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

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 techniques Pinzn, Dimas, Jr. Mnterey, Califrnia. Naval Pstgraduate Schl

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6 NAVAL POSTGRADUATE SCHOOL Mnterey, Califrnia THESiS ANALYSIS OF RADIATION DAMAGED AND ANNEALED GALLIUM ARSENIDE AND INDIUM PHOSPHIDE SOLAR CELLS USING DEEP LEVEL TRANSIENT SPECTROSCOPY TECHNIQUES by Dimas Pinzn, Jr. March 1991 Thesis Advisr: Sherif Michael Apprved fr public release; distributin is unlimited T254616

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8 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE la 2a REPORT SECURITY CLASSIFICATION UNCLASSIFIED 2b SECURITY CLASSIFICATION AUTHORITY DECLASSIFICATION /DOWNGRADING SCHEDULE REPORT DOCUMENTATION PAGE lb RESTRICTIVE MARKINGS 3 DISTRIBUTION /AVAILABILITY OF REPORT Apprved fr public release; distributin is unlimited 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S) Frm Apprved 0MB N a. NAME OF PERFORMING ORGANIZATION Naval Pstgraduate Sch 6b OFFICE SYMBOL (If applicable) EC 7a. NAME OF MONITORING ORGANIZATION Naval Pstgraduate Schl 6c. ADDRESS {City, State, arxi ZIP Cde) 7b ADDRESS (Oty, State, and ZIP Cde) Mnterey, CA Mnterey, CA a NAME OF FUNDING /SPONSORING ORGANIZATION 8b. OFFICE SYMBOL (If applicable) 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 8c. ADDRESS (City, State, and ZIP Cde) 10 SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK ELEMENT NO NO NO WORK UNIT ACCESSION NO }: mie (Include Security Classificatin) ANALYSIS OF RADIATION DAMAGED AND ANNEALED GAL ARSENIDE AND INDIUM PHOSPHIDE SOLAR CELLS USING DEEP LEVEL TRANSIENT SPECTROSCOPY TECHNIQUES 12 PERSONAL AUTHOR{S) PINZON. Jr.. Dimas 13a. TYPE OF REPORT 13b Master's Thesis TIME COVERED FROM TO 14 DATE OF REPORT (Year, Mnth, Day) 15 PAGE COUNT March 16 SUPPLEMENTARY NOTATION The vlews expressed in this thesis are thse f the authr and d nt reflect the fficial plicy r psitin f the Department f Defense r the US Gvernment. FIELD GROUP SUB-GROUP 18 SUBJECT TERMS (Cntinue n reverse if necessary and identify by blck number) Radiatin effects n slar cells; DLTS ; annealing f slar cells; gallium arsenide; indium phsphide 19 ABSTRACT (Cntinue n reverse if necessary and identify by blck number) Degradatin f slar cell perfrmance frm radiatin damage was fund t be reversed thrugh annealing prcesses. The mechanism behind the degradatin and recvery is based n deep-level traps, r defects, in the 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 level/cncentratin f the cell. Gallium Arsenide (GaAs) and Indium Phsphide (InP) slar cells were subjected t 1 MeV electrn irradiatin by a Dynamitrn linear acceleratin at tw fluence levels f 1E14 and 1E14 electrns/cm. The prcess f annealing included thermal annealing at 90 C with frward bias current and thermal annealing alne (fr GaAs). After each cycle, DLTS measurements were taken t determine the energy level f the traps and their cncentratin. Multiple cycles f irradiatin, annealing and DLTS were 17 COSATI CODES 20. DISTRIBUTION /AVAILABILITY OF ABSTRACT UNCLASSIFIED/UNLIMITED D SAME AS RPT DTIC USERS NAME OF RESPONSIBLE INDIVIDUAL MICHAEL, Sherif DD Frm 1473, JUN 86 Previus editins are bslete S/N 0102-LF i 21 ABSTRACT SECURITY CLASSIFICATION UNCTiAf^.STFTED 22b TELEPHONE (/nc/ude Area Cde) c OFFICE SYMBOL EC/Mi SECURITY CLASSIFICATION OF THIS PAGE UNCLASSIFIED

9 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE 19. cent. perfrmed t bserve the crrelatin between degradatin and recvery t trap energy level and cncentratin. The results shw that the lwer energy level traps are assciated with the recvery f the cells while the higher level traps are assciated with the verall permanent degradatin f the cells. Applying this infrmatin t future research culd allw fr significant increases in satellite missin life and ptentially increase missin paylad. DD Frm JUN 86 (Reverse) SECURITY classificatin f thls PAGE ii UNCLASSIFIED

10 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 Techniques by Dimas pinzn, Jr. Majr, United States Marine Crps B.S., Plytechnic Institute f Brklyn, 1975 M.S., University f Suthern Califrnia, 1985 Submitted in partial fulfillment f the requirements fr the degree f MASTER OF SCIENCE IN ELECTRICAL ENGINEERING (SPACE SYSTEMS) frm the NAVAL POSTGRADUATE SCHOOL.-March 199:

11 ABSTRACT Degradatin f slar cell perfrmance frm radiatin damage was fund t be reversed thrugh annealing prcesses. The mechanisms behind the degradatin and recvery is based n deep-level traps, r defects, in the 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 level/cncentratin f the cell. Gallium Arsenide (GaAs) and Indium Phsphide (InP) slar cells were subjected t 1 MeV electrn irradiatin by a Dynamitrn linear acceleratin at tw fluence levels f 1E14 2 and 1E15 electrns/cm. The prcess f annealing included thermal annealing at 90 C with frward bias current and thermal annealing alne (fr GaAs). After each cycle, DLTS measurements were taken t determine the energy level f the traps and their cncentratin. Multiple cycles f irradiatin, annealing and DLTS were perfrmed t bserve the crrelatin between degradatin and recvery t trap energy level and cncentratin. The results shw that the lwer energy level traps are assciated with the recvery f the cells while the higher level traps are assciated with the verall permanent degradatin f the cells. Applying this infrmatin t future research culd allw fr significant increases in satellite missin life and ptentially increase missin paylad. IV

12 TABLE OF CONTENTS I INTRODUCTION 1 A. BACKGROUND 1 B. RESEARCH PURPOSES 3 II PHOTOVOLTAIC 6 A. SEMICONDUCTOR THEORY 6 1. Bnding Mechanisms 6 2. Lattice Structure 7 3. Energy Bands and Band Gap Temperature Effects 13 B. PHOTOVOLTAIC EFFECT 15 1 Thery f Slar Cells Efficiency Factrs Affecting Slar Cell Efficiency..23 a. Bandgap Energy 24 b Temperature 24 c. Recmbinatin 27 C. CARRIER TRANSPORT 27 D. P-N JUNCTION 30 E P-N JUNCTION CAPACITANCE 32 III. SOLAR CELL RADIATION DAMAGE 34 A. ENVIRONMENT 34 B. THEORY OF RADIATION DAMAGE 38 C LATTICE STRUCTURE DAMAGE 40 IV. THEORY OF ANNEALING 43 A. RADIATION EFFECTS 43 V

13 B. RADIATION DEFECTS IN SOLAR CELLS DAMAGE EQUIVALENCE 47 C. SOLAR CELL ANNEALING 48 D. PREVIOUS ANNEALING RESEARCH 49 V. DEEP LEVEL TRANSIENT SPECTROSCOPY 51 A. DEEP-LEVEL TRANSIENT SPECTROSCOPY THEORY 51 B. DATA AND EQUATIONS 57 VI GALLIUM ARSENIDE SOLAR CELLS 65 A. GaAs CELL CHARACTERISTICS 65 B. EXPERIMENT OBJECTIVE AND PLAN 66 C. EXPERIMENTAL PROCEDURE AND RESULTS 68 D DLTS 69 E. CONCLUSIONS 70 VII INDIUM PHOSPHIDE SOLAR CELLS 73 A. InP CELL CHARACTERISTICS 73 B. EXPERIMENT OBJECTIVE AND PLAN 75 C. EXPERIMENTAL PROCEDURE AND RESULTS 75 D. DLTS 77 VIII CONCLUSIONS AND RECOMMENDATIONS 85 APPENDIX A PHYSICAL AND ELECTRICAL PROPERTIES OF SOME IMPORTANT SEMICONDUCTORS [REF. 5] 87 APPENDIX B I-V CURVES FOR MULTIPLE CYCLES OF IRRADIATED AND ANNEALED GaAs SOLAR CELLS APPENDIX C OPEN CIRCUIT VOLTAGE, SHORT CIRCUIT CURRENT, AND MAXIMUM POWER NORMALIZED PLOTS FOR GaAs SOLAR CELLS 110 APPENDIX D I-V CURVES FOR MULTIPLE CYCLES OF IRRADIATED AND ANNEALED InP SOLAR CELLS 132 VI

14 APPENDIX E OPEN CIRCUIT VOLTAGE, SHORT CIRCUIT CURRENT AND MAXIMUM POWER NORMALIZED PLOTS FOR InP SOLAR CELLS 148 APPENDIX F EQUATIONS AN SAMPLE CALCULATIONS FOR DLTS ON InP CELL ALONG WITH ENERGY AND CAPTURE CROSS SECTION PLOTS 155 REFERENCES 169 INITIAL DISTRIBUTION LIST 172 Vll

15 ACKNOWLEDGEMENT As we g thrugh life, there are a few special peple that share ur trials and tribulatins. It is fr this reasn, that I wish t express my heartfelt thanks t thse wh wrked with me n this research. First, t Dr. Sherif Michael wh intrduced me t the field f slar cell research. Thrughut his busy schedule there was always time fr me. His cnfidence and supprt made it all pssible. T Dr. Rudlf Panhlzer, fr cnvincing me after ur first chance meeting t enter the Space curriculum. His inspiratin helped me t achieve my gals. T Dr. Linda Halle, wh literally taught me abut Deep Level Transient Spectrscpy. The challenges f this research were always met and vercme thrugh her dedicatin and perseverence. She exemplifies her prfessin. T Karen Callaghan wh pulled it all tgether. Her exceptinal wrk and guidance thrugh the past tw and a half years helped make this a wrthwhile experience. Finally, and mst f all, t my wife Maureen, fifteen years f unwaivering lve and supprt she is the wind beneath my wings. I therefre dedicate this thesis t them, fr it is as much theirs' as it is mine. Vlll

16 I. INTRODUCTION A. BACKGROUND Since 1839 when the first phtvltaic effect was annunced by Bequerel, slar energy has becme an everincreasing facet in man's technlgy. The develpment f the first silicn slar cell in 1952 by Bell Labs plunged us int a new age f reliable pwer generatin particularly suited fr space ventures where the sun presents an inexhaustible surce f energy. Slar cells are the semicnductr devices which cnvert slar energy t electrical pwer using the phtvltaic effect. The majrity f spacecraft rbiting earth rely n slar pwer fr their paylad pwer requirements and these devices have becme an integral part f the space prgram. As a cnsequence, slar cells have been the subject f vast studies t increase efficiency f pwer utput and sustainability in the space envirnment. The advent f the space prgram created a great need fr independent pwer surces fr spacecraft. The success f the slar cell came abut with the Vanguard satellite in 1958 and as pwer demand increased with technlgy advances slar cell use quickly escalated. Slar cells present the mst viable alternative fr spacecraft pwer generatin based n reliability and cst. Over the past fur decades, slar cell

17 technlgy has advanced t such a degree that the pwer nw prvided by slar array designs are measured in kilwatts. A prblem, hwever, was t be encuntered. When the United States explded an atmic bmb within the Van Allen Belt in 1962 little was knwn abut the effects f radiatin n slar cells. Twenty-fur days after the explsin three f the satellites rbiting earth failed t perate due t pwer lss. The radiatin effects halted the phtvltaic energy cnversin f the cells. Despite the inexhaustible surce f energy presented by the sun, the pwer utput f the cells were limited ver the life f the spacecraft limited t the extent that spacecraft design is based n the end f life (EOL) pwer f the slar arrays. The radiatin effects t include damage t the lattice structure f the cell and its cmpensatin, have becme a critical issue causing extensive research in the area. T date, cmpensatin f radiatin damage has been minimal. The n n p cell was fund t be mre resistive t radiatin effects than the standard p n n. A cverglass with varying thickness was utilized and prvided limited shielding frm bmbarding electrns. Hwever, these effrts did nt extend the life f the slar cell t any appreciable extent. Develpment f ther III-V type cells (Gallium Arsenide and Indium Phsphide) prvided greater hardness against radiatin. The cst f manufacture versus life extensin has prhibited their wide use. What is needed is a prcess which wuld

18 actually reverse the damage f radiatin in the cells. If this culd be accmplished while n rbit, the prcess wuld present the mst attractive alternative t lst spacecraft. It wuld extend the life f the spacecraft, decrease design requirements and increase paylad. The cst-benefit wuld be mst attractive. The ptential fr n-rbit radiatin damage recvery became apparent when an annealing prcess was fund t restre the electrical degradatin experienced when the cells were subjected t radiatin damage [Ref. 1]. The recvery was significant enugh that the end f life (EOL) f a spacecraft culd be extended many times its present capability. This infrmatin pens the way fr greater peratinal endeavrs. The implicatins are that spacecraft can perate within the Van Allen Belts fr extended perids f time staying ff the lng-term damaging effects f radiatin n the cells (i.e., the Glbal Psitining System which passes thrugh the Van Allen Belts). Thus with this prcess, the verall cst benefits are realizable. B. RESEARCH PURPOSES This research is designed t prvide insight int the mechanism behind the structure defrmatin and refrmatin 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 established [Ref. 2]. 3

19 Research has established that after irradiatin at a fluence level f between 1E14 and 1E15 el/cm, the effects f damage caused by trapped electrns was reversed [Ref. 2] in GaAs and InP slar cells. Clark [Ref. 1] and Staats [Ref. 3] cnducted single annealing experiments t determine the ptimum mechanism fr recvery f radiatin-damaged GaAs cells. Cypranwski [Ref. 2] cntinued the research fr InP cells as well as investigating multiple cycles f radiatin and annealing n GaAs and InP cells. This research will explre 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. 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 and the envirnment in which the cells must perate. Cntinuing the prcess f radiatin damage, Chapter IV discusses the annealing fr slar cell recvery and utlines previus annealing research. The mechanism behind damage and recvery is further brught ut in Chapter V with the discussin f deep level transient spectrscpy and its relatinship t slar cell measurement

20 parameters. The experiment is discussed in detail fr GaAs in Chapter VI and InP in Chapter VII with cnclusins and recmmendatins fllwing in Chapter VIII. All pertinent graphs and equatins are fund within the appendices.

21 II. PHOTOVOLTAIC A. SEMICONDUCTOR THEORY In rder t understand the prcess f phtvltaics and slar cells, i.e., the nature f electrnic cnductin, it is necessary that sme fundamentals cncerning the material invlved are frmed. T this end, sme basics f semicnductr thery, the building blck f slar cells will be dealt with. The electrical prperties and physical characteristics f a material which lie intermediate between metals and insulatrs characterize a class f material knwn as semicnductrs 1. Bnding Mechanisms Chemically, semicnductrs have fur valence electrns. Since there are abut eight valence states with apprximately the same energy level, the valence shell is nly half filled. Therefre, the fur remaining empty states are filled by ne atm sharing ne electrn with each f fur neighbring atms, cmpleting the valence shell. This bnding is referred t as cvalent. It is the mechanism behind silicn crystals. Fr III-V cmpunds, i.e., GaAs and InP, the bnding mechanisms is a mixture f cvalent and inic bnding (the transfer f ne r mre electrns frm an

22 electrpsitive element t an electrnegative element, creating a psitive and negative in) The binding energy that is assciated with cvalent bnding is n the rder f a few electrn vlts per atm while the binding energy assciated with inic bnds (electrstatic attractin f ppsitely charged ins) is slightly higher. Insulatin r dielectrics are characterized by this binding energy. Fr silicn, hwever, the cvalent bnds are weaker than that f carbn because the valence electrns are in shells farther frm the nucleus. Therefre, the bnding energy is lwer. The same hlds true fr III-V cmpunds. The bnding energy fr GaAs and InP are higher hwever, than silicn because f their inic bnds. This becmes significant when band gap energy and its relatin t the light spectrum is discussed. This weaker bnding distinguishes the semicnductr frm the insulatr. It als distinguishes the semicnductr frm metals because the cvalent and inic bnding energy is greater than that f metallic bnding. 2. Lattice Structure A crystalline slid is characterized by an rderly, perfectly peridic array f atms knwn as the lattice structure. The basic building blck that defines the lattice structure f a crystal is the unit cell. By translating the unit cell, a translatinal symmetric lattice is generated. In ther wrds, the symmetry f the lattice is unchanged relative

23 t different crdinates. Because silicn, GaAs and InP are crystalline in nature, we can explit the symmetric characteristics when dealing with energy band gaps. Figure 2-1 shws the unit cell f silicn and GaAs. Length (a) is knwn as the lattice cnstant. When silicn crystallizes, it des s in a diamnd structure in which each atin is bund t its fur nearest neighbrs in a tetrahedral arrangement. Fr the III-V cmpunds, the atm f an element frm the third grup f the peridic table is surrunded by fur neighbring atms f an element frm the fifth grup and cnversely, s that the number f atms frm each grup is the same. By transferring an electrn frm a fifth grup atm t a third grup atm, each lattice site becmes ccupied by an in surrunded by fur ppsitely charged ins in a tetrahedral arrangement similar t the diamnd structure f silicn. This arrangement is knwn as a zinc-blende structure. The lattice structure plays an imprtant rle in semicnductr devices particularly in the generatin f band gaps. The atms f the lattice are in a state f cnstant vibratin. As a cnsequence, the atm imparts energy t the electrns surrunding it. The interactin f the electrn and the vibratinal energy cntributes t the frmatin f the energy bands and the band gap by causing the discrete energy levels f the atm t spread ut. This mechanism influences

24 SIMPLE CUBIC (P, etc) BODY-CENTERED CUBIC FACE- (NO, W, etc) CENTERED CUBIC (Ai;Au, etc) DIAMOND etc) [C, Ge, Si, ZINCBLENDE (GOAS, GOP, etc) Figure 2-1. Sme imprtant unit cells (direct lattices) and their representative elements r cmpunds; a is the lattice cnstant, [frm Ref. 5: p. 9]

25 the electrical and thermal cnductivity f the crystal and is the chief characteristic f the semicnductr. 3. Energy Bands and Band Gap As a direct cnsequence f translatinal symmetry, the discrete energy levels f the atm spread ut t frm tw majr energy bands the valance band and the cnductr band; each ne with its wn discrete electrn levels. The valance bands are thse ccupied by the electrns at 0 K while the cnductin bands are empty. At 0 K, a semicnductr has n delcalized electrns; all electrns are bund t individual atms [Ref. 4:p. 52]. Hence, the number f electrns available t carry current are almst nnexistent. Separating the tw majr energy bands is a gap f frbidden energy levels, better knwn as the bandgap. 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 pssess sufficient energy greater than the bandgap energy. Figure 2-2 is a diagrammatical representatin f the energy bands and the bandgap. The energy gap (band gap) fr semicnductr devices ranges frm t 2.5 ev. At rm temperature (300 K) and under nrmal atmsphere, the values f the bandgap are 1.12 ev fr silicn, 1.42 ev fr Gallium Arsenide and 1.35 ev fr Indium Phsphate [Ref. 5:p. 15 and Ref. 6:p. 42]. 10

26 ELECTRON ENERGY HOLE ENERGY DISTANCE Figure 2-2. Simplified band diagram f a semicnductr [frm Ref. 5: p. 15] 11

27 Once electrns crss the gap t the cnductin band, they mve freely and thereby carry current. The hle left behind in the valence band is filled by neighbring electrns, in effect causing the hle t mve arund the atms. This mtin can be cnsidered the mvement f a psitive charge. The net result is that current carried thrugh the semicnductr What distinguishes the semicnductr frm an insulatr is the fact that the bandgap energy is small (0 < E, < 2.5eV). It allws cnductin with small inputs f energy. Up t this pint, nly pure r intrinsic semicnductrs have been discussed, where the sle mechanism fr cnductin is the transprt f an electrn frm the valence band t the cnductin band. There is, hwever, what is knwn as extrinsic semicnductrs. Extrinsic semicnductrs lwer the bandgap energy by the intrductin f impurity atms r dpants int the semicnductr. If a dnr atm is intrduced (an atm with 5 valence electrns causing an excess f ne electrn when bnding ccurs) then little energy is required t bst the extra electrn t the cnductin band. If an acceptr atm is intrduced (an atm with 3 valence electrns 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 12

28 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 the cnductin band while the energy level assciated with a hle is lcated just abve the valance band. Dping a semicnductr with dnr r acceptr atms classifies the material nw as either n-type r p-type. When these tw types f material are placed in cntact with each ther, a junctin frms which prvides a necessary functin in slar cells and will be discussed in mre detail later. 4. Temperature Effects Cnductivity in intrinsic semicnductrs is characterized by a very strng temperature dependence. Unlike metals which increase cnductivity with decreasing temperature, a semicnductr increases cnductivity with increasing temperature. The increased temperature prvides thermal energy t break the bnded electrn away fr cnductin. In metals, heat is absrbed by the atm and transfrmed t lattice vibratin. Since the electrn cncentratin is temperature in dependent, electrn mbility tends t decrease. Semicnductr electrn cncentratin is very temperature dependent. It is the absrptin f the thermal energy which elevates the electrn past the energy bandgap. Electrn density increases expnentially with 13

29 - Dnr states Cnductin band Valence band Acceptr states B Figure 2-3. Representatin f discrete, lcalized impurity levels m an energy-level diagram fr the case f A, dnr and B, acceptr, impurities, [frm Ref. ll:p. 204] 14

30 temperature and tends t vercme the lattice vibratinal effects. As impurities are added, the temperature dependence f the electrn density becmes less. With heavy dping, the temperature dependence becme negligible and the semicnductr acts similar t the behavir f metals. Hwever, as will be dicussed later, the temperature effects in slar cells is quite different. B. PHOTOVOLTAIC EFFECT 1. Thery f Slar Cells When light falls incident n a semicnductr device, the phtn energy is either absrbed, reflected r passed thrugh. When absrbed, the phtns cllide with the atmic electrns imparting sufficient energy fr the electrns t break their bnds within the atmic structure. The disldged electrn leave "hles" in the structure, and while the electrns are bsted t the cnductin band, the hles are left behind in the valence band. These are nrmally referred t as electrn-hle pairs. If nthing else happens, 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, hwever, intrduces an internal electric field which separates and cllects the electrn-hle pairs befre they recmbine. This electric field is prduced by a p-n junctin frmed by the cntact between n-type and p- 15

31 type samples f the same material. n-type and p-type material is made, When the cntact between excess electrns frm the n-type regin will migrate ver int the p-type regin near the junctin and the hles frm the p-type regin will migrate t the n-type regin. 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 light-generated electrns and hles becme available, the ptential barrier separates them frcing electrns frm the p-regin where they are called minrity carriers t the n-regin where they are knwn as majrity carriers. 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 slar cell, which is a semicnductr device, will nw generate current thrugh electrical cntacts t an external circuit as shwn in Figure

32 Electrica Cntacts Light Generates Electrn and Hle Light Is Absrbed at Back Metal Cntact Tp Electrical Grid- KQ \0/e External Lad n-type Silicn- Junctinp-Type Silicn- I A Metal Cntact Electrn Hle Figure 2-4. 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, [frm Ref. 9: p. 14] 17

33 2. Efficiency The physical phenmenn f cnverting light r pht energy t electricity is knwn as the phtvltaic effect. This prcess is the basis f pwer generatin in slar cells. The energy assciated with light (phtns) necessary t free an electrn frm its atmic bnds, ranges frm t 2.5 ev based n the type f semicnductr used. As phtns strike the slar cell, ne f a number f effects will take place. The energy can be sufficient enugh t: - prduce an electrn-hle pair, - prduce an electrn-hle pair and generate heat in the frm f atmic vibratins, r - nt prduce an electrn-hle pair but generate heat. The energy can als be reflected r passed thrugh the cell withut being absrbed. Because f these events, mst f the energy that strikes the cell is lst befre it can be cnverted t electricity. The result is lw cnversin efficiency. In rder fr a phtn t be f significant use in the cnversin prcess, it must have sufficient energy t transfer t an electrn in rder fr the electrn t breach the bandgap. It is ideal thugh t have energy slightly greater than the bandgap t ensure the transitin f the electrn frm the valance band t the cnductin band. Figure 2-5 shws the visible light spectrum and the assciated energy. Nte that the smaller the bandgap, the greater the number f electrnhle pairs generated. T small a bandgap wuld result in 18

34 < Phtn energy Eph.eV Eg ^2.2 ev [GaP] 5.8 x 10'^ pairs per secnd Sun energy utilized in generatin f electrn-hle pairs in semicnductrs with different energy gaps.eg-1,45 ev 1.8 xlo pairs per secnd Energy spectrum f sun -Eg^l07eV [Si] 2.8 x 10'%airs per secnd Eg^0.68eV[Ga,Sb,Ge] 4.2 xi'^pairs per secnd Eg ^0.34 ev 5xi'^pairs per secnd ^Wavelength X, /im Figure 2-5. The energy spectrum f the sun n a bright, clear day at sea Ivel (excluding water vapr absrptin) and the parts f this spectrum utilizable in the generatin f electrn-hle pairs in semicnductrs with energy gaps f 2.25, 1.45, 1.07, 0.68 and 0.34 ev, respectively. Listed fr each f these cases is the number f electrn-hle pairs generated, btained under the assumptin f the existence f an abrupt absrptin edge with cmplete absrptin and zer reflectin n its high energy side, [frm Ref. 21:p ] 19

35 phtn energy being wasted as heat. It is, therefre, necessary that the material being used fr phtvltaic cnversin have an ptical bandgap. The idea is t match the bandgap characteristic f the slar cell with the slar spectrum such that the maximum amunt f energy in the sun's spectrum falls slightly abve the bandgap energy f the cell fr maximum efficiency. Frm Figure 2-6, maximum efficiency is illustrated as a functin f the bandgap energy fr varius cells. Nte where Gallium Arsenide and Indium, Phsphide fall in relatin t the maximum attainable efficiency f a cell under Air Mass Zer (AMO) cnditins. S, at 273 k, the desirable energy gap wuld be apprximately 1.4 ev. The parameters that characterize the perfrmance f a p-n junctin slar cell are: pen circuit vltage shrt circuit current V^^ Ig^ 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 Py f a cell is Pt = V,, I3, (2-1) With the cnversin lsses mentined abve the maximum practical (P^) pwer is smewhat less than P^. The I-V curve f Figure 2.7 shws the maximum utput pwer (P ). Anther slar cell parameter is the Fill Factr (FF) and is defined as: 20

36 >- u zuj u ENERGY GAP, ev Figure 2-6. Temperature-Dependent Maximum Efficiency as a Functin f Energy Gap fr a Few Phtvltaic Materials [frm Ref. 13 :p. 1-32] 21

37 Figure 2-7. Slar cell electrical utput characteristics (I-V curve) [frm Ref. 31] 22

38 p p FF = = (2-2) Under Air Mass Zer (AMO) cnditins, the sunlight 2 incident pwer is apprximately 1.36 Kw/m. Then the efficiency f a cell can be calculated as P V I FF ri = = (2-3) Sunlight Incident Pwer ^incident In rder t achieve high cnversin efficiency, the requirements are high V^^, Ig^, and FF (sharp crner in the I-V curve). Energy cnversin efficiencies f standard slar cells range between 12 and 17 percent; the main reasn being that, in the slar spectrum, 2 6 percent f the energy is in phtns having phtn energy f less than 1.1 ev (bandgap fr silicn) [Ref. 7:p. 60]. Frm Figure 2-5, 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 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. 3. Factrs Affecting Slar Cell Efficiency The upper limits f slar cell efficiency are bund by several factrs. Radiant energy passing thrugh the cell, as 23

39 well as reflectin, prduce n effect in the phtvltaic cnversin prcess. And, because sunlight is nt mnchrmatic, much f the radiant energy absrbed prduces heat. The remaining 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. This range wuld be between 1 and 2.5 ev as shwn in Figure 2.5. Silicn's bandgap energy is 1.1 ev while GaAs and InP are 1.42 and ev respectively. Nte frm Figure 2-6 that Gallium Arsenide's bandgap almst cincides with the peak efficiency assciated with the slar spectrum. b. Temperature Figure 2-6 shws that the slar cell efficiency decreases with increasing temperature, despite the fact that cnductivity in semicnductrs characteristically increases 24

40 30V c CD 20 LU C CO > c O 10 VGasr N^aP^^v^^^CdS Ge^ X^GaAs^ Semicnductr Temperature ( C) Figure 2-7. Slar cell efficiency versus temperature fr varius materials: Nte that all materials lse efficiency in the range shwn, [frm Ref. 9:p. 21] 25

41 with increasing temperature (Figure 2-7). Tw predminant factrs cause efficiency t drp as temperature rises (as thermal energy increases) : 1) lattice vibratins interfere with the free passage f charge carriers, and 2) the junctin begins t lse its pwer t separate charges [Ref. 8:p. 17], The first factr degrades perfrmance even at rm temperature. It is the secnd factr which ccurs at higher temperatures, that leads t the ersin f the phtvltaic effect. At higher temperatures, a great many electrns are brken frm their bnds. These electrns utnumber the free electrns supplied by dpants. Als created are the hles, frmed by the thermally-freed electrns. The n-type material begins t lse its n-type characteristic. The same prcess ccurs n the p-type side which lses its p-type characteristic. The effect is 1) the thermally agitated charge carriers have s much energy, that they crss ver the p-n junctin in bth directins as if the barrier field were nt there, and 2) ultimately, the junctin itself disappears because there are n lnger n- and p-type sides t create the barrier [Ref. 9:p ]. Thus, the efficiency diminishes. It can be shwn that temperature dependence can be reduced by larger bandgaps. Thus, GaAs cells are nly abut half as sensitive t increasing temperature as silicn cells [Ref. 10:p. 92]. 26

42 c. Recmbinatin The inadvertent randm encunter f lightgenerated electrn-hle pairs can lead t their rejining r recmbinatin befre they cntribute t current generatin. Recmbinatin ccurs by either direct r indirect methds. Direct recmbinatin ccurs when an electrn and a hle randmly encunter each ther. The electrn rebnds with the atm by falling back int a hle. The electrn's energy is lst as heat. This prcess ccurs mstly befre the electrn has a chance t crss the ptential barrier. Once acrss, direct recmbinatin is rare. Indirect recmbinatin ccurs when an electrnhle recmbinatin is influenced by ther factrs such as empty, r dangling bnds frm impurities r defects which capture the free electrns. This mechanism is mre prevalent. 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. C. CARRIER TRANSPORT There are tw majr mechanisms by which current flw in a semicnductr ccurs: drift and diffusin f charge carriers. Drift f charge carriers is caused by the mvement f free electrns and hles in the presence f an electric field. The charge carriers are accelerated by the electric field and acquire a velcity cmpnent in additin t their velcity 27

43 assciated with their thermal energy. This velcity can be expressed in relatin t the field strength by: v^ = electrn drift velcity = yn E (2.4) I) = hle drift velcity = yp E (2.5) where E is the electric field strength and y is the charge carrier's mbility cnstant. Since the mvement f charge causes current flw, drift current in the semicnductr can be expressed as Jrift = -q^^n + ^^p = qc^yn + PYp) ^ = ^E (2.6) where Jprift ^^ "^^^ current density (current flw per unit area) and is the semicnductr cnductivity cnstant. Table 2-1 gives electrical prperties f sme semicnductrs. The mre significant mechanism f current flw is that assciated with diffusin. This is the prcess whereby randm mvement f the particles exist due t cncentratin gradients. In ther wrds, the free charge carriers will diffuse frm a regin f high cncentratin t a regin f lw cncentratin which gives rise t a net flw f charge r diffusin current. Diffusin current flw can be expressed as: Jdiffusin.hles = q D ^ (2.7) dx ^diffusin.electrns = Q ^^ dn (2.8) dx where ^diffusin diffusin current density (fr hles r electrns) D = diffusin cnstant fr hles 28

44 = diffusin cnstant fr electrns dx dn dx = gradient f hle cncentratin = gradient f electrn cncentratin TABLE 2-1 ELECTRICAL PROPERTIES OF SEVERAL IMPORTANT SEMICONDUCTOR MATERIALS AT 3 00 K [frm Ref. 10:p. 42] Mbility ( cmvv s) DifTusin Cnstant (cm'/s) 1 Mnterial n, (cm-') M- Mr p (fl-cm) -(S cm"') Dr Si Ge GaAs 14 X lo" 2.5 x.lo" 9 X I0» X 10' 43 4 X 10' 4.4 X 10-' 2.2 X 10' 1.3 X lo* 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} = DT (2.9) 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. 29

45 D. P-N JUNCTION A p-n junctin is, fr ur purpses, cnsidered t be ne semicnductr (Si, GaAs, InP) with tw regins f different cnductivity type; n-type and p-type. The junctin frms at the regin where the cnductivity changes frm ne type t the ther. In the immediate neighbrhd f the junctin a depletin layer is frmed which, by virtue f charges mving acrss the junctin, sets up an electric field r ptential barrier. This barrier, as described earlier, ppses the further flw f free charge carriers. As mre carriers crss the junctin, the ptential barrier increases until the ppsitin allws n mre charge carriers acrss. Thus, a semi-permanent electric field is established in the regin f the junctin as shwn (Figure 2-8). The magnitude f the ptential barrier depends upn the width f the frbiddenenergy gap, the impurity cncentratin f dpant, and the temperature [Ref. ll:p. 270]. The quality f the ptential barrier is that it 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. S, when a light-generated electrn-hle pair is frmed, the electrn is driven t the n-type side and the hle is driven t the p-type side. Once the electrns are n 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 30

46 , \ n side p-side n Side p Side Neutral charge, biit extra (nnbnded) Ex Ira tiles electrns tree n In p-type side. n-type side. j (x^ 5 \^^^fl ^ 0) 0) / 1S^> '^ 1 ^1 X Psitive Ins Negative Ins 1 / ' iprn L ' / D 3 \ / f > L S / * f V t/ CO t /r "* ^_, v^vwv^ ^ ^ r^ c c vct:^0-.^^\ 1 >-- *j. jt» «/ \ u u, 1 \, / CO «I / ">-* /V \ s lii^-iiil t^ Wtien p and n are jined, electrns mve Irm nslde t fill hles n pside. ) < / > -TV -(^M O 1 / 3jUi ) Near the junctin, mst f the free electrns n the nslde have mved t the p-slde, creating a large psitive charge at the junctin. Large negative charge is created at the junctin because l the transfer f electrns t the p side t fill hles. Psitive charge begins t build n the nslde f the junctin because l the lss f electrns Electrn Hle Negative Charge Buildup + Psitive Charge Buildup O Silicn Atm <C» Dnr Atm Acceptr Atm Negative charge begins t build n the p-slde as electrns fill bnd vacancies (hles). Legend Q;:^^ Nrmal Bnd with 2 Electrns :< iy^'~(^ Bnd Missing an Electrn (i.e. a Hle) aj ct^ Bnd with Extra Electrn Irm Dnr Atm Once the junctin has fully frmed. It presents a barrier t additinal crssver f electrns t p side. -r-e Once the junctin has fully frmed. It presents a barrier t the pssible transfer f hles frm pside t nslde. Figure 2-8. During junctin frmatin, electrns mve frm the n-type silicn int the p-type, white hles mve in the ppsite directin. Mvement f electrns int the p-type silicn and hles int the n-type. silicn builds a fixed ptential barrier at the junctin, ppsing further mvement and creating a state f equilibrium, [frm Ref. 8:p. 12] 31

47 reaching the surface cntacts f the cell. Since a charge imbalance nw exists in the cell, current can flw thrugh a cnnected external circuit. E. 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. It, therefre, has assciated capacitance. The capacitance C f the junctin is given by A e C = (2.10) 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 cntact f the cell) and W is the width f the depletin regin. The acceptr r dnr density is the p-type r n-type regin adjacent t the depletin regin can be related t the capacitance per unit area by 1/2 (2.11) r N = ; (2.12) qea where N is the smaller value f acceptr density N^ r dnr density Ng, and V^ is the applied vltage (psitive in frward 32

48 bias), and V^ is barrier vltage. Using Ng assumes heavily dped n-regin while Np assumes heavily dped p-regin. Equatin (2.11) illustrates that the capacitance varies with the applied vltage. Therefre, measuring C as a 2 functin f reverse bias t a slar cell and pltting 1/C versus V^ will allw N, the dping density n the lightly dped side f the cell t be fund [Ref. 10:p. 68]. These expressins assume an abrupt junctin which is characteristic f cnventinal slar cells. 33

49 III. SOLAR CELL RADIATION DAMAGE A. SPACE ENVIRONMENT Thrughut its lifetime, a spacecraft in rbit is cntinually expsed t high-energy radiatin. The earth's rbital envirnment is characterized by the magnetsphere which is created thrugh the interactin f the slar wind and the terrestrial magnetic field as shwn in Figure 3-1. Earth's radiatin zne, referred t as the Van Allen Belts, cnsists f magnetically-trapped electrns and prtns, prviding the hstile envirnment respnsible fr the degradatin f slar cell efficiency. Figures 3-2 and 3-3 illustrate the distributin f the trapped prtns and electrns fr bth the inner and uter belts. The inner belt, smetimes referred t as the hard belt, cntains high energy prtns f energies t 700 MeV with electrn energies in the 2 kev t 1 MeV range. The uter belt called the sft belt, cnsists primarily f electrns frm 20 kev t 5 MeV and sme prtns ver 60 MeV [Ref. 12 :p ] 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 the primary cause f damage except during perids f high slar activity. During these 34

50 IHTERPLAHETARY MEDIUM MAGNETOSHEATH MAGNETOPAUSE MAGHETOTAfL NEUTRAL SHEET BOW SHOCK Figure 3-1. Crss sectin f the magnetsphere [frm Ref. 26:p. 46] 35

51 OMNIDIRECTIONAL FLUX (PROTONS/CM'-SEC) OMNIDIRECTIONAL FLUX (PROTONS/CM^SEC) Entriy > 100 M«Y 3 EMthRidii Figure 3-2. Distributin f trapped prtns [frm Ref. 26:p. 42] 36

52 n.uv itisiniikn ION >.s- mtv Figure 3-3. Distributin f trapped electrns [frm Ref. 26:p. 41] 37

53 perids, slar flare prtns may then add significantly t the ttal cell-damaging effect. T a great extend then, trapped electrns are the principle cause f slar cell degradatin which is a cntinuing prcess within the space envirnment. B. THEORY OF RADIATION DAMAGE The perfrmance f slar cells is subject t radiatin effects cnsisting f high energy r fast massive particles. The radiatin effects are prduced by electrns, prtns, neutrns, r ins. Because these particles have mass, energy and smetimes charge, these particles r ther particles generated by them can interact in several ways with slar cells [Ref. 13 :p. 3-1]. The dminant interactins are: - Inelastic Cllisins with Atmic Electrns. An energetic charged particle (electrn, prtn) lses its kinetic energy t a bund atmic electrn thrugh an inelastic cllisin. The atmic electrn experiences a transitin t an excited state (excitatin) r an unbund state (inizatin). This is the predminant mechanism by which the energetic charged particle lses its kinetic energy. - Elastic Cllisin with Atmic Nuclei. An atm can be displaced frm its lattice site by the culmbic interactins f energetic charged particles and the psitive charge f the atmic nucleus (Rutherfrd Scattering). The displaced atm may in turn cllide with ther atms causing them t displace if sufficient energy was transferred t the initial displaced atm. - Inelastic Cllisins with Atmic Nuclei. The inelastic cllisin f highly energetic prtns with the atmic nucleus causes the nucleus t be left in an excited state. Once excited, the nucleus emits energetic nuclens causing it t recil thrugh the lattice structure displacing itself. The reciling nucleus in turn cllides with ther nuclei causing their displacement. [Ref. 13 :p. 3-1] 38

54 Each interactin causes cell damage t ccur. 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 trapped by impurity atms in the glass frming clr centers. The subsequent result is a darkening f the cell cver glass reducing 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 inizatin radiatin than the phtn t create the same number f charge pairs. The interactin with the inizatin 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 t heat. The net effect wuld be an increase in temperature. High energetic, fast mving particles are capable f causing atmic displacements within the crystal lattice structure f slar cells. These displaced atms and their 39

55 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 [Ref. 13 :p. 3-7] and 25 ev fr GaAs [Ref. 14:p. 153]. 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 f a vacancy [Ref. 13:p. 3-7]. C. 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 [Ref. 15: p. 157]. The defects then can act as additinal recmbinatin centers causing a reductin in minrity carrier lifetime and diffusin length r they can 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. 40

56 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 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 [Ref. 13 :p. 3-9]. 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 then 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 41

57 (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 basically eliminated. The cmbinatin returns the crystal t its riginal lattice structure frmatin. This wuld be the ideal cnditin fr irradiated cells. A divacancy defect will ccur when tw vacancies cme tgether t frm a stable cmplex. These type defects increase rapidly with increasing electrn energy and appear t be f greater significance in the deterirating perfrmance f the cell [Ref. 13:p. 3-11]. The energy level assciated with this type defect is mst likely slightly abve the valance band based n p-type silicn [Ref. 13:p-3-ll]. The majr affect that these defects have is the frmatin f additinal recmbinatin centers which affect the lifetime and diffusin lengths in the cell. 42

58 IV. THEORY OF ANNEALING A. RADIATION 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. Impurity cncentratins, recmbinatin, diffusin lengths and minrity carrier lifetimes are the physical aspects f cell behavir while the electrical parameters include shrt circuit current (Igj.), pen circuit vltage (V^^.) and pwer utput (P). The principal effect f radiatin is the lattice defect damage caused. The displacement defects create additinal recmbinatin centers causing a reductin in minrity carrier diffusin length (minrity carrier lifetime). Since minrity carrier lifetimes are inversely prprtinal t the recmbinatin rates, the inverse lifetime is as fllws [Ref l:p-3-16] 1111 = + + (4.1) where Tn T' e Tr. p T = minrity carrier lifetime Tq = minrity carrier lifetime befre irradiatin Tg = minrity carrier lifetime due t electrn irradiatin T = minrity carrier lifetime due t prtn irradiatin 43