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A new MOS photon counting sensor operating in the above-breakdown regime Lester, Timothy Paul 1982

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A NEW MOS PHOTON COUNTING SENSOR OPERATING IN THE ABOVE-BREAKDOWN REGIME B.Sc, The University of Victoria, 1975 M.Sc, The University of British Columbia, 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES - ' Department of Electrical Engineering We accept this thesis as conforming TIMOTHY PAUL LESTER to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 1982 Timothy Paul Lester, 1982 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agr e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s un d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f PLJ-aTg-ttCQL- ^wGr/^f^A~JiKJr~r The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 ABSTRACT A MOS optical sensor that utilizes avalanche multiplication in silicon is proposed and investigated "both theoretically and experimentally. The above-breakdown operating regime is discussed and i t is shown how a MOS photosensor may be operated in a photon counting mode by pulsing i t into very deep deple-tion, beyond the point where avalanche "breakdown normally occurs. Avalanche discharges in such a MOS sensor are self-quenching due to the formation of an inversion layer. This self-quenching property suggests that a monolithic self-scanned array of MOS photon counting sensors should be possible. It is described how specially designed charge-coupled arrays (PC-CCD's) could be operated in this new regime. The high response of silicon in the visible and near infrared, compared with the responsive quantum efficiency of the commonly-used photocathode materials, gives the proposed imager a distinct advantage over presently-existing photon counting sensors in these spectral regions. It is shown that a PC-CCD must be fahricated on a p-type silicon sub-strate and illuminated from the back side in order to obtain a high avalanche initiation probability for the photogenerated carriers. It is also shown that a l l thermally activated, steady-state dark generation of carriers can be reduced to a negligible level by cooling the sensor to 100 K or less, while the generation due to interband tunneling may be reduced to an acceptable level by ensuring that the peak fields within the depletion region remain below approximately h.3 x 10^ Vcm "*". The dark generation due to band-to-band tunneling via trap states may make i t necessary to restrict the peak fields to even lower values. Re-triggering following a breakdown pulse, due to charge trapping or impact ionization of these traps during the avalanche, is also analysed. Optical coupling due to light emission during the avalanche i i i discharges is discussed and two methods for the prevention of this coupling between the image elements in linear arrays are described. MOS gates that break down either at the Si-SiO,, interface, or in the bulk at a n-p junction created by a buried n-channel, have been fabricated and operated above breakdown. The surface breakdown devices were operated .in a charge-injection mode while the bulk breakdown devices were operated in a charge transfer mode similar to that which would occur in a f u l l PC-CCD imager. The surface breakdown devices exhibited excessive dark count rates that were attributed to the high electric fields at the Si-SiO^ interface. The bulk breakdown detectors were found to be far superior. They had very sharply peaked pulse height distributions and considerably lower dark pulse rates. Operation up to 12 volts above breakdown with a corresponding avalanche in i t i a -tion probability greater than 0.9 was possible with these devices. Only a very weak temperature dependence of the dark pulse rate was observed, suggesting that a tunneling mechanism of dark carrier generation was limiting the performance of the bulk-breakdown devices. The magnitude of the dark count rate agreed with that expected for band-to-band tunneling through mid-gap states. These states, through a change in their occupancy during breakdown, were also believed to cause the re-triggering of avalanches that was observed when operating at high, above-breakdown voltages. These limita-tions on performance can be expected to be removed by employing improved processing techniques which would reduce the mid-gap trap levels by one or two orders of magnitude. i v TABLE OF CONTENTS Page ABSTRACT . i i ' LIST OF TABLES v i v i i LIST OF FIGURES x i v ACKNOWLEDGMENT 1 INTRODUCTION 1 2 BRIEF REVIEW OF LOW LIGHT LEVEL IMAGE SENSORS 3 2.1 ANALOG IMAGERS 1+ 2.1.1 The DQE f o r Analog CCD Sensors 8 2.1.2 Performance o f CCD Imagers C u r r e n t l y i n Operation 10 2.2 PHOTON COUNTING IMAGERS 13 2.2 .1 L i n e a r i t y and DQE of Photon Counting'Imagers lh 2.2.2 Photon Counting Imagers P r e s e n t l y i n Use l 6 3. THE PROPOSED PHOTON COUNTING SENSOR AND THEORY OF OPERATION 2k 3 . 1 THE AVALANCHE INITIATION PROBABILITY 32 3 . 1 . 1 T r i g g e r i n g P r o b a b i l i t y Theory 33 3 .1.2 Previous Experimental I n v e s t i g a t i o n s 39 3.2 DARK GENERATION OF TRIGGERING CARRIERS k2 3.2.1 Review of Recombination and Generation at Bulk h2 Defect or Impurity Centers 3.2.2 Steady State Bulk Generation: Low F i e l d Case 51 3.2.3 Steady State Generation at the S i l i c o n / S i l i c o n 5^-Dioxide I n t e r f a c e : Low F i e l d Case 3.2.1+ High F i e l d E f f e c t s 57 3.2 .5 Dark Generation Due t o Tunneling 65 3.2 .6 Dark Generation o f T r i g g e r i n g C a r r i e r s i n the 77 Non-Steady State TABLE OF CONTENTS cont'd Page It EXPERIMENTAL INVESTIGATION OF MOS STRUCTURES PULSED 100 ABOVE BREAKDOWN k.l SURFACE BREAKDOWN DEVICES 1 0 1 - 4 . 1 . 1 Design Considerations 1 0 1 h.1.2 Test S t r u c t u r e Designs and Mask Layouts 10k 4 . 1 . 3 Device F a b r i c a t i o n Ilk k.l.k Test Chamber and E l e c t r o n i c s 12k k.l.5 Modeling of the Completed Devices 128 k.l.6 Experimental Results and D i s c u s s i o n 133 1+. 2 BULK BREAKDOWN DEVICES 150 4 . 2 . 1 Design Considerations and Equations 1 5 3 k.2.2 Test S t r u c t u r e Design and F a b r i c a t i o n 156 U.2.3 Two Dimensional Modeling of the Completed Devices 167 k.2.k Experimental R e s u l t s and Discussion. 172 5 SUMMARY AND CONCLUSIONS 190 BIBLIOGRAPHY 198 APPENDIX A E l e c t r o n and hole i o n i z a t i o n c o e f f i c i e n t s 20k i n s i l i c o n APPENDIX B S i m p l i f i e d schematics f o r the high 207 voltage d r i v e , t i m i n g c i r c u i t r y , charge a m p l i f i e r and d i s c r i m i n a t o r APPENDIX C Methods used t o determine the doping p r o f i l e 2 1 1 and i n t e r f a c e s t a t e d e n s i t y . APPENDIX D Method used f o r the two-dimensional 2lk c a l c u l a t i o n of the p o t e n t i a l and f i e l d d i s t r i b u t i o n s i n the bulk breakdown devices v i LIST OF TABLES Page 3 . 1 Experimental values f o r the e f f e c t i v e mass and matrix "J6 elements f o r t u n n e l i n g through t r a p s t a t e s k.l P r o c e s s i n g d e t a i l s f o r f i r s t f a b r i c a t i o n 115 h.2 Processing d e t a i l s f o r second f a b r i c a t i o n 117 k.3 Device and t e s t wafer data 120 h.k Processing d e t a i l s f o r the bulk breakdown devices l 6 2 k.5 Data f o r wafer M66 l 6 6 V l l LIST OF FIGURES Page 2.1 Responsive quantum e f f i c i e n c y of d i f f e r e n t analog sensor 6 arrays as a f u n c t i o n o f wavelength 2.k Responsive quantum e f f i c i e n c y of d i f f e r e n t photocathode/ window combinations as a f u n c t i o n o f wavelength 3.1 Equivalent c i r c u i t f o r an avalanche diode o p e r a t i n g above breakdown, plus the b i a s and d e t e c t i o n c i r c u i t 3.2 Energy band diagram f o r a p-substrate MOS gate at the be-ginn i n g and end o f an avalanche discharge 3.1+ P o t e n t i a l w e l l diagram i l l u s t r a t i n g the b a s i c o p e r a t i o n o f a 4-phase PC-CCD 12 2.2 DQE f o r the T..I. kOO x 1+00 BCCD as a f u n c t i o n o f the t o -t a l i n t e g r a t e d i n c i d e n t s i g n a l , at s e v e r a l d i f f e r e n t wavelengths 2.3 The e f f e c t o f temporal sampling on the DQE o f a photon 17 counting detector 22 2.5 The DQE as a f u n c t i o n o f wavelength f o r a photon counting 23 det e c t o r w i t h a t r i - a l k . photocathode,. and f o r a r e a r i l l u m i n a t e d analog BCCD detector (T.I. liOO x 1+00 BCCD). 25 28 3.3 Equivalent c i r c u i t f o r an MOS gate o p e r a t i n g above break- 25 down 29 3.5 Expected performance of a PC-CCD- compared to e x i s t i n g pho- 31 ton counting systems employing a t r i - a l k . photocathode v i i i LIST OF FIGURES cont'd Page 3 - 6 Model of the impact i o n i z a t i o n t h a t occurs subsequent to 3l+ the i n t r o d u c t i o n of a t r i g g e r i n g c a r r i e r (or c a r r i e r p a i r ) at p o s i t i o n x i n the d e p l e t i o n region 3 . 7 The avalanche i n i t i a t i o n p r o b a b i l i t i e s P (x) and P^( x) f ° r 37 a p-substrate MOS gate 3 . 8 The avalanche i n i t i a t i o n p r o b a b i l i t y as a f u n c t i o n of sur- 38 face p o t e n t i a l f o r e l e c t r o n s o r i g i n a t i n g i n the'bulk and f o r holes o r i g i n a t i n g at the S i - S i O ^ i n t e r f a c e 3 - 9 The degrading e f f e c t of the dark count r a t e on the detec- 1+3 t i v e quantum e f f i c i e n c y 3 . 1 0 The four b a s i c Shockley-Read-Hall processes t h a t may occur 1+5 at a t r a p p i n g l e v e l 3.11 A c t i o n of an e l e c t r o n t r a p . The r e l a t i v e p o s i t i o n s of 1+5 E^ , E* and E„ are a l s o shown Fn T .Fp 3 . 1 2 Schematic diagram showing the d i s t r i b u t i o n of the cou- 58 lomb p o t e n t i a l w e l l around a t r a p p i n g center f o r d i f -f e r e n t e l e c t r i c f i e l d strengths 3.13 R a t i o of the f i e l d enhanced emission r a t e e y t o the zero 60 f i e l d emission r a t e e , as a f u n c t i o n of 3/T/kT o 3.ll+ Energy band diagram i l l u s t r a t i n g , the steady s t a t e gener- 6 3 a t i o n muchanisms i n v o l v i n g the t u n n e l i n g emission of e l e c t r o n s and/or holes by mid gap l e v e l s i x LIST OF FIGURES cont'd Page 3 . 1 5 Interband t u n n e l i n g generation r a t e versus the peak 72 + e l e c t r i c f i e l d m n p step j u n c t i o n s or p-substrate MOS gates, w i t h d i f f e r e n t l e v e l s o f substrate doping, T=100K 3 . 1 6 The interband t u n n e l i n g generation r a t e i n MOS s t r u c - 73 t u r e s , p l o t t e d as a f u n c t i o n o f the s i l i c o n s u rface p o t e n t i a l <j> , T=100K 3 . 1 7 Tunneling generation r a t e through t r a p s as a f u n c t i o n 78 of the peak e l e c t r i c f i e l d i n n +p step j u n c t i o n s or p-subs t r a t e MOS gates, T=100K 3 . 1 8 Energy band diagram f o r a p-substrate MOS gate i l l u s - 80 t r a t i n g the generation o f t r i g g e r i n g c a r r i e r s at the i n t e r f a c e , immediately f o l l o w i n g a d e p l e t i n g pulse 3 . 1 9 Energy band diagram f o r a p-substrate MOS gate i l l u s - 82 t r a t i n g the emission of t r i g g e r i n g c a r r i e r s from deep bulk t r a p s , immediately f o l l o w i n g a d e p l e t i n g pulse. 3.20 Model f o r the d e p l e t i o n r e g i o n of a p-substrate MOS 86 gate during breakdown 3.21 The increased emission o f e l e c t r o n s and holes by bulk 87 traps subsequent t o an avalanche discharge 3.22 C r o s s - s e c t i o n of MOS c a p a c i t o r showing e q u i p o t e n t i a l • 90 l i n e s i n the space charge region at the edge o f the f i e l d p l a t e .'LIST OF FIGURES cont'd 3.23 Four d i f f e r e n t MOS s t r u c t u r e s t o avoid premature a v a l -anche breakdown at the outer edge of the f i e l d p l a t e i n high r e s i s t i v i t y samples 3.2k The emission spectrum during reverse b i a s avalanche breakdown i n s i l i c o n . 3 . 2 5 I l l u s t r a t i o n of how deep a n i s o t r o p i c a l l y etched s l o t s may be used t o o p t i c a l l y i s o l a t e the i n d i v i d u a l p i x e l s i n a l i n e a r PC-CCD array f a b r i c a t e d on ( 1 1 0 ) s i l i c o n 3 . 2 6 I l l u s t r a t i o n o f how a n i s o t r o p i c a l l y etched v-grooves might be used t o provide the r e q u i r e d degree of o p t i c a l i s o l a t i o n i n l i n e a r arrays f a b r i c a t e d on ( 1 0 0 ) s i l i c o n k.l P o t e n t i a l d i s t r i b u t i o n perpendicular t o the i n t e r f a c e . f o r a surface-breakdown MOS gate, before and a f t e r break down k.2 Charge i n j e c t i o n t e s t d e v i c e , s t r u c t u r e 1 k.3 Charge i n j e c t i o n t e s t d e v i c e , s t r u c t u r e 2 k.k Charge t r a n s f e r t e s t d e v i c e , s t r u c t u r e 3 U.5 Copies o f the f i v e photomasks used to f a b r i c a t e the devices. k.6 F a b r i c a t i o n sequence f o r the surface-breakdown t e s t devices k.f T e f l o n a n o d i z a t i o n c e l l used i n the device f a b r i c a t i o n x Page 90 9k 97 98 102 105 106 107 110 112 1 1 3 122 x i LIST OF FIGURES cont'd Page h.Q C r o s s - s e c t i o n of the c o l d chamber used f o r the low 125 temperature device t e s t i n g h.9 Block diagram of the t e s t e l e c t r o n i c s 127 It. 10 Surface doping p r o f i l e f o r wafer P l - 7 , obtained from 129 C(v) data by the method described i n Appendix C It. 11 Surface doping p r o f i l e f o r wafer T2-k 130 It. 12 I n t e r f a c e s t a t e d e n s i t y f o r wafer P2-5 as a f u n c t i o n of 132 p o s i t i o n i n the band gap, obtained from C(V) measurements by the method o u t l i n e d i n Appendix C h.13 Test waveforms f o r the surface-breakdown, c h a r g e - i n j e c t - 13U i o n devices k.lh Voltage of f i r s t d e tectable breakdowns as a f u n c t i o n of I 3 6 the r e s e t v oltage f o r devices from the f i r s t f a b r i c a t i o n 1+.15 Voltage o f f i r s t d e t e c t a b l e breakdowns as a f u n c t i o n o f 137 the r e s e t voltage (second f a b r i c a t i o n ) It. 16 Maximum charge per pulse as a f u n c t i o n of the photogate 139 voltage it. 17 T y p i c a l pulse height d i s t r i b u t i o n f o r the s u r f a c e - lltO breakdown devices 18 Dark count r a t e as a f u n c t i o n o f the excess photogate l U 2 b i a s f o r the three r e s e t i n v e r s i o n c o n d i t i o n s , V = r +10V, +12V and +lltV x i i L I S T O F F I G U R E S cont'd Page it. 19 Dark and photon induced pulse r a t e s as a f u n c t i o n of li+3 excess photogate b i a s , f o r one of the b e t t e r devices from the f i r s t f a b r i c a t i o n it. 20 S h i f t i n photogate. p o t e n t i a l r e q u i r e d t o maintain a l i t 5 constant output, pulse s i z e o f 1 x 10 elect. , as a f u n c t i o n of the c y c l e time t it.2 1 Dark and photon induced pulse r a t e s as a f u n c t i o n of l i t 7 U.22 the photogate b i a s f o r two of the b e t t e r s u r f a c e - ihQ breakdown devices from the second f a b r i c a t i o n U.23 P o t e n t i a l d i s t r i b u t i o n p e r p e n d i c u l a r t o the surface f o r 1 5 1 a bulk-breakdown MOS gate, before and a f t e r breakdown, and at breakdown — • k.2h Bulk-breakdown, charge-transfer t e s t device 157 it. 25 F a b r i c a t i o n sequence f o r the bulk breakdown t e s t devices l 6 l k.26 Two-dimensional p o t e n t i a l d i s t r i b u t i o n under the photogate 169 f o r V = 100V and V = itOV g T it.27 R e s u l t s of the two-dimensional c a l c u l a t i o n o f the v a r i a - 170 t i o n of the avalanche i n i t i a t i o n p r o b a b i l i t y w i t h p o s i -t i o n under the photogate, T = 80K it.2 8 Test waveforms and.timing f o r the bulk-breakdown, charge- 1 7 3 t r a n s f e r devices it.29 Dark pulse r a t e as a f u n c t i o n of l / t ( i . e . , as a f u n c t i o n 176 of the number of r e s e t s per sec. of a c t i v e time) f o r a f i x e d r e s e t d u r a t i o n of t = 0 . 1 msec r x i i i LIST OF FIGURES cont'd 4.30 Dark pulse r a t e as a f u n c t i o n of the r e s e t d u r a t i o n f o r a f i x e d d u r a t i o n above breakdown o f t = 0.1 msec Page 177 4 . 3 1 Dark pulse r a t e as a f u n c t i o n o f the photogate b i a s and subs t r a t e temperature. The x's mark the approximate breakdown vo l t a g e (a) t r=. 0.1 msec , t = 10.0 msec (b) t = 1.0 msec , t = 1.0 msec 1 7 Q r a i f y 181 4 . 3 2 Red g a l l i u m arsenide phosphide LED source used f o r the photon induced pulse r a t e measurements 4 . 3 3 Dark and photon induced pulse r a t e s as .a f u n c t i o n o f the photogate b i a s f o r device M66/2-1. (a) t & = 1.0 msec , t = 0.2 msec —• - 183 (b) t = 10.0 msec , t =0.2 msec 184 a r (c) t & = 1.0 msec , t = 20.0 msec X85 188 4 . 3 4 Photon induced pulse r a t e as a f u n c t i o n of the photogate b i a s when the dark s u b t r a c t i o n i n c l u d e s those.counts r e -s u l t i n g from the detrapping f o l l o w i n g an avalanche discharge D l Device s t r u c t u r e used f o r the two-dimensional model. 2lh D2 Device s t r u c t u r e a f t e r conformal t r a n s f o r m a t i o n . 217 ACKNOWLEDGEMENT I would l i k e t o acknowledge the f o l l o w i n g people f o r t h e i r help and encouragement during the research and p r e p a r a t i o n o f t h i s t h e s i s : Gordon Walker, f o r h i s a s s i s t a n c e during the i n i t i a l stage o f t h i s p r o j e c t . My a d v i s o r , Dave P u l f r e y , f o r h i s c o n s t r u c t i v e c r i t i c i s m and support throughout the research. Garry T a r r , f o r many h e l p f u l d i s c u s s i o n s r e l a t i n g t o experimental and t h e o r e t i c a l aspects. The f i n a n c i a l a s s i s t a n c e provided by the U n i v e r s i t y of B r i t i s h Columbia f e l l o w s h i p s i s als o g r a t e f u l l y acknowledged. Very s p e c i a l thanks go to my w i f e , C a t h i e , f o r t y p i n g t h i s t h e s i s and f o r her patience during the lengthy p r e p a r a t i o n . 1 INTRODUCTION 1 The r e s e a r c h reported i n t h i s t h e s i s i n v o l v e s the i n v e s t i g a t i o n of a new mode of o p e r a t i o n f o r charge coupled .device (CCD) imagers t h a t enables the d i r e c t d e t e c t i o n of i n d i v i d u a l photons as they a r r i v e . Such photon counting imagery i s of great i n t e r e s t t o astronomers and those i n the space s c i e n c e s , e s p e c i a l l y f o r s a t e l l i t e - b o r n e o b s e r v a t o r i e s . One of the requirements of modern a s t r o p h y s i c s i s the d e t e c t i o n of very low photon f l u x e s w i t h optimum s e n s i t i v i t y , s p a t i a l r e s o l u t i o n and s p e c t r a l r e s o l u t i o n . The d e t e c t i o n of very f a i n t r a d i a t i o n i s fundamentally l i m i t e d by the q u a n t i f i e d nature of the r a d i a t i o n i t s e l f , so t h a t the a s t r o n -omer must a c c u r a t e l y t r a c k the source and use long exposures to r e c o r d enough photon events on each elemental image area, or " p i x e l " , to achieve the de-s i r e d photometric accuracy. In ground-based observations^ atmospheric t u r b u -lence and sky background determine the f a i n t e s t o b j e c t s f o r which u s e f u l photometric and spectroscopic i n f o r m a t i o n can be obtained. Observing from a space p l a t f o r m avoids the degrading atmospheric e f f e c t s , however, there i s s t i l l a low l e v e l background due t o i n t e g r a t e d s t a r l i g h t , z o d i a c a l l i g h t , and s c a t t e r e d l i g h t i n the o p t i c s . In a d d i t i o n to these low l e v e l backgrounds, i t i s very o f t e n impossible f o r the astronomer to avoid l o c a l i z e d b r i g h t regions w i t h i n the f i e l d . In spectroscopy there may be strong emission l i n e s next t o the region of i n t e r e s t w h i l e i n two-dimensional photometry there are o f t e n b r i g h t foreground s t a r s . Therefore, i n order t o r e a l i z e the f u l l p o t e n t i a l of observing from space and to o b t a i n the utmost from ground-based o b s e r v a t i o n s , a d e t e c t o r i s r e q u i r e d t h a t i s capable of r e c o r d -in g small c o n t r a s t d i f f e r e n c e s i n u l t r a f a i n t images w h i l e at the same time not being swamped by the s i g n a l from l o c a l i z e d b r i g h t areas. The imager must have maximum s e n s i t i v i t y , the lowest p o s s i b l e sensor n o i s e , a l a r g e dynamic range, good saturation characteristics, a very low dark signal, adequate resolution and spectral coverage, and a highly stable linear re-sponse. Various photoelectronic image sensors have been developed that at-tempt to f u l f i l l the above requirements. These detectors can be divided into two general categories: (1) detectors that integrate the image internally and give an analog out-put (2) photon counting imagers that allow external digital integration. Before discussing in detail the proposed photon counting detector, present-ly existing low light level imagers are reviewed briefly in chapter two. The detective quantum efficiency is derived for both analog CCD and photon counting sensors, and the present limitations of.these two imaging technique are examined. • • In chapter three the basic operation of the proposed photon counting imager is described and i t is shown.to have the potential for nearly opti-mum low light level performance in the visible and near infrared. Several problem areas are identified that require experimental investigation be-fore the fabrication of such an array is attempted, and the background theory necessary for a f u l l understanding of these issues is presented. The experimental investigation is discussed in chapter four. The design and fabrication of discrete photon counting MOS detectors is described and the experimental results obtained with these test devices are discussed. A summary of the main body of the thesis together with concluding remarks is given in chapter five. 2 BRIEF REVIEW OF LOW LIGHT LEVEL IMAGE SENSORS The f i e l d - of low l i g h t l e v e l imaging has progressed r a p i d l y i n the past few years. Advances i n s i l i c o n VLSI technology have made p o s s i b l e l a r g e , de-f e c t - f r e e s o l i d s t a t e image sensors, and the r a p i d l y growing microcomputer i n d u s t r y has made a v a i l a b l e a v a r i e t y o f low cost microprocessors and l a r g e memories f o r the manipulation and storage o f the vast amount of data one obtains from such l a r g e sensor a r r a y s . I t i s unnecessary to review i n d e t a i l a l l of the analog and photon counting imaging systems p r e s e n t l y i n o p e r a t i o n , because, by d i s c u s s i n g the general types of image sensors and i n t e n s i f i e r -sensor combinations used, i t i s p o s s i b l e to present a f a i r l y accurate p i c t u r e of the s t a t e of the a r t f o r low l i g h t l e v e l imaging. I t must, o f course, be remembered t h a t i n any r e a l imaging system the type o f sensor housing or i n t e n s i f i e r - s e n s o r assembly used, as w e l l as the readout, c o n t r o l , and data handling e l e c t r o n i c s , can have a marked i n f l u e n c e on the o v e r a l l performance. Analog imaging systems are d i v i d e d i n t o two general c a t e g o r i e s : (1) image sensors w i t h no p r e - d e t e c t i o n gain (2) sensors that i n t e g r a t e the s i g n a l a f t e r some form of image i n t e n s i f i -c a t i o n . The l a t t e r category i s discussed along w i t h photon counting systems since i t s implementation i s very s i m i l a r and i t s c h a r a c t e r i s t i c s are determined p r i m a r i l y by the image i n t e n s i f i e r . 2.1 ANALOG IMAGERS Low l i g h t l e v e l imagers i n t h i s ca tegory i n c l u d e t e l e v i s i o n p i c k - u p tubes [1,2], s e l f - s c a n n e d photo d iode a r r a y s [3,4], charge i n j e c t i o n d e v i c e (CID) a r r a y s [5,6] and charge coup led dev i ce (CCD) a r r a y s [7,8]. T e l e v i s i o n p i c k - u p tubes have been i n r o u t i n e o p e r a t i o n f o r the past t h r e e decades, however, i t was not u n t i l the l a t e 196o 's t h a t t e l e v i s i o n techn iques s t a r t e d t o r e p l a c e the r e l a t i v e l y i n e x p e n s i v e and w e l l e s t a b l i s h e d photographic methods f o r q u a n t i t a t i v e s c i e n t i f i c imag ing . T e l e v i s i o n p i c k - u p tubes o f f e r e d the advantages o f h i g h e r p o s s i b l e s i g n a l t o n o i s e i n the image, l i n e a r r e s p o n s e , and the p o s s i b i l i t y f o r post d e t e c t i o n image p r o c e s s i n g . These f e a t u r e s made t e l e v i s i o n techn iques s u p e r i o r t o : photography f o r low l i g h t l e v e l i m a g i n g , and by 1973 many groups i n astronomy were u s i n g t e l e -v i s i o n sensors f o r spect roscopy and t w o - d i m e n s i o n a l photometry [9].' Very p r o m i s i n g r e s u l t s were o b t a i n e d w i t h t h e s e t e l e v i s i o n type i m a g e r s , however, the newly developed s i l i c o n m o n o l i t h i c l i n e and X -Y sensor a r r a y s were b e -coming a v a i l a b l e at t h i s t ime and o f f e r e d some s i g n i f i c a n t improvements. S o l i d s t a t e imagers have more s t a b l e photometr ic p o r p e r t i e s , a h i g h l y l i n e a r response , and a w e l l d e f i n e d a b s o l u t e l y s t a b l e geometry. The advan -tage o f s m a l l p h y s i c a l s i z e i s negated by the requirement t h a t s i l i c o n mono-l i t h i c imagers be c o o l e d below 150 K i n o rder to reduce the dark leakage c u r r e n t t o a n e g l i g i b l e l e v e l . Such temperatures g e n e r a l l y r e q u i r e evacuated d e t e c t o r hous ings and s p e c i a l c h i p c a r r i e r s . The f i r s t s o l i d s t a t e imagers t o be used were s e l f - s c a n n e d photodiode a r r a y s . These sensors u t i l i z e the d e p l e t i o n r e g i o n c a p a c i t a n c e o f e l e c t r i c -a l l y i s o l a t e d p -n j u n c t i o n d iodes f o r the i n t e g r a t i o n and s to rage o f p h o t o -generated charge [10]. The i n d i v i d u a l photodiodes are coup led t o one o r a few v ideo l i n e s v i a MOS swi tches operated by o n - c h i p s h i f t r e g i s t e r s . Read -out occurs when the d iodes are r e b i a s e d s e q u e n t i a l l y through the v i d e o l i n e , resulting in a train of recharging current pulses. The number of electrons (or holes) collected per incident photon is referred to as the responsive quantum efficiency (RQE). The wide aperture linear photodiode arrays of 102U elements or more supplied by Reticon Corp. were particularly suitable for spectroscopy and are s t i l l in use today. These sensors have a high responsive quantum efficiency from U00 nm.to 900 nm (Fig. 2.1), very stable photometric properties, a 7 saturation level greater than 10 photogenerated carriers, and only slight image spreading above saturation. The most serious drawback to these arrays is the high level of readout noise and the large switching signal due to capacitive coupling between the video line and the shift register. Carefully designed, highly stable drive circuitry allows the switching transients to be largely removed, however, the Johnson-Nyquist•noise of the reset switches and the large video line capacitance results in typical r.m.s. noise levels of 700 to 1000 equivalent photoelectrons per pixel. This high level of read-out noise means that photodiode arrays are not well suited to very low light level imaging. However, the large saturation charge does allow one to obtain high signal to noise ratios for long exposures at moderate light levels, where one can accumulate large integrated signals. It also enables a dynamic range greater than 10 to 1 to be recorded in a single integration. In addition to high readout noise the two dimensional photodiode arrays suffer from con-siderable dead space losses since the many video lines and reset switches l i e within the active sensor area. In the mid 1970's imagers that utilized the newly discovered charge transfer principle became available. These sensors use arrays of MOS capac-itors for the integration of photogenerated charge. The gates of each capac-itor are biased so as to drive the bulk silicon underneath into deep deple-tion. The potential wells thus formed collect and store the photo-generated • 400 600 800 1000 INCIDENT WAVELENGTH (nm) FIGURE 2.1 Responsive quantum efficiency of different analog sensor arrays as a function of wavelength. 7 minority carriers. Depending on the type of readout employed, charge trans-fer devices are of either the CCD or CID variety. In CID imagers the individual sensing elements consist of a pair of gate electrodes that are connected in rows and columns. The signal from an indi-vidual pixel is obtained by pulsing the appropriate row of gates and sensing the voltage change on the appropriate column as the signal charge is trans-fered along the surface of the silicon from one gate to the other. The row and column selection is normally controlled by on-chip shift registers which results in a sequential readout. The above detection scheme leaves the sig-nal charge unchanged so that multiple nondestructive readouts are possible. The CID imager is reset for a new integration by injecting the signal charge into the bulk of the semiconductor where i t recombines with majority carriers.' The CID imager is not an inherently low noise device. Large switching spikes result from capacitve coupling between the row and column gates, and substantial signal attenuation by the column capacitance results in a typical rms readout noise of 800 to 1000 carriers per pixel. The noise may be greatly reduced by summing multiple nondestructive readouts. Unfortunate-l y , the lowest noise level that can be achieved in this way is limited by variations of the large switching signal, which in turn requires very stable, low noise drive circuitry. CID imagers have a linear response, however, there is a threshold effect which occurs after reset. The charge injection causes surface states to empty and subsequent signal charge is wasted refilling these states. To avoid this threshold probelm a small bias charge must be kept under the gates at a l l times. This bias signal must be read non-destructively and stored so that i t can be subtracted from the subsequent data exposure. Another draw-back to presently existing CID imagers is that they are front side illuminated which results in lower responsive quantum efficiencies, especially at short 8 wavelengths, due to absorption by the gate s t r u c t u r e . In the case of semi-transparent e l e c t r o d e s such as p o l y s i l i c o n , l o s s r e s u l t s from a b s o r p t i o n as w e l l as from wavelength-dependent i n t e r f e r e n e c e due to the m u l t i p l e r e f l e c t -ions at the v a r i o u s s i l i c o n - s i l i c o n d i o x i d e i n t e r f a c e s . Consequently, the s p e c t r a l t r a n s m i s s i o n curve and hence the responsive quantum e f f i c i e n c y o f the CID has a complex s t r u c t u r e throughout the v i s i b l e spectrum ( F i g . 2.1). The analog imager that p r e s e n t l y has the most p o t e n t i a l at low l i g h t l e v e l s i s the CCD. In CCD's the charge t r a n s f e r p r i n c i p l e i s used to t r a n s -port the o p t i c a l l y - c r e a t e d charge p a t t e r n over l o n g d i s t a n c e s across the s i l i c o n surface t o an on-chip a m p l i f i e r l o c a t e d at the edge of the sensor. This d e t e c t i o n method r e s u l t s i n a s i g n i f i c a n t r e d u c t i o n i n readout noise due to ( l ) s i g n a l d e t e c t i o n at a common low capacitance node and (2) the e l i m i n -a t i o n of s w i t c h i n g spikes w i t h i n the array. In a d d i t i o n , t h i n n e d , r e a r i l l u m i n a t e d CCD sensors are a v a i l a b l e t h a t have responsive quantum e f f i c i e n -c i e s approaching those of. t h e s e l f scanned photodiode a r r a y s . The main d i f -f i c u l t y w i t h the CCD i s the l o s s of charge due t o i n t e r f a c e - s t a t e t r a p p i n g as the s i g n a l i s t r a n s p o r t e d along the i n t e r f a c e . This problem may be par-t i a l l y overcome by i n t r o d u c i n g a b i a s charge or " f a t zero", however, a b e t t e r s o l u t i o n i s to avoid surface s t a t e s a l t o g e t h e r by t r a n s p o r t i n g the charge i n a b u r i e d channel l o c a t e d away from the i n t e r f a c e [11] . Because of the much lower d e n s i t y of bulk t r a p s , such b u r i e d channel CCD's (BCCD's) are capable of very high charge t r a n s f e r e f f i c i e n c i e s . 2 . 1 . 1 • The DQE For Analog CCD Sensors A more q u a n t i t a t i v e a p p r a i s a l of CCD imager performance at low l i g h t l e v e l s can be obtained by c a l c u l a t i n g t h e . d e t e c t i v e quantum e f f i c i e n c y , defined as: (S/N)* DQE = ? u t (2.1) ' (S/N)Jn in where, (S/N) , = signal to noise ratio after detection out (S/N). = signal to noise ratio before detection m A detector is performing optimally i f its DQE is equal to 1. For a l l image sensors, the DQE depends on the temporal and spatial modulation transfer functions. Such a dependence results from the non-zero width in both the temporal and spatial response of the detector. At very low light levels one need only consider time stationary images and to simplify the analysis even further only the zero spatial frequency DQE will be calculated. If the DQE as a function of spatial frequency is desired i t can be obtained from the spatial modulation transfer function (MTF) according to [12], DQE(f) = 5M|)_MTF2 where, f is the spatial frequency P(f) is the power spectrum of the noise. For optical signals the lowest possible noise before detection is merely the statistical photon noise, i.e. no sky or scattered light back-ground. In this case, (S/N). = (R t ) h (2.2) in p where, R^  = mean rate of arrival of photons per pixel t = integration time For a CCD imager the signal to noise in the output after subtracting the dark background i s , RQE R t ( S / N ) o u t = ~ E2 h <2'3> O U t (RQE R t + a + 2R,t)* p d 10 where, RQE = responsive quantum e f f i c i e n c y , equal to the r a t i o o f the number of c o l l e c t e d c a r r i e r s over the number of i n c i d e n t photons. Included i n t h i s f i g u r e are any dead space l o s s e s . a = rms readout noise of the CCD expressed as an equivalent number of photoelectron charges per p i x e l . R, =• dark leakage per p i x e l , d S u b s t i t u t i n g expressions ( 2 . 2 ) and ( 2 . 3 ) i n t o ( 2 . l ) y i e l d s the zero s p a t i a l . frequency DQE f o r a CCD, DQE(O) = ^ • (2.4) RQE + (a /R t ) + 2(R„/R ) p d p • Expression (2.1*) f o r the DQE i n d i c a t e s t h a t i n a d d i t i o n to readout n o i s e , excessive dark leakage a l s o degrades the performance of CCD imagers. F o r t u n a t e l y , by c o o l i n g s i l i c o n m o n o l i t h i c arrays to 150 K or lower the dark generation o f c a r r i e r s may be reduced t o a n e g l i g i b l e l e v e l . For f i x e d i n t e -g r a t i o n time,' a r i d / n e g l i g i b l e dark g e n e r a t i o n , the DQE approaches i t s maximum value (equal t o the detector* s RQE) as the sensor i r r a d i a n c e i n c r e a s e s . This i s as expected since at h i g h i n t e g r a t e d s i g n a l l e v e l s the s t a t i s t i c a l photon noise dominates. 2.1.2 Performance of CCD Imagers C u r r e n t l y In Operation Readout noise l e v e l s of 20 to 100 e l e c t r o n s rms have been achieved by s e v e r a l commercial CCD d e v i c e s , however, most o f these arrays are f r o n t side i l l u m i n a t e d . a n d the r e s u l t a n t responsive quantum e f f i c i e n c i e s are low. Texas Instruments has produced l a r g e r e a r i l l u m i n a t e d BCCD arrays s p e c i f i c a l l y de-signed f o r low l i g h t l e v e l imaging. 1*00 x 1*00 p i x e l prototype arrays [13] have been i n o p e r a t i o n f o r some time and r e c e n t l y the f u l l 800 x 800 element v e r s i o n has been completed. The 1*00 x 1*00 arrays are a c h i e v i n g readout n o i s e l e v e l s o f approximately 25 e l e c t r o n s rms [14] and have peak responsive quan-11 turn efficiencies of 0.7 at 700 nm (Fig. 2.1). The sensor is thinned to a thickness of approximately lOum over the active area leaving a thick rim for the support of the fragile membrane and for chip "bonding. The processing-induced stresses at the front side silicon-silicon dioxide interface can cause the membrane to buckle significantly, creating some stability problems. A thinned rear illuminated 512 x 320 pixel BCCD that is bonded to a glass sub-strate-window combination has recently been produced by RCA. The bonding process largely eliminates membrane buckling and stability problems and reportedly enhances the responsive quantum efficiency. The RQE of the RCA CCD's is the highest yet achieved on a routine basis. Unfortunately, the quoted readout noise levels are 70 to 100 electrons rms.[15]. The DQE for the T.I. 1+00 x kOO BCCD is plotted in Fig. 2.2 versus total integrated incident signal at various, wavelengths and.assuming negli-gible dark leakage. Curves of constant output signal to noise are also shown. From these i t is apparent that for integrated signal levels, such that (S/N) is greater than approximately 70, the T.I. BCCD is photon noise limited with a DQE within 10$ of the responsive.quantum efficiency. The saturation level for BCCD's such as the T.I. kOO x kOO is typically 5 x 10^ electrons. With a rms noise of 25 electrons the dynamic range becomes h 2 x 10 to 1, and the signal to noise for a level near saturation would be 700 against signal quantum noise. The CCD sensor appears to be a nearly ideal imager over a fairly wide spectral region around 700 nm. In practice, however, the internal charge integration and analog output can present some problems. In particular, non-linearities introduced by the signal electronics before the analog data is digitized must be eliminated or calibrated out. Stability of the signal electronics is also of concern, especially i f i t is necessary to subtract one frame from another in order to remove a large background signal. The 12 T 1 i r "X s 700 nm FIGURE 2.2 DQE for the T.I. kOO x UOO BCCD as a function of the total in-tegrated incident signal, at several different wavelengths. Curves of con-stant signal to noise in the output are also indicated. 13 response of CCD imagers as well as the transfer characteristics of the on-chip pre-amplifier have been found to be highly linear, however, some CCD sensors show a threshold effect. For example, some of the recent RCA BCCD's show a zero exposure intercept that deviates by as much as 170 electrons from the level given by the readout of multiple empty frames [15]. This threshold may result from long-lifetime bulk traps and has serious consequen-ces when trying to detect very faint images where l i t t l e or no background is present. 2.2 PHOTON COUNTING IMAGERS To avoid the problems of non-linearities and possible threshold effects associated with analog imagers and to obtain photon noise limited operation independent of the total integrated- signal, astronomers pioneered the develop-ment of intensified CCD's that operate in a photon counting mode. The re-quirements for photon counting are straightforward. Enough pre-readout gain must be provided in order to reliably discriminate single photon events above readout noise in the detector and achieve a low background or dark count rate. Further, the imaging device selected must be capable of being scanned rapidly enough so that at the maximum sensor irradiance to be measured, rarely will more than one photon be incident on any one pixel during a frame time. Lastly, the intensified detector must be interfaced with a computer type memory to accumulate photoevents according to their location in the image. Photon counting is obviously restricted to very faint images. In order to accommodate a large photon flux from an extended source the device must be scanned rapidly and there must be many small picture elements. However, this in turn dictates a large video signal bandwidth, which results in more readout noise per sample and necessitates higher intensifier gain so that the signal 11+ pulses will be clearly above the noise. It is possible, however, to operate some intensified detectors in a. charge integration mode so that higher photon fluxes can be measured. The integration time is set so as not to saturate the sensor and multiple frames may be summed without degradation due to sen-sor readout noise, provided there is sufficient gain in the image intensifier The intensifier gain required is somewhat less than for photon counting, but the pulse height distribution should be narrow since the dispersion in pulse heights introduces noise which increases roughly with the square root of the number of photon events recorded. The photon shot noise also increases with the square root of the number of photon events so that, provided the relative dispersion in pulse heights is small, photon noise limited operation is pos-sible. The noise contribution from cosmic ray and ion events, both of which produce very large pulses, can be a problem at very low light levels. Photon counting systems are able to reject these large events. Many of the early intensified imagers did not have enough gain to dis-criminate single photon events above readout noise and were operated in the above intensified charge integration mode. Instability and non-linearities introduced by the image intensifier, as well as "the noise due to cosmic ray and ion events, however, are limitations when operating in this mode and i t is preferable, i f possible, to photon count. 2.2.1. Linearity and.DQE of Photon Counting Imagers At low photon flux levels the DQE of an image photon counting system is constant and approximately equal to the responsive quantum efficiency of the intensifier photo-cathode. However, only one photon event may be detected per pixel per frame and as the photon flux increases, temporal sampling ef-fects introduce non-linearities and lower the DQE. These effects are exam-ined below for spatially and temporally invariant signals. 15 For an i n t e n s i f i e d . i m a g e r operating i n a photon counting mode, the mean event r a t e i s , n = R RQE n + n, , n J x « l (2 .5 ) p d d where, R^ = mean r a t e o f a r r i v a l o f i n c i d e n t photons per p i x e l RQE = responsive quantum e f f i c i e n c y of the photocathode n = p r o b a b i l i t y t h a t a photoelectron r e s u l t s i n an output s i g n a l p ulse above the d i s c r i m i n a t o r l e v e l n^ = mean number of e v e n t s / s e c / p i x e l due t o noise and thermionic a emission from the photocathode T = frame time The a r r i v a l of i n c i d e n t photons and the occurence of dark events obey Poisson s t a t i s t i c s , therefore,. the p r o b a b i l i t y t h a t there w i l l be a count i n frame time x i s , P = 1 - exp(-nx) The number of counts measured i n N frames i s , t h e r e f o r e , C = PN = [1 - exp(-nx)]N (2.6) and the mean square d e v i a t i o n i s , ( A C ) 2 = exp(-nx)[1 - exp(-nx)]N (2.7) Equation (2.6) shows the departure from l i n e a r i t y due to the f i n i t e frame r a t e . A f t e r c o r r e c t i n g f o r t h i s n o n l i n e a r i t y the mean number of counts i n N frames becomes, C* = -N £n[l - (C/N)] (2.8) and the mean square d e v i a t i o n becomes, ( A C ) 2 dC1 dC 2 ( A C ) 2 = [exp(nx) - 1]N (2 .9) Therefore, a f t e r s u b t r a c t i n g the dark count r a t e , the s i g n a l to noise i n the output i s , 16 (n - n,)xN (S/K) out {[exp(nx) - 1]N + ndTN}: (2.10) The signal to noise in the input i s , f(n - na>TH}* (2.11) i RQE n J Therefore, the zero spatial frequency DQE becomes, DQE(O) •= RQE n (n - nd)x (2.12) exp(nx) - 1 + n x Equation 2.12 shows the importance of a high RQE and n, and reveals the de-to be degraded by more than 10% the frame rate must be more than five times the maximum count rate to be measured. For event rates much lower than the frame rate (nx<<l), the DQE can be approximated by, Equation 2.13 reveals the degrading effect of the dark event flux n^, and shows the importance of choosing the optimum discriminator level for the photon flux to be measured. A higher discriminator level reduces the number of dark counts due to noise, but may also lower the probability n. 2.2.2 Photon Counting Imagers Presently in Use Presently existing photon counting imagers are of three basic types: (l) A high gain image intensifier tube optically coupled to a television camera tube or a silicon monolithic array [16,17]. gradation due to the finite frame time x. Figure 2.3 shows DQE/RQE n as a function of the event flux per frame nx(for n =0). In order for the DQE not DQE(O) - RQEn 1 + ( / n ) d 1 - (nd/n) (2.13) FIGURE 2.3 The e f f e c t o f temporal sampling on the DQE o f a photon counting detector. 18 (2) A special image tube that has as its anode either the silicon target of a vidicon or a solid state semiconductor array that directly detects photo-electron images from the photocathode [18,19,20,21]. (3) A microchannel plate (MCP) intensifier with a self-scanned multi-anode array [22], an x-y coincidence anode array or a resistive position sensitive anode [23,24,25]. In photon counting systems of the first category the image intensifier tubes can be either fibre-optically or lens coupled to the sensor. If they are lens coupled, multi-stage tubes, or tubes employing a microchannel plate intensifier must be used to overcome the large coupling losses. The temporal and spatial spreading of photon events caused by these image intensifiers limits the maximum photon flux that can be measured. The temporal spread results from output phosphor lag and can cause a.single event to appear in several successive frames. By subtracting the previous frame each time, a l l but the new events may be rejected, however, this also introduces a reduced sensitivity for subsequent detection of events in the same pixel. The spatial spreading can cause a single photon event to be recorded on several adjacent pixels in the detector. Not only does this lower the MTF but, be-cause of variations in size, the photon events are recorded with different statistical weights. This is a source of noise and lowers the DQE. The MTF and DQE can be restored by processing each frame prior to storage so as to detect the event centers. However, more than one pixel per photon event is inhibited during a frame time so that the linearity and DQE are more quickly affected by increasing photon flux than was previously indicated (equations 2.6 and 2.12). The speed with which a frame can be processed for event center detection typically limits frame rates to less than 100/sec for 500 x 500 pixels or more. .In photon counting systems of the second category, the troublesome out-19 put phosphor and o p t i c a l c oupling are e l i m i n a t e d by i n c o r p o r a t i n g w i t h i n the image tube a semiconductor array anode that d i r e c t l y detects the high energy photoelectrons. There i s no event.lag w i t h these imagers and event center d e t e c t i o n i s g e n e r a l l y not required. These image tubes are normally operated w i t h a c c e l e r a t i n g p o t e n t i a l s between 15 and 30 kV and t y p i c a l l y give an e l e c -tron-hole p a i r y i e l d t h a t i s l e s s than UOOO per i n c i d e n t photoelectron. In order to photon count, t h e r e f o r e , a low noise CCD sensor i s r e q u i r e d . Un-f o r t u n a t e l y , the l i f e t i m e s of CCD. imagers are very short when operated i n an electron-bombarded mode due to the damage introduced at the s i l i c o n - s i l i c o n d i o x i d e i n t e r f a c e . The t r a n s f e r channels o f a CCD are p a r t i c u l a r l y s e n s i t i v e to damage so t h a t ' i n t e r l i n e t r a n s f e r CCD's w i t h s h i e l d e d t r a n s f e r channels must be used, however, the 50$ dead space caused by the i n t e r l e a v e d channels reduces the photoelectron d e t e c t i o n p r o b a b i l i t y n. R e a r - i l l u m i n a t e d , e l e c -tron-bombarded CCD's appear to have much longer lifetimes'.[21,26], however, very few CCD's have so f a r been operated i n t h i s mode and the data a v a i l a b l e on o v e r a l l performance and l i f e t i m e i s l i m i t e d . The microchannel p l a t e i n t e n s i f i e r i s able t o d e l i v e r an output pulse 5 7 of 10 to 10 e l e c t r o n s , f a r i n excess of the noise l e v e l of common e l e c -t r i c a l a m p l i f i e r s and d i s c r i m i n a t o r s . This allows a multi-anode a r r a y t o be placed i n p r o x i m i t y focus at the output o f the MCP, with each anode connected to an i n d i v i d u a l counting c i r c u i t . The i n d i v i d u a l anode e l e c t r o d e s are t y p i c -a l l y 0.5mm to 1.0mm square and are separated by i n t e r p i x e l screening e l e c -trodes to prevent c r o s s - t a l k . Since a l l the p i x e l s are e f f e c t i v e l y read'out i n p a r a l l e l very high count r a t e s per p i x e l can be accommodated. The MCP 5 - 2 - 1 i t s e l f i s l i m i t e d t o approximately 10 . events mm sec a f t e r which the gain f a l l s o f f r a p i d l y because of the charge l o s t by the h i g h r e s i s t i v i t y channel w a l l s . An opaque photocathode deposited d i r e c t l y on the f r o n t face o f the MCP can be used w i t h these imagers. A f i e l d i s e s t a b l i s h e d i n f r o n t of the 20 MCP so as to collect the photoelectrons originating from the areas between channel openings. The most serious limitation to discrete anode MCP's is the small number of pixels (less than 500) achievable with currently existing ceramic and electronic technologies. To overcome this limitation, coincidence techniques may be used to determine the spatial location of an event by the simultaneous arrival of charge upon two orthogonal sets of electrodes. In this way 2N 2 circuits can handle an image having N pixels. Large coincidence anode arrays may be fabricated, however, the pulse pair resolution time limits the maximum system count rate. If two photon events occur within the coincidence-resolving time, four counts are generated, two at the actual event locations, and two at false mirror image locations. The only way to avoid false counts is to remain well below the maximum count rate, which limits the use of these sensors to extremely faint, low contrast images that do not have any localized bright regions. The photon counting system that has the greatest potential in terms of the maximum count rate per pixel (for large arrays) is a microchannel plate intensifier with a proximity focused, self-scanned anode array. The individual anodes store the charge from the MCP for a frame time and are interrogated using the same techniques as were developed for the self-scanned photodiode arrays. The high gain of the MCP makes very high frame rates possible. Unfortunately, this approach has not been pursued as active-ly as the coincidence anode technique and only small self-scanned anode ar-rays have so far been fabricated and tested. Spreading of the very large charge pulses leaving the MCP may make event center detection necessary for large arrays and thus limit the frame rate. • < From the above discussion i t is apparent that a l l of the presently existing photon counting imagers suitable for high resolution imaging have 21 r a t h e r low maximum frame r a t e s . Th is does not a f f e c t t h e i r DQE o r l i n e a r i t y when d e t e c t i n g ve ry f a i n t images, however, i t does l i m i t the dynamic range t h a t can be r e c o r d e d . A h i g h dark count r a t e w i l l lower the DQE and f u r t h e r l i m i t the dynamic range b u t , by c o o l i n g the photocathodes and choos ing the optimum d i s c r i m i n a t o r s e t t i n g ( a c c o r d i n g t o e q u a t i o n 2 . 1 3 ) t h i s d e g r a d a t i o n may be reduced t o a n e g l i g i b l e l e v e l . A l l o f the image photon c o u n t i n g systems u t i l i z e e i t h e r a semit ransparent o r opaque photoemiss ive s u r f a c e as the i n i t i a l l i g h t s e n s i t i v e element and, as i n d i c a t e d by equat ion ( 2 . 1 2 ) , i t i s the respons i ve quantum e f f i c i e n c y o f t h i s s u r f a c e t h a t u l t i m a t e l y l i m i t s the DQE at low l i g h t l e v e l s . F i g u r e 2.h shows the r e s p o n s i v e quantum e f f i c i e n c y versus wavelength f o r the most w i d e l y used photocathode m a t e r i a l s . Because o f the low RQE's o f a v a i l a b l e photocathodes longward of 600 nm, ana log CCD imagers are a b l e t o o f f e r s u p e r i o r performance i n the red s p e c t r a l r e g i o n s , p a r t i c u l a r l y f o r photon f l u x l e v e l s where a h i g h s i g n a l to n o i s e can be o b t a i n e d . T h i s i s shown more c l e a r l y i n F i g . 2 . 5 where the DQE versus wavelength i s p l o t t e d f o r bo th the Texas Instruments r e a r - i l l u m i n a t e d BCCD and a t y p i c a l photon c o u n t i n g imager equipped w i t h a t r i - a l k . p h o t o c a t h -ode. The DQE f o r an ana log CCD a l s o depends on the t o t a l i n t e g r a t e d s i g n a l w h i c h , i n t u r n , determines the output s i g n a l t o n o i s e . Curves o f constant s i g n a l t o n o i s e are used i n F i g . 2 . 5 t o show the wavelength dependence o f the DQE f o r the T . I . a r r a y . The curve f o r (S/N) >1000 r e p r e s e n t s the maximum DQE p o s s i b l e . The DQE f o r the p u l s e c o u n t i n g system i s shown f o r photon event r a t e s much lower than the frame r a t e and i s t h e r e f o r e independent o f the output s i g n a l t o n o i s e . INCIDENT WAVELENGTH (nm) FIGURE 2.4 Responsive quantum efficiency of different photdcathode/window combinations as a ro function of wavelength. 23 rear illuminated BCCD t o - : 25 el «c . rms, =0) photon counting system with tri.-alk. photocathode ( R D « frame rate) 200 400 600 800 1000 INCIDENT WAVELENGTH (nm) FIGURE 2.5 The DQE as a.function of wavelength for a photon counting detector with a tri.-alk. photocathode, and for a rear-illuminated analog BCCD detector (T.I. kOO x kOO BCCD). The total integrated incident signal required to give the indicated values of output signal to noise for the BCCD can be obtained . from Fig. 2.2. 2k 3 THE PROPOSED PHOTON COUNTING SENSOR AND THEORY OF OPERATION It has been demonstrated [27]-[31] that avalanche photodiodes can be used above the breakdown voltage in a photon counting (or Geiger tube) mode, provided the dark current is sufficiently small. When such an avalanche diode is suddenly biased above breakdown i t is in i t i a l l y non-conducting. Not until a carrier is injected into or generated within the high field region of the depletion layer can an avalanche be. initiated, so triggering the diode into reverse conduction. Furthermore, by cooling the avalanche diode to very low temperatures i t should, be possible to reduce the thermal generation rate of carriers to a.negligible level so that, virtually the only carriers available to initiate an avalanche will be those generated by incident photons. After a self-sustaining avalanche has been started the diode can be made ready to detect another photon, provided there is a suitable quenching circuit which momentarily reduces the diode bias and interrupts the avalanche. The equivalent circuit for an avalanche diode operating above breakdown is shown in Fig. 3.1 [35]. V denotes the breakdown voltage, R the diode D S series'impedance, R c the space charge, resistance during breakdown, and C^ the diode junction capacitance, including guard ring capacitance. The bias and detection circuit are represented by the applied voltage V , a stray shunt capacitance C^  and a load resistance R^, which, i f large, enough, will also serve to.quench the avalanche breakdowns. An avalanche discharge is repre-sented by the closing of switch S. As soon as an avalanche is initiated, C^ discharges towards with a time constant of approximately ^(C^ + C g). With a large enough load resistor, however, the current becomes very small in the vicinity of and statistical fluctuations in the number of carriers in the high field region of the diode depletion layer cause the avalanche to turn off. The mean time to turn off decreases as the circuit impedance in-25 o u t p u t FIGURE 3.1 Equivalent c i r c u i t f o r an avalanche diode o p e r a t i n g above break-down (shown i n dashed, box) plus the b i a s and d e t e c t i o n c i r c u i t . An avalanche discharge i s represented by the c l o s i n g of switch S. V, o p e n 1— closed FIGURE 3.3 E q u i v a l e n t c i r c u i t f o r an MOS gate o p e r a t i n g above breakdown. Charge i n j e c t i o n (or charge t r a n s f e r ) i s represented by the dashed conduction path and switch S . 26 creases [35,36]. T y p i c a l l y a l o a d r e s i s t o r o f 100 kft i s used f o r small area (~100 pm ) diodes. Once the avalanche has been quenched (S opens) C^ i s r e -charged t o V w i t h a time constant of approximately.R (C + C ). Since R i s a Jj d s 1J normally much l a r g e r than R , t h i s time constant determines the dead time per pulse. C l e a r l y there i s a compromise between mini m i z i n g R and s t i l l main-t a i n i n g a short quench time. Not every photogenerated c a r r i e r t h a t i s generated w i t h i n or d i f f u s e s t o the d e p l e t i o n l a y e r w i l l t r i g g e r the diode i n t o reverse conduction. A few w i l l t r a n s i t the high f i e l d region without s u f f e r i n g any i o n i z i n g c o l l i s i o n s w h i l e others may i n i t i a t e chains o f i o n i z i n g c o l l i s i o n s t h a t d i e out a f t e r only a few c a r r i e r s have been generated. In order t o e s t a b l i s h a s e l f - s u s -t a i n i n g avalanche, not only must the i n i t i a t i n g c a r r i e r cause at l e a s t one i o n i z a t i o n , but during each, subsequent t r a n s i t time some descendant must a l s o cause at l e a s t one i o n i z a t i o n . The p r o b a b i l i t y that a c a r r i e r w i l l have an i n f i n i t e number of descendants ( i . e . , w i l l t r i g g e r the diode i n t o reverse conduction) has been r e f e r r e d t o as the avalanche i n i t i a t i o n p r o b a b i l i t y [32]. The avalanche i n i t i a t i o n p r o b a b i l i t y i s zero at the breakdown voltage and, as would be expected, e v e n t u a l l y saturates to one as the diode i s b i a s e d f u r t h e r above breakdown. A s i l i c o n avalanche photodiode operated i n the above mode o f f e r s the unique p o s s i b i l i t y of a s o l i d s t a t e photon counting d e t e c t o r capable o f a very high DQE. Furthermore, because.of i t s s m a l l p o s s i b l e s i z e , such an avalanche diode could be the b a s i c element to an e n t i r e l y s o l i d s t a t e , h i g h performance, photon counting imager. A small m o n o l i t h i c or h y b r i d a r r a y o f avalanche photodiodes, each w i t h i t s own pulse counting c i r c u i t r y , would be of considerable i n t e r e s t . U l t i m a t e l y , however, one would l i k e to f a b r i c a t e l a r g e self-scanned arrays capable of high frame r a t e s . In t h i s case the diodes must be operated" i n the charge i n t e g r a t i o n mode ( i . e . , pulsed above breakdown and 27 then isolated for a frame time). Unfortunately, the requirement for high voltage reset switches and the need to prevent avalanche discharges during readout, severely complicates the design of such a self-scanned diode array. One is not restricted, however, to using an array of junction diodes. The image element of a solid state photon counting sensor could also be a metal-insulator-semiconductor capacitor that is pulsed into very deep deple-tion, such that the field in the depleted semiconductor is higher than that which would normally cause breakdown and the subsequent formation of an in-version layer. One important advantage of such an MIS breakdown image element is its inherent quenching mechanism. Once an avalanche has been initiated and large numbers of carriers are being generated, an inversion layer will build very rapidly until the potential across the semiconductor depletion region has dropped to a value too small to sustain the avalanche (Fig. 3 . 2 ) . The MIS capacitor will then remain in a partially discharged state until i t is reset by removing the charge that is forming the inversion layer under the gate. An equivalent circuit for such an MIS breakdown gate is shown in Fig. 3 - 3 . is the gate voltage above breakdown and <f^ . is the silicon sur-face potential at the onset of breakdown. Rg and R are the series and space charge impedance, C ^ is the depletion region capacitance, and C q x is the oxide capacitance. The closing of switch S^  represents the initiation of an aval-anche discharge while the closing of switch S^  represents charge transfer and reset. MOS gates of this sort could be integrated into a charge coupled array so that the readout, and simultaneous reset, would proceed exactly as in a normal C C D imager. The difference, of course, is that instead of creating only one carrier pair, a single photon is now able to trigger a mom-entarily sustained avalanche, thereby inducing a sizeable charge packet under the detection gate. Figure 3.1+ illustrates this new operating regime for CCD imagers. FIGURE 3.2 Energy band diagram for a p-substrate MOS gate at the beginning and end of an avalanche discharge. <J>s^  = silicon surface potential at the onset of breakdown. A((> = amount by which the surface potential exceeds breakdown in i t i a l l y . 29 - P1 - P 2 f— P 3 - P4 177^ 771 1^771 r77>7i J????. tT*rp XTpTA FIGURE 3.4 Potential well diagram illustrating the basic operation of a it-phase PC-CCD. Heavy solid line indicates the potential at the Si-SiO^ inter-face. (a) detection part of cycle. (b) end of detection phase, ready for charge transfer. (c) charge transfer and reset. 30 During the readout phase the imager i s operated exactly as a normal CCD. I t i s only during the detection part of the cycle i n the i n t e r v a l between read-outs that one or more phases i s held at a potential above breakdown. Since no avalanche discharges can occur during readout, image smearing i s not a problem. However, i n order to minimize dead time t h i s phase must l a s t for only a small f r a c t i o n of the t o t a l frame time. The array would, therefore, have to be organized for frame transfer into a separate storage and readout area. The large signal charge packets, and the fact that only t h e i r presence need be determined during readout, should make very high clocking rates pos-sib l e during frame transfer and readout. In addition to dead time, a certain amount of dead space may also be unavoidable. In order to define the i n d i v i d -ual pixels and prevent crosstalk, the regions between transfer channels and under at least one clock phase must be kept below.breakdown. Photogenerated carriers from these areas may not pass through a high f i e l d region before being collected i n the potential wells under the active gates, and thus, may be unable to tr i g g e r an avalanche discharge. The l i n e a r i t y and DQE for a photon counting CCD operating i n the break-down mode (hereafter referred to as a PC-CCD) are described by the same equations as were derived previously for photon counting imagers (equations 2.6 and 2.12), however, n now refers to the avalanche i n i t i a t i o n p r o b a b i l i t y , and the RQE describes the s i l i c o n response. I t i s reasonable to expect that the dead space i n a rear-illuminated PC-CCD would be less than 50$, perhaps as low as 25%, and that the RQE for each p i x e l could be at least as high as for the RCA or Texas Instruments CCD's. Assuming also that the dark count rate i s n e g l i g i b l e and that the avalanche i n i t i a t i o n p r o b a b i l i t y i s 0.9 or higher, the DQE versus wavelength for a PC-CCD would be approximately as shown i n Fig. 3.5- I t Is clear that the high responsive quantum e f f i c i e n c y t y p i c a l of s i l i c o n detectors would give the PC-CCD a d i s t i n c t advantage over 31 a FIGURE 3.5 Expected performance o f a PC-CCD compared t o e x i s t i n g photon c o u n t i n g systems employing a t r i . - a l k . photocathode. . 32 presently existing photon counting imagers in the visible and near infrared portion of the spectrum. The long wavelength response shown is based on room temperature RQE's and would be somewhat reduced at lower temperatures due to the decreased infrared absorption coefficients. This could be partly compen-sated for by optimizing the anti-reflection coating for these wavelengths and using a thicker substrate. By comparing Fig. 3.5 with Fig. 2.5 i t can be seen that a PC-CCD could also compete very favorably with analog CCD's, especially at very low light levels where high output signal to noise ratios are not possible. The new breakdown mode of operation for CCD's would appear relatively straightforward, however, before a successful PC-CCD imager can be developed the following important problems must be dealt with: (1) Maximizing the avalanche initiation probability. . (2) Reduction of the dark count rate to a negligible level. (3) Prevention of premature edge breakdown in the image elements, and achiev-ing planar, microplasma-free discharges. (U) Minimizing pixel cross-talk due to light emission during the avalanche discharges. 3.1 THE AVALANCHE INITIATION PROBABILITY The avalanche initiation probability has been defined as the probabiL--ity that a carrier, injected into or generated within the depletion layer of a diode biased above the breakdown voltage, will trigger a self-sustaining avalanche (i.e., one that would continue to grow indefinitely in the absence of any limiting mechanisms). Such a sustained avalanche i s , of course, not possible with an MOS breakdown detector. Once an avalanche has been initiat-ed in such a device, the buildup of space charge and the formation of the in-33 v e r s i o n l a y e r reduces the peak e l e c t r i c f i e l d and the corresponding values of the i o n i z a t i o n c o e f f i c i e n t s , u l t i m a t e l y to the poi n t at which the avalanche turns o f f . Before the e l e c t r i c f i e l d and i o n i z a t i o n r a t e s have been reduced s i g n i f i c a n t l y , however, the number o f c a r r i e r s i n the high f i e l d r e g i o n o f the d e p l e t i o n l a y e r w i l l have grown to the extent t h a t a s t a t i s t i c a l f l u c t u a t i o n t o zero, p r i o r to the generation o f a detectable s i g n a l charge i n the i n -v e r s i o n l a y e r , i s h i g h l y improbable [ 3 2 , 3 3 ] . Thus, to a very good a p p r o x i -mation, the p r o b a b i l i t y t h a t a c a r r i e r w i l l t r i g g e r an avalanche t h a t r e s u l t s i n a detectable p u l s e , i s the same as the avalanche i n i t i a t i o n p r o b a b i l i t y of an i d e a l i z e d device w i t h no current l i m i t i n g mechanisms, and f o r which the e l e c t r i c f i e l d and i o n i z a t i o n c o e f f i c i e n t s r e t a i n t h e i r i n i t i a l zero c u r ^ rent values. This i s an important s i m p l i f i c a t i o n since with, no current flow-i n g , the e l e c t r i c f i e l d d i s t r i b u t i o n i n the d e p l e t i o n l a y e r and the c o r r e s -ponding values o f the i o n i z a t i o n c o e f f i c i e n t s may be a c c u r a t e l y c a l c u l a t e d . The i o n i z a t i o n r a t e data f o r s i l i c o n used i n t h i s i n v e s t i g a t i o n i s given i n Appendix A. 3.1.1 T r i g g e r i n g P r o b a b i l i t y Theory Consider the d e p l e t i o n r e g i o n o f a planar avalanche diode (or MOS gate) that i s b i a s e d above the breakdown v o l t a g e , (shown s c h e m a t i c a l l y i n F i g . 3 .6) ; P (x) and P, (x) are the avalanche i n i t i a t i o n p r o b a b i l i t i e s , f o r e l e c t r o n s and e h holes r e s p e c t i v e l y , t h a t s t a r t at p o s i t i o n x i n the d e p l e t i o n l a y e r . P p ( x ) i - s l i k e w i s e the avalanche i n i t i a t i o n p r o b a b i l i t y f o r an e l e c t r o n - h o l e p a i r t h a t has been generated at p o s i t i o n x. The p r o b a b i l i t y that an e l e c t r o n o r hole ' w i l l s u f f e r an i o n i z i n g c o l l i s i o n i n the i n f i n i t e s i m a l d i s t ance 6x i s simply given by a (x)6x and a, (x)(Sx r e s p e c t i v e l y , where a and a, are the e l e c t r o n e h e h and hole i o n i z a t i o n r a t e s . The p r o b a b i l i t y ( l - P ) that n e i t h e r the e l e c t r o n P or the hole o f a p a i r generated at p o s i t i o n x are able to t r i g g e r a breakdown 3h F I E L D •eo p e(x) ; o <—eo—> x=0 1 ©o > P h(x) I < * ©o—> < ©o Pp(x) ©O I —¥ 1 < — © o > ©o—> a h(x) g(x) O I t * ©O a e ( x ) S x ©O x*Sx x=W DEPLETION REGION FIGURE 3.6 Model of the. impact ionization that occurs subsequent to the introduction of a triggering carrier (or carrier pair) at position X in-the depletion region. The probability^of. occurence is indicated in each case. 35 is given by the product, (1 - P ) = (1 - P )(1 - P. ) p e h therefore, P = P + P. - P A p e h e n Similarly, Oldham et.al. [31] show that the probability P g(x + 6x) that an electron starting at position x + 6x will trigger a sustained avalanche can be expressed as, P (x + fix) = P (x) + ct (x) 6x P (x) - P (x) a (x) 6x P (x) e e e p e e p or in differential form, after substituting (3.3) for P^(x), dP -T^ - = (1 - P )ao(P + Pv - P P.) (3.2) dx e e e h e h A similar expression can be derived for holes, dP - ± = _ ( i . + P H . P ^ ) (3.3) In the case of an idealized diode with no current limiting mechanisms, the zero current values for the ionization coefficients a (x) and a, (x) may be e h used. Therefore, provided the electric field distribution prior to break-down is known, (3.2) and (3-3) can be integrated with the boundary conditions P (0) = 0 (3.4) e Pjv) =0 (3.5) n Numerical techniques must, in general, be used to solve (3.2) -(3.5).- The most straightforward method is to use an assumed i n i t i a l value for P, (0) so that standard numerical techniques for the solution to systems h of differential equations may be used. The value for P^(0) c a n then be modified in an iterative procedure until the extra boundary condition P^ (w) = 0 is satisfied. Examples of the solution for the avalanche i n i t i a -tion probabilities Pg(x) and P^U) for an MOS gate biased above breakdown are 36 shown in Fig. 3.7. The corresponding band diagram is that shown in Fig. 3.2. 15 -3 A uniformly doped substrate with NA = 5.5 x 10 cm and room temperature ionization rates were used for this example. The parameter A<|>S is the amount by which the silicon surface potential exceeds the breakdown voltage. It is immediately obvious from Fig. 3-7 that, in silicon, electrons are far more effective than holes in triggering a sustained avalanche. This is simply due to the higher ionization coefficient for electrons (see Appendix A) and yields the well-known result that silicon avalanche detectors should "be designed in such a way that i t is predominantly the photogenerated electrons that initiate avalanche multiplication [ 3 4 ] . This means that photons must be absorbed in.the p-region adjacent to the high field region and that the substrate of an MOS avalanche detector or PC-CCD would have to be p-type, as in the example shown in Fig. 3.7- .Fortunately, this is stand-, ard practice with CCD imagers since electrons have a higher mobility in silicon and are the preferrred signal carrrier. The avalanche initiation probability for electrons entering the depletion layer from the neutral bulk (i.e., Pg'x'w) in Fig. 3 . 7 ) , is. shown as a function of the surface potential in Fig. 3.8. The triggering probability for holes originating from the silicon/silicon dioxide interface is also shown for comparison. It is apparent from the theoretical results shown in Fig; 3.8 that a large voltage above breakdown is required to reach saturation of the aval-anche initiation probability. In the example shown, an excess bias of 10 V or more would be required in order to operate in the plateau region of the electron triggering probability. The hole triggering probability has not even begun to saturate and is in fact increasing slightly superlinearly at these excess voltages. It would be desirable to operate a PC-CCD at some-what higher excess voltages to ensure that small variations in the breakdown voltage over the image area do not introduce large variations in response. 0 37 x/w interface FIGURE 3.7 The avalanche initiation probabilities P (x) and P (x) for a p-e h substrate MOS gate. A«> is the amount by which the surface potential exceeds s breakdown. W is the depletion layer width 15 -3 given in Appendix A, =5x10 -cm , T = 300K The ionization rate data used is FIGURE 3.8 The avalanche initiation probability as a function of surface potential for electrons originating in the bulk and for holes originating at the Si-Si02 interface. Same parameters as for Fig. 3.T. 39 In order t o s o l v e f o r P (x) and P. (x) u s i n g the coup led d i f f e r e n t i a l e n equat ions (3.2) and (3.3), the e l e c t r i c f i e l d d i s t r i b u t i o n through the d e p l e t i o n l a y e r must be known. M c l n t y r e [32] has shown, however, t h a t by making the approx imat ion = k a g , where k i s a constant independent o f f i e l d , (3.2) and (3.3) may be combined to g i ve i n t e g r a b l e e x p r e s s i o n s f o r P. (0) and P (w). The r e s u l t a n t express ions a f t e r i n t e g r a t i o n a r e : h e . . -- l n [ l - P h(0)] = ( i - T l O l n [P h(0) + f(w) + 1 - P h(0)] ( 3 . 6 ) 1 - P. (0) = [1 - P ( w ) ] k ( 3 . 7 ) n e w where f(w) = e x p [ ( l - k ) ? ] , and t, = / a (x )dx . 0 e From these e q u a t i o n s , the p r o b a b i l i t i e s P, (0) and P (w) may be c a l c u l a t e d as • h e a f u n c t i o n o f the two parameters k and £ w i thout hav ing t o know the exact f i e l d d i s t r i b u t i o n . U n f o r t u n a t e l y , the approx imat ion = kct^ i s ve ry poor f o r s i l i c o n , and i t was found necessary t o use equat ions (3.2) - (3-5) i n order t o o b t a i n s u f f i c i e n t l y accura te v a l u e s f o r P (w) and P, (0) when d e -e h s i g n i n g the MOS breakdown t e s t s t r u c t u r e s and a n a l y z i n g the e x p e r i m e n t a l r e s u l t s . 3.1.2 P r e v i o u s E x p e r i m e n t a l I n v e s t i g a t i o n s The p u l s e r a t e o f an avalanche photo diode b i a s e d above t h e breakdown v o l t a g e i s determined by the product o f the number o f c a r r i e r s t r a n s i t i n g the d e p l e t i o n l a y e r per u n i t t i m e , and the a p p r o p r i a t e avalanche i n i t i a t i o n p r o b a b i l i t y . By measur ing the v o l t a g e dependence o f the p u l s e r a t e under c o n d i t i o n s o f constant c a r r i e r i n j e c t i o n , the avalanche i n i t i a t i o n p r o b a b i l -i t y may be determined e x p e r i m e n t a l l y . Such measurements were made by K e i l and Bernt [27] by o b s e r v i n g the v o l t a g e dependence o f the p h o t o n - i n d u c e d p u l s e r a t e under constant i l l u m i n a t i o n . They found ev idence f o r s a t u r a t i o n 1+0 of the t r i g g e r i n g p r o b a b i l i t y i n some of the diodes they s t u d i e d but the value of excess b i a s at which s a t u r a t i o n occured i s much lower than expected. The diodes they studied,. however, were not f r e e from microplasmas, and the diode they reported showing s a t u r a t i o n had a dark count r a t e an order o f magnitude l a r g e r than the photon-induced pulse r a t e , making t h e i r t r i g g e r i n g p r o b a b i l i t i e s somewhat suspect. Oldham et a l . [31] have operated small area, d e f e c t - f r e e avalanche photodiodes above the breakdown voltage i n order to provide experimental v e r i f i c a t i o n o f t h e i r t h e o r e t i c a l l y p r e d i c t e d avalanche i n i t i a t i o n p r o b a b i l i -t i e s . The min i a t u r e avalanche diodes used were n +p abrupt j u n c t i o n devices w i t h a deeply d i f f u s e d n guard r i n g t o prevent premature edge breakdown and to d e fine the sma l l e s t p o s s i b l e breakdown area ( t y p i c a l l y 3-5 un i n diameter). The diodes were i l l u m i n a t e d from the n + s i d e w i t h 390 nm and 1050 nm r a d i a -t i o n i n order to provide hole and e l e c t r o n i n j e c t i o n r e s p e c t i v e l y . The high absorption c o e f f i c i e n t s at 390 nm ensured pure hole i n j e c t i o n ' f r o m the n e u t r a l r e g i o n of the n l a y e r so th a t the photon induced pulse r a t e pro-vided a d i r e c t measure of the avalanche i n i t i a t i o n p r o b a b i l i t y f o r holes en-t e r i n g the d e p l e t i o n r e g i o n . Pure e l e c t r o n i n j e c t i o n from the n e u t r a l p-type + bulk was not p o s s i b l e i n the case of i l l u m i n a t i o n from the n s i d e . However, Oldham et a l . argued that because of the small absorption c o e f f i c i e n t at 1050 nm and the much l a r g e r e l e c t r o n i o n i z a t i o n c o e f f i c i e n t s , the 1050 nm responses should be roughly p r o p o r t i o n a l to the avalanche i n i t i a t i o n proba-b i l i t y f o r e l e c t r o n s e n t e r i n g the d e p l e t i o n r e g i o n . The measured response at 390 nm was found t o f o l l o w the t h e o r e t i c a l hole t r i g g e r i n g p r o b a b i l i t y very c l o s e l y , however, only the l i n e a r r e g i o n of the avalanche i n i t i a t i o n p r o b a b i l i t y versus excess b i a s was covered, and since only a very rough estimate o f the absolute t r i g g e r i n g p r o b a b i l i t y was p o s s i b l e , the r e s u l t s do not, i n f a c t , provide good c o n f i r m a t i o n o f the kl theory. The response at 1050 nm did show some saturation, but considerably less than was theoretically predicted. This was thought to be due to the voltage dependence of the effective collecting volume for electrons and to uncertainties in the available ionization rate data. Further investigations are required in order to verify that the triggering probabilities saturate with increasing overvoltage as predicted by the theory, and that i t will be possible to operate an MOS gate in the plateau region of the electron trig-gering probability at reasonable excess biases. 1+2 3.2 DARK GENERATION OF TRIGGERING CARRIERS Photogeneration must be the dominant mechanism for the production of triggering carriers i f an MOS gate is to be operated above breakdown as a photon counting detector. The dark generation rate of triggering carriers must be made very small i f one wants to detect low photon fluxes. How small the dark generation rate needs to be can be determined by examining its ef-fect on the DQE of the sensor (Fig.' 3.9). In order for the DQE not to be reduced by more than 10$, the dark count rate must be less than 5$ of the event rate due to photogenerated carriers. In many cases i t would be de-sirable to detect photon fluxes at least as low as 0.1 per second per pixel, 2 for pixel areas on the order of 1000 um , and hence the dark count rate -1 —2 should be maintained at a level below 500 sec cm (corresponding to a dark - l 6 -2 leakage current of approximately 10 A cm ). A major effort will be re-quired to achieve such low dark count rates. Two basic mechanisms are responsible for the dark generation of car-riers within or adjacent to the surface space charge region of an MOS gate. The first involves thermally activated processes that occur at bulk defect or impurity trapping levels and at the Si-SiO^ interface states. The second mechanism, .applicable only in the high field region, involves band to band tunneling or tunneling between one band and a bulk trapping level or surface state. These generation mechanisms are described in more detail below. 3.2.1 Review of Recombination and Generation at Bulk Defect or Impurity Centers In a perfect (intrinsic) semiconductor there exists a forbidden gap be-tween the valence and conduction bands which is free of states that can be occupied by electrons. Thermal generation of carriers in such a material FIGURE 3.9 The degrading effect of the dark count rate on the detective quantum efficiency, plotted according to Eq. (2.13). kk r e q u i r e s t h a t an e l e c t r o n "be r a i s e d d i r e c t l y from the valence to conduction band. Semiconductor devices on the other hand are made from e x t r i n s i c mater-i a l t h a t i s doped w i t h i m p u r i t i e s having a low i o n i z a t i o n energy f o r e l e c -t r o n s and h o l e s , to give predominantly n or p type c o n d u c t i v i t y . In a d d i t i o n to these dopant i m p u r i t i e s , a number o f other unwanted i m p u r i t i e s w i t h h i g h -er i o n i z a t i o n energies are g e n e r a l l y present or are u n i n t e n t i o n a l l y i n t r o -duced during device processing. When the i o n i z a t i o n energy o f the i m p u r i t y i s higher i t may not be completely i o n i z e d at normal o p e r a t i n g temperatures and w i l l act as a t r a p or recombination-generation center. These energy l e v e l s are not only caused by i m p u r i t i e s but a l s o by a l a r g e v a r i e t y o f c r y s t a l d e f e c t s . The d i f f e r e n c e between shallow dopant l e v e l s , t r a p s and r e -combination-generation centers i s only q u a l i t a t i v e . Which r o l e the energy l e v e l w i l l p l a y depends on the temperature, the c o n c e n t r a t i o n of f r e e c a r -r i e r s and the r e l a t i v e cross s e c t i o n f o r the capture of m a j o r i t y and m i n o r i t y c a r r i e r s . Deep l e v e l s w i t h i n the band gap are g e n e r a l l y l o o s e l y r e f e r r e d to as simply " t r a p s " . The s t a t i s t i c s of c a r r i e r capture and emission by such intermediate energy l e v e l s has been worked out by Shockley and Read [37] and by H a l l [38]. For use i n the a n a l y s i s o f dark generation mechanisms t h i s theory w i l l be b r i e f l y reviewed. F o l l o w i n g the b a s i c concepts of Shockley and Read, four b a s i c processes are defined f o r centers w i t h a s i n g l e energy l e v e l w i t h i n the band gap ( F i g . 3.10): (a) E l e c t r o n capture from the conduction band (b) E l e c t r o n emission i n t o the conduction band (c) Hole capture from the valence band (d) Hole emission i n t o the valence band Processes (a) and (c) are described by two capture p r o b a b i l i t i e s c ^ s e c ^) and c^(sec ^ ) , w h i l e processes (b) and (d) are determined by the emission U5 (c) (d) * 1 . i — i l-O- i -<= 1__ _l i 1 I 1 i i l I =>- i — i < l i • 1 i i ' 1 1 r I ^ I 1 l 1 1 : i (a) (b) t 5 € 3 L9J FIGURE 3.10 The four "basic Shockley-Read-Hall processes that may occur at a trapping level. . The final state is indicated in the dashed boxes, the arrow indicates the direction of the electron transition. (a) electron capture (b) electron emission (c) hole capture (d) hole emission e J > - © . J L > -e- JL >.«=>. E t FIGURE 3.11 Action of an electron trap. The relative positions of E F n, E T and Epp are also shown. Electrons are trapped and re-emitted several times before finally disappearing through recombination. 1*6 p r o b a b i l i t i e s e (sec "*") and e (sec ^ ) r e s p e c t i v e l y . Energy l e v e l s are f u r -n p ther c h a r a c t e r i z e d by being donor l e v e l s or acceptor l e v e l s . A donor i s n e u t r a l when occupied by an e l e c t r o n and p o s i t i v e when ion i z e d , w h i l e an acceptor l e v e l i s n e g a t i v e l y charged when occupied by an e l e c t r o n and n e u t r a l when i o n i z e d . Doubly charged donors or acceptors are a l s o p o s s i b l e . In a d d i t i o n to the energy l e v e l , the capture c r o s s - s e c t i o n i s a b a s i c property of a given t r a p . E x p e r i m e n t a l l y , values f o r the c r o s s - s e c t i o n are obtained by measuring the capture r a t e c. I f the c a r r i e r s a l l have the same v e l o c i t y V q the capture r a t e would be simply, c = a v n,p n,p o 2 where a (cm ) i s the caoture c r o s s - s e c t i o n f o r e l e c t r o n s or holes. In n,p r e a l i t y the c a r r i e r s have a thermal d i s t r i b u t i o n o f v e l o c i t i e s and energy and furthermore, the capture c r o s s - s e c t i o n may depend on e l e c t r o n energy. The c r o s s - s e c t i o n s most f r e q u e n t l y quoted are obtained by d i v i d i n g the ob-served capture r a t e by the mean thermal v e l o c i t y , c * \-;3kT/m ) 2 v t h (3.8) where m* i s the c o n d u c t i v i t y e f f e c t i v e mass. The experimental values of a -12 -22 2 cover a considerable range, from-10 t o 10 cm . This range of capture c r o s s - s e c t i o n s can be q u a l i t a t i v e l y understood by c o n s i d e r i n g t h a t depend-ent on occupancy, a l e v e l may be e i t h e r Coulombically a t t r a c t i v e , n e u t r a l or r e p u l s i v e . I f the conc e n t r a t i o n o f centers i n the semiconductor i s N a c e r t a i n f r a c t i o n f ^ w i l l be i n the more negative s t a t e (e.g., i o n i z e d acceptors or n e u t r a l donors) and a f r a c t i o n ( l - f ) w i l l be i n the more p o s i t i v e s t a t e (e.g., n e u t r a l acceptors or i o n i z e d donors). In thermal e q u i l i b r i u m the occupancy f i s given by the Fermi-Dirac d i s t r i b u t i o n , hi fT • i1 + g e x p l - i T - J i ( 3 . 9 ) where E is the Fermi energy, E is the energy level of the center, and g F i is the spin degeneracy factor, usually assumed to be 2. The rate at which electrons and holes are captured depends on both the occupation of the centers and the density of free carriers. The rate at which carriers are emitted depends only on the occupation. The four rate equations cor-responding to processes (a) - (d) are, therefore, r a = c nn NT(1 - f T) r = e N f b n T T r c = C p P V T rd = 6 p N T ( l " V (3.10) (3.11) (3.12) (3.13) The electron concentration in the conduction band varies as dn „ = r - r = e N mf m - c n N m(l - f_) dt a b n T T n T T (3.1U) Similarly the rate of change of the hole concentration in the valence band is dt r d - Tc = e p N T ( L - V - W T (3.15) It is interesting to calculate the limiting electron and hole.lifetimes that occur when f^ is equal to zero and one respectively. From (3«lM» no n dni dt Cn NT (3.16) fT=o similarly from (3.15), po c Nm p T (3.17) U8 For more general values of f^ we need expressions for the emission rates e n and e^. By invoking the principle of detailed balance i t is possible to obtain a relation between the capture and emission probabilities. The principle of detailed balance states that in equilibrium r = r, and r = r,. a b c d. For the case of Boltzmann statistics (i.e., for the Fermi level sever-al kT below the conduction band edge) the electron concentration in the conduction band, in thermal equilibrium, is n = N exp kT = n. exp 1 E - E. _F i kT (3.18) where N is the effective density of states in the conduction band and E C • and E are the energy of the conduction band edge- and the intrinsic level i respectively. Equating r. and r and using (3.9) for f and expressions (3.18) for n gives n n g n. exp exp E m- E n T C kT V.'Ei kT (3.19) The emission probability of holes can be obtained similarly from p = N y exp fV EF) kT = n. exp 1 V V kT (3.20) k9 where Ny is the effective density of states in the valence hand and Ey is the energy level of the valence band edge. Thus, e ^ = Nvg exp P - n ig exp V E T kT V ET kT (3.21) As expected, the emission probabilities depend exponentially on the energy difference between the trap level and the respective band edge. Also, since the emission probabilities given by ( 3 . 1 9 ) and ( 3 - 2 1 ) are not .functions of the Fermi energy E_, the same expressions may be used in nonequilibrium sit-uations. For steady state, non-equilibrium conditions the rate of change of trapped charge is zero, therefore, dn _ dp_ dt dt Equating (3 .1 *0 for dn/dt and ( 3 . 1 5 ) for dp/dt enables the steady state occupancy f^ to be determined. e + c n f m = P t " , — (3.22) T e + e + c n + c p n p n p If this is reinserted into either (3 .1 *0 or ( 3 . 1 5 ) the net steady state rate of recombination or generation is obtained. , , (e e - c c np) N_ T j ^ d n ^ d p ^ np n P ^ T (3.23) dt d t . ' e + e + c n + c p n p n p Another question of importance is whether a particular energy level will behave as a trap, a recombination, or a generation center. Any energy level may contribute to either recombination or generation. The difference between traps and recombination-generation centers lies in the relative capture and emission rates for electrons and holes. Carriers will be cap-50 tured by traps, and reemitted into the band from which they came, several times before finally disappearing through recombination (Fig. 3.1l). In terms of the four rate equations (3.10) - (3.13) the conditions for electron traps are: r >> r, , r, >> r a d b c Similarly for hole traps r >> r^ , r, >> r c b d a For recombination centers the conditions are: r » r, , r >> r,_ a d c b and for generation centers r, >> r , r, >> r d a b c Stockmann [39] has shown that i t is possible to express these four sets of inequalities in the alternate form: . * electron traps i f , E w , E > E m (3.24) Fn Fp T hole traps i f , E* > E p n , (3.25) * recombination centers i f , E^ > E m > E ^ (3.26) Fn T ' Fp * generation centers i f , E„ > E m > E_ (3.27) Fp T Fn * Where E^ , is defined by, EJ 5 2 ET - J ^ - k T L n (c n/c ) (3.28) and Ep n and are the non-equilibrium, quasi Fermi levels that describe the electron and hole concentrations according to: n = n^ exp p = n i exp E - E. i Fn l kT 1 i Fp kT If the capture rates (i.e., the capture cross-sections) for holes and electrons are equal, Eq. (3.28) reduces to 51 * E_ - E. = E. - E_ T i i T * i n vhich case the c l a s s i f i c a t i o n l e v e l E^ i s i n the mirror image position of the l e v e l E^with respect to the i n t r i n s i c l e v e l E^. The treatment of intermediate levels thus f a r has been for centers with a single energy l e v e l only. In r e a l i t y , many defect or impurity centers have several donor and/or acceptor l e v e l s . Shockley and Last [40] have shown, however, that equations (3.10) - (3.23) can be generalized to the case of a mul t i l e v e l center,- and that the behaviour i s q u a l i t a t i v e l y very s i m i l a r to the single l e v e l case. I f the, number of lev e l s i s not too.great they are usually many kT apart at low temperatures and may be treated independently of each other. .. . . -. ( 3 . 2 . 2 Steady State Bulk Generation: Low F i e l d Case When defect or impurity centers are located within a reverse biased depletion region (where condition (3.27) holds) t h e i r occupancy i s only deter-mined by the emission p r o b a b i l i t i e s e n and e^ since capture i s n e g l i g i b l e due to the low c a r r i e r concentration i n such.a region. Setting n = p = 0 i n (3.22) gives F T - T^ir - ( T U T ^ I <3-29) n p n p and from (3.23) the volume rate of generation of electron-hole pairs becomes *B = r f t r N T ( 3 - 3 0 ) n p The centers must alternate between electron and hole emission. Eq. (3.29) relates the steady state occupancy to the r a t i o of the emission rates. From (3.19) and (3.21) t h i s r a t i o can be expressed as 52 n 1 Cn • —o — exp 2 g z c kT (3.31) For levels away from midgap the exponential factor very rapidly takes over, forcing levels i n the upper h a l f of the band gap to be predominantly empty and i n the lower h a l f to be f u l l of electrons. I f many different levels are present within the forbidden gap, the steady state emission of electrons and holes w i l l be dominated by those levels for which the electron and hole emission p r o b a b i l i t i e s are equal. From (3.31) the energy of these levels i s .2, VT1 E_ = E. + £f In Tmax l 2 kT (3.32) For s i m i l a r electron and hole capture cross-sections , E r p m a x l i e s very close to ( i . e . , mid gap).' Using expressions (3 . 1 9 ) and (3.2l) for e and e i n Eq. (3-30) for n p g^ with E m = E„ BB T Tmax gives n. SB 2T (3.33) where the eff e c t i v e l i f e t i m e T i s given by e { C U C / 2 NT (T T )' no po The t o t a l rate of generation per unit area of electron-hole pairs i s n.W GB = 2T~ where W i s the depletion layer width. The important thing to note from (3.33) i s that the temperature de-pendence of g„ i s determined mainly through n. which varies as B l 53 T 2 exp -E where E = E_- E„ Lowering the temperature should, therefore, be a very effective means of re-ducing the steady state thermal generation of carriers in the depletion region of a wide band gap semiconductor such as silicon. Typical bulk l i f e -• -U times T and x , after CCD processing, are on the order of 10 sec. which no po . 13 -1 -3 gives = 8.x 10 sec cm at room temperature. This is reduced by 20 orders of magnitude upon cooling to 100 K. It will., therefore, clearly be possible to reduce this type of generation to well below 500 carriers sec cm even for very wide depletion regions (several tens of microns). In addition to the generation occuring in the space charge region, one also has to consider the diffusion of minority carrier electrons from the neutral bulk. For thinned CCD's the diffusion length of these minority carriers is generally much greater than the substrate thickness, and i t is the condition of the back surface that determines the size of the electron injection current. The injection current can be obtained by solving the con-tinuity equation for minority carrier electrons in the neutral bulk, subject to the appropriate boundary conditions. The analysis may be simplified by making the following assumptions: (1) the minority carrier diffusion length in the bulk away from the surface is very much greater than the substrate thickness L so that recombination/ generation in the bulk can be neglected in comparison with recombination/ generation at the rear surface (i.e., L/x « s). (2) the rear silicon surface is a region of high electron hole recombination, characterized by a high value of surface recombination velocity s. With these assumptions the continuity equation for electrons becomes 5h ,2 \H= 0 n , d dx subject t o the boundary co n d i t i o n s = s[n - n(L)] , and n(0) = 0 D f n dx x=L where: n = e q u i l i b r i u m e l e c t r o n c o n c e n t r a t i o n o D = e l e c t r o n d i f f u s i v i t y . n x=0 = edge of the d e p l e t i o n r e g i o n L = th i c k n e s s of the n e u t r a l r e g i o n The e l e c t r o n i n j e c t i o n current i s , t h e r e f o r e , sn T -p. dn n d i f f " q n dx q Dn. ( s L + F T ( 3 ' 3 4 ) x=0 * n With a very high r e a r - s u r f a c e recombination v e l o c i t y , such t h a t s>>D /L, n J ,. » c a n tie approximated by n d i f f 2 n qD n. T = Vi — n 1 n d i f f q n L L N A L \ whi l e f o r a low r e a r - s u r f a c e recombination v e l o c i t y , — << s < ^—, J ,. „' x L n d i f f n becomes 2 n. T i v • = qsn = qs ^ — . n d i f f H o N n A 2 The n^ dependence ensures t h a t the m i n o r i t y c a r r i e r i n j e c t i o n d i f f u s i o n current can be reduced t o an e n t i r e l y n e g l i g i b l e l e v e l by c o o l i n g . 3.2.3 Steady State Generation at the S i l i c o n / S i l i c o n Dioxide I n t e r f a c e : Low F i e l d Case The d i s r u p t i o n o f the p e r i o d i c l a t t i c e s t r u c t u r e at the s i l i c o n / s i l i c o n d i o x i d e i n t e r f a c e introduces a high d e n s i t y of a v a i l a b l e energy s t a t e s i n the forbidden gap near the i n t e r f a c e . The d e n s i t y o f the i n t e r f a c e s t a t e s de-55 pends on the orientation of the silicon substrate and very critically on the oxidation and annealing processes that the silicon sample is subjected to. Silicon surfaces on a (100) crystal plane have been found to have the lowest interface state densities. For a properly annealed, thermally grown oxide on (100) silicon, the interface state density is in the range 9 11 -2 -1 10 - 10 cm eV with a distribution in energy which is relatively flat in the middle of the band gap and which peaks towards the conduction and valence band edges [41]. Although the physical origin of the interface states is different from that of the bulk centers, surface generation can be treated in a manner s i l i l a r to bulk generation. In the absence of an inversion layer, the concentration of both electrons and holes at the interface is very low and the steady state generation rate of electron hole pairs is given by an ex-pression similar to (3-30), E y n p (3.35) where N (E ) is the distribution of interface states per unit area per unit S -L energy. Using (3.19) and (3.21) for e and e (3.35) becomes n p E, n.c c N ( E j l n p s T Ey Cn 6 X P V E i kT + c exp P V ET kT dEn (3.36) The major contribution to the integral comes from those interface states within a few kT of the intrinsic level E . By further assuming that the electron and hole capture cross-sections are equal (i.e., a =a , c =c ), n p n p the integral can be evaluated approximately as 56 G =7* Trav^kT N (E.) n. s 2 th s 1 . 1 = | s n. (3.37) vhere s is the commonly used parameter called the surface recombination velocity. The assumption a =a is not really justified because experimental n p.. data indicates that the electron and hole capture cross-sections differ by as much as an order of magnitude. However, the error made by setting a =a is n p at most a factor of 2. Typically, the mid gap interface state density after 9 - 2 - 1 CCD processing is 10 cm eV . The capture cross-sections for electrons -lh 2 and holes by mid gap interface states are about 10 cm , therefore,the room temperature steady state generation of.electron hole pairs at the inter-face is Gg = 8 x 10^ cm ^sec \ corresponding to a surface recombination velocity of approximately 10 cm sec \ In p-type substrates i t is only the holes emitted from interface states that are able to traverse the depletion region and trigger a discharge. Since the temperature dependence of Gg is determined mainly by n^, cooling should be an effective means for reducing -1-2 G to well below. 500 sec cm s When an inversion layer is present, capture processes can no longer be neglected. For p-type substrates the effect of electron capture from the inversion layer is to keep the interface states f i l l e d up to a level considerably above the intrinsic level, and the hole emission rate, therefore, becomes extremely small. In this case the steady state occupancy can be shown to be f T = \ e x p [ — k r — - J + 1 ; Thus the position of the quasi fermi level for electrons, E ^ , determines the occupation of the interface states. 57 3 . 2 . 4 High Field Effects The high electric fields within the space charge region of an aval-anche diode or MOS gate, biased above breakdown, can substantially influence carrier emission from traps through either the Poole-Frenkel effect or tunneling. These field effects are illustrated schematically in Fig. 3.12 which shows the distortion of the coulomb potential well around a trapping center with increasing electric fields. At low fields carrier emission is thermally activated. As the field increases, the potential barrier is low-ered, thus enhancing the probability of thermal emission. At higher fields tunneling begins to dominate the emission process and finally, at very high fields, the barrier is lowered below the ground state of the trap and i t becomes delocalized. Delbcalization generally need not be considered, how-ever, since emission by tunneling increases very.rapidly with increasing field, and empties the traps before delocalization occurs. For a trap to experience the Poole-Frenkel effect i t must be coulomb attractive to the emitted carrier. If i t is neutral after carrier emission, barrier lowering will not occur due to the absence of the coulomb potential. The Poole-Frenkel effect can, therefore, only increase the emission rate of electrons from donor levels or holes from acceptor levels. The barrier lowering is similar to Schottky barrier lowering in a metal-semiconductor junction. The image charge, however, is fixed rather than mobile as in Schottky emission, resulting in a barrier lowering twice as great for the Poole-Frenkel effect. Referring to Fig. 3.12(b), ire = B/e" ( 3 . 3 8 ) where £ is the applied electric field and e is the high frequency dielectric constant. For silicon i t has been shown that the appropriate dielectric 58 FIGURE 3.12 Schematic diagram showing the distribution of the coulomb poten-t i a l well around a trapping center for different electric field strengths. (a) low field - thermal emission dominates (b) moderate field - thermal emission with reduced barrier (c) high field - tunnelling dominates (d) very high field - trap derealization 59 constant i s very c l o s e t o the s t a t i c value f o r f i e l d s up to at l e a s t 1.5 x 10^ V cm ^ [42]. Eq. (3.38) gives the maximum h a r r i e r l o w e r i n g i n the d i r e c t i o n o f the a p p l i e d f i e l d . In order t o c a l c u l a t e the r e s u l t i n g emission p r o b a b i l i t i e s , however, a three dimensional model i s r e q u i r e d . The three dimensional treatment of Poole-Frenkel emission from t r a p s has been developed by Hartke [43]. The r e s u l t i n g -expression f o r the b a r r i e r lowering., i n p o l a r c o o r d i n a t e s , i s A<j>pF(6) = e(6cos0)' (3.39) where the b a r r i e r i s lowered only f o r 0<6<TT/2. The r a t i o o f the f i e l d en-hanced emission r a t e e p F t o the zero f i e l d emission r a t e e , i s approximated by Hartke t o be 'PF ' kT 2 / 1 + fg/n 1 1 + - — - 1 kT j exp [ k T j (3.40) In d e r i v i n g (3.^0) Hartke assumes a s p h e r i c a l l y symmetric, f i e l d independent, attempt-to-escape frequency o f v/ku per u n i t s o l i d , angle where v i s given by the r e l a t i o n e Q = v exp (-AE/kT) AE = E - E m f o r donor l e v e l s c T = E m - E f o r acceptor l e v e l s T v For high f i e l d s or low temperatures where $-/Z » kT, (3.^0) may be ap p r o x i - . mated by "PF kT exp kT (3.41) F i g . 3.13.shows t h i s approximate form f o r e /e along w i t h the more accurate pr o value given by (3.^0)., p l o t t e d as a f u n c t i o n o f g/T/kT. The e f f e c t of Poole-Frenkel emission on the steady s t a t e generation i n 60 61 the depletion l a y e r can be-estimated as follows. From (3.30) and(3.40) the revised steady state generation (for the case of donor l e v e l s ) i s ye e no po lB ye + e NT ' no po (3 .42) As b e f o r e , the most e f f e c t i v e l e v e l s f o r steady s t a t e emission are those f o r which ye = e , i . e . , those l e v e l s at no po kT E m = E.+ 2± l n Tmax l 2 2 g c. (3 .43) Using expressions (3 . 1 9 ) and (3.21) f o r e^ Q and e ^ i n (3.42), w i t h E^ given by (3.43), gives 3B '2 Y " i 2x (3 .44) and the r a t e o f generation per u n i t area i s w 2x [ y ( x ) ] 2 dx (3 .45) 0 I d e n t i c a l expressions f o r g and G_. are obtained f o r acceptor l e v e l s . The steady s t a t e generation r a t e g . i s , t h e r e f o r e , i n c r e a s e d by a f a c t o r y when Poole-Frenkel high f i e l d e f f e c t s are i n c l u d e d . Using the approximate expression f o r y given i n (3.40) enables the temperature de-pendence of g to be expressed as g 'B 2 T exp fe/T.- E 2kT Therefore, provided the b a r r i e r l o w e r i n g g/£ i s only a small f r a c t i o n o f the energy gap, lowering the temperature should s t i l l be a very e f f e c t i v e means of reducing t h i s type of steady s t a t e generation. As w i l l be shown i n the 62 next s e c t i o n , the peak f i e l d i n the space charge r e g i o n o f s i l i c o n d iodes 7 -1 or MOS gates must be kept below approx imate ly 4.2 x 10 Vm i n order t o a v o i d s i g n i f i c a n t c a r r i e r g e n e r a t i o n due t o i n t e r b a n d t u n n e l i n g . The P o o l e - F r e n k e l b a r r i e r l o w e r i n g f o r a f i e l d o f t h i s magnitude i s O.lk eV, which i s indeed on ly a s m a l l f r a c t i o n of the s i l i c o n band gap. P o o l e - F r e n k e l e f f e c t s at the i n t e r f a c e can be t r e a t e d i n p r e c i s e l y the same manner, w i t h the r e s u l t t h a t the s u r f a c e recombinat ion v e l o c i t y i s h i n c r e a s e d by a f a c t o r y , G s = l ^ V t h k T N s ( E i ) V = ^ s n. (3.46) 2 PF i At ve ry h i g h f i e l d s i t becomes p o s s i b l e f o r e l e c t r o n s t o make t u n n e l i n g t r a n s i t i o n s between b u l k t r a p p i n g l e v e l s and e i t h e r b a n d , l e a d i n g t o e l e c -t r o n and h o l e e m i s s i o n p r o b a b i l i t i e s which are v i r t u a l l y independent o f temperature . I t a l s o becomes p o s s i b l e f o r e l e c t r o n s t o make t u n n e l i n g t r a n s i t i o n s from the va lence band i n t o empty i n t e r f a c e s t a t e s . Under s teady s t a t e c o n d i t i o n s these t u n n e l i n g processes may combine w i t h the t h e r m a l l y a c t i v a t e d e m i s s i o n from t r a p s or i n t e r f a c e s t a t e s , o r a two s t e p t u n n e l i n g process may occur from the va lence band i n t o a b u l k t r a p then from the t r a p i n t o the conduct ion band. These b a s i c s teady s t a t e t u n n e l i n g g e n e r a t i o n mechanisms are i l l u s t r a t e d i n F i g . 3.14. T u n n e l i n g mechanisms i n v o l v i n g more than one t r a p (examples o f which are i l l u s t r a t e d by the dashed l i n e s i n F i g . 3.l4) are a l s o p o s s i b l e but are expected t o be r e l a t i v e l y unimportant compared t o the s i n g l e l e v e l p r o c e s s e s . When t u n n e l i n g and P o o l e - F r e n k e l e f f e c t s are i n c l u d e d , the r a t e o f emiss ion o f h o l e s from donor l e v e l s becomes FIGURE 3.14 Energy band diagram'illustrating the proposed steady state gen-eration mechanisms involving the tunnelling emission of electrons and/or holes by mid gap levels. 6k where e° i s a hole emission p r o b a b i l i t y equal t o the p r o b a b i l i t y per u n i t pt time f o r t u n n e l i n g from the valence band t o an unoccupied donor l e v e l . The ra t e of emission o f el e c t r o n s becomes f - W")'M * v ( s , 1 V I < 3 - 4 8 ) where e + i s an emission p r o b a b i l i t y corresponding t o t u n n e l i n g from an II TJ occupied donor l e v e l t o the conduction band. Expressions (3.29) f o r f , and (3.30) f o r g , t h e r e f o r e , s t i l l h o l d provided the emission p r o b a b i l i t i e s B e and e are replaced by the new emission p r o b a b i l i t i e s e and e , de f i n e d n p n p b y : e*(x) = Y"(x)e + e + + ( x ) (3.49) n no nt e*(x) = e + e° (x) (3.50) p po pt For acceptor l e v e l s the new emission p r o b a b i l i t i e s are e*(x) = e + e°(x) (3.51) n no nt e*(x) = y(x)e + e'Ax) (3.52) p po pt The appropriate emission p r o b a b i l i t i e s t o be used i n expression (3-35) f o r * * + G are e (0) and e (0). For p-type substrates e .(0) i s , of course, s n p nt equal to zero. For shallow donor l e v e l s the e l e c t r o n emission p r o b a b i l i t y becomes very h i g h , and the rate determining step i n the steady s t a t e generation of el e c t r o n - h o l e p a i r s i s e i t h e r t h e r m a l l y a c t i v a t e d hole emission o r t u n n e l i n g from the valence band t o the t r a p . At low temperatures the p r o b a b i l i t y of hole emission by t u n n e l i n g may exceed the thermal emission p r o b a b i l i t y by many orders of magnitude i n the high f i e l d r e g i o n o f the d e p l e t i o n l a y e r . The t u n n e l i n g d i s t a n c e , however, i s c l o s e t o tha t f o r band to band t u n n e l i n g 65 and since the density of traps N^  is many orders of magnitude smaller than the density of states in the valence hand, tunneling through shallow donors is expected to be unimportant compared to interband tunneling. A similar argument holds for shallow acceptor levels. The situation is quite dif-ferent for deep bulk levels in the high field region. At low temperatures, thermal emission from these levels is generally negligible compared to the tunneling transitions. Thus, the generation of electrons and holes through deep levels in the high field region will proceed almost entirely by mechan-ism 2 in Fig. 3.14. Since the tunneling distances are approximately half that for band to band tunneling, this type of carrier generation can become significant. Tunneling through deep level traps is considered in more de-t a i l in section 3 .2.5. In the absence of an inversion layer, tunneling of electrons into unoccupied interface states, as in mechanism h in Fig. 3.14, can greatly in-crease the hole emission probability at low temperatures. This, together with the enhanced electron emission probability due to Poole-Frenkel barrier lowering, can substantially increase the.effective surface recombin-ation velocity. It may, therefore, be necessary to maintain the surface in strong inversion (i.e., E very close to the conduction band edge) in r n order to increase the tunneling distance for hole emission. 3 . 2 . 5 Dark Generation Due to Tunneling When the electric field in an insulator or semiconductor is suffic-iently high, the forbidden energy gap may be treated in the manner of a potential barrier of finite width w given by w = E /q£, 6 and thus i t is possible for the valence band electrons to make direct quan-tum mechanical tunneling transitions to the conduction band. Normally hot 66 e l e c t r o n e f f e c t s , such as impact i o n i z a t i o n and avalanche, precede t u n n e l i n g and the f i e l d never reaches a value where t u n n e l i n g becomes important. Observation o f l a r g e t u n n e l i n g currents i s r e s t r i c t e d t o specially-made, narrow p-n j u n c t i o n s i n h e a v i l y doped semiconductors, o f t e n r e f e r r e d t o as Esaki diodes [44]. In t h i s i n v e s t i g a t i o n , however, we are concerned w i t h extremely s m a l l reverse b i a s currents (of the order of 10 A) and, furthermore, the maximum f i e l d s are higher than those which would normally cause avalanche breakdown. I t i s t h e r e f o r e necessary t o consider i n t e r b a n d t u n n e l i n g as a p o s s i b l e dark generation mechanism even f o r j u n c t i o n s or MOS gates formed on r e l a t i v e l y l i g h t l y doped s u b s t r a t e s . Many t h e o r e t i c a l and experimental s t u d i e s o f i n t e r b a n d t u n n e l i n g have been report e d i n the l i t e r a t u r e . These s t u d i e s , however, are g e n e r a l l y d i r e c t e d at e x p l a i n i n g the current v o l t a g e c h a r a c t e r i s t i c s o f E s a k i t u n n e l diodes i n which the b u i l t - i n f i e l d i s l a r g e enough t o cause s i g n i f i c a n t t u n n e l i n g at zero b i a s . Such diodes g e n e r a l l y have degenerately doped n and .p regions. The only experimental r e s u l t s known t o the author on the t u n n e l -i n g generation of t r i g g e r i n g c a r r i e r s i n l i g h t l y doped avalanche diodes o p e r a t i n g above breakdown, are those o f H a i t z [36]. H a i t z measured the dark count r a t e f o r diodes known t o have very low d e n s i t i e s o f bulk t r a p p i n g l e v e l s and showed t h a t the observed dependence of the count r a t e on temper-ature and peak f i e l d could be described by an i n t e r b a n d t u n n e l i n g generation of c a r r i e r s . From H a i t z ' s dark count r a t e data and the quoted j u n c t i o n area, the reverse b i a s t u n n e l currents f o r h i s 30V breakdown (one-sided step -12 —2 j u n c t i o n ) diodes i s estimated t o be 2 x 10 A cm (before m u l t i p l i c a t i o n ) -8 -2 at breakdown i n c r e a s i n g t o 2 x 10 A cm at 10 V above breakdown. C l e a r l y , diodes or MOS s t r u c t u r e s t h a t have lower peak f i e l d s must be considered i f - l 6 -2 the dark generation i s t o be maintained below 10 A cm In one-sided step j u n c t i o n s or MOS gates, the peak f i e l d at break-67 down may be reduced by decreasing the su b s t r a t e doping. U n f o r t u n a t e l y , as regards f a b r i c a t i o n of a.PC-CCD, t h i s a l s o has the unde s i r a b l e e f f e c t of i n c r e a s i n g the breakdown v o l t a g e . In order t o examine more c l o s e l y the e f f e c t s of su b s t r a t e doping and d i f f e r e n t doping p r o f i l e s on the dark generation due to t u n n e l i n g , we need an accurate expression f o r the volume rate o f e l e c t r o n - h o l e p a i r generation t h a t my be i n t e g r a t e d over the deple-t i o n region. Interband t u n n e l i n g . c a l c u l a t i o n s can be c l a s s i f i e d i n t o two general categories according t o whether the t r a d i t i o n a l Zener f i e l d - e m i s s i o n model [45] or the more recent Fredkin-Wannier j u n c t i o n p o t e n t i a l model [46] i s used. In both p i c t u r e s of inter b a n d t u n n e l i n g the e x t e r n a l l y a p p l i e d f i e l d i s t r e a t e d as a p e r t u b a t i o n on the atomic f o r c e s . This i s j u s t i f i e d i n most cases s i n c e , at the highest f i e l d s normally encountered, the change i n e x t e r n a l p o t e n t i a l V over a l a t t i c e constant i s s m a l l compared t o the amplitude of the p e r i o d i c c r y s t a l p o t e n t i a l . E l e c t r o n s moving under the combined p o t e n t i a l s are normally represented as Bloch wave packets c o n s t r u c t -ed from the eigenstates o f the Hamiltonian f o r the unperturbed c r y s t a l , and can be t r e a t e d s e m i c l a s s i c a l l y as f r e e p a r t i c l e s a f f e c t e d only by the e x t e r n a l p o t e n t i a l V but responding according t o e f f e c t i v e dynamical laws. Considered c l a s s i c a l l y , , the e l e c t r o n then has, at any i n s t a n t , a band index n, a . c r y s t a l momentum k, and a p o s i t i o n r . The e f f e c t i v e dynamics represents, a quantum treatment of the c r y s t a l p o t e n t i a l and a c l a s s i c a l treatment of t h e ' e x t e r n a l p o t e n t i a l . With a f u l l quantum mechanical t r e a t -ment there e x i s t s the p o s s i b i l i t y of a change i n band index n by i n t e r -band t u n n e l i n g . WKB methods [47] or ord i n a r y time-dependent p e r t u r b a t i o n theory may be used t o i n c l u d e the s l o w l y v a r y i n g e x t e r n a l p o t e n t i a l i n the quantum mechanical c a l c u l a t i o n and a r r i v e at a t u n n e l i n g p r o b a b i l i t y . The Fredkin-Wannier model f o r inter b a n d t u n n e l i n g a p p l i e s s p e c i f i c -68 ally to Esaki diodes and considers the motion of Bloch electrons in an ex-ternal potential that changes over a short distance from one constant value to another. In such a model the tunneling probability for an electron colliding with the junction barrier is essentially defined in terms of the formalism of scattering theory and is expressed as a cross-section for scattering across to the other side. Since we require the volume rate of generation of electron-hole pairs in a high field region that extends over a considerable distance, the theoretical results based on the older field emission model will be easier to apply. Here the external potential is taken to be V(x) = -Fx, representing a constant field F = q£. Quasi-class-ically, under the influence of the constant electric field, the electrons cycle through the Brillouin zone at a constant rate k = F/h, with a period T = hK/F where K is the width of the Brillouin zone. The rate of leakage into the adjacent band is greatest when the k vector is at the band edge. The volume rate of generation due to Zener field emission is obtained by calculating a transition probability per unit time which is then inte-grated over the Brillouin zone. In indirect band gap materials, such as silicon, the tunneling cal-culations are complicated by the requirement for phonon cooperation. Tun-neling across an indirect energy gap involves a change in electron momentum perpendicular to.the tunneling direction. Since there is no force per-pendicular to the tunneling direction, this may only occur by the emission or absorption of a phonon. The values of the fundamental phonon energies in silicon that would conserve momentum in a tunneling transition are the phonon energies that occur at the same position in the Brillouin Zone as the conduction band minimum, and are [48]: 69 the transverse acoustic (TA) at 17.9 meV the longitudinal acoustic (LA) at U3.7 meV the longitudinal optic (LO) at 53.2 meV the transverse optic (TO) at 58.5 nieV The functional dependence of the phonon assisted tunneling probability vith electric field is very similar to the result for direct tunneling. The main difference is an additional prefactor for the probability of phonon scattering that may reduce the overall tunneling probability by as much as three orders of magnitude at any given field. Indirect phonon assisted tunneling has been considered by Kane [49] [50] using the constant electric field model. After summing the transition probability per unit time over a l l possible i n i t i a l and final states, the resulting expression for the volume rate of generation of electron-hole pairs applicable at large reverse bias, is g t = A^- E[M(Ep)]2{(u + l)exp[^ (Eg+ E p) 3 /2] + u expH^ (E - E )%]} (3.53) c g p where A is a constant and M(Ep) is the matrix element for phonon scattering. Bdepends on the reduced effective mass for tunneling and on the shape of the potential barrier in the forbidden gap. Kane assumes a triangular po-tential barrier, for which B - (3.54) E p is the phonon energy and u is the phonon occupation, given by U = exP(E1/kT) - 1 ( 3' 5 5 ) P TO The summation should extend over the four fundamental phonon energies mentioned earlier, as well as over the phonon energies involved in any multiple phonon scattering events. In s i l i c o n , however, i t has been established experimentally [51] [52] that the transverse acoustic and trans-verse optic phonons at 17-9 nieV and 58.5 nieV respectively, are the dominant scattering agents.for indirect tunneling. We w i l l make the further approx-imation that the matrix elements for phonon scattering are equal for these two phonons. In an actual diode or MOS gate the f i e l d c is not- constant but is a function of position x in the depletion region. The rate of tunneling generation per unit area therefore becomes w r G t g t(x) dx 0 AM' 2 ^ £(x) / 2 X {(u + l ) e x p [ ^ ( E + E ) / 2] TA,TO t U ; S P E g 0 + u exp[?7-x(E - E ) 3 / 2]} dx (3.56) ^ l t(x) g p J In practice the values of AM2 and B must be determined experimentally. Fairly reliable estimates for these values were obtained by f i t t i n g Haitz's [36] dark count rate data to ( 3 . 5 6 ) . The following formulas and numerical values were used in the calculations: w^  (width constant for Haitz's step junction) -6 -h = 0.23 x 10 mV 2 T (substrate temperature) = 196 K u (phonon occupation, at 196 K) = 0.52 for TA phonon at 1T-9 meV =0.03 for TO phonon at 58.5 meV E_ (band gap, at 196 K) = l . l U ev 7 1 £(x) = 2/w. [w_(V + V.)h - x] 1 1 a 1 where (V + V.) = applied voltage plus built-in voltage a l 2 The values of AM and B for best f i t (at large excess biases, where the avalanche initiation probability is close to one) are: AM2 = . 5.1 x 10 1 8 eV ^ V^secf 1 B = 1 . 8 9 x 109 eV _ 3 / / 2 V m"1 By using (3.54) for B the reduced effective mass for tunneling becomes * m = 0.077 m , which is in reasonable agreement with what, one would expect r o for tunneling from the light mass valence band in the light mass direction of the conduction band. With the above values for AM and B, ( 3 . 5 6 ) may be used to predict the generation rate due to interband tunneling for different substrate doping levels. Figure 3.15 shows the calculated generation rate of electron hole pairs versus peak electric field, for MOS gates operating above breakdown at a temperature of 100 K. The calculated generation rate versus surface potential is shown in Fig. 3 . l 6 . The corresponding band diagram is that shown in Fig. 3 . 2 . Although the generation rates shown are based on Haitz's data, they have been extrapolated to values eight orders of magnitude lower than the minimum generation rate he measured. Assuming the theoretical ex-pression used for. the extrapolation (Eq. 3.56) is accurate, the estimated error bars for Haitz's data lead to an error after extrapolation of approx-imately plus or minus one order of magnitude for the lowest generation rates indicated in Figures 3.15 and 3.l6. It is apparent from the results shown in Fig. 3 - 1 5 that the peak electric field at the Si-Si02 interface should 7 — 1 be kept below approximately U . 3 x 10 Vm in order to ensure a dark genera-- 1 - 2 tion rate less than 500 sec cm . 15 - 3 A substrate doping level below approximately 8 x 10 cm is required 10" 10-10" 10" 10' 10 o z < a 10 ce ui -1 10 .-2 O o X Pe(W) 0.98 0.90 0.50 0 N A = 2x10 1 6 cm"3 = 31.3 V NA = 1x1016 cm"3 Vb =' 50.8 V N A = 5x10 1 5 cm' 3 V b = 83.8 V 3.5 4.0 MAXIMUM FfELD 4.5 £max t105 V cm"1) 5.0 FIGURE 3.15 Interband tunnelling generation rate versus the peak electric field in n+p step junctions or p-substrate MOS gates, with different levels of substrate doping, T = 100K. ' The avalanche initiation probability P (W) is also indicated. 73 FIGURE 3.16 The interband tunnelling generation rate in MOS structures, plotted as a function of the silicon surface potential <j>s, T = 100K. rt to maintain the peak electric field below this value and yet s t i l l enable operation in the plateau region of the avalanche initiation probability (above P e( w) = 0 . 9 ) . From Fig. 3 . l 6 i t can be seen that the operating sur-face potentials for such an MOS gate l i e in the range 6 0 - 7 5 v. The actual gate operating voltages will of course be substantially higher than this due to the potential drop across the SiO^ layer. The interband tunneling discussed above is not the only tunneling dark current mechanism. As was pointed out in section 3 . 2 .k, electrons may also tunnel from the valence to conduction band via mid gap states. Price [53] has derived an effective first order matrix element.for the conventional field-emission process involving tunneling from defect or impurity levels within the band gap to the conduction band. The resulting probability per unit time that an electron, bound to a trap, is field ionized is found to have the same general form as that for interband tunneling transitions ex-cept that the energy gap is replaced.by the ionization energy of the impurity, namely the height of the barrier through which the electron must tunnel (i.e., E c - E,j). Using Price's matrix element for tunneling, Sah [54] de-termines the transition probability per unit time to be ent * \ ( E ^ ) 4 ( V V A V 3 / 2 } ( 3 ' 5 7 ) where A^ is a constant and M^  is the matrix element for tunneling from trap states. AE^ is the barrier lowering for coulomb attractive centers (equal to the Poole-Frenkel barrier lowering) and C^, is an effective field given by E T = 6 rE- AE_ T T ET (3.58) The tunneling emission rate from coulomb attractive centers is designated "by e*t. For neutral centers E^ = 0 and = £, and the designation is e° 75 By analogy w i t h the case of inte r b a n d t u n n e l i n g the e f f e c t i v e mass i n B may c be regarded as a reduced e f f e c t i v e mass f o r t u n n e l i n g , the dominant compon-ent o f which w i l l be the. e l e c t r o n mass i n the conduction band. For t u n n e l i n g from the valence band i n t o an empty t r a p or i n t e r f a c e s t a t e , a s i m i l a r expression t o (3.57) i s expected, except that the height o f the energy b a r r i e r , through which the e l e c t r o n t u n n e l s , i s now the d i f f e r - . , ence between the band gap and the i o n i z a t i o n energy of the i m p u r i t y l e v e l ( i . e . , E - E + E m = E_ - E ). The dominant component t o the e f f e c t i v e g c T T v mass i n t h i s case i s the hole mass i n the valence band. Thus, 2 ] (3.59) JT "V' " ~T The t r a n s i t i o n r a t e s f o r coulomb a t t r a c t i v e ( t o holes) and n e u t r a l centers are designated by e and e° r e s p e c t i v e l y . TP The only experimental work on t u n n e l i n g i n t o and out of deep l e v e l s has been d i r e c t e d . a t e x p l a i n i n g the excess current i n forward b i a s e d E s a k i diodes. Sah [54] has made a d e t a i l e d study o f the i m p u r i t y induced excess current i n gold doped s i l i c o n E s a k i j u n c t i o n s . The observed excess current was c o r r e l a t e d q u a n t i t a t i v e l y w i t h various two-step combinations o f Shock-ley-Read-Hall and t u n n e l i n g t r a n s i t i o n s u s i n g the t h e o r e t i c a l t u n n e l i n g rate 2 c a l c u l a t i o n due t o P r i c e . The estimated value o f A^M^ f o r the t u n n e l i n g t r a n s i t i o n s valence band t o t r a p t o conduction band (mechanisms 2 i n F i g . 3.1*0 obtained from Sah's data i s given i n t a b l e 3.1. Sah only r e p o r t s experimental data f o r one value o f f i e l d , t h e r e f o r e , no experimental value f o r B can be obtained from h i s r e s u l t s . The value o f B used by Sah was c a l c u l a t e d according t o (3-5*0 u s i n g the t r a n s v e r s e e l e c t r o n and l i g h t hole e f f e c t i v e masses. These masses and the.corresponding values f o r B are l i s t e d i n t a b l e 3.1. Chynoweth et a l . [55] have measured the f i e l d depend-ence of excess current i n s i l i c o n E s a k i diodes by v a r y i n g the n dopant con-76 centration. Their estimate of the effective mass to he used in (3.5*0. is 2 listed in table 3.1 along with the value for A^ M^ , required to obtain agree-ment with Sah's data. The steady state dark generation rate per unit area due to tunneling through deep bulk levels is ^Bt w g^Cx) dx (3.60) where g^,(x) for donor levels is Bt + , s e p t ( x ) e n t U ) N T n , n e p t U ) + e n t U ) and for acceptor levels is e L U ) e° (x) , T ( l> = -Pt' » T O M ) TABLE 3.1 Experimental values for the-effective mass and matrix element for tunneling through trap states. A ^ (eVrnV "''sec ^ ) */ */ m /m m /m c o v o B b c (Vm Bv* Sah 2.7 x 10 3 0.19 0.16 2.98 X 9 9 10* 2.73 x KT Chynoweth 6.5 x 10 3 a 0.3 3.7-+ x 10 9 * Value required to f i t Sah's data using 0.3 for m /mQ Calculated according to Eq. (3.5*0 77 The generation r a t e i s highest f o r those l e v e l s f o r which the t r a n s i -t i o n p r o b a b i l i t i e s e , and e ^ are equal. At f i e l d s trengths where the Poole-Frenkel b a r r i e r lowering i s s m a l l , these l e v e l s w i l l l i e c l o s e t o mid band. The d e n s i t y o f such deep l e v e l t r a ps w i l l depend on the q u a l i t y of the s t a r t i n g s i l i c o n wafer and on the bulk g e t t e r i n g steps i n c l u d e d i n the processing. T y p i c a l deep l e v e l i m p u r i t y / d e f e c t d e n s i t i e s a f t e r CCD pro-10 12 - 3 c e s s i n g l i e i n the range 10 - 10 cm . Figure 3 . 1 7 shows the c a l c u l a t e d 10 - 3 generation r a t e f o r = 10 cm versus peak e l e c t r i c f i e l d i n MOS gates w i t h d i f f e r e n t s u b s t r a t e doping l e v e l s . The generation r a t e per u n i t area was c a l c u l a t e d from ( 3 . 6 0 ) using the data i n Table 3 . 1 . The e x t r a p o l a t e d generation r a t e s are very u n c e r t a i n f o r these f i e l d s t r e n g t h s , as i n d i c a t e d by the l a r g e d i f f e r e n c e i n the r a t e s p r e d i c t e d from Sah's data and those p r e d i c t e d u s i n g the e f f e c t i v e mass estimate of Chynoweth et a l . I t i s apparent, however, t h a t t u n n e l i n g through deep traps w i l l be one of the dominant t r i g -g e r ing mechanisms i n the dark. P r e c i s e l y how important t h i s mechanism turns out to be w i l l depend very much on the d e n s i t y and energy l e v e l o f the deep im p u r i t y / d e f e c t centers present i n the high f i e l d r e g ion near the i n t e r -face and on the c o r r e c t value f o r t h e ' t u n n e l i n g e f f e c t i v e mass. 3 . 2 . 6 Dark Generation of T r i g g e r i n g C a r r i e r s i n the Non-Steady State So f a r only steady s t a t e dark generation mechanisms have been c o n s i d -ered. Immediately f o l l o w i n g the l a r g e d e p l e t i n g pulse above breakdown, how-ever, there i s a t r a n s i e n t during which the i n t e r f a c e s t a t e s and bulk t r a p s are r e l a x i n g t o t h e i r new steady s t a t e occupancy. During t h i s t r a n s i e n t there i s an enhanced emission of e i t h e r e l e c t r o n s or holes depending on the previous occupancy of the t r a p s , p r i o r to the d e p l e t i n g p u l s e . There i s a l s o a t r a n s i e n t f o l l o w i n g each avalanche discharge. During the discharge the occupancy of the bulk traps and i n t e r f a c e s t a t e s may be a l t e r e d by e i t h e r 78 3.5 4.0 4.5 MAXIMUM FIELD £ m n t f ( 1 0 5Vcm 1) FIGURE 3.17 Tunnelling generation rate through traps as. a function of the peak e l e c t r i c f i e l d i n n +p step junctions or p-substrate MOS gates, T = 100K. The results are extrapolated from the data given by Sah {54] and Chynoweth e t . a l . [55]. 79 direct capture of the mobile electrons and holes created by the avalanche, or by impact ionization. For short reset times, complete relaxation of the trap occupancy following an avalanche discharge may not be possible before the next pulse above breakdown occurs. Consider first the emission of holes from interface states. This is shown in Fig. 3.l8 for two different reset conditions corresponding to surface accumulation and surface inversion. When the surface is in accumu- • lation during reset the interface states empty down to the Fermi level by capturing holes. After the application of the depleting pulse above break-down, the density of both electrons and holes is very low at the interface. Electron capture i s , therefore, negligible and holes are emitted very rapid-ly as the levels nearest the valence band f i l l with electrons. These holes have avalanche initiation probability P. (0) and are immediately swept out h through the depletion layer. Unless i - s extremely small, an avalanche will be triggered within a very short time after the application of the de-pleting pulse. In order to achieve a low dark count rate, the silicon surface must be inverted during reset. In this case the interface states f i l l up to the Fermi level by capturing electrons from the inversion layer. In strong inversion this occurs very rapidly due to the high surface concen-tration of electrons, and hence the occupancy of the levels immediately prior to the pulse above breakdown will be insensitive to any previous aval-anche discharges. After the depleting pulse the inversion layer s t i l l re-mains.. Electron capture and emission, therefore, continue to determine the occupancy f^, forcing a l l the interface states below to be fu l l of elec-trons. The tunneling distance for hole emission i s , thus, large, and at low temperatures hole emission will be a very rare event. From the above discussion i t is apparent that a PC-CCD will require a 80 FIGURE 3.18 Energy band diagram for a p-substrate MOS gate illustrating the generation of triggering carriers at the interface, immediately following a depleting pulse. ( a ) pulsed from accumulation during reset (b) pulsed from inversion during reset. 81 circulating background charge or "fat zero" in order to suppress the dark generation of triggering carriers from interface states. In practice, however, the effectiveness of a circulating background charge may be limited by edge effects. At the boundaries of the breakdown area there is a transi-tion region where the surface is not in inversion before or after the de-pleting pulse. The dark generation from interface states in this region will be dominated by the steady state emission of electrons and holes, which may become significant at the high surface fields encountered above break-down. In addition, hot electrons incident on the interface during an aval-anche discharge may impact ionize some of the interface states resulting in an increased hole emission rate during the transient following the discharge. The non-steady state behaviour of the bulk trapping centers is more complex. Figure 3.19 shows the band diagrams for a typical PC-CCD gate during reset and after the depleting pulse above breakdown. After the de-pleting pulse, and in the absence of an avalanche discharge, the centers may only change their, charge state by the emission of electrons or holes. In this case the rate of change of trapped charge can be expressed as H T ~ f T ( x , t ) = e*(x) N T - [e*(x) + e*(x)] N Tf T(x,t) ( 3 . 6 3 ) * * where e n and e^ are defined by equations (3.^ 9) to (3.52). The return to equilibrium is, therefore, exponential with a time constant T ( X ) = *f * -1 [e (x) + e (x)] . The solution for f_(x,t) may be expressed as n p T f T(x,t) _ y X t w ) _ [ f T ( X j 0 o ) _ f T ( x > 0 ) ] exp -t/t(x) ( 3 . 6 4 ) where fT(x,») ±B the steady state occupancy given by ejx) T ' ' * * — en(x) + ep(x) 82 region 1 | region 2 FIGURE 3.19 Energy band diagram for. a p - s u b s t r a t e MOS gate i l l u s t r a t i n g the e m i s s i o n o f t r i g g e r i n g c a r r i e r s f rom deep b u l k t r a p s , immediate ly f o l l o w i n g a d e p l e t i n g p u l s e . The c o n d i t i o n d u r i n g r e s e t i s a l s o i n d i c a t e d . Region 1 remains i n d e p l e t i o n at a l l t imes (except f o r a r e g i o n v e r y near the i n t e r f a c e which may be i n v e r t e d ) . Region 2 a l t e r n a t e s between the e q u i l i b r i u m n e u t r a l c o n d i t i o n and d e p l e t i o n . 83 and f^(x,0) is the in i t i a l trap occupancy at the instant the gate is pulsed. At time t after the depleting pulse above breakdown, the mean dark event rate due to bulk traps (i.e., the probability per unit time that an avalanche discharge will be triggered) is R(t), = ANT | e*(x) f T(x,t) Pe(x) + e*(x)[l - f^x.t") ]Ph(x) dx (3.65) where P (x) and P, (x) are the electron and hole avalanche initiation prob-e h abilities, and A is the area. The difference between the i n i t i a l rate at t=0 and the rate that would be obtained with the steady state trap occupan-cy, fT(x,°°), is R(~) - R(0) = ANT [f T(x,») - f T(x,0)] w # • • # •[e (x)P (x) - e (x)P,(x)] dx (3.66) n e p h Equation (3-66) shows that a disturbance of the trap occupancy can cause either an increase or decrease in the breakdown rate, depending on the sign of the integrand. In order to interpret this result physically, the integral is divided into two parts. The first part is over those re-gions that remain in depletion during reset (region 1 in Fig. 3.19) and the second part of the integral is over those regions that alternate between de-pletion and the equilibrium neutral condition (region 2 in Fig. 3-19). Dur-ing reset the traps within-region 2 empty down to the equilibrium fermi level by capturing holes. This occurs very rapidly due to the high hole concentration in the p-type neutral bulk. Therefore, the trap occupancy in this region prior to each depleting pulse will be independent of any changes that may have occured during previous cycles. Following the depleting pulse, electrons and holes are emitted alternately. Initially holes are emitted at a higher rate than electrons (f^ (x,°°) > f^,(x,0)) as the trap 81* occupancy adjusts t o the new steady s t a t e i n d e p l e t i o n . In g e n e r a l , t h i s i ncreased hole emission w i l l r e s u l t i n a re d u c t i o n o f the breakdown r a t e since ^ ( x ) i s much smaller than P (x) i n region 2 (see F i g . 3-7). Only i f the traps are clo s e t o the valence band but above the e q u i l i b r i u m Fermi * * l e v e l d u r i ng r e s e t ( i . e . , f o r which e p(x)>>e n(x) and f ^ ( x , 0 ) - 0 ) , can the breakdown r a t e be increased. Except during periods of avalanche d i s c h a r g e , r e g i o n 1 remains depleted at a l l times. I t i s only during the t r a n s i e n t f o l l o w i n g each avalanche, t h e r e f o r e , t h a t the steady s t a t e occupancy i s d i s t u r b e d . Under avalanche breakdown c o n d i t i o n s , f r e e c a r r i e r concentrations o f the order of 10"^^cm 3 to l O ^ c m 3 are reached. Consequently, e l e c t r o n and hole cap-t u r e by traps becomes po s s i b l e , o r , s i m i l a r l y , the hot e l e c t r o n s and holes may impact i o n i z e the t r a p s . In e i t h e r case an exponential t r a n s i t i o n be-tween the i n i t i a l and f i n a l s t a t e s would be expected, which may be des-c r i b e d by an equation of the same form as (3.61*). i f the avalanche were to continue f o r time t ^ then the f r a c t i o n of centers i n the more negative s t a t e , upon t e r m i n a t i o n o f the avalanche, would be f A T ( x , t A ) = f A T(x,») - [f A T(x,») - f j ( x ) ] e x p - t A / x A ( x ) (3.67) where: f A (x,°°) = l i m i t i n g t r a p occupancy during an extended avalanche. f^,(x) = occupancy o f the traps immediately p r i o r t o the avalanche. T A ( X ) = time constant f o r the t r a n s i e n t . For the case t h a t the avalanche discharges are w e l l separated i n t i m e , the i n i t i a l occupancy i s equal t o the steady s t a t e occupancy i n d e p l e t i o n ( i . e . , f * ( x ) = f T(x,»)). Fol l o w i n g a discharge, the t r a p r e l a x a t i o n i n region 1 i s given by 85 " f T ( x , t ) = fT(x,«) - [fT(x,») - f A T ( x , t A ) ] e x p - t / x ( x ) (3.68) where t=0 i s now taken t o be the t e r m i n a t i o n o f the a v a l a n c h e . Making t h i s t ime t r a n s f o r m a t i o n i n (3.66) and u s i n g ( 3 . 6 8 ) g i v e s R^oo) - •R 1 ( t s ) = A N T [fT(x,») - f A T ( x , t A ) ] e x p - t s / x ( x ) w 1 - [ e * ( x ) P (x) - e * ( x ) P j x ) ] dx (3.69) n e p h where t i s the t i m e from the t e r m i n a t i o n o f t h e avalanche t o t h e next s p u l s e above breakdown (the i n t e g r a t i o n here i s over r e g i o n 1 o n l y ) . As b e f o r e , t h e r e can be e i t h e r an i n c r e a s e or decrease i n the breakdown r a t e , however, the magnitude o f t h e change now decays e x p o n e n t i a l l y w i t h i n -c r e a s i n g r e s e t d u r a t i o n . The f i e l d d i s t r i b u t i o n - , the v a r i a t i o n o f the i o n i z a t i o n c o e f f i c i e n t s a (x) and <x,(x), and the d i s t r i b u t i o n o f f r e e c a r r i e r s w i t h i n t h e space e h charge l a y e r d u r i n g breakdown are shown s c h e m a t i c a l l y i n F i g u r e s 3.20 ( a ) -( c ) . The boundary between r e g i o n s 1 and 2 i s a l s o i n d i c a t e d . I f charge t r a p p i n g i s t h e dominant process d u r i n g breakdown t h e n from F i g . 3.20 (c) i t can be seen t h a t , subsequent t o the d i s c h a r g e , t h e r e w i l l be an i n c r e a s e i n the e m i s s i o n o f e l e c t r o n s from t r a p s l o c a t e d near t h e S i - S i O ^ i n t e r f a c e , and an i n c r e a s e d h o l e e m i s s i o n r a t e f o r the remainder o f t h e t r a p s ' i n r e g i o n 1. T h i s i s shown s c h e m a t i c a l l y i n F i g . 3.21 ( b ) . F i g u r e 3.21(a) i n d i c a t e s the # v a r i a t i o n o f P (x) and P, (x) f o r r e f e r e n c e . F o r deep t r a p s (e (x) ~ e ( x ) ) e n n p the o v e r a l l e f f e c t o f the i n c r e a s e d e l e c t r o n o r h o l e e m i s s i o n shown i n F i g . 3.21(b) i s a s l i g h t r e d u c t i o n i n the t r i g g e r i n g r a t e R ( t ) . I f any charge i s t r a p p e d by s h a l l o w l e v e l s d u r i n g the avalanche d i s c h a r g e , the subsequent t r i g g e r i n g r a t e may be i n c r e a s e d . The s h a l l o w e s t l e v e l s , however, w i l l r e -l a x t o t h e i r s teady s t a t e occupancy b e f o r e the next p u l s e above breakdown occurs ( i . e . , ( e + e ) " ^ < t ) . n p s 86 FIGURE 3.20 Model for the depletion region of a p-substrate MOS gate during breakdown, (a) is the field distribution, (b) is the variation of the elec-tron and hole ionization coefficients and (c) is the density of hot electrons and holes. S i O 87 (a) t r i g g e r i n g p r o b a b i l i t y as a f u n c t i o n o f p o s i t i o n i n |the d e p l e t i o n r e g i o n . (bj c a r r i e r capture dominant d u r i n g breakdown. impact i o n i z a t i o n domin-ant d u r i n g breakdown. g i o n 2 FIGURE 3 . 2 1 The i n c r e a s e d e m i s s i o n o f e l e c t r o n s and h o l e s by b u l k t r a w subsequent t o an avalanche d i s c h a r g e . 7 P 88 The change i n occupancy that occurs i f impact i o n i z a t i o n of the traps i s dominant during breakdown i s more d i f f i c u l t to determine. In t h i s case there are two competing processes: l ) hot electrons or holes can knock o f f electrons from the traps, leading to a p o s i t i v e charge change or 2) hot c a r r i e r s can knock.off a hole, leading to a negative charge change. Figure 3.21(c) i l l u s t r a t e s th worst possible s i t u a t i o n following breakdown i . e . , f o r the case that the traps are charged i n the opposite sense to the free c a r r i e r density during the avalanche. As before, the only l e v e l s that w i l l -be a c t i v e l y emitting c a r r i e r s at the beginning of the next cycle are those # # _3_ for which (e + e ) > t . • n p s I t i s c l e a r that the o v e r a l l e f f e c t of an avalanche discharge w i l l depend very much on the r e l a t i v e sizes (as a function o f p o s i t i o n i n the depletion region) of the four' impact i o n i z a t i o n cross-sections, and two capture cross-sections, and on the d i s t r i b u t i o n of the hot c a r r i e r s during breakdown. The magnitude of the e f f e c t w i l l also depend on the duration of the avalanche, or more p r e c i s e l y , on the amount of charge t r a n s i t i n g the de-p l e t i o n region during an avalanche discharge. Without t h i s d e t a i l e d i n -formation a l l that can be s a i d i s . t h a t the r e s u l t i n g change i n occupancy i s not expected to lead to a large decrease i n the t r i g g e r i n g rate at the s t a r t of the next pulse. How large the increase w i l l be, i f any, w i l l depend on the reset duration, Haitz [36], by varying the shunt capacitance i n the high impedance re -set c i r c u i t of h i s small area n +p guard r i n g diodes, has measured the dark count rate as a function of the t o t a l charge crossing the junction during an avalanche. I n i t i a l l y the. count rate increased l i n e a r l y with i n c r e a s i n g shunt capacitance, however, some saturation of the count rate was evident for the highest charge l e v e l s reported, i n d i c a t i n g that the trap occupancy had approached the steady s t a t e v a l u e d u r i n g ava lanche . By e x t r a p o l a t i n g the l i n e a r count r a t e versus shunt c a p a c i t a n c e r e l a t i o n t o zero c a p a c i t a n c e , H a i t z was ab le t o determine the steady s t a t e dark g e n e r a t i o n r a t e f o r h i s d i o d e s . The maximum count r a t e s measured were a f a c t o r o f 20 l a r g e r than 1 5 - 2 t h i s and corresponded t o a charge o f 1 x 10 c a r r i e r s cm c r o s s i n g the j u n c t i o n d u r i n g the avalanche d i s c h a r g e s . Th is r e s u l t i s encouraging i n v iew o f t h e f a c t t h a t the s i z e o f the d i s c h a r g e p u l s e f o r an MOS gate i s t y p i c a l l y t h r e e orders o f magnitude lower than t h i s . 3.3 PREVENTION OF PREMATURE EDGE BREAKDOWN AND LOCALIZED MICROPLASMA BREAKDOWN Goetzberger and N i c o l l i a n [56] have s t u d i e d the. edge breakdown e f f e c t f o r s i l i c o n d i o x i d e / s i l i c o n MOS g a t e s . p u l s e d i n t o deep d e p l e t i o n . Wi th an ox ide t h i c k n e s s o f 1000S they found t h a t edge breakdown was un important f o r l6 -3 s u b s t r a t e dop ing l e v e l s g r e a t e r t h a n approx imate ly 5 x 10 cm" . Below t h i s doping l e v e l the e l e c t r i c f i e l d a t the o x i d e - s i l i c o n i n t e r f a c e i s enhanced at the edges o f the meta l gate c a u s i n g a r e d u c t i o n i n t h e breakdown v o l t a g e . F i g u r e 3 -22 i l l u s t r a t e s t h i s e f f e c t and shows the d i f f e r e n c e between h i g h and low semiconductor dop ing . A c c o r d i n g t o t h i s exp lanat ion ' . the edge b r e a k -down e f f e c t shou ld depend on the r a t i o o f d e p l e t i o n l a y e r w i d t h t o ox ide t h i c k n e s s . Rusu and Bu lucea [57] have made computer -a ided c a l c u l a t i o n s o f the breakdown v o l t a g e o f deeply d e p l e t e d MOS c a p a c i t o r s u s i n g the i o n i z a -t i o n i n t e g r a l method. The p o t e n t i a l s were c a l c u l a t e d from the t w o - d i m e n -s i o n a l P o i s s o n e q u a t i o n u s i n g f i n i t e d i f f e r e n c e s and s u c c e s s i v e o v e r - r e l a x -a t i o n . L e e ' s room temperature i o n i z a t i o n r a t e d a t a (Appendix A) and the : : . constant K approx imat ion (a, = ka ) were used t o c a l c u l a t e t h e i o n i z a t i o n h e i n t e g r a l . In a d d i t i o n t o u s e f u l d e s i g n p l o t s o f breakdown v o l t a g e versus 90 field plate o x i d e \ — — \ ^ — (a) High doping density, narrow depletion region, uniform fields. .-*. . ' ,•• . * • - . • • ' o x i d e \ (b) Low doping density, wide depletion region, high ;fringing field. FIGURE 3.22 Cross section of MOS capacitor showing equipotential lines in the space charge region at the-edge of the field plate. Edge breakdown occurs in (b) due to the high fringing field. \\j N 1 S,_N2_J SiO. Si \ -S i 3 N 4 (€2) ? Si (a) change of semiconductor doping, (b) V N2 composite dielectric, e l < e 2 insulator (Al 2 0 3 ) 7 Si Si (C) change of oxide thickness (d) separate guard ring field plate. FIGURE 3.23 Four different MOS structures to avoid premature avalanche breakdown at the outer edge of the field plate in high resistivity samples. 91 oxide thickness and substrate doping, Rusu and Bulucea obtain a universal c r i t e r i o n for f i e l d uniformity i n terms of the r a t i o of oxide thickness to the maximum (breakdown) width of the s i l i c o n depletion region. According to their.calculations t h i s r a t i o should be larger than 0.3 i n order not to have f i e l d concentration around the edges of the metal plate. I t was established i n section 3.2.5 that the substrate doping of a 15 -3 PC-CCD should be less than approximately 8 X 10 cm i n order to avoid interband tunneling. On such l i g h t l y doped substrates the oxide thickness required to s a t i s f y the above c r i t e r i o n for f i e l d uniformity becomes rather large, and i t may prove better to use some sort of guard r i n g i n order to prevent edge breakdown. Some of the ;possible guard r i n g structures that can be used on MOS devices are shown i n Fig. 3.23 [56]. In each case the action of the guard r i n g i s to cause a more gradual t r a n s i t i o n from the deeply depleted breakdown region to the undepleted (or s l i g h t l y depleted) surround-ing area, thereby, eliminating the high f r i n g i n g f i e l d s . In a PC-CCD, a l l but structure (a) i n Fig. 3.23 can be used both to define the transfer chan-nels and to prevent edge, breakdown. High f r i n g i n g f i e l d s i n the charge transfer d i r e c t i o n are avoided by.adjusting the po t e n t i a l b a r r i e r s between pixels to be only s l i g h t l y below breakdown (see Fig. 3.H). •In addition to premature edge breakdown, i t i s also possible for there to be l o c a l preferred sit e s for breakdown (so-called microplasmas) due to the presence of c r y s t a l defects. These c r y s t a l imperfections may cause a reduction i n the threshold energy required for i o n i z a t i o n [58], or they may become decorated with impurities leading to a l o c a l enhancement of the e l e c t r i c f i e l d [59] [60]. Consequently, the breakdown voltage i n the v i c i n -i t y of c r y s t a l defects i s lower than i n the surrounding area. In the early work on avalanche diodes such microplasmas were found to dominate the break-down ch a r a c t e r i s t i c s , and they have been the subject of many investigations. 92 Subsequent progress i n c r y s t a l growing and device f a b r i c a t i o n technology, however, has l e d t o the r o u t i n e f a b r i c a t i o n o f microplasma-free j u n c t i o n s t h a t breakdown uniform l y over the e n t i r e j u n c t i o n area. The f a b r i c a t i o n of uniform breakdown MOS gates f r e e from microplasmas may be more d i f f i c u l t . I t i s w e l l known th a t high temperature thermal o x i -d a t i o n of d i s l o c a t i o n - f r e e s i l i c o n wafers f r e q u e n t l y r e s u l t s i n the formation of Frank-type s t a c k i n g f a u l t defects at the S i - S i O ^ i n t e r f a c e [61]. These d e f e c t s , e s p e c i a l l y i f they become decorated w i t h i m p u r i t i e s , g r e a t l y i n -crease the leakage currents i n MOS and CCD s t r u c t u r e s [62] [63] and may a l s o r e s u l t i n l o c a l i z e d breakdown. I t has been found t h a t the o r i g i n o f o x i d a -t i o n induced s t a c k i n g f a u l t s (OSF's) i s e i t h e r r e s i d u a l saw and l a p p i n g damage or grown-in micro defects formed during c r y s t a l growth. Chemically e t c h i n g the wafer before o x i d a t i o n e l i m i n a t e s any mechanical damage but the grown-in defects are more d i f f i c u l t t o e l i m i n a t e . A number of procedures have been proposed t o suppress these n u c l e a t i o n centers and to s h r i n k e x i s t -i n g s t a c k i n g f a u l t s . P r e o x i d a t i o n g e t t e r i n g i n v o l v i n g a phosphorous or s i l i c o n n i t r i d e d e p o s i t i o n on the back side of the wafer [64] [65] i s a w e l l -known technique f o r the suppression o f SF n u c l e i . I t has a l s o been found that adding s m a l l amounts of c h l o r i n e i n the form of HCl or C^HCl^ t o the o x i d a t i o n atmosphere can suppress and s h r i n k OSF's, and can e l i m i n a t e grown-i n defects [62] - [69]. More r e c e n t l y i t has been shown t h a t the n u c l e a t i o n of OSF's on the f r o n t side of the wafer can be g r e a t l y suppressed by the g e t t e r i n g a c t i o n of mechanical damage on the back [70] [71], or by the get-t e r i n g a c t i o n o f t h e r m a l l y induced microdefects i n the inner p a r t of oxygen r i c h C z o c h r a l s k i wafers ( s o - c a l l e d i n t r i n s i c g e t t e r i n g ) [72] [73]. By us i n g a combination o f the above techniques, p a r t i c u l a r l y HCl o x i - . dation and back-surface damage, l a r g e CCD arrays have been f a b r i c a t e d t h a t are f r e e from any dark current anomalies. The same techniques should, t h e r e -93 f o r e , make p o s s i b l e the f a b r i c a t i o n o f l a r g e m i c r o p l a s m a - f r e e PC-CCD's 3.4 OPTICAL COUPLING BETWEEN IMAGE ELEMENTS • L i g h t e m i s s i o n d u r i n g avalanche breakdown i s a w e l l - k n o w n phenomenon and poses an important problem i n the proposed PC-CCD imager . Even i f o n l y a few photons are e m i t t e d . d u r i n g the avalanche d i s c h a r g e o f an image e lement , these photons would have a h i g h p r o b a b i l i t y o f b e i n g r e - a b s o r b e d and t r i g -g e r i n g the breakdown o f adjacent p i x e l s . These p i x e l s would then a l s o emit photons , thereby s t a r t i n g a c h a i n r e a c t i o n . In o rder t o prevent such a c h a i n r e a c t i o n and reduce the o p t i c a l c o u p l i n g between p i x e l s t o a n i g l i g i b l e l e v e l , the number o f photons e m i t t e d per d i s c h a r g e , t imes the p r o b a b i l i t y t h a t they w i l l t r i g g e r another p i x e l , must be made ve ry much l e s s than one. Breakdown r a d i a t i o n was f i r s t repor ted , i n s i l i c o n j u n c t i o n s as f a r back as 1955 [74], however, the mechanism f o r t h i s r a d i a t i o n has not been d e f i n i t e l y e s t a b l i s h e d . E x i s t i n g e x p l a n a t i o n s i n c l u d e r a d i a t i v e (phonon-a s s i s t e d ) recombinat ion o f the f r e e e l e c t r o n s and ho les p resent d u r i n g the breakdown [75], and r a d i a t i v e i n t r a b a n d t r a n s i t i o n s o f the hot e l e c t r o n s and h o l e s [75] [76] i n c l u d i n g r a d i a t i o n from the b r e m s s t r a h l u n g o f hot c a r -r i e r s i n the coulomb f i e l d o f charged i m p u r i t y cente rs [77]. For a l l the semiconductor m a t e r i a l s s t u d i e d the spectrum i s ve ry b r o a d , e x t e n d i n g t o energ ies both c o n s i d e r a b l y g r e a t e r than and l e s s than t h e . e n e r g y gap. The spectrum f o r s i l i c o n i s shown i n F i g . 3.2U [75]. The t o t a l l i g h t output has been shown t o i n c r e a s e l i n e a r l y w i t h breakdown c u r r e n t , however, t h e r e a re ve ry few r e p o r t e d es t imates o f the e m i s s i o n e f f i c i e n c y . I n i t i a l e s t i -8 mates f o r s i l i c o n p l a c e the e f f i c i e n c y at 10 v i s i b l e photons f o r every e l e c t r o n c r o s s i n g the j u n c t i o n [75]. I t i s the n e a r - i n f r a r e d photons w i t h 2 - 1 a b s o r p t i o n c o e f f i c i e n t s l e s s than 10 cm , however, t h a t w i l l be r e s p o n s i b l e 95 for the majority of the photon coupling between pixels. As can be seen from Fig. 3.2k, the emission efficiency for these photons is several orders of magnitude higher. Photon energies less than the band gap energy are normally attributed to intraband transitions, although such photons could also result from the recombination of hot carriers through deep traps. The spectrum in Fig. 3.2k was obtained from junctions containing many microplasma light spots. Such microplasmas imply regions of crystal damage and i t is well known that deep levels are associated with such structural defects. It is possible, therefore, that defect-free junctions would have a smaller emission e f f i c i -ency for infrared photons. Unfortunately, there are no reports as to .? whether the spectral distribution of the uniform glow from perfect junctions is any different from that reported earlier on avalanche diodes with micro-plasmas. Haitz [78] has made a quantitative investigation of the photon coupling mechanism and has found that the pulse rate of a small area avalanche diode operating above breakdown (detector) is increased significantly by the re-verse breakdown of another diode (emitter) on the same silicon wafer. The induced pulse rate was found to increase linearly with the breakdown current of the emitter, and to decrease with the square of the distance between emitting and detecting diodes. The range of diode separations measured was 0.06 - 0.6 cm. A square dependence over such distances implies that the interaction between the diodes was due to infrared radiation with an absorp-tion coefficient in silicon of 1 cm ^  or less, corresponding to photon energies equal to or less than the band gap energy [ 7 9 ] . Such infrared pho-tons can generate carriers either by phonon-assisted transitions from the valence band to the conduction band, or by generation from deep traps. The square dependence on distance also indicates that the coupling radiation 96 propogated d i r e c t l y from the em i t t e r t o the d e t e c t o r , and t h a t t o t a l i n -t e r n a l r e f l e c t i o n s at the top and bottom o f the s i l i c o n s l i c e were n e g l i -g i b l e . From an a n a l y s i s o f h i s photon c o u p l i n g data, H a i t z estimated the e f f i c i e n c y o f c o u p l i n g l i g h t generation to be 2 x 10 ^ photons (with an energy equal to or l e s s than the band gap) per e l e c t r o n c r o s s i n g the j u n c t i o n . The s i z e of the avalanche discharge pulses i n a PC-CCD exceeds 10^ el e c t r o n s even f o r very small area p i x e l s (25 um) . I t i s , t h e r e f o r e , c l e a r t h a t some s o r t o f . o p t i c a l b a r r i e r between p i x e l s w i l l be r e q u i r e d i n order t o reduce the p r o b a b i l i t y of an emitted photon t r i g g e r i n g another discharge. How complete the o p t i c a l i s o l a t i o n needs t o be w i l l depend on the s i z e and center t o center spacing of the p i x e l s . I t w i l l a l s o depend on the charge per u n i t area c r o s s i n g the j u n c t i o n during an avalanche discharge and hence on the amount of overvoltage employed. Fu r t h e r s t u d i e s on photon c o u p l i n g w i l l have to be made before the r e q u i r e d degree of o p t i c -a l i s o l a t i o n can be determined. Figure 3 - 2 5 , i l l u s t r a t e s how complete o p t i c a l i s o l a t i o n might be achieved i n a l i n e a r array organized f o r p a r a l l e l t r a n s f e r i n t o a separate readout channel. The PC-CCD i s f a b r i c a t e d on a 110 c r y s t a l p l a n e , and an a n i s o t r o p i c etch [80] i s used to cut deep v e r t i c a l w a l l grooves between p i x e l s . The grooves are etched t o the r e q u i r e d depth e a r l y on i n the f a b r i -c a t i o n w h i l e the wafer i s s t i l l f u l l t h i c k n e s s . The groove w a l l s can then be given the same o x i d a t i o n and annealing steps as the gate oxide. The f i n a l step i n the f a b r i c a t i o n would be to f i l l i n the grooves w i t h an opaque m a t e r i a l . A groove width o f 3 t o k microns and a depth to width r a t i o of 5 should be achievable by t h i s method. An a l t e r n a t e s t r u c t u r e that may be f a b r i c a t e d on 100 s i l i c o n , uses deep V-grooves [81] a n i s o t r o p i c a l l y . e t c h e d between the p i x e l s , as shown i n F i g . 3 . 2 6 . As.an automatic r e s u l t of extending the gate across the V-grooves, 97 readout register clocks Q Q Q output transfer photogate optical barriers opaque filler Al photogate : XvvXsT • field oxide FIGURE 3.25 I l l u s t r a t i o n o f how deep a n i s o t r o p i c a l l y etched s l o t s may be used to o p t i c a l l y i s o l a t e the i n d i v i d u a l p i x e l s i n a l i n e a r PC-CCD a r r a y f a b r i c a t e d on (110) s i l i c o n . 98 readout register clocks 9 9 9 r L_ I 2 123 I •1 h 23 I 2 " E l 1 1 output _ l V - groove barriers-transfer gate photogate Al photogate gate ox ide — f wafer thinned to this line at end of FIGURE 3.26 I l l u s t r a t i o n o f hov a n i s o t r o p i c a l l y e tched v -g rooves might be used t o p r o v i d e the r e q u i r e d degree o f o p t i c a l i s o l a t i o n i n l i n e a r a r r a y s f a b r i c a t e d on (100) s i l i c o n . 99 potential barriers of small lateral dimension are generated at the apex of each groove [82]. These potential barriers serve to define individual pixels, however, the oxide must be thick enough to prevent field enhance-ment and localized breakdown near the groove apex. Complete optical iso-lation between pixels is not possible with this structure since a thickness of silicon equal to the depletion layer width must exist under the apex of the grooves. Optical isolation of the pixels in a two dimensional array is more difficult. With two orthoganal sets of V-grooves, however, i t may be possible to achieve the required degree of optical isolation and yet s t i l l enable charge transfer along the channels [82]. 100 4 EXPERIMENTAL INVESTIGATION OF MOS STRUCTURES PULSED ABOVE BREAKDOWN I t i s apparent from the d i s c u s s i o n i n chapter three t h a t an e x p e r i -mental study on the above-breakdown op e r a t i n g regime of MOS s t r u c t u r e s i s r e q u i r e d before.the development of a f u l l PC-CCD array i s attempted. In p a r t i c u l a r , i t must be determined i f the avalanche i n i t i a t i o n p r o b a b i l i t y saturates as expected,. and i f i t i s p o s s i b l e t o o b t a i n the very low dark count ra t e s t h a t are r e q u i r e d . Data i s a l s o r e q u i r e d on the degree of photon c o u p l i n g as a f u n c t i o n of the s i z e of discharge pulse and p i x e l sep-a r a t i o n . In order t o i n v e s t i g a t e these i s s u e s , s m a l l area d i s c r e t e MOS devices, s u i t a b l e f o r operation above breakdown and at low temperatures, have been f a b r i c a t e d and t e s t e d . The t e s t devices were f a b r i c a t e d on p-type substrates- and i l l u m i n a t e d from the back s i d e . The i n v e s t i g a t i o n was conducted i n two p a r t s . For the i n i t i a l i n -v e s t i g a t i o n three very simple device s t r u c t u r e s were adopted t h a t r e q u i r e d a minimum of high temperature processing. F a b r i c a t i o n problems were en-countered t h a t prevented the operation of two of the three t e s t s t r u c t u r e s , however, the r e s u l t s obtained w i t h the remaining s t r u c t u r e i n d i c a t e d t h a t dark•generation o c c u r i n g at the Si-SiO i n t e r f a c e would be a major problem i n surface channel PC-CCD's. In the second part of the i n v e s t i g a t i o n these detr i m e n t a l surface e f f e c t s were l a r g e l y e l i m i n a t e d by going to a b u r i e d channel device s t r u c t u r e that breaks down at a bulk n-p j u n c t i o n away from the i n t e r f a c e . In a f u l l PC-CCD array the added complexity of t h i s s t r u c t u r e i s a l s o j u s t i f i e d by the higher c l o c k i n g . r a t e s , and hence higher frame r a t e s , t h a t are p e r m i s s i b l e w i t h b u r i e d channel CCD's. 101 4.1 SURFACE BREAKDOWN DEVICES 4.1.1 Design Considerations Figure h.l shows the potential distribution perpendicular to the interface for a surface breakdown MOS gate, and defines the various poten-tials and distances that will be refered to in the text. With these structures the peak field in the depletion region occurs at the Si-SiO^ interface. It was established in section 3.2.5 that this peak field should be kept below approximately k.3 x 1 0 ^ Vcm ^ in order to avoid significant interband tunneling, and that a substrate doping less than ap-15 —3 proximately 8 x 10 cm is required i f uniformly doped substrates are used. In order to reduce the dark generation due to the tunneling emission from traps and interface states to an acceptable level, the peak field at the interface, and corresponding substrate doping, may have to be even lower. As the substrate doping is lowered, however, the operating voltages increase rapidly (see Fig. 3-l6) and the depletion layer widths become comparable to the lateral dimensions of the photogate, making i t difficult to achieve uni-1 5 - 3 form planar breakdowns. For this study a substrate doping of N A =7x l0 cm was adopted, for which the calculated depletion layer width at breakdown (at 100K) is approximately 3 -5 ym. The actual depletion layer widths will be somewhat wider, and the corresponding peak fields lower, than those calcu-lated on the basis of a uniformly doped substrate. This is because boron doped substrates acquire a more lightly doped.surface layer, after thermal oxidation due to the out diffusion of boron [83], resulting in a structure analogous to an n+irp diode. It is vital that the field in the oxide remain below the breakdown field strength for SiO^. The breakdown field for thermal oxides grown in an 02/HCl ambient ranges from 7 x 10 Vcm to 1 x 101Vcm" [84,85]. Prior to an avalanche discharge the field in the gate oxide is given by, 102 S 1 O 9 P - silicon potential FIGURE 4.1 Potential d i s t r i b u t i o n perpendicular to the interface for a surface-breakdown MOS gate, before and after breakdown, at breakdown, and during reset. 103 ox e. max e. 1 1 where £ = peak f i e l d i n the s i l i c o n (at the S i - S i 0 o interface) max 2 •Q = positive fixed oxide charge ss = charge i n the inversion layer during reset. Subsequent to an avalanche discharge the inversion layer charge i s increased and the f i e l d i n the oxide becomes, e ' (Q_ - Q ) A* • £ + Si. + _ s - (4.1) ox e. max e. d i l ox For the substrate doping chosen, the charge (Qj~Q s s) required for strong i n --7 -2 version i s approximately 10 coul cm , while the peak.field i n the s i l i c o n at the interface w i l l be close to k x 10^ Vcm \ Putting these values i n . (k.l) gives, r (• A<p £' = 1 . 6 x 10 + r 1 Vcm ox d ox For t h i s investigation, a gate oxide thickness of 0.2um was chosen so as to enable operation several tens of volts above breakdown and s t i l l remain s u f f i c i e n t l y below the oxide breakdown f i e l d that leakage currents are min-imal [86,87]. In addition, with a gate oxide of t h i s thickness, the test devices w i l l not be destroyed i f they are inadvertently exposed to room l i g h t while deeply depleted. Further, there i s evidence that the SiO^ de-fect density at high e l e c t r i c f i e l d strengths, (2 - k x 10'^  Vcm "*") increases rapidly as the oxide thickness i s reduced below 0.2um [88]. During the periods of avalanche breakdown some of the hot electrons incident on the interface w i l l be injected into the conduction band of the 101+ adjacent SiO^ layer [89,90]. The injection probability, however, should be very small (<2 x 10 )[91], and in addition, i t has been found that trap-ping of the injected electrons is negligible in dry thermal oxides, so that no drift or stability problems are to be expected. 4.1.2 Test Structure Designs and Mask Layouts The three miniature surface breakdown devices used in the i n i t i a l in-vestigation are shown in Figures k.2 - k.k. Device 1 (Fig. k.2) has the simplest possible structure, consisting only of an MOS field plate with a thick oxide guard ring, and an ohmic contact to the substrate. In operation the gate is pulsed from a condition of strong inversion to a potential above that required for breakdown, and held there for a frame time. The gate potential is then returned to the original reset value so as to inject into the substrate any additional charge collected in the inversion layer as the result of an avalanche discharge. The avalanche discharge pulses can be detected simply by monitoring the substrate current, however, the large additional displacement currents during the rising and falling edges of the drive pulse complicate the detection. These drive pulse transients are primarily due to capacitive coupling between the relatively large area bond-ing pad and the substrate. In device 2 (Fig. k.3) the drive pulse transients are greatly reduced by providing a field shield underneath the bonding pad and interconnect line. Also, by omitting the thick field oxide, MOS devices with a field plate type guard ring may be fabricated, as in device 2b (Fig. U.3(b)). The charge injection mode of operation of devices 1 and 2 results in long reset times since the injected electrons must be given time to recom-bine with the majority carrier holes. At low temperatures the recombination time constant can be several miliseconds for long lifetime substrates. For 105 Amp. virt. gnd. -3-J10 jum}< 20x 20 urn (or 20x 40 urn) AI photogate (a) ohmic contact Si Op •'• p - silicon c V u a . A > (b) sb i "~7T\"" charge injection (C) FIGURE 4.2 Charge i n j e c t i o n test device, structure 1 (a) layout of the i n d i v i d u a l gates and v e r t i c a l structure (b) potential w e l l diagram i n deep depletion, before breakdown (c) during reset, charge i n j e c t i o n Amp. virt. gnd. shield gate Vs extends under photogate bonding pad ^J10jum|<-•SiO A l 2 0 3 20 x 20 Aim (or 20x40urn) Al photogate ohmic contact p - silicon 40x40 urn (or 40x 60 urn) Al photogate ohmic contact p - silicon FIGURE 4.3 Charge injection test device, structure 2 (a) layout and vertical structure (b) alternate structure obtained by omitting the thick field oxide 107 to shield gate Vs -Via \ V f — V i a to next device —H k— lOum Amp. virt. gnd. (a) 20x40um photogate guard ring and transfer gate A l2°3 p - silicon -Schottky output diode (b) ^ charge transfer to Schottky output diode -> (0 FIGURE 4.4 Charge transfer test device, structure 3 ( a ) layout of the individual gate and. vertical structure (b) potential well diagram in deep depletion before breakdown (c) during reset, charge transfer 108 t h i s reason a device that operates i n the charge transfer mode was included as one of the i n i t i a l test devices (Fig. U.*0. In these devices the signal charge i s transferred l a t e r a l l y along the interface to an output diode. During readout the guard ring, f i e l d plate serves as a transfer gate between .the output diode and the photogate. A sh i e l d gate i s provided around the breakdown gate and output diode i n order to interrupt any surface channels that would otherwise connect the devices to the bonding pad depletion regions. 1 No diffusions other than those used for bulk gettering purposes are required to fabricate the three test structures. The only remaining high temperature steps involved are the thick f i e l d and gate oxidations. The gates and interconnect l i n e s are aluminum. The f i r s t l e v e l undergoes an al l o y i n g step i n order to make any necessary ohmic contacts to the substrate, and i s then p a r t i a l l y anodized to form the insulator between f i r s t and second l e v e l metal [92-94]. The second l e v e l of aluminum i s not sintered so that MIS diodes may be formed [95]. This double l e v e l aluminum/Al^O^/ aluminum metalization was chosen over the more conventional polysilicon/SiO^/ aluminum scheme, p a r t l y because of a lack of p o l y s i l i c o n deposition f a c i l i -t i e s , and also because there are no high temperature steps involved during the double l e v e l aluminum metalization. The minimal high temperature pro-cessing required to fabricate the test devices f a c i l i t a t e s the maintenance of long bulk l i f e t i m e s . Several test devices of each type were l a i d out onto a three part die so that they could be fabricated simultaneously using a single set of photo-masks. The layouts were designed so as to provide a range of gate separa-tions for photon coupling measurements, and to have an arrangement of bond-ing pads suitable for mounting i n l 6 pin DIP packages. Five photomasks are required to fabricate the composite test chip, they are: 109 1 - gate oxide mask 2 - substrate contact mask 3 - first level aluminum mask . h - first to second level aluminum contact mask (vias) • 5 - second level aluminum mask Rubylith masters were generated manually on a coordinograph at a scale of 250 times. The photographic reduction and step and repeat operations were performed by Precision Photomask''". The five mask levels are shown in Fig. 4..5(a) - (e). The required first level aluminum pattern consists of various isolated features, (gates, field shields.etc.), however, the electrochemical anodiza-tion process requires electrical contact to each first level feature that is to he anodized. For this purpose mask 3 includes temporary anodizing • contacts that are extended to an aluminum bus in the scribe line area. Con-tact is made to this bus through the substrate during the anodization process. A protective photoresist mask is used to prevent the temporary contacts and aluminum bus, together with the first to second level vias, from being anodized [92]. Photoresist is also used to protect bare areas of silicon from the electrolyte (in this case the MIS contact, areas), as these would result in large leakage paths. A l l of these protected areas are included on mask k. The anodic Al^O^ layer formed is inert to the phosphoric acid etchant used to pattern aluminum, therefore, the removal of the anodization •contacts and bus does not require an additional photomask. These unpro-tected regions of.first level aluminum are etched away while patterning the second level of aluminum. The entire fabrication sequence is illustrated in Fig. k.6. ^ 5085 Isaballe street, St Hubert, Quebec, Canada. 110 FIGURE 4.5 Copies o f the f i v e photomasks used t o f a b r i c a t e the d e v i c e s . F i g u r e s ( a ) , ( b ) , and (d) are r e v e r s a l s o f the a c t u a l masks used . The l a s t number i n the dev i ce d e s i g n a t i o n s r e f e r s t o the gate numbers i n d i -c a t e d i n (e) (a) gate ox ide mask (b) s u b s t r a t e contac t mask (c) f i r s t l e v e l aluminum mask (d) v i a mask (e) second l e v e l aluminum mask I l l 112 J (e) .113 p- silicon Si03 ( l ) f i e l d o x i d a t i o n and gate ox ide window e t c h (2) gate o x i d a t i o n and contact window e t c h ohmic contact (3) f i r s t l e v e l A l d e p o s i t i o n and p a t t e r n e t c h , p l u s annea l _ O O a O o ° 0 ~ photoresist ^ ^ ^ ^ _a S-(k) s e l e c t i v e a n o d i z a t i o n o f f i r s t l e v e l A l Schottky output diode ( 5 ) second l e v e l A l d e p o s i t i o n and p a t t e r n e tch FIGURE 4.6 F a b r i c a t i o n sequence f o r the sur face -breakdown t e s t d e v i c e s . 11U 4.1.3 Device Fabrication Two lots of devices were fabricated on 2.2 - 2'5ft cm boron doped (100) Czochralski wafers, with chemo-mechanically polished front surfaces and bright etched rear surfaces. The processing details for the two fabrication runs are listed in Table U.l and U.2. Table U.3 lists the device wafers and test wafers used and gives the i n i t i a l bulk resistivities and the final gate and thick field oxide thicknesses. In both fabrications extensive use was made of dry HC1 oxidations in order to: (l) - suppress oxidation induced stacking faults and eliminate grown-in defects [66-69]. •(2) - getter lifetime-degrading impurities from the silicon [96-98]. (3) - passivate (i.e., neutralize) any mobile ionic sodium or potas-sium present in the oxide [99-101]. -Complete passivation of a l l mobile alkali ions is not critical to the suc-cessful operation of the present devices, since these ions will be "frozen-in" at the low operating temperature (below 100K). In. addition to the above benifits it has also been found that, subsequent to a hydrogen anneal (or aluminum "alneal"), HC1 oxides have lower surface state densities than oxides grown in pure 0^ [102]. Further, the defect density at high elec-tric field strengths is lower in HC1 oxides [103]. 115 TABLE 4.1 P r o c e s s i n g D e t a i l s For F i r s t F a b r i c a t i o n Step Operat ions D e t a i l s i n i t i a l c l e a n - hot xy lene w i t h u l t r a s o n i c a g i t a t i o n - RCA c l e a n s u r f a c e c l e a n - u p o x i d a t i o n temp. 1100°C c y c l e : 5 min 0^ U00 min 0 g + % HC1 5 min •1-1 s t r i p a l l ox ide f i e l d o x i d a t i o n - b u f f e r e d HF -•HC1/H 0 p a r t o f RCA c l e a n temp. 1100°C c y c l e : 5 min 0^ lUO min 0 2 + H a 400 min-0 + 5% HC1 5 min N 2 ox ide t h i c k n e s s , 1.00 urn gate window e t c h - neg r e s i s t , mask 1 - b u f f e r e d HF - s t r i p r e s i s t , hot HgSO^/H 0 2 - RCA c l e a n 1-2 gate o x i d a t i o n temp. 1100°C c y c l e : 5 min 0 2 62 min 0 2 + 5% HC1 5 min 0 2 15 min N "b s low p u l l i n N 2 ox ide t h i c k n e s s , 0.20 ym c o n t a c t e t c h - neg . r e s i s t , mask 2 - b u f f e r e d HF - r e s i s t s t r i p , hot HgSO^/H 0. RCA c l e a n - 2% HF d i p (20 sec) 116 TABLE 4.1 cont'd. Step 1-3 Operations aluminum evap. I aluminum etch I contact sinter plus hydrogen anneal Details electron beam evap.: substrate temp., 250°C evap. rate, 50-200 Ssec - 1 f i l m thickness, 1.0 ym neg. r e s i s t , mask 3 phosphoric/nitric etch, 60°C r e s i s t s t r i p , Microstrip temp. 1+50°C cycle: 10 min N g 30 min N 2 + 50$ H 2 1-1+ v i a photoresist aluminum anodization - Waycoat LSI 295 p o s i t i v e , mask 1+ : e l e c t r o l y t e , 25w/o APB-EG ° - 2 current, 0 . 5 mA cm formation voltage, 85 V soak time at 85 V, 2 min - r e s i s t s t r i p , hot acetone - Phosphoric etch, 1+0°C, 60 sec aluminum evaporation • tungsten filament evap.: I I substrate temp., 200°C evap. rate, 5 0 - 1 0 0 2sec -1 1 - 5 f i l m thickness 1 . 0 ym aluminum etch I I - neg. r e s i s t , mask 5 - phosphoric etch 60°C - r e s i s t s t r i p , Microstrip a Burnt hydrogen wet oxidation P u l l e d manually from the hot zone over a period of about 10 min. 25 weight % ammonium pentaborate dissolved i n (hot) ethylene g l y c o l (under an argon atmosphere to prevent oxidation). 117 TABLE 4.2 Proces s i n g Details For Second F a b r i c a t i o n Step Operations D e t a i l s i n i t i a l c lean - hot xylene w i t h u l t r a s o n i c ag ;i t at i o n - RCA cle a n surface clean-up temp. 1125°C o x i d a t i o n plus c y c l e : 5 min 0 d b phosphorus d i f f u s i o n 100 min Q>2 + H 2 mask kOO min 0 2 + 5% HC1 5 min N 2 s t r i p oxide o f f - HF vapor-etch (back side) 2-1 hack - HC1/H 20 2 p a r t of RCA c l e a n phosphorus g e t t e r temp. 1050°C a d i f f u s i o n source POCl^ pass over, 15°C i c y c l e : 5 min N g + 3% 0 2 3Q..min N 2 + 3% Q>2 + source N 5 min N 2 + 3% 0 2 s t r i p oxide o f f - HF vapor-etch ( f r o n t side) f r o n t - 10% HF, 60 sec. (phosphorous glaze s t r i p on back side) - HC1/H 20 2 part of RCA clean 2-2 a f i e l d o x i d a t i o n s l i c e s P2-0, P2-2: temp. 1125°C c y c l e : 10 min 0^ kO min 0 2 + H 2 2 5 min 0, 15 min N Oxide t h i c k n e s s , 0.52 ym s l i c e s P2-1, P2-3: temp. 1125°C 118 TABLE 4.2 cont'd. Step Operations Details 2 - 2 cont'd cycle: 10 min 0 ^ 73 min 0 2 + H 2 5 min 0 2 15 min N 2 oxide thickness, 0 . 7 2 ym gate window etch - neg. resist, mask 1 . - buffered HF (back side protected) - strip resist, hot H^O^/HgOg - RCA clean 2-3 a gate oxidation temp. 1125°C cycle: 10 min 0 2 49 min 0 2 + 5% HC1 5 min 0 2 5 min N2 c slow pull in N 2 oxide thickness, 0 . 1 8 ym contact window etch - neg. resist, mask 2 - buffered HF - strip resist, hot H 2 S 0^/H 2 0 2 - RCA clean - 2% HF dip 20 sec. aluminum evaporation electron beam evap: substrate temp., 250°C evap. rate, - 50 2sec film thickness, 1 . 0 ym 119 TABLE 4.2 cont'd. Step Operations Details 2-k cont'd aluminum etch I - neg. resist, masks 3 + 5 (double exposure) - phosphoric/nitric etch 60°C - strip resist, Microstrip aluminum etch II - neg. resist, masks U + 5 (double exposure) - phosphoric/nitric etch, 60°C - strip resist," Microstrip contact sinter. temp. U50°C cycle: 30 min hydrogen anneal o temp. 350 C cycle: 180 min etch off back side + n layer - white etch (front protected with wax) - hot trichloroethylene (to strip wax) Quartz furnace tube and boat pre-cleaned with O^/HCl gas flow for 2 hours, prior to loading devices. Burnt hydrogen wet oxidation. Pulled manually from the hot zone very slowly, over a period of about 20 min.. , followed by a fast pull once reaching a temperature of approximate-ly 6oo°c. 120 TABLE 4 . 3 Device And Test Wafer Data wafer use b u l k r e s i s t i v i t y (flcm) gate ox ide t h i c k n e s s V_. FB (um) . (V) f i e l d ox ide d V FB (V) t h i c k n e s s (pm) P l - 0 P l - 1 P l - 2 P I - 3 a n o d i z a t i o n t e s t s •2.5 - 0 . 2 0 P1-1+* P l - 5 P l - 6 dev ices 2.35 2.1+5 2.30 0 . 1 9 0 . 1 9 0 . 1 9 1 . 5 1 . 0 0 1 . 0 0 1 . 0 0 8 . 0 P l - T s u r f a c e s t a t e 2 .38 measurements 0 . 1 9 P 2 - 0 P 2 - 1 P 2 - 2 P 2 - 3 * P2-1+ P 2 - 5 dev ices p r o f i l e and s u r f a c e s t a t e measurements 2.1+5 2.32 2.35 2.22 2.2U 2.1+8 0 . 1 7 0 . 1 7 0 . 1 7 0 . 1 7 0 . 1 7 C 0 . 1 7 C 1 . 2 0 . 5 5 0.74 0 . 5 5 0.7I+ 5.3 Boron doped 2 " ( l 0 0 ) C z o c h r a l s k i w a f e r s , chemo-mechanical p o l i s h on f r o n t s u r f a c e , b r i g h t - e t c h e d r e a r s u r f a c e . Wafer t h i c k n e s s ~280pm. *Device wafers t e s t e d . b c Measured w i t h f o u r p o i n t probe b e f o r e p r o c e s s i n g . Th ickness o b t a i n e d from measured c a p a c i t a n c e i n s t r o n g accumula t ion (jising e-^/e- =3.8).. Th ickness o b t a i n e d . f r o m . c o l o u r , accuracy approx imate l y ± 0 . 0 2 p m . 121 ( l ) F i r s t f a b r i c a t i o n run P r i o r to device p r o c e s s i n g the wafers were o x i d i z e d i n an O^/HCl ambient t o remove any surface damage and provide some i n i t i a l g e t t e r i n g o f i m p u r i t i e s . This oxide was then s t r i p p e d and the t h i c k f i e l d and gate oxides were grown, again u s i n g HC1. A f i e l d oxide t h i c k n e s s o f 1 ym was chosen i n order to ensure t h a t the s i l i c o n beneath the edges of the metal-i z a t i o n would remain w e l l below breakdown during device o p e r a t i o n . A 15 minute n i t r o g e n anneal .was i n c l u d e d at the end of the gate o x i d a t i o n i n order t o minimize the p o s i t i v e ' f i x e d s u r f a c e - s t a t e charge Q [104]. A f t e r ss opening both the ohmic and MIS contact windows the f i r s t l e v e l o f aluminum was deposited ( v i a e l e c t r o n beam evaporation) i n a p l a n e t a r y evaporator. The substrates were heated t o 250°C during the evaporation'to f u r t h e r im-prove step coverage [105]. In order t o achieve tapered m e t a l i z a t i o n edges and a l l e v i a t e step coverage problems during the second l e v e l m e t a l i z a t i o n , n i t r i c a c i d was added t o the phosphoric a c i d etchant used t o p a t t e r n the f i r s t l e v e l of aluminum [106]. The n i t r i c a c i d causes the p h o t o r e s i s t t o lose adherence and g r a d u a l l y l i f t from the edge inwards during e t c h i n g , r e -s u l t i n g i n the d e s i r e d edge p r o f i l e . A f t e r p a t t e r n i n g the f i r s t l e v e l of aluminum the s l i c e s were given a U50°C contact s i n t e r i n order t o make ohmic contact t o the an o d i z a t i o n bus and t o anneal out any x-ray damage caused by the e l e c t r o n beam evaporation. A hydrogen anneal t o reduce sur-face s t a t e d e n s i t i e s was a l s o i n c l u d e d at t h i s time, s i n c e an a c t i v e metal " a l n e a l " f o l l o w i n g the second m e t a l i z a t i o n i s not p o s s i b l e , as t h i s would s i n t e r the MIS contacts and destroy t h e i r r e c t i f y i n g property. A f t e r a p p l y i n g the v i a p h o t o r e s i s t the wafers were anodized i n d i v i d -u a l l y , i n an e l e c t r o l y t e of 25 w/o ammonium pentaborate i n ethylene g l y c o l , u sing the s p e c i a l t e f l o n wafer h o l d e r shown i n F i g . h.'J.. The anodic oxide -2 l a y e r s were formed at a low constant current d e n s i t y of 0.5 mA cm and h e l d 122 FIGURE 4.7 Teflon anodization cell used in the device fabrication. 123 for only a few minutes at the final voltage while the current decayed, since both high current density and a prolonged soak time at constant vol-tage are reported to result in pore formation [107], The results of some in i t i a l anodization tests, on wafers with large photoresist patterns, had indicated that the anodic oxide could be formed to a voltage of 120 V before the resist mask started to break down and l i f t at the edges. Unfortunately, during the anodization of the device wafers i t was found that the small pho-toresist features lifted at a much lower voltage. Parts of the via photo-resist pattern lifted completely at approximately 60 V on the first device wafer anodized. Re-baking the photoresist at a higher temperature enabled the anodization to be extended to about 85•V on the remaining two wafers. However, after depositing and patterning the second level of aluminum i t was found that the breakdown voltage of the'-AlgO layer was only hO V, less than half the formation voltage. The second level of aluminum was evaporated from a tungsten filament since the MIS contacts preclude the annealing of x-ray damage resulting from an electron beam evaporation. The cause of the low breakdown strength of the anodic Al^O^ layer is not certain, but is thought to be due to annealing hillocks present in the first level of aluminum prior to the anodization [108,109]. Such hillocks are the result of compressive stresses in the aluminum film following the contact sinter. Even i f these features are properly anodized, the increased fields present at the .apex of the sharp hillocks could cause premature break-1 down. Because of the low breakdown voltage of the anodic oxide layer, only the simple MOS gates with thick oxide guard rings (device structure l l ) were operational above breakdown. (2) Second fabrication run On this fabrication run the double level Al-Al o0_-Al metalization 12k scheme was abandoned and only device structure 1 was fabricated. In add-ition to the i n i t i a l HC1 oxidation a phosphorus getter diffusion [110,111] was also included prior to device fabrication, in order to try and improve bulk lifetimes. Furthermore, to help reduce the number of impurities intro-duced during processing, the wafer boat and furnace tube were cleaned with an O^/HCl gas flow for two hours before each high temperature operation. Devices were fabricated with two different thicknesses of field (i.e., guard ring) oxide, 0. 5^ um and 0 .74pm., The gate oxidation cycle was identical to the previous fabrication. After opening the contact windows a single level of aluminum was deposited via electron beam and patterned. In order to achieve the desired pattern in one level of aluminum using the existing masks, double exposures and two photoresist operations were required (see Table k.2). After etching the. aluminum pattern the slices were given a 30 minute contact sinter and aluminum "alneal" at ^ 50°C in N^ , followed by a o + 350 C hydrogen anneal in pure for 3 hours. The back-side n layer (phosphorus.getter) was then etched away, completing the processing. 4.1.4 Test Chamber and Electronics For testing, the individual die were mounted in modified ceramic l 6 pin DIP packages. To enable back-side illumination of the devices the metal bottoms of the DIP packages were replaced by glass and the test chips were glued to this using a transparent epoxy (Araldite high vacuum epoxy). The package pins were then bent backwards, to facilitate illumination of the de-vices through the glass . ' Figure 4.8 shows a cross-section of the cold chamber used for the low temperature device testing. Cooling is accomplished with a liquid nitrogen heat pipe that protrudes into an evacuated housing. The front (window) end of the housing is removable, so that the packaged devices can be clamped to Cross-section of the cold chamber used for the low temperature device testing. 126 an aluminum cold finger on the end of the heat pipe. The test socket is connected to electrical feedthroughs on the back of the chamber with 3 mil teflon insulated copper wire. The liquid nitrogen heat pipe also cools a canister of zeolite sorption material within the test chamber. After insert-ing the test devices the chamber is rough-pumped and then sealed off. During the cool-down the sorption pump evacuates the chamber further and once cold will maintain the vacuum below 10 torr. The vacuum provides insulation and ensures that no moisture is able to condense and freeze on the devices. A copper, constantan thermocouple is used to.monitor the temperature of the cold finger. In operation the-cold finger reaches a stable temperature of 80 K. A power resistor was added during the testing of the bulk channel devices, enabling the substrate temperature to be altered over a moderate temperature range from 80 K to ihO K. , A block diagram of the test electronics is shown in Fig. 4.9 • Schema-tics for the driver, amplifier,, descriminator and timing circuitry are given in Appendix B. The driver supplies a very clean trapezoidal waveform with no overshoot or undershoot. The ramp rates on the leading and trailing edges may be varied independently from lO^Vsec 1 to 5 x lO^Vsec The up-per level may be varied from +20 V to +150 V while the lower level may be varied from -90 V to +50 V. The amplifier used to detect the avalanche charge pulses is housed in an aluminum box on the back of the cold chamber. It consists basically of a low noise wide-band J-FET input op-amp (LF 356) operated as a current to voltage amplifier, followed by further voltage amplification and then a high speed sample and hold smplifier (LH0053), operated as a preset integrator. The output of the current amplifier is monitored on an oscilloscope and the integrator output is passed to a des-criminator circuit and counter. The current integrator may be taken out of the preset mode to start integration anywhere along the positive or nega-OSCILLOSCOPE PULSE COUNTERS No. of events No. of frames DESCRIMINATOR CURRENT AMP. AND INTEGRATOR TIMING \ 1 HIGH VOLTAGE DRIVER AND INTEGRATOR START PULSE GEN. COLD CHAMBER J Pi » 1 FIGURE 4.9 Block diagram o f the t e s t e l e c t r o n i c s . 128 t i v e going edge of the d r i v e pulse and the d u r a t i o n of the i n t e g r a t i o n may-be v a r i e d independently o f the d r i v e r waveform. Before b e i n g p r e s e t , the i n t e g r a t o r goes i n t o a h o l d mode momentarily w h i l e the de s c r i m i n a t o r i s 3 a c t i v a t e d . The l e v e l o f noise at the de s c r i m i n a t o r v a r i e d from 3 x 10 ele c t r o n s r.m.s. f o r short (0.2msec) i n t e g r a t i o n s t o approximately 1.5 x 10^ e l e c t r o n s r.m.s. f o r longer (2msec) i n t e g r a t i o n s . 4.1.5 Modeling of the Completed Devices In order t o i n t e r p r e t the r e s u l t s and make comparisons w i t h t h e o r y , an accurate doping p r o f i l e through the d e p l e t i o n region-under the gate, and accurate gate oxide and f i e l d oxide thicknesses are r e q u i r e d . The f i e l d oxide thickness was. determined t o w i t h i n +0.02 ym from i t s c o l o u r . The doping p r o f i l e and gate oxide t h i c k n e s s were determined from C-V data accord i n g to the method o u t l i n e d i n Appendix C. These l a t t e r measurements were made on wafers t h a t had r e c e i v e d the same high temperature p r o c e s s i n g as the device s l i c e s and that had a n e a r l y i d e n t i c a l s t a r t i n g r e s i s t i v i t y (see Table 4 . 3 ) . The measured doping p r o f i l e s f o r the two f a b r i c a t i o n runs are shown i n Figures 4.10 and 4.11. To s i m p l i f y the c a l c u l a t i o n o f e l e c t r i c f i e l d s trength as a f u n c t i o n of p o s i t i o n i n the d e p l e t i o n r e g i o n , the doping p r o f i l e s were approximated by the two s t r a i g h t l i n e segments i n d i c a t e d . By making the d e p l e t i o n approximation i t can then be shown t h a t the e l e c t r i c f i e l d i s given by: qN, q(N - N ) £ l s ( y ) = e U ~ y ) " € 2d ( d l ~ y ) » ° l y ^ d i ( 4 ' 2 ) s s 1 q N 1 £ 2 s(y) = — (w - y) , d l l y (4.3) e £ = — £ ' (4.4) ox e. Is i W (jum) FIGURE 4.10 Surface doping profile for wafer Pl-7, obtained from C(V) data by the method de-scribed in Appendix C. The solid line shows the approximate profile used to model the devices. T r r~ r~——i— 1 1 1 r I 1— 1 i i i i » t t 1 0 0.4 0.8 1.2 1.6 2.0 W (jum) FIGURE 4.11 Sur face doping p r o f i l e f o r wafer P2-4 and the approximate p r o f i l e used f o r d e -v i c e m o d e l i n g . 131 where y is the position in the depletion region, measured from Si-Si0 2 interface, and N^ , and d^ are the parameters given in Figures 4.10 and 4.H.. The depletion layer width w is given by w = -e - I d + e. ox l e. ox l + e . N d l d o x + ~ W T d l l 1 1 2e QTd_ 2e (V - V_) \h + -Mr^ + 5 \ (4.5) e i q N l q IN. where is the amount of charge present in the surface inversion layer and V_ is the flat band voltage. The silicon surface potential is given by, FB *N1 2 ^ V V P ' *s = 2Tv ~ ~ 6 l d i s s (4.6) In addition to the device structure parameters, the.interface state density and bulk lifetime were also determined for the devices from the second fabrication. These measurements were made on test wafer P2-5. The measured interface state density is shown in Fig. 4.12. The method used, described in Appendix C, limited the range over which the interface state density could be determined to those energies near mid-gap and towards the valence band edge, whereas, the interface states of interest are those nearer the conduction band. The densities of these interface states, however, are typically lower that those near the valence band [102]. The bulk lifetime was estimated by monitoring the substrate displacement current of the 1 mm dia MOS gates, following a depleting pulse at room temperature. The i n i t i a l value of the decay current was measured on a Keithly model 602 electrometer (in the fast mode) and related to the bulk lifetime through Eq. 3.33. The depletion region width w was obtained from Eq. 4.5 using the doping profile 10 >11 \ 101 0 o l/l i r WAFER P2-5 o \ O 300 K x 223 K • 173 K \ 0.1 0.2 0.3 E - E v (eV) 0.4 0.5 0.6 0.7 FIGURE 4.12 I n t e r f a c e s t a t e d e n s i t y f o r wafer P2-5 as a f u n c t i o n o f p o s i t i o n i n the hand g a p , o b t a i n e d from C(V) measurements by the method o u t l i n e d i n Appendix C. The t r u e i n t e r f a c e s t a t e d e n s i t y i s rep resented by the upper envelope o f the t h r e e s e t s o f d a t a . 133 data from wafer P2-H. The c o n t r i b u t i o n t o the decay c u r r e n t f rom i n t e r f a c e s t a t e s was min imized by p u l s i n g the gates from a c o n d i t i o n o f s t r o n g i n -v e r s i o n . The measured b u l k l i f e t i m e a c c o r d i n g t o t h i s method was 60 y s e c . Be fo re any h i g h v o l t a g e t e s t s were conducted on the t e s t dev ices the f l a t - b a n d v o l t a g e s f o r the gate and f i e l d ox ides were determined by d r i v i n g the photogate w i t h a t r i a n g u l a r waveform (+15 V) and o b s e r v i n g the d i s p l a c e -ment c u r r e n t on an o s c i l l o s c o p e . S ince the v o l t a g e ramps are l i n e a r the d i s -placement c u r r e n t i s p r o p o r t i o n a l t o the c a p a c i t a n c e . The f l a t - b a n d v o l t a g e s f o r the t h i c k and t h i n ox ide r e g i o n s may be determined s e p a r a t e l y by u s i n g s t r o n g i l l u m i n a t i o n and measur ing the v o l t a g e s o f the two i n f l e c t i o n s i n the C-V c u r v e , co r respond ing t o i n v e r s i o n under the t h i c k and t h i n o x i d e s , r e -s p e c t i v e l y . To w i t h i n the accuracy o f the measurements, a l l o f the dev i ces t e s t e d , from a g i ven w a f e r , were found to have the same f l a t band v o l t a g e s . The gate and guard r i n g , f l a t band v o l t a g e s are g i v e n i n : T a b l e h.3. The f l a t band v o l t a g e s d i d not change w i t h t i m e , even a f t e r the dev ices had been operated above breakdown, and c y c l e d between room temperature and 80 K, many t i m e s . 4 . 1 . 6 E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n The above breakdown t e s t i n g was conducted at a temperature o f 80 K. Examples o f the d r i v e r waveform used and the t y p i c a l output p u l s e s o b t a i n e d are i l l u s t r a t e d i n F i g . U.13. The i n t e g r a t i o n was s t a r t e d d u r i n g the p o s -i t i v e go ing ramp, s l i g h t l y b e f o r e c r o s s i n g the breakdown v o l t a g e . The l a r g e d r i v e p u l s e d isp lacement c u r r e n t s due t o c a p a c i t i v e c o u p l i n g between the bonding pad and the s u b s t r a t e made i t necessary t o l i m i t the ramp r a t e t o 1 x 10^ Vsec i n o rder not t o s a t u r a t e the c u r r e n t a m p l i f i e r . In accordance w i t h the t h e o r e t i c a l d i s c u s s i o n i n chapter 3, i t was found t h a t when the dev ices were p u l s e d i n t o deep d e p l e t i o n from a r e s e t 13h active phase I AVALANCHE DISCHARGE integrate (0.5 - 2 msec) (a) — 7 / — 1 -> <— 1 -1000 msec r 0 (b) (c) + 5V •(d) FIGURE 4.13 Test waveforms for the surface-breakdown, charge-injection devices ( a ) high voltage driver (b) output of the current to voltage amplifier. Substrate displacement current (c) output of the preset integrator (d) discriminator output, threshold = 0 V 135 condition corresponding to surface accumulation, breakdown always occurred during the voltage ramp, within a few microseconds of crossing the breakdown voltage. Once initiated, the breakdown continued for the remainder of the ramp duration. Pulsing the diodes from a reset condition corresponding to inversion (under the thin oxide region of the gate) increased the mean delay time to breakdown by about a factor of 3 and resulted in discrete breakdown pulses. However, not until the silicon under the thick oxide-guard ring was also inverted during reset could appreciable delays to breakdown be achieved, enabling the devices to be pulsed several volts above breakdown. When operating in the latter mode the reset inversion layer charge present under the guard ring, bonding pad and interconnect line is transfer-red to the thin oxide gate region during the depleting pulse, thereby, in-creasing the gate potential required to cause breakdown in the underlying silicon. Since no inversion layer charge remains under the guard ring after the depleting pulse, the increased gate potential causes the guard ring to be more deeply depleted. These effects are shown in Figures 4 . l 4 and 4 . 1 5 , for devices from the two fabrication runs. The silicon surface potential under the guard ring, calculated using ( 4 . 6 ) and the doping profile data in Figures 4 . 1 0 and 4 . 1 1 is also indicated. The change in breakdown voltage V . for a given change in reset voltage, when the guard ring is heavily in-verted during reset, is given by AV ( 4 . 7 ) where d g gate oxide thickness field oxide thickness area of the thin oxide gate region area of the guard ring, bonding pad and interconnect line 136 140 2 130 o > 120 110 10 z o < Ul oc CD 111 _I CO < o u 100 t— UJ O U. O UJ O < I-_ i o > DEVICE O P1-4/3-5 60 o — o — - o P1-4/2-3 gate area = 20 x 40 jjm t r = 100 msec 62.5 V 59.9 V 4 6 RESET VOLTAGE O a. ui o CO V r (volts) FIGURE 4.14 Voltage of first detectable breakdowns as a function of the reset voltage for devices from the first fabrication. The solid line in-dicates the calculated slope for the case that the guard ring is strongly inverted during reset. The silicon surface potentials under the guard ring and under the active region of the gate are also indicated. 137 -2 0 2 4 6 8 RESET VOLTAGE Vp (volts) FIGURE 4.15 Voltage of first detectable breakdowns as a function of the reset voltage (second fabrication). 138 The c a l c u l a t e d sloue AV ,/AV from (h.j) i s i n d i c a t e d by the s o l i d l i n e i n gb r Figures h.lh and U.15. The close agreement between the c a l c u l a t e d and ob-served slopes indicates that premature edge breakdown was not occuring. I f i t were, one would expect the slope AV ^/AV^ to be greater than that c a l c u -l a t e d from ( 4 . 7 ) , since the guard r i n g becomes more deeply depleted ( i . e . , more e f f e c t i v e i n preventing edge breakdown). as the reset voltage i s i n -creased. With further increases i n reset voltage, or as the f i e l d oxide thickness i s reduced, a point i s eventually reached where the s i l i c o n under the guard r i n g , bonding pad, and interconnect l i n e also break down. The thinner f i e l d oxide on wafers P2-0 and P2-2 prevented operation of these devices above the gate breakdown voltage when the guard r i n g was h e a v i l y i n -verted during reset. Figure k.l6 shows the maximum charge, per pulse as a function of the gate voltage f o r one of the 20 x 20 ym gates from wafer P2-3. The pulse height d i s t r i b u t i o n (for V - V , = 5 V) is-shown i n F i g . U.17. The charge S gb measurements were obtained from the discriminator s e t t i n g using the c a l c u l a -ted gain of the current a m p l i f i e r - i n t e g r a t o r combination (9-36 x 10^ e l e c t . V - ^"). The discharge pulses increase l i n e a r l y with excess gate voltage, as expected, however, the maximum charge pulses are smaller than those pre-di c t e d from I QI - A«i(v-v (4-8) and the pulse height d i s t r i b u t i o n i s considerably wider than a n t i c i p a t e d . These e f f e c t s are thought to be due to the build-up of p o s i t i v e space charge during an avalanche (e.g., holes d r i f t i n g through the low f i e l d regions of the depletion region). The build-up of space charge l i m i t s the avalanche discharge.current to the point where s t a t i s t i c a l f l u c t u a t i o n s can cause the number of c a r r i e r s i n the high f i e l d region to drop to zero, thus terminat-FIGURE 4.16 Maximum charge .per pulse as a function of the photogate voltage. The dashed indicates the expected variation, according to Eq. U.8. T 1 1 1 1——i 1 1 1 r 0 0.4 0.8 1.2 1.6 2.0 DESCRIMINATOR LEVEL ( 10 6 elect.) FIGURE 4.17 Typical pulse height distribution for the surface-breakdown devices. The dif-ferential distribution was obtained by graphically differentiating the integral distribution. V - V = 5V. 1 4 1 ing the avalanche. (l) Results From First Fabrication Six test chips (78 devices) were examined from wafer PI-4. The dark count rates, at a given excess bias, were found to differ by less than a factor of 2 , for a l l but a few devices which had anomalously high count rates. Except for these "bad" devices i t was found that even after the guard ring was inverted during reset, the dark count rate at a given excess gate bias continued to decrease as the reset voltage (i.e. , the inversion layer charge) increased. This decrease continued until the guard ring also started to break down. This effect is shown in Fig. 4 . 1 8 for one of the better devices from wafer Pl-4. The silicon surface potential 4>s was cal-culated from (4 .5) and (4 .6 ) . A l l of the count rates presented in this dis-cussion have been corrected for dead time and temporal sampling effects (according to Eq. 2 . 7 )» and are expressed as counts/sec. The dark count rates shown in Fig. 4 .18 are very high, increasing supralinearly as the gate bias is increased. 100 counts sec ^ for the 40 x 20 ym gate corres-7 - 1 - 2 ponds to 1 . 2 5 x 10 counts sec cm , more that 4 orders of magnitude larger - 1 - 2 than the desired maximum dark count rate of 500 sec cm - In spite of the high dark event rate i t was possible to operate these first devices under low level illumination in a photon counting mode. Fig. 4 . 1 9 shows a typical example of the count rate under illumination, plotted as a function of the excess gate bias. The devices were illuminated with a red gallium arsenide-phosphide LED (TIL 2 2 0 , X = 620 nm) run at very low current densities and pulsed on during.the integration only. The entire back' side of the chip was illuminated and no attempt was made to determine the level of illumination or to estimate the number of carriers generated, per light pulse, within a carrier diffusion length of the gate. Therefore, 200 SILICON SURFACE POTENTIAL 63 64 150 o • » c 3 O U 100 < OC z O 5 0 o 3£ < T Device P1-4/3-5 gate area P 20x40 um tj = 1.0 msec t „ = 300 msec • x V r r *10 V J i T <ps (volts) 65 1 I f i I V r = *12V \ J V r : *14V 5 _L EXCESS 2 3 GATE BIAS (volts) FIGURE 4.18 Dark count r a t e as a f u n c t i o n o f the excess photogate b i a s f o r the t h r e e r e s e t i n v e r s i o n c o n d i t i o n s , = +10V, +12V, +lVv. The c a l c u -l a t e d s i l i c o n s u r f a c e p o t e n t i a l b e f o r e breakdown <|> i s a l s o i n d i c a t e d . s 1U3 150 TT DEVICE P1-4/3-5 I gate area = 20x 40 jum tj = 1.0 msec t r - 300 msec V„ = 14 V 100 i dark pulse rate photon- induced pulse rate ( dark subtracted ) o V IA •V tfl •» c o U \ Ul I-< * 50 z :> o o i O l — 1 2 EXCESS PHOTOGATE BIAS Vn -V_K (volts) g go FIGURE 4.19 Dark and photon induced pulse rates as a function of excess photogate bias, for one of the better devices from the first fabrication. 144 no determination o f the expected pulse r a t e could be made. The l i g h t - i n d u c e d pulse r a t e s were always observed t o in c r e a s e s u p r a l i n e a r l y w i t h i n c r e a s i n g gate b i a s , showing no s i g n of s a t u r a t i o n . In order t o o b t a i n consistent r e s u l t s when measuring the dark and photon .induced pulse r a t e s i t was found necessary to. operate the devices w i t h a reset d u r a t i o n of 100 msec or longer. With s h o r t e r r e s e t times there was a charging e f f e c t which caused a p o s i t i v e s h i f t i n the gate p o t e n t i a l s re-, q u i r e d t o generate a given s i z e of breakdown pulse ( i . e . , t o reach a given pre-breakdown surface p o t e n t i a l <j> ). The s h i f t i n gate p o t e n t i a l r e q u i r e d s 6 to maintain a constant breakdown pulse s i z e - o f 1 x 10 e l e c t r o n s , c o r r e s -ponding t o an excess gate b i a s of approximately 1 v o l t , i s p l o t t e d as a f u n c t i o n o f the c y c l e time t i n F i g . 4 . 2 0 . S u f f i c i e n t i l l u m i n a t i o n was used to ensure a breakdown every c y c l e . Assuming t h a t a f i x e d amount of charge i s trapped per c y c l e and t h a t the amount of trapped charge decays e x p o n e n t i a l l y w i t h a time constant x between avalanche discharge p u l s e s , the s h i f t i n gate p o t e n t i a l a f t e r many c y c l e s i s expected to be given by, V ( t ) - V (») = V .En exp - i t Ix (A.9) g s g o 1=1 s where V q i s the s h i f t i n gate p o t e n t i a l due t o a s i n g l e discharge. As i n d i c a t e d i n F i g . 4 . 2 0 the observed s h i f t s i n gate voltage can be f i t very c l o s e l y by Eq. ( 4 . 9 ) , w i t h V - 0 . 5 5 V and x = 40 msec. o The charging e f f e c t shown i n F i g . 4 . 2 0 was only observed when the devices were pulsed from a r e s e t c o n d i t i o n corresponding t o d e p l e t i o n or i n -v e r s i o n under the t h i n oxide region of the gate. When pulsed from accumu-l a t i o n no p o s i t i v e s h i f t i n the gate p o t e n t i a l could be detected. I n t e r f a c e s t a t e s cannot be r e s p o n s i b l e f o r t h i s charge t r a p p i n g s i n c e the i n v e r s i o n l a y e r ensures t h a t the only empty l e v e l s a v a i l a b l e t o t r a p e l e c t r o n s l i e very c l o s e t o the conduction band. The detrapping time constant f o r these 145 0.1 I _J I _J I 0 10 20 30 40 PERIODE OF ONE FULL CYCLE t s (msec) FIGURE 4.20 Shift in photogate potential required to maintain a constant output pulse size of 1 x 10^ elect., as a function of the cycle time t . s The solid line shows the "best (visual) f i t to Eq. 4.9. The dashed line shows the shift after one pulse. 146 levels is very short. This then suggests that the electrons are being trapped in the silicon near the interface, in the region that remains in depletion during reset (see section 3 . 2 . 6 ) . Howeverj with charge trapping of this magnitude, and a detrapping time constant of 40 msec, a large in-crease in the avalanche pulse rate would be expected as the reset time is decreased. Such an effect was not apparent. Very l i t t l e , i f any, increase in pulse rate could be detected when going from a cycle time of 1 sec to 5 msec. For this reason i t is believed that the charging effect was due to electron injection into oxide traps near the Si-SiO^ interface. (2 ) Results From Second Fabrication Five test chips (65 devices) were examined from wafer P 2 - 3 . The dark count rates, at a given excess bias were approximately an order of magnitude lower than those obtained with the devices from wafer P l - 4 , however, the variations in dark count rate from device to device were larger. No devices were found with anomalously high count rates and a build-up of negative charge at the Si-SiO^ interface, when operating above breakdown, was not observed with these devices. No shift in the gate po-tential required for a given pulse size could be detected for cycle times as short as 3 msec. The dark and photon-induced pulse rates for two of the better devices are shown in Figures 4 . 2 1 and 4 . 2 2 . The devices had not been thinned so that the rear illumination provided virtually pure electron injection from the neutral bulk. The photon induced count rate in this case should follow the electron avalanche initiation probability Pe(w). The theoretically de-termined probability Pe(w), calculated according to ( 3 . 2 ) - ( 3 . 5 ) and the ionization rate data of Appendix A, is also shown in Figures 4 . 2 1 and 4 . 2 2 . The electric field £(y), was calculated from equations ( 4 . 2 ) - ( 4 . 5 ) , 11+7 100 80 60 u v tn *N •A ••* C -3 o o 40 ui < z O o 20 DEVICE P2-3/4-10 gate area t i 1 i = 20 x 20 vm = 2.0 msec = 10 msec = 6.00 V = 113.4 V dark pulse rate photon induced pulse rate ( dark subtracted ) i * JL £ X _L_ JL X 113 115 117 PHOTOGATE VOLTAGE 119 (volts) 121 FIGURES 4.21 and 4.22 Dark and photon induced pulse rates as a function of the photogate bias for two of the better surface-breakdown devices from the second fabrication. The dashed line indicates the calculated variation of P (w), arbitrarily f i t through the first two experimental points. 11+8 100 DEVICE P2-3/4-12 60 gate area t 1 20 x 20 urn 2.0 msec 10 msec 7.00 V 123.3 V u 60 in *s Ift *y c 3 O v hi < 40 i dark pulse rate photon-induced pulse rate (dark subtracted) I z => O u 20 i / / / J. i. X _l_ J . 123 125 127 PHOTOGATE VOLTAGE 129 (volts) 131 FIGURE 4.22 lU9 using the doping profile data in Fig. l+.ll. Since no absolute experimental triggering probabilities were determined, the theoretical curves were arbitrarily f i t from the observed breakdown voltage (voltage of first de-tectable breakdown pulses) through the first two experimental points. The remaining points deviate by an increasing amount from the theoretical curve. This indicates a large degree of re-triggering, due to either charge trapping or impact ionization of traps, during the periods of avalanche discharge, as discussed in section 3 . 2 . 6 . Provided the traps are not chargedto satur-ation the degree of re-triggering should be roughly proportional to the product of the count rate and the size of the discharge pulses, leading to 4 the type of rapidly increasing count rate observed. The estimated bulk lifetime of 60 ysec reflects predominantly the mid gap trap densities and thus, may not be an indication of the density of those traps responsible for the re-triggering. By taking count rate data i at different temperatures i t may have proved possible to characterize these traps, however, the high, and varied, fields present in the depletion region would greatly complicate the interpretation of such data. It was not thought that, the surface breakdown devices warranted such an investigation, since the likelihood of a successful surface channel PC-CCD is small due to interface state effects. The need to maintain the periphery of the active region in inversion during reset, and the very large inversion layer charge required, severely complicates the design of a low dark count rate surface 9 - 2 - 1 channel PC-CCD. The low mid gap interface state density of 7 x 10 cm eV measured on test wafer P 2 - 5 indicates that the annealing treatment used was nearly optimum and that the observed behaviour was not due to an exception-ally large density of interface states. Any further reduction in the inter-face state density of a PC-CCD, using existing techniques, would be at best an order to magnitude. 150 4.2 BULK BREAKDOWN DEVICES • By introducing a t h i n l a y e r of n-type s i l i c o n between the substrate and the i n s u l a t o r of a p-substrate MOS gate i t i s p o s s i b l e to form a poten-t i a l minimum i n the n-layer, away from the Si-SiO^ i n t e r f a c e ( F i g . 4 . 2 3 ) . In order to accomplish t h i s i t i s e s s e n t i a l f o r the p-n junction to be maintained i n reverse bias so that the t h i n l a y e r of n-type material would be f u l l y depleted i n the absence of any stored charge. This v e r t i c a l 4 structure forms the basis for a buried channel CCD, i n which separate n-regions define the i n d i v i d u a l t r a n s f e r channels. The reverse bias i s pro-vided by a d.c. contact at the output end of each n-type channel. As was the case with a surface channel CCD i t i s p o s s i b l e to pulse the i n d i v i d u a l gates of a buried channel CCD so as t o cause the p-type bulk to be deeply depleted, beyond the point where breakdown would normally occur. With a s u f f i c i e n t l y t h i c k n-layer the p o t e n t i a l minimum w i l l s t i l l be l o -cated away from the i n t e r f a c e i n t h i s deeply depleted c o n d i t i o n , so t h a t , once t r i g g e r e d , the avalanche discharge w i l l be confined to the bulk n-p junction. The f i e l d s at the surface of the semiconductor (where the bands bend upwards), and i n the i n s u l a t o r , can be kept r e l a t i v e l y low provided the n-layer has the correct thickness and doping density. Figure 4 . 2 3 shows the p o t e n t i a l d i s t r i b u t i o n perpendicular to the i n t e r f a c e f o r a bulk break-down MOS gate, and defines the various p o t e n t i a l s and distances that w i l l be r e f e r r e d to. Like the surface breakdown devices, t h i s structure i s s e l f -quenching since the electrons generated during the avalanche c o l l e c t i n the p o t e n t i a l w e l l , thereby reducing the p o t e n t i a l d i f f e r e n c e across the n-p junction. 151 w SiO* after breakdown e breakdown n - silicon p - silicon potential FIGURE 4.23 Potential distribution perpendicular to the surface for a bulk-breakdown MOS gate, before and after breakdown, at breakdown, and during reset. The compensated region containing the stored charge Q resulting from an avalanche discharge is also indicated. 1 5 2 In addition to the much lower oxide f i e l d strengths, and the fact that breakdown now occurs i n the bulk of the semiconductor away from the i n -t e r f a c e , the bulk breakdown MOS structure has the further advantage that c a r r i e r s generated v i a i n t e r f a c e states can no longer t r i g g e r an avalanche. Holes generated at the i n t e r f a c e migrate l a t e r a l l y along the s i l i c o n surface and escape out of the sides of the channel to the p-type bulk where they recombine. Electrons generated v i a i n t e r f a c e states d r i f t through the low f i e l d surface region and are c o l l e c t e d i n the p o t e n t i a l w e l l . Only i f c a r r i e r s are generated on the bulk side of the p o t e n t i a l minimum can an avalanche be triggered. For t h i s reason back-side i l l u m i n a t i o n i s manda-tory f o r a buried channel PC-CCD. Inherent i n the buried channel CCD structure i s the a b i l i t y to c o n t r o l the bulk f r i n g i n g f i e l d s and reduce premature edge breakdown. In order to f u l l y deplete the n-channel the i n d i v i d u a l t r a n s f e r gates must extend com-p l e t e l y across the channel, and out over the p-type substrate. When pulsed above breakdown these gates are p o s i t i v e with respect to the substrate, and hence cause the p - s i l i c o n adjacent to the n-channel t o be depleted, thereby lowering the bulk f r i n g i n g f i e l d s . Reducing the oxide thickness increases the gate voltage required f o r breakdown, which i n turn causes the p-type s i l i c o n on e i t h e r side of the channel to become more deeply depleted. Pro-vided the l a t e r a l n-p t r a n s i t i o n i s not too abrupt, i t should be po s s i b l e to sele c t an oxide t h i n enough to prevent edge breakdown along the sides of the n—channels, but s t i l l s u f f i c i e n t l y t h i c k to prevent breakdown i n the p-type substrate at the edges of the gates. As with the surface channel CCD, high f r i n g i n g f i e l d s i n the charge t r a n s f e r d i r e c t i o n can be avoided by keeping the adjacent t r a n s f e r gate only s l i g h t l y below breakdown. 153 4.2.1 Design Consideration and Equations Although the bulk n-p junction w i l l generally not be abrupt, the re-s t r i c t i o n s on the peak e l e c t r i c f i e l d i n the depletion region, and on the substrate doping, are roughly the same as were determined for the surface 1 5 - 3 breakdown devices.. A substrate doping of'N^ < 7 x 10 cm was therefore also adopted for the bulk breakdown devices. Several factors determine the appropriate thickness and doping of the n-layer. I t i s desirable to mini-mize the dopant concentration (per cm ) i n t h i s layer.as f a r as possible i n order to f a c i l i t a t e long minority c a r r i e r l i f e t i m e s and low trap densities, but, at the same time, the dopant dose (per cm ) must be high enough that the potential minimum i s located away from the interface when the gate i s deeply depleted. On the other hand, i f the dopant dose i s too great the f i e l d s at the interface w i l l be very high during.charge t r a n s f e r , and the s i l i c o n may break down at the surface. I t i s also desirable to minimize the junction curvature at the edges of the n-region ( i . e . , use a deep n-layer) as t h i s relaxes the problem of co n t r o l l i n g edge breakdown along the sides of the n-channel. Also a high junction curvature may cause the n-channel to breakdown prematurely at the output and, before the channel depletion volt-, age i s reached. In order to arrive at some actual quantitative s p e c i f i c a t i o n s for the n-layer and the oxide thickness, i n i t i a l guesses were made on the basis of the above considerations, and then modified according to the results of one dimensional calculations of the potential and f i e l d d i s t r i b u t i o n s normal to the surface. The required gate voltages i n deep depletion were determined by calculating the avalanche i n i t i a t i o n p r o b a b i l i t y P (w) according to e equations (3.2) - (3-5) and the ion i z a t i o n rate data i n Appendix A. The equations required to calculate the potential and f i e l d d i s t r i b u t i o n s were obtained as follows. 15k The p o t e n t i a l s and distances used i n the f o l l o w i n g d e r i v a t i o n are defined i n F i g . k.23. Using the depletion'approximation, the Poisson equations f o r the i n s u l a t o r , the n-type top l a y e r and the p-type s u b s t r a t e become d2<f> (y) — i r - = 0 - - d o x±yio (A.. 10) dy 2 d <(> . (y) / \ — ^ " = - ^  , 0<y (4.11) dy s where p(y) i s the volume charge d e n s i t y i n the s i l i c o n as- a f u n c t i o n o f the •distance from the S i - S i O ^ i n t e r f a c e , and d» and i> .. are the e l e c t r o s t a t i c 2 ox s i p o t e n t i a l s i n the i n s u l a t o r and i n the s i l i c o n , r e s p e c t i v e l y . The e l e c t r o -s t a t i c p o t e n t i a l of the substrate i s taken .to be 0 . The boundary c o n d i t i o n s needed to solve (1+.10) and (l+.ll) are •ox(-dox) = v g ; • ( 4 - 1 2 ) W 0 ) = * s i ( 0 ) = *s <4'13> d<j> (0 ) d(f. . ( 0 ) ox T s i . ... e. — = e — 5 (4.14) 1 dy s dy <|>si(w) ==• 0 (4.15) d<f> .(w) - f ~ = 0 (4.16) By u s i n g p a r t i a l i n t e g r a t i o n and the boundary c o n d i t i o n s (U . 1 2 ) - ( U . l 6 ) <f> (y) and <j> .(y) can be expressed as ox s i * (y + a ) ; w ox ox g e i p(y) dy (4.17) 155 1 Jw p(y) dy - yp(y) dy (4.18) 'w while the electric field in the silicon becomes w p(y) dy (4.19) s ' where w may be determined by an iterative procedure from boundary condition (4.13), which becomes w w j [ yp(y) dy + -f^ s i J p(y) dy - V = 0 g (4.20) The position of the potential minimum y^ can likewise be determined from Vm p(y) dy = 0 (4.21) w The normal procedure for generating the n-layer is to ini t i a l l y pre-dope the surface by ion implantation (or a low temperature furnace predeposi-tion) and then drive the dopant in at a high temperature. The resulting doping profile in this case is approximately Gaussian, and p(y) becomes P(y) = 9. N(0) exp -(y/e) - 9.N. ( 4.22) -3, where N(0) is the surface concentration of the n-layer dopant (cm ) and N is the bulk acceptor doping density. The parameter 6 is related to the junction depth according to 6 = y [In 1(0) - In N j " ^ (4.23) Approximating the doping profile by (4.22) enable the integrals appearing in (4.17) - (4.21) to be replaced by 156 b b P ( y ) d y = N(0) 3 e r f ( y / 3 ) - N Ay} a • b 2 N y 2 b yp(y) dy = {N(0) | [1 - exp - ( y / B ) 2 ] - -§- } (A.24) (4.25) On the b a s i s of the one dimensional c a l c u l a t i o n s the f o l l o w i n g s p e c i f i c a t i o n s w e r e determined f o r the oxide t h i c k n e s s , n-channel j u n c t i o n depth, and n - l a y e r surface c o n c e n t r a t i o n to be used w i t h a s u b s t r a t e 1 5 - 3 doping of = 7 x 10 cm : d = 0.5 ym ox y^ = 2.0 urn N(0) = 3.2 x 1 0 l 6 t o 4.0 x 1 0 l 6 cm" 3 An oxide t h i c k n e s s of 0-5 ym was chosen as t h i s i s the minimum th i c k n e s s p e r m i s s i b l e due to processing c o n s t r a i n t s t h a t are' discussed i n the next s e c t i o n . The j u n c t i o n depth was r e s t r i c t e d t o 2 ym because the maximum temp-erature of the d r i v e - i n furnace was l i m i t e d t o 1150°C, and t o d r i v e the n-l a y e r i n much f u r t h e r would have r e q u i r e d very l o n g d r i v e - i n times. A l s o , i f the n-layer i s deeper the surface c o n c e n t r a t i o n must be lower, and con-t r o l over the u n i f o r m i t y of t h i s d i f f u s i o n becomes more d i f f i c u l t . 4.2.2 Test S t r u c t u r e Design and F a b r i c a t i o n The b ulk breakdown device used i n t h i s i n v e s t i g a t i o n i s shown i n F i g . 4.24. I t i s b a s i c a l l y the same as the previous surface breakdown t e s t s t r u c t u r e shown.in F i g . 4.4, except that a n - d i f f u s i o n now defines the t r a n s f e r channel and only a s i n g l e t h i c k n e s s . o f oxide i s used. The a d d i t i o n -a l n+ and p+ d i f f u s i o n s are r e q u i r e d i n order to make good ohmic contacts t o the n-channel and p-substrate. Because of the s i m i l a r i t y o f the two device s t r u c t u r e s i t was p o s s i b l e to f a b r i c a t e the bulk breakdown t e s t 157 o J 1 f \ — > \ (b) c ft) •» o . a. j I V. V. charge transfer to output diode (0 FIGURE 4.24 Bulk-breakdown, charge-transfer test device ( a ) vertical structure. Layout is identical to the surface-breakdown test device shown in Fig. U.4 (b) potential well diagram in deep depletion, before breakdown (c) during reset, charge transfer 158 structure using the existing masks. Double exposures (to two different masks) were required to define the n+ and p+ diffusions and to etch the n+ and p+ contact windows. The fabrication sequence for the bulk breakdown devices is illustrated in Fig.. U.25 and the processing details are listed in Table h.k. As before, the devices were fabricated on 2.2 - 2.5^ cm boron doped (100) Czochralski wafers with chemo-mechanically polished front surfaces. The back sides, however, had a rough, sand-blasted surface fin-ish. This heavily damaged layer of silicon getters lifetime-degrading im-purities from the bulk silicon during device processing. The heavy phos-phorus concentration introduced into the back side during the n+ contact predeposition also helps to getter impurities. A l l dry oxidations were carried out with HC1 added to the oxidation atmosphere. The fabrication again calls for an Al-Al^^-Al double level metali-zation. However, there are no MIS contacts this time so that the contact sinter and hydrogen anneal may be performed as a last step in the device processing, thereby avoiding any anodization problems due to hillock formation in the first level of aluminum. Also, the interlevel vias are opened by selectively etching the A l ^ ^ anodic oxide layer [94], rather than masking these areas with positive resist during the anodization. The maximum forma-tion voltage is then only restricted by the electrolyte used, and by the thickness of Si02 over the areas of the wafer that are exposed to the electro-lyte but not covered with aluminum. Bare areas of silicon exposed to the electrolyte were avoided by opening the p+ and n+ contact windows in separ-ate operations (see Fig. k.25). The 25 w/o APB-EG electrolyte used can sup-port anodization up to 350 V before side reactions start to occur [112]. A formation voltage of 220 V was chosen for device fabrication to ensure that the anodic oxide would support a 100 V potential difference between the two gate levels. The SiO gate oxide must then be at least 0.5pm thick to pre-159 vent anodization of the silicon. Considerable difficulty was encountered in controlling the low temp-erature phosphorous predeposition used to form the transfer channels. Initial tests, conducted to determine the best combination of predeposition temperature and time, indicated that achieving the desired dopant concen-tration would be somewhat of a hit or miss operation, due to the poor temper-ature stability of the phosphorous predeposition furnace after loading the wafer boat. Ideally the channel should have been pre-doped by ion implanta-tion and then simultaneously annealed and driven in; however, an ion-implant-er was not readily available. Instead an attempt was made, to fabricate some successful test devices by using a furnace predeposition, and processing several wafers with different doping times. -Nine wafers {M.6h - WJ2) were processed. During the n-channel pre-deposition step the wafers were split into three groups and given 8 , 12, and 20 minute predepositions as T80°C. Four point probe resistivity measurements, conducted after the drive-in and the removal of a l l masking oxides, indicated that only wafers M 6 5 , 6 6 , 72 (20 min. predep.) had re-ceived sufficient phosphorous dopant, and that even these had a more lightly doped n-channel than desired. The incorrectly doped wafers were continued along with the good wafers and used for testing during the aluminum anodi-zation and via etch. M72 was inadvertently destroyed while spin drying, during a later RCA clean. Selectively etching the anodic Al^O^ to form the interlevel vias, also proved to be very difficult. The negative resist used (Waycoat 200 negative) could not withstand the 80°C CrO^/phosphoric acid etch for more than about 10-15 minutes before l i f t i n g , while the Al^O^ etch rate was much lower than expected, requiring approximately 10 min. for complete removal of the 220 V films. Also, the end point could not be determined visually: i6o only by probing the v i a areas very g e n t l y and measuring the e l e c t r i c a l r e s i s t a n c e t o the u n d e r l y i n g aluminum was i t p o s s i b l e to determine the com-p l e t i o n o f the etch. The good device wafers (M65,66) were given a 10 min v i a etch a f t e r which probing i n d i c a t e d that bare aluminum had been exposed. However, a f t e r d e p o s i t i n g the second l e v e l o f aluminum i t was discov e r e d t h a t the A1,,0 had not been completely removed. Apparently the contact probe must have broken through' a t h i n remaining l a y e r of oxide. Unfortun-a t e l y , since the n+ contact windows had already been opened, i t was not p o s s i b l e t o simply remove a l l the aluminum and Al^O^ and repeat the metal-i z a t i o n procedure. Instead i t was a l s o necessary t o remove the SiO^ gate oxide and r e - o x i d i z e the wafers. T h i s , however, consumed a s i g n i f i c a n t p o r t i o n of the n-channel and f u r t h e r reduced the channel doping (cm ). On the second attempt at et c h i n g the Al^O^ v i a s , the CrO^/phosphoric a c i d etch was followed by an etch i n s t r a i g h t phosphoric a c i d at 50°C u n t i l bubbles could be observed (approximately 2 min), i n d i c a t i n g that the u n d e r l y i n g aluminum was being etched and that the Al^O had been completely removed. Only wafer M66 was s u c c e s s f u l l y completed i n t h i s way. The r e s i s t l i f t e d on M6p during the CrO^/phosphoric a c i d etch. Table U.5 l i s t s the various thickness and doping parameters measured on wafer M66 at the completion of the processing. The f i n a l n -layer dopant dose (cm ) was c o n s i d e r a b l y low-er than-desired but i t was f e l t t h a t the devices would s t i l l be o p e r a t i o n a l above breakdown. phosphorous i i masking oxidation - phosphorous predep boron 1 n - channel 2. n-channel drive in an oxidation - boron predep. phosphorous 3. oxidation - phosphorus predep. gate oxide /•:•• ,. ,•. , 1 . 1 1 \ n" k. strip a l l oxides - gate oxidation - open substrate contacts. v. _ ' • " / 5. deposit and pattern first level of Aluminum j g W ^ F ^ ^ & W ,,„,,„ „,(E^\,,,, „ , ,,,,, * P I \ n" ^_ 2.-'/ >• * v ; s 6. Aluminum anodization and via etch. , . • • - , , J ^ U V ^ 7- open n channel contacts. 8. deposit and pattern second level of Aluminum plus anneal. FIGURE 4.25 Fabrication sequence for the bulk-breakdown test devices ON H 162 TABLE 4.4 Processing Details For The Bulk Breakdown Devices Step Operations Details i n i t i a l clean n masking oxide channel window etch channel predep. hot xylene with ultrasonic agitation RCA clean temp, cycle: 1150°C 30 min 0, c 5 min Nr oxide thickness, 0.10 urn neg. resist, mask 1 buffered HF resist strip, hot B^SO^/H^ RCA clean temp. T80°C source POCl^ pass over, 15°C boat and tube predoped at 1050°C for 1 h slices cycle: M6T, 69, TO 5 min N 8 min N slices cycle: slices cycle: TO + 3% °2 + 3% °2 + 3% °2 71 + 3% °2 + 3% °2 + 3% °2 12 + 3% °2 + 3% °2 + 3% °2 M6U, 68, Tl 5 min L2 min N2 5 min N 2 M65, 66, T2 5 min N2 20 min N 2 5 min N2 phosphorus glaze strip, 10$ HF, 15 sec. HC1/H202 part of RCA clean 163 TABLE 4.4 cont'd. Step Operations Details n drive-in and a temp. . 1150°C oxidation cycle: 2U5 min Q>2 + 3% HC1 kO min 0^ + H 2 10 min N2 + p diff. window - neg. resist, masks 2+5 (double etch exposure) - buffered HF p - resist strip, hot H SO^ /H 0 - RCA clean + p pre-dep temp. 1000°C source BBr^ pass over, 15°C cycle: 5 min N 2 + 3% 0 2 5 min( N2 + 3% 0 2 + Source N, 30 min N 2 + Source N 2 5 min N 2 - boron glaze stripy HF/H 0( l : l ) , 30 sec - HC1/H202 part of RCA clean p + drive-in and a temp. 1100°C oxidation cycle: . 5 min 0 2 120 min 0 2 + H 2 ' 5 min N2 3 n + diff. window etch - neg. resist, masks 2+3 (double 2 exposure) - buffered HF - resist strip, hot H SO^ /H 0. - RCA clean 161+ TABLE 4.4 cont'd. Step Operations D e t a i l s 3 cont'd n+ pre-dep. temp. 1050°C source POCl^ pass over, 15°C c y c l e : 5 min N 2 + 3% 0 2 20 min N 2 + 3% 0 2 + Source N 2 15 min N 2 + 3% 0 2 s t r i p a l l masking - HF/H 20(1:1) oxides - HC1/H"202 part o f RCA cle a n gate o x i d a t i o n a temp. 1150°C c y c l e 3 min 0 2 1+0 min 0 2 + R"2 30 min 0 2 + y % HCl 10 min N 2 1+ + p contact window - neg. r e s i s t , masks 2 + 5 (double etch exposure) - b u f f e r e d HF - r e s i s t s t r i p , hot H 2S0^/ H 0 2 etch o f f back side - white etch ( f r o n t p r o t e c t e d w i t h wax) + n l a y e r - hot t r i c h l o r e t h y l e n e - hot H 2S0 u/H 20 2 - RCA clean aluminum evap. I - tungsten f i l a m e n t evap. substrate temp. 250°C evap. r a t e 150 2sec ^ 5 - f i l m t h i c k n e s s 1.2 ym aluminum etch I - neg. r e s i s t , mask 3 p h o s p h o r i c / n i t r i c etch,60 C r e s i s t s t r i p , M i c r o s t r i p 16 5 TABLE 4.4 cont'd Step Operations D e t a i l s a n o d i z a t i o n : e l e c t r o l y t e , 25 w/o APB-EG c u r r e n t , 1 mA cm ^ formation v o l t a g e , 220 V 6 v i a etch soak time at 220V, 5 min - neg. r e s i s t , mask k - CrO /H PO e t c h , 80°C, 10 min . 0 - phosphoric e t c h , 50 C, 2 min r e s i s t s t r i p , M i c r o s t r i p 7 + n contact window - neg. r e s i s t , masks 2 + 3 (double etch exposure) - b u f f e r e d HF - r e s i s t s t r i p , M i c r o s t r i p aluminum evap. I I - tungsten f i l a m e n t evap. sub s t r a t e temp. 2 5 0 ^ 0 evap. r a t e 150 Xsec ^ - f i l m t h i c k n e s s 1 . 0 ym 8 aluminum etch I I - neg. r e s i s t , mask 5 - phosphoric e t c h , 60°C - r e s i s t s t r i p , M i c r o s t r i p contact s i n t e r temp. 1J00°C plus anneal c y c l e : 60 min H^ Quartz furnace tube and boat pre-cleaned w i t h O^/HCl gas flow f o r 2 hours, p r i o r to l o a d i n g devices. 166 TABLE 4.5 Data f o r Wafer M66 Bulk resistivity (before processing) 2.1+2 ficm a 15 —3 Substrate doping 5-8 x 10 cm Channel doping (surface concentration) 3.0 x 10 cm Junction depth (from bevel and stain) 1.63 um Oxide thickness (from colour) . 0.52 ym Channel breakdown voltage -65 V Determined from low temperature deep depletion C-V data using the shield gate of the operational devices (see Appendix C). b Determined from four point probe resistivity measurements and the junction depth, assuming a Gaussian profile for the n-layer. 16 7 4.2.3 Two Dimensional Modeling of the Completed Devices Unlike the surface breakdown devices i t was not c e r t a i n that the bulk breakdown devices could be operated i n such a way as to completely eliminate premature edge breakdown. This i s due to the l i m i t e d voltage range over which the t r a n s f e r gate can be operated. I t must, at a l l times, be suf-f i c i e n t l y negative with respect, to the channel output to ensure complete depletion of the n-layer. The degree of depletion i n the bulk s i l i c o n under the t r a n s f e r gate i s , therefore, l i m i t e d by the breakdown voltage of the channel output diode. In order to compare the experimentally observed pulse rates with those predicted from the theory i t i s necessary to have some idea o f the p o t e n t i a l d i s t r i b u t i o n i n the bulk breakdown structure and the uniformity of the breakdown voltage. The approximate two dimensional model shown i n F i g . Dl (Appendix D) was used f o r t h i s purpose. A zero gate separation was used and the t r a n s f e r gate and n-layer were assumed to be i n f i n i t e i n extent. The l a t e r assumption i s j u s t i f i e d because v a r i a t i o n s i n the doping p r o f i l e and degree o f depletion, at distances greater than 10 ym (the t r a n s f e r gate width) from the edge of the breakdown region, have a n e g l i g i b l e e f f e c t on the p o t e n t i a l d i s t r i b u t i o n under the photogate. A zero gate separation i s j u s t i f i e d , since the actual gate separations (0.25 ym) are more than an order of magnitude l e s s than the depletion region width and are not ex-pected to s i g n i f i c a n t l y a l t e r the p o t e n t i a l d i s t r i b u t i o n or the peak break-down f i e l d s away from the Si-SiO^ i n t e r f a c e . The use of zero gate separations does, however, r e s u l t i n higher l a t e r a l f i e l d s at the surface of the s i l i c o n , i n the t r a n s i t i o n region from one gate to the other. The p o t e n t i a l d i s t r i -bution under the photogate (across i t s 20 ym width) and under the t r a n s f e r gate on e i t h e r side was c a l c u l a t e d by the method described i n Appendix D. The depletion approximation was used i n order to l i n e a r i z e the two dimen-168 sional Poisson equations and make possible an analytical solution. A Guassian doping profile was assumed, enabling the integrals to be replaced by (J+.2U) and (U.25). The following parameters were used to model the devices from wafer M66 . T = 80 K NA = 5-8 x 10 1 5 cm-3 1 6 "3 N(0) = 2.7 x 10 cm-3 d = 0.52 ym ox -y = 1.63 urn • N(0) has been adjusted slightly from the measured value (Table U.5) in order to obtain agreement between the calculated and observed n-layer depletion voltage. Figure k.26 shows the resulting potential distribution for V = 100 V. A transfer gate voltage of = hO V relative to the substrate was used as this is close to the maximum allowed with a channel output breakdown voltage of 65 V. The avalanche initiation probabilities ^(o) a n < i ^ e ( w ) a s a function of position x under the photogate are shown in Fig. k.27. These quantities were obtained by integrating equations (3.2) - (3.5). along the lines (a) - (g) shown in Fig. 26, as described in Appendix D. The posi-tion x refers to the starting position of the carrier involved: The avalan-che initiation probabilities for photogate voltages of 103V and 108V are also shown. These results indicate that premature edge breakdown has not been completely eliminated; however, the calculated increase in avalanche in-itiation probability towards the edge of the photogate corresponds to only a 3% increase in the peak field. Since the uniformity of the triggering probability improves as the gate is biased farther above breakdown, this degree of premature edge breakdown is not expected to be important in a SiO, ov 0 potential minimum at surface T p- silicon Ijjm (vertical scat*) 1 I L_ OV 10 LATERAL POSITION X (urn) FIGURE 4.26 Two-dimensional potential distribution under the photogate for V =100 V and V T= kO V. The lines along which the avalanche initiation probabilities shown in Fig.' k.21 were calculated, are also shown. O N vo i 1— r— 1 1— 1 1 1 1 r 0 2 4 6 8 10 LATERAL POSITION UNDER PHOTOGATE X (|im) FIGURE 4.27 Results of the two-dimensional c a l c u l a t i o n of the v a r i a t i o n of the avalanche i n -i t i a t i o n p r o b a b i l i t y with p o s i t i o n under the photogate, T = 80 K. Points a - g f o r the 100 V data correspond t o the f i e l d l i n e s a - g i n F i g . 4 . 2 6 . 171 PC-CCD. As regards the t e s t d e v i c e s , however, i t means th a t the measured photon induced pulse r a t e s can no longer be used t o determine P (w) versus e excess b i a s d i r e c t l y . I n i t i a l l y the r a p i d i n c r e a s e i n pulse r a t e i s due p r i m a r i l y to the i n c r e a s i n g e f f e c t i v e t r i g g e r i n g area. At higher excess biases the i n c r e a s e i n photon induced pulse r a t e f o l l o w s P (w) more e c l o s e l y . As was discussed i n s e n t i o n 4 . 2 . 1 , the f i n a l n - l a y e r dopant dose on wafer ¥.66 was lower than d e s i r e d . As a consequence o f t h i s t h ere i s a region around the edge o f the photogate where the p o t e n t i a l minimum i s l o c a t e d at the i n t e r f a c e r a t h e r than i n the b u l k . As the photogate i s bi a s e d f u r t h e r above breakdown t h i s region extends inwards. The c a l c u l a t e d extent f o r V = 100 V and V m = 1+0 V i s i n d i c a t e d i n F i g . 1+.26, however, g T i t s width i s s e n s i t i v e t o the n-channel doping, parameters used so t h a t i t i s not c e r t a i n how wide t h i s r e g i o n i s i n the a c t u a l t e s t devices. Although holes generated by i n t e r f a c e s t a t e s are able to t r i g g e r breakdowns when the n-channel i s too l i g h t l y doped, t h e i r c o n t r i b u t i o n to the dark pulse r a t e should be very s m a l l . This i s because the i n t e r f a c e remains depleted o f el e c t r o n s and holes during reset so that the i n t e r f a c e s t a t e s remain f i l l e d to approximately mid gap. Since the f i e l d s i n the s i l i c o n are very low at the i n t e r f a c e , the steady s t a t e generation r a t e - 1 -2 of holes should be w e l l below 500 sec cm (see s e c t i o n 3 .2.3) . Subsequent to an avalanche discharge the i n t e r f a c e s t a t e s above mid gap are a l s o f i l l e d w i t h e l e c t r o n s so tha t the hole emission r a t e i s t e m p o r a r i l y reduced even f u r t h e r . With a c o r r e c t l y doped n-channel there i s s t i l l a region at the edge of the photogate where the p o t e n t i a l minimum i s at the i n t e r f a c e , how-ever, i t i s very narrow and l i e s w e l l o u t side the area where P (o)>0. 172 4.2.4 Experimental Results and D i s c u s s i o n The y i e l d o f o p e r a t i o n a l devices on wafer M66 was very low. This was p r i m a r i l y due to misalignment between masking l e v e l s , p a r t i c u l a r l y the two metaliza.tion masks and the v i a mask, and t o p i n h o l e s i n the SiO^ and Al^O^ oxides. The misalignment was a r e s u l t o f the r a t h e r l a r g e fcUym) step and repeat e r r o r s on the masks themselves and not due t o alignment e r r o r s during the p h o t o r e s i s t operations. Out of the 80 t e s t d i e 10 were found upon v i s u a l i n s p e c t i o n t o be c o r r e c t l y a l i g n e d . These 10 d i e were packaged and f u r t h e r t e s t e d f o r f a t a l defects such as i n t e r l e v e l shorts or shorts t o the substrate. This reduced the number of good t e s t d i e t o k. The f i r s t device t e s t e d at high voltages s u f f e r e d a d e s t r u c t i v e breakdown of the Al^O^ l a y e r , r e s u l t i n g i n a short between the t r a n s f e r gate and the f i e l d gate. The remaining 3 t e s t d ie ( l 8 devices) were f u l l y o p e r a t i o n a l above breakdown. The f o l l o w i n g operating voltages were used f o r the above breakdown device t e s t i n g ( s e e F i g . k.2h): v ^ = -6ov sub V , = 0 V (Amu. v i r t . gnd.) out -V = -75 V sh V T = -30 V V = -32 to +58 V p The measured f l a t band'voltage was -2.0 V on both the p-substrate and the n-channel. Charge t r a n s f e r to the channel output takes place at the end of the negative-going photogate reset pulse. I n t e g r a t i o n of the channel current was, t h e r e f o r e , s t a r t e d during the negative-going ramp, at V = -20 V. Figure 4.28 i l l u s t r a t e s the t i m i n g used and the t y p i c a l output pulses ob-6 — l tained. A rasp r a t e of 5 x 10 Vsec was used on both the positive and negative-going drive pulse edges. The f i r s t detectable breakdowns under the photogate occurred at 173 .A. active phase |< t „ (0.5-10 msec) integ. level I . . . . I < t p (0.1-20 msec) reset transferred charge due to breakdown during previous active phase. — | |V-tn - f i ~ tegrate ( 50-100 jusec) • hold ( 0.05 - 20 msec) •Vgb-60V (a) (b) (O 45V '(d)' FIGURE 4.28 Test waveforms and timing for the bulk-breakdown, charge-trans-fer devices. ( a ) high voltage driver (photogate) (b) output of the current to voltage amplifier, Channel output current. (c) output of the preset integrator (d) discriminator output, threshold = 0 V Ijk approximately = +kl V (a gate potential of V g = .101'V relative to the substrate), in reasonable agreement with the value for V . predicted from go the two-dimensional calculations.. The photogate voltage could be extended to approximately +58 V before the p-type bulk under the 10 ym wide line connecting the photogate to its bonding pad also started to break down. Be-cause the shield gate is biased so as to accumulate the p-substrate, the photogate interconnect line first breaks." down at the point where i t steps up over the shield gate (see Fig. -U.U(a)). In contrast to the surface breakdown devices, the pulse height dis-tribution for the bulk devices was very sharply.peaked at a l l photogate biases except those very close to V Typically the pulse heights varied by less than + 1 0 $ .(total variation) except for the odd low pulse that was assumed to be due to a discharge occuring during-the rising or falling edge of the drive pulse. The dark pulse rates showed considerable variation over the 1 8 oper-ational devices. A l l of the devices, however, had dark pulse rates that were considerably lower than those of the previous surface breakdown de-vices, in spite of the fact that the measured bulk lifetime (after process-ing) for wafer M66 was approximately 5 ysec, a factor of 10 lower than for the surface breakdown devices. The bulk lifetime was estimated from the room temperature leakage current of the n-p channel junction (60 nA cm at 20 V reverse bias) and from room temperature charge collection measurements under the photogate. Both methods gave essentially the same bulk lifetime. Out of a l l 1 8 devices, two in particular exhibited dark pulse rates that were a factor of two lower than the rest, devices M66/2-1 and M 6 6 A - 3 . The majority of the dark and photon-induced pulse rate measurements were made on device M66/2-1. As before, a l l of the pulse rates presented and referred to in the following discussion are those obtained after correcting for dead time 175 and temporal sampling effects. At any given excess gate bias i t was found that the dark pulse rate decreased i f the duration at or above breakdown t (see Fig. It. 28) was in-creased while holding the reset duration t constant. This result is shown r in Fig. It. 29. The dark pulse rates have been plotted as a function of l / t , i.e., the number of resets per second of active time. It is apparent that the dark pulse rate increases linearly with the number of resets. The lim-it - 1 —2 iting dark pulse rate at (l/t ) = 0 is approximately 2 x 1 0 sec cm at cL (V - V , ) = 1 0 V, only a factor of ho larger than the desired maximum dark count rate. In accordance with the above result i t was also found that the dark pulse rate increased to a limiting value as the reset duration was in-creased, while holding t constant, Fig. it. 30. a In order to obtain further insight into the mechanism responsible for the dark pulse rate, a heater was installed on the end of the liquid nitrogen heat pipe, enabling operation up to lUO K. The results of dark pulse rate measurements at 8 0 K , 1 0 0 K , 1 2 0 K , and lltOK are presented in Figures It. 31(a) and (b). Over this temperature range there was essentially no variation in the limiting dark count rate (i.e., when operated with short reset times, t = 0 . 1 msec, and long active times, t = 1 0 msec), as shown in Fig. It. 31 (a). Furthermore, the rapid increase in pulse rate with increasing gate bias always started at the same gate bias even though the breakdown voltage had increased by approximately 5 volts from 8 0 K to lltOK. This temp-erature independent supralinear behaviour of the dark pulse rate strongly suggests a tunneling mechanism for the dark generation of triggering carriers. The dark generation at V = 117 V, however, is approximately S eight orders of magnitude higher than the rate obtained by extrapolating Haitz's [36] interband tunneling data according to Eq.(3.56), as described in section 3.2.5. For this reason i t is believed that the tunneling genera-176 (No. resets / sec. active time) FIGURE 4.29 Dark pulse rate as a function of l / t . (i.e., as a function of the number of resets per sec. of active time) for a fixed reset duration of t = 0.1 msec, r — , DEVICE M66/2-1 t Q = 1.0 msec T = 80 K 5 1 ^ — — \ / I .1 I I / ^ - o — ° o o J L P , . . _ { 5 t"/ Vp =43V . o „ _ _ n o — p 5 5 O 1 2 3 4 RESET DURATION t p (msec) FIGURE A.30 Dark pulse r a t e as a f u n c t i o n o f the r e s e t d u r a t i o n f o r a f i x e d d u r a t i o n above breakdown of t = 1.0 msec a 178 T 1 1 r DEVICE M 6 6 / 2 - 1 t r = 0.1 msec u w c ' 3 O ^ 1 Ul < cc z o o o 10.0 msec 140 K O o _J_ 120 K 100 K 60 K 101 105 109 PHOTOGATE BIAS 113 (volts) 117 FIGURE 4.31 (a) Dark pulse rate as a function of the photogate bias and substrate temperature. The x's mark the approximate breakdown voltage. t =0.1 msec r , t =10.0 msec a 179 8 0 8 4 o 0 m « •» c § 8 u ui $ 4 z 8 0 12 8 L 4 U 0 * -101 - T 1— r DEVICE M66/2-1 t r = 1.0 msec t „ = 1.0 msec JL O o H 140 K O o H 120 K O 100 K ° 60 K 105 109 PHOTOGATE BIAS 113 1.17 Vg (volts) FIGURE 4.31 (b) t =1.0 msec r , t = 1.0 msec a 180 tion of triggering carriers is occurring through deep traps. The observed generation rates are in general agreement with those extrapolated from Sah's [54] data, according to equations (3.5T)-(3.62), provided a mid gap trap 12 13 -3 density of 10 -10 cm is assumed. Such a density of mid gap levels is consistent with the 5 usee bulk lifetimes measured on wafer M66 . Referring back to Fig. h.29 i t can be seen that the increase in pulse rate- with decreasing t is such as to maintain a constant ratio between a the pulse rates at different gate biases. This implies that the increase in dark generation is due to a change in the occupancy of those traps involved in the tunneling, leading to an enhanced tunneling emission rate of either electrons or holes following the reset. This conclusion is substantiated by the lack of any strong temperature dependence of the dark pulse rate when operating with long (l msec) reset times and shorter ( l msec) active times, Fig. k.31(b). The slight decrease in dark pulse rate with increasing temperature, seen in Fig. k.31(b), cannot be explained at present, nor has • it been possible to envisage a mechanism whereby the occupancy of the traps involved in the tunneling generation changes during reset so as to in-crease the subsequent generation rate. The problem is basically that the conditions during reset are not sufficiently different from those above breakdown to make possible a large change in. occupancy. The entire high field region remains in depletion during reset and the peak field is less than a factor of 1.5 lower than in the deeply depleted condition. Figure U.32 shows the red gallium arsenide phosphide LED.source used to make the photon induced pulse rate measurements. Light emerging from the 500um dia pinhole on the integrating sphere was imaged at 10 times reduction on to the rear of the 300um thick devices, using an f/2 l 6 mm lens. A photo-diode mounted in the integrating sphere was used to monitor the light inten-sity. . An absolute calibration of the number of photogenerated electrons per 00 182 second reaching the edge of the photogate d e p l e t i o n region from the n e u t r a l bulk was determined from charge i n t e g r a t i o n measurements. For these measure-ments the devices were operated i n the charge i n t e g r a t i o n mode w i t h the f o l -lowing gate p o t e n t i a l s : V . sub = -30 V V out = 0 V (amp. v i r t . gnd. ) V s h = -1+5V VT = -1+5V V = -1+7 t o +20V P By op e r a t i n g the t r a n s f e r gate at -15V r e l a t i v e t o the s u b s t r a t e the e f f e c t i v e c o l l e c t i o n area i s r e s t r i c t e d to the area of n-channel under the photogate and t r a n s f e r gate. The p-substrate around the n-channel i s h e l d i n accumulation at the surface by the t r a n s f e r gate, thus p r o v i d i n g a b a r r i e r to the photogenerated c a r r i e r s c o l l e c t e d i n the surface d e p l e t i o n r e g i o n outside t h i s area. The e f f e c t i v e c o l l e c t i n g area, measured under an o p t i c a l microscope, was 1+5 urn x 65um. The measured area of the photogate was 22ym x !+2um, 31.6% of the effective c o l l e c t i n g area. 60 min. integrations were made using the same l e v e l of i l l u m i n a t i o n as was used for the above-break-down tests. The measured s i g n a l v o l t a g e s were converted t o a charge measure-ment using the c a l c u l a t e d gain of the current a m p l i f i e r i n t e g r a t o r combina-t i o n . 60 min dark i n t e g r a t i o n s r e s u l t e d i n zero measurable charge. Figures 1+. 33(a) - (c) show t y p i c a l examples of the photon induced pulse r a t e f o r the f o l l o w i n g three operating c o n d i t i o n s : • (a) t = 1.0 msec, t = 0.2 msec . a r (b) t = 10.0 msec, t =' 0.2 msec a r (c) t = 1 . 0 msec, t ^ = 2 0 . 0 msec The i n j e c t i o n l e v e l obtained from charge integration measurements, as- des-c r i b e d above, i s i n d i c a t e d i n each case. The i n d i c a t e d u n c e r t a i n t y i n t h i s 183 70 60 50 ~ 40 u M c 3 O £ 30 < I 20 O o r~ DEVrCE *r T 1 M66/2-1 0.2 msec 1.0 msec 60 K measured injection level -2.—\ZZ-\-2-\-Z-ZZ—ZZ — Z2 light (dark subtracted) meas. inj. level 10 • light (dark subtracted) dark • „ o ° 100 104 PHOTOGATE BIAS 108 Vg (volts) 112 FIGURE 4.33 (a) Dark and photon induced pulse rates as a function of the photogate bias f o r device M66/2-1. The measured i n j e c t i o n l e v e l i s from charge i n t e g r a t i o n measurements below breakdown. t = 1 . 0 msec a , t = 0 . 2 msec r « 184 4.0 S 2.0 in to c o U Ul < •z 3 1.0 O O i 100 FIGURE 4.33 (b) > J I light (dark subtracted) I dark § S 104 108 PHOTOGATE BIAS Vg (volts) i 112 t = 10.0 msec a , t = 0.2 msec ' r 185 70 60 DEVICE M66/2-1 20.0 msec 1.0 msec T s 80 K 50 u m c : 40 measured injection level i I i & 30 111 0E light (dark subtracted) § 20 O O 10 L dark - a . o _L 100 104 PHOTOGATE BIAS 108 Vg (volts) 112 FIGURE 4.33 (c) t = 1 . 0 msec , t = 20.0 msec a * -v. 186 level reflects the level of noise in the charge, amplifier only, and not the uncertainty in the estimated ratio of collecting area to photogate area. Initially the photon induced pulse rate begins to saturate with increasing photogate bias as expected, however, at approximately V - V = 7 V the g gb increase turns supralinear.. Up to that point the level to which the pulse rate appears to be saturating is in reasonable agreement with the measured injection level. As with the surface breakdown devices the supralinear" behavior of the photon induced pulse rate at high excess gate biases is attributed to either carrier capture by traps or impact ionization of the traps, during the periods of avalanche discharge. By comparing Figures k.33(a) and (c) i t can be seen that the supralinear behavior of the photon induced pulse rate changes very l i t t l e as the reset duration t is increased from 0.2 msec to 20.0 msec. This indicates that the detrapping time constant during reset (at 80K) is much longer than 20 msec. In Fig. 4.33(b) the supralinear behavior starts more abruptly and at a somewhat higher excess gate bias. It is felt that this is due to the longer active time t and a shorter de-St trapping time constant due to tunneling under the high field conditions that exist after the discharge (i.e., at V ). Since the detrapping time constant is much longer than 20 msec during reset and somewhat longer than .10 msec during the active time, the following experiment was devised to obtain a true measure of the number of pulses triggered by photogenerated carriers. The devices were operated with an active time of t = 1.0 msec and a reset time of t =2.0 msec. The LED a r source was pulsed on during the active time of every second cycle and two separate counts were accumulated; one for those cycles with the LED on, and the other for those cycles with the LED off. The 2.0 msec reset allows time for the photogenerated carriers in the bulk to recombine before the next pulse above breakdown. The counts accumulated w i t h the LED o f f a r e , t h e r e f o r e , due only t o the dark counts and the counts r e s u l t i n g from the de.trapping f o l l o w i n g an avalanche discharge. These counts can then be subtracted from those obtained w i t h the LED on t o a r r i v e at the counts due t o photogenerated c a r r i e r s . I n order t o minimize coincidence l o s s e s , the l i g h t l e v e l was adjusted so th a t fewer than 3% of the frames contained counts. The r e s u l t s o f such measurements are shown i n F i g . h.3h. In order to compare these r e s u l t s w i t h those p r e d i c t e d from the theory, a f u l l three dimensional c a l c u l a t i o n of the p o t e n t i a l d i s t r i b u t i o n and v a r i a t i o n o f P (w) under the photogate i s r e q u i r e d . Such c a l c u l a t i o n s have not been made. Instead, the two dimensional r e s u l t s were used i n such a way as t o approximate a three dimensional s o l u t i o n . For these c a l -c u l a t i o n s a photogate 20ym wide by Ul+ym l o n g , but w i t h h e m i s p h e r i c a l ends, was assumed. This gives the same t o t a l area as a 20ym x l+Oym gate. The v a r i a t i o n of the avalanche i n i t i a t i o n p r o b a b i l i t y , along any l i n e normal to the perimeter and extending i n t o the l o n g i t u d i n a l center l i n e o f the gate, was assumed to be the same as th a t given by the two dimensional s o l u t i o n shown i n F i g . k.27. Using t h i s c o n s t r u c t i o n , the expected v a r i a t i o n of the photon induced pulse r a t e w i t h gate bi a s ( f o r r e a r i l l u m i n a t i o n , i . e . , pure e l e c t r o n i n j e c t i o n ) was c a l c u l a t e d from the double i n t e g r a l P (w) dx dz JJ E The c a l c u l a t e d v a r i a t i o n of the photon induced pulse r a t e i s shown by the s o l i d l i n e i n F i g . The c a l c u l a t e d curve has been s h i f t e d by +1.85V, and has been a r b i t r a r i l y f i t through the experimental p o i n t at V = 110 V, as no measurement of the absolute i n j e c t i o n l e v e l was made. The d e v i a t i o n of the f i r s t two experimental p o i n t s from the low volt:-:, t a i l of the c a l c u l a t e d curve i s an expected r e s u l t s i n c e space charge e f f e c 188 FIGURE 4.34 Photon-induced pulse rate as a function of the photogate bias when the dark subtraction includes those counts resulting from the detrap-p i n g following an avalanche discharge. The solid line shows the variation of the photon-induced pulse rate, calculated using the results of the two-dimensional modeling. The calculated curve has been shifted by +I.85 V and fitted through the experimental point at V = 110 V. 189 have been neglected. At small excess gate b i a s e s the b u i l d - u p of space charge s i g n i f i c a n t l y reduces the number of discharges t h a t r e s u l t i n pulses l a r g e r than the 5 x 10 e l e c t , d i s c r i m i n a t o r l e v e l used f o r these measure-ments. A l s o , the e f f e c t i v e breakdown area i s reduced i n the low v o l t a g e t a i l which f u r t h e r lowers the s i z e of the discharge pulse s . The e x c e l l e n t agreement between the c a l c u l a t e d and observed v a r i a t i o n of the photon induced pulse r a t e w i t h gate b i a s f o r the remainder of the experimental p o i n t s i n d i c a t e s t h a t the avalanche i n i t i a t i o n p r o b a b i l i t y i s a c c u r a t e l y described by the theory due t o Oldham e t . a l . [ 3 1 ] , equations (3 . 2 ) - ( 3 . 5 ) ' The upper experimental po i n t at V = 1 1 2 V corresponds t o an avalanche i n i t i a t i o n p r o b a b i l i t y f o r e l e c t r o n s , P (w), that ranges from 0 . 9 at the center of the photogate t o 0..9T at the edge. 190 5 SUMMARY AND CONCLUSIONS A s o l i d s t a t e photon counting sensor, based on the above-breakdown operating regime of MOS s t r u c t u r e s , has been proposed and i n v e s t i g a t e d both t h e o r e t i c a l l y and experimentally. I t has a l s o been de s c r i b e d how s p e c i a l l y designed charge-coupled arrays may be operated i n t h i s new regime, r e s u l t i n g i n the r e a l i z a t i o n o f an e n t i r e l y s o l i d s t a t e high performance photon counting imager. In order t o demonstrate the need f o r such an imager and i t s p o t e n t i a l advantages, the general p r o p e r t i e s of s t a t e - o f - t h e - a r t analog and photon counting imagers are reviewed b r i e f l y i n chapter two. I t i s shown th a t CCD imagers are s u p e r i o r t o other types o f analog detectors f o r u l t r a low l i g h t l e v e l imaging, l a r g e l y as a r e s u l t of the low l e v e l s o f readout noise (a<25 el e c t r o n s r.m.s.) that are being achieved w i t h current CCD sensors. A q u a n t i t a t i v e means of a p p r a i s i n g the performance of low l i g h t l e v e l sensors (the DQE) i s introduced and i t i s shown th a t analog CCD sensors are very n e a r l y an optimum detector over a wide range of wavelengths, centered at TOO nm, provided the s t a t i s t i c a l photon noise dominates the s i g n a l t o noise i n the output. For current CCD imagers t h i s c o n d i t i o n i s met f o r an output s i g n a l to noise g r e a t e r than approximately TO t o 1. At very low'photon f l u x e s , photon counting i s g e n e r a l l y the p r e f e r r e d imaging technique. This.not only makes p o s s i b l e a DQE t h a t i s independent of the t o t a l i n t e g r a t e d s i g n a l but i t avoids some of the l i n e a r i t y , s t a b i l i t y , and t h r e s h o l d problems o f t e n encountered w i t h analog imagers. I t i s shown, however, that temporal sampling e f f e c t s introduce n o n - l i n e a r i t i e s and lower the DQE i f the photon a r r i v a l r a t e per p i x e l i s allowed t o approach the frame r a t e of the imager. Many of the e x i s t i n g photon counting systems 1 9 1 require real-time frame processing to detect the photon event centers, r e s u l t i n g i n a l i m i t e d frame rate ( t y p i c a l l y 100 sec "*") and a low dynamic range. A l l of the image photon counting systems u t i l i z e e i t h e r a semi-transparent or opaque photoemmisive surface as the i n i t i a l l i g h t s e n s i t i v e element. I t i s the l i m i t e d responsive quantum e f f i c i e n c y of the commonly used photocathode material (RQE<0.2) that u l t i m a t e l y l i m i t s the DQE o f photon counting imagers at very low l i g h t l e v e l s . The proposed s o l i d state photon counting sensor and i t s theory of operation are discussed i n chapter three. The above-breakdown operating regime i s discussed and i t i s shown how an MOS photosensor may be operated i n a photon counting (or Gieger tube) mode by pu l s i n g i t i n t o very deep depletion, beyond the point where avalanche breakdown normally occurs. Operation above the breakdown voltage has been previously demonstrated, how-ever, only p-n photodiodes have been operated i n t h i s mode so f a r . Further-more, there has been no attempt to optimize these devices as low l i g h t l e v e l photon counting sensors, nor has a monolithic imaging array of such detectors been considered. The MOS photon counting sensor i s shown to have an inherent self-quenching property that g r e a t l y s i m p l i f i e s i t s incorporation into such an array. The proposed photon counting CCD (PC-CCD) has the p o t e n t i a l f o r achieving a DQE that i s independent of the t o t a l ' integrated s i g n a l and which i s nearly equal to the photon-noise l i m i t e d DQE's being achieved with analog CCD imagers. Also, the large s i z e of the s i g n a l charge packets generated by the photon induced avalanche discharges should enable high c l o c k i n g rates to be used during readout, and make poss i b l e a high frame rate. The following major problem areas i n the development o f a succe s s f u l PC-CCD imager were i d e n t i f i e d : (1) maximizing the avalanche i n i t i a t i o n p r o b a b i l i t y (2) reduction of the dark pulse rate to an acceptable l e v e l 192 (3) achieving planar micro-plasma-free avalanche discharges (k) prevention of optical coupling due to light emission during the avalanche discharges. In the remainder of chapter 3 the theoretical background required for a f u l l understanding of these problems is introduced and the existing experimental data is reviewed. It is shown that a PC-CCD must be fabricated on a p-type silicon substrate and illuminated from the back side in order to obtain a high triggering probability for the photogenerated carriers. A l l of the possible dark generation mechanisms have been discussed in detail. It is shown that a l l thermally activated steady state dark genera-tion mechanisms that occur in the bulk can be reduced to a negligible level by cooling the sensor to low temperatures (100 K or lower). The generation of possible triggering carriers (holes) by interface states can be controlled by maintaining an inversion charge at the silicon surface. The generation of possible triggering carriers by interband tunneling may be reduced to an acceptable level by ensuring that the peak fields within the depletion region are below approximately k.3 x 10^ Vcm \ Operation above breakdown with peak fields as low or lower than this requires wide depletion regions (i.e., a low substrate doping) which in turn results in large (60-70V) potentials across this region. Due to the potential drop across the oxide the MOS gate used to generate these depletion regions must be operated at s t i l l higher voltages so that specially designed charge transfer arrays are re-quired for operation in the above-breakdown regime. The generation of triggering carriers by band to band tunneling through trap states is also examined. There is very l i t t l e existing data upon which to base estimates for the dark generation due to this mechanism but by ex-trapolating data obtained with high field Esaki diodes, order-of-magnitude estimates can be made. Such estimates indicated that tunneling through 193 traps would l i k e l y be the dominant steady s t a t e dark generation mechanism and t h a t , depending on the t r a p d e n s i t y , peak f i e l d s lower than 3 x 1 0^ Vcm" may be r e q u i r e d . A c h i e v i n g the lowest p o s s i b l e t r a p d e n s i t y i s e s s e n t i a l f o r minimizing t h i s type of dark generation. F o l l o w i n g the d e p l e t i n g pulse above breakdown, there i s a t r a n s i e n t s i t u a t i o n d u r ing which the dark pulse r a t e may be e i t h e r increased or de- : creased from i t s steady s t a t e value depending on the c o n d i t i o n s during reset and on the energy and capture c r o s s - s e c t i o n s o f the t r a p p i n g l e v e l s . A s i m i l a r t r a n s i e n t s i t u a t i o n e x i s t s a f t e r each breakdown p u l s e , due t o charge t r a p p i n g or impact i o n i z a t i o n o f the t r a p s during the avalanche discharge. T h e o r e t i c a l expressions are d e r i v e d t o d e s c r i b e the change i n pulse r a t e during these t r a n s i e n t s . A low d e n s i t y of t r a p s i s r e q u i r e d t o minimize the p o s s i b i l i t y o f r e - t r i g g e r i n g due t o increased c a r r i e r emmission f o l l o w -i n g an avalanche discharge. • The c o n t r o l of f r i n g i n g f i e l d s and the p r e v e n t i o n of premature edge breakdown i s discussed b r i e f l y , along w i t h the p r o c e s s i n g techniques used t o prevent or e l i m i n a t e l a t t i c e defects t h a t might l e a d t o l o c a l i z e d micro-plasma breakdown. A review o f the e x i s t i n g data on l i g h t emission during avalanche breakdown i n d i c a t e s t h a t some form of o p t i c a l b a r r i e r between the i n d i v i d u a l p i x e l s i n an a r r a y w i l l be r e q u i r e d . Two methods f o r a c h i e v i n g a h i g h de-gree of o p t i c a l i s o l a t i o n between the p i x e l s i n l i n e a r arrays are described. The experimental i n v e s t i g a t i o n of MOS s t r u c t u r e s o p e r a t i n g i n the above-breakdown regime i s reported i n chapter four. This i n v e s t i g a t i o n was d i r e c t e d p r i m a r i l y at problems ( l ) and (2) above. MOS s t r u c t u r e s t h a t breakdown at the s i l i c o n surface were s t u d i e d i n i t i a l l y . An extension of the gate metal over the t h i c k f i e l d oxide was used to prevent edge breakdown and the devices s t u d i e d were r e s e t by i n j e c t -19b ing the charge into the substrate. A gate oxide thickness greater than 0.2 ym was shown to be necessary. Difficulties encountered during the double level Al-Al^O^-Al metalization indicated that the aluminum anodization should precede any contact sinter or annealing treatments and that selective etching rather than selective anodization should be used to form the first to second level metal vias. In order to obtain appreciable delays to breakdown the surface-break-down devices had to be pulsed from a reset condition corresponding to in-version under both the active region of the gate and the guard ring. When the guard ring is not inverted during reset the interface states around the edge of the breakdown area are unoccupied above mid gap. In the deeply de-pleted condition the breakdown area extends outwards into this edge region, resulting in a large dark pulse rate which is due to the increased hole emission from the unoccupied interface states under the high field conditions that exist in deep depletion. The low interface state density measured on the test samples indicates that i t will not be possible to reduce this form of dark generation to an acceptable level by further reductions in the inter-face state density. Inverting the guard ring during reset results in a large reduction of the dark pulse rate but its effectiveness is limited because the inversion layer charge is transferred to the active (thin oxide) region of the photo-gate after pulsing above breakdown thus allowing the interface states in the edge region to empty. Also, this charge transfer increases the gate voltage required for breakdown under the photogate and results in very high oxide field strengths. The dark pulse rates of the test devices continued to de-crease as the inversion layer charge during reset was increased, until the point where the guard ring also started to break down or the higher oxide fields resulted in a destructive breakdown of the gate oxide. The lowest 195 dark p u l s e r a t e s measured on t h e s u r f a c e breakdown d e v i c e s , a t excess b i a s e s s u f f i c i e n t t o g i ve a t r i g g e r i n g p r o b a b i l i t y l a r g e r than 0.5, were 3 o r d e r s of magnitude h i g h e r than the maximum d e s i r e d dark p u l s e r a t e o f - 1 - 2 500 sec cm . For the above reasons MOS s t r u c t u r e s t h a t breakdown at the s i l i c o n s u r f a c e were r u l e d out as p o s s i b l e image elements f o r a PC-CCD. These problems can be avo ided by go ing t o an MOS s t r u c t u r e t h a t b reaks down i n the b u l k away from the S i-Si02 i n t e r f a c e . I t i s shown t h a t such a s e l f -quenching , bu lk -breakdown MOS gate can be made by forming a l i g h t l y doped n -channe l at the s i l i c o n s u r f a c e , as i n the b u r i e d channel CCD s t r u c t u r e . Oxide f i e l d s t r e n g t h s are ve ry low i n the bu lk -breakdown s t r u c t u r e so t h a t the dark g e n e r a t i o n by i n t e r f a c e s t a t e s i s n e g l i g i b l e at the low (<100 K) o p e r a t i n g temperatures . Fur thermore , w i t h a c o r r e c t l y doped n - c h a n n e l the p o t e n t i a l minimum l i e s i n the b u l k o f the n - c h a n n e l away from the S i - S i O ^ i n t e r f a c e so t h a t the c a r r i e r s e m i t t e d by i n t e r f a c e s t a t e s are unable to t r i g g e r a breakdown. The r e s u l t s o f t w o - d i m e n s i o n a l model ing o f the com-p l e t e d t e s t dev i ces i n d i c a t e d t h a t the n - c h a n n e l had not been s u f f i c i e n t l y doped and t h a t the p o t e n t i a l minimum was l o c a t e d a t the S i - S i O ^ i n t e r f a c e i n the deep ly d e p l e t e d c o n d i t i o n above breakdown. The r e s u l t s o f the model ing , d i d , however, c o n f i r m t h a t the degree o f premature edge-breakdown i n the f a b r i c a t e d dev i ces would not be e x c e s s i v e . In g e n e r a l , the b e h a v i o r o f the bu lk -breakdown MOS p u l s e c o u n t i n g d e -t e c t o r s was found t o be f a r s u p e r i o r t o the sur face -breakdown d e v i c e s . The dark p u l s e r a t e s were c o n s i d e r a b l y l o w e r , i n s p i t e o f poorer b u l k l i f e t i m e s a n d , i n c o n t r a s t t o t h e s u r f a c e d e v i c e s , the p u l s e h e i g h t d i s t r i b u t i o n was very s h a r p l y peaked. Only a very weak temperature dependence o f the dark p u l s e r a t e was o b -s e r v e d , sugges t ing a t u n n e l i n g mechanism. The dark count r a t e w a s , however, e i g h t o rders o f magnitude h i g h e r than t h a t p r e d i c t e d f o r the d i r e c t band t o 196 band tunneling generation of triggering carriers. The limiting dark genera-tion mechanism for the bulk-breakdown devices studied (peak fields =3.3 x 10 Vcm )^ i s , therefore, believed to be interband tunneling through trap states. The measured dark pulse rates are in general agreement with those predicted from the theory and existing data obtained with high field Esaki 12 13 -3 diodes, provided a mid gap trap density of 10 to 10 cm is assumed. The measured bulk lifetime of 5 usee is consistent with this density of mid gap generation centers. The number of dark pulses detected was also found to be linearly re-lated to the number of resets, suggesting that the tunneling emission of triggering carriers in the high field region is increased following a reset. There i s , however, no apparent mechanism to explain the change in trap oc-cupancy during reset required to cause this increased emission. The photon induced pulse rate measurements indicated that retriggering following an avalanche discharge was s t i l l a problem. After making a simple dark subtraction the measured pulse rates did, however, show some i n i t i a l signs of saturation with increasing gate bias. The level to which the pulse rates appeared to be saturating, before the increases turned supralinear, was. in general agreement with the measured electron injection level. By pulsing the LED light source on every second cycle it- was possible to make a dark subtraction that included the counts due to re-triggering following an avalanche discharge. When this was done i t was found that the photon induced pulse rate saturated precisely as predicted by the theory. These photon induced pulse rate measurements were extended up to gate biases 12V above breakdown, corresponding to an electron triggering probability greater than 0.9. The re-triggering following the avalanche discharges constitutes a form of positive feedback and is an undesirable effect as i t would cause 197 severe non-linearities in the response of a PC-CCD. 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[105] A.J. Learn, Thin Solid Films, 2 0 , 2 6 l ( 1 9 7 U ) . [106] A.J. Learn, J. Electrochem. Soc. , 1 2 3 , 39U ( 1 9 7 6 ) . [107] J.S.L. Leach, and P. Neuford, Corrosion Sci. , 9 , U l 3 ( 1 9 6 9 ) . [108] P. Chaudhari, J. Appl. Phys. , U5_, U339 ( 1 9 7 U ) . [109] C J . Dell'Oca, and A.J. Learn, Thin Solid Films, 8 , RU7 (l97lK [110] T.E. Seidel, R.L. Meek, and A.G. Cullis, J.Appl. Phys., U 6 , 600 ( 1 9 7 5 ) . [ I l l ] R.L. Meek, and T.E. Seidel, J. Phys. Chem. Solids, 3 6 , 7 3 1 ( 1 9 7 5 ) . 203 [112] R.W. Santway, and R.S. A l w i t t , J . Electrochem. Soc. , 117, 1282 (1970). [IA [2A [3A [4A [5A [6A [1C [2C [3C [4C [5C [ID [2D G.A. Baraff, Phys. Rev., 128, 2507 (1962). G.A. Baraff, Phys. Rev., 133, A26 (196U). C.R. Crowell, and S.M. Sze, Appl. Phys. L e t t . , 9, 2U2 (1966). G. E. Stillman, and C.M. Wolfe, i n "Semiconductors and Semimetals vol . 1 2 1 ' PP325-3U0, Academic Press, New York (1977), and references therein. C.A. Lee, R.A. Logan, R.L. Bardorf, J . J . Kleimack, and W. Wiegmann, Phys. Rev., 13b, A 7 6 I (196U). J. Conradi, S o l i d State Electron., 17, 99 (l9lb). S.M. Sze, "Physics of Semiconductor Devices," p.372,Wiley, New York (1969). E.H. N i c o l l i a n , M.H. Hanes, and J.R. Brews, IEEE Trans Electron. Devices, ED-20, 380 (1973). C.N. Berglund, IEEE Trans. Electron. Devices, ED-13, 701 (1966). R. Castagne, C.R. Acad. S c i . , B267, 866 (1968). M. Kuhn, Solid-State Electron., 13, 873'(1970). K.M. De Meyer, and G.J. Declerck, IEEE Trans. Electron.. Devices, ED-28, 313 (1981). H. W. Hanneman, and L.J.M. Esser, P h i l i p s Res. Rep., 30, 56 (1975). 2C-1+ APPENDIX A Electron and hole ionization coefficients in silicon For small electric field strengths the free carriers in a semiconduc-tor are able to remain in thermal equilibrium with the lattice through im-purity and acoustic phonon scattering, and conduction occurs at the band edges. At higher field strengths optical phonon emission dominates the scattering process and the drift velocity saturates. The current is no longer ohmic, however, conduction s t i l l occurs at the band.edges. At s t i l l higher field strengths (-lO'V/cm in silicon) the carriers gain energy from the field faster than they can ld'se i t by emitting phonons. At these and higher fields the carriers are no longer in equilibrium with the lattice and their energy relative to the band edge increases until they have ac-quired the threshold energy for impact ionization. The electron and hole ionization coefficients are used to describe the average distance a carrier will travel before generating an electron-hole pair by impact ionization. The most general theory for the ionization rates is a modification of Baraff's theory [1A,2A] due to Crowell and Sze [3A]. The assumptions made by Baraff to obtain-a numerical solution were: (1) The energy bands in momentum space are parabolic. (2) Only scattering by, and emission of, optical phonons is important, i.e., the lattice temperature was assumed to be very low. The resulting energy loss i s , therefore, equal to the optical phonon energy E . (3) The mean-free-path for optical phonon emission X is independent of energy. (h) The mean-free-path for impact ionization is constant for electron ener-gies greater than the threshold ionization energy E^. (5) The scattering is spherically symmetric. 205 Crowell and Sze l a t e r improved upon t h i s theory by including o p t i c a l phonon absorption thereby enabling the temperature dependence of the i o n i -zation c o e f f i c i e n t s to be determined. They suggested that an average energy loss per c o l l i s i o n <Er> could be used i n place of E^ i n Baraff's Theory, and give the following expression for the temperature dependence of X and E ' r <E > r E jjp = tanh r r_ 2kT X X (Al) where X q i s the low temperature l i m i t to the mean-free-path for o p t i c a l phonon generation. They also give the following approximation to Baraff's numerical solution for the io n i z a t i o n c o e f f i c i e n t s a (correct to within ±2% f o r 0 . 0 1<r< 0 . 0 6 and 5<x<l6) , aX = exp ( i l . 5 r 2 - 1.17r + 3.9x 10-1* ) 2 + (l*6r 2 - 11.9r + 1.75 x 1 0 - 2 ) + ( - 7 5 7 r 2 + 7 5 . 5 r - 1.92) x (A2) <Er> E where r = — and x = —FT , Ej qcX ' There i s considerable uncertainty as to the exact magnitude and f i e l d v a r i a t i o n of the electron and hole i o n i z a t i o n rates i n s i l i c o n . [ 4 A ] . The ioni z a t i o n rates used i n t h i s work are those measured at room temperature by Lee e t . a l . [5A]. These are the most widely quoted i o n i z a t i o n rates, and the only ones that can be f i t to Baraff's theory with a reasonable value for the parameter X, the accepted value of E =3/2 E , and the measured o p t i c a l phonon energy of E r = 0 . 0 6 3 eV. The ioniz a t i o n rates were transformed to the appro-pria t e temperature using Crowell's and Sze's modification to Baraff's theory, Equations (Al) and (A2). The parameters used i n (Al) and (A2) that f i t Lee's data are [6A]: E = 0.063 eV r E z (300K) = 1 . 6 eV (electrons) = 76 2 \ (holes) = U9 S 207 APPENDIX B S i m p l i f i e d schematics f o r the high voltage d r i v e , timing c i r c u i t r y , charge a m p l i f i e r and discriminator. RAMP RATE J_ X CONT. ~ ~ A O o driver output o B o C INTEGRATOR CONT. PULS GEN.. 209 O A surface devices co-£x>-4>o bulk devices o comp. pulse counter 2 TIMING surface dev. bulk *1 10 100 R2 100 10 *3 10 10 .47 1 c 2 1 .1 C 3 .47 .1 210 68 n 2.7 r - W W 1 — D o-2.7 220P PMI 1 CMP01 com p.o-pulse counter 1 DESCRIMIN ATOR input o preset o-integ. o-* low noise •*15 10 •15 -15 o o 0 4.7; preset level 10 '3 I! 8 12 5 7 0053 1 1 9 4 10 3 MC1741 -O E - O D CURRENT AMP. AND INTEGRATOR 211 APPENDIX C Methods used to determine the doping p r o f i l e and i n t e r f a c e s t a t e d e n s i t y ( l ) Doping P r o f i l e The doping p r o f i l e s were obtained by the w e l l known dC/dV - method based on the f o l l o w i n g formulae ( lC) v = € S / C S C (C2) where N = doping d e n s i t y w = d e p l e t i o n l a y e r width ( i . e . , d i s t a nce from the semiconductor sur-face at which the doping d e n s i t y i s determined) C . = space charge capacitance per u n i t area <J> = semiconductor surface p o t e n t i a l The negative s i g n a p p l i e s f o r n-type substrates and the p o s i t i v e s i g n f o r p-type. Equations ( Cl) and (C2) are based on the d e p l e t i o n approximation, which becomes i n v a l i d f o r s m a l l values o f w where the m a j o r i t y c a r r i e r con-c e n t r a t i o n can no longer be neglected i n comparison to the doping d e n s i t y . This l i m i t s the determination o f the doping d e n s i t y to values o f w g r e a t e r . than 2 where i s the e x t r i n s i c Debye le n g t h [2C]. D 1 qN In d e p l e t i o n the space charge capacitance i s r e l a t e d t o the measured high frequency MOS capacitanc C„„ according t o HF 212 provided the measuring frequency i s high enough t h a t the i n t e r f a c e s t a t e s do not c o n t r i b u t e t o the o v e r a l l capacitance. C i s the oxide capacitance which, i n the case of a low i n t e r f a c e s t a t e d e n s i t y , can be approximated by the measured capacitance i n strong accumulation. In order to use Eq. ( C l ) i t i s f u r t h e r necessary to o b t a i n a r e l a t i o n s h i p between the surface poten-t i a l <f>£ and the a p p l i e d voltage V . Berglund (3C)-has shown t h a t the s u r -face p o t e n t i a l may be determined to w i t h i n an a d d i t i v e constant by i n t e -g r a t i n g the measured C(V) curve from a p o i n t corresponding to s t r o n g accumu-l a t i o n , V , toward d e p l e t i o n , 3,C C • rvg , c (v * s ( y = j I 1 - + K I ( C 4 ) v o x acc The additve constant drops out when performing the d e r i v a t i v e i n ( C l ) . I t i s customary to use pulsed C-V measurements i n order t o prevent the formation of an i n v e r s i o n l a y e r and enable the doping p r o f i l e to be ob-t a i n e d to greater depths. Because of the l a c k of such measuring equipment, a d i f f e r e n t method was used here. Samples w i t h s e v e r a l 1 m mdia MOS c a p a c i t o r s were mounted i n l6 p i n DIP packages and cooled to 80K i n the c o l d chamber used f o r the device t e s t i n g . Under t o t a l darkness the i n v e r s i o n l a y e r charge c o l l e c t s so slowly that i t was p o s s i b l e t o o b t a i n the C (V) curve p o i n t by. point w i t h a capacitance b r i d g e . The measuring frequency used was 500 kHz. (2) I n t e r f a c e State Density The i n t e r f a c e s t a t e d e n s i t y was obtained by combining q u a s i - s t a t i c C-V measurements w i t h high frequency C-V measurements, as discussed by Castagne [40]. The d i f f e r e n c e between the q u a s i - s t a t i c (low frequency) capacitance C and the high frequency capacitance C„„ i s d i r e c t l y r e l a t e d t o the s u r -213 face state density as follows C (<p ) C C C C „ /. \ ss s . LF ox HF ox u ox LF ox HF where N is the interface state density per unit area per eV and C is the ss ss capacitance due to interface states. The interface state densities obtained from Eq. (C5) are only valid when the MOS sample is in depletion. In in-version the minority carriers are not able to follow the high frequency ac signal used to measure C^, while in accumulation the interface states nr closest to the band edge are able to follow the ac signal, so that C can ss no longer be determined. The constant in Eq. (Ch), needed to determine ij) (V ), was obtained by plotting- l/C versus (<j> - K ), which results in a S § S C S X straight line in depletion (with uniformly doped samples). l/C • goes to 0 s c as <J>g goes to 0 , therefore, the intercept gives K^ . As with the doping profile measurements the interface state density was measured on 1 mm dia, p-substrate, MOS capacitors. The high frequency capacitance measurements were made with a 1 MHz (Boonton) capacitance meter. The quasi-static C(V) curves were obtained by measuring the MOS displacement _2 current in response to a linear voltage ramp (10 V/sec), as described by Kuhn [5C]. The displacement current was measured on a Keithley model 602 electrometer (in the fast mode). In addition to the room temperature C(V) curves, quasi-static and high frequency C-V measurements were also made at 173K and 223K in order to obtain interface state densities closer to the valence band edge. At these lower temperatures the energy range over which the interface state information is valid becomes quite narrow because the deep levels can no longer follow the slow voltage ramp used for the quasi-static measurement (see Fig. k.20). 21k APPENDIX D Method used for the two-dimensional calculation of the potential and field distributions in the bulk breakdown devices The structure for which the solutions will be derived is shown in Fig. Dl -L/2 0-X +L/2 V„ ox -5*- x y n-type p-type ~L FIGURE Dl Device structure used for the two-dimensional model. The method is analogous to that described by Meyer and Declerck . [ID] for ob-taining potential distributions in BCCD structures, and uses the super-position principle in such a way that a l l boundary conditions are satisfied. This is not the case in the method of Meyer and Declerck. They use the superposition principle in the oxide and n-layer only, and then match the solution in the substrate in such a way that the potential goes to zero at the edge of the depletion region. Their solution, however, does not satisfy the additional boundary condition grad <f>(x,w) = 0 and the potential dis-tribution in the substrate cannot be accurately determined, particularly i f 215 the substrate doping density i s comparable t o t h a t of the n - l a y e r as i t i s v i t h the b u l k breakdown devices. In the method discussed below, the s u p e r p o s i t i o n p r i n c i p l e i s used throughout. This i n f a c t r e s u l t s i n a simpler s o l u t i o n as i t e l i m i n a t e s the complicated matching c o n d i t i o n between t h e n - l a y e r and the s u b s t r a t e s o l u t i o n s . A zero gate separation i s assumed as shown i n F i g . D l . By making the d e p l e t i o n approximation and using, the s u p e r p o s i t i o n p r i n c i p l e i t i s p o s s i b l e to o b t a i n the s o l u t i o n f o r the e l e c t r o s t a t i c p o t e n t i a l as the sum of two p a r t s , <i> ,(x,y) '= • (x,y) + <f>f. (x,y) (Dl) <t»ox(x,y) = <f> (x,y) + +Q X(x,y) (D2) where <|>h(x,y) i s the s o l u t i o n t o the homogeneous "problem obtained by s e t t i n g the charge d e n s i t i e s equal t o zero, i . e • 5 t o the problem, 2 h V <f> (x,y) = 0 , -d < y (D3) w i t h boundary c o n d i t i o n , (D4) and <j>' i s a p a r t i c u l a r s o l u t i o n f o r the case V = V = 0, i . e . , t o the one dimensional problem, , -d < y < 0 ox (D5) -Biz) s 0 < y (D6) 216 with boundary conditions d)P (-d ) = 0 (D7) Tox ox *Px(0) - 4(o) a<l>p (o) Hv.(o) (D8) OX 'SI f T. n. e . — r = e — (D9) i By s 9y The additional boundary conditions needed to obtain d> and d> . are ox r s i <J> (x,w) = 0 (D10) S i . (x,w) — l y — = 0 (DH) 34 .(x,w) = 0 (D12) By The particular problem posed by Equations (D5)-(D9) is straight-for-ward. By using partial integration and the three boundary conditions, d>P (x,y) and <i>P.(x,y) can be expressed as ox si * C(x'y) = C l ( y + dox }'• " dox < y K ° ( D 1 3 ) r 7 1 f y re. 1 ^(x.y) = J j p(y)dy - - yp(y) dy + -C y + d l ,0<y 3 0 (D14) ox I s For the solution to the homogeneous problem posed by Equations (D3) and (DU), Meyer and Declerck use a method derived from the theorem of image forces [2D]. For the gate structure shown in Fig. Dl, however, there is an easier solution based on conformal mapping techniques. By using the trans-formations, x' = x , y' = y + d ' J ox z" = In {Zz] I Ify , z' = x» + iy' (D15) 217 the e l e c t r o s t a t i c s problem i s transformed to that shown i n Fig. D 2 , for which the following solution can be obtained by inspection, (V - V ) 4>h(x",y") =• V T + 6 i r T y" (D16) ^\\\X\\\\\\\\\\\\\\\X\\\ ^L — CO + 00 V +00 TT g . \ f FIGURE D2 Device structure after conformal transformation. After applying the inverse transformation the solution becomes (V - V J <f>h(xsy) ;an ry + d > ox r y + d 1 ox - tan [x - L/2J I x + L/ 2 j ( D 1 7 ) The constant C can now be obtained from B.C. ( D l l ) , w s j l I / \ j x 3J (x,w) \ 1 " - I 7 ( e s J + "V" J (D18) and w i s determined by an i t e r a t i v e procedure from B.C. (DIO), which becomes <j> (x,w) - -w yp(y) dy - — d e. ox 1 6 s „ 13<j>h(x,w) 0 p(y) dy - {w + — d } L oxJ 3y = 0 (D19) where the derivative of (D17), with respect to y, i s 218 3 < T(x,y) = y (x - L/2) + (y + d ) S - 1 ox (x - L/2) (x + L/2) + (y + d ) ^ - l (x + L/2) (D20) Boundary condition (D12) follows automatically from B.C. (DIO). In order to solve f o r P (w) and P, (0) equations (3.2) - (3.5) were e h integrated along a l i n e s t a r t i n g from a point at the p o t e n t i a l minimum ( i n the bulk or at the in t e r f a c e ) and following the d i r e c t i o n of the e l e c t r i c f i e l d vector (see Figures k.26 i n t e x t ) . The x and y components of the e l e c t r i c f i e l d were obtained from the x and y derivatives of <|> .(x,y), as S X follows, • . . • Mx,y) 3<f>si(x,y) dx H (x,y) + 9x — y + d e ox s !2i ax (D21) £ y(x,y) 9* s i(x,y) 3y . ^ > + i j o ( y ) i y t ! i 0 i (D22) dC^/dx can be obtained from B.C. (D12) as follows, 3x e. 1-1 »,h, v _ i w + d ( x ? v ) e ox 9x s ' (D23) where the d e r i v a t i v e of (D17) with respect to x i s 84>n(x,y) = 3x f i ^ ^ ! + (y + d ) (y + d o x ) [ ( y + d Q x ) ox'J - 1 (D24) 

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