Analysis of radiation damaged and annealed gallium arsenide and indium phosphide solar cells using deep level transient spectroscopy.

Transcription

1 Calhun: The NPS Institutinal Archive Theses and Dissertatins Thesis Cllectin Analysis f radiatin damaged and annealed gallium arsenide and indium phsphide slar cells using deep level transient spectrscpy. Bruening, Jseph A. Mnterey, Califrnia. Naval Pstgraduate Schl

2

3 D»,n: pv kwx LIBRARY N/ EQUATE SCHOOL :.r GA H Mpu,

4

5

6 Apprved fr public release; distributin is unlimited. Analysis f Radiatin Damaged and Annealed Gallium Arsenide and Indium Phsphide Slar Cells Using Deep Level Transient Spectrscpy by Jseph A. 3ruening Lieutenant United States Navy B.S., The Ohi State University, 1982 Submitted in partial fulfillment f the requirements fr the degree f MASTER OF SCIENCE IN ASTRONAUTICAL ENGINEERING (SPACE SYSTEMS) frm the NAVAL POSTGRADUATE SCHOOL September 1993 ^) ii

7 [classified uriry Classificatin f this page REPORT DOCUMENTATION PAGE Reprt Security Classificatin: Unclassified lb Restrictive Markings Security Classificatin Authrity > Declassificatin/Dwngrading Schedule Perfrming Organizatin Reprt Number(s) Name f Perfrming Organizatin aval Pstgraduate Schl 6b Office Symbl 31 3 Distributin/Availability f Reprt Apprved fr public release; distributin is unlimited. 5 Mnitring Organizatin Reprt Number(s) 7a Name f Mnitring Organizatin Naval Pstgraduate Schl Address (city, slate, and ZIP cde) [nterey CA Name f Funding/Spnsring Organizatin 6b Office Symbl (if applicable) 7b Address (city, state, and ZIP cde) Mnterey CA Prcurement Instrument Identificatin Number ddre&s (city, state, and ZIP cde) 10 Surce f Funding Numbers Prgram Element N Prject N Task N Wrk Unit Accessin N Title (include security classificatin) ANALYSIS OF RADIATION DAMAGED AND ANNEALED GALLIUM ARSENIDE AND 4DIUM PHOSPHIDE SOLAR CELLS USING DEEP LEVEL TRANSIENT SPECTROSCOPY Persnal Authr(s) BRUEN1NG, Jseph, A. a Type f Reprt aster's Thesis 13b Time Cvered Frm T 1 4 Date f Reprt (year, mnth, day) 1993 September 15 Page Cunt 126 Supplementary Nutin The views expressed in this thesis are thse f the authr and d nt reflect the fficial plicy r psitin the Department f Defense r the U.S. Gvernment. Csati Cdes 18 Subject Terms (cntinue n reverse if necessary and identify by blck number) eld Grup Subgrup Radiatin damage in slar cells; DLTS; Annealing; Heterjunctin; gallium arsenide; indium phsphide Abstract (cntinue n reverse if necessary and identify by blck number) )wer lss in spacecraft slar cells due t radiatin damage was investigated. The mechanisms behind the degradatin and cvery is based n deep-level defects in the crystalline lattice structure f the slar cell. Thrugh a prcess knwn as Deep svel Transient Spectrscpy (DLTS), a crrelatin can be made between damage/recvery and trap energy f the cell. rsenide (GaAs/Ge) and Indium Phsphide (InP) slar cells were subjected t 1 MeV electrn irradiatin, t fluences f 1E16 ectrns/enr. ltinjectin annealing.»p energy level and grwth. Attempts at recvery included thermal annealing, alne, and with an applied frward bias current, and Gallium Varius cycles f irradiatin, annealing and DLTS were perfrmed, in an attempt t crrelate damage t The results shw that DLTS cannt be perfrmed n GaAs/Ge, and n recvery was apparent in these cells. DLTS Lwer energy level defects are lalysis f InP indicated excellent phtinjectin annealing recvery at a variety f temperatures. sciated with the recvery f the cells while the higher energy traps are indicative f permanent degradatin in the InP slar Us. Applying this infrmatin t future research culd increase satellite missin life, and significantly reduce space missin >sts. Distributin/Availability f Abstract "X unclassified/unlimited _ same as reprt _ DT1C users a Name f Respnsible Individual [ICHAEL, Sherif 21 Abstract Security Classificatin Unclassified 22b Telephne (include Area Cde) c Office Symbl EC/Mi ) FORM 1473,84 MAR 83 APR editin may be used until exhausted All ther editins are bslete security classificatin f this paj Unclassifie i

8 ABSTRACT Pwer lss in slar cells due t radiatin damage was investigated. The mechanisms behind the degradatin and recvery is based n deep-level defects in the crystalline lattice structure f the slar cell. Thrugh a prcess knwn as Deep Level Transient Spectrscpy (DLTS), a crrelatin can be made between damage/recvery and trap energy f the cell. Gallium Arsenide (GaAs/Ge) and Indium Phsphide (InP) slar cells were subjected t 1 MeV electrn irradiatin, t fluences f 1E16 electrns/ cm 2. Attempts at recvery included thermal annealing, alne, and with an applied frward bias current, and phtinjectin annealing. Varius cycles f irradiatin, annealing and DLTS were perfrmed, in an attempt t crrelate damage t trap energy level and grwth. The results shw that DLTS cannt be perfrmed n GaAs/Ge, and n recvery was apparent in these cells. DLTS analysis f InP indicated excellent phtinjectin annealing recvery at a variety f temperatures. Lwer energy level defects are assciated with the recvery f the cells while the higher energy traps are indicative f permanent degradatin in the InP slar cells. Applying this infrmatin t future research culd increase satellite missin life, and significantly reduce space missin csts. 111

9 ..... r.1 TABLE OF CONTENTS I INTRODUCTION 1 A. BACKGROUND 1 B. SOLAR CELL TECHNOLOGY 8 C. RESEARCH PURPOSES 9 II PHOTOVOLTAICS 12 A. PHOTOVOLTAIC EFFECT Energy Bands and Bandgap Semicnductr Dping 15 B. P-N JUNCTION 16 C. P-N JUNCTION CAPACITANCE 21 III SOLAR CELLS 24 A. THEORY OF SOLAR CELLS Cnversin Efficiency Factrs Affecting Efficiency 29 a Bandgap Energy 30 c. Temperature 30 b Recmbinatin 32 B. SOLAR CELL RADIATION DAMAGE Space Envirnment Radiatin Effects Lattice Structure Damage 36 4 Damage Equivalence 43 a. NIEL 44 C. SOLAR CELL ANNEALING 47 IV

10 .. v \J-»r\ i NAVAL POSTGRADUATE SCHOOL IV. DEEP LEVEL TRANSIENT SPECTROSCOPY 5"?" T.ER^ FS 93943^! A. DEEP-LEVEL TRANSIENT SPECTROSCOPY Defect Levels and Traps 50 B. DLTS THEORY Defect Annealing 61 V. GALLIUM ARSENIDE SOLAR CELLS 70 A. GaAs SOLAR CELL CHARACTERISTICS 70 B. EXPERIMENTAL OBJECTIVE AND PLAN 74 C. EXPERIMENTAL PROCEDURE AND RESULTS Antiphase Dmains and DLTS 89 VI INDIUM PHOSPHIDE SOLAR CELLS 94 A. InP SOLAR CELL CHARACTERISTICS 94 B. EXPERIMENTAL OBJECTIVE AND PLAN 95 C. EXPERIMENTAL PROCEDURE AND RESULTS 101 VII CONCLUSIONS AND RECOMMENDATIONS 112 REFERENCES 116 INITIAL DISTRIBUTION LIST 119

11

12 I. INTRODUCTION A. BACKGROUND The fundamental requirements fr a spacecraft pwer supply are lw cst, weight rati. lng-term pwer generatin with a high pwer-t Slar arrays are uniquely suited t meet these requirements, and the standard pwer surce fr spacecraft cntinues t be phtvltaic arrays. Fr the last thirty years, spacecraft missins have grwn mre diverse and cmplex; with a crrespnding increase in pwer requirements. Spacecraft slar arrays are specifically sized t prvide missin end-f-life (EOL) pwer requirements. The design and perfrmance f an array are thus determined by the efficiency f the slar cells that cmprise the array. Slar cells are the semicnductr devices which cnvert slar energy t electrical pwer thrugh a prcess knwn as the phtvltaic effect. The actual phtvltaic cnversin efficiency f a slar cell is limited by perating envirnment factrs, such as temperature, incident phtn energy, and radiatin damage. Array engineering design cnsideratins can effectively minimize thermal and quantum efficiency lsses. Radiatin damage t slar cells is the primary factr in determining spacecraft EOL pwer. In an effrt t ptimize their perfrmance, slar cells have been the subject f extensive research t increase their

13 efficiency, radiatin tlerance, and sustainability in the space envirnment. An earth-rbit expses spacecraft t radiatin effects that cause damage t the slar cell crystal lattice structure that reduce the cell's p-n junctin cnversin efficiency. Slid state design attempts t cmpensate fr radiatin damage have prgressed slwly. The n-n-p junctin silicn cell is mre resistant t radiatin damage than the standard p n n. As shwn in Figure 1-1, prtective cell cverglass, f varying thicknesses in cmprmise fr weight cnsideratins, prvides adequate shielding frm bmbarding prtns. Hwever, these effrts have nt extended the life f silicn slar cells t any appreciable extent. Develpment f ther III-V cmpund type cells (gallium arsenide and indium phsphide) prvided greater radiatin hardness t incident electrns. Until recently, high manufacturing csts fr these materials have discuraged large scale prductin. Current advances in the slid state electrnics industry have greatly increased the demand fr III-V materials, with a crrespnding decrease in manufacturing csts. Gallium arsenide has been discvered t have a particularly wide range f applicatins, and is rapidly becming mre ecnmically attractive. Hwever, radiatin damage t slar cells reduces their theretical cnversin efficiency (Figures 1-2 and 1-3), and what is needed is a prcess which wuld actually reverse the degradatin in the cells.

14 '» > 2 3< U r~ y*v i 1 ' 1 ' 1 1 CUftVl»*CIO«f 07 ^> "* 1 T 1 I 06 t MAXIMUM ro«ir P I n n ciacun viuci iv c i t fc * ae z c c 100 «90 * SH0RI ClOCUil CUMIN! (Itc) SHIELD THICKNESS "» "> Figure 1-1 A. 100 J 90 <? 80- i i ' ec 60 1 ' ' ' """1 '." " "T^ 1 * I >l*l «F 1 1»IH V V \ \ \ \\ >y ^Sas *»^^~^. CELLS 16. U - J*** CJ&4fn CELL 20(1 tmml - 2 < 30 $ 20 *, ^\^ - ^» N. ^^CELLSJ6rt I0mm _...J 1 1 lliul 1 A lllilll TIME AFTER LIFTOFF (DAYS) Figure 1-1 B. Figure 1-1. The prtective effect f cverglass shielding n the perfrmance parameters f Silicn slar cells. (A.) After 417 days in rbit; and (B.) Nrmalized maximum pwer cnserved by additinal shielding. The cverglass screens primarily prtn damage. [Ref 1: p ]

15 7""» U A \3 00 cd O cd «J3 hh cd cd <-, Ih cd Q 2 rs * CO?h S U <~ // 7/ T ' i c/i c a> 7> > c w re Addendum) Hanbk Radiatin u 1 9 a. -i Handbk) Radiatin el] CO -3" fe a t A E )»- <+eej E P / ** e a / / J / c / <+- ij - CO / < / *- «/ 1 a / / ii a. < >-* Cu <S CO i f\ / J / / 2 J O 6 1 /^- X^ 1 A A. i -* " 1 * O CO r-h 1-H *n *n i i» i (%) XDU3I0IJJ3 U0ISJ3AU03 I e <& c cd Figure 1-2. The degradatin f Silicn, Gallium Arsenide, and Indium Phsphide slar cells due t electrn and prtn irradiatin. [Ref 2: p. IV-9]

16 G O i <L> <L> O C <L> P E c u W > (%) XuapijjH Figure 1-3. The predicted degradatin f Silicn, Gallium Arsenide, and Indium Phsphide slar cells due t 1 MeV electrn irradiatin. [Ref 2: p. IV-34]

17 If this culd be accmplished while n rbit, the prcess wuld present the mst attractive alternative spacecraft missins lst t inadequate pwer supply. Cell damage recvery wuld extend the life f the spacecraft, decrease array design mass and size requirements, and increase paylad. The ecnmic advantages prmise great ptential fr research in this area. The ptential fr n-rbit radiatin damage recvery became apparent when an annealing prcess was fund t restre the electrical pwer generatin lss experienced when the cells were subjected t radiatin damage. The recvery was significant enugh that the end f life (EOL) f a spacecraft culd be extended well beynd present capability, and greatly reduce the size f the deplyed array. Currently, a spacecraft will experience abut a 30 percent reductin in pwer after 10 years in gesynchrnus rbit and designers crrect fr this by deplying an array that initially generates 13 percent f EOL pwer (Figure 1-4). Reducing the beginning f life (BOL) array size has extrardinary financial implicatins nt nly because excess slar cells wuld n lnger have t be purchased and assembled, but mre s frm the great savings realized in lifting less mass int rbit. Thus, with an effective pwer recvery prcess, the verall financial benefits are significant.

18 Nnrrflcclivc (black) Vilet Cnventinal 30 - u j i iii ml i i» ' mil ' 10' I0 U «I I '"I 10' i i mil 10" l-mevnuence(e-/cm? ) Figure 1-4. Maximum pwer utput f cnventinal, vilet, and nnreflective silicn slar cells as a functin f 1-MeV electrn irradiatin. [Ref 3: p. 336]

19 B. SOLAR CELL TECHNOLOGY T date, virtually all spacecraft slar arrays have been cnstructed using silicn slar cells. Many design methds have been implemented t imprve the rbital life f silicn cells: cverglass, vertical junctins, back-surface-fields, thin cells, etc. Little satisfactry imprvement has been made in extending the life f silicn arrays. The fundamental prblems f silicn technlgy are its bandgap, respnsible fr its lw cnversin efficiency, and intlerance fr radiatin. This has made deplyment f slar arrays that are ver-designed (in size and mass) the nly acceptable slutin t meeting spacecraft end-f-life pwer demands. Silicn has significant advantages in cst, demnstrated perfrmance, and simplicity [Ref. 4]. Table 1-1 indicates the cmparative advantages f the mst prmising materials fr replacing silicn as the predminant slar cell substrate. TABLE 1-1 ELECTRICAL PROPERTIES OF COMMON PHOTOVOLTAIC MATERIALS Slar Cell Bandgap Eg (ev) Efficiency BOL ( %) Specific Pwer BOL (W/kg) Annealing Temp ( C) 25 C 60 C 2 5 C 60 C Nte (1) Silicn GaAs InP (1) Minimum demnstrated temperatures fr recvery with n minrity carrier injectin.

20 Gallium arsenide has recently been fund t have many applicatins in the micr-electrnics industry and is expected t replace silicn in many areas. The cst f gallium arsenide has drpped t a level where it is becming cmpetitive with silicn fr space slar array applicatins. Nt nly are gallium arsenide slar cells mre radiatin tlerant than silicn, it has a higher cnversin efficiency, and a lwer thermal annealing temperature. The mst attractive parameters in a spacecraft slar cell, ther than lw cst, are radiatin tlerance and high phtelectric cnversin efficiency. Minimizing the deplyed mass f the slar array is als a critical issue due t the high launch csts assciated with getting the spacecraft int rbit. Launch csts are generally measured in thusands f dllars per kilgram, but fail t include the additinal expenses f array assembly, array stwed size, and additinal attitude cntrl fuel t suppress the dynamic respnse f the deplyed array. C. RESEARCH PURPOSES This research is seeks t investigate the slid state mechanisms invlving the lattice structure degradatin and recvery f gallium arsenide (GaAs) and indium phsphide (InP) slar cells thrugh the use f Deep Level Transient Spectrscpy (DLTS). Preliminary investigatin int the feasibility f annealing electrn-damaged slar cells has been widely accepted fr several years. Research has established

21 that after irradiatin at a fluence level f between 1E14 and 1E15 el/cm 2, the effects f damage caused by trapped electrns was reversed in GaAs and InP slar cells. Previus research cnducted single annealing experiments t determine the ptimum mechanism fr recvery f radiatindamaged GaAs cells. Cypranwski [Ref. 5] cntinued the research fr InP cells as well as investigating multiple cycles f radiatin and annealing n GaAs and InP cells. Pinzn [Ref. 6] explred the frward biased current and heat annealing f GaAs and InP cells that have been electrn damaged by lking int the lattice structure, via DLTS, t determine the mechanisms that affect the damage and annealing prcess. The purpse f this investigatin was t reprduce the research f Cypranwski and Pinzn, in an effrt t determine the ptimum parameters fr annealing gallium arsenide and indium phsphide slar cells. Beginning with Chapter II, fundamentals f semicnductr thery and the phtvltaic effect are intrduced. This infrmatin prvides a fundatin n which the thesis is based. Other imprtant cncepts such as p-n junctin and carrier transprt are als discussed. Chapter III deals with radiatin effects n slar cells, the envirnment in which the cells must perate and utlines previus annealing research. Chapter IV cntinues t explain the mechanisms behind damage and recvery thrugh a discussin f deep level transient spectrscpy and its relatinship t slar cell measurement 10

22 parameters. The experiment is discussed in detail fr GaAs in Chapter V, and InP in Chapter VI, with cnclusins and recmmendatins fllwing in Chapter VII. 11

23 II. PHOTOVOLTAICS A. PHOTOVOLTAIC EFFECT T understand hw a slar cell cnverts light energy t electricity, it helpful t first cnsider the effect f putting a great many atms clse tgether in a slid. The behavir f the bulk material can be regarded as a cumulative effect f what is ccurring in the individual atms. In a slar cell incident light phtns cllide with atmic electrns, lsing energy with each cllisin. The electrns that gain sufficient energy frm these cllisins can change t a higher energy band. 1. Energy Bands and Band Gap In slids the ptential energy experienced by a valence electrn is discretely quantized as a functin f its psitin in the atmic lattice. When atms are brught clse enugh tgether that their wave functins verlap, the energy level f each system splits int tw distinct energy levels (Figure 2-1), and the splitting increases as the separatin between atms decreases. Crystallgraphic symmetry effects frce the energy levels f the atm t frm tw majr energy bands, the valance band and the cnductr band; each ne with its wn distinct levels f permissible electrn energy. Figure 2-2 represents the energy band bending caused by equilibrium f Fermi levels acrss the junctin. 12

24 >- ac us 2 2 O CB- p-type n-type CB UJ DISTANCE Figure 2-1. Schematic f a p-n junctin immediately after frmatin. [Ref. 8: p. 138] ELECTRON ENERGY Figure 2-2. Schematic f a p-n junctin at equilibrium, [Ref. 8: p. 141] 13

25 Semicnductrs are cvalent slids that may be regarded as "insulatrs" because the valence band is cmpletely full and the cnductin band is empty f electrns at 0 K. Thus, at 0 K, a semicnductr has n delcalized electrns; all electrns are bund t individual atms, leaving nne available t carry current. Separating the tw energy bands is a gap f frbidden energy levels, better knwn as the bandgap (E g ). In rder fr an electrn t escape the valence band and crss the band gap int the cnductin band t carry current, it must absrb enugh energy t raise its energy level t that f the cnductin band. It must absrb enugh energy t jump the bandgap. The energy gap (band gap) fr semicnductr devices ranges frm t 2.5 ev. In situatins where all the levels f an islated band are filled except fr thse near the very tp, the dnr level, it is cnvenient t think in terms f hles representing the absence f electrns in an therwise cmpletely filled band. Since the absence f a negatively charged electrn is equivalent t the presence f a psitive charge, hles behave as if they are psitively charged. Once electrns crss the gap t the cnductin band, they mve freely and thereby carry current. Each electrnic excitatin int the cnductin band leaves behind a hle in the valence band. These hles, acting as psitive charge carriers, als 14

26 cntribute t the cnductivity. The net result is that current carried thrugh the semicnductr. 2. Semicnductr Dping Semicnductrs are distinguishable frm insulatrs by the fact that the bandgap energy is small (0 <E g < 2.5eV). A narrw bandgap allws electrical cnductin with small inputs f energy. The cnductivity f semicnductrs arising frm thermal excitatin as called intrinsic cnductivity. Anther way t enhance cnductivity is phtexcitatin in semicnductrs with a bandgap equivalent t the energy f incident phtns, als knwn as phtcnductin. Extrinsic semicnductrs lwer the bandgap energy margin by the intrductin f impurity atms r dpants int the semicnductr. If a dnr atm is intrduced int the crystal lattice (an atm with an excess f ne valence electrn), then little energy is required t bst the extra electrn t the cnductin band. If an acceptr atm is intrduced (an atm with fewer valence electrns than the hst lattice, causing excess hles) then little energy is required t mve electrns in the valence band t the hle site. The net effect is less energy required fr cnductin. Therefre, a semicnductr's electrical prperties can be imprved by adding impurities t the material. Figure 2-3 is a representatin f what happens t the bandgap when impurities, either dnr r acceptr are intrduced. Nte that the quantum state f the excess electrn is lcated slightly belw 15

27 the cnductin band while the energy level assciated with a hle is lcated just abve the valance band. Dping a semicnductr with either impurity dnr (excess valence electrns) r acceptr (deficient valence electrns) atms classifies the material nw as either n-type r p-type, respectively. When these tw types f material are placed in cntact with each ther, a p-n junctin frms. B. P-N JUNCTION P-n junctin semicnductrs (Si, GaAs, InP) have a regin dped t different cnductivity levels. At the junctin there is a change frm n- t p-type material ver a regin f space. The structure shwn in Figure 2-3 is an ideal abrupt junctin in which the transitin takes place suddenly. Hwever, the graded, r diffused, junctin is mre characteristic f real junctins. The degree f grading depends n the fabricatin prcess. The GaAs/Ge samples studied in this thesis were fabricated by metal-rganic chemical vapr depsitin (MOCVD) which can prduce an almst perfectly abrupt junctin. The Indium Phsphide samples used were thermally diffused and can be expected t have a less distinct transitin at the junctin. The fllwing discussin will cnsider an n*p junctin which the n-side is much mre heavily dped than the p-side (i.e. N D >> N A ), since this is the cnfiguratin f the Indium Phsphide samples that were mre extensively investigated. 16

28 Electrn energy Cnductin band Cnductin band End f rd p regin I Junctin I regin i n regin End f rd Unbiased electrn current Reverse biased current Frward biased current Thermal Recmbinatin Thermal Recmbinatin Thermal Recmbinatin Figure 2-3. Electrn energy -level diagram fr an unbiased p-n junctin. [Ref 9: p. 387] 17

29 When n- and p-type semicnductrs cme int cntact, a nn-equilibrium charge state exists. There will initially be an excess f electrns in the n-side relative t the p-side and an excess f hles in the p-side relative t the n-side. Charge cncentratin gradients acrss the junctin cause diffusin t ccur. Electrns will diffuse acrss the junctin int the p-side and hles will diffuse int the n- side. A regin in the p-side, near the junctin, thus becmes deficient in free hles. Similarly, diffusin f electrns frm the n-side f the junctin leads t a lss f electrns. The p-side, therefre, has an excess f negatively charged inized acceptr centers, and the n-side has an excess f psitively charged inized dnrs. Since these inized atms are at a fixed psitin in the lattice, a regin f psitive space charge (with cncentratin N D ) is created in the n-side near the junctin and ne f negative space charge (with cncentratin N A ) is created n the p-side. This gives rise t a layer depleted in carriers, which is knwn as a depletin layer. The width f the depletin layer (W) is given by 2 e V(N A + N D ) w = (2.1) qn A N D where V is the ptential difference acrss the junctin, q is the electrnic charge, and is the permittivity f the junctin material [Ref. 8]. The magnitude f the ptential barrier depends upn the width f the frbidden-energy gap, 18

30 the impurity cncentratin f dpant, and the temperature. Equatins 2.2, and 2.3 give the depletin widths (xnp f each ) side f the junctin (i.e. W = x p + x n ). Fr the n*p junctin, since N D >> N A, ne can see that the width will be mstly cmprised f the p-material. V ^s *n - N A N a + N D W (2.2) xv K p - N D N a + N D W (2.3) The creatin f the tw space charge regins f ppsite sign establishes a built-in electric field. The resultant electric field is directed frm the n-side t the p-side. The frce exerted by this field ppses the further diffusin f carriers and, in this way, the develpment f this field brings abut a cnditin f equilibrium in the junctin. The built-in electric field depends directly n the dping levels present in the junctin (the higher the dping levels are, the higher the electric field is). This effect can lead t junctin breakdwn if the cncentratins are high enugh. The dping levels which we will cnsider («I0 17 cm' 3 n the p- side and «10 18 cm" 3 n the n-side) prduce electric fields f the rder f 10 7 V/m. Charge cncentratin gradients lead t variatins in electric field causing the field t be nnunifrm ver junctin width. Electric fields f this strength 19

31 can ften mask the electrnic prperties f the junctin, particularly when measuring the junctin capacitance. The initial electrn cncentratin gradient acrss the junctin induces a diffusin current frm the n + int the p- regin. This diffusin results in the inizatin f a regin f dpant atms abut the junctin which cnstitutes a fixed space charge. The space charge creates an electric field in ppsitin t the diffusin current. The end result is an equilibrium situatin where the current induced by the electric field f the inized dpant atms balances the diffusin current, and a ptential gradient exists acrss the junctin increasing frm the p int the n + regin. The magnitude f this ptential difference is referred t as the built in vltage- V bi. This ptential creates an energy barrier against charge migratin. As a result f the energy barrier created by V bi, a prtin f the dide near the junctin is depleted f free charge carriers and is referred t as the depletin regin. The depletin regin may be visualized as a parallel plate capacitr. The ptential barrier ppses the crssing f majrity charge carriers but minrity carriers are nt hindered frm crssing. Minrity carriers are in fact driven by the field t the ppsite side f the junctin. Thus, when a lightgenerated electrn-hle pair is frmed, the electrn is driven t the n-type side, and the hle is driven t the p-type side. 20

32 Once the electrns are h the n-type side and the hles are n the p-type side, they can mve arund withut being prevented by the recmbinatin prcess frm reaching the surface cntacts f the cell. Since a charge imbalance nw exists in the cell, current can flw thrugh a cnnected external circuit. C. P-N JUNCTION CAPACITANCE The p-n junctin is a duble layer f ppsitely charge carriers separated by a small distance (the depletin regin) and thus has the prperties similar t a parallel plate capacitr. The junctin capacitance can be expressed using the simple parallel-plate capacitr equatin (since there are n free charge carriers in the depletin layer f the junctin) and is given by A C = (2.4) W where A is the area f the junctin in the slar cell, e is the permittivity f the cell (e = Ke where K is the dielectric cnstant f the cell), and W is the width f the depletin regin. The acceptr r dnr density in the p-type r n-type regin adjacent t the depletin regin can be related t the capacitance per unit area by r <3 en 1/2 I (2.5) 2(V b - V.) 21

33 r 2(V b - V a )C 2 N = ; (2.6) qea 2 where N is the smaller value f acceptr density N A r dnr density N B, and V a is the applied vltage (psitive fr frward bias), and V b is barrier vltage. Using N a assumes heavily dped n-regin while N assumes heavily dped p-regin. Equatin (2.6) illustrates that the capacitance varies with the applied vltage. Therefre, measuring C as a functin f reverse bias t a slar cell and pltting 1/C 2 versus V a will allw N, the dping density n the lightly dped side f the cell t be fund. These expressins assume an abrupt junctin which is characteristic f cnventinal slar cells. When an external vltage is applied, equatin (2.4) is mdified t becme W 2 = 2 e(v bi - V) (2.7) q n a where V b j is the built-in (diffusin) ptential, V is an applied bias ptential (negative fr reverse bias) acrss the junctin, e is the dielectric cnstant f the junctin, q is the electrnic charge, and N A is the dping level f the p- material. This gives rise t the junctin capacitance q c N A A 2 c 2 m (2.8) 2 (V bi - V) 22

34 In summary, a reverse bias will increase the depletin width and s decrease the capacitance. The effect f an applied bias vltage n the depletin regin's capacitive prperties is critical in the study f slar cells, and their phtelectric cnversin behavir. 23

35 III. SOLAR CELLS A. THEORY OF SOLAR CELLS When a slar cell is illuminated, the phtn energy is either absrbed, transmitted, r reflected. Absrbed phtns that d nt have sufficient energy t frm electrn-hle pairs simply cntribute t lattice phnn energy as heat. Electrnhle pair frmatin requires phtns with a minimum threshld energy. Due t the narrw range f phtn energies acceptable fr phtcnductin, mst sunlight that strikes the cell is lst befre it can be cnverted t electricity. Sme phtns d result in electrn-hle pairs, but if n electric field is present, the electrns will eventually recmbine with the hles. The net effect f the absrptin prcess being nthing mre than a heating up f the semicnductr. The slar cell p-n junctin intrduces an internal electric field which separates and cllects the electrn-hle pairs befre they recmbine. A charge field is created which sets up a barrier fr further net charge mvement. In ther wrds, the barrier prevents ther free charges frm migrating acrss the junctin. This barrier knwn as the ptential barrier r depletin regin, plays an imprtant rle in the generatin f electricity. As electrn hle pairs becme available, the ptential barrier separates them, frcing electrns frm the p-regin where they are called minrity 24

36 carriers t the n-regin where they are knwn as majrity carriers. Light incident n the cell creates electrn-hle pairs, which are separated by the ptential barrier, creating a vltage that drives a current thrugh an external circuit. The hles transprt frm the n-regin t the p-regin. An electrn in the n-regin is called a majrity carrier and a hle in the n-regin is called minrity carrier. Fr the p- regin, the ppsite is true (hles are majrity carriers and electrns are minrity carriers). It is the minrity carrier which must pass thrugh the barrier. Since there are fewer carriers f ppsite charge t recmbine with, the minrity carrier, has a high prbability f reaching the respective regin surface. The net result is a vltage difference between either end f the cell. The high number f available pairs at the slar cell junctin will generate a current flw. 1. Cnversin Efficiency In rder fr a phtn t be f significant use in the cnversin prcess, it must have transfer sufficient energy t an electrn in rder fr the electrn t breach the bandgap. A phtn cllisin transfer f energy slightly greater than the bandgap is preferred, t ensure the transitin f the electrn t the cnductin band. Since, in space, the energy spectrum f sunlight is fixed, the phtvltaic material must be selected with an ptimum bandgap. Figure 3-1 illustrates the relative bandgaps f varius materials. 25

37 c fs > 0> O0 - s - TT K v in ^t &> h ^ (j.uih^d^s^.uid ^ix) xn j ujqj m Figure 3-1. Energy density vs. ptimum wavelength fr varius semicnductr materials. The curves are the nminal slar energy spectrum available at Earth rbit. [Ref 10: p. 213] 26

38 . The maximum efficiency bandgap fr space slar cells (Air Mass Zer) is abut 1.4 ev, at rm temperature (300 K) The bandgaps f silicn (1.12 ev), and indium phsphide (1.35 ev), are belw this theretical threshld, and gallium arsenide (1.42 ev) has a significant advantage. The parameters that characterize the perfrmance f a p-n junctin slar cell are: pen circuit vltage shrt circuit current V^ I sc fill factr FF The efficiency f a cell is the rati f the cell's maximum utput pwer t the pwer incident n the cell frm radiant energy. The theretical maximum pwer P T f a cell is Pt = V c I sc (3.1) With the cnversin lsses mentined abve the maximum practical (P m ) pwer is smewhat less than P. t The I-V curve f Figure 3-2 shws the maximum utput pwer (P m ), ccurs fr zer series resistance, and infinite shunt resistance. Anther slar cell parameter is the Fill Factr (FF) and is defined as: Pm Pm FF = = (3.2) Vc Isc Pt Fr rbiting spacecraft, at air mass zer (AMO) cnditins, sunlight nminal incident pwer is 1.36 Kw/m 2. 27

39 e -06 ^i ^ > V (VOLTS) "l re- Figure 3-2. Theretical current-vltage (I-V) characteristics fr slar cells that includ series and shunt resistances. Inset shws the equivalent circuit. [Ref. 8:p. 243] 28

40 Slar cell efficiency can be calculated as Pm V^ I sc FF EFF = = (3.3) ^incident Sunlight Incident Pwer In rder t achieve high cnversin efficiency, the requirements are high V^, I sc, and FF (sharp crner in the I-V curve). Energy cnversin efficiencies f standard slar cells range between 12 and 20 percent, due primarily t limited material absrbtivity. In the slar spectrum, 26 percent f the energy is in phtns having phtn energy f less than 1.1 ev (bandgap fr silicn). Frm Figure 3-1, it can als be seen that apprximately 4 percent f the energy is in phtns having phtn energy less than 1.45 ev (bandgap fr GaAs). Of the remaining 60 percent (thse phtns with energy greater than 1.45 ev), any energy greater than the 1.45 ev required t generate an electrn-hle pair is absrbed by the atmic structure and prduces heat in the frm f atmic vibratins. Thus, apprximately 25 percent f the energy in these phtns is wasted. Slar cell efficiency f 15 t 18 percent fr standard GaAs is typical. 2. Factrs Affecting Efficiency The upper limits f slar cell efficiency are bund by several factrs. Radiant energy passing thrugh the cell, as well as reflectin, prduce n effect in the phtvltaic cnversin prcess. Sunlight is nt mnchrmatic, much f the radiant energy absrbed prduces heat. The remaining 29

41 energy causes the electrn-hle pairs t generate current. The factrs affecting the prductin f electrn-hle pairs t generate current are discussed. Althugh sme f the factrs are inherent t the cell, imprvement is achieved thrugh gd design and material selectin, a. Bandgap Energy As nted earlier, the smaller the bandgap f the cell, the greater the number f available phtns there are with enugh energy t create electrn-hle pairs. Hwever, shuld the bandgap be t small, mst f the radiant energy wuld be wasted as heat. The mst desirable range fr the bandgap wuld be the range that matched the peak f the slar spectrum. Silicn's bandgap energy is 1.1 ev while GaAs and InP are 1.42 and 1.35 Ev respectively. Nte frm Figure 3-1 that Gallium Arsenide's bandgap almst cincides with the peak phtn bandgap assciated with the slar spectrum. b. Temperature Figure 3-3 shws hw slar cell efficiency decreases with increasing temperature, despite the fact that cnductivity in semicnductrs characteristically increases with increasing temperature. Tw predminant factrs cause efficiency t drp as temperature rises (as intrinsic cnductivity increases) : 1) lattice vibratin phnn energy cntributes t randm electrn energy levels, interfering with charge carrier migratin; and 2) the junctin electric field becmes less effective in separating pair charges. [Ref. 12] 30

42 r, ^, 1, ^ r t i ' 1 U ^ S3 >H CO w r* / in 1 si L g d ^ /, - «2 & PI - W P > rature MOC * S ^ At ) /^ / g >> fcu t 4-1 H *> O d > 4 u - j - i i. i II d M < 1 t c < On v t m H -t i _ cn «^ O - > OS d 00 d d d d t d d d OX) 4-1 D u (VU1) Jtl9JJtl3 H93 Figure3-3. The effect f perating temperature n the cnversin perfrmance f an InP slar cell. [Ref. 11: p. 43] 31

43 The first factr degrades perfrmance even at rm temperature. As temperature increases, the secnd phenmenn is predminant in reducing the electric field gradient at the p-n junctin. At higher temperatures, as many electrns are freed frm their bnds. These electrns utnumber the free electrns supplied by dpants. Als created are electrn-hle pairs, frmed by the thermal excitatin. The n-type material begins t lse its n-type characteristics. The same prcess ccurs n the p-type side which lses its p-type characteristics. The effect is 1) the thermally excited charge carriers have sufficient energy t freely crss ver the p-n junctin in bth directins as if the barrier field were nt there, and 2) ultimately, the depletin regin disappears because there are n lnger n- and p-type sides t create the barrier. These lsses in junctin efficiency eventually lead t a cmplete failure f the phtelectric effect. [Ref. 12] Thermal effect degradatin can be reduced by selecting a larger bandgap, t prvide a wider respnse t variatins at the depletin regin. Thus, GaAs cells are nly abut half as sensitive t increasing temperature as silicn cells. [Ref. 9] c. Recmbinatin The phtn generated electrn-hle pairs can randmly recmbine befre they cntribute t current generatin. Recmbinatin ccurs by either direct r indirect 32

44 . methds. Direct recmbinatin ccurs when an electrn and a hle randmly encunter each ther. The electrn rebinds with an atm when it encunters a hle, emitting energy as heat. Randm recmbinatin generally ccurs befre the electrn has time t crss the depletin barrier. Once acrss, direct recmbinatin is rare. Recmbinatin can als ccur when a free charge carrier has a cllisin, reducing its energy and increasing the prbability that it will fall int a bnd. Indirect recmbinatin ccurs when an electrn-hle recmbinatin is encuraged by ther influences, such as empty, r dangling bnds present frm impurities r defects (traps) which capture the free electrns. This is the predminant mechanism assciated with radiatin degradatin in slar cells, since radiatin intrduces defects int the crystalline lattice, and thus increases the pprtunity fr recmbinatin C. SOLAR CELL RADIATION DAMAGE 1. Space Envirnment A spacecraft in the earth's rbital envirnment is cnstantly expsed t magnetically-trapped electrns and prtns, slar-flare prtns, and csmic rays. The cumulative effect is a dynamic envirnment causing degradatin f slar cell efficiency n-rbit. In lwer earth-rbits, bth gemagnetically trapped electrns and prtns play significant rles in cell damage. At higher altitudes (near gesynchrnus rbit) the high energy trapped electrns are 33

45 the primary cause f damage, except during perids f high slar activity, when slar flare prtns add significantly t the ttal cell-damaging effect. The effect variatins in trapped radiatin at different rbital altitudes can be seen in Figure 3-4. The use f slar cell cverglass effectively screens ut mst prtns (Figure 1-1), and trapped electrns are the principle cause f slar cell degradatin in the space envirnment. 2. Radiatin Effects The perfrmance f slar cells is represented in terms f engineering utput parameters. The effect f radiatin n the cells can then be described in terms f changes in these perfrmance parameters. These parameters deal with bth the physical and electrical characteristics f the cell and give insight int the mechanisms invlved. Dpant impurity cncentratins, recmbinatin, diffusin lengths and minrity carrier lifetimes are the physical aspects f cell behavir while the electrical parameters include shrt circuit current (I sc ), pen circuit vltage (V^) and pwer utput (P). The damage phenmena can be categrized by tw majr types f radiatin damage: inizatin and atmic displacement. Inizatin ccurs mainly in the slar cell cver glass. There is a reductin f transmittance f the cver glass due t its darkening. When inizing radiatin excites an rbital electrn t the cnductin band, the electrn may becme 34

46 » V ih C/5 rh F 1^ <4H w a> ^H <+H O 1 CO VH T3 T3 C C W ctf T3 CO i-h 3 <4H u ^ 00 ^ * 5 «xj < O ^6 *E) *n m (%) XDU9I0IJJ3 U0ISJ9AU03 Figure 3-4. The effect f rbital altitude radiatin expsure) n spacecraft slar cells. [Ref. 11: p. 31] (cumulative 35

47 trapped by impurity atms in the glass, frming clr centers. The subsequent result is a darkening f the cell cver glass, which reduces the illuminizatin f the cell. Inizing radiatin will als excite the electrns in the cell frm the valance band t the cnductin band, creating electrn-hle pairs similar t the phtvltaic prcess. This is the beneficial effect f inizatin. Hwever, much greater energy is required frm the inizing radiatin than frm the slar phtn t create the same number f charge pairs. The interactin with the inizing radiatin and the atmic electrn is inelastic; therefre, the electrn experiences a transitin t an excited state. If the energy transfer between the tw is nt sufficient t mve the electrn t the cnductin band, the effect will be temprary. The electrn will eventually recmbine with a hle, lsing its energy as heat. The net effect wuld be an increase in temperature. 3. Lattice Structure Damage Cnsiderable lattice damage takes place as radiative particles strike a slar cell. This damage is usually in the frm f crystal defects (vacancies, interstitials, vacancyimpurity cmplexes, defect clusters). The creatin f these defects in the crystal lattice intrduces additinal energy states which are fund in the band gap. The defects then can act as additinal recmbinatin centers, causing a reductin in minrity carrier lifetime and diffusin length; r they can 36

48 . act as additinal impurities, changing the net impurity cncentratin f the cell. In either case, the damage results in a deteriratin n the cell's perfrmance ver time. Figure 3-6 shws the effect f several types f radiatin n a single defect type. High energetic, fast mving particles are capable f causing atmic displacements within the crystal lattice structure f slar cells. These displaced atms and their assciated vacancies will eventually frm permanent stable defects within the crystal lattice. These defects prduce the significant changes within the cell which affect the equilibrium carrier cncentratins and the minrity carrier lifetime and subsequently cell efficiency. The displacement energy required t eject an atm frm its lattice site is n the rder f 13 ev fr silicn and 25 ev fr GaAs. Because the displacement f an atm invlves the frmatin f a vacancy, the frmatin f an interstitial atm and ther electrnic and vibratinal lsses, the displacement energy can be expected t be much higher than the energy f frmatin fr a vacancy. [Ref. 12] The principal effect f radiatin damage is the damage caused t the crystal lattice. Radiatin induced displacement defects create additinal recmbinatin centers causing a reductin in minrity carrier diffusin length (minrity carrier lifetime) 37

49 tduibiihtt' I Figure 3-5. The effect f 1 MeV electrn radiatin expsure n the current-vltage (I-V) curve fr Gallium Arsenide (GaAs/Ge). Pst-Rad curve resulted frm a single expsure t a fluence f 1E15. 38

50 +-> c 2 Lj 3 O <U 00 u In CO \ tns C/3\ CA u *\ a, \ M > \ v " Oh > s *-H \. s \ cr> i CN t CM 8V > CO c O tu ^-i O N.g M electrns V \ S \ D " W) D W c N a a s c G O Q CO» > CN (i-iu) 9}Q}{ uipnpjiuj lspij f7h O CM Figure 3-6. The effect f displacement damage in InP caused by different energies f incident radiatin. The damage is measured by the grwth rate f a single type f defect (the trapping center knwn as H4). [Ref. ll:p. 45] 39

51 The diffusin length can be measured experimentally. It is a measure f the amunt f displacement damage in the base f the slar cell. Limitatins d exist. Lw energy prtns d cnsiderable displacement damage within the junctin depletin regin withut changing the cell's diffusin length, but seriusly reducing slar cell I sc and V^. In additin, the relatinship between diffusin length and I sc and VK are nt well defined, and diffusin length is mre difficult t measure than I sc r V c. Therefre, t better evaluate the mechanism, radiatin effects are expressed in terms f the electrical pwer generatin parameters, rather than slid state effects. Radiatin will cause significant degradatin in base resistivity, shrt circuit current (I sc ), pen circuit vltage (V c ) and subsequently the maximum pwer pint (Pma X ). The degradatin in I sc and V c will result in a decreased I-V curve as shwn in Figure 3-5. The maximum pwer (Pma X ) is fund using equatin: P max = (FF) I sc V c. The fill factr is relatively unaffected by electrn radiatin. The reductin in slar cell spectral respnse due t radiatin induced defects is shwn in Figure 3-7. The direct result f electrn displacement damage, which is f primary interest t this research, is the creatin f vacancies and interstitials. Once an interactin ccurs, the radiative particle may have sufficient energy t prduce 40

52 4 *» ' i 1 > CD 00 S-. CO XJ i i u (D (D ( -i_) c u CO * CJ c CO (X (0 C «T> a (0 + J-< c: L, a C CO c L-, i -4-J u d (D.. CJ U-H U a CD O i 7^^ /> /w "X > - DO \\\ c -l-j (0 *-( 0) O \\\ 1m l* W +-> ^ Cm N a 1 E CM * < 1E U in 1 2 * b r < X ^ II XI X ^ II CO ~^ u II S- - * 3- CD CO 0) > pn CD > CD S II S O O CO E c x: r^ c <p CO > c0 m CD j * > ZO C tt c c c Xuaiijj3 inrqu^nfr i^ujq^u] 03 Figure 3-7. The effect f radiatin induced defects n the spectral respnse f an InP slar cell. The 1 MeV fluences shwn are rutinely encuntered by spacecraft in Earth rbit. [Ref. ll:p. 33] 41

53 secndary displacements within the crystal. Therefre, the distributin f vacancies will nt be unifrm because the vacancies frm secndary displacements will be relatively clse t the assciated primary vacancy. The interstitials, n the ther hand, will mve randmly thrughut the crystal until it lses its energy and cmes t rest in the interstices f the atm. It therefre seems reasnable that the interstitials will have a mre unifrm distributin within the crystal. Vacancies and interstitials are extremely mbile and unstable at rm temperature. Displacement damage is caused by the varius cmbinatins available t a vacancy within the crystal. A vacancy can cmbine with anther atm such as impurity atms frming clse cupled vacancy-xygen pairs, vacancy dnr pairs, r vacancy-acceptr pairs. In the case f vacancy-xygen and vacancy-dnr pairs, the defects are electrically active and can becme negatively charged by accepting an electrn frm the cnductin band. The energy levels f these defects are slightly belw the cnductin band. Fr vacancy-acceptr pairs, the defects can becme psitively charged by accepting a hle frm the valance band (giving up an electrn t the valance band). The energy level f this defect is slightly abve the valance band. If a vacancy cmbines with an interstitial, the damage is functinally eliminated. The cmbinatin returns the 42

54 crystal t its riginal lattice structure frmatin. This wuld be the ideal cnditin fr irradiated cells. The majr effect these defects have is the frmatin f additinal recmbinatin centers which affect the lifetime and diffusin lengths in the cell. The diffusin cnstant (D) is significant because it relates the mean distance that a minrity carrier travels befre recmbinatin, r diffusin length (L), and the mean time f recmbinatin (T), r minrity carrier lifetime by the expressin L 2 = DT (3.4) The cncept f diffusin length is used t describe the thery f peratin f semicnductrs and t calculate the effect f radiatin. As will be discussed later, the effects f radiatin n slar cell perfrmance is due t the change in minrity carrier lifetime which decreases the diffusin length. 4. Damage Equivalence The energies assciated with electrns and prtns within the space envirnment vary ver a wide range. In rder t evaluate the effects f radiatin damage in slar cells, it is necessary t describe the varius types f radiatin in terms f an envirnment that can be reprduced under labratry cnditins. The cncept f damage equivalence is, therefre, based n the 1 MeV electrn fluence fr slar cell degradatin. The damage prduced in slar cells by electrns f varius energies is related t the damage prduced, under 43

55 . labratry cnditins, by 1 MeV electrn by the damage cefficients <p c = critical fluence, and K L = diffusin length damage cefficient. Similarly, the damage prduced by prtns f varius energies is standardized t 10 MeV prtns which have the apprximately same penetratin range in silicn as 1 MeV electrns. It is thus pssible t cnstruct a mdel in which the varius surce cmpnents f a radiatin envirnment can be described in terms f an equivalent fluence. a. NIEL The many variables invlved when measuring radiatin damage t materials result in wide variatins in predicting specific perfrmance degradatin. A preferred methd f mdeling radiatin damage is that f Nninizing Energy Lss (NIEL) NIEL is the amunt f energy a primary knckn atm can impart int displacements. The rati f the NIEL fr 3 MeV prtns t 1 MeV electrns in InP is abut 750. This agrees with the rati f the H4 defect intrductin rates, suggesting a linear dependency f displacement damage n NIEL fr p-type InP. The effect f irradiatin in prtn and electrn envirnments is usually discussed in terms f an equivalent 1 MeV fluence. This equivalent fluence is determined by first reducing the prtn spectrum t an equivalent 10 MeV prtn fluence, which is then reduced t an equivalent 1 MeV electrn fluence by a damage equivalency factr. The measured equivalency factr fr p-type Si is abut 3500, and abut 1000 fr GaAs. Frm the present results, the equivalency factr fr p-type InP is expected t be equal t the rati f the NIEL fr 10 MeV prtns t 1 MeV electrns, which is abut 300. [Ref. 2:p. 50] The effect f nninizing energy lss fr varius energy ranges f incident radiatin is shwn in Figure 3-8 fr silicn, and in Figure 3-9 fr InP. 44

56 (3/ iu-a9>0 r iain Figure 3-8. The calculated energy dependence f the nninizing energy lss (NEIL) fr prtns and electrns in Silicn. [Ref. 2:p. 39] 45

57 Oh U U-i CO CO O - J - &U V a W bfi G ih N i-h c ih c fc T) <D <*) cj 1 < EJ O 3 i < U JJ_l_li - - c:> C/5 e (3/zUi-A*J0 sst ASiaua SuiziutuM > V D G w p Oh Figure 3-9. The calculated energy dependence f the nninizing energy lss (NIEL) fr prtns and electrns in Indium Phsphide. [Ref. 2:p. 50] 46

58 C. SOLAR CELL ANNEALING Lattice damage and assciated electrical degradatin f radiatin-damaged slar cells can, t sme extent, be reversed. This is dne by thermal and/r electrical defect annealing a prcess by which heat and/r current is intrduced t the cell, causing the energy level f the cell t increase. The recvery is due t atmic mvement within the crystal causing the lattice structure t return t its riginal cnditin. Althugh the crystal is nt 100% restred, the annealing prcess achieves sufficient recvery t extend the life f the cell's usefulness (Figure 3-10). This is accmplished via : 1) recmbinatin f crystal vacancies and interstitials are effected, creating fewer atmic dislcatins and 2) the rearrangement f dislcatins t a lwer energy cnfiguratin withut changing in the actual number f dislcatins present. Bth prcesses prvide a mre stable crystal with a partial eliminatin f the radiatin induced lattice defects and a decrease in recmbinatin centers within the depletin regin. Increasing the temperature f the bulk slar cell thrugh the additin f heat is knwn as thermal annealing. It is the mst cmmn methd f defect annealing. The energy level increase is a functin f annealing temperature. Research cnducted by L, et al [Ref. 17], shws that peridic thermal annealing at temperatures as lw as 200 C cnsiderably reduces the radiatin damage t GaAs cells. 47