Radiation damage evaluation on AlGaAs/GaAs solar cells

IEEE T ansac ions on Nuclea Science, Vol. 35, No. 4, Augus 1988 1067 RADIATION DAMAGE EVALUATION ON ALGAAS/GAAS SOLAR CELLS E. G. Mo eno, R. Alcubilla, L. P a and L. Cas a ie Depa amen o de Elec dnica. U.P.C. Jo ge Gi ona Salgado s/n - Ba celona 08034 - SPAIN Abs ac A piecewise model o e alua e adea ion damage on AlGaAs based sola cells has been de eloped, which gi es comple e elcc Lca1 pa ame e s o he cells in he ope a ing empe a u e ange. Di e en s uc u es, including g aded band gap and double he e o ace can be analyzed. The cell s uc u e is sliced in o laye s o cons an pa ame e s, allowing he model o ake in o accoun nonuni o m damage p oduced by low ene gy p o ons wi hou excess compu e ime. P o on damage coe icien s as well as p o on damage a ios can be calcula ed o ene gies be ween 30 and lo4 keV wi h only wo adjus able pa ame e s. In addi ion, coi adia ion expe imen s wi h di e en ene gy p o ons can be simula ed, by imp o ing he con en ional me hod o deg ada ion compu e ing. In oduc ion Gallium A senide sola cells a e conside ed as especially sui able o space pu poses because o hei high e iciency and adia ion esis ance. The use o GaAs sola cells in space powe sys ems scheduled o 7 yea s o ope a ing li e ime 111 equi es p edic ion capabili ies o he expec ed sola cell deg ada ion. This wo k mus include bo h labo a o y es measu emen s and simula ion wo k o be e unde s anding o he unde lying phenomena as well as o de elop ools o acili a e cell design. The common me hod o p edic sola cell deg ada ion in space is o ela e he damage p oduced by any kind o pa icles, o damage p oduced by pa icles o e e ence, usually 1 MeV elec ons o 10 MeV p o ons, and o calcula e he o al equi alen luence 121. Al hough he equi alence damage me hod has been ex ensi ely used, cases o ailu e when GaAs sola cells a e conce ned ha e been de ec ed, mainly due o he di e en deg ada ion beha iou o hese cells in compa ison wi h Silicon cells, in pa icula i coi adia ion wi h low and high ene gy p o ons is conside ed 111. In he wo k epo ed he e he ocus is placed on he elec ical beha iou o he sola cell in he p esence o ha m ul adia ion en i onmen assumed o concen a e i s e ec s in he mino i y ca ie li e ime deg ada ion. I has been ound ha many o he expe imen al da a o deg ada ion o elec ical cha ac e is ics may be explained by assuming a mino i y ca ie li e ime deepness- dependen om he su ace on which pa icles a e impinging. The shape o he li e ime inside he sample, will be ob iously dependen on he ype and ene gy o he pa icles, as well as on he kind o i adia ion, i.e. i he pa icles ha e no mal o iso opic incidence. Manusc ip ecei ed on Feb ua y 5, 1988 A e y i s in e es o he wo k is o p o ide a ool o calcula e he expec ed deg ada ion o sola cells in any kind o i adia ion en i onmen , by simply knowing he expe imen al esul s a e no mal i adia ion wi h a monoene ge ic pa icle luence a 1 MeV elec ons and 10 MeV p o ons. Damage p oduced by hese pa icles is easily measu ed in ea h labo a o ies. The model should be capable o explain he ailu e o con en ional p edic ion models when co-i adia ion wi h di e en ene gy p o ons is conce ned. Sola cell model Comple e simula ion o sola cells equi es sol ing a se o non linea di e en ial equa ions including Poisson, anspo and con inui y equa ions o bo h ca ie ypes. The solu ion needs complica ed and ime consuming nume ical me hods. Simple models assume cons an alue pa ame e in each egion o he cell hen inding analy ical solu ions. Howe e hey a e no able o explain adequa ely he cell deg ada ion by low ene gy p o ons, because he non uni o mi y o he damage. These p e ious analy ical models o GaAs cell deg ada ion, ei he calcula e he mean alue o ca ie li e ime in each egion cell as a unc ion o pa icle luence and ene gy, o i hey akes in o accoun he non uni o mi y o he damage, hey a e only able o calcula e he sho ci cui cu en educ ion 131. Al e na i ely, cell deg ada ion a e ominidi ec ional adia ion can be compu ed om he expe imen al deg ada ion cu e a e no mal adia ion, by calcula ing he o al damage in he cell 141. Again, he non uni o mi y o he damage is neglec ed. The model he e p esen ed is basPO on a piecewise qpp oach ah di ides he cell s uc u e in an adap a i e numbe o slices, Inside a pa icula slice he semiconduc o pa ame e s a e cons an , consequen ly, i is easy o ind an analy ical solu ion o he semiconduc o anspo equa ions wi h sui able bounda y condi ions o he in e aces wi h he adjacen slices. Mo e speci ically, he bounda y condi ions applied o cu en con inui y a e ela ed o in e ace ecombina ion eloci ies, S, and he bounda y condi ions applied o mino i y ca ie concen a ion a e €o a P ype egion gi en by whe e n is he eLec on concen a ion in p- ype slice and E, is he conduc ion band ene gy le el, Nimp he dopan concen a ion and m* he elec on e ec i e mass. The selec ed p ocedu e o pe o m he 0018-9499/88/08~107$01.00 0 1988 IEEE 1068 cell s uc u e di ision is shown in Figu e 1. The emi e , base and deple ion egions a e sliced in o laye s when he dopan Aluminium concen a ion a e cons an . This me hod is able o accomoda e s uc u es wi h AlGaAs laye s a he op o he bo on o he cell as well as o conside a iable gap s uc u es. DEPLETION EMITTER REGION BASE II Fig. 1 Di ision o sola cell s uc u e in o slices. As i will be shown la e , he adia ion is expec ed o c ea e e y sha p li e ime a ia ions in he semiconduc o bulk. Fo his eason, a selec ion o he slices and spacial dis ibu ion mus be pe o med in o de o place a g ea e numbe o slices in he semiconduc o egion whe e sha pe a ia ions in he li e ime a e p esen . Finally, he compu e p og am ha has been de elopped calcula es he o al I(V) cha ac e is ics by adding he con ibu ions o he emi e , base and space cha ge egions unde AM0 illumina ion condi ions. Spec al esponse is, o cou se, an ou pu o he p og am. All he pa ame e s o he model a e analy ically ela ed o he empe a u e, composi ion o he semiconduc o (Aluminium concen a ion) and dopan concen a ion (Nimp). Table I shows he de ini ion o pa ame e s and he dependeces conside ed in he model. Analy ical exp essions ha e been gi en elsewhe e 15 I. Table I. Elec ical Pa ame e Band ene gy E ec i e mass ml*,, mi (XAL) In insic conc. ni (Band ene gy, m* ,Temp) Ca ie mobili y l+ (Nimp m* I Temp) Ca ie li e ime Tn Tp (Nimp, m* , Temp) Dielec ic cons an E (XAL, Temp) Abso ion coe icien a (h. Band ene qy) EG, EL, Ex (XAL, Temp) __ Re lec i i y R ( h, ARC) Radia ion e ec s I is well known ha he elec on and p o on adia ion c ea es de ec s in he semiconduc o bulk ha ac s as ecombina ion cen e s o ca ie s. The e a e se e al ypes o ecombina ion cen e s, each one cha ac e ized by he cap u e c oss sec ion and he si ua ion in he gap. These ecombina ion cen e s modi y he ca ie li e ime whe e TO Qi as ollows 11 - = 7 + Nl i h 01 is he mino i y ca ie li e ime be o e i adia ion (BOL) is he cap u e c oss sec ion o he i ype cen e Ni is he desi y o he i ype cen e V h is he he mal eloci y Fo sake o simplici y we will ake only one ype o cen e , placed a he cen e o he gap, wi h he same cap u e c oss sec ion o bo h ypes o ca ie s. Because he ange o he 1 MeV elec ons is much g ea e han he hickness o he GaAs cell, i is commonly assumed ha he ecombina ion cen e densi y is uni o m h ough he cell s uc u e. In ha case he mino i y ca ie li e ime ! a e an elec on luence o @e 1 MeV e-/cm can be ela ed o he Begining O Li e li e ime as ollows (3) -= i+KO~ h ee whe e Ke is he li e ime deg ada ion cons an , aking in o accoun he cap u e c oss sec ion o he cen e and he p opo ionali y be ween he de ec s and he densi y o ecombina ion cen e s. The i adia ion wi h p o ons leads o a mo e complex si ua ion, on he one hand because he ange alue is compa able o he cell dep h and, on he o he hand because o he nonuni o m dis ibu ion o he de ec s along he ange. Mo e p ecisely, he numbe o p ima y collisions o a p o on, wi h ins an aneous ene gy E, is he ecip ocal o he mean ee pa h, 1(E), 161 (4) whe e O(E) is he nuclea s opping c oss sec ion, and N is he a omic densi y. Each p ima y collision p oduces a ce ain numbe o a omic displacemen s, (E), ela ed o he ins an aneous ene gy h ough he Kinchin and Pease heo y. The o al numbe o a omic displacemen s p oduced by he p o on pe uni y pa h leg h is (5) To ela e he ins an aneous ene gy, E, o a p o on wi h inciden ene gy Eo o he pene a ion, x, we ha e i ed he ange da a, R(Eo), o Ande sen and Ziegle 171 ob aining 175' (R-x) E= (7) 1 + .67*(R-~)'.~' Fo iso opic i adia ion he unc ion ~(R-X) has Po be 'a e ac ed €o all he inciden angles as ollows 1 Hence he li e ime alue a e a p o on luence o oP p'/cm2 is , whe e KP ac s o he p o ons as Ke o he elec ons. Bo h cons an s, K and IC.?, a e used o adjus he model o ge expe imen al esul s. To ake in o accoun he co e glass e ec s on he dis ibu ion unc ion C(Eo,x) he coo dina e o igin is displaced o a deepness o xo om he su ace. xo is calcula ed as he GaAs hickness needed in o de o ha e he same s opping powe as he co e glass. Once he unc ion T(To,x) has been calcula ed, a disc e iza ion p ocedu e ollows, conce ning he whole cell s uc u e. The disc e iza ion is au oma ically pe o med acco ding o he alue o he inciden ene gy and he i adia ion ype. Figu e 2 shows he esul s o such a disc e isa ion o i adia ions wi h a luence o 10l1 cm-2 di ec ional and iso opic, a wo di e en ene gies. As expec ed, he shape o he disc e iza ion is ,in) hg in he iso opic case. U ~51 0 6.5 1.0 1.5 2.0 Dep h (l~ m) Fig. 2 Hole li e ime educ ion a e lo1' 10 MeV p o on/cm2 i adia ion. - ii~l mdi -_ iso opic. Resul s The model has been used o simula e he elec ical beha iou o an he e o ace AlGaAs sola cell epo ed in he li e a u e 111,181, in o de o check i s capabili ies. These cells ha e been quali ied by he NASDA o space use, so i s beha iou unde i adia ion a e well known. The main physical pa ame e s and he elec ical pe o mance BOL a 28OC a e lis ed in Table 11. Se ies and shun esis ences, and in insic ca ie li e ime a e chosen o ma ch expe imen al esul s 181 a his empe a u e. Figu e 3 shows he sho ci cui cu en , open ci cui ol age, and maximum powe plo ed as a unc ion o he empe a u e. Expe imen al poin s epo ed in e e ence 8 a e also supe posed. To calcula e he beha iou unde i adia ion we s a se ing he alues o Ke and KP. This is done in o de o i he expe imen al esul s a e no mal i adia ion by 1 MeV elec ons and 10 MeV p o ons espec i ely. The o me is shown in Figu e 4 wi h expe imen al poin s aken om (8). Figu e 5 shows he spec al esponse BOL, a e 1 MeV elec on no mal i adia ion a a luence o 5 1015 cm-2, and a e combina ed no mal i adia ion wi h 1 MeV elec on and 10 MeV p o on a luences o 1069 , 1Ol5 cm-2 and 5 10l2 cm-2, espec i ely ,"I 60 60 iM LM Tempe a u e (OC) FI,~ { Tempe a u e cha ac e is ics o P,, Iy l,,, b'OL. !oo - - &i 0 "Eo U Id W n .: 60 c ?I c E W g40 I I 10 l4 10 l5 10 Ib 1 MeV elec on luence (cm-') n m3i ": i- -. -< '1 F, ~ I MeV e ec on ELuence. 1 'I 111 / 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Wa eleng h ( .I m) . q Spec al esponse o sola cell (a) be o e i adia ion (b) a e 5-1015 cm-2 1MeV elec on i adia ion (c) a e 5-1015 cm-2 1MeV elec on and 5-1012 cm-2 loMeV p o on i adia ion. These p e ious adjus emen s allow us o calcula e he deg ada ion o he sola cell 1070 GaAs laye pe o mances a e p o on i adia ion o a bi a y ene gy and luence, iso opic o di ec ional. Figu e 6 shows he e iciency deg ada ion as a unc ion o p o on ene gy o se e al luences. Two ea ly conclusions can be gi en, i s he e is an ene gy ha p oduces maximum deg ada ion, a ound 200 keV, and second, o high ene gy p o ons iso opic i adia ion p oduces wo se damage. Thickness (!.nu) 0.5 Impu i y concen a ion (cm-3) 1018 In e ace ec eloci y (cm/s) 104 Emi e p- ype Base n- ype Gene al Elec ical cha ac supe posi ion o he damage p oduced by he di e en pa icle ypes o calcula e he o al equi alen luence. E o s p oduced by his assump ion can be impo an , mainly when low ene gy p o ons is conce ned. Co-i adia ion expe imen s wi h se e al ene gy p o ons ha e been pe o med showing his misma ch 111. Table 11. Cell pa ame e s Impu i y concen a ion (cm-3) 1018 Su ace ec eloci y (cm/s) 106 Thickness (p) 6.0 I Impu i y concen a ion (~m-~) 4.1016 Ac i e laye ______~.__ Thickness (pn) 200 Subs a e Impu i y concen a ion (cm-3) 1018 -1 Back su ace ec eloci y (cm/s) 1010 Size (cmL) 2x2 Con ac su ace co e ed (%) 3 ARC Si3Nq Se ies esis ence ( 52 ) 0.4 Shun esis ence ( 52 ) 250 __ -~ __ . __ ___ Isc (mA) 125. oc (V) 0.97 Fill Fac o 0.77 Pmax (mw) 94.8 ____._____I - - - .. . - I Mo eo e , we can calcula e he deg ada ion o he cell in any kind o adia ion en i onmen by calcula ing he de ec s accumula ed a each dep . This allows us o p edic he cell li e ime in a gi en o bi . Damage coe icien s Damage coe icien s a e de ined as he luence o 10 MeV p o ons equi ed o educe one elec ical cell pa ame e (usually Isc, Voc! o Pma,) a empe a u e T by pe cen , di ided by he luence o p o ons o ene gy E equi ed o ha e he same educ ion in he chosen pa ame e , a he same empe a u e. P o on damage a ios a e de ined in a simila way o he damage coe icien s, bu aking 1 MeV elec ons as e e ence pa icles. Bo h pa ame e s a e ex ensi ely used o p edic he use ul li e o pho o ol aic a ays in space o a gi en o bi , con e ing he o al i adia ion in an equi alen luence o e e ence pa icles. Howe e , his me hod has some d awbacks. Fi s , he damage coe icien s a e no uniquely de ined o a gi en ene gy. They depend on he i adia ion kind (no mal o iso opic) and on pe cen deg ada ion conside ed. So he e a e se e al alue ables and hei handling is di icul . Second, damage coe icien s depend s ongly on he physical s uc u e o he cell conside ed. Ex apola ion o ano he cell ype, e en simila , is no possible. Fo his eason hey a e no sui able o pu poses o op imiza ion s uc u es. Mo eo e he me hod applies The me hod p oposed in his wo k, based on he use o a powe ul simula ion model i ed bo h expe imen al esul s BOL, and a e 1 MeV elec on and 10 MeV p o on i adia ion, can o e come he abo e men ioned d awbacks. As an example, deg ada ion p oduced by combina ed i adia ion wi h se e al ene gy p o ons has been calcula ed. Fi s ly he p o on damage coe icien s ha e been ob ained om he cu es o Figu e 6, o = 20 % o Pmax, and hey a e shown in Figu e 7. These esul s closely ag ee wi h hose epo ed in 0- 0.1 1 10 P o on ene gy (MeV) Fig. b Pmax deg ada ion e sus o on ene gy o (a) 1O1O cm-2 (b) lop1 cm-2 and (c) 1012 cm-2 luences. - - no mal - iso opic. 100 ul +J c .-I U .-I u w m 0 U 10 01 0 m E m n 0.1 F I <3 . 7 0 -10 0 -10 0 -10 Fig. 8 /' i Iso opic 0.1 1 10 P o on ene gy (MeV) 20% Pmax damage coe icien s. < 100 keV I 0.1 1 .o 10 Ene gy (MeV) Di e ences be ween emaining Pmax calcula ed h ough he PDM me hod and by he model. Coi adia ion o se e al ene gy p o ons and (a) 100 KeV, (b) 500 KeV and (c) 10 MeV p o ons. All he luences causes 20% Pmax deg ada ion. e e ence 4. A e ha , deg ada ion p oduced by co-i adia ion wi h 0.1, 0.5 and 10 MeV p o ons and p o ons o di e en ene gies a luences which causes 20 % Pmax deg ada ion has been calcula ed (a) by he con en ional equi alen damage me hod, and (b) by di ec calcula ion o ca ie li e ime deg ada ion. The di e ence be ween bo h me hods is shown in Figu e 8. As we can see, hese di e ences a e mo e impo an o co-i adia ion wi h low ene gy and high ene gy p o ons. Conclusion We ha e de eloped a ma hema ical model o GaAs sola cells. This model is able o p edic elec ical pe o mance deg ada ion a e p o on o elec on i adia ion o low and medium ene gies. This in o ma ic ool allows us o o e come he main disad an ages o he con en ional me hod o p edic ion, i.e. he damage coe ien me hod. Mo eo e , only wo pa ame e s a e necesa y o adjus he model o expe imen al alues, Ke and K , bo h easily measu eable in ea h lago a o ies, 1071 wi h 1 MeV elec on and 10 MeV p o ons i adia ion, o ins ance. The qbili y o he model o i expe imen al esul s o monoene ge ic pa icle luence on he e o ace AlGaAs sola cells has been p o ed. Resul s o co-i adia ion expe iences wi h se e al ene gy pa icles has been also p esen ed. The p og am can be now used o pe o m s udies o i adia ion ha dness wi h ano he AlGaAs cell ypes like g aded band gap o double he e o ace cells. Re e ences N. Taka a, K. To iyama e al., "Ene gy dependence o p o on i adia ion damage in GaAs sola cells and e ec s O combina ed adia ion on hem". 5 h Eu op. Symp. Pho Gen. in Space. 1986. pp. H.Y. Tada, J.R. Ca e J ., B.E. Anspaugh and R.G. Downing, "Sola Cell Radia ion Handbook" 3 d Edi ion, JPL Publica ion 82-69, No embe 1982. 425-433. 131 J.Y. Young, "A model o p o on damage in Silicon and GaAs sola cells". 17 h IEEE Pho . Spec. Con . 1984. pp. 1084-1087. 141 B.E. Anspaugh and R.G. Downnig , "Radia ion e ec s in Gallium A senide sola Cells using iso opic and no mally inciden adia ion". 17 h IEEE Pho . Spec. Con . 1984. pp. 23-30. 151 L. P a , E.G. o e no and L. Cas a ie , "He e o ace Gallium A senide sola cells induced deg ada ion. Analy ical model". IEEE T ans. on NUC. Sci., Vol. NS-33. 161 Yu. V. Bulgako and M.A. Kumako ,"Spa ial dis ibu ion o adia ion de ec s in ma e ials wi h beams o monoene ge ic pa icles". So ie Physics Semicond. Vol. 2 No 11. 1969. pp. 1334-137. 171 H.H. Ande sen and J.F. Ziegle , "zid ogen __- elemen s". Vol. 3. pe gamon P ess Inc. 1977. 181 S. Ma suda, M. O oda e al., "De elopemen o AlGaAs/GaAs sola cells wi h space quali ica ions". 17 h IEEE Pho . Spec. Con . 1984. pp. 97-102. No 3. 1986. pp. 1058-1065. - s 0 P pin 9 - PEK~ s_ _qn_C-__ _a ~ce s --An22