estimated esistivity detectin limit f the Chage Stage Methd as estimated in Table I. The ρ DC measued with the chage stage methd is ~300 times lage than the ρ ASTM ~10 18 Ω-cm value fm standad handbks [27]; this is cnsistent with a eslutin limit f the cnstant vltage methd f ~ Ω-cm, as indicated in Table I. TFE is knwn as a nn-pla plyme, with a vey lw plaizability evidenced by its lw dielectic cnstant f 2.1 [27, p. 120] and a small magnitude ise pedicted f the bund chage. Respnse f the lng chain plymes and mdificatins f defects ccu slwly f TFE, as evidenced by the elatively lng plaizatin decay time τ ~18 h and the slw pedicted ise f the bund chage. (iii) The alumina samples had a lwe dak cuent esistivity f ~ Ω-cm than measued f eithe the TFE FR4 plymes, with vey lage and me apid plaizatin. Alumina is a ceamic with ne f the highest dielectic cnstants f cmmn ceamics, with a value f abut 10 [27]. This led t a pedicted lage initial ise in the bund chage, which cincided with a elatively apid decay f fee chage. Such behavi can ccu because the plaizatin decay cnstant τ ~6 h is nt t much shte than τ DC ~20 h.

12 2201 IEEE Tans. n lasma Sci., 34(5) Octbe 2006, DOI: /TS Mateial TABLE II. COMARISON OF DARK CURRENT AND OLARIZATION DECAY CONSTANTS [10] Dak Cuent Resistivity ( Ω-cm) ρ DC Measued τ DC Decay Times (days) Measued τ, Tabulated τ ASTM Rati f Decay Times τ DC / τ τ DC / τ ASTM Kaptn (KA001 lyimide) Tefln (TFE) Tefln (FE) Tefln (FA) Tefzel (ETFE) Uethane tting Cmpund (Cnthane EN-11) FR4 inted Cicuit Bad TFE Cmpsite Alumina (Al 2 O 3 ) VI. CRITICAL DECAY RATES AND RESISTIVITY VALUES FOR SACECRAFT CHARGING ALICATIONS In the space envinment, chage is depsited n the suface f the spacecaft as it bits. Hence, the bital tatinal peidicity f the spacecaft sets the elevant time scale f the pblem. Typical bits f nea-eath satellites ange fm 1 t 24 hus, while tatins ae usually up t 100 times shte. F example, satellite bit tatin peid detemines the fequency with which sufaces ae expsed t high intensity adiatin belts in the magnetsphee t sunlight whee they ae subject t phtemissin. Spacecaft n inteplanetay missins can be cntinuusly expsed t chaging cnditins f days t yeas. Chage accumulated n the insulating spacecaft sufaces typically dissipates thugh the insulat t a cnducting substate. As highly insulating spacecaft mateials accumulate chage, thei extemely lw chage mbility causes that chage t accumulate whee depsited and lcal electic fields t ise until the leakage cuent fm the insulats t cnducts equals the accumulatin cuent fm the envinment ( until the insulat actually beaks dwn and geneates a chage pulse). Mdeately insulating mateials have enhanced cnductivity, which allws chage t dissipate me apidly. The chage will migate t adjacent cnducting sufaces, giving ise t fame chaging instead f diffeential chaging leading t chage dissipatin when cmbined with cuents fm ppsitely chages cmpnents. Hence, the magnitude f esistivity f insulating mateials diectly detemines hw accumulated diffeential chage will distibute acss the spacecaft, hw apidly diffeential chage imbalance will dissipate, and what equilibium ptential an islated insulat will adpt unde given envinmental cnditins. T bette undestand the chaging phenmena, ne then needs t elate esistivity chage mbility t a suitable time scale. The chage stage decay time t the cnducting substate depends n the (macscpic) esistivity equivalently the (micscpic) chage mbility f the insulat. If the chage decay time exceeds the bit time, nt all chage will be dissipated befe bital cnditins act again t futhe chage the satellite and chage can accumulate. As the insulat accumulates chage, the electic field ises until the insulat beaks dwn and geneates a pulse. Thus, chage stage decay times in excess f ~1 h ae pblematic, as is specifically stated in NASA Handbk 4002 [3]. Figue 6 shws a plt f decay time as a functin f esistivity, using Eq. 1 with 1, f a elevant ange f esistivity values. Cnsideing these esults, maginally dangeus cnditins begin t ccu f mateials with esistivities in excess f ~10 16 Ω-cm with 2< <4, when τ exceeds ~1 h. Me sevee chaging cnditins ccu f ρ Ω-cm, when decay times exceed ~1 day. VII. CONCLUSION It is clea fm the evidence pesented in this pape that it is essential f accuate mdeling f spacecaft chaging t have accuate and apppiate values f the esistivity f insulats used in the cnstuctin f spacecaft. Hweve, the existing guidelines d nt adequately addess these issues, and lead designes int false secuity. The bulk esistivity values f insulats used t mdel spacecaft chaging have taditinally been btained fm the handbk [25,27] values fund by the classical ASTM/IEC methds [5,6]. Values f typical spacecaft insulat mateial esistivities fund in handbks ae in the ange f t Ω-cm [25,27]. These esistivity values cespnd t decay times f ~1 sec t ~3 days, suggesting that in many cases chage cllected by cmmn spacecaft insulats will dissipate abut as fast as the chage is enewed. It has been shwn hee that classical methds f highly insulating mateials ae ften nt applicable t situatins encunteed in spacecaft chaging [1,2,7-9,12]. Measuements pesented in this and elated studies have fund that esistivity detemined fm the Chage Stage Methds is typically 10 1 t 10 4 lage than values btained fm classical ASTM/IEC methds f a vaiety f thin film insulating samples, including plyimides, Myla TM, Tefln TM, silicate glasses, and cicuit bads [7-10]. These highe Chage Stage esistivities f typical spacecaft insulats ae in the ange f Ω-cm t Ω-cm and have cespnding decay times fm minutes t decades, clealy in

13 Dennisn et al.: METHODS FOR RESISTIVITY MEASUREMENTS RELATED TO SACECRAFT CHARGING 2202 the ange whee maginal me seius spacecaft chaging pblems ae expected t ccu based n Figue 6. It is theefe impeative t evise the elevant engineeing design guidelines f mitigatin f spacecaft chaging and the elated mateials databases befe futhe pblems ccu in space. NASA Handbk 4002 [3] deals extensively with ecmmendatins f detemining what level f esistivity mateials pse isk f spacecaft chaging and hw t measue esistivities f mateials. Based n the esults descibed in this pape, the pimay ecmmended changes t NASA Handbk 4002 deal with impved methds t detemine esistivity f excellent dielectics. The ecmmended changes suggest that a peliminay measuement f esistivity be made using electmetes in a esistance cnstant vltage mde f sht peids f time fllwing the guidelines in the ASTM standad. If the peliminay measuement f esistivity yields a value geate than ~10 14 Ω-cm (equivalent t a decay time f ~1 sec) if the measued esistivity is fund t cntinue changing f me than a few minutes, additinal measuements shuld be cnducted. Tw highe pecisin test methds ae ecmmended f these additinal measuements, the Electmete Cnstant Vltage Methd and the Chage Stage Methd. These highe pecisin tests must be cnducted in stingent test cnditins unde vacuum with appaatus that ae well designed t minimize pblems fm sample cntaminatin, tempeatue, humidity, vibatin, electmagnetic intefeence, dielectic beakdwn and the cnfunding vaiables as utlined in ASTM D [5] and ASTM 618 [25]. The highe pecessin tests must als be cnducted f lng enugh time peids t assue that the mateial has becme fully plaized, times that may be fm minutes t mnths depending n the mateials being tested. Based n the maximum measuable esistivities f the diffeent methds as shwn in Table I, we cncluded that such a Cnstant Vltage Methd test is usually applicable t mateials with esistivities in a ange f Ω-cm>ρ>10 17 Ω- cm ( equivalently 1 sec>τ>10 h), while the Chage Stage Methd is the methd f chice f vey high esistance mateials with ρ>10 16 Ω-cm τ>1 h. The ppsed mdificatins als impve Handbk 4002 by incpating the new knwledge f chage stage ppeties. The Chage Stage Methd has been develped t measue the esistivity in a me applicable cnfiguatin and with acceptable eliability f excellent dielectics with vey high esistivities Ω-cm, whee classical ASTM [5] and IEC [6] methds each thei limits f applicability [1]. Instumentatin and methds have been successfully develped t measue esistivity with the Chage Stage Methd. The simple, macscpic, physics-based mdel descibed hee with Eqs. 9 and 12 is based n fist pinciples (Gauss Law, the cnstitutive elatins f macscpic electic fields, the definitins f basic mateials ppeties including esistivity and dielectic cnstant, and a simple capacit gemety f the dielectics). It can be used t accuately fit the time-dependant data f a vaiety f test methds and extact physically meaningful fitting paametes, including the plaizatin decay cnstant, the dak cuent decay cnstant, the initial pemittivity, and the pemittivity f the fully plaized sample. This allws clea sepaatin f the decay time (sec) SAFE MARGINAL ROBLEM 1 day esistivity (hm-cm) plaizatin cuent and the dak cuent. The mdel als accuately pedicts dispaities between diffeent methds and explains thei eslutin limits. Finally, the mdel als clealy detemines which test methds ae apppiate f inceasing levels f esistivity. ACKNOWLEDGMENT The auths wuld like t acknwledge vey helpful discussins n these standads with Hank Gaett and Al Whittlesey. The chage stage measuements descibed in this pape wee made at the Jet pulsin Labaty, Califnia Institute f Technlgy, unde a cntact with the Natinal Aenautics and Space Administatin. The cnstant vltage measuements wee made by the Mateials hysics Gup at Utah State Univesity. The majity f the suppt f this wk was fm a cntact fm the NASA Space Envinments and Effects (SEE) gam. This wk was lagely initiated by the late Rbb Fedeicksn, wh was the diving fce behind develpment f the chage stage methd and u cnstant mtivatin t undestand these pcesses in tems f fundamental physics. JRD and NWG wuld like t ecgnize Rbb as thei fiend and ment, and as a maj influence n thei scientific caees. REFERENCES [1] J.R. Dennisn, A. Rbb Fedeicksn, Nelsn W. Geen, asanna Swaminanthan and Jeilyn Bunsn, Test tcl f Chage Stage Methds, NASA Space Envinments and Effects gam, Cntact N. NAS , Measuement f Chage Stage Decay Time and Resistivity f Spacecaft Insulats, Apil 1, 2002 t Januay 31, [2] J.R. Dennisn, A. Rbb Fedeicksn, and Nelsn W. Geen, Cmments n Engineeing Design Guidelines: Resistivity Measuements Related t Spacecaft Chaging, NASA Space Envinments and Effects gam, Cntact N. NAS , Measuement f Chage Stage Decay Time and Resistivity f Spacecaft Insulats, Apil 1, 2002 t Januay 31, h Figue 6. Decay time as a functin f esistivity base n a simple capacit mdel and Equatin (1). Hee is set t 1. Maginal chaging pblems ccu f mateials with esistivities ( me ppely ρ ) in excess f ~ Ω-cm, when the decay time τ exceeds ~1 h. Me seius chaging pblems ccu f ρ Ω-cm, when decay times exceed ~1 day.