UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An experimental and theoretical investigation of the characterstics of dark illuminated junction diodes… Pinson, William Edwin 1956

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1956_A7 P4 E9.pdf [ 4.06MB ]
Metadata
JSON: 831-1.0103760.json
JSON-LD: 831-1.0103760-ld.json
RDF/XML (Pretty): 831-1.0103760-rdf.xml
RDF/JSON: 831-1.0103760-rdf.json
Turtle: 831-1.0103760-turtle.txt
N-Triples: 831-1.0103760-rdf-ntriples.txt
Original Record: 831-1.0103760-source.json
Full Text
831-1.0103760-fulltext.txt
Citation
831-1.0103760.ris

Full Text

AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF THE CHARACTERISTICS OF DARK A*TD ILLUMINATED JUNCTION DIODES OF GERMANIUM AND SILICON by WILLIAM EDWIN PINSON B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1954. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of P h y s i c s We accept t h i s t h e s i s as conforming t o the standard r e q u i r e d from candidates f o r the degree o f MASTER OF APPLIED SCIENCE THE UNIVERSITY OF BRITISH COLUMBIA September, 1956 ABSTRACT Measurements have been made on a v a r i e t y of germanium and s i l i c o n j u n c t i o n diodes i n order t o determine departures from the i d e a l behavior both under i l l u m i n a t e d and dark c o n d i t i o n s . The diodes i n c l u d e d a l l o y e d , grown and d i f f u s e d j u n c t i o n types and the experimental study was l a r g e l y c o n f i n e d t o forward v o l t a g e . C a r r i e r s i n j e c t e d by a forward v o l t a g e i n t o the b u l k regions o f a p-n j u n c t i o n i n Ge or S i reduce the r e s i s t a n c e s o f these r e g i o n s , A model o f a photodiode c o n s i s t i n g o f an i d e a l diode (Shockley, 1949) i n s e r i e s w i t h t h i s c a r r i e r modulated r e s i s t a n c e produces good agreement w i t h the e x p e r i -m e n t a l l y observed dark chs.; i n one Ge a l l o y diode the agreement was exact up t o at l e a s t 0,7V forward v o l t a g e . For l a r g e forward c u r r e n t s ( d e n s i t y o f i n j e c t e d c a r r i e r s comparable t o i n j e c t e d c a r r i e r d e n s i t y ) t l i e Shockley ex* p r e s s i o n r e l a t i n g I and V i s no longer v a l i d nor conse« que n t l y i s the c o n d u c t i v i t y modulation theory. This theory, making use of the experimental dark chs, and the experimental dynamic c a p a c i t y measurements, i s able t o deduce many o f the parameters o f the diode m a t e r i a l e # g , y ^ , Pn 'Vo* The chs. o f the diode dark a n d i l l u m i n a t e d have been found to i n t e r s e c t a t l a r g e forward c u r r e n t s . T h e o r e t i c a l i n v e s t i g a t i o n o f the c o n d i t i o n f o r crossover i n v a r i o u s models o f the diode i s made. The p h y s i c a l meaning o f t h i s ( i i ) t c o n d i t i o n i s t h a t a t some forward v o l t a g e the r e s i s t a n c e .of the diode i s s u f f i c i e n t l y reduced on i l l u m i n a t i o n t o o f f s e t the e f f e c t of the opposed i n t e r n a l photo-e.m.f... For an i d e a l diode the r e l a t i o n between the s h o r t c i r c u i t photo-current and open?-circuit photo»e.nuf# (photochs.) should simply be the same as the dark forward chs., except f o r a r e v e r s a l of s i g n of the c u r r e n t . The f a c t t h a t the experimental photochs. f a l l s below the i d e a l photochs. i s a t t r i b u t e d to i n t e r n a l r e s i s t a n c e i n the diode and an expression i s developed from t h i s assumption; the t h e o r e t i c a l expression i s l a r g e l y c o n s i s t e n t w i t h experiment. S e v e r a l other models are examined f o r the n o n - i d e a l behavior o f j u n c t i o n diodes which attempt t o take i n t o account the p o s s i b l e e f f e c t s o f the r e s i s t a n c e of the bulk m a t e r i a l and o f the electrode-.semiconductor c o n t a c t ; the i m p l i c a t i o n s o f n o n ^ l i n e a r recombination are a l s o i n v e s t i * gated. I t i s found t h a t none of these a l t e r n a t i v e models i s as s u c c e s s f u l as the c o n d u c t i v i t y - m o d u l a t i o n scheme i n e x p l a i n i n g the dark;, the i l l u m i n a t e d and the photocharac-t e r i s t i c s * \J' O^JJUSJJ^M j B . C . v i i i ACKNOWLEDGMENTS I am indebted t o P r o f e s s o r R. E. Burgess f o r g u i d i n g t h i s research and f o r t a k i n g a constant i n t e r e s t i n the work. H i s knowledge of the f i e l d of semiconduct-i n g devices has c e r t a i n l y served as an i n s p i r a t i o n w h i l e h i s a v a i l a b i l i t y f o r d i s c u s s i o n at a l l times has been a b i g f a c t o r i n the s u c c e s s f u l completion of t h i s t h e s i s , I would a l s o l i k e t o thank Dr, M. B, P r i n c e of N a t i o n a l Semiconductors I n c . f o r a S i d i f f u s e d j u n c t i o n ; Dr. J . N. Shive o f B e l l T e i phone L a b o r a t o r i e s f o r the l o a n of a I I 85 Ge grown j u n c t i o n ; Miss B e t t y P i n s o n , my s i s t e r , f o r her a s s i s t a n c e i n t y p i n g the t h e s i s . The support of the Defence Research Board through the summer of 1956 i s g r a t e f u l l y acknowledged. This research has been c a r r i e d out under the auspices of Defence Research Board Grant 9512-22, rl TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1 LIST OF COMMON SYMBOLS . . 7 CHAPTER I . EXPERIMENTAL METHODS AND RESULTS 10 Diodes jised i n experiments 10 Dark c h a r a c t e r i s t i c s . . . . . . . . . . . . 012 I l l u m i n a t e d c h a r a c t e r i s t i c s • • • , • . . • • 1 3 P h o t o c h a r a c t e r i s t i e s . • • • • • • • • . . , . 1 6 Dynamic c a p a c i t y of space charge l a y e r , • • ,19 Photocurrent a f u n c t i o n of i l l u m i n a t i o n • • • 22 L i g h t Sources . . • » • • • • • « , . . • • • • 2 4 I I . THEORY AND DISCUSSION. . , • • • * , « • » • #26 Model IA ~ I d e a l diode i n s e r i e s w i t h n a constant R s . . « , . . . . • » • • Model I B - Model IA shunted by a constant r e s i s t a n c e , * . . « . » * • • • • 28 Model 2 - C o n d u c t i v i t y modulation . . . . . 33 Dark c h a r a c t e r i s t i c s . • • * • • « * • • • ' 3 3 High l e v e l e f f e c t s . » . » • • • « 37 Guides i n a n a l y s i s o f I n I _ - R • 40 p l o t . Comparison of theory and e x p e r i -ment, • • • ' • • • • • • • » » » • 4 1 P j j i T p , L p c a l c u l a t i o n from the c o n d u c t i v i t y modulation theory • . 43 P h o t o c h a r a c t e r i s t i c s . » • • • • • • • • 4 ^ Crossover . . . • . • • • • • « • • • • 50 i v Page Model 3 Two i d e a l diodes opposed to one another • « » « • • « « « « • « « 52 Model 4 I d e a l diode i n s e r i e s w i t h Bethe-type diode , « • « • « • • • • • 55 Model 5 Nonlinear c a r r i e r recombination to p r e d i c t dark I-V chs. . . . . 60 ^APPENDIX I Complete expression f o r c o n d u c t i -v i t y modulation assuming P(d) = P n.. . . . . . . . . . . 65 REFERENCES. . « , • • , . . . . . . « 67 V LIST OF ILLUSTRATIONS F i g u r e F a c i n g Page A. C r o s s - s e c t i o n of diodes 10 B. Normal c i r c u i t f o r measuring dark c h a r a c t e r i s t i c s 12 C. P u l s e r and bridge set-up f o r measuring dark 12 c h a r a c t e r i s t i c s D. Normal c i r c u i t f o r measuring i l l u m i n a t e d character- 15 i s t i c s E. CRO d i s p l a y b e f o r e , a t , and a f t e r crossover 16 F. Diagram r e l a t i n g crossover t o i l l u m i n a t e d 16 c h a r a c t e r i s t i c s 1. Crossover of i l l u m i n a t e d , a n d dark c h a r a c t e r i s t i c s 16 f o r Ge a l l o y diode(1N77A) G. Normal c i r c u i t f o r measuring p h o t o c h a r a c t e r i s t i c s 17 H. C i r c u i t f o r measuring p h o t o c h a r a c t e r i s t i c s f o r 17 pul s e d l i g h t 2. P h o t o c h a r a c t e r i s t i c s of Ge a l l o y diode (1N77A) 18 f o r d i f f e r e n t l i g h t i n g techniques I . C i r c u i t f o r measuring dynamic c a p a c i t y o f diodes 19 3. E f f e c t o f frequency on measured dynamic c a p a c i t y 21 f o r Ge grown j u n c t i o n (TPC5) J . C i r c u i t f o r determining i f photocurrent i s a 22 f u n c t i o n of i l l u m i n a t i o n 4. Dependence o f s h o r t - c i r c u i t photocurrent on 22 i n t e n s i t y of i l l u m i n a t i o n LA. Model 1: I d e a l Diode i n S e r i e s w i t h constant R s on 26 5. Comparison of dark c h a r a c t e r i s t i c s w i t h Model IA 27 f o r three d i f f e r e n t constant r e s i s t a n c e s 6. Comparison of experimental p h o t o c h a r a c t e r i s t i c s 27 w i t h those p r e d i c t e d by Model IA f o r three d i f f e r e n t constant r e s i s t a n c e s IB. Model IB: Model IA shunted by a constant r e s i s t a n c e 28 v i LIST OF ILLUSTRATIONS j - -F i g u r e F a c i n g Page 7. Comparison of Nat. Fab. s o l a r c e l l c h a r a c t e r - 29 i s t i e s w i t h Model IB 2A. Model 2: I d e a l diode i n s e r i e s w i t h decreasing on33 r e s i s t a n c e 2B. Representation o f excess hole d e n s i t y i n 35b n-region 2C. Diagram f o r comparing the L n l n - R _ p l o t w i t h 36 equation 7 o f Model 2. _ B 2D. Approximate p h y s i c a l r e p r e s e n t a t i o n o f the e f f e c t 40 to on R s of the boundary c o n d i t i o n f o r hole d e n s i t y 2K at d, (the n-region t o e l e c t r o d e contact) 8. R s modulated by hole i n j e c t i o n f o r Ge grown 41 diode ( B e l l 1H85) 9. R s modulated by hole i n j e c t i o n f o r Ge grown 41 diode ( C l e v i t e 1N188A) 10. R s modulated by h o l e i n j e c t i o n f o r Ge a l l o y 41 diode (1N77A) IT. Dark c h a r a c t e r i s t i c s c o r r e c t e d by c o n d u c t i v i t y 41 modulation theory, Ge a l l o y diode (1N77A) 12. A n a l y s i s of dynamic c a p a c i t y measurements f o r 47 a Ge a l l o y diode (1N77A) 2L. Table o f numerical r e s u l t s f o r c o n d u c t i v i t y 47 modulation theory f o r Ge all<ky diode (1N77A) 2M. F i g u r e i n d i c a t i n g the d i r e c t i o n of f l o w f o r 48 curre n t through the j u n c t i o n caused by l i g h t and f o r c u r r e n t due t o an e x t e r n a l forward v o l t a g e 2N. F i g u r e showing t h a t f o r s h o r t - c i r c u i t current 49 due to l i g h t f a l l i n g on the diode v e r y l i t t l e modulation o f n-region r e s i s t a n c e can take p l a c e by hole i n j e c t i o n from the t r a n s i t i o n r e g i o n because the c u r r e n t flows away from the n-region 13. P h o t o c h a r a c t e r i s t i c s of Ge grown j u n c t i o n 50 (1N188A) 14. P h o t o c h a r a c t e r i s t i c s of Nat. Fab. s o l a r c e l l 50 v i i LIST OF ILLUSTRATIONS Figur e F a c i n g Page 2 0 . Table of date f o r c a l c u l a t i n g R S c at 5 1 crossover 1 5 . Diagram showing t h a t R S L R s at crossover 5 1 3A. Model 3: Two i d e a l diodes opposed to one 5 2 another 1 6 . Comparison of dark c h a r a c t e r i s t i c s w i t h character- 54 i s t i e s c a l c u l a t e d from a model of two i d e a l diodes opposed to one another f o r Ge grown j u n c t i o n (TPC5) 4A. Model 4: I d e a l diode i n s e r i e s w i t h Bethe-type 55 diode 1 7 . Comparison of dark c h a r a c t e r i s t i c s w i t h c h a r a c t e r - 58 i s t i c s c a l c u l a t e d from Model 4 f o r Nat, Fab. S i s o l a r c e l l 18. Comparison of dark c h a r a c t e r i s t i c s w i t h character- 58 i s t i c s c a l c u l a t e d f o r Model 4 f o r Ge grown j u n c t i o n (TPC5) 5A. F i g u r e showing how l i f e t i m e v a r i e s w i t h d e n s i t y 6 2 o f i n j e c t e d c a r r i e r s f o r n o n l i n e a r recombination l i m i t e d by the Shockley-Read recombination theory 5B. F i g u r e showing t h a t has an extremum f o r i n j e c t e d 6 2 c a r r i e r d e n s i t y equal t o (ac)-£ CD INTRODUCTION The r e g i o n o f t r a n s i t i o n from p t o n-»type m a t e r i a l 'in a s i n g l e c r y s t a l o f a semiconducting m a t e r i a l such as Ge or S i , a c t s as a r e c t i f y i n g b a r r i e r to the f l o w o f cu r r e n t through the r e g i o n . T h i s t r a n s i t i o n l a y e r together w i t h the n and p-type regions on e i t h e r s i d e of i t i s c a l l e d a p-n j u n c t i o n or diode, Shockley (1949) developed a t h e o r e t i c a l r e l a t i o n be-tween the v o l t a g e a p p l i e d to the j u n c t i o n (he assumed i t t o equal the d i f f e r e n c e i n Fermi L e v e l s on e i t h e r s i d e o f the t r a n s i t i o n region) and the c u r r e n t through the j u n c t i o n oV I = I 0 ( e x p kT . i ) where I = reverse s a t u r a t i o n c u r r e n t . This r e l a t i o n was o v a l i d i f e x c i t a t i o n o f e l e c t r o n s and holes was due t o thermal energy alone and i f s m a l l c u r r e n t s flowed, i . e . the p e r t u r b a t i o n of the d e n s i t y o f holes ( e l e c t r o n s ) i n the n(p) r e g i o n was much l e s s than the e q u i l i b r i u m d e n s i t y o f e l e c t r o n s (holes) i n the n(p) r e g i o n . Cummerow (1954) considered t h i s same j u n c t i o n when photons w i t h an energy) the energy gap o f the semiconductor f e l l on or near the j u n c t i o n , c r e a t i n g h o l e - e l e c t r o n p a i r s which d i f f u s e d t o the j u n c t i o n and caused a photocurrent and photo-e.m.f.. H i s theory showed t h a t t h i s photo-c u r r e n t flowed i n a d i r e c t i o n apposite t o the forward dark c u r r e n t through the diode g i v i n g f o r the t o t a l diode c u r r e n t (2) a! I =1 (exp k T - l ) « BL L O where L = i n t e n s i t y of i l l u m i n a t i o n . H a l l (1952)^ consider-ed a d i f f e r e n t type o f j u n c t i o n c o n s i s t i n g o f a l a y e r o f v n e a r - i n t r i n s i c semiconductor sandwiched between h e a v i l y doped p-and n-regions. For h i g h l e v e l i n j e c t i o n and w i t h the half-?thickness o f the middle wafer s m a l l compared w i t h L (the d i f f u s i o n length) he obtained a dark chs. exo o I = I p 2kT Bornemann et a l (1955) f o r a m e t a l l i c contact t o n-germanium and w i t h the assumptions t h a t T i s i n f i n i t e and a l l the current was hole c u r r e n t } o b t a i n e d an expression f o r I which showed t h a t the e x p o n e n t i a l term i n the dark c u r r e n t - v o l t a g e chs. changed g r a d u a l l y from exp qV/kT f o r low c u r r e n t to exp qV/2kT f o r h i g h c u r r e n t . Kleinman (1956) obtained a semi-empirical expression f o r the dark chs. o f a s i m i l a r S i P-I-N diode which contains an e x p o n e n t i a l term l y i n g between exp qV/kT and qV/2kT. The photochs. f o r a diode (Lebovec, 1948) r e l a t e s the s h o r t - c i r c u i t c u r r e n t t o the o p e n - c i r c u i t v o l t a g e q voc I s c ^ o ( e x P " ^ r - 1 ) I t may be d e r i v e d from the general i l l u m i n a t e d chs. of Cummerow by c o n s i d e r i n g t h i s equation f o r the two s p e c i a l cases of s h o r t - c i r c u i t c u r r e n t and o p e n - c i r c u i t v o l t a g e and (3) e l i m i n a t i n g l i g h t (L) from the two equations. T h i s photo-chs. has the. g r e a t advantage t h a t the e f f e c t s of l i g h t on a j u n c t i o n can be measured without measuring the l i g h t i n t e n s i t y . The problems t h a t i n i t i a t e d the present i n v e s t i g a t i o n were: (1) the experimental dark chs. o f s m a l l area Ge j u n c t i o n s f e l l below the i d e a l chs. p r e d i c t e d by the Shockley theory except very near the o r i g i n . (2) the photochs. of s m a l l area Ge j u n c t i o n s i n some diodes agreed almost e x a c t l y w i t h the Shockley-Cummerow theory w h i l e i n other s i m i l a r diodes the photochs. f e l l below the t h e o r e t i -c a l photochs., though not so much as the dark c h s 0 (3) Seed (1954) shov/ed i n h i s paper on Ge grown j u n c t i o n s the i l l u m i n a t e d chs, (the I~V chs. when a l i g h t i s s h i n i n g on the diode and a forward v o l t a g e i s a p p l i e d to i t ) c r o s s i n g the dark chs,. Cummerow's the o r y i n d i c a t e d t h a t the i l l u m i -nated c h s 0 should be a constant c u r r e n t d i f f e r e n c e (BL) below the dark chs. Why then d i d the dark a n d i l l u m i n a t e d chs. cross ? Our experimental i n v e s t i g a t i o n s confirmed the existence o f the crossover e f f e c t and showed t h a t the vol t a g e o f t h i s crossover p o i n t increased w i t h i n c r e a s i n g i l l u m i n a t i o n . (4) Shockley*s theory I n d i c a t e s t h a t the c u r r e n t through the diode i n the dark should s a t u r a t e when a reverse v o l t a g e i s a p p l i e d t o the j u n c t i o n . I n none o f the diodes X4) *did the reverse c u r r e n t s a t u r a t e (become constant) and i n some f o r a g i v e n reverse v o l t a g e i t i n c r e a s e d w i t h time, (5) The experimental photochs. o f the S i s o l a r b a t t e r y i n d i c a t e d an exponential term of the form exp qV/3kT over 2 decades of c u r r e n t . Why should the experimental chs. o f t h i s broad area device depart so markedly from the i d e a l photochso? (6) A l l the dark chs. had e x p o n e n t i a l terms f o r medium forward v o l t a g e s (0.4V) l e s s than qV/2kT, the minimum slope p r e d i c t e d by any o f the t h e o r i e s . The problem t h a t r e q u i r e d s o l u t i o n f i r s t was t h a t o f the dark forward chs. o f the s m a l l area Ge j u n c t i o n s . To e x p l a i n the dark forward chs. s e v e r a l models f o r the diode were mathematically examined (and compared w i t h experiment: Model IA An i d e a l diode o f the Shockley type i n s e r i e s w i t h a constant r e s i s t a n c e . Model IB As i n IA but i n a d d i t i o n a shunt r e s i s t a n c e across the diode. T h i s model was proposed by P r i n c e (1955) to e x p l a i n chs. of the s o l a r b a t t e r y . Model 2 C o n d u c t i v i t y modulation of the n-.ahd p-regions by i n j e c t e d c a r r i e r s o f the opposite type (Shulman and McMahon, 1953; P r i n c e , 1956; Kleinman, 1956). Model 3 Two i d e a l diodes of the Shockley type, opposing one another, one r e p r e s e n t i n g the main p-n j u n c t i o n , the other r e p r e s e n t i n g the n-region t o e l e c t r o d e contact,. C5) Model 4 One i d e a l diode o f the Shockley type represent-i n g the main j u n c t i o n and an e m p i r i c a l diode proposed by Bethe to e x p l a i n p o i n t - c o n t a c t r e c t i f i e r s (Torrey and Whitmer, 1954) r e p r e s e n t i n g the n-region t o metal contact. Model 5 Non-linear recombination of c a r r i e r s causing the departure from the Shockley theory (Kleinman, 1956)* An approximate theory f o r c o n d u c t i v i t y modulation of the n-region by hole i n j e c t i o n from the p-region produces good agreement w i t h the e x p e r i m e n t a l l y observed dark chs.; i n one Ge a l l o y diode the agreement was exact up t o a t l e a s t 0.7V forward v o l t a g e . From the dark chs. and the dynamic c a p a c i t y measure-ments o f the diode t h i s theory was able t o p r e d i c t f o r a Ge a l l o y diode P n » T p , v ^ Q , and other parameters. Chs. of the diode, dark and i l l u m i n a t e d , have been found to i n t e r s e c t at l a r g e forward c u r r e n t s . T h e o r e t i c a l i n v e s t i g a t i o n of the c o n d i t i o n f o r crossover i n va r i o u s models of the diode i s made. The p h y s i c a l meaning of t h i s c o n d i t i o n i s t h a t a t some forward v o l t a g e the r e s i s t a n c e o f the diode i s s u f f i c i e n t l y reduced on i l l u m i n a t i o n t o o f f s e t the e f f e c t of the opposed i n t e r n a l photo-e.m.f.. For an i d e a l diode the r e l a t i o n between the sh o r t c i r c u i t photo-current and o p e n - c i r c u i t photo-e.m.f. (photochs.) should simply be the same as the dark forward chs., except f o r a r e v e r s a l o f s i g n of the c u r r e n t . The f a c t t h a t the experimental photochs. f a l l s below the i d e a l <6) •photochs. i s a t t r i b u t e d t o i n t e r n a l r e s i s t a n c e i n the diode and an expression i s developed from t h i s assumption; the t h e o r e t i c a l e xpression i s l a r g e l y c o n s i s t e n t w i t h experiment. By u s i n g a p o i n t l i g h t source and the inverse-square law f o r l i g h t , "B" of the short c i r c u i t c u r r e n t I g c w r i t t e n as - BL i s found t o be a s l o w l y v a r y i n g f u n c t i o n of l i g h t , v i z . B:<o<in where n v a r i e s from «0.15 f o r very s m a l l l i g h t i n t e n s i t i e s t o 0.10 f o r l a r g e l i g h t i n t e n s i t i e s on the Ge diodes ( F i g . 4 ) , However except f o r v e r y low i n t e n s i t y o f l i g h t n i s approximately constant at 0.10. None of the other models g i v e s the diode chs., p a r t i c u -l a r l y the dark chs.. The most s u c c e s s f u l of them, Model 4, appears to be only an e x e r c i s e at c u r v e - f i t t i n g due t o one e x t r a disposable parameter. Model 5 i f used together w i t h the c o n d u c t i v i t y modulation theory, would seem to be p h y s i c a l l y v a l i d , f o r l i f e t i m e does depend on d e n s i t y of c a r r i e r i n j e c t i o n . (7) LIST OF COMMON SYMBOLS A area o f p-n j u n c t i o n b r a t i o - of e l e c t r o n t o hole m o b i l i t y B a parameter w i t h dimensions of c u r r e n t / l i g h t i n t e n s i t y Bg i s the same parameter f o r the semiconductor-electrode j u n c t i o n d length of n-region Dp n d i f f u s i o n constant f o r holes ( e l e c t r o n s ) i n n(p) regi o n g r a t e o f c a r r i e r generation per u n i t volume I c u r r e n t through diode I Q a parameter w i t h dimensions of c u r r e n t (q P nLp/Dp) which t h e o r e t i c a l l y i s equal to the s a t u r a t i o n reverse c u r r e n t I L c u r r e n t through device when i t i s i l l u m i n a t e d (v/ith o r without an a p p l i e d v o l t a g e or an e x t e r n a l impedance), I c u r r e n t through device i n dark ( w i t h an e x t e r n a l a p p l i e d v o l t a g e ) , I s h o r t c i r c u i t c u r r e n t through the device when i t i s i l l u m i n a t e d , 3T c u r r e n t d e n s i t y through device J p n hole ( e l e c t r o n ) c u r r e n t d e n s i t y through the device k Boltzmann's constant L i n t e n s i t y of i l l u m i n a t i o n (8) Lg r e f e r s t o l i g h t i n t e n s i t y on j u n c t i o n at semicon-duct o r - e l e c t r o d e contact L p > n d i f f u s i o n l e n g t h f o r holes ( e l e c t r o n s ) * (D T ) ^ v p,n p,n/ e q u i l i b r i u m d e n s i t y of holes and e l e c t r o n s i n i n t r i n s i c m a t e r i a l e q u i l i b r i u m e l e c t r o n d e n s i t y i n n-region N J J donor d e n s i t y i n n-region P n e q u i l i b r i u m hole d e n s i t y i n n-region Pp e q u i l i b r i u m hole d e n s i t y i n p-region the excess d e n s i t y of holes at a plane x i n "the h-region over the e q u i l i b r i u m density»(because of charge n e u t r a l i t y t h i s i s the excess e l e c t r o n d e n s i t y at the plane x a l s o j q e l e c t r o n i c charge r r a t e of c a r r i e r recombination per u n i t volume R r e s i s t a n c e R Q e q u i l i b r i u m r e s i s t a n c e of n(p) r e g i o n R i n t e r n a l s e r i e s r e s i s t a n c e of the device s T absolute temperature V v o l t a g e when the context makes c l e a r what vo l t a g e i s meant V Q e x t e r n a l v o l t a g e a p p l i e d t o t e r m i n a l s of the device V. the d i f f e r e n c e between the Fermi L e v e l s on e i t h e r side of the space-charge r e g i o n . <9) r Voc ° P e n c i r c u i t v o l t a g e across the device when i t i s i l l u m i n a t e d x the d i s t a n c e measured from the n-edge o f the space-charge r e g i o n —12 £ q d i e l e c t r i c constant f o r f r e e space (8.85 x 10 f/m) £ d i e l e c t r i c constant ( 1 6 ^ f o r Ge, 12£v f o r S i ) JJp hole m o b i l i t y | J n e l e c t r o n m o b i l i t y p r e s i s t i v i t y of the n(p) r e g i o n C~ bulk c o n d u c t i v i t y o f n ( p ) - r e g i o n undisturbed by c a r r i e r i n j e c t i o n dT(flt) bulk c o n d u c t i v i t y o f n ( p ) - r e g i o n at a plane, x u n i t s from the n-edge of the j u n c t i o n hole l i f e t i m e i n n-region yjjQ e q u i l i b r i u m d i f f e r e n c e i n e l e c t r o s t a t i c p o t e n t i a l across the j u n c t i o n f a c i n g p. 10 L i g h t J u n c t i o n leads FIG.Ai L i g h t n Indium Drop leads FIG * A i i j L i g h t Boron l a y e r — " 2x10-* cms. t h i c k , dontact (10) CHAPTER I (EXPERIMENTAL PROCEDURE AND RESULTS DIODES USED IN EXPERIMENT The f o l l o w i n g i s a l i s t of the diodes on which experiments were conducted: (1) Two T r a n s i s t o r Products C5, Ge grown j u n c t i o n s ( F i g . A i ) . These were the f i r s t diodes examined and they were subjected to most of the experimental procedures. A paper by Seed (1954) i n d i c a t e d crossover i n the TPG5 diodes and l e d us to more c a r e f u l l y examine the phenomenon. ( 2 ) A S y l v a n i a 1N77A Ge a l l o y j u n c t i o n ( F i g . A i i ) . Most experimental procedures were done on one o f these diodes. (3) A N a t i o n a l F a b r i c a t e d Products S l S i s o l a r b a t t e r y ( F i g . A i i i ) . This c e l l i s made by d i f f u s i n g o f boron i n t o n-type Si., The reverse chs. of t h i s c e l l was not i d e a l f o r even one or two kT/q v o l t s of reverse v o l t a g e . The photochs. w i t h a slope q/3kT over 2 decades o f c u r r e n t was a l s o very d i f f e r e n t from theGe diodes. (4) C l e v i t e LN188A Ge grown j u n c t i o n ( F i g . A i ) . Dark and photochs. were done. This j u n c t i o n had a s m a l l reverse curr e n t t h a t s a t u r a t e d w e l l 0 (5) B e l l Telephone L a b o r a t o r i e s 1N85 Ge grown j u n c t i o n ( F i g , A i ) . This diode i s not commercially a v a i l a b l e but Or-. Shive k i n d l y made one a v a i l a b l e f o r t h i s work. This diode t i l ) was not r e c e i v e d u n t i l l a t e i n the research and there was only time f o r a dark chs. t e s t on i t . A pparently the p u b l i s h e d chs. do not p r e d i c t crossover, (Shive and Zuk, 1955), (6) Two l a b o r a t o r y model c i r c u l a r d i f f u s e d b o r o n - s i l i c o n diodes ( F i g . Ali±)9 and one r e c t a n g u l a r diode of the same type. These diodes were made i n the same way as the s o l a r b a t t e r y . These were a l s o r e c e i v e d l a t e i n the r e -search and when t e s t s showed t h a t t h e i r dark chs. were even more complex than the dark chs. o f the s o l a r c e l l , e.g. a t about 500mV forward v o l t a g e there was a p o i n t of i n f l e c t i o n f o r the c i r c u l a r diodes, they were no longer considered.(These samples provided by B e l l Telephone L a b s ) , (7) A, Hughes fused«alloy A l - S i s m a l l area diode (HD6005) ( F i g . A i i ) . Considerable work was done on the diode but the apparatus was not s e n s i t i v e enough t o a c c u r a t e l y measure the c u r r e n t f o r s m a l l a p p l i e d v o l t a g e s . The cover-i n g coat of p a i n t was scraped o f f the diode t o make i t capable of being i l l u m i n a t e d but the geometry prevented much l i g h t from f a l l i n g on the j u n c t i o n . F o r both reasons i t was f i n a l l y d i s carded. f a c i n g p. 12 FIG.B Pu l s e r FIG.C (12) DARK CHARACTERISTICS The normal experimental set-up f o r measuring the dark chs. i s shown i n F i g . B, The diode was placed i n o o a thermos i n an o i l bath at 25 C, • 1 C „ The potentiom-e t e r proved t o be the most accurate and dependable way o f measuring v o l t a g e across the diode, p a r t i c u l a r l y f o r sm a l l c u r r e n t s . For ve r y small c u r r e n t s a K e i t h l e y VTVM across a shunt o f s e v e r a l megohms was used to measure the cu r r e n t . At l a r g e currents the diode heated. To t e s t the e f f e c t o f t h i s h e a t i n g on the dark chs. the p u l s e r and brid g e set-up o f F i g . C was employed. Diode c u r r e n t and volta g e were computed from the bridge parameters at balance and from the v o l t a g e of the p u l s e . P u l s e d u r a t i o n was 1 ms. a t a r e p e t i t i o n frequency of 60 per s e c . Thi s technique showed t h a t h e a t i n g o f the diode d i d not s u b s t a n t i a l l y a l t e r the dark chs. ( i f the diode was i n the o i l bath) up to about IV forward v o l t a g e . Two d i f f i c u l t i e s decreased the accuracy of t h i s type of measure-ments u n c e r t a i n t y of the balance p o i n t ; measurement o f vol t a g e of pulse on the CRO screen. This same bridge set-up w i t h the p u l s e r and CRO r e -p l a c e d by a d.c. source and de t e c t o r was a l s o used t o measure the diode chs. f o r very s m a l l c u r r e n t s and t o check measurements made w i t h the normal method. 013) The s m a l l s i g n a l a.c. (300 c p . s . ) r e s i s t a n c e ) d V / d I > of the Ge grown j u n c t i o n (TPC5) at s m a l l forward d.c. bias v o l t a g e s and i n the dark decreased w i t h i n c r e a s i n g temperature. However beyond 250mV t h i s a.c. r e s i s t a n c e was almost constant over a temperature range between 20° C. and 30° C, I t can be concluded from t h i s f a c t t h a t f o r a given v o l t a g e the dark c u r r e n t w i l l i n c r e a s e w i t h tempera-t u r e . ILLUMINATED CHARACTERISTICS The i l l u m i n a t e d chs. i s most proper t o a photodiode because i t r e l a t e s , c u r r e n t , v o l t a g e a n d l i g h t . T h i s chs. •was measured w i t h constant l i g h t and w i t h p u l s e d l i g h t . For constant l i g h t and f o r a forward c u r r e n t the same experimental set-up was used as i n F i g . B. For negative currents the b a t t e r y was removed and the current f e d through a measured v a r i a b l e r e s i s t a n c e . The i l l u m i n a t e d chs. was l o c a t e d at the i n t e r s e c t i o n s of the l o a d l i n e s drawn from the v a r i a b l e r e s i s t a n c e s and of the measured voltage across the diode. The constant l i g h t method was s u i t a b l e f o r low l i g h t i n t e n s i t y but f o r g r e a t e r i n t e n s i t y the l i g h t heated the diode and the c o o l i n g o i l w i t h r e -s u l t i n g u n c e r t a i n t y i n the measurements. For these h i g h e r i n t e n s i t i e s a chopped or pu l s e d l i g h t source was used t o e l i m i n a t e h e a t i n g by the l i g h t . An attempt t o c o o l the diode by blowing compressed a i r (14) over i t was not s u c c e s s f u l . Best r e s i o l t s were obtained by p l a c i n g the diode i n a l i g h t petrolatum bath i n a l u c i t e c o n t a i n e r , the o i l being c o n s t a n t l y s t i r r e d . I n a d d i t i o n an i n c h of l u c i t e was p l a c e d between the l i g h t and the c o n t a i n e r . The l u c i t e was an i d e a l l i g h t f i l t e r f o r the Ge diode. I t s t r a n s m i s s i o n p r o p e r t i e s f o r a \. i n c h f i l t e r are as f o l l o w s : 80-85% t r a n s m i s s i o n up to 1.5 microns; 30-35% i n bands up t o 2 microns; 0 beyond 2 microns. Assuming an energy gap i n Ge o f 0.7 e.v. t h i s means t h a t wave lengths up t o 1.8 microns w i l l be e f f e c t i v e i n producing liole« e l e c t r o n p a i r s ; hence the l u c i t e w i l l t r a n s m i t p r a c t i c a l l y a l l these photons and stop a l l those mainly r e s p o n s i b l e f o r h e a t i n g the diode,. The l i g h t petrolatum c o o l a n t had t r a n s -m i s s i o n chs. s i m i l a r t o the l u c i t e except between 1 and 2 microns i n which range i t absorbed more photons than the l u c i t e . A l i g h t chopper was s u c c e s s f u l l y employed t o reduce h e a t i n g of the diode by h i g h i l l u m i n a t i o n . The chopper con-s i s t e d o f an aluminum d i s c w i t h one c i r c u l a r hole a t the o circumference 0.5 cms. i n diameter and subtending a 10 angle at the centre o f the d i s c . The d i s c r o t a t e d a t 2840 rpm - 10 rpm. The 500 watt p r o j e c t i on lamp was the l i g h t source and the diode was i n the o i l bath w i t h one i n c h o f l u c i t e between i t and the chopper. The s h o r t -c i r c u i t c u r r e n t , being p r o p o r t i o n a l t o the l i g h t i n t e n s i t y , f a c i n g p. 15 (15) f u r n i s h e d a convenient way of measuring t h i s i n t e n s i t y . This was done by h o l d i n g the chopper s t a t i o n a r y and n o t i n g the maximum sho r t c i r c u i t c u r r e n t t h a t the diode would supply f o r a given l i g h t i n t e n s i t y ( F i g . D). The i l l u m i n a t e d chs, may be obtained i n the f o l l o w i n g way. F i r s t the dark chs. i s obtained. Then w i t h the s e t -up o f F i g . D the s h o r t - c i r c u i t c u r r e n t i s noted f o r the given i l l u m i n a t i o n . Then the v a r i a b l e r e s i s t o r i s s e t to gi v e the d e s i r e d dark c u r r e n t through the diode (the diode should be covered f o r t h i s measurement). T h i s dark c u r r e n t g i v e s a p o i n t on the dark chs. The r e s i s t a n c e of the c i r -c u i t f a c i n g the diode i s then computed and a lo a d l i n e drawn through t h i s p o i n t . With the l i g h t f a l l i n g on the diode the CRO measures the departure from the dark chs. v o l t a g e (AV). The i n t e r s e c t i o n of the l o a d l i n e and the voltage l i n e , equal t o the sum of the dark v o l t a g e andftVj g i v e s the de-s i r e d p o i n t on the i l l u m i n a t e d chs. Since the method i s l a b o r i o u s and the i l l u m i n a t e d chs. do not provide any important i n f o r m a t i o n except when crossover of the dark and the i l l u m i n a t e d chs. occurs o n l y f o r the 1N77A Ge a l l o y diode, were i l l u m i n a t e d chs. made. The technique e x p l a i n e d above i s used to f i n d the cu r r e n t s and vol t a g e s a t the crossover p o i n t s as w e l l as the s h o r t - c i r c u i t c u r r e n t corresponding to the i l l u m i n a t i o n used. As crossover i s approached the CRO d i s p l a y f o r the 1F77A i s as f o l l o w s i n F i g . E. f a c i n g p, 16 ' ' t J V U Crossove 3 i i i i i FIG.E 10 m a . 2 0 0 m v . 4 0 U mv. FORWARD V61TAGE F.3G.1 (16) F i g . E i i i represents the crossover pointsfrom the f o l l o w i n g argument. I f we accept t e n t a t i v e l y t h a t F i g . E i i i r epresents the crossover p o i n t s then these p o i n t s f o r v a r i o u s i l l u m i n a t i o n s are shown i n F i g . F (L >L o>L n-»0). Assume t h a t the maximum l i g h t i n t e n s i t y i s L g and t h a t the dark c u r r e n t corresponds t o p o i n t 0 on the dark chs.. When l i g h t f i r s t begins t o f a l l on the diode, from 0 the vo l t a g e moves out along the l o a d l i n e to the c u r v e t l . As the l i g h t i n c r e a s e s the volt a g e r e t u r n s along the l o a d l i n e t o 3, the maodmum I n t e n s i t y . Then the l i g h t ceases g r a d u a l l y (because of chopping) and the vo l t a g e r e t u r n s to 1 and 0. Crossover f o r thus occurs when 0 and 3 are on the same h o r i z o n t a l l i n e ( F i g . E i i i ) . Three of the crossover p o i n t s f o r the 12T77A diode are shown i n F i g . 1 and the R g and R g L f o r two of the p o i n t s are shown i n Table 20. Crossover occured also i n the TPC5 Ge grown j u n c t i o n , the only other diode t e s t e d f o r the e f f e c t . PHOTCCHARACTERISTIC The ge n e r a l photodiode equation i s I L = I Q (exp kT _ i ) _ BL I f 1 = 0 and V= V o c the ge n e r a l equation becomes q voc 0 = I 0 (exp - 1) - BL f a c i n g p. 17 L i g h t FIGo G Licrht >- V Diode CRO C17) I f V = 0 and 1= I s c then the g e n e r a l equation becomes E l i m i n a t i n g EL from these equations we get the photochs. q voc I M " x o C « P " » " - i ) which v e r y c o n v e n i e n t l y has no term i n v o l v i n g i l l u m i n a t i o n . F i g . G i n d i c a t e s the normal experimental set«up. The O n same pre c a u t i o n s were taken to keep the diode at 25 C. as f o r the i l l u m i n a t e d chs., i . e . l u c i t e f i l t e r , s t i r r e d o i l o bath h e l d a t 25 C. The 500 watt p r o j e c t i o n lamp served as l i g h t source. As maximum l i g h t i n t e n s i t y was approached i t was impossible t o h o l d the temperature of the diode and even of the o i l bath constant. To approach as c l o s e as p o s s i b l e to s h o r t - c i r c u i t c u r r e n t heavy copper l e a d s , a low r e s i s t -ance shunt and a very s e n s i t i v e galvanometer were used. I n order t o reduce h e a t i n g of the diode by the l i g h t and i n order t o reach g r e a t e r i n t e n s i t y of i l l u m i n a t i o n two pulsed l i g h t i n g techniques were used. The f i r s t was the chopper technique w i t h the 500 watt lamp explained i n the i l l u m i n a t e d chs. s e c t i o n . The second was an e l e c t r o n i c p h o t o f l a s h lamp. The experimental set-up f o r both these l i g h t sources i s shown i n F i g . H. f a c i n g p. 18 1 4, 100 10 1 ma 100 10 .1 P KO TO C BARA CTE'RIS T H Ge ALLOY DIODE (IN' J S O P 77A) f o r d i f f l i g h t i n g arent methods / ,/Phot y"0.56 5flashh q/kT ^500 W. Ch L i g h t Slope 0.8 jpped 5Cq/kT £-500 W. / ^ S l o p e Steady L i ght 0 300 mv. 400mv, Voc M P I G . 2 as) The o p e n - c i r c u i t v o l t a g e and the v o l t a g e drop across the low r e s i s t a n c e are both read on the CRO and I g c c a l c u -l a t e d . Both I s c and V o c must be obtained from the CRO because the pulses of l i g h t are s o s h o r t . The photochs. from the three techniques f o r the Ge a l l o y 12T77A diode are shown i n F i g , 2, For the same current the three m e t h o d B appear to giv e d i f f e r e n t v a l u e s o f V Q C, T h i s discrepancy may r e s u l t from the d i f f i c u l t y i n measuring the o p e n - c i r c u i t v o l t a g e and s h o r t - c i r c u i t c u r r e n t on the CRO and i n the case o f the p h o t o f l a s h by changing i n t e n s i t y of the f l a s h . Because a tru e s h o r t - c i r c u i t c u r r e n t cannot be achieved i n p r a c t i c e the e f f e c t o f R s c ^ 0 on I s c i s now c a l c u l a t e d . R a„ i n c l u d e s the r e s i s t a n c e of the e x t e r n a l c i r c u i t and a l s o the r e s i s t a n c e o f the contacts and bulk semi-conductor. The g e n e r a l equation f o r the photodiode i s s I = I 0 ( e x p kT - 1) - BL which f o r R„^-^0 becomes TBL 1 + VRs</^  I sc 1+R f /R sc o where k T / q I 0 f a c i n g p. 19 0 t,o 45V — — * A A / W — — © -Diode V admittance ~*7rn Bridge -O " G--O -O Detectojr - O FIG0 I (19) I n a l l the photochs, an attempt was made to keep R Q / R > 50 (R i s the r e s i s t a n c e of the e x t e r n a l c i r c u i t ) . For some l a r g e c u r r e n t s t h i s was i m p o s s i b l e , DYNAMIC CAPACITY OF SPACE-CHARGE LAYER As e x p l a i n e d i n the s e c t i o n on Model 2 two dynamic c a p a c i t i v e e f f e c t s are present i n p-n j u n c t i o n s . The measured dynamic c a p a c i t y i s the sum o f these two p l u s any s t r a y c a p a c i t y . F i g . ( I ) i l l u s t r a t e s the experiment-a l set-up f o r measuring t h i s t o t a l sum. The diode c i r c u i t allows a reverse d.c, b i a s v o l t a g e t o be a p p l i e d t o the diode (the bridge i s assumed to have n e g l i g i b l e d.c. r e s i s t a n c e } w h i l e s t i l l a l l o w i n g the s m a l l s i g n a l dynamic c a p a c i t y o f the diode t o be measured on the bridge at t h a t b i a s , The accuracy of the experiment was l i m i t e d by the d e t e c t o r . F o r f r e q u e n c i e s o f the order o f 20 Kc, which should be used to makeuu~r p4l, a narrow bandwidth wave analyser would seem to be the I d e a l d e t e c t o r . For f r e -quencies such thattA>T p>l, the exact formula f o r Q D must be used (see Shockley, 1950,p. 316). The three c a p a c i t i v e e f f e c t s present are (Shockley, 1949): (1) C Q S t r a y c a p a c i t y » important f o r l a r g e reverse v o l t a g e s on the diode. (2) C D D i f f u s i o n c a p a c i t y = Aq 2p nL p/2kT exp qV/kT (20) i f U J T ^ I - import.-mt only f o r small reverse v o l t -ages because of the exponential ter® i a V. (3) C s Space-charge n e u t r a l i s a t i o n capacitance -important at a l l voltages but dominant i n the middle region of reverse voltage. Fox* an a l l o y Junction wita abrupt t r a n s i t i o n from p to n-region X f o r a grown j u n c t i o n s [ i s - v )J where a^HD - H A i n the depletion l a y e r . F i g , (12) shows the dynamic capacity raeasureaaenis o f the 1M77A Ge a l l o y diode. Tho following procedure i s used i n analysing the data. F i r s t a p l o t o f l a C m e a 8 -l a V r e v i s made. A l a C s - In according to the theory should have a ^ slope f o r an a l l o y j unction and a 1/3 slope f o r a grown Junction. For the Ge a l l o y j unction considered t h i s l i n e with slope \ i s placed so that f o r voltages > S o o t h e diffe r e n c e between i t and the point© of measured capaci-tance i s acanstant (and equal to C Q) ( F i g . 12), facing p . 21 .IV I V 10 V REVERSE V O L T A G E • F I G . $ £21) I n c a l c u l a t i n g C D both area and p n must be known. These may be c a l c u l a t e d from the procedure o u t l i n e d i n Model 2 o r i f area i s known and i n t u r n p n may be c a l -c u l a t e d from the expe r i m e n t a l l y observed C g and the formula f o r C g, I f C U T ,O^1 then the approximate formula f o r d i f f u -s i o n capacitance may be used t o c a l c u l a t e C D f o r s m a l l v o l t a g e s , C r j + C 0 i s then s u b t r a c t e d from the measured capacitance values f o r v o l t a g e s ^ 5^ 0, The v o l t a g e d i f f e r -ence between these p o i n t s and the l i n e w i t h slope 1? should be constant a i d equal to'+o , For l e s s than 0,1 V reverse v o l t a g e the a.c. s i g n a l can d i s t u r b the reverse v o l t a g e o p e r a t i n g p o i n t ; i f too sm a l l an a.c, s i g n a l i s a p p l i e d the ba l a i ce p o i n t cannot be detected. Thus there i s c o n s i d e r a b l e u n c e r t a i n t y i n such low vo l t a g e capacitance measurements and hence i n d e r i v e d from them. The p o s s i b i l i t y o f e r r o r i n i s f u r t h e r i n c r e a s e d by u n c e r t a i n t y i n the p o s i t i o n of the In C s - In V r e v l i n e w i t h slope £ and by the f a c t t h a t because t^Tp<^ci the formula f o r C Q i s not exact. The measured dynamic c a p a c i t y d i d not appear to var y w i t h frequency up t o 100 Kc., a t l e a s t f o r reverse v o l t a g e s > 0,5V. F i g . 3 f o r Ge grown j u n c t i o n (TPC5) shows the d i f f e r e n c e between c a p a c i t y measured a t 100 Kc, and at 1 megacycle. The f a c t t h a t the slope i s l e s s a t a mega-c y c l e than a t 100 Kc. leads to the c o n c l u s i o n t h a t the frequency should be low, i . e . 100 Kc. f o r good C g f a c i n g p. 2 2 D PoDmx Source o f L i g h t —3ram.—«• Diode D i f f u s i n g Screen n F I G . J Ammeter 100 cm, 50 20cms. 10.0 5 Distance from l i g h t to ScrBen F I G . 4 £22) measurements , A t 100 Kc. the slope i s about l/39. the value p r e d i c t e d by the C g formula f o r the grown j u n c t i o n . Weak i l l u m i n a t i o n of the diode had very l i t t l e e f f e c t on the measured capacitance. With i l l u m i n a t i o n on the Oe grown j u n c t i o n (TPC5) corresponding t o 150 microamps sh o r t -c i r c u i t c u r r e n t the c a p a c i t y was the same as f o r the diode i n the dark, PHOTOCURRENT A FUNCTION OF ILLUMINATION Does "B" i n the formula f o r the s h o r t - c i r c u i t c u r r e n t of an i l l u m i n a t e d diode - ( l g c = » BL)« v a r y with i n t e n s i t y of i l l u m i n a t i o n (L) of the photodiode? The experimental set-up of F i g . J based on the inverse-square»law f o r a p o i n t source of l i g h t was used t o t e s t t h i s . The d i f f u s i n g screen, c o n s i s t i n g o f a sheet of paper, i n s u r e d t h a t the l i g h t f e l l evenly onthe j u n c t i o n , i,e„ the e f f e c t o f diode o r i e n t a t i o n w i t h respect to the l i g h t was reduced. The inverse«square-law a p p l i e d to the dependence o f L on the d i s t a n c e (D) between the p o i n t source and t h i s screen. The d i s t a n c e between the screen and j u n c t i o n was minimized. Because only weak p o i n t sources of l i g h t were a v a i l a b l e and because the d i f f u s i o n screen reduced the l i g h t i n t e n s i t y even more, the maximum I s c f o r the Ge diodes was about 10 microamps and f o r the S i s o l a r c e l l , 1mA, Some of the r e s u l t s are shown i n F i g , 4, ((23) Before the d i f f u s i n g screen was used the r e s u l t s were erratic and slopes on the I n T „ - In D p l o t « 2,4 were measured. The r e s u l t s may be summarized; (1) Por the N a t i o n a l F a b r i c a t e d s o l a r c e l l the slope of the In I g c - In D p l o t was 2,00, Thus "B" appears to be constant w i t h changing i n t e n s i t y o f i l l u m i n a t i o n , (2) For the Ge a l l o y j u n c t i o n (1N77A) and the Ge grown j u n c t i o n (TPC5) the slope of the I n I „ - i n D p l o t sc 1.7 f o r very weak i l l u m i n a t i o n (0,01 microamps s h o r t - c i r c u i t c u r r e n t ) and i n c r e a s e d t o between 2.05 and 2,15 f o r a 200^fold i n c r e a s e i n i l l u m i n a t i o n . The g r e a t e r p a r t of the slope (n) was c l o s e to the higher value which appeared t o be a l i m i t i n g v a l u e , (n/2 - 1) B<=<L where n i s the s l o p e . Therefore f o r Ge diodes s i n c e n > 2 except f o r the weakest l i g h t , "B" i n c r e a s e s w i t h i l l u m i n a t i o n . P o s s i b l e causes of departure from the inverse-square-law ares (1) The s h o r t - c i r c u i t c u r r e n t i s l e s s than i d e a l because of i n t e r n a l diode r e s i s t a n c e . (2) D i f f u s i n g screen not completely d i f f u s i n g , i . e , a component of d i r e c t t r a n s m i s s i o n i s present. As a r e s u l t the o r i e n t a t i o n o f the j u n c t i o n may cause >C24) g e o m e t r i c a l changes i n i n t e n s i t y as the d i s t a n c e of the l i g h t source from the diode i s changed* LIGHT SOURCES The photochs. and i l l u m i n a t e d chs. were done almost e x c l u s i v e l y w i t h a 500 watt, 120V, GJE. tungsten p r o j e c t i o n Itemp, 3200° K c o l o r temperature. The i n t e n s i t y o f illumi« n a t i o n was v a r i e d by changing the volt a g e on the lamp by means of a v a r i a c and a l s o by changing the d i s t a n c e between diode and l i g h t . The p o i n t sources of l i g h t i n c l u d e d : (1) A s m a l l tungsten lamp probably out o f an automobile h e a d l i g h t (12-16V; 4 w a t t s ) . (2) Tungsten p o i n t l i g h t ( S y l v a n i a A2/DC/S). (3) Tungsten P o i n - U o - L i t e ; 120 C.P.; made by Ediswan, England, The i n t e n s i t y was v a r i e d i n a l l these lamps by changing the dist a n c e from l i g h t source t o diode. The high i n t e n s i t y e l e c t r o n i c p h o t o f l a s h lamp was an Ascor S p e e d l i g h t , Model A - 202 w i t h a G.E. FT 120, #80 lamp. The f l a s h l a s t s 1/1300 sec. and has a peak l i g h t output of 6 4 X 10 lumens. The l i g h t a r i s e s from a discharge of 2000V through xenon gas o r a mixture o f argon and neon gas. T h i s l a r g e e l e c t r i c a l discharge ; c o u p l e d to the CRO and i n t e r -f e r e d w i t h the measurement of Vrt_ and I on the CRO. One *•"•» sc gre a t advantage of t h i s l i g h t was t h a t i t caused noheating. (25) A carbon arc was t r i e d but i t s i n t e n s i t y c ould not be kept constant enough. Measurements were made of the photochs. u s i n g a Na arc source to see i f the frequency of the l i g h t changed the chs. Wo change i n the photochs. were n o t i c e d so i t was assumed throughout t h a t wavelength d i d not a f f e c t the i l l u m i n a t e d and photochs. (26) GHAPTER 2 THEORY AND DISCUSSION ^THEORETICAL MODELS FOR PREDICTING CHARACTERISTICS OF DIODES MODEL I •IDEAL DIODE IN SERIES WITH CONSTANT R S Model I c o n s i s t s of an i d e a l p-n j u n c t i o n i n s e r i e s w i t h a f i x e d r e s i s t a n c e ( F i g . I A ) . The i d e a l j u n c t i o n has an i l l u m i n a t e d c h a r a c t e r i s t i c of the form (Cummerow, 1954) (exp kT _ I= I 0 (exp 1) - BL (1) The bulk Ge and the contacts c o n s t i t u t e the R g # -YL-Oh' -©• •AAAr - I F F i g . IA The dark c h a r a c t e r i s t i c i s found by s e t t i n g L = 0 i n (1) I I Q (exp kT . i ) (2) The p h o t o c h a r a c t e r i s t i c , which r e l a t e s the sho r t c i r c u i t c u r r e n t t o the open c i r c u i t v o l t a g e at any i l l u m i n a t i o n i n t e n s i t y , i s -aCR s Isc) -S^oc E S C = I 0 (exp kT - exp kT ) (3) f a c i n g p. 27 100-10 1 ma. 100 10 200 bv. 400 mv. FI&16 1 A, f i d e / Slo a l Dioc pe ajk' ie A / i >^ > ''Exper: Dark ( .mental : h s . . • Comparison of Dark Chs. w i t h Model I A.:'; of Ideal- Diode i n S e r i e s W l t i l U ;consta * r -' J 200wv. 400 600mv. #00 FORWARD VOLTAGE . FIG. 5 ( 2 7 ) which reduces, i f Rglsc * s s m a l l compared w i t h kT/q, t o oc - 1) (4) i +- Q^o Rs kT An attempt t o o b t a i n the i d e a l diode chs. from the experimental dark chs. u s i n g s e v e r a l values o f R_ i s shown have a l s o been computed and p l o t t e d i n F i g . . Th i s model does not p r e d i c t the experimental dark chs. ( F i g . 6 ). N e i t h e r i s there any experimental evidence f o r the r a p i d change i n the slope o f the l n l s c - V o c p l o t a t moderate cu r r e n t s r e q u i r e d by the theory ( F i g . G ). The same conclusions apply t o the other s m a l l area Ge devices t e s t e d . The chs. of the l a r g e area d i f f u s e d S i j u n c t i o n s v a r y w i d e l y but i t can be s a i d t h a t n e i t h e r the dark nor photochs. of any of them i s p r e d i c t e d by Model I . F i g . 5 suggests t h a t i f R g decreases as the c u r r e n t through the device i n c r e a s e s the f i t would improve. Therefore the next step i s to c a l c u l a t e the e f f e c t on RQ o f i n j e c t e d c a r r i e r s ( c o n d u c t i v i t y modulation). i n F i g . 6~ . The photochs. f o r these same values of R, f a c i n g p. 28 R s WW-— V - I R s — ^ b r -F i g . IB (28) MODEL IB MODEL IA SHUNTED BY A CONSTANT RESISTANCE. Model IB d i f f e r s from Model IA i n having a shunt r e s i s t a n c e across the diode i n a d d i t i o n t o a r e s i s t a n c e i n s e r i e s w i t h the diode ( P i g . I B ) . The shunt r e s i s t a n c e was added t o e x p l a i n the almost l i n e a r r e l a t i o n between I and V over a considerable range of reverse v o l t a g e ( ^ 4 V o l t s ) f o r the Nat. Fab. S l S i S o l a r B a t t e r y ( P r i n c e , 1955). Making use o f the gene r a l r e l a t i o n between I , V and L (Cummerow, 1954) <3V I - I Q (exp M - 1) - BL (4) the c i r c u i t equation f o r F i g . IB i s q(V - I R S ) I = I Q (exp m 1) - BL Hr V - I R a Rsh (5) This may be transformed t o the g e n e r a l I-V chs. IR f l) (6) S e t t i n g L = 0 we o b t a i n the dark chs. (7) f a c i n g p. 29 200 ma. 150' * D 100 ["""SHUNTED CONST AW1] 50 ma. 'COMPARISON OF SOLAR CELL CHS.WITH MODEL IB OF AN IDEAL.Dion IN SERIES WITH A, .00 TANT R AND ALSO V/ITH A R x. Above subst : — e qua L i y i e l d point <b Kxnerimer: must 7.5 .n. 3 6 -n_t 430 H ^  values i t u t e d i OTT these t a l P t s . 5C0mv. I V FORWARD VOLTAGE FIG.fc (29) F i n a l l y the photochs,. i s 1 +• R 3 R s h -qjsc5§ q v o c - I 0 exp = i exp "ET" - Vpc (8) Rsh To check the above theory w i t h experiment, values are needed f o r R g, R s h and I . The p l o t of the experimental I-V chs. should approach a s t r a i g h t l i n e w i t h slope R f o r s l a r g e forward v o l t a g e . T h i s i s so because the i d e a l diode a c t s almost as a short c i r c u i t . For l a r g e reverse v o l t a g e the i d e a l diode i s p r a c t i c a l l y an open c i r c u i t and so the slope of the chs. i s very n e a r l y R^Rs^- R 0» the r e s i s t a n c e near the o r i g i n , equals (dV) T)V = 0 .1=0 which y i e l d s R 0 = R c + ( R s h ) ( k T / q I 0 ) (9) ° R s h + k T / q V Regrouping Rsh+Rs -I = k T / q o R Sh -R s - Rp I (Ro - V j (10) From the measured values of R s u b s t i t u t e d i n ( 1 0 ) , I may be computed. A c t u a l l y the I-V chs. do not become s t r a i g h t l i n e s i n e i t h e r the f a r forward or reverse v o l t a g e d i r e c t i o n s , ( F i g . 7 ) , nor i s R q a c c u r a t e l y known. Hence I computed i n t h i s way i s not exact. (30) I may a l s o be estimated from a l n l j ) - V p l o t f o r the s o l a r b a t t e r y . A q/kT slope i s drawn on the l n I D - V graph so t h a t the v o l t a g e d i f f e r e n c e between i t and the dark chs. ( I D R s ) i s a minimum. (R g i s the s e r i e s r e s i s -tance measured i n the f a r forward d i r e c t i o n ) . I i s the i n t e r c e p t of t h i s q/kT l i n e w i t h the l n I D a x i s . I Q e s t i -mated t h i s way was about 0,5 mA; by the f i r s t method, about 0.34 mA. Equation (7) f o r moderate forward currents and beyond Is almost e q u i v a l e n t to the forward dark chs. o f Model IA (V 0 - I R s ) / R s h I o « V I 0 i . e . has no e f f e c t s ince the diode i s of v e r y low r e s i s t a n c e . Therefore i f Model IA i s not s u c c e s s f u l i n p r e d i c t i n g the forward dark chs. n e i t h e r w i l l t h i s model be. The i n t r o d u c t i o n of Rs-h was only p a r t i a l l y s u c c e s s f u l i n p r e d i c t i n g the reverse chs. Nowhere was there a t r u l y l i n e a r s e c t i o n of t h i s reverse chs.; beyond 4 v o l t s the cu r r e n t i n c r e a s e d more q u i c k l y («4 Y " 8 8 -8 Y - 300 mA). The best f i t f o r s m a l l I and V between Equation 7 and the experimental dark chs. was obtained f o r the parame-t e r s shown i n F i g . (7). The R needed t o o b t a i n t h i s f i t s (7.5 ohms) was much 'larger than the R_ (3.2 ohms) t h a t AV/ftI o f the f a r forward chs. g i v e s . Thus we conclude t h a t R„ must decrease as I i n c r e a s e s . Q u i t e p o s s i b l y s t h i s decrease i s due t o m i n o r i t y c a r r i e r i n j e c t i o n as C31) developed i n the next s e c t i o n . This modulation could take place i n three ways: (1) Hole modulation of n-region. Since the r e s i s t a n c e of the n-region i s probably < 1-^ h o l e modulation cannot wholly account f o r the e x p e r i m e n t a l l y observed l a r g e decrease i n R , s (2) E l e c t r o n modulation of p-region. The f a c t t h a t the p-region i s about 2 x 10 cms. t h i c k accounts f o r i t s h i g h r e s i s t a n c e . The acceptor d e n s i t y a t the surface i s about 18 +3 10 /cms. but t h i s d e n s i t y f a l l s o f f as ( P r i n c e , 1956) P = P e r f c x (11) o . \ f 4 D t where P i s acceptor d e n s i t y at d i s t a n c e x below surface P 0 i s acceptor d e n s i t y a t surface D i s d i f f u s i o n constant f o r i m p u r i t y (boron) at temperature of d i f f u s i o n t t o t a l time o f d i f f u s i o n 10 w3 o Since n^ i s about 1.4 x 10 cm a t 300K f o r S i , —3 a t the surface i s 200 cm and no c o n d u c t i v i t y modulation w i l l take place there. However, i n accordance w i t h (11) n i n c r e a s e s r a p i d l y w i t h x and assuming L to be equal p n t o the width o f the p - r e g i o n , there may be c o n s i d e r a b l e modulation over the main p a r t of the p-region by e l e c t r o n s * (3) The c o n t a c t r e s i s t a n c e i s probably the main p a r t o f R ( P r i n c e , 1954). T h i s contact r e s i s t a n c e may r e s u l t s (32) *from a t r a n s i t i o n l a y e r o f c a r r i e r d e p l e t i o n m a t e r i a l between the S i and metal e l e c t r o d e . T h i s near d e p l e t i o n r e g i o n may be c o n d u c t i v i t y modulated by i n j e c t e d c a r r i e r s c a r r y i n g r i g h t across the p or n-region. E l e c t r o n s e s p e c i a l l y , c o u l d e a s i l y cross the t h i n p-region and modulate the p t o metal contact. MODEL 2 . I D E A L DIODE I N S E R I E S WITH D E C R E A S I N G R ' i • s CONDUCTIVITY MODULATION - DARK CHS. The second, and most s a t i s f a c t o r y model, consists of an i d e a l junction i n series with a resistance which decreases with increasing current. The diode w i l l f i r s t be considered not illuminated. Assuming the n-region to be much nearer i n t r i n s i c than the highly-doped p-region, the decrease i n resistance r e s u l t s from (non-equilibrium) hole i n j e c t i o n into the n-region (conduc-t i v i t y modulation). Thus the t o t a l series resistance i s the sum of the resistance of the contacts, of the p-region, and the decreasing bulk resistance of the n-region. The equivalent c i r c u i t i s shown i n F i g . 2A. _ ^ V q , C>l r v w F i g . 2A Calculation of conductivity modulation requires that the two boundary conditions f o r hole density at the p-n junction and at the n-region electrode contact be known. The kind and q u a l i t y of the electrode contact f o r the commercial diodes experimented with was unknown. Hence the comparison of theory and experiment could not be exact. ( 3 4 ) The mathematical theory developed here i s f o r low-l e v e l i n j e c t i o n of holes i n t o the n-region ( p « N D ) „ The f o l l o w i n g assumptions are made: (a) One-dimensional ho l e f l o w ( x ) . T h i s assumption a p p l i e s w e l l to the Ge grown j u n c t i o n s , where the area o f the j u n c t i o n and n-region i s constant. I t a p p l i e s w i t h l e s s reason t o the Ge a l l o y j u n c t i o n s , where the j u n c t i o n i s more h e m i s p h e r i c a l i n shape and area i s not constant. One-dimensional hole f l o w would not seem to apply a t a l l t o the l a r g e area d i f f u s e d type S i j u n c t i o n s . Borneman et a l (1955) w i t h two a d d i t i o n a l assumptions, have shown t h a t the g e n e r a l shape o f the I-V chs. does not depend on the geometry. I n other words, whether the hole f l o w i s one, two or three dimensional, the r e s u l t i n g equation should be the same except f o r a constant m u l t i p l y i n g f a c t o r determined by the dimensions of the system. (b) The h o l e c u r r e n t i s by d i f f u s i o n only; i . e . J = -qD dp/dx. The d i f f e r e n t i a l equation f o r h o l e s i s P P P (c) Up , D , T » L & r e independent of p, n and o f x. « v P P p (d) The boundary c o n d i t i o n a t x= 0 i s P = p n exp kT J V,= j u n c t i o n v o l t a g e = ( a p p l i e d v o l t a g e - I R S ) . (35) a (e) The boundary c o n d i t i o n a t x = d i s P = P n which i m p l i e s a high r a t e o f recombination a t the e l e c t r o d e contact to the n-region, ( f ) J^J p ( 0 ) ; (Jn«l=0); i . e . the c u r r e n t i s c a r r i e d e n t i r e l y by holes a t the j u n c t i o n . (g) L o c a l n e u t r a l i t y i s maintained. T h i s i m p l i e s (n - p ) = ( n n - p n ) = N D and<r= <r*+• q p P ( b + 1)6 p, (h) Resistances of electrode-semiconductor contacts are n e g l i g i b l e . Making use o f these assumptions a g e n e r a l equation f o r R s i s developed i n Appendix 1. Since t h i s exact expression does not le n d i t s e l f to easy g r a p h i c a l a n a l y s i s an approximate expression i s developed below. The 8 p o f Appendix 1 i s r e p l a c e d by the approximate expression 8 P = P n (exp - 1) exp ^P <x) which g i v e s at x = d CJV -d_ *p(d) = p B (exp * T - 1) exp LP (2) which i s compatible w i t h 6 p(0)= 0 i f d/Lp»qV/kT. Making use o f the approximate b p o f equation 1, the f o l l o w i n g r e l a t i o n s j and F i g . 2B <T4= q p ^ b i ^ ^ - P n ) (3) <r(x) = <To+ q u P ( b + l ) b p (4) R« = f dx  3 h A?Tx) ( 5 ) f a c i n g p, 3 5 b (35)b S E E F A C I N G P A G E .the approximate c o n d u c t i v i t y modulation R_ f o r low l e v e l hole i n j e c t i o n i s R s - h i 1" f exp d/Lp +• In/In ~[ ( 6 ) A<r- L 1 1 - v i i - J I n equation (6) i f I 1 < l D < 1^ exp d/Lp then R P~ Lp I n I T exp d/Lp = R n n e ( 7 ) On a I n I D - H e p l o t t h i s i s the equation o f a s t r a i g h t l i n e w i t h slope - A c r 0 / L p and w i t h an i n t e r c e p t on the I n I D a x i s of 1^ exp d/Lp. Here R ] _ i n e i s the r e s i s t a n c e i n d i c a t e d by t h i s s t r a i g h t l i n e . I t i s seen t h a t o n l y i f exp d/Lp» 1 w i l l there be an appreciable s t r a i g h t p o r t i o n i n the p l o t of equation ( 6 ) „ f a c i n g p. 36 FIG. 2C (36) S e t t i n g R l i n e = R s of equation(6) ( P i g . 2C) S E R P A C I N G P A G E we f i n d I l i n e " I X exp cVLp ^  [ X " fe^] (8A) = 1 + 1_ f o r I I s r a a l l (8B) I x exp d/Lp I D . I l i n e Here I i i n e i s the cu r r e n t corresponding t o R i i n e . The experimental R S i s obtained from a I n I D - V p l o t by f i n d i n g the dif f e r e n c e , A V , o f the forward v o l t a g e o f the i d e a l chs. (slope ..: q/kT and pas s i n g through I 0 at V= 0) f o r a given c u r r e n t I D and the forward v o l t a g e o f the dark chs. f o r the same c u r r e n t and t a k i n g R S = A V / I B . Next I n I D i s p l o t t e d as a f u n c t i o n o f t h i s R S . The next step i s s u b j e c t t o some u n c e r t a i n t y . F i r s t we do not know the k i n d and q u a l i t y of the contact and hence we don't know the b.c. a t the contact but i t i s customary i n commercial diodes t o aim f o r the h i g h recombi-n a t i o n contact we haveassumed; i . e . t h a t p(d)= p n . ( I n the approximate theory p ( d ) = p n (exp qV^/kT - 1) exp -d/Lp which i s not imposed but a r i s e s from r e j e c t i o n o f one (37) s o l u t i o n of the d i f f e r e n t i a l equation),, Second, the u n c e r t a i n t y i n R s measured i s g r e a t e s t f o r small c u r r e n t s , p a r t l y because of u n c e r t a i n t y i n l o c a t i n g the q/kT s l o p e . This means t h a t the low c u r r e n t end of the In I D - R g p l o t i s not too u s e f u l i n deducing I-j_, HIGH LEVEL EFFECTS, Before proceeding w i t h the a n a l y s i s of the In I D - R g p l o t making use of the low l e v e l i n j e c t i o n theory, i t seemed appropriate t o consider the e f f e c t s which a r i s e from h i g h l e v e l i n j e c t i o n of h o l e s ( p ( 0 ) > > Ng) at l a r g e forward c u r r e n t s and cause d e v i a t i o n s from the assumptions of the theory given above, (1) High l e v e l hole i n j e c t i o n ( p > N D) leads t o a change i n the boundary c o n d i t i o n at the j u n c t i o n (x= 0) and as a r e s u l t to a d i f f e r e n t form f o r J p , S p and R g. Throughout t h i s s e c t i o n we may w r i t e J p ( 0 ) < ^ c $ p ( 0 ) p(0) A t x - 0 the f o l l o w i n g equation i s approximately tr u e from c o n s i d e r a t i o n o f quasi»Fermi l e v e l s at the j u n c t i o n 2 & p(p+ N D) =- n± expkT (9) When p > N D ( h i g h l e v e l i n j e c t i o n ) t h i s leads t o the b.c. at x= 0 „ p = n^ e x p 2 k T (10) (38) >and thus t o an equation f o r S p , w i t h exp qV/2kT i n s t e a d of exp qV/kT as the e x p o n e n t i a l term. Borneman et a l , (1955) i n a d d i t i o n to assumption a, c, e, f , g, h l i s t e d above f o r low l e v e l i n j e c t i o n have assumed t h a t f o r h i g h l e v e l i n j e c t i o n r - i s i n f i n i t e and J = 0 throughout the n-region, so o b t a i n i n g f o r %p * P = 2D£EBT-1 - J l + 4 p „ n n (exp k ? * , i j f 1 (11) 2 L I ( i V . i - P r , ) 2 J J '= n i I t i s i n t e r e s t i n g to note t h a t equations (12) and (10), a r r i v e d at by d i f f e r e n t approaches, are e q u i v a l e n t . Hence on a I n I D - V p l o t f o r v e r y h i g h l e v e l h o l e i n j e c t i o n ( i . e , exp qV/kT >> l / i ^ ) the i d e a l diode no longer has an q/kT slope but a q/2kT slope. For intermediate values of hole i n j e c t i o n the slope i s between q/kT and q/2kT. Since we do not know the c u r r e n t c o e f f i c i e n t f o r t h i s q/2kT chs.,AV and Rfl cannot be determined f o r the, h i g h l e v e l case, (2) T p w i l l v a r y w i t h 6p. I n f a c t , f o r h i g h l e v e l i n j e c t i o n , T p i s almost constant and much l e s s than f o r low l e v e l i n j e c t i o n . T h i s value o f T p i s d i r e c t l y opposed t o Borneman's s i m p l i f y i n g assumption t h a t T p i s i n f i n i t e (and J n i s zero) but i f d/L p i s s m a l l enough the approxi-mation i s v a l i d . (39) I n Model 5 we consider the e f f e c t on the chs. o f c a r r i e r recombination t h a t v a r i e s n o n l i n e a r l y w i t h i n -j e c t e d hole d e n s i t y ( i . e . a T p which i s not co n s t a n t ) . The exponent o f the expo n e n t i a l term f o r the diode chs. v a r i e s between 3/2 q/kT and 1/2 q/kT, w i t h an extremum o c c u r i n g f o r some S p which i s not n e c e s s a r i l y the maximum % p. (3) p p and Dp w i l l a l s o v a r y f o r h i g h l e v e l i n j e c t i o n . \) p of the low l e v e l case i s f o r l a t t i c e and i m p u r i t y s c a t t e r i n g of holes w h i l e f o r the h i g h l e v e l case there i s i n a d d i t i o n c a r r i e r - c a r r i e r s c a t t e r i n g which w i l l reduce the hole m o b i l i t y . ( H a l l , 1952; Morin and M a i t a , 1954). (4) For the r e l a t i v e l y l a r g e a p p l i e d v o l t a g e f o r h i g h l e v e l hole i n j e c t i o n d r i f t c u r r e n t w i l l tend t o predominate over d i f f u s i o n c u r r e n t . The c r i t e r i o n f o r t h i s t o happen i s t h a t the e l e c t r i c f i e l d i n the n-region exceeds kT/qLp, Borneman e t a l i n t h e i r assumptions take d r i f t and d i f f u s i o n c u r r e n t s i n t o account but then by assuming J n = 0 they consider only hole c u r r e n t . When d r i f t c u r r e n t predominates, however, i t seems l i k e l y t h a t t h i s c u r r e n t should be c a r r i e d comparably by hol e s and by e l e c t r o n s and so J n may not be n e g l i g i b l e compared w i t h J p # The i n c l u s i o n of these a d d i t i o n a l e f f e c t s i n a theory v a l i d f o r h i g h l e v e l i n j e c t i o n becomes very complicated and c o u l d not r e a d i l y be checked e x p e r i m e n t a l l y , so i t has not been attempted. f a c i n g p. 40 DIACR;KS FOR APPENDIX 1 Doundary Condition at d pld)»p n &pjp n(exp qV/kT - 1) 6t> DIAGRAMS. FOR EQN. 7 Doundary Condition at d p(d)=p n(cxp qV/kT -1) exp -d/Lp + p n p n(exp qV/kT - 1) FIG.2D FIG..2E d d FIG.2F SI1ALL CURRENT FIG.2G Rs approx. equal since b„'c not important yet FIG.2H 1=1. exp d/L. FIG,21 RR i s l e s s i n Fig.21 than i n Fig.2H FIG.2J Very l a r g e I FI|5>a2K Tlie r a t i o between Ro of Fig.ZK and Rs of F i g . 2 J i s be com. i n g ^ s m a l l . APPROXIMATE PHYSICAL REPRESENTATION OF THE EFFECT ON R 6F THE BOUNDARY CONDITION FOR HOLE DENSITY AT d (40) GUIDES IN ANALYSIS OF l n l _ , - R PLOT The f o l l o w i n g guides apply p r i m a r i l y t o the comparison o f the approximate R g of equation (7) w i t h experiment. The s u b s t i t u t i o n o f equation (7) f o r the R g developed i n Appendix 1 appears j u s t i f i e d f o r two reasons. F i r s t , the b.c. at x= d o f equation (7) a c t u a l l y may represent the p h y s i c a l s i t u a t i o n . Second, f o r 1-Q=1I exp ^/L^ and d / L p» 1 equation (7) g i v e s Rg=(yA<r«)(0.70) w h i l e Appendix 1 g i v e s Rs-(yA<To) (0.82). F i g s . 2D to K attempt a p h y s i c a l p i c t u r e o f the d i f f e r e n c e s between equation (7) and the equation i n Appendix 1. R g of equation (7) should b e ^ R g of Appendix 1, arid t h i s d i f f e r e n c e should be more marked the l a r g e r I D , f o r a t l a r g e I D the b.c. a t d becomes more important. I f R g given by the two equations are not too much d i f f e r e n t f o r I 1 exp d/Lp which i s a f a i r l y l a r g e c u r r e n t , we seem j u s t i f i e d i n assuming the agreement w i l l be even b e t t e r f o r s m a l l e r v a l u e s of c u r r e n t . F o r h i g h l e v e l h o l e i n j e c t i o n n e i t h e r formula i s v a l i d . Guide 1. I f the l n I D - R g p l o t was l i n e a r f o r a good di s t a n c e t h i s l i n e a r p o r t i o n may be considered c o i n c i d e n t w i t h the » Atf"o/L l i n e . Equation (7) p r e d i c t s t h i s i f Guide 2. I f the l n I D - R s p l o t has a p o i n t o f i n f l e c t i o n w i t h shallow curves on e i t h e r s i d e , the - A t f i / L p slope would be ^ . the slope of the l n I D - R g curve at the p o i n t of i n f l e c t i o n . A t the same time the c u r r e n t d i f f e r e n c e f a c i n g p. 41 50 ma 10 •D 1 ma .1 ma ma, Re I'onu: LAT"7.D BY1 JECTJON i Diode -:-1NI33A •• — HOLE .IN. -Ge- GrowGlevite LV°2.4 KX i . Lope'^-lolr QQ .m"~I o Experi *• Experi correc penta1 P nental P bed by e > S * in .S-SboJ 10 A, 100 10 I ma 100 10, \>k Rs MOD HOLE I Ge A l l Sy"1 , 1 U LA TED BY. NJECTION ; oy Diode N77A ^/Lr»12 ma. . 1 I y\ -r\ ^ « T 32. U X l i l i 7 Ex: erj Exper: Pts. J e:qr .mental p t s . N ^ Lmental ibrrecte «a J FIG.10 RS modula HOLE INJE "Ge Grovm B e l l 1N#5 1 ted by GTION Diode \ s j Slope=-\ 2 1 ohm ^ 7.3 o Experime Points n t a l \ 5s FIG.8 10 1 ma ID 100 10 1,0 ^5lope< 1/kT > c per 3. me irk Chs ntal • DARK < &ARACT ERISTIC CORREt TI.VIT' THEOR" Ge Al' :TED BY COKDUC f MODULATION : n v D'i or]'p • • — ( 1»77J i)- See F i c.lO v. t cons1 ;ant *. 2UL imv. : 4uu ou mv. Su FORWARD VOLTAGE FIG.11 (41) between the « A &o /Lp l i n e and the experimental p o i n t s f o r s m a l l c u r r e n t s should equal I j and be constant. The - A /Lp slope would be the experimental slope a t the p o i n t of i n f l e c t i o n i f d/L - 1 f o r then the c o r r e c -t i o n term o f equation (8) would begin before the ^ c o r r e c -t i o n had become unimportant. Thus the l n l _ . - R_ curve jj s would begin to bend up before i t had reached i t s minimum - A <r0 /Lp s l o p e . However even i n t h i s case R g o f equation (7) and R n n e may be compared q u i t e e x a c t l y u s i n g the c o r r e c t i o n term o f equations (8) and the f o l l o w i n g procedure. Guide 3. A t e n t a t i v e s t r a i g h t l i n e i s drawn through t h % p o i n t of i n f l e c t i o n and p a r a l l e l to the s t r a i g h t l i n e p o r t i o n o f the l n I D - R s p l o t . I x exp d/L p i s the i n t e r c e p t o f t h i s l i n e on the l n l D a x i s . S t a r t i n g w i t h a value of R g where I j / I - j ^ g << 1 and making use o f 8A, V I p j i s added to 1/IT_ exp d/Lp ( t h i s i s done ve r y e a s i l y g r a p h i c a l l y by adding them on a piece of semilog paper turned upside down) and the r e s u l t compared w i t h I l i n e f o r t h i s p o i n t . T h i s i s repeated f o r a few other p o i n t s , u s i n g 8A or SB, The comparison o f these c o r r e c t e d p o i n t s w i t h the ~ A<^/L p l i n e w i l l suggest how the f i t may be improved. A new s t r a i g h t l i n e i s drawn and the process repeated. The r e s u l t s of t h i s type of a n a l y s i s are shown i n F i g s . (% ,°). COMPARISON OF THEORY AND EXPERIMENT Agreement between R. o f equation (7) and experimental (42) R v a r i e s . The approximate theory i n d i c a t e d t h a t the s l n l p - R G p l o t should be a s t r a i g h t l i n e or have the geom e t r i c a l form,* o f F i g . 2C, This shape appears i n the l n l - R p l o t s of a l l the Ge and S.^  diodes except f o r two Ge grown diodes. The curves f o r both of these diodes appear t o bend up i n s t e a d of down at the low curren t end o f the l n I D - R G p l o t . F o r these s m a l l current R G depends c r i t i c a l l y on the p o s i t i o n o f the q/kT slope of the i d e a l diode on the l n I D - V p l o t , but even w i t h the slope tangent to the dark chs,, the l n I D - R G curve s t i l l bends up. The Ge a l l o y diode agreed p e r f e c t l y w i t h the approxi« mate theory o f equation (7) ( F i g s J Q , l l ) , The l n l - R O D S p l o t o f the 1 N 85 Ge grown j u n c t i o n was ve r y n e a r l y a s t r a i g h t l i n e w i t h a gradual bending up at the high c u r r e n t end. ( F i g , 8 ). Equation (8) d i d not f u l l y c o r r e c t t h i s departure from the s t r a i g h t l i n e p o r t i o n of the curve, assumed to be c o i n c i d e n t w i t h the - A<Z/l>^ slope. A care-f u l f i t t i n g u s i n g the equation (8) was done on another Ge grown diode w i t h the poorer r e s u l t s i n d i c a t e d i n ( F i g . 9 )„ A q u a l i t a t i v e C43) ^check on the other diodes, both Ge and S i , i n d i c a t e d f a i r agreement w i t h the theory. (Why the theory should p r e d i c t the s o l a r b a t t e r y dark chs. i s not c l e a r . See d i s c u s s i o n o f c o n d u c t i v i t y modulation o f s o l a r b a t t e r y a t end o f s e c t i o n on Model L & ) C o n d u c t i v i t y modulation o f the n-region by holes i n j e c t e d from the p-region seems to be the major cause of the d i f f e r e n c e between the measured dark chs. and the i d e a l diode chs. ( I ' I Q (exp qV/kT - 1), a t l e a s t up to h i g h l e v e l hole i n j e c t i o n . P n , T p , L p , CALCULATED FROM THE CONDUCTIVITY MODULATION THEORY The f o l l o w i n g a n a l y s i s f o r an a l l o y type diode i l l u s t r a t e s the amount of in f o r m a t i o n t h a t may be d e r i v e d from the c o n d u c t i v i t y modulation theory v i a the - A<f«/Lp l i n e d i s c u ssed above. I f equation (7) and (8) are used t o determine the best - A<r«/L_ l i n e , i n the process R and P o I 1 are f i x e d by the c u r v e - f i t t i n g . The a l l o y j u n c t i o n was chosen to be analysed f o r two reasons: (1) i t s e x c e l l e n t agreement w i t h equation ( 7 ) ; ( 2 ) o n l y f o r a l l o y j u n c t i o n s can the c o n d u c t i v i t y modulation r e s u l t s and the dynamic c a p a c i t y r e s u l t s be combined t o g i v e a maximum o f i n f o r -mation. J u n c t i o n type diodes may be analysed s i m i l a r l y and they have the advantage t h a t the j u n c t i o n area i s known; however dynamic capacitance measurements o f them do not (44) g i v e a check on p n and as happens f o r the a l l o y type. F i r s t a comparison i s made between e x p e r i m e n t a l l y determined q u a n t i t i e s and the groups o f symbols they correspond to i n theory. Then a second comparison i s made between the experimental q u a n t i t i e s and the i n f o r -mation d e r i v e d from them, the comparison developing from most c e r t a i n t o l e s s c e r t a i n experimental r e s u l t s , and then from these d e r i v i n g secondary r e s u l t s . E x p e r i m e n t a l l y Determined Corresponds i n Theory t o Group of Symbols S = slope of the s t r a i g h t l i n e = «AO« (13) p o r t i o n o f the l n I D - ^  p l o t or the slope determined by curve-f i t t i n g . I R s Q = i n t e r c e p t of s t r a i g h t l i n e = I± e x p f P ^ A ^ | ( 1 4 ) w i t h L n I D a x i s : , where R= Oa *- ^ R = unmodified r e s i s t a n c e of the o bul k n-region. I n f e r r e d from l n I D - V p l o t or the curve f i t t i n g o f Guide 3. IT_ = c u r r e n t i n t e r c e p t of the s t r a i g h t _ I R = 0 ( 1 5 ) l i n e p o r t i o n w i t h R = R Q a x i s . e x P [ R o A < ' ^ L p ] (45) E x p e r i m e n t a l l y Determined Corresponds i n Theory t o group of Symbols I Q = s a t u r a t i o n c u r r e n t o f i d e a l diode; = Aqp nDp/i_p (16) equal t o the d i f f e r e n c e i n c u r r e n t near the o r i g i n on a l n I D - V p l o t between the q/kT slope o f an i d e a l diode and the measured dark c h s # Should be constant but i n c r e a s e s some-what as the o r i g i n i s approached, 2 I o / I l = ( b ^ 1 ) BOg f o r equation (7) (17) = ( b ^ 1 ) p n c Q t h d/Lp f o r Appendix 1 (18) D i f f e r e n t i a l capacitance measurements on t h i s same diode w i t h the reverse v o l t a g e as v a r i a b l e y i e l d a c a p a c i -t a n c e C m e a s r C o + c s + c D w h e r e Cfl = the dynamic c a p a c i t y due t o — A g i ^ g l ^ 1 9 y 2(vi-V)j space charge, (most important f o r l a r g e reverse v o l t a g e s ) . 2 L i 2kT C D = t h e d i f f u s i o n capacitance r e - =r Aq pnLp exp qV/kT (20) s u i t i n g from the f a i l u r e of i n -j e c t e d c a r r i e r s t o f o l l o w the a.c, f i e l d , ( This C Q i s most important f o r s m a l l v o l t a g e s ) . The formula on the r i g h t i s an approximation v a l i d i f u ) T ^ l or 2. ( 4 6 ) CQ~ s t r a y c a p a c i t y and assumed constant, (Important f o r l a r g e reverse v o l t a g e where C"D, C s—»-0) Because the experimental q u a n t i t i e s are not e q u a l l y c e r t a i n , the f o l l o w i n g development i s ordered t o place the more c e r t a i n experimental q u a n t i t i e s i n the key p o s i t i o n s . For example, area, one of the most v i t a l q u a n t i t i e s , can onl y be measured d i r e c t l y by opening the diode. Hence the area i s regarded as an unknown and adjusted t o make the other r e s u l t s c o n s i s t B n t , R Q i s a l s o u n c e r t a i n , but i n the a l l o y j u n c t i o n s i t can be i n f e r r e d w i t h more c e r t a i n t y than area. Derived Experimental I x = 1 I R = 0 exp ^ R^SI (21) 2 2 A / p n = p ^ - _ v ] (23) n ? L qf- J Secondary Derived 2 2 T P = A D p | S l l (24) 2 L l ° J i ( CD)v=0 =. Aq_pD__(DpTp) (25) 2kT 0Z = qC ^ i f t i + WpPn 5 ( 2 6 ) 1 (27) R = le n g t h of n-region (28) {jCTo) (Average Area of n-region) f a c i n g p. 47 T70V I D T REVERSE VOLTAGE FIG.12 Lp/A«r. R o To . n i b I I 32 o 7 114.5 4. 20;: 10"^ amps 1.95X101" 2 e14 0 . 1 8 _ n l . J V sec 3.^.0x10-4 amps Area Pn n n T P 2e93x10-7 l 0 7 4 x l 6 1 8 2 a 20x^0-° 1. 7 x l 0 - 6 vsec0 ohra r n " x 0„076 ohra-m. L P 'cD)v*o Apparent width of n-rep-ion Anp.Width V A * 0 from InV-IpC nlot 8.9x10" 5 ra. 141 p£ 0 0 053x10" 3 rn. Should \ 6 )e. equal 3.5 0.14 V NUMERICAL RESULTS OF CONDUCTIVITY HODTTLATION THEORY FOR Ge ALLOY . DIODE (1N77A) TA^LE 2L (47) I n equation (23) f o r l a r g e neg. V, i s n e g l i g i b l e , and assuming a value f o r C Q which i s c o n s i s t e n t w i t h the I n C m e a s ^ - In V p l o t ( F i g . \ 2 ) , A i s computed to be con« s i s t e n t w i t h p n i n (22). From these T p and C D may be computed and C m e a s ^ c o r r e c t e d , f o r small v o l t a g e s , by c D + c o to giv e C g, The V d i f f e r e n c e between the c o r r e c t e d C s and the l i n e w i t h slope 1/2 should y i e l d a constant v a l u e o f ^ K ( F i g . \^ ), Th i s was on l y approximately t r u e e x p e r i m e n t a l l y . The assumption t h a t the slope of the s t r a i g h t l i n e on the In C s - In V p l o t i s L/2 f o l l o w s from the abruptness of t r a n s i t i o n In an a l l o y j u n c t i o n , R Q should be c o n s i s t e n t w i t h (28). From ^Po the d e n s i t y o f acceptors i n the p-region may be found. The numerical r e s u l t s f o r the Ge a l l o y diode are give n i n Table 2K. ( F i g , U ) i n d i c a t e s the agreement between the i d e a l q/kT slope and the dark chs. c o r r e c t e d by the c o n d u c t i v i t y modulation R o f equation ( 7 ) . f a c i n g p tight t R « -—sfa B a t t e r y —I'l^ — F I G 0 m (48) PHOTOCHARACTERISTIC The photochs. i s given by (Cummerow, 1 9 5 4 ) -qlscRsc? qVpc I s c = I Q (exp kT „ exp «T ) (29) The measured open c i r c u i t v o l t a g e i s the tru e j u n c t i o n v o l t a g e but the measured sh o r t c i r c u i t c u r r e n t i s not t r u l y a s.c. c u r r e n t because of the r e s i s t a n c e of the n-region ( R s c ) , c o n t a c t s , and cu r r e n t measuring apparatus. Rgc* i s the sum o f these three r e s i s t a n c e s . I t i s important t o d i s t i n g u i s h between three con-d i t i o n s of r e s i s t a n c e t h a t the n-region may be i n , v i z ; Rs» HSL> Rsc« R s i s the c o n d u c t i v i t y modulated r e s i s t a n c e of the n-region i n the dark f o r some forward c u r r e n t . R O T i s the c o n d u c t i v i t y modulated r e s i s t a n c e of the n-region i l l u m i n a t e d f o r the same forward c u r r e n t . The f o l l o w i n g argument demonstrates t h a t R S L i s always l e s s than R s f o r a given forward c u r r e n t , SEE FACING PAGE F i g . 2M I n Figs.2'Myl5the forward c u r r e n t ( I p ) due t o the a p p l i e d v o l t a g e i s o f f s e t by the cu r r e n t due t o i l l u m i -n a t i o n which flows i n the reverse d i r e c t i o n . These two curr e n t s add a l g e b r a i c a l l y to g i v e I x the c u r r e n t at f a c i n g p. 49 •FIGa 2N (49) -which R s and R g L are compared.. Since l p i s b i g g e r than I x more holes are i n j e c t e d from the p i n t o the n-region f o r the i l l u m i n a t e d than f o r the dark case. Since the r e s i s t a n c e i s l e s s the more holes i n j e c t e d R S L w i l l be ' l e s s than R g. There may be a f u r t h e r r e d u c t i o n i n R S L because of the photoconductive modulation o f R s over the whole n-region, R i s the r e s i s t a n c e of the n-region when the s.c. cur r e n t due t o i l l u m i n a t i o n i s f l o w i n g . I g c flows i n the opposite d i r e c t i o n to the forward I D and thus the case f o r R s c i s t o t a l l y d i f f e r e n t than f o r R g and ( P i g . 2M) 0 SEE FACING PAGE F i g . 2N Holes are not i n j e c t e d i n t o the n-region from the p-region s i n c e the cu r r e n t i s f l o w i n g the opposite way. On the other hand there may be some i n j e c t i o n of hol e s from the contact i n t o the n-region, depending on the q u a l i t y o f contact. A l s o present i s photoconductive r e d u c t i o n of the n-region r e s i s t a n c e by the l i g h t and thus R i s somewhat l e s s than R n„ sc ° The I n I g c - V Q C p l o t s f o r the Ge diodes are almost s t r a i g h t l i n e s w i t h slopes roughly between q/kT f a c i n g p. 50 Fl8?14 PHOTOCMAK'ACTERIST.IQ OF Ge GROWN JN . / UNiddA) / / - O Experimental /£/ Photochs * / / Dark Slope q/kl JdO-fL / i n fl) ^01 rRg C shown, i s t a n c e r? I 0 exp q l . "Is r e s -squired 3 CR s c A T _ / Ph< / / i >tochs. 'agree with / n slope. i . . . _ '• - . r- r>h / V *1&0 ohms > -lOOmv..' 200mv, FlS5l3 (50) and 0.85 q/kT ( P i g . 13). The S i broad area j u n c t i o n s have p l o t s w i t h two s t r a i g h t l i n e p o r t i o n s ; one sh o r t p o r t i o n w i t h a slope = q/kT and a l o n g p o r t i o n w i t h slope = 1/3 q/kT. Por the Ge diodes the l Q e x p q | l s c | R g ^ l c T c o r r e c t i o n b r i n g s the experimental I n I s c - V Q C p l o t c l o s e r t o the q/kT l i n e ( F i g . 14) but because Rs'c i s unknown no q u a n t i t a t i v e check can be made. The two slopes f o r the S i devices &£e c o n s i s t ^ ent w i t h the theory, f o r the I f o r the broad area S i devices i s much g r e a t e r than f o r the s m a l l area Ge devices and f o r S i the c o r r e c t i o n term i s very l a r g e ( F i g . 14). Equation (12) f o r h i g h l e v e l i n j e c t i o n of holes i n t o the n-region cannot be used to p r e d i c t photochs. w i t h I n I0_» V_rt slopes <q/kT since as shown above there i s very l i t t l e h ole i n j e c t i o n f o r the photochs. CROSSOVER Crossover o f the dark and i l l u m i n a t e d chs. ( 1 ^ —11) f o r l a r g e enough c u r r e n t s i s p o s s i b l e i n the c o n d u c t i v i t y modu-l a t i o n model (and l i k e w i s e i n Models IA and IB) i f f o r a given forward c u r r e n t i s s u f f i c i e n t l y s m a l l e r than R g, Equations 30, 31 and 32 and F i g . (15) I D ~ I 0 (exp ^  - 1) (30) qCV - IrRgr) \ = 1 0 ( e x p * ? . - 1) - BL (31) I = (crossover c o n d i t i o n ) (32) f a c i n g p. 51 Diode Isc L Xover I Xover V I R S at Xover I ! 0 R s (egn34, RSL R s Sylv. 1N77A Ge Allov -1 B1 mA 3.7 mA . 286rnv. 86mv0 1.27'A., 23 21.4 0 o93 it « -6.5 MA .5a8 mA ,311rnv0 102mvo 1 027 A. 17 06 14 05 0,83 TPC5 Ge Grown -0.36mA 0o62mA 236mv 41 mv 0,25 A 0 66 48 0 o73 R<?r CALCULATED FROM CROSSOVER POINTS TABLE 20 1 I 0 ( e x p qV/kT IT + • I s c I x D I A G R A M SHOWINCJk^ / I n THAT RQT<R_ at/i . 7 ^ XOVER * L h '/ i . e . ( I n ^ I ^ ) / r ^ R a i 0 FIG.I5 (51) g i v e at crossover i s s ^ B L _ exp I exp K T . „ e x p fc":—• | (33) ^o *o which g i v e s R C J L kT m [ BL exp M -t- exp kT (34) Since R gj j< R s and I x i s p o s i t i v e the R.H.S. o f equation (33) i s p o s i t i v e . Therefore at a g i v e n i l l u m i -n a t i o n there c o u l d be some value of c u r r e n t f o r which the equation i s s a t i s f i e d . Table 2?0 l i s t s I , V, R g and Rg^ f o r crossover f o r d i f f e r e n t l i g h t i n t e n s i t i e s f o r the 1 N 77A Ge a l l o y j u n c t i o n . Crossover was a l s o observed i n the T.P^CS Ge grown j u n c t i o n . Whether crossover takes place or not appears to depend on the degree of p h o t o e x c i t a t i o n and where i t occurs on theGe device^ f o r both these f a c t o r s a f f e c t -1 f a c i n g p. 52 _ + 1 n ... 1 n 1 FIG.3A (52) MODEL'3 .TWO IDEAL DIODES OPPOSED TO ONE ANOTHER The t h i r d model consists., of two i d e a l p-n j u n c t i o n s opposing one another ( F i g . 3A). An i d e a l j u n c t i o n obeys the equation (Shockley, 1949; Cummerow, 1954). One j u n c t i o n represents the main p-n j u n c t i o n of the photodiode w h i l e the other represents a j u n c t i o n a t the contact between the e l e c t r o d e and n-type semiconductor. I n p r a c t i c a l diodes some l i g h t w i l l u s u a l l y f a l l on t h i s end contact and produce a p h o t o v o l t a i c e f f e c t . Thus the model d e p i c t i n g t h i s s i t u a t i o n i s as i n F i g . 3A i n which L 2 i s assumed to be p r o p o r t i o n a l t o L (the l i g h t i n t e n s i t y ) . Using the f o l l o w i n g equations f o r each diode alone i n F i g . 3A I = I 0 (exp kT - 1) - EL (1) I L = I 0 (exp kT - 1) - BL (2) -qV2 I L = I 2 ( 1 " exp K B 2 L 2 (3> the g e n e r a l equation f o r t h i s model i s * n ' B L t I o e x P (4) 1+<I 0/I 2)exp qV/kT where X 2 i s the s a t u r a t i o n c u r r e n t o f the end diode. (53) For l a r g e forward^voltage the c u r r e n t approaches a s a t u r a t i o n value determined e n t i r e l y by the end diode The dark chs, found by s e t t i n g L, L g = 0 i n equation ( 4 ) , i s * * * * * ~ (6) l - K l o / I g ) exp kT For l a r g e forward v o l t a g e I D = I g . The r e l a t i o n between r and V Q C i s a l g e b r a i c a l l y q u i t e complex and i s omitted here but a t l a r g e l i g h t i n t e n s i t i e s I S C ^ B L i f I 2 » I G (7) i . e , s t i l l l i n e a r - f u n c t i o n of Ir but V — & 1 x 1 l 2 B L = v s (8) q IoBgLg which i s a constant s a t u r a t i o n v a l u e . Crossover of the dark and i l l u m i n a t e d chs, found by equating I D t o I L , w i l l occur a t the forward v o l t a g e g i v e n by kT/q l n f L g B I g ~]= crossover v o l t a g e = V g (9) Thus crossover f o r a l l i l l u m i n a t i o n s should occur a t the same v o l t a g e V (assuming L 2<*L). V s should be the f a c i n g p. 54 IA. 100 10 JB I ma. 100 10 .1 MA, COMPARISON OF DARK b l S . WITH CHS. CALCULATED FROM' hA MODEL OF 2 IDEAL DIODES OPPOSED TO ONE r^T^bki ANOTHER 4^:50AM G H Ox-own (TP C5) drr< /^Calculated ' Dark! Chs. 200mv. 400mv, FORWARD VOLTAGE FIG.16 • ( 6 4 ) maximum open c i r c u i t v o l t a g e t h a t the diode can develop. E x p e r i m e n t a l l y the crossover v o l t a g e i n c r e a s e d w i t h i n -c r e a s i n g i n t e n s i t y of i l l u m i n a t i o n . F u r t h e r , experimental open c i r c u i t v o l t a g e s were observed which were much g r e a t e r than the v o l t a g e s at crossover. Thus the model i s incon-s i s t e n t w i t h experiment. Even more s e r i o u s was the f a i l u r e t o p r e d i c t the dark chs. ( F i g . 16). A number of other s e t s of values f o r I and I 2 than the p a i r shown i n ( F i g . 16) were t r i e d i n the attempt t o get the dark chs. but w i t h no b e t t e r r e s u l t s . However the experimental f a c t remains t h a t a r e c t i f y -i n g b a r r i e r o f t e n e x i s t s between a metal and n-type semi-conductor contact. Therefore we looked f o r another model t h a t would (1) i n c l u d e t h i s experimental f a c t , (2) p r e d i c t crossover, (3) g i v e b e t t e r agreement w i t h the dark chs. f a c i n g p. 55 IDEAL DIODE BETHE DIODE — V" FIG.4A (55) MODEL' 4 IDEAL DIODE IN SERIES WITH BETHE-TYPE DIODE For p o i n t - c o n t a c t r e c t i f i e r s Bethe (Torrey and Whitmer, 1948) had suggested chs. of the form I D = I 2 exp k T (exp kT _ i ) 0 ^ « 1 (1) The contact between the n-region and metal e l e c t r o d e might approximate to t h i s chs. and i n f a c t , G i a n o l a (1955) has suggested t h i s r e p r e s e n t a t i o n f o r the S i s o l a r b a t t e r y . These suggestions l e d t o the f o u r t h model. The f o u r t h photodiode model c o n s i s t s o f an i d e a l p-n j u n c t i o n i n s e r i e s w i t h a diode o f the Bethe type ( F i g . 4A) f o r which I L = I o (exp kT - 1) - BL (2) q/3V2 -gVg =-I2 exp( kT ) ( 1 - exp kT )+B^2 (3) The forward d i r e c t i o n o f the end contact depends on whether/3 £ 1/2 and so B g reverses i t s e l f f o r fi = 1/2. Thus i t seems p l a u s i b l e by analogy w i t h j u n c t i o n diode theory t h a t B 2 i s p o s i t i v e when B < 1/2 and negative when @> 1/2, When(3-1/2 the Bethe diode i s a symmetrical n o n l i n e a r r e -s i s t a n c e and not a r e c t i f y i n g element. The g e n e r a l c h s . f o r t h i s model ( F i g . 4A) i s (56) Ic exp k ? 0 J (4) [ l L 1 - B L i ' I 0 J When/3= 0 t h i s reduces t o equation (4) of the previous s e c t i o n s i n c e i t g i v e s the case of the i d e a l diodes i n s e r i e s o p p o s i t i o n . I n the dark chs. l e t X ^ V ^ + l ) ( 5 ) Then the dark chs. may be expressed [q/SV —, r «.qV -j exp kT Krai exp KT-t-1 (6) which f o r l a r g e forward c u r r e n t where l«"X«exp kT g i v e s /3+1 0+1 R + \ k r I D = I 2 _ I 0 exp (7) Now l e t us consider the photochs. i n which the diode i s i l l u m i n a t e d but no e x t e r n a l v o l t a g e i s a p p l i e d . I f I S c - I 0 (exp qV o c/kT - 1) (8) then I g c f o r the diode can be expressed For the f i r s t - o r d e r approximation (weak i l l u m i n a t i o n ) t h i s assumed the i d e a l form f o r a photochs. C57) I 8 C - - A (exp -KT~ - i ) (io) * 0 ^ 2 For the next order o f approximation (11) X s i c ^ s c ~ x + ( W*2>U s e - I s c -y \ I (12) For I s c ^ I S c t ^ 6 1 1 " t ^ 1 6 photochs. approaches q V 0 0 ( l -/3) I 8 C = - A 2 exp kT (13) which suggests t h a t f o r s t r o n g i l l u m i n a t i o n the s h o r t c i r c u i t c u r r e n t i n c r e a s e s l e s s r a p i d l y than f o r an i d e a l photochs. From (13) and the experimental photochs. both /3 and Ag may be estimated. Equation (10) and thephotochs. may a l s o be combined t o f i n d A 1; A* i s the constant d i f f e r -ence between the q/kT slope and the measured photochs. as V-»0. A l t e r n a t i v e l y A ' = qR^/kT where R Q i s the dynamic diode r e s i s t a n c e as (V, I - * 0 ) , A^ may be estimated from equation (11), I D cannot be obtained as an e x p l i c i t f u n c t i o n of V and so i t appears impossible t o see i f t h i s model p r e d i c t s crossover (Ip-Ig)» ' A r i l S O N U f ™ DARK TED FRO: :ns V/ITH Experim-e n t a l Dark Chs. '•al e.u-^Dark ch; values t I 0=l«ilnla ma, l a t e d from valuep -below derived)}''. — from photochs(Fi£. I 0 = l « 3 2 m a . 14) l 2 t = l o 4 2 r n a o -& =Q.J>1 c a l c u l a t e d T rota-t i v e best f i t 1 cx 12-1.90 3 .(Dark) ma /3=.35 200mv. 4 0 0 m v . FORWARD VOLTAGE F I G . 1 ? f a c i n g p. 58 FORWARD VOLTAGE FIG. 13' (58) This model p r e d i c t s f o r hi g h i n t e n s i t y of i l l u m i -n a t i o n V 0 ( p(kT/q) In ( B L / I 0 ) (14) This r e s u l t of a l o g a r i t h m i c a l l y i n c r e a s i n g o p e n - c i r c u i t photo e, m. f , agrees b e t t e r w i t h experiment than does Model 3 which p r e d i c t s a constant V f o r h i g h l i g h t i n t e n -oc s i t y . The comparison o f Model 4 and experiment was a l o n g process because most o f the equations were i m p l i c i t f u n c t i o n s o f c u r r e n t and v o l t a g e . The dark chs. of the TP C5 Ge grown j u n c t i o n and the Nst. Fab. s o l a r b a t t e r y were compared w i t h the t heory ( F i g s . 17, 18). The agreement was very good up to 300 mV forward v o l t a g e f o r the G5 diode ( F i g . 18). F o r the s o l a r b a t t e r y the photochs. and equation 13 l e a d t o 0.67 but the best agreement w i t h the dark chs. i s f o r p=. 0.35. The experimental dark chs. and the t h e o r e t i c a l chs. c a l c u l a t e d f o r both va3.ues o f a r e shown i n F i g . 17. Equation (12) p r e d i c t s t h a t the photochs. w i l l be a t 28.75 mA when the measured photochs. i s 28 mA f o r the TPC5 j u n c t i o n . A c t u a l l y the d i f f e r e n c e appears t o be s e v e r a l times t h i s amount. T h i s model g i v e s a b e t t e r f i t t o the dark chs, than Model (3) a n d i t a l s o shows t h a t the photochs. w i l l depart s l i g h t l y from the i d e a l (but l e s s than experiment i n d i c a t e s ) . However there are two weaknesses i n t h i s Model: (59) (1) There i s no p h y s i c a l reason In grown j u n c t i o n s and i n the d i f f u s e d S i j u n c t i o n s f o r assuming a Bethe-type chs. f o r the contact between the n - m a t e r i a l and e l e c t r o d e . /3 i s an a d d i t i o n a l e m p i r i c a l parameter; the model does not r e l a t e / 3 t o any p h y s i c a l parameters. (2) Agreement wi t h the dark chs. i s b e t t e r than i n Model 3, but t h i s may be only the r e s u l t o f adding the a d d i t i o n a l parameter (ft ) t o the I Q and I g of Model 3, i . e . we can c u r v e - f i t b e t t e r w i t h 3 than w i t h 2 parameters, (60) MODEL 5 ^NONLINEAR CARRIER RECOMBINATION TO PREDICT DARK I-V GHS. Ba s i c to the theory f o r the d, c, I-V c h a r a c t e r i s t i c s o f an i d e a l p-n j u n c t i o n diode i s the steady-state equation o f c o n t i n u i t y . For holes i t i s ^ • J p = q(g - r ) (1) For the one-dimensional case w i t h holes i n j e c t e d by an a p p l i e d forward v o l t a g e from the p-type i n t o the n-type r e g i o n of the j u n c t i o n , and assuming t h a t the r a t e of recombination i s d i r e c t l y p r o p o r t i o n a l t o the excess concen-t r a t i o n of h o l e s , the equation o f c o n t i n u i t y becomes q(P - P n ) - - ^ ( 2 ) T " d x , . ' P This equation leads to a chs. of the form I = A J p ( 0 ) = I Q (exp kT _ i ) ( 3) X where I Q«A q ( D p / T p ) 2 p n ( 4 ) For c u r r e n t s reasonably g r e a t e r than I Q the slope of the l n I D - V p l o t should be q/kT. The l n I D - V p l o t s f o r the Ge and S i devices t e s t e d always had a slope l e s s then q/kT (Figs.11,17), Kleinman (1956) a t t r i b u t e d t h i s departure from q/kT slope to c a r r i e r recombination t h a t v a r i e d n o n l i n e a r l y w i t h i n j e c t e d c a r r i e r d e n s i t y . (61) ^With t h i s assumption one form t h a t the steady-state c o n t i n u i t y equation may take f o r h i g h l e v e l i n j e c t i o n ( i n which r w i l l g r e a t l y exceed g) i s - £ p = -Kq(8p) V (5) dx Th i s leads t o an I~V dark chs. of the form qV(V+-l)' J ? = q ( 2 K D p P n v ^ ) ^ exp ^  2 ^ (K = a constant) (6) V = l g i v e s agreement w i t h the l i n e a r t h e o r y f o r l a r g e f o r -ward v o l t a g e s . What values o f v are c o n s i s t e n t w i t h a p h y s i c a l l y mean-i n g f u l theory? The Shockley-Read (S-R) theory of recombi-n a t i o n (Shockley-Read, 1952) by means o f a s i n g l e t r a p p i n g l e v e l l y i n g between the conduction and valence bands i s ex-amined here. I n t h i s theory U= (g - r ) ~ g i s the net r a t e of recombination f o r holes i n j e c t e d i n t o the n-region. Hence the c o n t i n u i t y equation i s d J g = , q U = -qK(6p) V (7) dx A l i f e t i m e f p i s d e f i n e d i n the S-R theory by T D=&£=l(fcp) ,~ V (8) • TT fC U KBy the S-R theory -r . T o (1+ aSp) 'P " (1+cop) (9) f a c i n g p. 62 toq S p FIG. 5A (a,c are p o s i t i v e parameters with d i m -ensions ox BKWhose value depends on the n-material) FIG. 5B (62) I n F i g , 5A are shown the ge n e r a l f e a t u r e s of a l o g T^ l o g Sp p l o t w i t h the l i m i t e d values o f T p g i v e n i n the S-R theory. SEE FACING PAGE P i g . 5A The p o i n t s o f i n f l e c t i o n on the curves of Ln T - l o g 6 p w i l l i n d i c a t e f o r what values of l o g %p, ( l . - v ) i s an extremum. (1 -V ) - d(m T) _ * P ( a - c) (10) d ( l n b p ) (1+ a S p ) ( l + cSp) 1 - V has an extremum f o r 6 p = 1 (11) \Tac whence the extremum of V i s g i v e n by V m = 2 \Tc~ (12) a^-*-\Tc" Sm FACING PAGE F i g . 5B (63) Thusv might vary from 0 to 2, depending on the values o f a and c. The same co n c l u s i o n can be immediately seen from equation (9) where i f a-» 0,T»r-l/p or i f c — * 0 , T p ~ p , and i f a * c,7y>«constant f o r a l l o p . With these l i m i t s f o r v , the I-V chs. f o r n o n l i n e a r recombination may vary between the extremes 1 I ~ exp 2 kT f o r c « a 3 £Y I ~ exp 2 kT f o r c » a and i n g e n e r a l v a r i e s as exp ( V + l ) .gV - 2 - kT from equation ( 6 ) . Thus on the b a s i s of recombination process which v a r i e s n o n l i n e a r l y w i t h c o n c e n t r a t i o n of i n j e c t e d c a r r i e r s as given by the Shockley-Read theory we can p r e d i c t the f o l l o w i n g about the dark chs.: (see F i g . SB) (a) The slope of the In I D - v p l o t can vary only between 1 /2 q/kT and 3/2 q/kT, (b) The slope of the In 1^ - V p l o t should go through a p o i n t of i n f l e c t i o n f o r i n j e c t i o n d e n s i t i e s c o r r e s -ponding to equation (11), The theory i s c o n t r a d i c t e d i n p a r t by the e x p e r i -mental r e s u l t s : (1) O n a l l Ge and S i devices t e s t e d the In I D - V p l o t ( 6 4 ) had a slope < L/2 q/kT f o r v o l t a g e s of the order of 0.3 V i n a l l cases ( F i g s . 11,13,16,17). V i o l a t e s ( a ) . (2) On no device was the slope>q/kT ( F i g s . 11,13,14,17). (a) suggests slopes up to 3/2 q/kT could e x i s t . (3) No p o i n t of i n f l e c t i o n had appeared f o r the h i g h e s t c u r r e n t d e n s i t i e s ( F i g s . 5,11,17). (b) suggests there should be a p o i n t of i n f l e c t i o n f o r these l a r g e c u r r e n t s . The c o n c l u s i o n i s t h a t n o n l i n e a r combination alone, given by the Shockley-Read recombination t h e o r y , w i l l hot e x p l a i n the e x p e r i m e n t a l l y observed dark chs. (65) APPENDIX I For low l e v e l hole i n j e c t i o n i n t o the n-region the d i f f e r e n t i a l equation f o r hole d e n s i t y i n the n-region i s ~ (P - VTl) = 0 (1) °* D P T P The gen e r a l s o l u t i o n f o r t h i s equation i s -x x 6p= (p - p n ) = A exp Lp+B exp Lp (2) The two boundary c o n d i t i o n s assumed to apply at the end of the n-region are P= P n a t x= d (3) oV P = P n (exp kT ) at x= 0 (4) which when s u b s t i t u t e d i n (.2) y i e l d f o r bp gV d - x & p = p n ( e x p kT - 1) s i n h Lp (5) s i n h d/Lp Using the r e l a t i o n s K- I dx, C6) <T (x) = «£ + qtfp(b"+i) 5p (7) assuming n e u t r a l i t y throughout the n-region and op o f (5) (66) "2" In P-h c o t h d +V1 -v- p P - * - c o t h 2L " 1+P (8) w h e r e P = ID I-L s i h h d / L p (9) a n d I , - kT . A <r~ c o t h d (10) 1 q T b T i l L ~ L p When d / L p > 4 we c a n c o m p a r e t h e v a l u e s o f R s f o r a c u r r e n t I 0 = e x p d A i p u n d e r t w o b o u n d a r y c o n d i t i o n s a t x = d . I f p ( x ) = p n I n 3 + ^ 5 = 0,86 L, A-CTo (11) Equation (7) of Model 2 g i v e s f o r the same c u r r e n t but w i t h the b.c, at x= d determined by & p=&p(0) exp « x/Lp R s=0,70 (12) Thus as expected the i m p o s i t i o n o f the b.c, p(d) = p n y i e l d s a higher r e s i s t a n c e than vfc en a l a r g e r hole d e n s i t y at the contact i s considered, s i n c e the main p a r t of the spreading r e s i s t a n c e a r i s e s from the r e g i o n near x = d where the c o n d u c t i v i t y i s always <5l i f p(d) = p n„ (67) REFERENCES Borneman et a l , Journ. App. Phys. 26, 1021-1028 (1955) Cummerow R. L., Phys. Rev. 94, 1525-1529 (1954) G i a n o l a U . , Journ. App. Phys. 2>7, 51-54 (195^) H a l l R. N., Proc. I n s t n Radio Engrs 40, 1512-1518 (1952) Kleinman D. A., B e l l S yst. Tech, J . 35, 685-706 (1956) Lehovec , Phys- Rev. 74, 463-471 (1948) Morin F. J . and M a l t a J.P,, P;ftys. Rev. 94, 1525-1529 (1954) P r i n c e M. B., Journ. App. Phys. 26, 535-540 (1955) P r i n c e M. B,, B e l l S yst. Tech. J 35, 661-685 (1956) Seed R. J , , " P h o t o s e n s i t i v e Ge Devices and Some Device A p p l i c a t i o n s " , T r a n s i s t o r P r o d u c t s , (1954) Shive J . N. and Zuk P., B e l l L a b o r a t o r i e s Record 33, 445, Dec.(1955). Shockley W., B e l l S yst. Tech. J 28, 435-489 (1949) Shockley W., " E l e c t r o n s and Holes i n Semiconductors", D. Van Nostrand, 1950, p. 316 Shulman R. G., and McMahon M.E., Journ. App. Phys. 24, 1267-1272 (1953) Torrey H.C. and Whitmer C.A., " C r y s t a l R e c t i f i e r s " , McGraw H i l l Book Co., 1948, p.46 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0103760/manifest

Comment

Related Items