@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Pinson, William Edwin"@en ; dcterms:issued "2012-01-31T19:07:08Z"@en, "1956"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """Measurements have been made on a variety of germanium and silicon junction diodes in order to determine departures from the ideal behavior both under illuminated and dark conditions. The diodes included alloyed, grown and diffused junction types and the experimental study was largely confined to forward voltage. Carriers injected by a forward voltage into the bulk regions of a p-n junction in Ge or Si reduce the resistances of these regions, A model of a photodiode consisting of an ideal diode (Shockley, 1949) in series with this carrier modulated resistance produces good agreement with the experimentally observed dark chs.; in one Ge alloy diode the agreement was exact up to at least 0,7V forward voltage. For large forward currents (density of injected carriers comparable to injected carrier density) the Shockley expression relating I and V is no longer valid nor consequently is the conductivity modulation theory. This theory, making use of the experimental dark chs, and the experimental dynamic capacity measurements, is able to deduce many of the parameters of the diode material e.g. Ƭ𝞺, Pո,Ψo. The chs. of the diode dark and illuminated have been found to intersect at large forward currents. Theoretical investigation of the condition for crossover in various models of the diode is made. The physical meaning of this condition is that at some forward voltage the resistance of the diode is sufficiently reduced on illumination to offset the effect of the opposed internal photo-e.m.f.. For an ideal diode the relation between the short circuit photo-current and open-circuit photo-e.m.f. (photochs.) should simply be the same as the dark forward chs., except for a reversal of sign of the current. The fact that the experimental photochs falls below the ideal photochs is attributed to internal resistance in the diode and an expression is developed from this assumption; the theoretical expression is largely consistent with experiment. Several other models are examined for the non-ideal behavior of junction diodes which attempt to take into account the possible effects of the resistance of the bulk material and of the electrode-semiconductor contact; the implications of non-linear recombination are also investgated. It is found that none of these alternative models is as successful as the conductivity-modulation scheme in explaining the dark, the illuminated and the photocharacteristics."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/40401?expand=metadata"@en ; skos:note "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 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 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<= 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 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 > 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 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 ^ 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 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 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+ 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) 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 "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0103760"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Physics"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "An experimental and theoretical investigation of the characterstics of dark illuminated junction diodes of germanium and silicon."@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/40401"@en .