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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  TIMOTHY PAUL LESTER 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 to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  1982  Timothy Paul Lester, 1982  In p r e s e n t i n g  this  thesis i np a r t i a l  fulfilment of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e of B r i t i s h Columbia, I agree that it  freely  the L i b r a r y s h a l l  a v a i l a b l e f o r reference and study.  agree that p e r m i s s i o n for  University  f o r extensive  I further  copying o f t h i s  thesis  s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e h e a d 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 . understood that for  make  financial  I t i s  copying o r p u b l i c a t i o n o f t h i s  gain  shall  n o t b e a l l o w e d w i t h o u t my w r i t t e n  permission.  Department o f  PLJ-aTg-ttCQL-  The U n i v e r s i t y o f B r i t i s h 2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  thesis  Columbia  ^wGr/^f^A~JiKJr~r  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 i s shown how a MOS photosensor may be operated in a photon counting mode by pulsing i t into very deep depletion, beyond the point where avalanche "breakdown normally occurs.  Avalanche  discharges i n such a MOS sensor are self-quenching due to the formation of an inversion layer. This self-quenching property suggests that a monolithic selfscanned array of MOS photon counting sensors should be possible. It i s 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 commonlyused photocathode materials, gives the proposed imager a distinct advantage over presently-existing photon counting sensors in these spectral regions. It i s shown that a PC-CCD must be fahricated on a p-type silicon substrate and illuminated from the back side in order to obtain a high avalanche initiation probability for the photogenerated carriers.  It i s 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  iii discharges i s 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 i n 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.  iv  TABLE OF CONTENTS Page ABSTRACT  .  i i '  LIST OF TABLES  vi vii  LIST OF FIGURES xiv ACKNOWLEDGMENT 1  INTRODUCTION  1  2  BRIEF REVIEW OF LOW LIGHT LEVEL IMAGE SENSORS  3  2.1  2.2  3.  ANALOG IMAGERS  1+  2.1.1  The DQE f o r A n a l o g CCD S e n s o r s  2.1.2  Performance  8  o f CCD Imagers C u r r e n t l y i n O p e r a t i o n  10  PHOTON COUNTING IMAGERS  13  2.2.1  L i n e a r i t y and DQE o f Photon Counting'Imagers  lh  2.2.2  Photon C o u n t i n g Imagers P r e s e n t l y i n Use  l6  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 Investigations  39  3.2  DARK GENERATION OF TRIGGERING CARRIERS  k2  3.2.1  h2  Review o f Recombination  and G e n e r a t i o n at B u l k  Defect o r Impurity Centers 3.2.2  Steady S t a t e B u l k G e n e r a t i o n :  3.2.3  Steady S t a t e G e n e r a t i o n a t t h e S i l i c o n / S i l i c o n Dioxide Interface:  Low F i e l d Case  51 5^-  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 G e n e r a t i o n Due t o T u n n e l i n g  65  3.2.6  Dark G e n e r a t i o n o f T r i g g e r i n g C a r r i e r s i n t h e  77  Non-Steady S t a t e  TABLE OF CONTENTS c o n t ' d Page  It  EXPERIMENTAL INVESTIGATION OF MOS STRUCTURES PULSED  100  ABOVE BREAKDOWN k.l  101  SURFACE BREAKDOWN DEVICES - 4 . 1 . 1 Design C o n s i d e r a t i o n s  1+. 2  5  101  h.1.2  T e s t S t r u c t u r e Designs and Mask L a y o u t s  10k  4.1.3  Device F a b r i c a t i o n  Ilk  k.l.k  T e s t Chamber and E l e c t r o n i c s  12k  k.l.5  M o d e l i n g o f t h e Completed D e v i c e s  128  k.l.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  133  BULK BREAKDOWN DEVICES  150  4.2.1  D e s i g n C o n s i d e r a t i o n s and E q u a t i o n s  153  k.2.2  T e s t 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 D i m e n s i o n a l M o d e l i n g o f t h e Completed D e v i c e s  167  k.2.k  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 .  172  SUMMARY AND CONCLUSIONS  190  BIBLIOGRAPHY  198  APPENDIX A  E l e c t r o n and h o l e i o n i z a t i o n c o e f f i c i e n t s in  APPENDIX B  20k  silicon  S i m p l i f i e d schematics f o r t h e high voltage drive, timing c i r c u i t r y ,  207  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 t h e doping p r o f i l e  211  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 t h e t w o - d i m e n s i o n a l c a l c u l a t i o n o f t h e 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 t h e b u l k breakdown d e v i c e s  2lk  vi LIST OF TABLES Page  3.1  E x p e r i m e n t a l v a l u e s f o r t h e e f f e c t i v e mass and m a t r i x elements  "J6  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  Processing details f o r f i r s t fabrication  115  h.2  P r o c e s s i n g 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  D e v i c e and t e s t w a f e r d a t a  120  h.k  P r o c e s s i n g d e t a i l s f o r t h e b u l k breakdown d e v i c e s  l62  k.5  D a t a f o r w a f e r M66  l66  V l l  LIST OF FIGURES  Page 2.1  R e s p o n s i v e quantum e f f i c i e n c y o f d i f f e r e n t a n a l o g s e n s o r  6  a r r a y s as a f u n c t i o n o f w a v e l e n g t h  2.2  DQE f o r t h e T..I. kOO x 1+00 BCCD as a f u n c t i o n o f t h e t o t a l integrated incident s i g n a l , at several  12  different  wavelengths  2.3  The e f f e c t o f t e m p o r a l s a m p l i n g on t h e DQE o f a photon  17  counting detector  2.k  R e s p o n s i v e quantum e f f i c i e n c y o f d i f f e r e n t p h o t o c a t h o d e /  22  window c o m b i n a t i o n s as a f u n c t i o n o f w a v e l e n g t h  2.5  The DQE as a f u n c t i o n o f w a v e l e n g t h f o r a photon c o u n t i n g detector with a t r i - alk.  23  photocathode,. and f o r a r e a r  i l l u m i n a t e d a n a l o g BCCD d e t e c t o r ( T . I . liOO x 1+00 BCCD).  3.1  Equivalent c i r c u i t  f o r an a v a l a n c h e diode o p e r a t i n g above  breakdown, p l u s t h e b i a s and d e t e c t i o n  3.2  25  circuit  Energy band diagram f o r a p - s u b s t r a t e MOS g a t e a t t h e b e -  28  g i n n i n g and end o f an a v a l a n c h e d i s c h a r g e  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 b r e a k -  25  down  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 t h e b a s i c o p e r a t i o n o f a 4-phase PC-CCD  3.5  E x p e c t e d 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  29  31  viii  LIST OF FIGURES c o n t ' d Page 3-6  3l+  Model o f the impact i o n i z a t i o n t h a t o c c u r s subsequent t o the i n t r o d u c t i o n o f a t r i g g e r i n g c a r r i e r ( o r 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  3.7  The  a v a l a n c h e 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 ^ ( )  The  f°  x  a p-substrate 3.8  region  MOS  r  37  gate  a v a l a n c h e 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 o f s u r -  face p o t e n t i a l f o r electrons o r i g i n a t i n g i n the'bulk  38  and  f o r h o l e s 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  d e g r a d i n g e f f e c t o f t h e dark count r a t e on the d e t e c -  1+3  t i v e quantum e f f i c i e n c y 3.10  The  f o u r b a s i c S h o c k l e y - R e a d - H a l l p r o c e s s e s t h a t may  at a t r a p p i n g 3.11  occur  1+5  level  A c t i o n o f an e l e c t r o n t r a p .  The  r e l a t i v e positions of  1+5  Schematic diagram showing the d i s t r i b u t i o n o f the cou-  58  E^ , E* and E„ are a l s o shown Fn T .Fp 3.12  lomb p o t e n t i a l w e l l around a t r a p p i n g c e n t e r ferent e l e c t r i c f i e l d 3.13  for dif-  strengths  R a t i o o f t h e f i e l d enhanced e m i s s i o n r a t e e y t o  the zero  60  f i e l d e m i s s i o n r a t e e , as a f u n c t i o n o f 3/T/kT o 3.ll+  Energy band diagram i l l u s t r a t i n g , the s t e a d y s t a t e genera t i o n muchanisms i n v o l v i n g the t u n n e l i n g e m i s s i o n o f e l e c t r o n s and/or h o l e s by mid  gap l e v e l s  63  ix  LIST OF FIGURES c o n t ' d Page  3.15  I n t e r b a n d t u n n e l i n g g e n e r a t i o n r a t e v e r s u s t h e peak + electric field  m  72  n p step j u n c t i o n s or p-substrate  MOS g a t e s , w i t h d i f f e r e n t l e v e l s o f s u b s t r a t e d o p i n g , T=100K 3.16  The i n t e r b a n d t u n n e l i n g g e n e r a t i o n 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 t h e s i l i c o n s u r f a c e p o t e n t i a l <j> , T=100K 3.17  T u n n e l i n g g e n e r a t i o n r a t e t h r o u g h t r a p s as a f u n c t i o n  78  o f t h e peak e l e c t r i c f i e l d i n n p s t e p j u n c t i o n s o r p+  s u b s t r a t e MOS g a t e s , T=100K 3.18  Energy band diagram f o r a p - s u b s t r a t e 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 3.19  following a depleting pulse  Energy band diagram f o r a p - s u b s t r a t e MOS gate i l l u s -  82  t r a t i n g t h e 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 from deep bulk t r a p s , immediately 3.20  following a depleting pulse.  Model f o r t h e d e p l e t i o n r e g i o n o f a p - s u b s t r a t e MOS  86  gate d u r i n g breakdown 3.21  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 p s subsequent t o an avalanche  3.22  discharge  C r o s s - s e c t i o n o f MOS c a p a c i t o r showing e q u i p o t e n t i a l l i n e s i n t h e space charge r e g i o n a t t h e edge o f t h e f i e l d plate  87  • 90  x .'LIST OF FIGURES c o n t ' d  Page  3.23  Four d i f f e r e n t MOS  structures  t o a v o i d premature  anche breakdown at t h e o u t e r edge o f t h e f i e l d in high r e s i s t i v i t y  3.2k  The e m i s s i o n  aval-  90  plate  samples  spectrum d u r i n g r e v e r s e b i a s a v a l a n c h e  9k  breakdown i n s i l i c o n . 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 e t c h e d s l o t s  97  may be used t o o p t i c a l l y i s o l a t e t h e 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 ( 1 1 0 ) 3.26  silicon  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 e t c h e d v-grooves  98  might be used t o p r o v i d e t h e 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 ( 1 0 0 ) 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 . f o r a surface-breakdown MOS  silicon  interface  102  g a t e , b e f o r e and a f t e r b r e a k  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  105  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  106  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  U.5  C o p i e s o f t h e f i v e photomasks  3  107  used t o f a b r i c a t e the  devices. k.6  Fabrication  110 112  sequence f o r t h e surface-breakdown t e s t  113  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 d e v i c e  fabrication  122  xi LIST OF FIGURES c o n t ' d Page  h.Q  C r o s s - s e c t i o n o f t h e c o l d chamber used f o r t h e low  125  temperature device t e s t i n g  h.9  B l o c k diagram o f t h e t e s t e l e c t r o n i c s  127  It. 10  S u r f a c e d o p i n g p r o f i l e f o r w a f e r P l - 7 , o b t a i n e d from  129  C(v)  d a t a by t h e method d e s c r i b e d i n Appendix C  It. 11  S u r f a c e d o p i n g p r o f i l e f o r w a f e r 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 w a f e r P2-5 as a f u n c t i o n o f  132  p o s i t i o n i n t h e band gap, o b t a i n e d from C(V) measurements by t h e method o u t l i n e d i n Appendix C h.13  T e s t waveforms f o r t h e s u r f a c e - b r e a k d o w n , c h a r g e - i n j e c t ion  k.lh  1+.15  r e s e t v o l t a g e f o r d e v i c e s from t h e f i r s t  I36  fabrication  V o l t a g e 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 the  It. 16  devices  V o l t a g e 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 the  13U  137  r e s e t v o l t a g e (second f a b r i c a t i o n )  Maximum charge p e r p u l s e as a f u n c t i o n o f t h e p h o t o g a t e  139  voltage it. 17  lltO  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 surfacebreakdown d e v i c e s  18  Dark count r a t e as a f u n c t i o n o f t h e e x c e s s p h o t o g a t e bias f o r the three reset i n v e r s i o n conditions, V  = r  +10V, +12V and +lltV  lU2  xii  LIST  OF  FIGURES  cont'd  Page  it. 19  Dark and photon i n d u c e d p u l s e r a t e s as a f u n c t i o n o f e x c e s s photogate from t h e f i r s t  it. 20  li+3  b i a s , f o r one o f t h e b e t t e r d e v i c e s fabrication  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 m a i n t a i n a c o n s t a n t output, p u l s e s i z e o f 1 x 10  lit 5  e l e c t . , as a  f u n c t i o n o f t h e c y c l e time t  it.21  Dark and photon i n d u c e d p u l s e r a t e s as a f u n c t i o n o f  U.22  t h e p h o t o g a t e b i a s f o r two o f t h e b e t t e r s u r f a c e breakdown d e v i c e s from t h e second  U.23  ihQ  fabrication  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 a bulk-breakdown MOS  lit 7  151  g a t e , b e f o r e and a f t e r breakdown,  and a t breakdown  —  •  k.2h  Bulk-breakdown, c h a r g e - t r a n s f e r t e s t d e v i c e  157  it. 25  F a b r i c a t i o n sequence f o r t h e b u l k breakdown t e s t d e v i c e s  l6l  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 t h e photogate  169  f o r V = 100V g it.27  and V = itOV T  R e s u l t s o f the two-dimensional t i o n o f t h e avalanche  it.29  80K  T e s t waveforms a n d . t i m i n g f o r t h e b u l k - b r e a k d o w n , c h a r g e transfer  170  i n i t i a t i o n probability with posi-  t i o n under t h e p h o t o g a t e , T =  it.28  c a l c u l a t i o n of the v a r i a -  173  devices  Dark p u l s e r a t e as a f u n c t i o n o f l / t  ( i . e . , as a f u n c t i o n  o f t h e number o f r e s e t s p e r s e c . o f a c t i v e t i m e ) f o r a f i x e d r e s e t d u r a t i o n o f t = 0 . 1 msec r  176  xiii LIST OF FIGURES c o n t ' d  Page 4.30  Dark p u l s e r a t e as a f u n c t i o n o f t h e 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  4.31  Dark p u l s e r a t e as a f u n c t i o n o f t h e p h o t o g a t e b i a s and substrate temperature. breakdown  The x's mark t h e approximate  voltage  (a)  t = . 0.1 msec  , t = 10.0 msec  (b)  t = 1.0 msec  , t = 1.0 msec a  r  r 4.32  Red g a l l i u m a r s e n i d e  1 7 Q  ify  phosphide LED s o u r c e u s e d f o r t h e  photon i n d u c e d p u l s e r a t e measurements  4.33  177  181  Dark and photon i n d u c e d p u l s e r a t e s as .a f u n c t i o n o f t h e p h o t o g a t e b i a s f o r d e v i c e M66/2-1. (a)  t = 1.0 msec  , t = 0.2 msec  (b)  t = 10.0 msec a t = 1.0 msec  , t = 0 . 2 msec r , t = 20.0 msec  (c) 4.34  &  &  —• -  Photon i n d u c e d p u l s e r a t e as a f u n c t i o n o f t h e p h o t o g a t e b i a s when t h e dark s u b t r a c t i o n i n c l u d e s t h o s e . c o u n t s r e s u l t i n g from t h e d e t r a p p i n g  183 184 X85  188  f o l l o w i n g an a v a l a n c h e d i s c h a r g e  Dl  D e v i c e s t r u c t u r e used f o r t h e t w o - d i m e n s i o n a l model.  2lh  D2  Device s t r u c t u r e a f t e r conformal transformation.  217  ACKNOWLEDGEMENT  I w o u l d l i k e t o acknowledge t h e f o l l o w i n g p e o p l e f o r t h e i r h e l p and encouragement d u r i n g t h e r e s e a r c h and p r e p a r a t i o n o f t h i s thesis: Gordon W a l k e r , f o r h i s a s s i s t a n c e d u r i n g t h e i n i t i a l  stage  of t h i s project. 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 s u p p o r t t h r o u g h o u t t h e r e s e a r c h . G a r r y 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 e x p e r i m e n t a l and t h e o r e t i c a l  The  aspects.  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 o f B r i t i s h  Columbia f e l l o w s h i p s i s a l s o g r a t e f u l l y acknowledged. Very s p e c i a l t h a n k s go t o 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 h e r p a t i e n c e d u r i n g t h e l e n g t h y p r e p a r a t i o n .  1  1  INTRODUCTION  The r e s e a r c h r e p o r t e d i n t h i s t h e s i s i n v o l v e s t h e i n v e s t i g a t i o n o f a new  mode o f o p e r a t i o n f o r charge c o u p l e d .device (CCD)  imagers t h a t e n a b l e s  t h e d i r e c t d e t e c t i o n o f i n d i v i d u a l photons as t h e y a r r i v e .  Such photon  c o u n t i n g imagery i s o f g r e a t i n t e r e s t t o astronomers and t h o s e i n t h e space sciences, e s p e c i a l l y for satellite-borne observatories. One  o f t h e r e q u i r e m e n t s o f modern a s t r o p h y s i c s i s t h e d e t e c t i o n o f  v e r y 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  detection of very f a i n t r a d i a t i o n i s  l i m i t e d by t h e q u a n t i f i e d n a t u r e o f t h e r a d i a t i o n i t s e l f ,  fundamentally  so t h a t t h e a s t r o n -  omer must a c c u r a t e l y t r a c k t h e source and use l o n g exposures t o r e c o r d enough photon e v e n t s on each e l e m e n t a l s i r e d photometric  accuracy.  image a r e a , o r " p i x e l " , t o a c h i e v e t h e  de-  I n ground-based o b s e r v a t i o n s ^ a t m o s p h e r i c t u r b u -  l e n c e and sky background determine t h e f a i n t e s t o b j e c t s f o r w h i c h u s e f u l photometric  and s p e c t r o s c o p i c i n f o r m a t i o n can be o b t a i n e d .  a space p l a t f o r m a v o i d s t h e d e g r a d i n g  Observing  from  a t m o s p h e r i c e f f e c t s , however, t h e r e  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 t h e o p t i c s .  I n a d d i t i o n t o t h e s e low l e v e l b a c k g r o u n d s ,  i t i s v e r y o f t e n i m p o s s i b l e f o r t h e astronomer t o a v o i d 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  t h e r e may  be s t r o n g  emission  l i n e s n e x t t o t h e r e g i o n o f i n t e r e s t w h i l e i n t w o - d i m e n s i o n a l photometry there are o f t e n b r i g h t foreground  stars.  Therefore,  i n order to  realize  t h e f u l l p o t e n t i a l o f o b s e r v i n g from space and t o o b t a i n t h e utmost f r o m 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 c a p a b l e ing  of record-  s m a l l 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 a t t h e same t i m e  not b e i n g swamped by t h e s i g n a l from l o c a l i z e d b r i g h t a r e a s .  The  imager  must have maximum s e n s i t i v i t y , t h e l o w e s t p o s s i b l e s e n s o r 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 response. Various photoelectronic image sensors have been developed that attempt 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 output  (2)  photon counting imagers that allow external digital integration.  Before discussing in detail the proposed photon counting detector, presently existing low light level imagers are reviewed b r i e f l y 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 i s shown.to have the potential for nearly optimum low light level performance in the visible and near infrared.  Several  problem areas are identified that require experimental investigation before the fabrication of such an array i s 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 i s 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 i n chapter five.  2  The  BRIEF REVIEW OF LOW LIGHT LEVEL IMAGE SENSORS  f i e l d - o f l o w l i g h t l e v e l imaging has p r o g r e s s e d r a p i d l y i n t h e p a s t  few y e a r s .  Advances i n s i l i c o n VLSI t e c h n o l o g y 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 s e n s o r s , and t h e 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 l o w c o s t m i c r o p r o c e s s o r s and l a r g e memories f o r t h e m a n i p u l a t i o n and s t o r a g e o f t h e v a s t amount o f d a t a one o b t a i n s from such l a r g e s e n s o r a r r a y s .  I t i s unnecessary t o review i n d e t a i l  a l l o f t h e a n a l o g and photon c o u n t i n g 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  t h e g e n e r a l t y p e s o f image s e n s o r s and i n t e n s i f i e r -  sensor c o m b i n a t i o n s used, i t i s p o s s i b l e t o p r e s e n t a f a i r l y a c c u r a t e p i c t u r e of t h e s t a t e o f t h e a r t f o r low l i g h t l e v e l imaging.  I t must, o f c o u r s e ,  be remembered t h a t i n any r e a l imaging system t h e t y p e o f s e n s o r h o u s i n g o r i n t e n s i f i e r - s e n s o r assembly u s e d , as w e l l as t h e r e a d o u t , c o n t r o l , and d a t a h a n d l i n g 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 t h e o v e r a l l  performance.  A n a l o g i m a g i n g systems a r e d i v i d e d i n t o two g e n e r a l c a t e g o r i e s : (1)  image s e n s o r s w i t h no p r e - d e t e c t i o n g a i n  (2)  s e n s o r s t h a t i n t e g r a t e t h e s i g n a l a f t e r some form o f image i n t e n s i f i cation.  The l a t t e r c a t e g o r y i s d i s c u s s e d a l o n g w i t h photon c o u n t i n g systems s i n c e i t s i m p l e m e n t a t i o n i s v e r y 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 a r e d e t e r m i n e d p r i m a r i l y by t h e 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 c a t e g o r y 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 i o d e a r r a y s (CID)  arrays  [3,4], charge i n j e c t i o n  [5,6] and charge c o u p l e d d e v i c e (CCD) a r r a y s  device  [7,8].  T e l e v i s i o n p i c k - u p t u b e s have been i n r o u t i n e o p e r a t i o n f o r t h e p a s t t h r e e d e c a d e s , however,  i t was not u n t i l t h e l a t e 196o's t h a t  television  t e c h n i q u e s s t a r t e d t o r e p l a c e t h e 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 p h o t o g r a p h i c 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 i m a g i n g .  Television pick-up  tubes o f f e r e d t h e 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 t h e image, l i n e a r r e s p o n s e , and t h e p o s s i b i l i t y f o r p o s t 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 t e c h n i q u e s 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 s e n s o r s f o r s p e c t r o s c o p y and t w o - d i m e n s i o n a l photometry  [9].' V e r y  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 t y p e i m a g e r s , however, t h e newly d e v e l o p e d s i l i c o n m o n o l i t h i c l i n e and X - Y s e n s o r a r r a y s were b e coming a v a i l a b l e a t t h i s t i m e 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 p h o t o m e t r i c p o r p e r t i e s , a h i g h l y l i n e a r r e s p o n s e , 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 a d v a n -  t a g e o f s m a l l p h y s i c a l s i z e i s negated by t h e r e q u i r e m e n t t h a t s i l i c o n monol i t h i c imagers be c o o l e d b e l o w 150 K i n o r d e r t o reduce t h e d a r k l e a k a g e current to a n e g l i g i b l e l e v e l .  Such t e m p e r a t u r e s 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 h o u s i n g s 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 arrays.  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 p h o t o d i o d e  These s e n s o r s u t i l i z e t h e 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  electric-  a l l y i s o l a t e d p - n j u n c t i o n d i o d e s f o r t h e i n t e g r a t i o n and s t o r a g e o f p h o t o g e n e r a t e d charge [10].  The i n d i v i d u a l p h o t o d i o d e s a r e c o u p l e d t o one o r a  few v i d e o l i n e s v i a MOS s w i t c h e s o p e r a t e d by o n - c h i p s h i f t r e g i s t e r s .  Read-  out o c c u r s when t h e d i o d e s a r e r e b i a s e d s e q u e n t i a l l y t h r o u g h t h e 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 i s 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 i n 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 i n 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. greater than 10  It also enables a dynamic range  to 1 to be recorded in a single integration.  In addition  to high readout noise the two dimensional photodiode arrays suffer from considerable 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 depletion.  The potential wells thus formed collect and store the photo-generated •  400  600 INCIDENT  800 WAVELENGTH  1000 (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 i s obtained by pulsing the appropriate row of gates and sensing the voltage change on the appropriate column as the signal charge i s transfered 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 i s 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 r e f i l l i n g 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 drawback to presently existing CID imagers i s that they are front side illuminated which results in lower responsive quantum efficiencies, especially at short  8  w a v e l e n g t h s , due transparent  t o a b s o r p t i o n by the g a t e s t r u c t u r e .  I n t h e case o f semi-  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 t o t h e m u l t i p l e r e f l e c t i o n s 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 . s p e c t r a l t r a n s m i s s i o n c u r v e and hence t h e r e s p o n s i v e the CID has The  Consequently, the  quantum e f f i c i e n c y  of  a complex s t r u c t u r e t h r o u g h o u t t h e v i s i b l e spectrum ( F i g . 2.1).  analog  imager t h a t p r e s e n t l y has the most p o t e n t i a l at low  l e v e l s i s t h e CCD.  light  I n CCD's t h e charge t r a n s f e r p r i n c i p l e i s used t o t r a n s -  p o r t t h e o p t i c a l l y - c r e a t e d charge p a t t e r n o v e r l o n g d i s t a n c e s a c r o s s s i l i c o n s u r f a c e t o an o n - c h i p a m p l i f i e r l o c a t e d at t h e edge o f t h e  the sensor.  T h i s 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 r e a d o u t n o i s e t o ( l ) s i g n a l d e t e c t i o n at a common low c a p a c i t a n c e a t i o n of s w i t c h i n g spikes w i t h i n the array. i l l u m i n a t e d CCD  node and  rear  quantum e f f i c i e n -  c i e s a p p r o a c h i n g t h o s e o f . t h e s e l f scanned p h o t o d i o d e a r r a y s . f i c u l t y w i t h the CCD  (2) the e l i m i n -  In a d d i t i o n , t h i n n e d ,  s e n s o r s are a v a i l a b l e t h a t have r e s p o n s i v e  due  The  main d i f -  i s the l o s s o f 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 a l o n g the i n t e r f a c e . t i a l l y overcome by i n t r o d u c i n g  a  T h i s problem may  be  par-  b i a s charge or " f a t z e r o " , however, a  b e t t e r s o l u t i o n i s t o a v o i d s u r f a c e 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  c h a n n e l l o c a t e d away from t h e i n t e r f a c e [11] .  o f the much l o w e r d e n s i t y o f b u l k t r a p s , such b u r i e d are c a p a b l e o f v e r y h i g h charge  2.1.1  • The  DQE  For A n a l o g CCD  Because  c h a n n e l CCD's (BCCD's)  transfer efficiencies.  Sensors  A more q u a n t i t a t i v e a p p r a i s a l o f CCD  imager performance a t low  light  l e v e l s can be o b t a i n e d 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:  DQE  =  (S/N)* ?  (2.1) '  u t  (S/N)J  n  in  where,  (S/N)  , out  (S/N).  m  =  signal to noise ratio after detection  =  signal to noise ratio before detection  A detector i s performing optimally i f i t s DQE i s 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 w i l l be calculated.  If the DQE  as a function of spatial frequency i s desired i t can be obtained from the spatial modulation transfer function (MTF) DQE(f) =  according to [12],  5M|)_MTF  2  where, f i s the spatial frequency P(f) i s 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 background.  In this case, (S/N). in  =  (R t ) p  (2.2)  h  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 )  out O U t  =  ~  E  2  (RQE R t + a p  h  + 2R,t)* d  <'> 2  3  10  where,  RQE  =  r e s p o n s i v e quantum e f f i c i e n c y , e q u a l t o t h e r a t i o o f t h e number o f c o l l e c t e d c a r r i e r s o v e r t h e number o f i n c i d e n t photons.  a  =  I n c l u d e d i n t h i s f i g u r e a r e any dead space l o s s e s .  rms readout n o i s e o f t h e CCD  expressed  number o f p h o t o e l e c t r o n charges p e r R, d  =•  dark l e a k a g e p e r (2.2)  S u b s t i t u t i n g expressions f r e q u e n c y DQE  for a  as an e q u i v a l e n t  pixel.  pixel,  and  (2.3)  i n t o ( 2 . l ) y i e l d s t h e zero s p a t i a l .  CCD,  DQE(O)  = RQE  ^ • + (a /R t ) + 2(R„/R ) p d p  • E x p r e s s i o n (2.1*) f o r t h e DQE n o i s e , e x c e s s i v e dark l e a k a g e  (2.4)  i n d i c a t e s that i n a d d i t i o n to  a l s o degrades t h e performance o f CCD  readout 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 a r r a y s t o 150 K o r l o w e r t h e  dark  g e n e r a t i o n o f c a r r i e r s may  inte-  be r e d u c e d t o a n e g l i g i b l e l e v e l .  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 , t h e DQE v a l u e ( e q u a l t o t h e detector* s RQE) i s as expected  For f i x e d  approaches i t s maximum  as t h e s e n s o r i r r a d i a n c e i n c r e a s e s .  s i n c e 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  This photon  n o i s e dominates.  2.1.2  Performance of CCD  Imagers C u r r e n t l y I n  Operation  Readout n o i s e l e v e l s o f 20 t o 100 e l e c t r o n s rms s e v e r a l commercial CCD  have been a c h i e v e d  d e v i c e s , however, most o f t h e s e a r r a y s a r e f r o n t s i d e  i l l u m i n a t e d . a n d t h e r e s u l t a n t r e s p o n s i v e quantum e f f i c i e n c i e s a r e low. Instruments  Texas  has produced l a r g e r e a r i l l u m i n a t e d BCCD a r r a y s s p e c i f i c a l l y  s i g n e d f o r low l i g h t l e v e l i m a g i n g .  1*00 x 1*00 p i x e l p r o t o t y p e a r r a y s  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 t h e f u l l 800 x 800 v e r s i o n has been completed. l e v e l s of approximately  by  The  [13] element  1*00 x 1*00 a r r a y s are a c h i e v i n g readout  25 e l e c t r o n s rms  [14]  de-  noise  and have peak r e s p o n s i v e 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 processinginduced 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 substrate-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. CCD's is the highest yet achieved on a routine basis.  The RQE of the RCA 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 i n Fig. 2.2 versus total integrated incident signal at various, wavelengths and.assuming negligible dark leakage.  Curves of constant output signal to noise are also  shown. From these i t i s apparent that for integrated signal levels, such that (S/N)  is greater than approximately 70, the T.I. BCCD i s 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 i s 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 f a i r l y 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 i s digitized must be eliminated or calibrated out.  Stability of the signal  electronics i s also of concern, especially i f i t i s 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 i n tegrated incident signal, at several different wavelengths. Curves of constant signal to noise in the output are also indicated.  13 response of CCD imagers as well as the transfer characteristics of the onchip 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 consequences 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 development of intensified CCD's that operate in a photon counting mode. The requirements for photon counting are straightforward.  Enough pre-readout gain  must be provided in order to reliably discriminate single photon events above readout noise i n 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 w i l l 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 w i l l be clearly above the noise.  It i s possible, however, to operate  some intensified detectors in a. charge integration mode so that higher photon fluxes can be measured. The integration time i s set so as not to saturate the sensor and multiple frames may be summed without degradation due to sensor readout noise, provided there is sufficient gain i n 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 i s small, photon noise limited operation i s possible.  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 discriminate 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 i s 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 effects introduce non-linearities and lower the DQE.  These effects are exam-  ined below for spatially and temporally invariant signals.  15  F o r an i n t e n s i f i e d . i m a g e r o p e r a t i n g i n a photon c o u n t i n g mode, t h e mean event r a t e i s , n where,  =  (2.5)  R RQE n + n, , n x « l p d d J  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 p e r p i x e l  RQE  =  r e s p o n s i v e quantum e f f i c i e n c y o f t h e photocathode  n  =  p r o b a b i l i t y t h a t a p h o t o e l e c t r o n r e s u l t s i n an o u t p u t s i g n a l p u l s e above t h e d i s c r i m i n a t o r l e v e l  n^  =  mean number o f e v e n t s / s e c / p i x e l due t o n o i s e and t h e r m i o n i c a  e m i s s i o n from t h e photocathode T  =  frame t i m e  The a r r i v a l o f i n c i d e n t photons and t h e occurence o f dark e v e n t s obey P o i s s o n s t a t i s t i c s , t h e r e f o r e , . t h e p r o b a b i l i t y t h a t t h e r e w i l l be a count i n frame time x i s , P  =  1 - exp(-nx)  The number o f c o u n t s measured i n N frames i s , C  =  PN  =  therefore,  [1 - exp(-nx)]N  (2.6)  and t h e mean square d e v i a t i o n i s , (AC)  2  =  exp(-nx)[1 - exp(-nx)]N  (2.7)  E q u a t i o n (2.6) shows t h e d e p a r t u r e from l i n e a r i t y due t o t h e 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 t h e mean number o f c o u n t s  i n N frames becomes, C*  =  (2.8)  -N £n[l - (C/N)]  and t h e mean square d e v i a t i o n becomes,  (AC)  2  dC dC  1 2  (AC)  2  =  [exp(nx) - 1]N  (2.9)  T h e r e f o r e , a f t e r s u b t r a c t i n g t h e dark count r a t e , t h e s i g n a l t o n o i s e i n t h e output i s ,  16 (n - n,)xN (S/K) out  {[exp(nx) - 1]N + n TN}  (2.10)  :  d  The signal to noise in the input i s ,  f(n - n >TH}* a  i  RQE  (2.11)  nJ  Therefore, the zero spatial frequency DQE becomes, (n - n )x d  DQE(O) •=  RQE n  (2.12)  exp(nx) - 1 + n x  Equation 2.12 shows the importance of a high RQE and n, and reveals the degradation 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  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, 1 - (n /n) ( d d  DQE(O) -  RQEn  1  +  / n )  (2.13)  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 i n 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].  FIGURE 2.3 detector.  The e f f e c t o f t e m p o r a l s a m p l i n g on t h e DQE  o f a photon c o u n t i n g  18 (2) A special image tube that has as i t s anode either the silicon target of a vidicon or a solid state semiconductor array that directly detects photoelectron 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 f i r s t category the image intensifier tubes can be either fibre-optically or lens coupled to the sensor.  I f 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 i s 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 o u p l i n g a r e 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 t h e image tube a semiconductor a r r a y anode t h a t d i r e c t l y d e t e c t s t h e h i g h energy photoelectrons.  There i s no e v e n t . l a g w i t h t h e s e imagers and event c e n t e r  d e t e c t i o n i s g e n e r a l l y not r e q u i r e d .  These image tubes a r e n o r m a l l y  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 g i v e an e l e c t r o n - h o l e p a i r y i e l d t h a t i s l e s s than UOOO p e r i n c i d e n t p h o t o e l e c t r o n .  In  o r d e r t o photon count, t h e r e f o r e , a l o w n o i s e CCD sensor i s r e q u i r e d . Unf o r t u n a t e l y , t h e l i f e t i m e s o f CCD. imagers a r e v e r y s h o r t when o p e r a t e d  i n an  electron-bombarded mode due t o t h e damage i n t r o d u c e d a t t h e s i l i c o n - s i l i c o n dioxide interface. to  The t r a n s f e r channels  o f a CCD a r e p a r t i c u l a r l y  sensitive  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, t h e 50$ dead space caused b y t h e i n t e r l e a v e d channels reduces t h e p h o t o e l e c t r o n d e t e c t i o n p r o b a b i l i t y n.  Rear-illuminated, elec-  tron-bombarded CCD's appear t o have much l o n g e r l i f e t i m e s ' . [ 2 1 , 2 6 ] , however, v e r y few CCD's have so f a r been o p e r a t e d  i n t h i s mode and t h e d a t a 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 m i c r o c h a n n e l 5  p l a t e i n t e n s i f i e r i s a b l e t o d e l i v e r an output  pulse  7  o f 10 t o 10 e l e c t r o n s , f a r i n excess o f t h e n o i s e l e v e l o f 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 . T h i s a l l o w s a m u l t i - a n o d e a r r a y t o be p l a c e d i n p r o x i m i t y focus a t t h e output o f t h e MCP, w i t h each anode c o n n e c t e d to an i n d i v i d u a l c o u n t i n g 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 a r e t y p i c -  a l l y 0.5mm t o 1.0mm square and a r e s e p a r a t e d b y i n t e r p i x e l s c r e e n i n g e l e c t r o d e s t o prevent in  parallel  cross-talk.  Since a l l t h e p i x e l s are e f f e c t i v e l y read'out  v e r y h i g h count r a t e s p e r p i x e l can b e 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 t h e gain  f a l l s o f f r a p i d l y because o f t h e charge l o s t b y t h e h i g h r e s i s t i v i t y walls.  channel  An opaque photocathode d e p o s i t e d d i r e c t l y on t h e f r o n t f a c e o f t h e  MCP can be used w i t h t h e s e imagers.  A f i e l d i s established i n front o f 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 i s 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) i s 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 selfscanned photodiode arrays. rates possible.  The high gain of the MCP makes very high frame  Unfortunately, this approach has not been pursued as active-  ly as the coincidence anode technique and only small self-scanned anode arrays 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 .  T h i s does not a f f e c t t h e i r DQE o r  when d e t e c t i n g v e r y f a i n t i m a g e s , however, i t t h a t can be r e c o r d e d .  linearity  does l i m i t t h e dynamic range  A h i g h dark count r a t e w i l l l o w e r t h e DQE and f u r t h e r  l i m i t t h e dynamic range b u t , by c o o l i n g t h e p h o t o c a t h o d e s and c h o o s i n g t h e 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 may be reduced t o a n e g l i g i b l e l e v e l .  degradation  A l l o f t h e 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 s e m i t r a n s p a r e n t o r opaque p h o t o e m i s s i v e 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 a n d , as i n d i c a t e d  by e q u a t i o n  (2.12),  i t i s t h e r e s p o n s i v e 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 t h e DQE a t low l i g h t l e v e l s .  F i g u r e 2.h shows t h e r e s p o n s i v e quantum  e f f i c i e n c y v e r s u s w a v e l e n g t h f o r t h e most w i d e l y used p h o t o c a t h o d e m a t e r i a l s . Because o f t h e l o w RQE's o f a v a i l a b l e p h o t o c a t h o d e s longward o f 6 0 0 nm, a n a l o g CCD imagers a r e a b l e t o o f f e r s u p e r i o r performance i n t h e r e d 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 t o 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 t h e DQE  v e r s u s w a v e l e n g t h i s p l o t t e d f o r b o t h t h e Texas I n s t r u m e n t s  rear-illuminated  BCCD and a t y p i c a l photon c o u n t i n g imager e q u i p p e d w i t h a t r i - a l k . ode.  photocath-  The DQE f o r an a n a l o g CCD a l s o depends on t h e 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 , d e t e r m i n e s t h e 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 a r e used i n F i g . 2 . 5 t o show t h e w a v e l e n g t h dependence o f t h e DQE f o r t h e T . I . DQE p o s s i b l e .  array.  The c u r v e f o r (S/N)  >1000 r e p r e s e n t s t h e maximum  The DQE f o r t h e 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 l o w e r t h a n t h e frame r a t e and i s t h e r e f o r e independent the output s i g n a l to n o i s e .  of  INCIDENT  WAVELENGTH  (nm)  FIGURE 2.4 Responsive quantum efficiency of different photdcathode/window combinations as a function of wavelength.  ro  23  rear illuminated BCCD t o - : 25 e l « c . rms, =0) photon counting system tri.-alk. photocathode ( R « frame rate)  with  D  200  400 INCIDENT  600 800 WAVELENGTH (nm)  1000  FIGURE 2.5 The DQE as a.function of wavelength for a photon counting detector with a t r i . - a l k . 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 i n a photon counting (or Geiger tube) mode, provided the dark current i s sufficiently small.  When such an avalanche  diode is suddenly biased above breakdown i t is i n i t i a l l y non-conducting. Not until a carrier is injected into or generated within the high f i e l d 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 w i l l 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 i s a suitable quenching circuit which momentarily reduces the diode bias and interrupts the avalanche. The equivalent circuit for an avalanche diode operating above breakdown denotes the breakdown voltage, R the diode  is shown in Fig. 3.1 [35]. V D  S  series'impedance, R the space charge, resistance during breakdown, and C^ the c  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, w i l l also serve to.quench the avalanche breakdowns. An avalanche discharge is represented 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 i n  the high f i e l d region of the diode depletion layer cause the avalanche to turn off.  The mean time to turn off decreases as the circuit impedance i n -  25  o u t p u t  FIGURE  3.1 E q u i v a l e n t c i r c u i t f o r an a v a l a n c h e d i o d e o p e r a t i n g above b r e a k down (shown i n dashed, box) p l u s t h e b i a s and d e t e c t i o n c i r c u i t . An a v a l a n c h e d i s c h a r g e i s r e p r e s e n t e d by t h e c l o s i n g o f s w i t c h S.  V,  o p e n  1  FIGURE  — closed  3.3 E q u i v a l e n t c i r c u i t f o r an MOS g a t e o p e r a t i n g above breakdown. Charge i n j e c t i o n ( o r charge t r a n s f e r ) i s r e p r e s e n t e d b y t h e dashed c o n d u c t i o n p a t h and s w i t c h S .  26  c r e a s e s [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 s m a l l a r e a  (~100 pm ) d i o d e s . charged t o V  Once t h e avalanche has been quenched (S opens) C^ i s r e -  w i t h a t i m e c o n s t a n t o f a p p r o x i m a t e l y . R (C a  + C ). S i n c e R i s  Jj d  s  1J  n o r m a l l y much l a r g e r than R , t h i s time c o n s t a n t d e t e r m i n e s t h e dead t i m e p e r pulse.  C l e a r l y t h e r e i s a compromise between m i n i m i z i n g R  and s t i l l  main-  t a i n i n g a s h o r t quench t i m e . Not e v e r y p h o t o g e n e r a t e d c a r r i e r t h a t i s g e n e r a t e d w i t h i n o r 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 t h e diode i n t o reverse conduction. w i l l t r a n s i t t h e h i g h f i e l d r e g i o n w i t h o u t s u f f e r i n g any i o n i z i n g  A few  collisions  w h i l e o t h e r s may i n i t i a t e c h a i n s 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 o n l y a few c a r r i e r s have been g e n e r a t e d .  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 a v a l a n c h e , n o t o n l y must t h e i n i t i a t i n g c a r r i e r cause a t l e a s t one i o n i z a t i o n , b u t d u r i n g each, subsequent cause a t l e a s t one i o n i z a t i o n . i n f i n i t e number o f descendants  t r a n s i t t i m e some descendant must a l s o  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 have an ( i . e . , w i l l t r i g g e r t h e diode i n t o reverse  c o n d u c t i o n ) has been r e f e r r e d t o as t h e a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y [ 3 2 ] . The a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y i s zero a t t h e breakdown v o l t a g e and, as would be e x p e c t e d , e v e n t u a l l y s a t u r a t e s t o one as t h e d i o d e 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 a v a l a n c h e p h o t o d i o d e o p e r a t e d i n t h e above mode o f f e r s t h e unique p o s s i b i l i t y o f a s o l i d s t a t e photon c o u n t i n g d e t e c t o r c a p a b l e o f a v e r y h i g h DQE.  F u r t h e r m o r e , 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 d i o d e c o u l d be t h e b a s i c element t o 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 c o u n t i n g imager.  A small monolithic or hybrid array o f  avalanche p h o t o d i o d e s , each w i t h i t s own p u l s e c o u n t i n g c i r c u i t r y , would be o f 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 t o f a b r i c a t e l a r g e  s e l f - s c a n n e d a r r a y s c a p a b l e o f h i g h frame r a t e s .  I n t h i s case t h e d i o d e s must  be operated" i n t h e charge i n t e g r a t i o n mode ( i . e . , p u l s e d 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 i s pulsed into very deep depletion, such that the f i e l d in the depleted semiconductor i s higher than that which would normally cause breakdown and the subsequent formation of an i n version layer.  One important advantage of such an MIS breakdown image element  is i t s inherent quenching mechanism. Once an avalanche has been initiated and large numbers of carriers are being generated, an inversion layer w i l l 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 w i l l then remain in a partially discharged state until i t i s 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 .  i s the gate voltage above breakdown and <f^. i s the silicon sur-  face potential at the onset of breakdown.  R  g  and R  are the series and space  charge impedance, C ^ is the depletion region capacitance, and C capacitance.  q x  is the oxide  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, i s that instead of  creating only one carrier pair, a single photon is now able to trigger a momentarily 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>^ = silicon surface potential at the onset of breakdown. A((> = amount by which the surface potential exceeds breakdown i n i t i a l l y . s  29  - P1 - P2  f—  177^771  1^771 r77>7i J????.  tT*rp  P3 - P4  XTpTA  FIGURE 3.4 Potential well diagram illustrating the basic operation of a itphase PC-CCD. Heavy solid line indicates the potential at the Si-SiO^ interface. (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 e x a c t l y as a normal CCD. I t i s only during the detection part of the c y c l e i n the i n t e r v a l between readouts that one o r more phases i s h e l d at a p o t e n t i a l above breakdown.  Since  no avalanche discharges can occur during readout, image smearing i s not a problem.  However, i n order t o minimize dead time t h i s phase must l a s t f o r  only a small f r a c t i o n of the t o t a l frame time.  The array would, t h e r e f o r e ,  have t o be organized f o r frame t r a n s f e r i n t o a separate storage and readout area.  The l a r g e s i g n a l charge packets, and the f a c t that only t h e i r presence  need be determined during readout, should make very high c l o c k i n g r a t e s poss i b l e during frame t r a n s f e r and readout.  In a d d i t i o n t o dead time, a c e r t a i n  amount o f dead space may a l s o be unavoidable.  I n order t o define the i n d i v i d -  u a l p i x e l s and prevent c r o s s t a l k , the regions between t r a n s f e r channels and under at l e a s t one clock phase must be kept below.breakdown.  Photogenerated  c a r r i e r s from these areas may not pass through a high f i e l d region before being 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 s under the a c t i v e gates, and thus, may be unable t o t r i g g e r an avalanche discharge. The l i n e a r i t y and DQE f o r a photon counting CCD operating i n the breakdown mode ( h e r e a f t e r r e f e r r e d t o as a PC-CCD) are described by the same equations as were derived p r e v i o u s l y f o r photon counting imagers (equations 2.6 and 2.12), however, n now r e f e r s t o 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 t o expect that  the dead space i n a r e a r - i l l u m i n a t e d PC-CCD would be l e s s than 50$, perhaps as low as 25%, and that the RQE f o r each p i x e l could be at l e a s t as high as f o r the RCA o r 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 f o r a PC-CCD would be approximately as shown i n F i g . 3.5-  I t I s c l e a r t h a t the high responsive quantum e f f i c i e n c y  t y p i c a l o f 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 E x p e c t e d performance o f a PC-CCD compared t o e x i s t i n g p h o t o n c o u n t i n g systems e m p l o y i n g a t r i . - a l k . p h o t o c a t h o d e . .  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 achieving 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, w i l l 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 i n i t i a t -  ed in such a device, the buildup of space charge and the formation of the i n -  33 version the  l a y e r reduces t h e peak e l e c t r i c f i e l d and t h e c o r r e s p o n d i n g v a l u e s o f  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 t o the p o i n t at which the avalanche  turns o f f .  B e f o r e t h e 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 r e d u c e d  s i g n i f i c a n t l y , however, t h e number o f c a r r i e r s i n t h e h i g h f i e l d r e g i o n o f t h e depletion  l a y e r w i l l have grown t o t h e e x t e n t t h a t a s t a t i s t i c a l  fluctuation  t o z e r o , p r i o r t o t h e g e n e r a t i o n o f a d e t e c t a b l e s i g n a l charge i n t h e i n version  l a y e r , i s h i g h l y improbable [ 3 2 , 3 3 ] .  Thus, t o a v e r y good a p p r o x i -  m a t i o n , t h e 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 a v a l a n c h e t h a t i n a d e t e c t a b l e p u l s e , i s t h e same as t h e a v a l a n c h e i n i t i a t i o n  results  probability  o f an i d e a l i z e d d e v i c e w i t h no c u r r e n t l i m i t i n g mechanisms, and f o r w h i c h 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.  T h i s i s an i m p o r t a n t s i m p l i f i c a t i o n s i n c e with, no c u r r e n t f l o w -  ing, 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 depletion  l a y e r and t h e c o r r e s -  ponding v a l u e s o f t h e 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 The i o n i z a t i o n r a t e d a t a f o r s i l i c o n  calculated.  used i n t h i s i n v e s t i g a t i o n i s g i v e n i n  Appendix A.  3.1.1  Triggering  P r o b a b i l i t y Theory  Consider the depletion  r e g i o n o f a p l a n a r a v a l a n c h e d i o d e ( o r MOS  t h a t i s b i a s e d above t h e breakdown v o l t a g e , (shown s c h e m a t i c a l l y P ( x ) and P, ( x ) a r e t h e a v a l a n c h e i n i t i a t i o n e h holes r e s p e c t i v e l y ,  that  has been g e n e r a t e d a t p o s i t i o n x. ' 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  hole i o n i z a t i o n rates.  layer.  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 The p r o b a b i l i t y t h a t an e l e c t r o n  and  Pp( ) i x  pair  s  that  or hole  i n t h e i n f i n i t e s i m a l d i s t a n c e 6x i s s i m p l y  g i v e n by a ( x ) 6 x and a, (x)(Sx r e s p e c t i v e l y , where a e h and  3.6);  i n Fig.  p r o b a b i l i t i e s , f o r electrons  s t a r t at p o s i t i o n x i n the depletion  l i k e w i s e the avalanche i n i t i a t i o n  gate)  and a, a r e t h e e l e c t r o n e h  The p r o b a b i l i t y ( l - P ) t h a t n e i t h e r t h e e l e c t r o n P or t h e h o l e o f a p a i r g e n e r a t e d a t p o s i t i o n x a r e a b l e t o t r i g g e r a breakdown  3h  FIELD  p (x) ; e  •eo  o  1  ©o  >  P (x) h  I  <  <  *  ©o—>  ©o  Pp(x)  <—eo—>  ©O  I —¥ <—©o  O I  1  ©o—>  >  a (x) g(x) h  t ©O  *  a (x)Sx e  ©O x*Sx  x=0 DEPLETION  x=W  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 i s indicated in each case.  35  is given by the product, (1 - P ) = (1 - P )(1 - P. ) p e h therefore, Pp  =  P e P. h- P e An +  Similarly, Oldham et.al. [31] show that the probability P (x + 6x) that an g  electron starting at position x + 6x w i l l 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 i n differential form, after substituting (3.3) for P^(x), dP -T^- = (1 - P )a (P + P - P P.) dx e e e h eh o  (3.2)  v  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 f i e l d distribution prior to break-  down i s known, (3.2) and (3-3) can be integrated with the boundary conditions P (0) = 0 e P j v ) =0 n  (3.4) (3.5)  Numerical techniques must, in general, be used to solve (3.2) (3.5).- The most straightforward method i s 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 i n 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 P (x) and P^U) for an MOS gate biased above breakdown are g  36  shown in Fig. 3.7. The corresponding band diagram is that shown in Fig. 3.2. 15  A uniformly doped substrate with N  A  = 5.5 x 1 0  ionization rates were used for this example.  -3  cm  and room temperature  The parameter  A<|> is the amount S  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 i s 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 f i e l d 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 i s apparent from the theoretical results shown in Fig; 3.8 that a large voltage above breakdown is required to reach saturation of the avalanche initiation probability. In the example shown, an excess bias of 1 0 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 somewhat higher excess voltages to ensure that small variations in the breakdown voltage over the image area do not introduce large variations in response.  37 0  interface  FIGURE 3.7  x/w  The avalanche initiation probabilities P (x) and P (x) for a pe h substrate MOS gate. A«> i s the amount by which the surface potential exceeds The ionization rate data used i s s breakdown. W i s the depletion layer width 15 -3 given in Appendix A, =5x10 -cm , T = 300K  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 S i - S i 0 2 interface. Same parameters as for Fig. 3.T.  39  In o r d e r t o s o l v e f o r P (x) e  and P. (x) n  u s i n g the coupled d i f f e r e n t i a l  e q u a t i o n s (3.2) and (3.3), t h e 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 t h r o u g h t h e d e p l e t i o n l a y e r must be known. making t h e a p p r o x i m a t i o n field,  Mclntyre  [32] has shown, however, t h a t by  = k a , where k i s a c o n s t a n t independent  of  g  (3.2) and (3.3) may be combined t o g i v e i n t e g r a b l e e x p r e s s i o n s  P. (0) and P (w). h e  The r e s u l t a n t e x p r e s s i o n s a f t e r i n t e g r a t i o n a r e : . . -  - l n [ l - P (0)]  =  ( i - T l O l n [ P ( 0 ) + f(w)  1 - P. (0)  =  [1 - P ( w ) ]  h  n  where f(w)  for  h  e  + 1 - P (0)] h  (3.6)  (3.7)  k  w = e x p [ ( l - k ) ? ] , and t, = / a ( x ) d x 0  .  e  From t h e s e e q u a t i o n s , t h e 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 t h e two parameters k and £ w i t h o u t h a v i n g t o know t h e e x a c t field distribution.  Unfortunately,  the approximation  = kct^ i s v e r y poor  f o r s i l i c o n , and i t was found n e c e s s a r y t o use e q u a t i o n s (3.2) - (3-5) i n o r d e r t o o b t a i n s u f f i c i e n t l y a c c u r a t e 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 t h e 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 t h e e x p e r i m e n t a l results. 3.1.2  Previous Experimental  Investigations  The p u l s e r a t e o f an a v a l a n c h e photo d i o d e b i a s e d above t h e breakdown v o l t a g e i s d e t e r m i n e d b y t h e p r o d u c t o f t h e number o f c a r r i e r s t r a n s i t i n g t h e d e p l e t i o n l a y e r p e r u n i t t i m e , and t h e a p p r o p r i a t e a v a l a n c h e i n i t i a t i o n probability.  By m e a s u r i n g t h e v o l t a g e dependence o f t h e p u l s e r a t e under  c o n d i t i o n s of 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 d e t e r m i n e d e x p e r i m e n t a l l y . and B e r n t  Such measurements were made b y K e i l  [27] b y o b s e r v i n g t h e v o l t a g e dependence o f t h e  p u l s e r a t e under c o n s t a n t i l l u m i n a t i o n .  photon-induced  They found e v i d e n c e f o r  saturation  1+0 o f t h e t r i g g e r i n g p r o b a b i l i t y i n some o f t h e d i o d e s t h e y s t u d i e d b u t t h e v a l u e o f excess b i a s a t w h i c h s a t u r a t i o n o c c u r e d i s much l o w e r t h a n e x p e c t e d . The d i o d e s t h e y s t u d i e d , . however, were n o t f r e e from m i c r o p l a s m a s , and t h e d i o d e t h e y r e p o r t e d showing s a t u r a t i o n had a d a r k count r a t e an o r d e r o f magnitude l a r g e r t h a n t h e p h o t o n - i n d u c e d p u l s e 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 s u s p e c t . Oldham e t a l . [31] have o p e r a t e d s m a l l a r e a , d e f e c t - f r e e a v a l a n c h e p h o t o d i o d e s above t h e breakdown v o l t a g e i n o r d e r t o p r o v i d e e x p e r i m e n t a l 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 ties.  probabili-  The m i n i a t u r e a v a l a n c h e d i o d e s used were n p a b r u p t j u n c t i o n d e v i c e s +  w i t h a deeply d i f f u s e d n  guard r i n g t o p r e v e n t premature edge breakdown and  t o d e f i n e t h e s m a l l e s t p o s s i b l e breakdown a r e a ( t y p i c a l l y 3-5 un i n d i a m e t e r ) . The d i o d e s were i l l u m i n a t e d from t h e 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 o r d e r t o p r o v i d e h o l e 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 h i g h  a b s o r p t i o n c o e f f i c i e n t s a t 390 nm e n s u r e d pure h o l e i n j e c t i o n ' f r o m t h e neutral region of the n  l a y e r so t h a t t h e photon i n d u c e d p u l s e r a t e p r o -  v i d e d a d i r e c t measure o f t h e a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y f o r h o l e s ent e r i n g the d e p l e t i o n region.  Pure e l e c t r o n i n j e c t i o n from t h e n e u t r a l p-type +  b u l k was n o t p o s s i b l e i n t h e case o f i l l u m i n a t i o n from t h e n  side.  However,  Oldham e t a l . argued t h a t because o f t h e s m a l l a b s o r p t i o n c o e f f i c i e n t a t 1050 nm and t h e 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 , t h e 1050 nm responses s h o u l d be r o u g h l y p r o p o r t i o n a l t o t h e a v a l a n c h e i n i t i a t i o n  proba-  b i l i t y for electrons entering the depletion region. The measured r e s p o n s e a t 390 nm was found t o f o l l o w t h e t h e o r e t i c a l h o l e t r i g g e r i n g p r o b a b i l i t y v e r y c l o s e l y , however, o n l y t h e l i n e a r r e g i o n o f the  a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y v e r s u s e x c e s s b i a s was c o v e r e d , and  s i n c e o n l y a v e r y rough e s t i m a t e o f t h e a b s o l u t e 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 , t h e r e s u l t s do n o t , i n f a c t , p r o v i d e good c o n f i r m a t i o n o f t h e  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 i n 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 w i l l be possible to operate an MOS gate i n the plateau region of the electron t r i g 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 i s 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 i t s effect 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  should be maintained at a level below 500 sec -l6  leakage current of approximately 10  —2  cm  (corresponding to a dark  -2  A cm  ).  A major effort w i l l be re-  quired to achieve such low dark count rates. Two basic mechanisms are responsible for the dark generation of carriers within or adjacent to the surface space charge region of an MOS  gate.  The f i r s t 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 f i e l d region, involves band to band tunneling or tunneling between one band and a bulk trapping level or surface state. 3.2.1  These generation mechanisms are described in more detail below. 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 . 1 3 ) .  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 t h e v a l e n c e t o c o n d u c t i o n band.  S e m i c o n d u c t o r d e v i c e s on t h e o t h e r hand a r e 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 h a v i n g a l o w 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 , t o g i v e p r e d o m i n a n t l y t o t h e s e dopant er  n o r p type c o n d u c t i v i t y .  In a d d i t i o n  i m p u r i t i e s , a number o f o t h e r unwanted i m p u r i t i e s w i t h h i g h -  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  duced d u r i n g d e v i c e p r o c e s s i n g .  intro-  When t h e i o n i z a t i o n energy o f t h e i m p u r i t y  i s h i g h e r i t may n o t be c o m p l e t e l y i o n i z e d a t normal o p e r a t i n g and w i l l a c t as a t r a p o r r e c o m b i n a t i o n - g e n e r a t i o n  center.  temperatures  These energy  l e v e l s a r e n o t o n l y caused b y i m p u r i t i e s b u t a l s o by a l a r g e v a r i e t y o f crystal defects.  The d i f f e r e n c e between s h a l l o w 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 .  l e v e l w i l l p l a y depends on t h e t e m p e r a t u r e ,  Which r o l e t h e energy  the concentration of free car-  r i e r s and t h e r e l a t i v e c r o s s s e c t i o n f o r t h e c a p t u r e o f m a j o r i t y and m i n o r i t y carriers.  Deep l e v e l s w i t h i n t h e band gap a r e g e n e r a l l y l o o s e l y r e f e r r e d  t o as s i m p l y " t r a p s " .  The s t a t i s t i c s o f c a r r i e r c a p t u r e and e m i s s i o n b y such  i n t e r m e d i a t e energy l e v e l s has been worked o u t b y S h o c k l e y and Read [37] and by H a l l  [38].  F o r use i n t h e a n a l y s i s o f dark g e n e r a t i o n mechanisms t h i s  t h e o r y w i l l be b r i e f l y  reviewed.  F o l l o w i n g t h e b a s i c concepts o f S h o c k l e y and Read, f o u r b a s i c  processes  are d e f i n e d f o r c e n t e r s w i t h a s i n g l e energy l e v e l w i t h i n t h e band gap ( F i g . 3.10): (a)  E l e c t r o n c a p t u r e from t h e c o n d u c t i o n band  (b)  E l e c t r o n e m i s s i o n i n t o t h e c o n d u c t i o n band  (c)  Hole c a p t u r e from t h e v a l e n c e band  (d)  Hole e m i s s i o n i n t o t h e v a l e n c e band  Processes  (a) and ( c ) a r e d e s c r i b e d by two c a p t u r e p r o b a b i l i t i e s c ^ s e c  and c ^ ( s e c ^ ) , w h i l e p r o c e s s e s  ^)  (b) and (d) a r e d e t e r m i n e d b y t h e e m i s s i o n  U5  * .  (c)  1  i—i  l-O- i 1__  _l  i I i l -<==>- i — l  (d)  1 1  i I  i  i  <  •  1  i  i  1  '  (b)  I ^ I  1 1  l  1  : i  t  (a)  r  1  3  5  €  L9J  FIGURE 3.10 The four "basic Shockley-Read-Hall processes that may occur at a trapping level. . The final state i s indicated i n the dashed boxes, the arrow indicates the direction of the electron transition. (a) (c)  electron capture hole capture  (b) electron emission (d) hole emission  e J  > - © .  JL  > -e-  JL  >.«=>.  E t  FIGURE 3.11 Action of an electron trap. The relative positions of E , E and Epp are also shown. Electrons are trapped and re-emitted several times before finally disappearing through recombination. F n  T  1*6 p r o b a b i l i t i e s e ( s e c "*") and e ( s e c ^) r e s p e c t i v e l y . n p  Energy l e v e l s a r e f u r -  t h e r c h a r a c t e r i z e d by b e i n g donor l e v e l s o r a c c e p t o r l e v e l s .  A donor i s  n e u t r a l when o c c u p i e d by an e l e c t r o n and p o s i t i v e when i o n i z e d , w h i l e an a c c e p t o r l e v e l i s n e g a t i v e l y charged when o c c u p i e d b y 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 o r a c c e p t o r s a r e a l s o p o s s i b l e .  In a d d i t i o n t o t h e energy l e v e l , t h e c a p t u r e c r o s s - s e c t i o n i s a b a s i c property of a given trap.  Experimentally, values f o r the c r o s s - s e c t i o n are  o b t a i n e d b y measuring t h e c a p t u r e r a t e c. velocity V  t h e c a p t u r e r a t e would be s i m p l y ,  q  c where  a  n,p  I f t h e c a r r i e r s a l l have t h e same  n,p  = a v n,p o  2 (cm ) i s t h e c a o t u r e c r o s s - s e c t i o n f o r e l e c t r o n s o r h o l e s . I n  r e a l i t y t h e c a r r i e r s have a t h e r m a l 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 f u r t h e r m o r e , t h e c a p t u r e 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 a r e o b t a i n e d b y d i v i d i n g t h e obs e r v e d c a p t u r e r a t e by t h e mean t h e r m a l * \;3kT/m )  2  velocity,  c v  (3.8)  th  where m* i s t h e c o n d u c t i v i t y e f f e c t i v e mass.  -12 cover a c o n s i d e r a b l e range, from-10  The e x p e r i m e n t a l v a l u e s o f a  -22 t o 10  2 cm .  T h i s range o f c a p t u r e  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 u n d e r s t o o d by c o n s i d e r i n g t h a t dependent on occupancy, a l e v e l may be e i t h e r C o u l o m b i c a l l y a t t r a c t i v e , n e u t r a l o r repulsive. I f t h e c o n c e n t r a t i o n o f c e n t e r s i n t h e semiconductor  isN  a certain  f r a c t i o n f ^ w i l l be i n t h e more n e g a t i v e s t a t e ( e . g . , i o n i z e d a c c e p t o r s o r 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 t h e 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). occupancy f  i s g i v e n by t h e F e r m i - D i r a c  In thermal e q u i l i b r i u m the  distribution,  hi  T • i g l-iT-Ji  f  where E  F  + 1  (3.9)  e x p  i s the Fermi energy, E i s the energy level of the center, and g 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. are emitted depends only on the occupation.  The rate at which carriers The four rate equations cor-  responding to processes (a) - (d) are, therefore, r r  a  = c n n NT(1 - f )  (3.10)  b  = e N f n T T  (3.11)  T  r  c  r  d  =  C  p  =  6  p T  P  N  (3.12)  V T  "  ( l  (3.13)  V  The electron concentration in the conduction band varies as  dn „ = r - r = e N f - c n N ( l - f_) dt  a  b  n TT m  n  m  T  Similarly the rate of change of the hole concentration dt  r  d - Tc  =  e  p T N  ( L  - V  -  (3.1U)  T  m  W  in the valence band is  T  (3.15)  It i s interesting to calculate the limiting electron and hole.lifetimes that occur when f^ i s equal to zero and one respectively.  no  n dni dt f =o  From (3«lM»  (3.16) C  n T N  T  similarly from (3.15), po  c N p T m  (3.17)  U8 For more general values of f^ we need expressions for the emission rates e and e^.  n  By invoking the principle of detailed balance i t i s possible to  obtain a relation between the capture and emission probabilities. The principle of detailed balance states that in equilibrium r  = r, a b  and  r = r,. c d.  For the case of Boltzmann statistics (i.e., for the Fermi level several kT below the conduction band edge) the electron concentration i n the conduction band, in thermal equilibrium, i s  n  where N and E i  =  N  exp  =  n. exp  kT E - E. _F i kT  1  (3.18)  i s the effective density of states in the conduction band and E C • are the energy of the conduction band edge- and the intrinsic level  respectively.  Equating r. and r  and using (3.9) for f  and expressions  (3.18) for n gives E - E T C kT m  n  exp  g  n  n.  n  V.' i E  exp  kT  (3.19)  The emission probability of holes can be obtained similarly from  p  exp  =  N  =  n. exp  y  1  fV  E  F)  kT  V V kT  (3.20)  k9 where Ny is the effective density of states in the valence hand and Ey i s the energy level of the valence band edge. Thus, e ^ P  =  Ng v  -  exp  n g exp  V  V  i  T kT  E  E  T  (3.21)  kT  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 s i t uations. For steady state, non-equilibrium conditions the rate of change of trapped charge i s 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. f  e + c n = " , — T e + e + c n + cp n p n p P  m  (3.22)  t  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_ Tj^dn^dp^ np n P ^ T dt d t . ' e + e + c n + cp n p n p  (3.23)  Another question of importance i s whether a particular energy level w i l l 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 w i l l 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  a  >> r , , r, >> r d b c  Similarly for hole traps r  c  >> r^ b  , r , >> r d a  For recombination centers the conditions are: r  a  » r, , r >> r,_ d c b  and for generation centers r, >> r d a  , r, >> r b c  Stockmann [39] has shown that i t i s possible to express these four sets of inequalities in the alternate form:  .  * E ,E >E Fn Fp T E* > E ,  electron traps i f ,  w  hole traps i f ,  m  p n  *  T  and Ep and  (3.25)  m  (3.26)  m  (3.27)  recombination centers i f , E^ > E > E ^ Fn T ' Fp * generation centers i f , E„ > E > E_ Fp T Fn * Where E^, i s defined by, EJ 5 2 E  (3.24)  - J ^ - k T L n (c /c ) n  (3.28)  are the non-equilibrium, quasi Fermi levels that describe the  n  electron and hole concentrations according to: E  n  = n^ exp  p  =  i  - E. i l  kT 1  n exp  Fn  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 p o s i t i o n of the l e v e l E^with respect t o the i n t r i n s i c l e v e l E^. The treatment of intermediate l e v e l s thus f a r has been f o r centers with a s i n g l e energy l e v e l only.  I n 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 t o the case o f a m u l 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 t o the s i n g l e l e v e l case.  I f the, number of l e v e l s i s not too.great they are  u s u a l l y many kT apart at low temperatures and may be t r e a t e d independently of each other. 3.2.2  ..  . .  -  . Steady State Bulk Generation:  ( Low F i e l d Case  When defect or impurity centers are l o c a t e d w i t h i n a reverse biased depletion region (where c o n d i t i o n (3.27) holds) t h e i r occupancy i s only determined 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 n  - (TUT^I  p  <3  29)  n p  and from (3.23) the volume r a t e o f generation o f electron-hole p a i r s becomes  *B = r f t r n  N  T  ( 3  -  3 0 )  p  The centers must a l t e r n a t e between e l e c t r o n and hole emission.  Eq. (3.29)  r e l a t e s the steady state occupancy t o the r a t i o o f the emission r a t e s . (3.19) and (3.21) t h i s r a t i o can be expressed as  From  52  1 n • — exp 2 g c C  n  —oz  (3.31)  kT  For l e v e l s away from midgap the exponential f a c t o r very r a p i d l y takes over, f o r c i n g l e v e l s i n the upper h a l f of the band gap t o be predominantly empty and i n the lower h a l f t o be f u l l of e l e c t r o n s .  I f many d i f f e r e n t l e v e l s  are present w i t h i n the forbidden gap, the steady s t a t e emission o f e l e c t r o n s and holes w i l l be dominated by those l e v e l s f o r which the e l e c t r o n and hole emission p r o b a b i l i t i e s are equal. VT  From (3.31) the energy o f these l e v e l s i s .2,  1  E_ Tmax  = E. + £f I n l 2  (3.32)  kT  For s i m i l a r e l e c t r o n and hole capture cross-sections , to  E  rp  m a x  l i e s very c l o s e  ( i . e . , mid gap).'  Using expressions ( 3 . 1 9 ) and (3.2l) f o r e and e i n Eq. (3-30) f o r n p g^ w i t h E = E„ B T Tmax gives m  B  n. S  B  (3.33)  2T  where the e f f e c t i v e l i f e t i m e T i s given by e  {  C  U  C  /  2  N  T  (T  T  no po  )'  The t o t a l r a t e o f generation per u n i t area o f e l e c t r o n - h o l e p a i r s i s n.W G  B  =  2T~  where W i s the d e p l e t i o n l a y e r width. The important t h i n g t o note from (3.33) i s t h a t the temperature dependence of g„ i s determined mainly through n. which v a r i e s as B l  53  T exp  -E  2  where  E  = E_- E„  Lowering the temperature should, therefore, be a very effective means of reducing 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 no po . 13  gives  = 8.x 10  sec. which  -1 -3  sec  cm  at room temperature.  orders of magnitude upon cooling to 100 K.  This i s reduced by 20  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 i n 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 i s generally much greater than the substrate thickness, and i t i s 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 i n the bulk away from the surface is very much greater than the substrate thickness L so that generation i n the bulk can be neglected in comparison with generation at the rear surface (i.e., L/x  (2)  recombination/ recombination/  « s).  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= n ,d  0  dx  s u b j e c t t o t h e boundary D  where:  n D  conditions  f  n dx  o n  =  s[n - n(L)]  = equilibrium electron  The  and n(0) = 0  concentration  = electron d i f f u s i v i t y .  x=0 = edge o f t h e d e p l e t i o n L  ,  x=L  = thickness  region  of the neutral  region  electron i n j e c t i o n current i s , therefore, T  ndiff "  dn n dx  sn  -p. q  qD  x=0  n. ( s L + F T *  ( 3  n  '  3 4 )  With a v e r y h i g h r e a r - s u r f a c e r e c o m b i n a t i o n v e l o c i t y , such t h a t s>>D / L , n J ,. » c a n tie a p p r o x i m a t e d by ndiff 2 n qD n. T = Vi — n 1 ndiff n L L N A L \ w h i l e f o r a low r e a r - s u r f a c e r e c o m b i n a t i o n v e l o c i t y , — << s < ^—, J ,. „' x L ndiff n becomes 2 n. T i • = qsn = qs ^ — . ndiff o N A 2 q  v  H  n  The  n^  dependence ensures t h a t t h e 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  c u r r e n t 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 S t a t e G e n e r a t i o n a t t h e S i l i c o n / S i l i c o n D i o x i d e  Interface:  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 structure 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 introduces forbidden  a h i g h d e n s i t y o f a v a i l a b l e energy s t a t e s i n t h e  gap n e a r t h e i n t e r f a c e .  The d e n s i t y o f t h e 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 c r i t i c a l l y on the oxidation and annealing processes that the silicon sample i s 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 i s in the range  9 10  11 - 10  -2 -1 cm  eV  with a distribution in energy which i s 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 i s 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 i s given by an ex-  pression similar to (3-30), (3.35)  E  n  y  p  where N (E ) i s the distribution of interface states per unit area per unit S  energy.  -L  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  VkT i E  Ey  C  n  6 X P  + c exp P  VkTT  dE  n  (3.36)  E  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* T r a v ^ k T N (E.) n. s 2 th s 1 . 1 = | s  vhere s  n.  (3.37)  is the commonly used parameter called the surface recombination  velocity.  The assumption a =a i s 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 i s n  at most a factor of 2.  p  Typically, the mid gap interface state density after  9-2-1 CCD processing i s 10  cm  eV  . The capture cross-sections for electrons -lh  and holes by mid gap interface states are about 10  2 cm , therefore,the  room temperature steady state generation of.electron hole pairs at the interface i s G  g  = 8 x 10^ cm ^sec \ corresponding to a surface recombination  velocity of approximately 10 cm sec \  In p-type substrates i t i s only the  holes emitted from interface states that are able to traverse the depletion region and trigger a discharge.  Since the temperature dependence of G i s g  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  [—kr—-  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 f i e l d 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. thermally activated.  At low fields carrier emission i s  As the f i e l d increases, the potential barrier i s low-  ered, thus enhancing the probability of thermal emission.  At higher fields  tunneling begins to dominate the emission process and f i n a l l y , at very high fields, the barrier i s 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 f i e l d , 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.  I f i t is neutral after carrier emission,  barrier lowering w i l l 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. lowering is similar to Schottky barrier lowering in a junction.  The barrier  metal-semiconductor  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"  (  3.38)  where £ i s the applied electric f i e l d 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 potent i a l well around a trapping center for different electric f i e l d strengths. (a) (b) (c) (d)  low field - thermal emission dominates moderate f i e l d - thermal emission with reduced barrier high f i e l d - tunnelling dominates very high f i e l d - trap derealization  59  c o n s t a n t i s v e r y c l o s e t o t h e s t a t i c v a l u e f o r f i e l d s up t o a t l e a s t 1.5 x 10^ V cm ^ [42]. Eq. (3.38) g i v e s t h e 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 t h e 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  e m i s s i o n p r o b a b i l i t i e s , however, a t h r e e d i m e n s i o n a l model i s r e q u i r e d . The t h r e e d i m e n s i o n a l t r e a t m e n t has been developed by H a r t k e  o f P o o l e - F r e n k e l e m i s s i o n from t r a p s  [43]. The r e s u l t i n g -expression f o r t h e 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> (6)  =  pF  e(6cos0)'  (3.39)  where t h e b a r r i e r i s lowered o n l y f o r 0<6<TT/2. hanced e m i s s i o n r a t e e  p F  The r a t i o o f t h e f i e l d en-  t o t h e zero f i e l d e m i s s i o n r a t e e , i s  approximated  by Hartke t o be  'PF  ' kT  2  /1  1  In d e r i v i n g  +  1  +  - —  kT  -  fg/n  1 exp [kTj j  (3.^0) Hartke assumes a s p h e r i c a l l y s y m m e t r i c , f i e l d  attempt-to-escape  (3.40)  independent,  frequency o f v/ku p e r u n i t s o l i d , angle where v i s g i v e n by  the r e l a t i o n e  Q  =  v exp (-AE/kT)  AE  =  E  =  E  c T m  - E - E  T m  v  f o r donor l e v e l s f o r acceptor  For h i g h f i e l d s o r l o w temperatures  levels  where $-/Z »  kT, (3.^0) may be a p p r o x i - .  mated by "PF  Fig.  kT  exp  (3.41)  kT  3.13.shows t h i s approximate form f o r e  /e pr  a l o n g w i t h t h e more a c c u r a t e o  v a l u e g i v e n 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 o f P o o l e - F r e n k e l e m i s s i o n on t h e s t e a d y s t a t e g e n e r a t i o n i n  60  61  the d e p l e t i o n l a y e r can b e - e s t i m a t e d as f o l l o w s . the r e v i s e d steady s t a t e g e n e r a t i o n  From (3.30) and(3.40)  ( f o r t h e case o f donor l e v e l s ) i s  ye  l  e no po ye + e T ' no po  B  (3.42)  N  As b e f o r e , t h e most e f f e c t i v e l e v e l s f o r s t e a d y s t a t e e m i s s i o n a r e t h o s e f o r w h i c h ye = e , i . e . , those l e v e l s a t no po 2 g . kT E.+ 2± l n l 2 c  E  Tmax m  Using expressions by  =  ( 3 . 1 9 ) and (3.21) f o r e ^  (3.43)  Q  and e ^ i n ( 3 . 4 2 ) , w i t h E^ g i v e n  (3.43), gives '2 Y  3  B  " i 2x  (3.44)  and t h e r a t e o f g e n e r a t i o n p e r u n i t a r e a i s w [y(x)]  2x  2  (3.45)  dx  0 I d e n t i c a l expressions for g The factor y  and G_. a r e o b t a i n e d f o r a c c e p t o r  levels.  s t e a d y s t a t e g e n e r a t i o n 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 when P o o l e - F r e n k e l h i g h f i e l d e f f e c t s a r e i n c l u d e d .  Using the  approximate e x p r e s s i o n f o r y g i v e n i n (3.40) e n a b l e s t h e t e m p e r a t u r e dependence o f g  t o be e x p r e s s e d as  g'B  2 T exp  fe/T.- E 2kT  T h e r e f o r e , p r o v i d e d t h e b a r r i e r l o w e r i n g g/£ i s o n l y a s m a l l f r a c t i o n o f the energy gap, l o w e r i n g t h e t e m p e r a t u r e s h o u l d s t i l l be a v e r y e f f e c t i v e means of reducing t h i s type o f steady s t a t e generation.  As w i l l be shown i n t h e  62 next s e c t i o n , t h e peak f i e l d i n t h e space charge r e g i o n o f s i l i c o n d i o d e s 7  -1  o r MOS gates must be k e p t below a p p r o x i m a t e l y 4.2 x 1 0 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 i n d e e d o n l y a s m a l l f r a c t i o n o f t h e 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 a t t h e i n t e r f a c e can be t r e a t e d i n  precisely  t h e same manner, w i t h t h e r e s u l t t h a t t h e s u r f a c e r e c o m b i n a t i o n v e l o c i t y  is  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  n.  2  i  PF  s  (  E  i  )  V  (3.46)  A t v e r y 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 temperature.  e m i s s i o n p r o b a b i l i t i e s w h i c h are v i r t u a l l y It  independent  of  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 t h e v a l e n c e band i n t o empty i n t e r f a c e s t a t e s .  Under s t e a d y  s t a t e c o n d i t i o n s t h e s e t u n n e l i n g p r o c e s s e s may combine w i t h t h e  thermally  a c t i v a t e d e m i s s i o n from t r a p s o r 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 p r o c e s s may o c c u r from t h e v a l e n c e band i n t o a b u l k t r a p t h e n from t h e i n t o the conduction band.  These b a s i c s t e a d y s t a t e t u n n e l i n g  mechanisms a r e i l l u s t r a t e d i n F i g . 3.14.  trap  generation  T u n n e l i n g mechanisms i n v o l v i n g  more t h a n one t r a p (examples o f w h i c h a r e i l l u s t r a t e d by t h e dashed l i n e s i n F i g . 3.l4) a r e a l s o p o s s i b l e b u t a r e e x p e c t e d t o be r e l a t i v e l y  unimportant  compared t o t h e 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 a r e i n c l u d e d , t h e r a t e e m i s s i o n o f h o l e s from donor l e v e l s becomes  of  FIGURE 3.14 Energy band diagram'illustrating the proposed steady state generation mechanisms involving the tunnelling emission of electrons and/or holes by mid gap levels.  6k where e° i s a h o l e e m i s s i o n p r o b a b i l i t y e q u a l t o t h e p r o b a b i l i t y p e r u n i t pt t i m e f o r t u n n e l i n g from t h e v a l e n c e band t o an u n o c c u p i e d donor l e v e l .  The  r a t e o f e m i s s i o n o f e l e c t r o n s becomes  f - W")' * v  ( s , 1  M  where e  +  V  <3  I  -  48)  i s an e m i s s i o n p r o b a b i l i t y c o r r e s p o n d i n g t o t u n n e l i n g from an  II TJ  o c c u p i e d donor l e v e l t o t h e c o n d u c t i o n 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 p r o v i d e d t h e e m i s s i o n B  probabilities  e and e a r e r e p l a c e d by t h e new e m i s s i o n p r o b a b i l i t i e s e and e , d e f i n e d n p n p by: e*(x) n  =  e*(x) p  =  Y  "(x)e  + e (x) no n t +  +  e + e° ( x ) po p t  (3.49)  (3.50)  For a c c e p t o r l e v e l s t h e new e m i s s i o n p r o b a b i l i t i e s a r e e*(x) n  =  e + e°(x) no n t  (3.51)  e*(x) p  =  y(x)e  (3.52)  + e'Ax) po p t  The a p p r o p r i a t e e m i s s i o n p r o b a b i l i t i e s t o be u s e d i n e x p r e s s i o n (3-35) f o r * * + G a r e e (0) and e ( 0 ) . F o r p-type s u b s t r a t e s e .(0) i s , o f c o u r s e , s n p nt equal t o zero. For s h a l l o w donor l e v e l s t h e e l e c t r o n e m i s s i o n p r o b a b i l i t y becomes v e r y h i g h , and t h e r a t e d e t e r m i n i n g s t e p i n t h e s t e a d y s t a t e g e n e r a t i o n o f electron-hole p a i r s i s e i t h e r thermally a c t i v a t e d hole emission o r tunneling from t h e v a l e n c e band t o t h e t r a p .  A t low t e m p e r a t u r e s t h e p r o b a b i l i t y o f  h o l e e m i s s i o n by t u n n e l i n g may exceed t h e t h e r m a l e m i s s i o n p r o b a b i l i t y by many o r d e r s o f magnitude i n t h e h i g h f i e l d r e g i o n o f t h e 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 t h a t f o r band t o band t u n n e l i n g  65  and since the density of traps N^ i s 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 f i e l d 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 f i e l d region w i l l proceed almost entirely by mechanism 2 i n 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 i n mechanism h in Fig. 3.14, can greatly i n 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 recombination velocity.  It may, therefore, be necessary to maintain the surface  in strong inversion (i.e., E  very close to the conduction band edge) i n n order to increase the tunneling distance for hole emission. r  3.2.5  Dark Generation Due to Tunneling When the electric field in an insulator or semiconductor i s suffic-  iently high, the forbidden energy gap may be treated i n the manner of a potential barrier of finite width w given by w  = E /q£, 6  and thus i t i s possible for the valence band electrons to make direct quantum 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 and t h e f i e l d never reaches  i o n i z a t i o n and a v a l a n c h e , p r e c e d e t u n n e l i n g  a v a l u e where t u n n e l i n g becomes i m p o r t a n t .  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 s e m i c o n d u c t o r s , Esaki diodes  [44].  o f t e n r e f e r r e d t o as  I n t h i s i n v e s t i g a t i o n , however, we a r e concerned  e x t r e m e l y s m a l l r e v e r s e b i a s c u r r e n t s ( o f t h e o r d e r o f 10  with  A) and,  f u r t h e r m o r e , t h e maximum f i e l d s a r e h i g h e r t h a n t h o s e w h i c h w o u l d n o r m a l l y cause avalanche breakdown.  I t i s t h e r e f o r e necessary t o consider interband  t u n n e l i n g as a p o s s i b l e dark g e n e r a t i o n mechanism even f o r j u n c t i o n s o r 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 e x p e r i m e n t a l 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 r e p o r t e d i n t h e l i t e r a t u r e .  These s t u d i e s , however, a r e g e n e r a l l y  directed at e x p l a i n i n g the current voltage c h a r a c t e r i s t i c s of Esaki tunnel d i o d e s i n w h i c h t h e 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 a t zero b i a s . .p r e g i o n s .  Such d i o d e s g e n e r a l l y have d e g e n e r a t e l y doped n and  The o n l y e x p e r i m e n t a l r e s u l t s known t o t h e a u t h o r on t h e t u n n e l -  i n g g e n e r a t i o n o f 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, a r e t h o s e o f H a i t z [36]. H a i t z measured t h e dark count r a t e f o r d i o d e s known t o have v e r y low d e n s i t i e s o f b u l k t r a p p i n g l e v e l s and showed t h a t t h e observed  dependence o f t h e count r a t e on temper-  a t u r e and peak f i e l d c o u l d be d e s c r i b e d by an i n t e r b a n d t u n n e l i n g g e n e r a t i o n of c a r r i e r s .  From H a i t z ' s dark count r a t e d a t a and t h e quoted j u n c t i o n a r e a ,  t h e r e v e r s e b i a s t u n n e l c u r r e n t s f o r h i s 30V breakdown ( o n e - s i d e d s t e p -12 —2 j u n c t i o n ) d i o d e s i s e s t i m a t e d 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 a t 10 V above breakdown. Clearly, d i o d e s o r MOS  s t r u c t u r e s t h a t have l o w e r peak f i e l d s must be c o n s i d e r e d i f -2  -l6  t h e dark g e n e r a t i o n i s t o be m a i n t a i n e d b e l o w 10 I n o n e - s i d e d s t e p j u n c t i o n s o r MOS  A cm  g a t e s , t h e peak f i e l d a t b r e a k -  67  down may be r e d u c e d by d e c r e a s i n g  the s u b s t r a t e doping.  Unfortunately,  as r e g a r d s f a b r i c a t i o n o f a.PC-CCD, t h i s a l s o has t h e u n d e s i r a b l e e f f e c t o f i n c r e a s i n g t h e breakdown v o l t a g e .  I n o r d e r t o examine more c l o s e l y t h e  e f f e c t s o f s u b s t r a t e d o p i n g and d i f f e r e n t d o p i n g p r o f i l e s on t h e dark generation  due t o t u n n e l i n g , we need an a c c u r a t e  expression  f o r t h e volume  r a t e o f e l e c t r o n - h o l e p a i r g e n e r a t i o n t h a t my be i n t e g r a t e d o v e r t h e d e p l e 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 g e n e r a l  c a t e g o r i e s a c c o r d i n g t o whether t h e 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] o r t h e more r e c e n t F r e d k i n - W a n n i e r j u n c t i o n p o t e n t i a l model [ 4 6 ] i s used.  In both p i c t u r e s o f interband 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  i s t r e a t e d as a p e r t u b a t i o n on t h e atomic f o r c e s . most cases s i n c e , a t t h e h i g h e s t  f i e l d s normally  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 c o n s t a n t amplitude o f t h e p e r i o d i c c r y s t a l p o t e n t i a l . combined p o t e n t i a l s a r e n o r m a l l y  represented  ed from t h e e i g e n s t a t e s o f t h e H a m i l t o n i a n  field  This i s j u s t i f i e d i n e n c o u n t e r e d , t h e change  i s s m a l l compared t o t h e  E l e c t r o n s moving under t h e as B l o c h wave p a c k e t s  f o r the unperturbed  construct-  crystal,  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 o n l y by t h e 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.  C o n s i d e r e d c l a s s i c a l l y , , t h e e l e c t r o n t h e n h a s , a t any i n s t a n t , a band i n d e x 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  r e p r e s e n t s , a quantum t r e a t m e n t o f t h e 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 t r e a t m e n t o f t h e ' e x t e r n a l p o t e n t i a l . W i t h a f u l l quantum m e c h a n i c a l t r e a t ment t h e r e e x i s t s t h e p o s s i b i l i t y o f a change i n band i n d e x n by i n t e r band t u n n e l i n g .  WKB methods  [ 4 7 ] o r o r d i n a r y time-dependent p e r t u r b a t i o n  t h e o r y may be used t o i n c l u d e t h e 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 t h e quantum m e c h a n i c a l c a l c u l a t i o n and a r r i v e a t a t u n n e l i n g p r o b a b i l i t y . The F r e d k i n - W a n n i e r model f o r i n t e r 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 i n an external 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 i n 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 i n a high f i e l d region that extends over a considerable distance, the theoretical results based on the older f i e l d emission model w i l l be easier to apply.  Here the external potential i s  taken to be V(x) = -Fx, representing a constant f i e l d F = q£.  Quasi-class-  i c a l l y , under the influence of the constant electric f i e l d , 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 f i e l d emission is obtained by calculating a transition probability per unit time which is then integrated over the Brillouin zone. In indirect band gap materials, such as s i l i c o n , the tunneling calculations are complicated by the requirement for phonon cooperation.  Tun-  neling across an indirect energy gap involves a change i n 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 i n 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 f i e l d i s very similar to the result for direct tunneling. The main difference i s 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 f i e l d . Indirect phonon assisted tunneling has been considered by Kane [49] [50] using the constant electric f i e l d 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, i s  g  t  =  A^-  E[M(E )] {(u + l ) e x p [ ^ (E + E ) 2 ] 2  3/  p  g  p  + u expH^ (E - E )%]} c g p  (3.53)  where A i s a constant and M(E ) i s the matrix element for phonon scattering. p  Bdepends on the reduced effective mass for tunneling and on the shape of the potential barrier i n the forbidden gap. Kane assumes a triangular potential barrier, for which  B E  p  -  (3.54)  i s the phonon energy and u i s the phonon occupation, given by U  =  ex (E /kT) - 1 P 1  P  ( 3  '  5 5 )  TO  The summation should extend over the four fundamental phonon energies mentioned e a r l i e r , as w e l l as over the phonon energies involved i n 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 transverse optic phonons at 17-9 nieV and 58.5 nieV r e s p e c t i v e l y , are the dominant scattering agents.for i n d i r e c t tunneling.  We w i l l make the further approx-  imation that the matrix elements f o r phonon scattering are equal f o r these two phonons. In an actual diode or MOS gate the f i e l d c i s not- constant but i s a function of p o s i t i o n x i n the depletion region.  The rate of tunneling  generation per unit area therefore becomes w r G  g (x) dx  t  t  0 2 AM'  ^ £(x)  / 2  X {(u + l ) e x p [ ^ ( E + E ) ] TA,TO / 2  t  E  g  U  ;  S  P  0  + u exp[?7-x(E - E ) ^ t(x) g p l  In practice the values o f AM  3/2  ] } dx J  and B must be determined  2  (3.56)  experimentally.  F a i r l y r e l i a b l e 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 i n the c a l c u l a t i o n s : w^  (width constant f o r Haitz's step junction) = 0.23 x  10-6  mV  -h 2  T  (substrate temperature)  = 196 K  u  (phonon occupation, at 196 K) = 0.52 f o r TA phonon at 1T-9 meV =0.03 f o r TO phonon at 58.5 meV  E_  (band gap, at 196 K) = l . l U ev  71  £(x) = 2/w. [w_(V 1 1 a  + V.)  h  1  - x]  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: AM  2  B  = . 5.1 x 10 =  1 . 8 9 x 10  eV^V^secf  18  9  eV  _3//2  V  1  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 f i e l d , for MOS gates operating above breakdown at a temperature of 100 K.  The calculated generation rate versus surface  potential i s 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 expression used for. the extrapolation (Eq. 3.56) is accurate, the estimated error bars for Haitz's data lead to an error after extrapolation of approximately plus or minus one order of magnitude for the lowest generation rates indicated in Figures 3.15 and 3.l6.  It i s apparent from the results shown  in Fig. 3 - 1 5 that the peak electric f i e l d at the Si-Si02 interface should be kept below approximately U . 3 x 10 tion rate less than 500 sec  - 1 - 2  cm  7  Vm  —1  in order to ensure a dark genera-  .  A substrate doping level below approximately 8 x 10  15  -3  cm  is required  10"  P (W) e  10-  O  0.98  o  0.90  X  0.50 N  0 10"  A  = 2x10 cm" = 31.3 V 16  3  10"  10'  N V  A  b  = 1x10 cm" =' 50.8 V 16  3  10  o z <  N = 5x10 c m ' V = 83.8 V A  -1 ce 10  15  3  b  a  ui  .-2 10 3.5  4.0 MAXIMUM  FfELD  £  4.5 max t10 V cm" ) 5  5.0  1  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 i n i t i a t i o n 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>, T = 100K. s  rt  to maintain the peak electric f i e l d below this value and yet s t i l l enable operation in the plateau region of the avalanche initiation probability (above P ( ) w  0.9).  =  e  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 w i l l 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 f i r s t 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 f i e l d ionized is found to have the same general form as that for interband tunneling transitions except 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 - E,j). c  Using Price's matrix element for tunneling, Sah [54] de-  termines the transition probability per unit time to be  e  nt  *  \  ( 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 f i e l d given by r  E  T  =  6  E- AE_ T T E  T  (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 t h e case o f i n t e r b a n d t u n n e l i n g t h e e f f e c t i v e mass i n B  may c  be r e g a r d e d 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 , t h e dominant component o f w h i c h w i l l be the. e l e c t r o n mass i n t h e c o n d u c t i o n  band.  F o r t u n n e l i n g from t h e v a l e n c e band i n t o an empty t r a p o r i n t e r f a c e s t a t e , a s i m i l a r e x p r e s s i o n t o (3.57) i s e x p e c t e d , e x c e p t t h a t t h e h e i g h t o f t h e energy b a r r i e r , t h r o u g h which t h e e l e c t r o n t u n n e l s , i s now t h e d i f f e r - . , ence between t h e band gap and t h e i o n i z a t i o n energy o f t h e i m p u r i t y l e v e l (i.e., E  g  - E  c  + E  = E_ - E ). T v  T m  The dominant component t o t h e e f f e c t i v e  mass i n t h i s case i s t h e h o l e mass i n t h e v a l e n c e band.  2  J  T  "V'  "  Thus,  ]  (3.59)  ~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 h o l e s ) and n e u t r a l c e n t e r s are d e s i g n a t e d by e  and e°  respectively.  TP  The o n l y e x p e r i m e n t a l work on t u n n e l i n g i n t o and out o f 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 t h e excess c u r r e n t i n f o r w a r d 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 s t u d y o f t h e i m p u r i t y induced  c u r r e n t i n g o l d doped s i l i c o n E s a k i j u n c t i o n s .  excess  The o b s e r v e d excess c u r r e n t  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 v a r i o u s t w o - s t e p c o m b i n a t i o n s o f Shockl e y - R e a d - H a l l 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 t h e t h e o r e t i c a l t u n n e l i n g r a t e  2 c a l c u l a t i o n due t o P r i c e .  The e s t i m a t e d v a l u e o f A^M^  f o r the tunneling  t r a n s i t i o n s v a l e n c e band t o t r a p t o c o n d u c t i o n band (mechanisms 2 i n F i g . 3.1*0  o b t a i n e d from Sah's d a t a i s g i v e n i n t a b l e 3.1.  experimental  Sah o n l y r e p o r t s  d a t a f o r one v a l u e o f f i e l d , t h e r e f o r e , no e x p e r i m e n t a l  f o r B can be o b t a i n e d from h i s r e s u l t s .  value  The v a l u e o f B used by Sah was  c a l c u l a t e d a c c o r d i n g t o (3-5*0 u s i n g t h e t r a n s v e r s e e l e c t r o n and l i g h t e f f e c t i v e masses.  These masses and t h e . c o r r e s p o n d i n g  l i s t e d i n t a b l e 3.1.  hole  values f o r B are  Chynoweth e t a l . [55] have measured t h e f i e l d depend-  ence o f excess c u r r e n t i n s i l i c o n E s a k i diodes by v a r y i n g t h e 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 agreement with Sah's data. The steady state dark generation rate per unit area due to tunneling through deep bulk levels i s w g^Cx)  ^Bt  dx  (3.60)  where g^,(x) for donor levels i s Bt +  , s  pt  e  e  (  pt  x  )  e  U )  n t  +  e  U  N  )  nt  T  ,  n  n  U )  and for acceptor levels is  ,T  TABLE 3.1  (l  >  e L U ) e° (x)  =  -Pt'  »  T  O  M  )  Experimental values for the-effective mass and matrix element  for tunneling through trap states.  */  A ^ (eVrnV "''sec ^) Sah  2.7  10  3  Chynoweth  6.5 x 1 0  3  x  a  */  m /m c o  m /m v o  0.19  0.16  B*  B c  b  v  (Vm 2.98  9  X  10*  0.3  3.7-+ x  * Value required to f i t Sah's data using 0.3 for m /m Calculated according to Eq. (3.5*0  Q  2.73 10 9  x  9 KT  77  The  generation  rate i s highest  f o r those l e v e l s f o r which the  t i o n p r o b a b i l i t i e s e , and e ^ are e q u a l .  transi-  At f i e l d s t r e n g t h s where t h e  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 close to band.  The  mid  d e n s i t y o f such deep l e v e l t r a p s w i l l depend on t h e q u a l i t y o f  t h e s t a r t i n g s i l i c o n w a f e r and on t h e b u l k g e t t e r i n g s t e p s i n c l u d e d i n t h e 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  c e s s i n g l i e i n t h e range 10  10  -  10  generation  rate for  = 10  10  12  -3  cm  Figure 3.17  cm  v e r s u s peak e l e c t r i c f i e l d i n MOS The  generation  c a l c u l a t e d from ( 3 . 6 0 ) u s i n g t h e d a t a i n T a b l e 3 . 1 .  generation  shows t h e c a l c u l a t e d  -3  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 . was  .  pro-  gates  r a t e per u n i t The  area  extrapolated  r a t e s a r e v e r y u n c e r t a i n f o r t h e s e 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 t h e l a r g e d i f f e r e n c e i n t h e r a t e s p r e d i c t e d from Sah's d a t a 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 e s t i m a t e o f Chynoweth e t a l . I t i s a p p a r e n t , however, t h a t t u n n e l i n g t h r o u g h deep t r a p s w i l l be one  o f t h e dominant t r i g -  g e r i n g mechanisms i n t h e dark. P r e c i s e l y how  t h i s mechanism t u r n s  important  out t o be w i l l depend v e r y much on the d e n s i t y and energy l e v e l o f the deep impurity/defect centers present  i n the h i g h f i e l d r e g i o n n e a r t h e  inter-  f a c e and on t h e c o r r e c t v a l u e 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 G e n e r a t i o n  of T r i g g e r i n g C a r r i e r s i n the Non-Steady S t a t e  So f a r o n l y s t e a d y s t a t e dark g e n e r a t i o n mechanisms have been c o n s i d ered.  Immediately f o l l o w i n g t h e l a r g e d e p l e t i n g p u l s e above breakdown, how-  e v e r , t h e r e i s a t r a n s i e n t d u r i n g which the i n t e r f a c e s t a t e s and b u l k a r e r e l a x i n g t o t h e i r new  s t e a d y s t a t e occupancy.  traps  During t h i s t r a n s i e n t  t h e r e i s an enhanced e m i s s i o n o f e i t h e r e l e c t r o n s o r h o l e s depending on previous  occupancy o f t h e t r a p s , p r i o r t o t h e d e p l e t i n g p u l s e .  a l s o a t r a n s i e n t f o l l o w i n g each a v a l a n c h e d i s c h a r g e .  During the  t h e occupancy o f t h e b u l k t r a p s and i n t e r f a c e s t a t e s may  the  There i s discharge  be a l t e r e d by e i t h e r  78  3.5 MAXIMUM  4.0 FIELD  £  4.5 (10 Vcm ) 5  m n t f  1  FIGURE 3.17 Tunnelling generation r a t e through traps as. a f u n c t i o n o f 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 o r p-substrate MOS gates, T = 100K. The r e s u l t s 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 f i r s t 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 i s very low at the interface. Electron capture i s , therefore, negligible and holes are emitted very rapidly 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 - extremely small, an avalanche s  w i l l be triggered within a very short time after the application of the depleting 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 concentration of electrons, and hence the occupancy of the levels immediately prior to the pulse above breakdown w i l l be insensitive to any previous avalanche discharges. After the depleting pulse the inversion layer s t i l l remains.. Electron capture and emission, therefore, continue to determine the occupancy f^, forcing a l l the interface states below trons.  to be f u l l of elec-  The tunneling distance for hole emission i s , thus, large, and at low  temperatures hole emission w i l l be a very rare event. From the above discussion i t is apparent that a PC-CCD w i l l require a  80  Energy band diagram for a p-substrate MOS gate illustrating the generation of triggering carriers at the interface, immediately following a depleting pulse.  FIGURE 3.18  (a) (b)  pulsed from accumulation during reset 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 i s a transi-  tion region where the surface is not in inversion before or after the depleting pulse.  The dark generation from interface states i n this region  w i l l be dominated by the steady state emission of electrons and holes, which may become significant at the high surface fields encountered above breakdown. In addition, hot electrons incident on the interface during an avalanche discharge may impact ionize some of the interface states resulting i n 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 ~f (x,t) T  T  *  where e  n  =  e*(x) N  T  - [e*(x) + e*(x)] N f (x,t) T  T  (3.63)  *  (3.^9) to (3.52). The return to  and e^ are defined by equations  equilibrium i s , therefore, exponential with a time constant T ( X ) = *  *f  [en (x) + ep (x)] f (x,t)  -1  _  T  where f (x,») ± T  B  . The solution for f_(x,t) may be expressed as T  y  _  X t w )  [ f T  (  X j 0 o )  _ f (  x > 0  ) ] exp -t/t(x)  the steady state occupancy given by ejx)  T  T  ' '  * e (x) n  +  *— e (x) p  (3.64)  82  region 1 | region 2  FIGURE 3 . 1 9 Energy band d i a g r a m f o r . a p - s u b s t r a t e MOS g a t e i l l u s t r a t i n g t h e 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 from deep b u l k t r a p s , i m m e d i a t e l y 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 . R e g i o n 1 remains i n d e p l e t i o n at a l l times (except f o r a r e g i o n v e r y near t h e i n t e r f a c e w h i c h may be i n v e r t e d ) . Region 2 a l t e r n a t e s between t h e 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 i n i t i a l trap occupancy at the instant the gate i s 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 w i l l be triggered) i s  R(t), =  AN | e*(x) f (x,t) P (x) + e*(x)[l - f^x.t") ]P (x) dx T  T  e  h  (3.65)  where P (x) and P, (x) are the electron and hole avalanche initiation probe 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 occupancy, f (x,°°), i s T  R(~) - R(0)  =  AN  [f (x,») - f ( x , 0 ) ] T  T  w  T  # •  •#  •[e (x)P (x) - e (x)P,(x)] dx n e p h  (3.66)  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 f i r s t part is over those re-  gions that remain i n depletion during reset (region 1 in Fig. 3.19) and the second part of the integral is over those regions that alternate between depletion 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 i n the p-type neutral bulk.  Therefore, the trap occupancy in  this region prior to each depleting pulse w i l l be independent of any changes that may have occured during previous cycles.  Following the depleting  pulse, electrons and holes are emitted alternately. I n i t i a l l y holes are emitted at a higher rate than electrons (f^(x,°°) > f^,(x,0)) as the trap  81*  occupancy a d j u s t s t o t h e new s t e a d y s t a t e i n d e p l e t i o n .  In general, t h i s  i n c r e a s e d h o l e e m i s s i o n w i l l r e s u l t i n a r e d u c t i o n o f t h e breakdown r a t e since ^ ( x )  i s much s m a l l e r t h a n P ( x ) i n r e g i o n 2 ( s e e F i g . 3-7).  Only  i f t h e t r a p s a r e c l o s e t o t h e v a l e n c e band b u t above t h e e q u i l i b r i u m Fermi  *  *  l e v e l d u r i n g r e s e t ( i . e . , f o r w h i c h e ( x ) > > e ( x ) and f ^ ( x , 0 ) - 0 ) , can t h e p  n  breakdown r a t e be i n c r e a s e d . E x c e p t d u r i n g p e r i o d s o f a v a l a n c h e d i s c h a r g e , r e g i o n 1 remains depleted at a l l times. avalanche,  I t i s o n l y d u r i n g t h e t r a n s i e n t f o l l o w i n g each  t h e r e f o r e , t h a t t h e steady s t a t e occupancy i s d i s t u r b e d .  Under  a v a l a n c h e breakdown c o n d i t i o n s , f r e e c a r r i e r c o n c e n t r a t i o n s o f t h e o r d e r o f 10"^^cm  to lO^cm  3  a r e reached.  3  C o n s e q u e n t l y , e l e c t r o n and h o l e cap-  t u r e by t r a p s becomes p o s s i b l e , o r , s i m i l a r l y , t h e h o t e l e c t r o n s and h o l e s may impact i o n i z e t h e t r a p s .  I n e i t h e r case an e x p o n e n t i a l t r a n s i t i o n b e -  tween t h e i n i t i a l and f i n a l s t a t e s would be e x p e c t e d , w h i c h may be desc r i b e d by an e q u a t i o n o f t h e same form as (3.61*). continue  f o r t i m e t ^ t h e n t h e f r a c t i o n o f c e n t e r s i n t h e more n e g a t i v e s t a t e ,  upon t e r m i n a t i o n o f t h e a v a l a n c h e , f  i f t h e a v a l a n c h e were t o  A T  (x,t ) A  =  would be  f (x,») - [f (x,») - f j ( x ) ] e x p - t / x ( x ) AT  AT  A  A  (3.67)  where: f  (x,°°) = l i m i t i n g t r a p occupancy d u r i n g an extended  A  f^,(x) = occupancy o f t h e t r a p s i m m e d i a t e l y T ( X ) = time constant A  avalanche.  p r i o r t o t h e avalanche.  for thetransient.  For t h e case t h a t t h e a v a l a n c h e d i s c h a r g e s  are w e l l separated i n time, the  i n i t i a l occupancy i s e q u a l t o t h e s t e a d y s t a t e occupancy i n d e p l e t i o n  (i.e.,  f * ( x ) = f (x,»)). T  F o l l o w i n g a d i s c h a r g e , t h e t r a p r e l a x a t i o n i n r e g i o n 1 i s g i v e n by  85  "f (x,t)  =  T  f (x,«) - [f (x,») - f T  T  A T  (x,t )]exp  (3.68)  -t/x(x)  A  where t = 0 i s now t a k e n t o be t h e t e r m i n a t i o n o f t h e a v a l a n c h e . t i m e t r a n s f o r m a t i o n i n ( 3 . 6 6 ) and u s i n g ( 3 . 6 8 )  R^oo) - • R ( t ) 1  s  = AN  [f (x,») - f T  T  w  where t  s  1  A T  Making t h i s  gives  (x,t )]exp A  -t /x(x) s  - [ e * ( x ) P (x) - e * ( x ) P j x ) ] n e p h  (3.69)  dx  i s t h e t i m e from t h e t e r m i n a t i o n o f t h e a v a l a n c h e t o t h e n e x t  p u l s e above breakdown ( t h e i n t e g r a t i o n h e r e i s o v e r r e g i o n 1 o n l y ) . 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 o r d e c r e a s e however, t h e magnitude o f t h e change now decays  As  i n t h e breakdown r a t e ,  exponentially with i n -  creasing reset duration. The f i e l d d i s t r i b u t i o n - , t h e v a r i a t i o n o f t h e 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 t h e 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 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 (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 .  t r a p p i n g i s t h e dominant p r o c e s s  If  space 3.20(a)charge  d u r i n g breakdown t h e n from F i g . 3 . 2 0 ( c )  it  can be seen t h a t , subsequent t o t h e 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 t h e 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 n e a r 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 t h e r e m a i n d e r 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 . 2 1 ( b ) . 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 . e n the o v e r a l l e f f e c t  F i g u r e 3.21(a) i n d i c a t e s  F o r deep t r a p s (e ( x ) ~ e ( x ) ) n p  o f t h e 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 is  ).  I f any  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 t h e a v a l a n c h e d i s c h a r g e , t h e  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 . lax  the  #  charge  subsequent  The s h a l l o w e s t l e v e l s , however, w i l l  re-  t o t h e i r s t e a d y s t a t e occupancy b e f o r e t h e n e x t 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) i s the f i e l d distribution, (b) is the variation of the electron and hole ionization coefficients and (c) i s the density of hot electrons and holes.  87  (a)  (bj  t r i g g e r i n g p r o b a b i l i t y as a function of position i n |the d e p l e t i o n r e g i o n .  c a r r i e r c a p t u r e dominant d u r i n g breakdown.  Si O  impact i o n i z a t i o n dominant 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 subsequent t o an a v a l a n c h e d i s c h a r g e . 7  traw P  88  The  change i n occupancy t h a t o c c u r s i f impact i o n i z a t i o n o f the  i s dominant d u r i n g breakdown i s more d i f f i c u l t t o determine. there  are two  electrons  competing p r o c e s s e s :  l)  hot  2)  hot  charge change.  Figure  worst p o s s i b l e s i t u a t i o n f o l l o w i n g breakdown i . e . ,  f o r the case t h a t the t r a p s are charged i n the o p p o s i t e c a r r i e r d e n s i t y d u r i n g the avalanche.  As b e f o r e ,  sense t o the  free  the o n l y l e v e l s t h a t  a c t i v e l y e m i t t i n g c a r r i e r s at t h e b e g i n n i n g o f t h e next c y c l e are  f o r which (e  case  can knock o f f  from the t r a p s , l e a d i n g t o a p o s i t i v e charge change or  3.21(c) i l l u s t r a t e s t h  be  In t h i s  e l e c t r o n s or h o l e s  c a r r i e r s can k n o c k . o f f a h o l e , l e a d i n g t o a n e g a t i v e  traps  #  # _3_ + e ) > t n p s  will-  those  . •  I t i s c l e a r t h a t the  o v e r a l l e f f e c t o f an a v a l a n c h e d i s c h a r g e  will  depend v e r y much on the r e l a t i v e s i z e s (as a f u n c t i o n o f p o s i t i o n i n t h e d e p l e t i o n r e g i o n ) o f the four' impact i o n i z a t i o n c r o s s - s e c t i o n s , and c a p t u r e c r o s s - s e c t i o n s , and breakdown.  The  on t h e d i s t r i b u t i o n o f the hot  magnitude o f the  two  c a r r i e r s during  e f f e c t w i l l a l s o depend on t h e  duration  of  the a v a l a n c h e , o r more p r e c i s e l y , on the amount o f charge t r a n s i t i n g the p l e t i o n region formation not  during  an avalanche d i s c h a r g e .  a l l t h a t can be  Without t h i s  detailed i n -  s a i d i s . t h a t t h e r e s u l t i n g change i n occupancy i s  expected t o l e a d t o a l a r g e decrease i n the t r i g g e r i n g r a t e a t t h e  o f the next p u l s e . the r e s e t  How  de-  l a r g e the i n c r e a s e w i l l be,  i f any,  will  start  depend  on  duration,  Haitz set c i r c u i t  [36],  by v a r y i n g the shunt c a p a c i t a n c e i n the h i g h  of h i s small area n p +  guard r i n g d i o d e s , has  count r a t e as a f u n c t i o n o f the t o t a l charge c r o s s i n g the an avalanche.  measured t h e junction  I n i t i a l l y the. count r a t e i n c r e a s e d l i n e a r l y w i t h  shunt c a p a c i t a n c e , the highest  impedance r e -  however, some s a t u r a t i o n o f the count r a t e was  charge l e v e l s r e p o r t e d ,  dark  during  increasing evident  i n d i c a t i n g t h a t the t r a p occupancy  had  for  approached t h e s t e a d y s t a t e v a l u e d u r i n g a v a l a n c h e .  By e x t r a p o l a t i n g t h e  l i n e a r count r a t e v e r s u s shunt c a p a c i t a n c e r e l a t i o n t o z e r o c a p a c i t a n c e , H a i t z was a b l e t o determine t h e s t e a d y 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 diodes.  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  1 t h i s and c o r r e s p o n d e d t o a charge o f 1 x 10 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 .  5  -  than  2  c a r r i e r s cm  crossing the  This r e s u l t i s encouraging i n  v i e w o f t h e f a c t t h a t t h e s i z e o f t h e d i s c h a r g e p u l s e f o r an MOS g a t e i s t y p i c a l l y t h r e e o r d e r s o f magnitude l o w e r t h a n t h i s .  3.3  PREVENTION OF PREMATURE EDGE BREAKDOWN AND LOCALIZED MICROPLASMA BREAKDOWN  G o e t z b e r g e r and N i c o l l i a n [56]  have s t u d i e d t h e . 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 .  W i t h an  o x i d e t h i c k n e s s o f 1000S t h e y f o u n d t h a t edge breakdown was u n i m p o r t a n t  l6 s u b s t r a t e d o p i n g l e v e l s g r e a t e r t h a n a p p r o x i m a t e l y 5 x 10  for  -3 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 at 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  a t t h e edges o f t h e m e t a l g a t e 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 - 2 2 i l l u s t r a t e s t h i s e f f e c t and shows t h e d i f f e r e n c e between h i g h and low s e m i c o n d u c t o r d o p i n g .  A c c o r d i n g t o t h i s e x p l a n a t i o n ' . t h e edge b r e a k -  down e f f e c t s h o u l d depend on t h e 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 thickness.  Rusu and B u l u c e a [57]  oxide  have made c o m p u t e r - a i d e d c a l c u l a t i o n s  of  t h e breakdown v o l t a g e o f d e e p l y d e p l e t e d MOS c a p a c i t o r s u s i n g t h e 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 t h e 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 ation.  over-relax-  L e e ' s room t e m p e r a t u r e i o n i z a t i o n r a t e d a t a ( A p p e n d i x A) and t h e  c o n s t a n t K a p p r o x i m a t i o n (a, = k a ) were u s e d 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 integral. I n 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 v e r s u s  :  :.  90  field  plate  o x i d e  \ \  .-*..',•• . * • - . •  — ^  •'  o x i d e  —  —  \  (a)  (b) Low doping density, wide depletion region, high fringing f i e l d .  High doping density, narrow depletion region, uniform fields.  ;  FIGURE 3.22 Cross section of MOS capacitor showing equipotential lines i n the space charge region at the-edge of the f i e l d plate. Edge breakdown occurs in (b) due to the high fringing f i e l d .  SiO.  \\j  N  1  S,_ 2_J N  \-Si N 3  Si (a) change of semiconductor doping,  (€ )  ?  2  Si  (b)  V 2  composite dielectric, e  N  l  < e  2 insulator ( A l  Si (C) change of oxide thickness  4  2  0 ) 3  7  Si (d)  separate guard ring f i e l d 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 u n i v e r s a l c r i t e r i o n f o r f i e l d u n i f o r m i t y i n terms of the r a t i o of oxide thickness t o the maximum (breakdown) width of the s i l i c o n d e p l e t i o n region.  According  to t h e i r . c a l c u l a t i o n s t h i s r a t i o should be l a r g e r than 0.3 i n order not t o have f i e l d concentration around the edges o f the metal p l a t e . I t was e s t a b l i s h e d i n s e c t i o n 3.2.5 that the substrate doping of a 15  PC-CCD should be l e s s than approximately 8 X 10 interband tunneling.  -3  cm  i n order t o avoid  On such l i g h t l y doped substrates the oxide  thickness  required t o s a t i s f y the above c r i t e r i o n f o r f i e l d u n i f o r m i t y becomes rather l a r g e , and i t may prove b e t t e r t o use some sort of guard r i n g i n order t o prevent edge breakdown.  Some o f t h e p o s s i b l e guard r i n g s t r u c t u r e s that can ;  be used on MOS devices are shown i n F i g . 3.23 [56].  In each case the a c t i o n  of the guard r i n g i s t o cause a more gradual t r a n s i t i o n from the deeply depleted breakdown region t o the undepleted (or s l i g h t l y depleted) surroundi n g area, thereby, e l i m i n a t i n g the high f r i n g i n g f i e l d s .  In a PC-CCD, a l l  but s t r u c t u r e (a) i n F i g . 3.23 can be used both t o define the t r a n s f e r channels and t o prevent edge, breakdown.  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 are avoided by.adjusting the p o t e n t i a l b a r r i e r s between p i x e l s to be only s l i g h t l y below breakdown (see F i g . 3.H). •In a d d i t i o n t o premature edge breakdown, i t i s a l s o p o s s i b l e f o r there to be l o c a l p r e f e r r e d s i t e s f o r breakdown ( s o - c a l l e d microplasmas) due t o the presence o f 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 f o r i o n i z a t i o n [58], or they may become decorated w i t h i m p u r i t i e s l e a d i n g t o 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.  I n the e a r l y  work on avalanche diodes such microplasmas were found t o dominate the breakdown c h a r a c t e r i s t i c s , and they have been the subject of many i n v e s t i g a t i o n s .  92  Subsequent p r o g r e s s i n c r y s t a l growing and d e v i c e  f a b r i c a t i o n technology,  however, has l e d t o t h e r o u t i n e f a b r i c a t i o n o f m i c r o p l a s m a - f r e e t h a t breakdown u n i f o r m l y o v e r t h e e n t i r e j u n c t i o n The  junctions  area.  f a b r i c a t i o n o f u n i f o r m breakdown MOS g a t e s 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 t h a t h i g h t e m p e r a t u r e t h e r m a l o x i -  d a t i o n o f 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 t h e 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 t h e y become d e c o r a t e d 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  r e s u l t i n l o c a l i z e d breakdown.  [62] [63] and may a l s o  I t has been found t h a t t h e o r i g i n o f o x i d a -  t i o n i n d u c e d 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 o r grown-in m i c r o d e f e c t s etching the wafer before  formed d u r i n g c r y s t a l growth.  o x i d a t i o n e l i m i n a t e s any m e c h a n i c a l damage b u t t h e  grown-in d e f e c t s a r e more d i f f i c u l t t o e l i m i n a t e .  A number o f p r o c e d u r e s  have been proposed t o suppress t h e s e n u c l e a t i o n c e n t e r s ing stacking f a u l t s .  Chemically  and t o s h r i n k  exist-  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 o r  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 t h e back s i d e o f t h e w a f e r [64] [65] i s a w e l l known t e c h n i q u e f o r t h e s u p p r e s s i o n  o f SF n u c l e i .  I t has a l s o been found  t h a t a d d i n g s m a l l amounts o f c h l o r i n e i n t h e form o f H C l o r C^HCl^ t o t h e 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 growni n defects  [62] - [ 6 9 ] .  More r e c e n t l y i t has been shown t h a t t h e n u c l e a t i o n  o f OSF's on t h e f r o n t s i d e o f t h e w a f e r can be g r e a t l y s u p p r e s s e d by t h e g e t t e r i n g a c t i o n o f m e c h a n i c a l damage on t h e back [70] [ 7 1 ] , o r by t h e g e t t e r i n g a c t i o n o f thermally induced microdefects  i n t h e i n n e r p a r t o f oxygen  r i c h Czochralski wafers ( s o - c a l l e d i n t r i n s i c gettering) By u s i n g a c o m b i n a t i o n o f t h e above t e c h n i q u e s ,  [72] [ 7 3 ] .  p a r t i c u l a r l y HCl o x i - .  d a t i o n and b a c k - s u r f a c e damage, l a r g e CCD a r r a y s have been f a b r i c a t e d t h a t are f r e e from any dark c u r r e n t a n o m a l i e s .  The same t e c h n i q u e s s h o u l d ,  there-  93 f o r e , make p o s s i b l e t h e 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 P C - C C D ' 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 a v a l a n c h e breakdown i s a w e l l - k n o w n phenomenon and poses an i m p o r t a n t problem i n t h e p r o p o s e d PC-CCD i m a g e r .  Even i f  only  a few photons are e m i t t e d . d u r i n g t h e a v a l a n c h e d i s c h a r g e o f an image e l e m e n t , t h e s e photons w o u l d 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 t h e breakdown o f a d j a c e n t p i x e l s .  These p i x e l s w o u l d t h e n a l s o emit  photons, thereby s t a r t i n g a chain r e a c t i o n .  I n o r d e r t o p r e v e n t such a  c h a i n r e a c t i o n and reduce t h e 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 , t h e number o f photons e m i t t e d p e r d i s c h a r g e , t i m e s t h e  probability  t h a t t h e y w i l l t r i g g e r a n o t h e r p i x e l , must be made v e r y much l e s s t h a n o n e . Breakdown r a d i a t i o n was f i r s t r e p o r t e d , 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, t h e mechanism f o r t h i s r a d i a t i o n has not been definitely established.  E x i s t i n g explanations include r a d i a t i v e  (phonon-  a s s i s t e d ) r e c o m b i n a t i o n o f t h e f r e e e l e c t r o n s and h o l e s p r e s e n t d u r i n g t h e 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 t h e h o t and h o l e s  electrons  [75] [76] i n c l u d i n g r a d i a t i o n from t h e b r e m s s t r a h l u n g o f h o t  r i e r s i n t h e coulomb f i e l d o f charged i m p u r i t y c e n t e r s  car-  [77]. F o r a l l t h e  s e m i c o n d u c t o r m a t e r i a l s s t u d i e d t h e spectrum i s v e r y b r o a d , e x t e n d i n g t o e n e r g i e s b o t h c o n s i d e r a b l y g r e a t e r t h a n and l e s s t h a n t h e . e n e r g y gap. s p e c t r u m 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  The  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,  there  a r e v e r y few r e p o r t e d e s t i m a t e s o f t h e e m i s s i o n e f f i c i e n c y .  esti-  Initial  8 mates f o r s i l i c o n p l a c e t h e e f f i c i e n c y a t 10 electron crossing the junction  [75].  It 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 t h a n 10 cm  v i s i b l e photons f o r  every  i s t h e n e a r - i n f r a r e d photons  with  , 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 i s 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 i s 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 microplasmas. 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) i s increased significantly by the reverse 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 absorption coefficient i n silicon of 1 cm ^ or less, corresponding to photon energies equal to or less than the band gap energy [ 7 9 ] . Such infrared photons 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 t h e e m i t t e r t o t h e 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 a t t h e t o p and bottom o f t h e s i l i c o n s l i c e were n e g l i gible.  From an a n a l y s i s o f h i s photon c o u p l i n g d a t a , H a i t z e s t i m a t e d t h e  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 g e n e r a t i o n t o be 2 x 10 ^ photons ( w i t h an energy e q u a l t o o r l e s s t h a n t h e band gap) p e r e l e c t r o n c r o s s i n g t h e j u n c t i o n . The s i z e o f t h e avalanche  d i s c h a r g e p u l s e s i n a PC-CCD exceeds 10^  e l e c t r o n s even f o r v e r y s m a l l a r e a p i x e l s ( 2 5 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 o r d e r t o reduce t h e p r o b a b i l i t y o f an e m i t t e d photon t r i g g e r i n g discharge.  another  How complete t h e 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  t h e s i z e and c e n t e r t o c e n t e r s p a c i n g o f t h e p i x e l s .  I t w i l l a l s o depend  on t h e charge p e r u n i t a r e a c r o s s i n g t h e j u n c t i o n d u r i n g an a v a l a n c h e d i s c h a r g e and hence on t h e amount o f o v e r v o l t a g e employed.  Further studies  on photon c o u p l i n g w i l l have t o be made b e f o r e t h e 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 can be  determined.  F i g u r e 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 e t c h [80] i s used t o c u t deep v e r t i c a l w a l l grooves between pixels.  The grooves a r e etched t o t h e r e q u i r e d depth  c a t i o n w h i l e the wafer i s s t i l l  f u l l thickness.  e a r l y on i n t h e f a b r i -  The groove w a l l s can then  be g i v e n t h e same o x i d a t i o n and a n n e a l i n g s t e p s as t h e gate o x i d e . f i n a l s t e p i n t h e f a b r i c a t i o n would be t o f i l l material.  A groove w i d t h o f 3 t o k microns  The  i n t h e grooves w i t h an opaque  and a depth t o w i d t h r a t i o o f 5  s h o u l d be a c h i e v a b l e 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 t h a t 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 t h e p i x e l s , as shown i n Fig.  3.26.  As.an automatic  r e s u l t o f e x t e n d i n g t h e gate a c r o s s t h e V - g r o o v e s ,  97 readout register Q Q Q  clocks  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 e t c h e d s l o t s may be u s e d t o o p t i c a l l y i s o l a t e t h e 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  9  9  register  9  clocks  I  r  I  I  1 1  output  h  •1  2  transfer gate  2  photogate L_  123 V - groove  23  barriers-  Al  gate  wafer  FIGURE 3.26  thinned  _l  "El  to  this  ox ide  line  at  photogate  — f  end  of  I l l u s t r a t i o n o f h o v a n i s o t r o p i c a l l y e t c h e d v - g r o o v e s might be used t o p r o v i d e t h e 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 f i e l d enhancement 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 i s 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 t h e d i s c u s s i o n i n c h a p t e r t h r e e t h a t an m e n t a l s t u d y on t h e above-breakdown o p e r a t i n g regime o f MOS required before.the  experi-  structures i s  development o f a f u l l PC-CCD a r r a y i s a t t e m p t e d .  In  p a r t i c u l a r , i t must be d e t e r m i n e d i f t h e a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y s a t u r a t e s 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 t h e v e r y low count r a t e s t h a t are r e q u i r e d .  D a t a i s a l s o r e q u i r e d on t h e degree o f  photon c o u p l i n g as a f u n c t i o n o f t h e s i z e o f d i s c h a r g e aration.  p u l s e and p i x e l sep-  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  devices, s u i t a b l e f o r operation have been f a b r i c a t e d and t e s t e d . t y p e s u b s t r a t e s - and The  dark  above breakdown and at low The  MOS  temperatures,  t e s t d e v i c e s were f a b r i c a t e d on  p-  i l l u m i n a t e d from the back s i d e .  i n v e s t i g a t i o n was  conducted i n two  v e s t i g a t i o n three very simple  parts.  For t h e i n i t i a l i n -  d e v i c e s t r u c t u r e s were adopted t h a t  a minimum o f h i g h t e m p e r a t u r e p r o c e s s i n g .  required  F a b r i c a t i o n problems were  c o u n t e r e d t h a t p r e v e n t e d the o p e r a t i o n o f two  en-  of the three t e s t s t r u c t u r e s ,  however, t h e r e s u l t s o b t a i n e d w i t h the r e m a i n i n g s t r u c t u r e i n d i c a t e d t h a t dark•generation  occuring  at the S i - S i O  i n s u r f a c e c h a n n e l PC-CCD's.  i n t e r f a c e would be  a major problem  I n t h e second p a r t o f t h e i n v e s t i g a t i o n t h e s e  d e t r i m e n t a l s u r f a c e 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 g o i n g t o a b u r i e d channel device the i n t e r f a c e .  s t r u c t u r e t h a t b r e a k s down at a b u l k n-p  j u n c t i o n away from  I n a f u l l PC-CCD a r r a y t h e added c o m p l e x i t y  i s a l s o j u s t i f i e d by t h e h i g h e r  of t h i s  c l o c k i n g . r a t e s , and hence h i g h e r  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 c h a n n e l CCD's.  structure  frame r a t e s ,  101 4.1 4.1.1  SURFACE BREAKDOWN DEVICES Design Considerations Figure h.l  shows the potential distribution perpendicular to the  interface for a surface breakdown MOS gate, and defines the various potentials and distances that w i l l be refered to in the text. With these structures the peak f i e l d in the depletion region occurs at the Si-SiO^ interface.  It was established in section 3.2.5 that this peak  f i e l d 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 ap15 proximately 8 x 10  —3 cm  i s 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 f i e l d 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 d i f f i c u l t to achieve uni15-3 form planar breakdowns.  For this study a substrate doping of N = 7 x l 0 A  cm  was adopted, for which the calculated depletion layer width at breakdown (at 100K) i s approximately 3-5 ym.  The actual depletion layer widths w i l l be  somewhat wider, and the corresponding peak fields lower, than those calculated 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 i n a structure analogous to an n irp diode. +  It i s v i t a l that the f i e l d in the oxide remain below the breakdown f i e l d strength for SiO^.  The breakdown f i e l d for thermal oxides grown in an  0 /HCl ambient ranges from 7 x 10 Vcm 2  to 1 x 10 Vcm" 1  [84,85].  an avalanche discharge the f i e l d in the gate oxide i s given by,  Prior to  102  S1O9  P - silicon  potential  FIGURE 4.1 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 breakdown, at breakdown, and during reset.  103  ox  e. max 1  where £ max •Q  ss  e. 1  = peak f i e l d i n the s i l i c o n (at the S i - S i 0 i n t e r f a c e ) 2 o  =  p o s i t i v e f i x e d oxide charge  =  charge i n the i n v e r s i o n l a y e r during r e s e t .  Subsequent t o an avalanche discharge the i n v e r s i o n l a y e r charge i s increased and the f i e l d i n the oxide becomes, e £  ox  (Q_ - Q  '  e. max i  +  )  A*  Si. _ +  e. l  s  •  -  (4.1)  d ox  For the substrate doping chosen, the charge ( Q j ~ Q ) r e q u i r e d f o r strong i n ss  -7 version i s approximately 10  -2 coul cm  , while the p e a k . f i e l d i n the s i l i c o n  at the i n t e r f a c e w i l l be close t o k x 10^ Vcm \ (k.l)  P u t t i n g these values i n .  gives,  r (•  £'  ox  =  1.6  x 10  A<p  + r d ox  1  Vcm  For t h i s i n v e s t i g a t i o n , a gate oxide thickness o f 0.2um was chosen so as t o enable operation s e v e r a l tens o f v o l t s 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 minimal [86,87].  I n a d d i t i o n , w i t h a gate oxide o f t h i s t h i c k n e s s , the t e s t  devices w i l l not be destroyed i f they are i n a d v e r t e n t l y exposed t o 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 r a p i d l y as the oxide thickness i s reduced below 0.2um [88]. During the periods o f avalanche breakdown some o f the hot electrons incident on the i n t e r f a c e w i l l be i n j e c t e d i n t o the conduction band o f the  101+  adjacent SiO^ layer [89,90]. very small (<2 x 10  The injection probability, however, should be  )[91], and i n 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 i n the i n i t i a l i n -  vestigation are shown in Figures k.2 - k.k.  Device 1 (Fig. k.2) has the  simplest possible structure, consisting only of an MOS  f i e l d plate with a  thick oxide guard ring, and an ohmic contact to the substrate.  In operation  the gate i s 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 i n 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 bonding pad and the substrate.  In device 2 (Fig. k.3) the drive pulse transients  are greatly reduced by providing a f i e l d shield underneath the bonding pad and interconnect line.  Also, by omitting the thick f i e l d oxide, MOS  devices  with a f i e l d plate type guard ring may be fabricated, as i n 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 recombine 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  (a)  20 urn (or 20x 40 urn) AI photogate  Si Op  •'•  ohmic contact p - silicon  .  c  A  i  >  (b)  sb  V  u a  "~7T\"" charge  FIGURE 4.2 (a) (b) (c)  injection  Charge i n j e c t i o n t e s t device, s t r u c t u r e 1  layout o f the i n d i v i d u a l gates and v e r t i c a l s t r u c t u r e p o t e n t i a l w e l l diagram i n deep d e p l e t i o n , before breakdown during r e s e t , charge i n j e c t i o n  (C)  Amp. virt. gnd.  shield gate V under photogate bonding pad s  extends  ^J10jum|<-  •SiO  Al 0 2  3  20 x 20 Aim (or 20x40urn) Al photogate  ohmic contact  p - silicon  4 0 x 4 0 urn (or 40x 60 urn) Al photogate  ohmic contact  p - silicon  FIGURE 4.3 Charge injection test device, structure 2 (a) (b)  layout and vertical structure alternate structure obtained by omitting the thick f i e l d oxide  107  to  shield gate  V  —H k—  s  lOum  -Via Amp. virt. gnd.  \Vf—Via  to  20x40um  photogate  next  (a)  device  guard  ring  and  transfer gate Al  p - silicon  -Schottky diode  2°3  output  (b)  ^  charge transfer to Schottky output diode  FIGURE 4.4 Charge transfer test device, structure 3 (a) (b) (c)  layout of the individual gate and. vertical structure potential well diagram in deep depletion before breakdown during reset, charge transfer  -> (0  108  t h i s reason a device that operates i n the charge t r a n s f e r mode was included as one of the i n i t i a l t e s t devices ( F i g . U.*0.  I n these devices the s i g n a l  charge i s t r a n s f e r r e d l a t e r a l l y along the i n t e r f a c e t o an output diode. During readout the guard ring, f i e l d p l a t e serves as a t r a n s f e r gate between .the output diode and the photogate.  A s h i e l d gate i s provided around the  breakdown gate and output diode i n order t o i n t e r r u p t any surface channels that would otherwise connect the devices t o the bonding pad d e p l e t i o n regions. 1  No d i f f u s i o n s other than those used f o r b u l k g e t t e r i n g purposes are  required t o f a b r i c a t e the three t e s t s t r u c t u r e s .  The only remaining high  temperature steps involved are the t h i c k f i e l d and gate o x i d a t i o n s . gates and interconnect l i n e s are aluminum.  The  The f i r s t l e v e l undergoes an  a l l o y i n g step i n order t o make any necessary ohmic contacts t o the s u b s t r a t e , and i s then p a r t i a l l y anodized t o form the i n s u l a t o r between f i r s t and second l e v e l metal  [92-94].  The second l e v e l o f aluminum i s not s i n t e r e d  so that MIS diodes may be formed [95].  This double l e v e l aluminum/Al^O^/  aluminum m e t a l i z a t i o n was chosen over the more conventional p o l y s i l i c o n / S i O ^ / aluminum scheme, p a r t l y because o f a l a c k o f p o l y s i l i c o n d e p o s i t i o n 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 m e t a l i z a t i o n .  The minimal high temperature pro-  cessing required t o f a b r i c a t e the t e s t 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 t e s t devices o f each type were l a i d out onto a three part d i e so that they could be f a b r i c a t e d simultaneously u s i n g a s i n g l e set o f photomasks.  The layouts were designed so as t o provide a range of gate separa-  t i o n s f o r photon coupling measurements, and t o have an arrangement o f bondi n g pads s u i t a b l e f o r mounting i n l 6 p i n DIP packages.  Five photomasks  are required t o f a b r i c a t e the composite t e s t c h i p , they are:  109 1  - gate oxide mask  2  -  substrate contact mask  3  -  f i r s t level aluminum mask  h  -  f i r s t to second level aluminum contact mask (vias)  •5 -  second level aluminum mask  Rubylith masters were generated manually on a coordinograph 250 times.  .  The photographic  at a scale of  reduction and step and repeat operations were  performed by Precision Photomask''". The five mask levels are shown i n Fig. 4..5(a) - (e).  The required f i r s t level aluminum pattern consists of various isolated features, (gates, f i e l d shields.etc.), however, the electrochemical anodization process requires electrical contact to each f i r s t 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 i s made to this bus through the substrate during the anodization process. A protective photoresist mask i s used to prevent the temporary contacts and aluminum bus, together with the f i r s t to second level vias, from being anodized [92].  Photoresist i s also used to protect bare areas of silicon  from the electrolyte (in this case the MIS contact, areas), as these would result i n large leakage paths. on mask k.  A l l of these protected areas are included  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 C o p i e s o f t h e f i v e photomasks used t o f a b r i c a t e t h e d e v i c e s . F i g u r e s ( a ) , ( b ) , and (d) a r e r e v e r s a l s o f t h e a c t u a l masks u s e d . The l a s t number i n t h e d e v i c e d e s i g n a t i o n s r e f e r s t o t h e gate numbers i n d i c a t e d i n (e) (a) (b) (c) (d) (e)  gate o x i d e mask s u b s t r a t e c o n t a c t mask f i r s t l e v e l aluminum mask v i a mask second l e v e l aluminum mask  Ill  112  J (e)  .113  Si0  3  p- silicon (l)  f i e l d o x i d a t i o n and g a t e o x i d e window e t c h  (2)  g a t e o x i d a t i o n a n d c o n t a c t 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  anneal  photoresist _OO O a  ^  (k)  o° ~ 0  ^  ^  ^  _a S-  selective anodization of f i r s t l e v e l A l  Schottky  (5)  output  diode  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 t c h  FIGURE 4.6  F a b r i c a t i o n sequence f o r t h e s u r f a c e - b r e a k d o w n t e s t  devices.  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 l i s t e d in Table U . l and U.2.  Table U.3 l i s t s 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 f i e l d 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 potassium present in the oxide [99-101]. Complete passivation of a l l mobile alkali ions i s not c r i t i c a l to the successful operation of the present devices, since these ions w i l l be "frozenin" at the low operating temperature (below 100K).  In. addition to the above  benifits i t 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-  t r i c f i e l d strengths i s lower in HC1 oxides  [103].  115 TABLE 4.1  Step  P r o c e s s i n g D e t a i l s For F i r s t  Operations  i n i t i a l clean  Fabrication  Details  - hot x y l e n e w i t h u l t r a s o n i c  agitation  - RCA c l e a n surface clean-up  temp.  oxidation  cycle:  1100°C 5 min 0^  U00 min 5 min s t r i p a l l oxide  •1-1  + %  g  HC1  - b u f f e r e d HF p a r t o f RCA c l e a n  -•HC1/H 0 field  0  oxidation  temp.  1100°C  cycle:  5 min 0^ lUO min 0  + H  2  400 min-0  5  a  + 5% HC1  min N  2  o x i d e 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 gate o x i d a t i o n  temp.  1100°C  cycle:  5 min 0  62  min 0  2  + 5% HC1  2  5 min 0  2  15 min N "b  1-2  slow p u l l i n N contact etch  2  o x i d e t h i c k n e s s , 0.20 ym - n e g . 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 , h o t HgSO^/H 0. RCA c l e a n - 2% HF d i p  (20 s e c )  116 TABLE 4.1 c o n t ' d .  Step  Operations aluminum evap. I  Details e l e c t r o n beam evap.: substrate temp., 250°C evap. r a t e , 50-200 S s e c  -1  f i l m t h i c k n e s s , 1.0 ym aluminum etch I 1-3  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 resist strip, Microstrip  contact s i n t e r plus  temp.  hydrogen anneal  cycle:  1+50°C 10 min N 30 min N  g  2  + 50$ H  2  v i a photoresist  - Waycoat LSI 2 9 5 p o s i t i v e , mask 1+  aluminum anodization  : e l e c t r o l y t e , 25w/o APB-EG ° -2  1-1+  c u r r e n t , 0 . 5 mA cm formation v o l t a g e , 85 V soak time at 85 V, 2 min -resist  s t r i p , hot acetone  - Phosphoric e t c h , 1+0°C, 6 0 sec aluminum evaporation II  • tungsten filament evap.: substrate temp., 200°C evap. r a t e , 5 0 - 1 0 0  2sec  -1  f i l m thickness 1 . 0 ym  1-5  aluminum etch I I  - neg. r e s i s t , mask 5 - phosphoric etch 60°C - resist strip, Microstrip  a  Burnt hydrogen wet o x i d a t i o n P u l l e d manually from the hot zone over a period o f about 10 min. 25 weight % ammonium pentaborate d i s s o l v e d i n (hot) ethylene g l y c o l (under an argon atmosphere t o prevent o x i d a t i o n ) .  117  TABLE 4.2 P r o c e s s i n g D e t a i l s F o r Second F a b r i c a t i o n  Details  Operations  Step  initial  clean  - h o t x y l e n e w i t h u l t r a s o n i c ag; i t a t i o n - RCA c l e a n  surface clean-up  temp.  oxidation plus  cycle:  1125°C 5 min 0 b  d  phosphorus d i f f u s i o n  100 min Q> + H  mask  kOO min 0  2  2-1  s t r i p oxide o f f  - HF v a p o r - e t c h  hack  - HC1/H 0 2  phosphorus g e t t e r a diffusion  2  + 5% HC1  2  5 min N  2  2  (back s i d e )  p a r t o f RCA c l e a n  temp.  1050°C  source  P O C l ^ pass o v e r , 15°Ci  cycle:  5 min N  g  + 3% 0  3Q..min N  2  + 3% Q> + source N  2  + 3% 0  5 min N  2  2  2  s t r i p oxide o f f  - HF v a p o r - e t c h  (front side)  front  - 10% HF, 60 s e c . (phosphorous g l a z e s t r i p on back s i d e ) - HC1/H 0 2  a f i e l d oxidation  2  p a r t o f RCA c l e a n  s l i c e s P2-0, P2-2: temp. cycle:  1125°C 10 min 0^ kO min 0  2-2  2  + H  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 P 2 - 1 , P2-3: temp.  1125°C  2  118  TABLE 4.2 cont'd.  Step  Operations  Details 1 0 min 0 ^  cycle:  2-2  7 3 min 0  cont'd  5 min 0  + H  2  2  2  1 5 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  a gate oxidation  temp.  1125°C  cycle:  1 0 min 0  2  49 min 0 5 min 0  + 5% HC1  2  2  5 min N 2  c  2-3  slow pull in N contact window etch  2  oxide thickness, 0 . 1 8 ym - neg. resist, mask 2 - buffered HF - strip resist, hot H S 0 ^ / H 0 2  - RCA clean - 2% HF dip 2 0 sec.  aluminum evaporation  electron beam evap: substrate temp., 250°C evap. rate, - 50 2sec film thickness, 1 . 0 ym  2  2  119  TABLE 4.2 c o n t ' d .  Step  Operations aluminum etch I  2-k  Details - neg. resist, masks 3 + 5 (double exposure)  cont'd  - 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.  cycle: hydrogen anneal  etch off back side + n layer  U50°C  30 min o  temp.  350 C  cycle: 180 min - 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  D e v i c e And T e s t Wafer Data  bulk resistivity (flcm)  gate oxide thickness  wafer  use  Pl-0 Pl-1 Pl-2 PI-3  anodization tests  P1-1+* Pl-5 Pl-6  devices  2.35 2.1+5 2.30  0.19 0.19 0.19  Pl-T  surface state measurements  2.38  0.19  P2-0 P2-1 P2-2 P2-3*  devices  2.1+5 2.32 2.35 2.22  0.17 0.17 0.17 0.17  P2-1+ P2-5  p r o f i l e and surface state measurements  2.2U 2.1+8  0.17 0.17  (um)  .  V_. FB (V)  field  oxide  thickness (pm)  d  V FB (V)  -0.20  •2.5  1.5  1.2  1.00 1.00 1.00  0.55 0.74 0.55 0.7I+  8.0  5.3  C  C  Boron doped 2 " ( l 0 0 ) C z o c h r a l s k i w a f e r s , c h e m o - m e c h a n i c a l p o l i s h on f r o n t surface, bright-etched rear surface. Wafer t h i c k n e s s ~280pm. *Device wafers t e s t e d . b  Measured w i t h f o u r p o i n t probe b e f o r e  c  T h i c k n e s s 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 a c c u m u l a t i o n (jising e-^/e- =3.8).. Thickness o b t a i n e d . f r o m . c o l o u r ,  processing.  accuracy approximately  ±0.02pm.  121 (l)  F i r s t f a b r i c a t i o n run  P r i o r t o d e v i c e p r o c e s s i n g t h e w a f e r s were o x i d i z e d i n an O^/HCl ambient t o remove any s u r f a c e damage and p r o v i d e some i n i t i a l g e t t e r i n g o f impurities.  T h i s o x i d e was t h e n s t r i p p e d and t h e t h i c k f i e l d and g a t e  o x i d e s were grown, a g a i n u s i n g HC1.  A f i e l d o x i d e t h i c k n e s s o f 1 ym was  chosen i n o r d e r t o ensure t h a t t h e s i l i c o n b e n e a t h t h e edges o f t h e m e t a l i z a t i o n w o u l d r e m a i n w e l l below breakdown d u r i n g d e v i c e o p e r a t i o n .  A 15  minute n i t r o g e n a n n e a l .was i n c l u d e d a t t h e end o f t h e gate o x i d a t i o n i n order t o minimize  t h e 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].  After  ss o p e n i n g b o t h t h e ohmic and MIS c o n t a c t windows t h e f i r s t l e v e l o f aluminum was d e p o s i t e d The  ( v i a e l e c t r o n beam e v a p o r a t i o n )  i n a planetary  evaporator.  s u b s t r a t e s were h e a t e d t o 250°C d u r i n g t h e e v a p o r a t i o n ' t o  prove s t e p coverage [105].  f u r t h e r im-  I n o r d e r t o a c h i e v e t a p e r e d m e t a l i z a t i o n edges  and a l l e v i a t e s t e p coverage problems d u r i n g t h e second l e v e l m e t a l i z a t i o n , nitric  a c i d was added t o t h e p h o s p h o r i c  f i r s t l e v e l o f aluminum [106].  a c i d e t c h a n t used t o p a t t e r n t h e  The n i t r i c  l o s e adherence and g r a d u a l l y l i f t  a c i d causes t h e p h o t o r e s i s t t o  from t h e edge inwards d u r i n g e t c h i n g , r e -  s u l t i n g i n t h e d e s i r e d edge p r o f i l e .  A f t e r patterning the f i r s t l e v e l of  aluminum t h e s l i c e s were g i v e n a U50°C c o n t a c t s i n t e r i n o r d e r t o make ohmic c o n t a c t t o t h e a n o d i z a t i o n bus and t o a n n e a l out any x - r a y damage caused by t h e e l e c t r o n beam e v a p o r a t i o n .  A hydrogen a n n e a l t o reduce s u r -  f a c e 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 a t t h i s t i m e , s i n c e an a c t i v e m e t a l " a l n e a l " f o l l o w i n g t h e second m e t a l i z a t i o n i s n o t p o s s i b l e , as t h i s w o u l d s i n t e r t h e MIS c o n t a c t s and d e s t r o y 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 t h e v i a p h o t o r e s i s t t h e w a f e r s were a n o d i z e d u a l l y , i n an e l e c t r o l y t e o f 25 w/o ammonium p e n t a b o r a t e u s i n g t h e s p e c i a l t e f l o n w a f e r h o l d e r shown i n F i g . h.'J.. l a y e r s were formed a t a l o w c o n s t a n t  individ-  i n ethylene  glycol,  The a n o d i c o x i d e -2 c u r r e n t d e n s i t y o f 0.5 mA cm and h e l d  122  FIGURE 4.7  Teflon anodization c e l l 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 voltage are reported to result i n pore formation [107],  The results of some  i n 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 photoresist features l i f t e d at a much lower voltage.  Parts of the via photo-  resist pattern l i f t e d completely at approximately 6 0 V on the f i r s t 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 half the formation voltage.  layer was only hO V, less than  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 i s not certain, but is thought to be due to annealing hillocks present i n the f i r s t 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 break1  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 0_-Al metalization o  12k scheme was abandoned and only device structure 1 was fabricated. In addition 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 f i e l d (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 i n 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 i n 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 devices through the glass  .  '  Figure 4.8 shows a cross-section of the cold chamber used for the low temperature device testing.  Cooling i s accomplished with a liquid nitrogen  heat pipe that protrudes into an evacuated housing.  The front (window) end  of the housing i s 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 i s 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 inserting 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 w i l l maintain the vacuum below 10  torr.  The vacuum provides insulation  and ensures that no moisture i s 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 i n Fig. 4.9 • Schematics 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 t r a i l i n g  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 i s 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 i s passed to a descriminator 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 No.  COLD CHAMBER  COUNTERS of events  CURRENT AMP. AND INTEGRATOR  DESCRIMINATOR  J Pi »  No.  of frames  1  TIMING 1 \  HIGH VOLTAGE DRIVER AND INTEGRATOR START PULSE GEN.  FIGURE 4.9 B l o c k diagram o f the t e s t  electronics.  128  t i v e g o i n g edge o f t h e d r i v e p u l s e and t h e d u r a t i o n o f t h e i n t e g r a t i o n maybe v a r i e d i n d e p e n d e n t l y  o f t h e d r i v e r waveform.  Before being 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 m o m e n t a r i l y w h i l e t h e d e s c r i m i n a t o r i s 3 activated.  The l e v e l o f n o i s e a t t h e d e s c r i m i n a t o r v a r i e d from 3 x 10  e l e c t r o n s r.m.s. f o r s h o r t (0.2msec) i n t e g r a t i o n s t o a p p r o x i m a t e l y  1.5 x  10^ e l e c t r o n s r.m.s. f o r l o n g e r (2msec) i n t e g r a t i o n s . 4.1.5  Modeling  o f t h e Completed D e v i c e s  I n o r d e r t o i n t e r p r e t t h e r e s u l t s and make comparisons w i t h an a c c u r a t e doping p r o f i l e t h r o u g h t h e d e p l e t i o n r e g i o n - u n d e r a c c u r a t e gate o x i d e and f i e l d o x i d e t h i c k n e s s e s a r e r e q u i r e d .  theory,  t h e g a t e , and The f i e l d  o x i d e t h i c k n e s s was. d e t e r m i n e d t o w i t h i n +0.02 ym from i t s c o l o u r .  The  d o p i n g p r o f i l e and gate o x i d e t h i c k n e s s were d e t e r m i n e d from C-V d a t a ing  t o t h e method o u t l i n e d i n Appendix C.  accord  These l a t t e r measurements were  made on w a f e r s t h a t had r e c e i v e d t h e same h i g h t e m p e r a t u r e p r o c e s s i n g as t h e d e v i c e s l i c e s and t h a t 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 ( s e e Table 4 . 3 ) .  The measured doping p r o f i l e s f o r t h e two f a b r i c a t i o n runs a r e  shown i n F i g u r e s 4.10 and 4 . 1 1 .  To s i m p l i f y t h e 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 t r e n g t h as a f u n c t i o n o f p o s i t i o n i n t h e d e p l e t i o n r e g i o n , t h e doping p r o f i l e s were a p p r o x i m a t e d by t h e two s t r a i g h t l i n e segments i n d i c a t e d . making t h e d e p l e t i o n a p p r o x i m a t i o n  By  i t can t h e n be shown t h a t t h e e l e c t r i c  f i e l d i s g i v e n by: qN, £  ls  (  y  )  e  =  £ (y)  =  £  =  2s  ox  q(N - N ) U  s  qN —  ~  y  "  € 2d s  ( d  1  l~  y  )  »  °l ^ i y  d  ( 4  '  2 )  1  (w - y ) ,  e — £ ' e. I s i  )  d  l  l  y  (4.3)  (4.4)  W  (jum)  FIGURE 4.10 Surface doping profile for wafer Pl-7, obtained from C(V) data by the method described in Appendix C. The solid line shows the approximate profile used to model the devices.  I  0  T  r  r~  r~——i—  1  1  1  r  1—  1  i  i  i  »  t  t  0.4  i  0.8 W  1.2  1.6  (jum)  FIGURE 4.11 S u r f a c e d o p i n g p r o f i l e f o r w a f e r P2-4 v i c e modeling.  and t h e a p p r o x i m a t e p r o f i l e u s e d f o r  de-  1  2.0  131 where y is the position in the depletion region, measured from S i - S i 0 interface, and N^,  2  and d^ are the parameters given in Figures 4.10 and  4.H.. The depletion layer width w i s given by  w  e = - e.I d ox + l  e. ox l  e. N l 1  +  d  l ox d  2e Q d_ T  +  ~  -Mr^ + e  where  +  i  q  l  N  W  T l 1 d  25e (V - V_) q IN.  \h \  (4.5)  is the amount of charge present in the surface inversion layer and  V_ is the flat band voltage. FB  *1 N  *s  =  2T  v  s  2  The silicon surface potential is given by,  ^  V  ~~ 6 l  V d  P  '  (4.6)  i  s  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  i WAFER o  r P2-5  \ \  \  10  10  o l/l  O x •  0.1  300 K 223 K 173 K  0.2  0.3 E - E v  0.4  0.5  0.6  0.7  (eV)  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 w a f e r P2-5 as a f u n c t i o n o f p o s i t i o n i n t h e h a n d g a p , o b t a i n e d from C(V) measurements by t h e method o u t l i n e d i n A p p e n d i x 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 r e p r e s e n t e d by t h e upper envelope o f t h e t h r e e s e t s o f d a t a .  133  d a t a from w a f e r P2-H.  The c o n t r i b u t i o n t o t h e decay c u r r e n t f r o m i n t e r f a c e  s t a t e s was m i n i m i z e d by p u l s i n g t h e g a t e s from a c o n d i t i o n o f s t r o n g i n version.  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 .  B e f o r e any h i g h v o l t a g e t e s t s were conducted on t h e t e s t d e v i c e s t h e f l a t - b a n d v o l t a g e s f o r t h e g a t e and f i e l d o x i d e s were d e t e r m i n e d by  driving  t h e p h o t o g a t e 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 t h e 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 i n c e t h e v o l t a g e ramps a r e l i n e a r t h e 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 t h e 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 t h e t h i c k and t h i n o x i d e r e g i o n s may be d e t e r m i n e d 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 m e a s u r i n g t h e v o l t a g e s o f t h e two i n f l e c t i o n s i n t h e C-V c u r v e , c o r r e s p o n d i n g t o i n v e r s i o n under t h e t h i c k and t h i n o x i d e s , spectively.  re-  To w i t h i n t h e a c c u r a c y o f t h e measurements, a l l o f t h e d e v i c e s  t e s t e d , from a g i v e n w a f e r , were found t o have t h e same f l a t band v o l t a g e s . The g a t e and guard r i n g , f l a t band v o l t a g e s a r e 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 t h e d e v i c e s had been o p e r a t e d above breakdown, and c y c l e d between room t e m p e r a t u r e 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 c o n d u c t e d at a t e m p e r a t u r e o f 80 K.  Examples o f t h e d r i v e r waveform used and t h e t y p i c a l o u t p u t 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 t h e p o s -  i t i v e g o i n g ramp, s l i g h t l y b e f o r e c r o s s i n g t h e breakdown v o l t a g e .  The  large  d r i v e p u l s e d i s p l a c e m e n t 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 t h e b o n d i n g pad and t h e s u b s t r a t e made i t n e c e s s a r y t o l i m i t t h e ramp r a t e 1 x 10^ Vsec  i n o r d e r not t o s a t u r a t e t h e c u r r e n t  to  amplifier.  I n a c c o r d a n c e w i t h t h e t h e o r e t i c a l d i s c u s s i o n i n c h a p t e r 3, i t was found t h a t when t h e d e v i c e s 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  (a)  — 7 / — ->  r 0  1  < — 1 -1000 msec  I  AVALANCHE DISCHARGE  (b)  integrate (0.5 - 2 msec)  (c)  + 5V  •(d)  FIGURE 4 . 1 3  devices (a) (b) (c) (d)  Test waveforms for the surface-breakdown, charge-injection  high voltage driver output of the current to voltage amplifier. Substrate displacement current output of the preset integrator 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 i s transferred to the thin oxide gate region during the depleting pulse, thereby, i n 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 i n breakdown voltage V . for a given change i n reset voltage, when the guard ring i s heavily i n verted during reset, is given by  AV  where dg  gate oxide thickness f i e l d oxide thickness area of the thin oxide gate region area of the guard ring, bonding pad and interconnect line  (4.7)  136  140  60  DEVICE  2 130 o >  O o—o—-o  gate 10  120  P1-4/3-5 P1-4/2-3  area = 20 x 40 jjm t  r  = 100 msec  z o < Ul  oc CD  110  111 _I  CO  <  o  u 100 t—  UJ O  O a.  U.  O  ui o  UJ  O <  I_i  CO  o >  4 RESET  62.5  V  59.9  V  6 VOLTAGE  V  r  (volts)  FIGURE 4.14 Voltage of f i r s t detectable breakdowns as a function of the reset voltage for devices from the f i r s t fabrication. The solid line i n dicates the calculated slope for the case that the guard ring i s 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 RESET  4 VOLTAGE  V  p  6 (volts)  8  FIGURE 4.15 Voltage of f i r s t detectable breakdowns as a function of the reset voltage (second fabrication).  138 The  c a l c u l a t e d s l o u e AV ,/AV from (h.j) gb r h.lh  Figures served  and U.15.  i s i n d i c a t e d by the s o l i d l i n e i n  The c l o s e agreement between t h e c a l c u l a t e d and ob-  s l o p e s i n d i c a t e s t h a t premature edge breakdown was n o t o c c u r i n g .  If  i t were, one would expect t h e s l o p e AV ^/AV^ t o be g r e a t e r t h a n t h a t c a l c u l a t e d from ( 4 . 7 ) ,  s i n c e t h e guard r i n g becomes more deeply  more e f f e c t i v e i n p r e v e n t i n g creased.  depleted  edge breakdown). as t h e r e s e t v o l t a g e  (i.e.,  is in-  With f u r t h e r i n c r e a s e s i n r e s e t v o l t a g e , o r as t h e f i e l d  oxide  t h i c k n e s s i s reduced, a p o i n t i s e v e n t u a l l y r e a c h e d where t h e s i l i c o n t h e guard r i n g , b o n d i n g p a d , and i n t e r c o n n e c t l i n e  a l s o break down.  t h i n n e r f i e l d o x i d e on wafers P2-0 and P2-2 p r e v e n t e d devices  under The  operation o f these  above t h e gate breakdown v o l t a g e when t h e guard r i n g was h e a v i l y i n -  verted during reset. F i g u r e k.l6 shows t h e maximum charge, p e r p u l s e as a f u n c t i o n o f t h e gate v o l t a g e f o r one o f t h e 20 x 20 ym gates from wafer P2-3. height  distribution  -  (for V S  measurements were o b t a i n e d  V , = 5 V) gb  The p u l s e  is-shown i n F i g . U.17.  The charge  from t h e d i s c r i m i n a t o r s e t t i n g u s i n g t h e c a l c u l a -  t e d g a i n o f t h e c u r r e n t a m p l i f i e r - i n t e g r a t o r c o m b i n a t i o n (9-36 x 10^ e l e c t . V ^"). -  The d i s c h a r g e p u l s e s  increase l i n e a r l y with  expected, however, t h e maximum charge p u l s e s dicted  excess gate v o l t a g e , as  a r e s m a l l e r than t h o s e  pre-  from  IQ  -  I -«iv-v A  and t h e p u l s e h e i g h t  (  (4 8)  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 a r e t h o u g h t t o be due t o t h e b u i l d - u p o f p o s i t i v e space charge d u r i n g an avalanche ( e . g . , h o l e s the d e p l e t i o n r e g i o n ) . discharge.current  d r i f t i n g t h r o u g h t h e low f i e l d r e g i o n s o f  The b u i l d - u p o f space charge l i m i t s t h e a v a l a n c h e  t o t h e p o i n t where s t a t i s t i c a l  number o f c a r r i e r s i n t h e h i g h  f l u c t u a t i o n s can cause t h e  f i e l d r e g i o n t o drop t o z e r o , thus  terminat-  FIGURE 4.16 Maximum charge .per pulse as a function of the photogate voltage. indicates the expected variation, according to Eq. U.8.  The dashed  T  0  1  1  1  0.4 0.8 DESCRIMINATOR  1——i  LEVEL  1  1  1.2 1.6 ( 1 0 elect.)  1  r  2.0  6  FIGURE 4.17 Typical pulse height distribution for the surface-breakdown devices. The d i f ferential distribution was obtained by graphically differentiating the integral distribution. V  - V  = 5V.  141  ing the avalanche.  (l)  Results From First Fabrication  Six test chips ( 7 8 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 i s shown in Fig. 4 . 1 8 for one of the The silicon surface potential 4> was cal-  better devices from wafer Pl-4. culated from (4.5)  and ( 4 . 6 ) .  s  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 i n Fig. 4.18 are very high, increasing supralinearly as the gate bias i s increased. 100 counts sec ^ for the 40 x 2 0 ym gate corres7  ponds to 1 . 2 5 x 10  -1  counts sec  -2  cm  , more that 4 orders of magnitude larger -1  than the desired maximum dark count rate of 500 sec -  -2  cm  In spite of the high dark event rate i t was possible to operate these  f i r s t devices under low level illumination i n 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,  SILICON 200  Device gate  SURFACE  <p  POTENTIAL  63  64  T  T  (volts)  s  65  1  P1-4/3-5  area P 20x40 um tj = 1.0 msec t „ = 300 msec  f  I  i  150  o  I  • »  c 3 O U  V r *10 V  100  r  J  V  r  = *12V  \  < OC  J  z O o  5 0  V  r  : *14V  i  5  3£  <  •x  _L EXCESS  FIGURE 4.18  2 GATE  BIAS  3 (volts)  Dark count r a t e as a f u n c t i o n o f t h e e x c e s s p h o t o g a t e 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 ,  = +10V, +12V,  +lVv.  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 also s  The c a l c u indicated.  1U3  DEVICE gate  P1-4/3-5  area tj t V„ r  100  I  TT  150  i  = = =  dark  20x 40 jum 1.0 msec 300 msec 14 V  pulse  rate  photon- induced pulse ( dark subtracted )  rate  o  \  V IA •V  tfl •»  c o U  Ul I-  <  *  50  z :> o o  i  Ol— 1 EXCESS  2 PHOTOGATE  BIAS  V -V_ g go n  K  (volts)  FIGURE 4.19 Dark and photon induced pulse rates as a function of excess photogate bias, for one of the better devices from the f i r s t fabrication.  144  no d e t e r m i n a t i o n o f t h e expected  p u l s e r a t e c o u l d be made.  The l i g h t - i n d u c e d  p u l s e r a t e s were always observed  to increase s u p r a l i n e a r l y with increasing  gate b i a s , showing no s i g n o f s a t u r a t i o n . In o r d e r t o o b t a i n c o n s i s t e n t r e s u l t s when m e a s u r i n g t h e dark and photon .induced p u l s e r a t e s i t was  found n e c e s s a r y to. o p e r a t e t h e d e v i c e s w i t h a  r e s e t d u r a t i o n o f 100 msec o r l o n g e r .  With s h o r t e r r e s e t times there  was  a c h a r g i n g e f f e c t w h i c h caused a p o s i t i v e s h i f t i n t h e gate p o t e n t i a l s r e - , q u i r e d t o generate  a g i v e n s i z e o f breakdown p u l s e ( i . e . , t o r e a c h a g i v e n  pre-breakdown s u r f a c e p o t e n t i a l <j> ). s  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 6  t o m a i n t a i n a c o n s t a n t breakdown p u l s e s i z e - o f 1 x 10 ponding t o an excess  gate b i a s o f a p p r o x i m a t e l y i n Fig. 4.20.  f u n c t i o n o f t h e c y c l e time t  used t o ensure a breakdown every c y c l e .  electrons, corres-  1 v o l t , i s p l o t t e d as a  Sufficient illumination  was  Assuming t h a t a f i x e d amount o f  charge i s t r a p p e d p e r c y c l e and t h a t t h e amount o f t r a p p e d charge decays e x p o n e n t i a l l y w i t h a time c o n s t a n t x between avalanche  discharge pulses,  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 e x p e c t e d V  where V  q  g  ( t ) - V (») s g  V  .E o 1=1  n  exp - i t Ix s  c l o s e l y by Eq.  the observed  shifts  by, (A.9)  i s t h e 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 d i s c h a r g e .  indicated i n F i g . 4.20  The  =  t o be g i v e n  As  i n gate v o l t a g e can be f i t v e r y  ( 4 . 9 ) , w i t h V - 0 . 5 5 V and x = 40 msec. o  c h a r g i n g e f f e c t shown i n F i g . 4 . 2 0 was  o n l y observed when t h e  d e v i c e s were p u l s e d from a r e s e t c o n d i t i o n c o r r e s p o n d i n g t o d e p l e t i o n o r i n v e r s i o n under t h e t h i n o x i d e r e g i o n o f t h e g a t e .  When p u l s e d from accumu-  l a t i o n no p o s i t i v e s h i f t i n t h e gate p o t e n t i a l c o u l d be d e t e c t e d .  Interface  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 o n l y 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 v e r y c l o s e t o t h e c o n d u c t i o n band.  The  d e t r a p p i n g time c o n s t a n t f o r t h e s e  145  0.1 I 0  _J  10  PERIODE  _J  I  20 OF ONE  FULL  I 40  30  CYCLE  t  s  (msec)  FIGURE 4.20 Shift i n 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 . shows the shift after one pulse.  The dashed line  146  levels i s 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 i n crease in the avalanche pulse rate would be expected as the reset time i s 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 ( 6 5 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 i n 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 i n 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 i n this case should follow  the electron avalanche initiation probability P (w). e  The theoretically de-  termined probability P (w), calculated according to ( 3 . 2 ) e  ( 3 . 5 ) and the  ionization rate data of Appendix A, i s also shown in Figures 4 . 2 1 and 4 . 2 2 . The electric f i e l d £(y), was calculated from equations ( 4 . 2 )  -  (4.5),  11+7  100 DEVICE  P2-3/4-10  gate area t i  80  60 u tn  = = = = =  20 x 20 vm 2.0 msec 10 msec 6.00 V 113.4 V  i  dark  pulse  rate  1  photon induced pulse rate ( dark subtracted )  i  v  *N  •A ••* C  -3  o o 40  ui  < z O o  *  20  X  JL 113  £  _L_ 115 PHOTOGATE  JL  117 VOLTAGE  X  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 f i r s t two experimental points.  11+8  100  DEVICE  P2-3/4-12  gate area t 1  60  i  dark  20 x 20 urn 2.0 msec 10 msec 7.00 V 123.3 V  pulse  rate  u 60 photon-induced pulse rate (dark subtracted)  in  *s Ift  *y  c  3 O  I  v  hi <  40  z => O  u  i  20  /  J.  123  FIGURE 4.22  /  /  i.  X  _l_  125 PHOTOGATE  J.  127 VOLTAGE  129 (volts)  131  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 f i r s t detectable breakdown pulses) through the f i r s t 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  channel PC-CCD. The low mid gap interface state density of 7 x 1 0 cm  - 1  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 exceptionally 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  i n t r o d u c i n g a t h i n l a y e r o f n-type s i l i c o n between t h e  and t h e i n s u l a t o r o f a p - s u b s t r a t e  MOS  substrate  gate i t i s p o s s i b l e t o form a p o t e n -  t i a l minimum i n the n - l a y e r , away from the S i - S i O ^ i n t e r f a c e ( F i g . 4 . 2 3 ) . In o r d e r t o a c c o m p l i s h 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  m a i n t a i n e d i n r e v e r s e b i a s so t h a t the t h i n l a y e r o f n-type m a t e r i a l would be  fully  depleted  i n the absence o f any  s t o r e d charge.  This  vertical  4  s t r u c t u r e forms the b a s i s f o r a b u r i e d channel CCD, regions  define the i n d i v i d u a l t r a n s f e r channels.  v i d e d by  a d.c.  As was  contact  deeply  The  the case w i t h  a s u r f a c e channel CCD  n-  reverse bias i s pro-  at the output end o f each n-type  i n d i v i d u a l gates o f a b u r i e d c h a n n e l CCD be  i n which s e p a r a t e  channel.  i t i s p o s s i b l e to pulse  so as t o cause the p - t y p e b u l k  d e p l e t e d , beyond the p o i n t where breakdown would n o r m a l l y  the to  occur.  With a s u f f i c i e n t l y t h i c k n - l a y e r the p o t e n t i a l minimum w i l l s t i l l be l o c a t e d away from the i n t e r f a c e i n t h i s d e e p l y  depleted  once t r i g g e r e d , t h e avalanche d i s c h a r g e w i l l be junction.  The  n - l a y e r has the  i n the i n s u l a t o r , can be k e p t r e l a t i v e l y low  correct thickness  and  doping d e n s i t y .  the p o t e n t i a l d i s t r i b u t i o n perpendicular g a t e , and  referred to.  confined to the bulk  Figure  provided  t o the i n t e r f a c e f o r a b u l k  d e f i n e s the v a r i o u s p o t e n t i a l s and  the  4 . 2 3 shows break-  distances that w i l l  be  L i k e the s u r f a c e breakdown d e v i c e s , t h i s s t r u c t u r e i s s e l f -  quenching s i n c e the e l e c t r o n s g e n e r a t e d d u r i n g t h e avalanche c o l l e c t p o t e n t i a l w e l l , thereby reducing junction.  n-p  f i e l d s at the s u r f a c e o f the semiconductor (where the bands  bend upwards), and  down MOS  c o n d i t i o n , so t h a t ,  the p o t e n t i a l d i f f e r e n c e a c r o s s t h e  i n the n-p  151  w  after  e  SiO*  n - silicon  breakdown  breakdown  p - silicon  potential  FIGURE 4.23 Potential distribution perpendicular to the surface for a bulkbreakdown MOS gate, before and after breakdown, at breakdown, and during reset. The compensated region containing the stored charge Q resulting from an avalanche discharge i s also indicated.  152  In a d d i t i o n t o t h e much lower o x i d e f i e l d s t r e n g t h s , and t h e f a c t t h a t breakdown now o c c u r s i n t h e b u l k o f t h e semiconductor  away from t h e i n -  t e r f a c e , t h e b u l k breakdown MOS s t r u c t u r e has t h e f u r t h e r advantage t h a t c a r r i e r s g e n e r a t e d v i a i n t e r f a c e s t a t e s can no l o n g e r t r i g g e r an a v a l a n c h e . Holes g e n e r a t e d at t h e i n t e r f a c e m i g r a t e l a t e r a l l y a l o n g t h e s i l i c o n s u r f a c e and escape out o f t h e s i d e s o f t h e channel t o t h e p-type b u l k where t h e y recombine.  E l e c t r o n s generated v i a i n t e r f a c e s t a t e s d r i f t through t h e low  f i e l d s u r f a c e r e g i o n and a r e c o l l e c t e d i n t h e p o t e n t i a l w e l l .  Only i f  c a r r i e r s a r e g e n e r a t e d on t h e b u l k s i d e o f t h e p o t e n t i a l minimum can an avalanche be t r i g g e r e d .  F o r t h i s r e a s o n b a c k - s i d e i l l u m i n a t i o n i s manda-  t o r y f o r a b u r i e d c h a n n e l PC-CCD. Inherent i n t h e b u r i e d channel CCD s t r u c t u r e i s t h e a b i l i t y t o c o n t r o l the b u l k f r i n g i n g f i e l d s and reduce premature edge breakdown.  In order t o  f u l l y d e p l e t e t h e n-channel t h e i n d i v i d u a l t r a n s f e r gates must extend comp l e t e l y a c r o s s t h e c h a n n e l , and out over t h e p-type s u b s t r a t e .  When p u l s e d  above breakdown t h e s e gates a r e p o s i t i v e w i t h r e s p e c t t o t h e s u b s t r a t e , and hence cause t h e p - s i l i c o n a d j a c e n t t o t h e n-channel t o be d e p l e t e d , t h e r e b y lowering the bulk f r i n g i n g f i e l d s .  Reducing t h e o x i d e t h i c k n e s s i n c r e a s e s  the gate v o l t a g e r e q u i r e d f o r breakdown, which i n t u r n causes t h e p-type s i l i c o n on e i t h e r s i d e o f t h e channel t o become more d e e p l y d e p l e t e d .  Pro-  v i d e d t h e l a t e r a l n-p t r a n s i t i o n i s not t o o a b r u p t , i t s h o u l d be p o s s i b l e t o s e l e c t an o x i d e t h i n enough t o p r e v e n t edge breakdown a l o n g t h e s i d e s o f t h e n—channels, b u t s t i l l  s u f f i c i e n t l y t h i c k t o p r e v e n t breakdown i n t h e p-type  s u b s t r a t e a t t h e edges o f t h e g a t e s . fringing fields  As w i t h t h e s u r f a c e channel CCD, h i g h  i n t h e charge t r a n s f e r d i r e c t i o n can be a v o i d e d b y k e e p i n g  the a d j a c e n t t r a n s f e r gate o n l y s l i g h t l y below breakdown.  153 4.2.1  Design Consideration and Equations Although the bulk n-p j u n c t i o n w i l l g e n e r a l l y not be abrupt, the r e -  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 r e g i o n , and on the substrate doping, are roughly the same as were determined f o r the surface 15-3 breakdown devices.. A substrate doping of'N^ < 7 x 10 a l s o adopted f o r the bulk breakdown devices.  cm  was therefore  Several f a c t o r s 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 p o s s i b l e i n order t o f a c i l i t a t e  long m i n o r i t y c a r r i e r l i f e t i m e s and low t r a p d e n s i t i e s ,  but, at the same time, the dopant dose (per cm ) must be high enough that the p o t e n t i a l minimum i s l o c a t e d away from the i n t e r f a c e 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 i n t e r f a c e 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 a l s o d e s i r a b l e t o minimize the  j u n c t i o n curvature at the edges o f the n-region  ( i . e . , use a deep n-layer)  as t h i s relaxes the problem o f c o n t r o l l i n g edge breakdown along the sides o f the n-channel.  Also a high j u n c t i o n curvature may cause the n-channel t o  breakdown prematurely at the output and, before the channel d e p l e t i o n volt-, age i s reached. In order t o a r r i v e at some a c t u a l q u a n t i t a t i v e s p e c i f i c a t i o n s f o r the n-layer and the oxide t h i c k n e s s , i n i t i a l guesses were made on the b a s i s o f the above considerations, and then modified according t o the r e s u l t s o f one dimensional the surface.  c a l c u l a t i o n s o f 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 normal t o The required gate voltages i n deep depletion were determined  by c a l c u l a t i n g 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 t o e equations  (3.2) - (3-5) and the i o n i z a t i o n r a t e data i n Appendix A.  The  equations required t o c a l c u l a t e 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 were obtained as f o l l o w s .  15k  The defined  p o t e n t i a l s and d i s t a n c e s  i n F i g . k.23.  used i n t h e f o l l o w i n g d e r i v a t i o n a r e  Using the depletion'approximation, the Poisson  e q u a t i o n s f o r t h e i n s u l a t o r , t h e n-type t o p l a y e r and t h e p - t y p e  substrate  become d<f>  (y)  2  — i r -  =  - -  0  d ox  ±yio  (A.. 10)  dy  2 d <(> . (y)  — ^ "  / \  =-^  , 0<y  (4.11)  where p ( y ) i s t h e volume charge d e n s i t y  i n t h e s i l i c o n as- a f u n c t i o n o f t h e  dy  •distance  s  i n t e r f a c e , and d» and i> .. a r e t h e e l e c t r o s t a t i c ox s i  from t h e S i - S i O ^ 2  p o t e n t i a l s i n t h e i n s u l a t o r and i n t h e s i l i c o n , r e s p e c t i v e l y .  i s t a k e n .to be 0 . The boundary  s t a t i c p o t e n t i a l of the substrate  conditions  (1+.10) and ( l + . l l ) a r e  needed t o s o l v e  •ox - ox (  W  The e l e c t r o -  d  )  d<j>  e.1 — ox dy <|> (w) si  v  *si  =  0 )  =  (0)  g (  ; 0  )  •  ( 4  *s  =  -  1 2 )  < ' > 4  d(f. . ( 0 )  = es — sdy 5i  13  .  ... (4.14)  T  ==• 0  (4.15)  = 0  (4.16)  d<f> .(w)  - f ~  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 t h e boundary c o n d i t i o n s  (U.12) - ( U . l 6 )  <f> ( y ) and <j> . ( y ) c a n be e x p r e s s e d as ox si *  (y ox  g  a ox ) ;  +  e  i  w  p(y) dy  (4.17)  155  1  p(y) dy -  w  yp(y) dy 'w  J  (4.18)  while the electric field i n the silicon becomes w (4.19)  p(y) dy s '  where w may be determined by an iterative procedure from boundary condition  (4.13), which  becomes w  j  [ yp(y) dy + s  w  -f^  i  J  p(y) dy - V g  = 0  (4.20)  The position of the potential minimum y^ can likewise be determined from  Vm  p(y) dy w  (4.21)  = 0  The normal procedure for generating the n-layer i s to i n i t i a l l y predope the surface by ion implantation (or a low temperature furnace predeposition) and then drive the dopant i n at a high temperature.  The resulting  doping profile i n this case i s approximately Gaussian, and p(y) becomes P(y)  =  9. N(0) exp -(y/e)  - 9.N.  ( 4.22)  where N(0) i s the surface concentration of the n-layer dopant (cm-3, ) and N is the bulk acceptor doping density.  The parameter 6 i s related to the  junction depth according to 6  = y [In 1(0) - In N j " ^  Approximating the doping profile by in  (4.17) - (4.21)  (4.22)  to be replaced by  (4.23) enable the integrals appearing  156  b  b P(y)dy  =  N(0) 3 e r f ( y / 3 ) -  N y}  (A.24)  A  a •  2  b  y p ( y ) dy  =  {N(0) |  Ny [1 - exp - ( y / B ) ] - - § - } 2  b  (4.25)  2  On t h e b a s i s o f the one d i m e n s i o n a l  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 t h e o x i d e t h i c k n e s s , n - c h a n n e l j u n c t i o n d e p t h , and n - l a y e r s u r f a c e c o n c e n t r a t i o n t o be used w i t h a s u b s t r a t e doping o f  = 7 x 10 d  ox y^  1 5 - 3 cm  = 0.5  ym  = 2.0  urn  N(0) = 3.2  x 10  An o x i d e t h i c k n e s s o f 0-5  :  l 6  t o 4.0  ym was  x 10  l 6  cm"  3  chosen as t h i s i s t h e minimum t h i c k n e s s  p e r m i s s i b l e due t o p r o c e s s i n g c o n s t r a i n t s t h a t are' d i s c u s s e d i n t h e next section.  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 t h e maximum temp-  e r a t u r e o f the d r i v e - i n f u r n a c e was  l i m i t e d t o 1150°C, and t o d r i v e the  l a y e r i n much f u r t h e r w o u l d have r e q u i r e d v e r y l o n g d r i v e - i n t i m e s .  n-  Also,  i f the n - l a y e r i s deeper t h e s u r f a c e c o n c e n t r a t i o n must be l o w e r , and  con-  t r o l over the u n i f o r m i t y o f 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 D e s i g n and F a b r i c a t i o n The b u l k breakdown d e v i c e 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  Fig.  4.24.  I t i s b a s i c a l l y t h e same as t h e p r e v i o u s s u r f a c e breakdown t e s t  s t r u c t u r e shown.in F i g . 4.4, t r a n s f e r channel  except t h a t a n - d i f f u s i o n now  defines the  and o n l y a s i n g l e t h i c k n e s s . o f o x i d e 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 o r d e r t o make good ohmic c o n t a c t s t o t h e n-channel and p - s u b s t r a t e . d e v i c e s t r u c t u r e s i t was  Because o f the s i m i l a r i t y o f the  two  p o s s i b l e t o f a b r i c a t e t h e b u l k breakdown t e s t  157  o  J  1  f  \  —  >  (b)  \  c ft)  •» o . a.  j  V. I  V.  charge transfer to output diode  FIGURE 4.24 Bulk-breakdown, charge-transfer test device (a) (b) (c)  vertical structure. Layout i s identical to the surface-breakdown test device shown in Fig. U.4 potential well diagram in deep depletion, before breakdown during reset, charge transfer  (0  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 l i s t e d 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. ish.  The back sides, however, had a rough, sand-blasted surface f i n -  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 A l - A l ^ ^ - A l double level metalization.  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 f i r s t 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 electrolyte but not covered with aluminum.  Bare areas of silicon exposed to the  electrolyte were avoided by opening the p+ and n+ contact windows in separate 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 temperature phosphorous predeposition used to form the transfer channels. I n i t i a l tests, conducted to determine the best combination of predeposition temperature and time, indicated that achieving the desired dopant concentration would be somewhat of a h i t or miss operation, due to the poor temperature 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 i n ; however, an ion-implanter 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 received 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 anodization 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 d i f f i c u l t .  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 the 220 V films.  10 min. for complete removal of  Also, the end point could not be determined visually:  i6o o n l y by p r o b i n g t h e v i a areas v e r y g e n t l y and measuring t h e e l e c t r i c a l r e s i s t a n c e t o t h e u n d e r l y i n g aluminum was i t p o s s i b l e t o d e t e r m i n e t h e comp l e t i o n o f the etch.  The good d e v i c e w a f e r s (M65,66) were g i v e n a 10 min  v i a e t c h a f t e r w h i c h p r o b i n g i n d i c a t e d t h a t b a r e aluminum h a d been exposed. However, a f t e r d e p o s i t i n g t h e second l e v e l o f aluminum i t was d i s c o v e r e d t h a t t h e A1,,0  had not been c o m p l e t e l y removed.  Apparently the contact  probe must have b r o k e n through' a t h i n r e m a i n i n g l a y e r o f o x i d e .  Unfortun-  a t e l y , s i n c e t h e n+ c o n t a c t windows had a l r e a d y been opened, i t was n o t p o s s i b l e t o s i m p l y remove a l l t h e aluminum and A l ^ O ^ and r e p e a t t h e m e t a l i z a t i o n procedure.  I n s t e a d i t was a l s o n e c e s s a r y t o remove t h e S i O ^ gate  o x i d e and r e - o x i d i z e t h e w a f e r s .  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 o f t h e n-channel and f u r t h e r r e d u c e d t h e c h a n n e l  doping  (cm  ).  On  t h e second attempt at e t c h i n g t h e A l ^ O ^ v i a s , t h e CrO^/phosphoric a c i d e t c h was f o l l o w e d by an e t c h i n s t r a i g h t p h o s p h o r i c c o u l d be observed  a c i d a t 50°C u n t i l b u b b l e s  (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 b e i n g etched and t h a t t h e Al^O  had been c o m p l e t e l y  Only wafer M66 was s u c c e s s f u l l y completed i n t h i s way. on M6p d u r i n g t h e CrO^/phosphoric a c i d e t c h .  removed.  The r e s i s t  lifted  T a b l e U.5 l i s t s t h e v a r i o u s  t h i c k n e s s and doping parameters measured on w a f e r M66 a t t h e c o m p l e t i o n o f the p r o c e s s i n g .  The f i n a l n - l a y e r dopant dose (cm  ) was c o n s i d e r a b l y low-  er t h a n - d e s i r e d b u t i t was f e l t t h a t t h e d e v i c e s w o u l d s t i l l be o p e r a t i o n a l above breakdown.  phosphorous  i  i v. _  masking oxidation - phosphorous predep  5.  •  '  "  /  deposit and pattern f i r s t level of Aluminum  boron  ,,„,,„ „,(E^\,,,, „ , ,,,,,  j g W ^ F ^ ^ & W 1  n - channel  *  >•  2.  n-channel drive in an oxidation - boron predep.  6.  P  *  I  \  v  n"  ;  ^_  2.-'/ s  Aluminum anodization and v i a etch.  phosphorous  , V  3.  oxidation - phosphorus predep.  .••-,,J^U  ^  7-  open n  channel contacts.  8.  deposit and pattern second level of Aluminum plus anneal.  gate oxide /•:•• . •. , ,  1  k.  .  1  ,  1 \  n"  strip a l l oxides - gate oxidation - open substrate contacts.  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 i n i t i a l clean  Details hot xylene with ultrasonic agitation RCA clean  n  masking oxide  temp,  1150°C  cycle:  30 min 0, c  5 min N  r  oxide thickness, 0.10 urn channel window etch  neg. resist, mask 1 buffered HF resist strip, hot B^SO^/H^ RCA clean  channel predep.  temp.  T80°C  source  POCl^ pass over, 15°C  boat and tube predoped at 1050°C for 1 h  M6T, 69, TO TO 5 min N + 3%  slices cycle:  8 min N  + 3% + 3%  M6U, 68, 71 Tl 5 min + 3%  slices cycle:  °2 °2 °2  °2  L2 min N + 3% °2 5 min N + 3% 2  °2  2  66, 12T2  slices  M65,  cycle:  5 min N + 3% 2  20 min N 5 min N  2  + 3%  2  + 3%  °2 °2 °2  phosphorus glaze strip, 10$ HF, 15 sec. HC1/H 0 part of RCA clean 2  2  163 TABLE 4.4 cont'd.  Step  Operations n  drive-in and  Details a  oxidation  temp.  . 1150°C  cycle:  2U5 min Q> + 3% HC1 2  kO min 0^ + H 10 min N +  2  2  - neg. resist, masks 2 + 5  p d i f f . window etch  (double  exposure) - buffered HF - resist strip, hot H SO^/H 0  p  - RCA clean + p  temp.  pre-dep  1000°C  source  BBr^ pass over, 15°C  cycle:  5 min N  2  5 min N (  30 min N  2  2  + 3% 0  2  + 3% 0  2  + Source N, 2 + Source N 2  5 min N  2  - boron glaze stripy HF/H 0 ( l : l ) , 30 sec - HC1/H 0 part of RCA clean 2  p  +  drive-in and  a  oxidation  temp.  2  1100°C  cycle:  . 5 min 0  2  120 min 0  2  5 min N 3  n  +  diff. window etch  + H ' 2  2  - neg. resist, masks 2 + 3  (double  exposure) - buffered HF - resist strip, hot H SO^/H 0. - RCA clean  161+ TABLE 4.4  Step  3 cont'd  cont'd.  Operations  Details  n+ pre-dep.  temp.  1050°C  source  P O C l ^ pass o v e r , 15°C  cycle:  5 min N + 3% 0 2  20 min N  2  + 3% 0  15 min N  2  + 3% 0  + Source N  2  2  s t r i p a l l masking  - HF/H 0(1:1)  oxides  - HC1/H" 0 p a r t o f RCA c l e a n  gate o x i d a t i o n  2  2  a  2  temp.  1150°C  cycle  3 min 0  +  p c o n t a c t window etch  2  1+0 min 0  2  + R"  30 min 0  2  + % HCl  10 min N 1+  2  2  y  2  - neg. r e s i s t , masks 2 + 5  (double  exposure) - b u f f e r e d HF - resist  e t c h o f f back s i d e +  n  layer  s t r i p , hot H S0^/ H 0 2  2  - w h i t e e t c h ( f r o n t p r o t e c t e d w i t h wax) - hot t r i c h l o r e t h y l e n e - hot H S 0 / H 0 2  u  2  2  - RCA c l e a n aluminum evap. I  5  - tungsten  f i l a m e n t evap.  s u b s t r a t e temp.  250°C  evap. r a t e  150  2sec ^  - f i l m t h i c k n e s s 1.2 ym aluminum e t c h I  - neg. r e s i s t , mask 3 phosphoric/nitric resist  etch,60 C  strip, Microstrip  2  16 5  cont'd  TABLE 4.4  Step  Operations  anodization  Details  :  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 soak t i m e a t 220V, 5 min 6  via  etch  r e s i s t , mask k  -  neg.  -  CrO /H PO  e t c h , 80°C, 10 min  .  -  0  e t c h , 50 C, 2 min  phosphoric  resist strip, Microstrip + 7  n c o n t a c t window etch  - neg. r e s i s t , masks 2 + 3  (double  exposure) - b u f f e r e d HF - resist  aluminum evap. I I  strip, Microstrip  - tungsten  f i l a m e n t evap.  s u b s t r a t e temp. evap. r a t e  150  250^0  Xsec ^  - f i l m t h i c k n e s s 1 . 0 ym 8  aluminum e t c h I I  - neg. r e s i s t , mask 5 - phosphoric - resist  contact  sinter  temp.  plus  anneal  cycle:  Q u a r t z f u r n a c e t u b e and b o a t p r e - c l e a n e d p r i o r to loading devices.  e t c h , 60°C  strip, Microstrip 1J00°C 60 min H^  w i t h O^/HCl gas f l o w f o r 2 h o u r s ,  166  TABLE 4.5  Data f o r Wafer M66  Bulk resistivity (before processing)  2.1+2 ficm 5-8  x 10  15 cm—3  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  Substrate doping Channel doping  a  (surface concentration)  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 4.2.3  7  Two D i m e n s i o n a l Modeling o f the Completed D e v i c e s U n l i k e t h e s u r f a c e breakdown d e v i c e s i t was not c e r t a i n t h a t t h e b u l k  breakdown d e v i c e s c o u l d be o p e r a t e d i n such a way as t o c o m p l e t e l y e l i m i n a t e premature edge breakdown.  T h i s i s due t o t h e l i m i t e d v o l t a g e range  which t h e t r a n s f e r gate can be o p e r a t e d .  I t must, at a l l t i m e s , be s u f -  f i c i e n t l y n e g a t i v e w i t h respect, t o t h e channel output t o ensure d e p l e t i o n o f the n-layer.  over  The degree o f d e p l e t i o n i n t h e b u l k  complete silicon  under the t r a n s f e r gate i s , t h e r e f o r e , l i m i t e d by t h e breakdown v o l t a g e o f the c h a n n e l output d i o d e . I n o r d e r t o compare t h e e x p e r i m e n t a l l y o b s e r v e d p u l s e r a t e s w i t h those p r e d i c t e d from t h e t h e o r y i t i s n e c e s s a r y t o have some i d e a o f t h e p o t e n t i a l d i s t r i b u t i o n i n t h e b u l k breakdown s t r u c t u r e and t h e u n i f o r m i t y o f the breakdown v o l t a g e .  The approximate  two d i m e n s i o n a l model shown i n F i g .  D l (Appendix D) was used f o r t h i s purpose.  A zero gate s e p a r a t i o n was  and t h e t r a n s f e r gate and n - l a y e r were assumed t o be i n f i n i t e The l a t e r assumption  i s j u s t i f i e d because  i n extent.  v a r i a t i o n s i n the doping  profile  and degree o f d e p l e t i o n , at d i s t a n c e s g r e a t e r t h a n 10 ym ( t h e t r a n s f e r width)  used  gate  from t h e edge o f the breakdown r e g i o n , 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 t h e photogate.  A zero gate s e p a r a t i o n i s  j u s t i f i e d , s i n c e t h e a c t u a l gate s e p a r a t i o n s (0.25 ym) a r e more than an o r d e r o f magnitude l e s s than t h e d e p l e t i o n r e g i o n w i d t h and a r e not exp e c t e d t o s i g n i f i c a n t l y a l t e r t h e p o t e n t i a l d i s t r i b u t i o n o r t h e peak b r e a k down f i e l d s away from t h e S i - S i O ^ i n t e r f a c e .  The use o f zero gate s e p a r a t i o n s  does, however, r e s u l t i n h i g h e r l a t e r a l f i e l d s a t t h e s u r f a c e o f t h e s i l i c o n , i n t h e t r a n s i t i o n r e g i o n from one gate t o t h e o t h e r . b u t i o n under t h e photogate  ( a c r o s s i t s 20 ym width)  The p o t e n t i a l  distri-  and under t h e t r a n s f e r  gate on e i t h e r s i d e was c a l c u l a t e d by t h e method d e s c r i b e d i n Appendix D. The d e p l e t i o n a p p r o x i m a t i o n was used i n o r d e r t o l i n e a r i z e t h e 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 N  A  = 5-8 x 1 0  15  cm  16  N(0) = 2.7 x 10  -3  "3  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 i s close to the maximum allowed with a channel output breakdown voltage of 65 V. The avalanche initiation probabilities ^ ( o )  a n <  i ^ ( ) w  a s  e  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 i n avalanche i n i t i a t i o n 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 i s biased farther above breakdown, this degree of premature edge breakdown is not expected to be important i n a  SiO,  potential minimum at  surface  T  p- silicon OV  ov  Ijjm (vertical scat*)  1 0  10 LATERAL  POSITION  I  L_  X (urn)  FIGURE 4.26 Two-dimensional potential distribution under the photogate for V = 1 0 0 V and V = kO V. The lines along which the avalanche initiation probabilities shown i n Fig.' k.21 T  were calculated, are also shown.  ON  vo  i  0  1—  r—  2 LATERAL  1  4 POSITION  1—  UNDER  1  6 PHOTOGATE  1  1  X  1  8 (|im)  FIGURE 4.27 R e s u l t s o f t h e two-dimensional c a l c u l a t i o n o f t h e v a r i a t i o n o f t h e a v a l a n c h e 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 t h e p h o t o g a t e , T = 80 K. P o i n t s a - g f o r t h e 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 .  r  10  171  PC-CCD.  As r e g a r d s  t h e t e s t d e v i c e s , however, i t means t h a t t h e measured  photon i n d u c e d p u l s e r a t e s can no l o n g e r b e used t o determine excess b i a s d i r e c t l y .  P (w) v e r s u s e  I n i t i a l l y t h e r a p i d i n c r e a s e i n p u l s e r a t e i s due  p r i m a r i l y t o 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  b i a s e s t h e i n c r e a s e i n photon i n d u c e d p u l s e r a t e f o l l o w s P (w) more e closely. As was d i s c u s s e d i n s e n t i o n 4 . 2 . 1 , t h e f i n a l n - l a y e r dopant dose on wafer ¥.66 was l o w e r t h a n d e s i r e d .  As a consequence o f t h i s t h e r e i s a  r e g i o n around t h e edge o f t h e photogate  where t h e p o t e n t i a l minimum i s  l o c a t e d a t 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 t h e p h o t o g a t e i s  b i a s e d f u r t h e r above breakdown t h i s r e g i o n extends i n w a r d s . The c a l c u l a t e d e x t e n t f o r V = 100 V and V = 1+0 V i s i n d i c a t e d i n F i g . 1+.26, however, g T m  i t s w i d t h i s s e n s i t i v e t o t h e n-channel doping, parameters used so t h a t i t i s not c e r t a i n how w i d e t h i s r e g i o n i s i n t h e a c t u a l t e s t d e v i c e s . Although holes generated by i n t e r f a c e s t a t e s are able t o t r i g g e r breakdowns when t h e n - c h a n n e l i s t o o l i g h t l y t h e dark p u l s e r a t e s h o u l d be v e r y s m a l l .  doped, t h e i r c o n t r i b u t i o n t o  T h i s i s because t h e  interface  remains d e p l e t e d o f e l e c t r o n s and h o l e s d u r i n g r e s e t so t h a t t h e s t a t e s remain f i l l e d t o a p p r o x i m a t e l y mid gap.  interface  Since the f i e l d s i n the  s i l i c o n a r e v e r y low a t t h e i n t e r f a c e , t h e s t e a d y s t a t e g e n e r a t i o n r a t e -1 -2 o f h o l e s s h o u l d be w e l l below 500 sec t o an avalanche  cm  (see s e c t i o n 3 . 2 . 3 ) .  Subsequent  d i s c h a r g e t h e i n t e r f a c e s t a t e s above mid gap a r e a l s o  w i t h e l e c t r o n s so t h a t t h e h o l e e m i s s i o n r a t e i s t e m p o r a r i l y r e d u c e d further.  W i t h a c o r r e c t l y doped n-channel t h e r e i s s t i l l  edge o f t h e photogate  filled even  a region at the  where t h e p o t e n t i a l minimum i s a t t h e i n t e r f a c e , how-  e v e r , i t i s v e r y narrow and l i e s w e l l o u t s i d e t h e a r e a where P (o)>0.  172  4.2.4  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 y i e l d o f o p e r a t i o n a l d e v i c e s on w a f e r M66 was  p r i m a r i l y due t o misalignment  v e r y low.  This  between masking l e v e l s , p a r t i c u l a r l y t h e  m e t a l i z a . t i o n masks and t h e v i a mask, and t o p i n h o l e s i n t h e S i O ^ and oxides.  The misalignment  was  the p h o t o r e s i s t operations.  and not due t o a l i g n m e n t  two  Al^O^  a r e s u l t o f t h e r a t h e r l a r g e fcUym) s t e p  r e p e a t e r r o r s on t h e masks themselves  was  and  errors during  Out o f t h e 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 d e f e c t s such as i n t e r l e v e l s h o r t s o r s h o r t s t o t h e substrate.  T h i s reduced t h e number o f good t e s t d i e t o k.  The  first  t e s t e d a t h i g h v o l t a g e s s u f f e r e d a d e s t r u c t i v e breakdown o f t h e  Al^O^  l a y e r , r e s u l t i n g i n a s h o r t between t h e t r a n s f e r gate and t h e f i e l d The  r e m a i n i n g 3 t e s t d i e ( l 8 d e v i c e s ) were f u l l y The  gate.  o p e r a t i o n a l above breakdown.  f o l l o w i n g o p e r a t i n g v o l t a g e s were u s e d f o r t h e above breakdown  device t e s t i n g ( e s e  v  device  ^ =  Fig.  k.2h):  -6ov  sub V , = 0 V (Amu. out V = -75 V sh V = -30 V  virt.  gnd.)  T  V  = -32 t o +58  p  V  The measured f l a t b a n d ' v o l t a g e n-channel.  -2.0 V on b o t h t h e p - s u b s t r a t e and  reset pulse.  I n t e g r a t i o n of t h e c h a n n e l  t h e r e f o r e , s t a r t e d d u r i n g t h e n e g a t i v e - g o i n g ramp, at V  = -20  6  A rasp r a t e of 5 x 10  ob-  —l Vsec  was used on both the p o s i t i v e and  negative-going d r i v e pulse edges. The f i r s t d e t e c t a b l e breakdowns under the photogate occurred at  of  current  V.  F i g u r e 4 . 2 8 i l l u s t r a t e s the t i m i n g used and t h e t y p i c a l output p u l s e s  tained.  the  Charge t r a n s f e r t o t h e c h a n n e l output t a k e s place at the end  t h e n e g a t i v e - g o i n g photogate was,  was  173  active |<  phase t„ (0.5-10 msec) •Vg -60V b  (a)  I  integ. level  .  .  .  I  <  .  t (0.1-20 msec) reset p  transferred charge due to breakdown during previous active phase.  (b)  .A.  — |  -fi~  |V-tn tegrate ( 50-100 jusec) • hold ( 0.05 - 20 msec)  (O  45V  '(d)'  FIGURE 4.28 Test waveforms and timing for the bulk-breakdown, charge-transfer 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 i t s bonding pad also started to break down. Because the shield gate is biased so as to accumulate the p-substrate, the photogate interconnect line f i r s t 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 distribution 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 $ . ( t o t a l variation) except for the odd low pulse that was assumed to be due to a discharge occuring during-the rising or f a l l i n g edge of the drive pulse. The dark pulse rates showed considerable variation over the 1 8 operational devices.  A l l of the devices, however, had dark pulse rates that  were considerably lower than those of the previous surface breakdown devices, in spite of the fact that the measured bulk lifetime (after processing) for wafer M66 was approximately 5 ysec, the surface breakdown devices.  a factor of 10 lower than for  The bulk lifetime was estimated from the  room temperature leakage current of the n-p channel junction ( 6 0 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 creased while holding the reset duration t in Fig. It. 29.  (see Fig. It. 28) was i n -  constant.  This result is shown  r 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. iting dark pulse rate at ( l / t ) = 0 i s approximately  it 2 x 1 0 sec  The lim—2  1  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 i n 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, i s 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. r e s e t s / 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  T  5  = 1.0 msec  1  ^  —  —  = 80 K  \  /  I  .1 I I  P  ,.._{  5  V  t"/ /o o O  ^  - „o —_  _ °  o —  n  p  =43V  .  5  p  5  o J 1  L 2  3 RESET  DURATION  t  p  4 (msec)  FIGURE A.30 Dark p u l s e r a t e as a f u n c t i o n o f t h e 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 = 1.0 msec a  178  1  T DEVICE  t  1  r  o  M66/2-1  = 0.1 msec  r  10.0 msec  140 K O  120 K u  w  c ' 3 O  ^  1  Ul  < cc  100 K  z o o  60 K  o 101  105 PHOTOGATE  _J_  109 BIAS  113 (volts)  117  FIGURE 4.31 (a) Dark p u l s e r a t e as a f u n c t i o n o f t h e photogate b i a s and s u b s t r a t e temperature. The x's mark t h e approximate breakdown v o l t a g e . t  r  = 0 . 1 msec  , t = 1 0 . 0 msec a  179  1—  -T  8  DEVICE t  r  t„  r  M66/2-1  o H  = 1.0 msec = 1.0 msec  140 K O O  0 8  o H  120 K  4  O  o m  0  « •»  c § 8 u  100 K  °  ui  $  4  z  8  0  12  8  60 K  L  4U  0*101  JL  105 PHOTOGATE  109 V BIAS  FIGURE 4.31 (b) t  r  =1.0 msec  , t  a  = 1.0 msec  113 g  (volts)  1.17  180  tion of triggering carriers is occurring through deep traps.  The observed  generation rates are i n general agreement with those extrapolated from Sah's [54]  data, according to equations (3.5T)-(3.62), provided a mid gap trap 12  13  density of 10 -10  -3 cm  i s assumed.  Such a density of mid gap levels is  consistent with the 5 usee bulk lifetimes measured on wafer M 6 6 . Referring back to Fig. h.29 i t can be seen that the increase in pulse rate- with decreasing t i s 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 • i t been possible to envisage a mechanism whereby the occupancy of the traps involved in the tunneling generation changes during reset crease the subsequent generation rate.  so as to i n -  The problem i s 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  f i e l d region remains i n depletion during reset and the peak f i e l d is less than a factor of 1.5 lower than i n 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 intensity. . An absolute calibration of the number of photogenerated electrons per  00  182  second r e a c h i n g t h e edge o f t h e p h o t o g a t e d e p l e t i o n r e g i o n from t h e n e u t r a l b u l k was d e t e r m i n e d from charge i n t e g r a t i o n measurements.  F o r t h e s e measure-  ments t h e d e v i c e s were o p e r a t e d i n t h e charge i n t e g r a t i o n mode w i t h t h e f o l l o w i n g gate V  . = -30 V sub  V out V  sh  V  T  V  potentials:  P  = 0 V (amp. v i r t . gnd. ) = -1+5V = -1+5V = -1+7 t o +20V  By o p e r a t i n g t h e t r a n s f e r gate a t -15V r e l a t i v e t o t h e s u b s t r a t e t h e e f f e c t i v e c o l l e c t i o n a r e a i s r e s t r i c t e d t o t h e a r e a o f n - c h a n n e l under t h e photogate and t r a n s f e r g a t e . i n accumulation  The p - s u b s t r a t e around t h e n-channel i s h e l d  a t t h e s u r f a c e by t h e t r a n s f e r g a t e , t h u s 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 s u r f a c e 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 a r e a , measured under an o p t i c a l  microscope,  was 1+5 urn x 65um.  The measured a r e a o f t h e p h o t o g a t e was 22ym x  !+2um, 31.6%  of the e f f e c t i v e c o l l e c t i n g area.  60  min. i n t e g r a t i o n s 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 f o r the down t e s t s .  above-break-  The measured s i g n a l v o l t a g e s were c o n v e r t e d t o a charge measure-  ment using the c a l c u l a t e d g a i n o f t h e c u r r e n t a m p l i f i e r i n t e g r a t o r combination.  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. F i g u r e s 1+. 33(a) - ( c ) show t y p i c a l examples o f t h e photon  induced  pulse rate 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  a (b)  t  = 10.0 msec, t  a (c)  The  = 0.2 msec . r  t  injection  =' 0.2 msec r  = 1 . 0 msec,  t ^ = 2 0 . 0 msec  l e v e l obtained from charge i n t e g r a t i o n 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  r~ DEVrCE *r  60  T  1 M66/2-1 0.2 msec 1.0 msec 60 K  50 measured  injection  level  -2.—\ZZ-\-2-\-Z-ZZ—ZZ — Z2 ~ 40 u M  light (dark  subtracted)  c  3 O  £ 30 <  I  20  O  meas. inj. level  o  •  10  • 100  „ 104 PHOTOGATE  light (dark  o  subtracted)  dark ° 108  BIAS  V  g  112 (volts)  FIGURE 4.33 (a) Dark and photon i n d u c e d p u l s e r a t e s as a f u n c t i o n o f t h e photogate b i a s f o r d e v i c e 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  a  = 1 . 0 msec  , t  r  = 0 . 2 msec  184 «  4.0  I J light (dark subtracted)  S in  2.0  I  to c o U  Ul  <  i  •z 3 1.0 O O  i  dark  § S  100  FIGURE 4.33 t  a  104 PHOTOGATE (b) >  = 1 0 . 0 msec  , t  ' r  = 0.2 msec  BIAS  V  g  108 (volts)  112  185  70 DEVICE  M66/2-1 20.0 msec 1.0 msec  60 T  s  80 K  50  I measured  injection  level  : 40 u m  i  i  c & 30  light (dark subtracted)  111 0E  § 20 O O  10  L dark o  _L  -a.  100  104 PHOTOGATE  BIAS  FIGURE 4.33 ( c ) = 1 . 0 msec  t a  ,t *  -v.  = 2 0 . 0 msec  V  g  108 (volts)  112  186 level reflects the level of noise in the charge, amplifier only, and not the uncertainty i n the estimated ratio of collecting area to photogate area. I n i t i a l l y 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 i s i n 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 i s 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  i s increased from 0.2 msec to  20.0 msec. This indicates that the detrapping time constant during reset (at 80K) i s 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 i s felt that this i s due to the longer active time t  and a shorter de-  St  trapping time constant due to tunneling under the high f i e l d conditions that exist after the discharge (i.e., at V ). Since the detrapping time constant i s 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  b e f o r e t h e next p u l s e above breakdown.  The counts accumulated w i t h t h e LED  o f f a r e , t h e r e f o r e , due o n l y t o t h e dark counts and t h e counts from t h e de.trapping f o l l o w i n g an avalanche d i s c h a r g e .  resulting  These counts can  t h e n be s u b t r a c t e d from t h o s e o b t a i n e d w i t h t h e LED on t o a r r i v e a t t h e counts due t o p h o t o g e n e r a t e d c a r r i e r s .  I n order t o minimize coincidence  l o s s e s , t h e l i g h t l e v e l was a d j u s t e d so t h a t f e w e r t h a n 3% o f t h e frames contained counts.  The r e s u l t s o f such measurements a r e shown i n F i g . h.3h.  I n o r d e r t o compare t h e s e r e s u l t s w i t h t h o s e p r e d i c t e d from t h e 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 and v a r i a t i o n o f P (w) under t h e photogate i s r e q u i r e d . have not been made.  distribution  Such c a l c u l a t i o n s  I n s t e a d , t h e two d i m e n s i o n a l r e s u l t s were used i n  such a way as t o approximate a t h r e e d i m e n s i o n a l s o l u t i o n .  For these  cal-  c u l a t i o n s a p h o t o g a t e 20ym wide b y Ul+ym l o n g , b u t w i t h h e m i s p h e r i c a l e n d s , was assumed.  T h i s g i v e s t h e same t o t a l a r e a as a 20ym x l+Oym g a t e .  The  v a r i a t i o n o f t h e a v a l a n c h e i n i t i a t i o n p r o b a b i l i t y , a l o n g any l i n e normal t o t h e p e r i m e t e r and e x t e n d i n g i n t o t h e l o n g i t u d i n a l c e n t e r l i n e o f t h e g a t e , was assumed t o be t h e same as t h a t g i v e n by t h e two d i m e n s i o n a l 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 o f the  photon i n d u c e d p u l s e r a t e w i t h g a t e b i 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 t h e double  JJ  integral  PE (w) dx dz  The c a l c u l a t e d v a r i a t i o n o f t h e photon i n d u c e d p u l s e r a t e i s shown by t h e solid line i n Fig.  The c a l c u l a t e d c u r v e 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 t h r o u g h t h e e x p e r i m e n t a l p o i n t a t V  = 110 V,  as no measurement o f t h e a b s o l u t e 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 o f t h e f i r s t two e x p e r i m e n t a l p o i n t s from t h e low volt:-:, t a i l o f t h e c a l c u l a t e d c u r v e i s an expected r e s u l t s i n c e space charge  effec  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 detrapp i n g following an avalanche discharge. The solid line shows the variation o f the photon-induced pulse rate, calculated using the results of the twodimensional modeling. The calculated curve has been shifted by +I.85 V and fitted through the experimental point at V = 110 V.  189  have been n e g l e c t e d .  At s m a l l excess g a t e b i a s e s t h e b u i l d - u p o f space  charge s i g n i f i c a n t l y reduces t h e number o f d i s c h a r g e s t h a t r e s u l t i n p u l s e s l a r g e r t h a n t h e 5 x 10 ments.  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 t h e s e measure-  A l s o , t h e e f f e c t i v e breakdown a r e a i s reduced i n t h e 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 o f the d i s c h a r g e p u l s e s . The e x c e l l e n t agreement between t h e c a l c u l a t e d and o b s e r v e d v a r i a t i o n of  t h e photon i n d u c e d p u l s e r a t e w i t h g a t e b i a s f o r t h e r e m a i n d e r o f t h e  experimental p o i n t s i n d i c a t e s 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 a c c u r a t e l y d e s c r i b e d by t h e t h e o r y due t o Oldham e t . a l . [ 3 1 ] , e q u a t i o n s (3.2) - ( 3 . 5 ) '  The upper e x p e r i m e n t a l p o i n t a t V  = 1 1 2 V c o r r e s p o n d s t o an  a v a l a n c h e 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), t h a t ranges from at t h e c e n t e r o f t h e p h o t o g a t e t o 0..9T  a t t h e edge.  0.9  190  5  SUMMARY AND  CONCLUSIONS  A s o l i d s t a t e photon c o u n t i n g s e n s o r , b a s e d on t h e above-breakdown o p e r a t i n g regime o f MOS  s t r u c t u r e s , has been p r o p o s e d and i n v e s t i g a t e d  b o t h t h e o r e t i c a l l y and e x p e r i m e n t a l l y . s p e c i a l l y designed charge-coupled  I t has  a r r a y s may  a l s o been d e s c r i b e d  how  be o p e r a t e d i n t h i s new  regime,  r e s u l t i n g i n t h e 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 h i g h performance photon c o u n t i n g imager. I n o r d e r t o demonstrate t h e need f o r such an imager and i t s p o t e n t i a l advantages, t h e g e n e r a l p r o p e r t i e s o f s t a t e - o f - t h e - a r t a n a l o g and photon c o u n t i n g imagers a r e r e v i e w e d b r i e f l y i n c h a p t e r two.  I t i s shown t h a t  imagers a r e s u p e r i o r t o o t h e r t y p e s o f a n a l o g d e t e c t o r s f o r u l t r a low  CCD  light  l e v e l i m a g i n g , l a r g e l y as a r e s u l t o f t h e low l e v e l s o f readout n o i s e (a<25 e l e c t r o n s r.m.s.) t h a t are b e i n g a c h i e v e d w i t h c u r r e n t CCD  sensors.  q u a n t i t a t i v e means o f a p p r a i s i n g the performance o f low l i g h t l e v e l ( t h e DQE)  i s i n t r o d u c e d and i t i s shown t h a t a n a l o g CCD  nm,  sensors  s e n s o r s are v e r y  n e a r l y an optimum d e t e c t o r over a wide range o f w a v e l e n g t h s , TOO  A  c e n t e r e d at  p r o v i d e d t h e s t a t i s t i c a l photon n o i s e dominates t h e s i g n a l t o n o i s e  i n the output.  F o r c u r r e n t 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 t o n o i s e g r e a t e r t h a n a p p r o x i m a t e l y TO t o 1. At v e r y low'photon f l u x e s , photon c o u n t i n g i s g e n e r a l l y t h e p r e f e r r e d imaging t e c h n i q u e .  T h i s . n o t o n l y makes p o s s i b l e a DQE  t h a t i s independent  o f t h e t o t a l i n t e g r a t e d s i g n a l but i t a v o i d s some o f t h e l i n e a r i t y , and t h r e s h o l d problems o f t e n encountered  w i t h a n a l o g imagers.  stability,  I t i s shown,  however, t h a t t e m p o r a l s a m p l i n g e f f e c t s i n t r o d u c e n o n - l i n e a r i t i e s and the DQE  lower  i f the photon a r r i v a l r a t e p e r p i x e l i s a l l o w e d t o approach t h e  frame r a t e o f t h e imager.  Many o f the e x i s t i n g photon c o u n t i n g systems  191  r e q u i r e r e a l - t i m e frame p r o c e s s i n g t o d e t e c t t h e photon event  centers,  r e s u l t i n g i n a l i m i t e d frame r a t e ( t y p i c a l l y 1 0 0 s e c "*") and a low dynamic range.  A l l o f t h e 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 semi-  t r a n s p a r e n t o r opaque photoemmisive s u r f a c e as t h e i n i t i a l l i g h t element.  sensitive  I t i s t h e l i m i t e d r e s p o n s i v e quantum e f f i c i e n c y o f t h e commonly  used photocathode m a t e r i a l (RQE<0.2) t h a t u l t i m a t e l y l i m i t s t h e DQE o f photon c o u n t i n g imagers a t v e r y low l i g h t  levels.  The proposed s o l i d s t a t e photon c o u n t i n g sensor and i t s t h e o r y o f operation are discussed i n chapter three.  The above-breakdown o p e r a t i n g  regime i s d i s c u s s e d and i t i s shown how an MOS photosensor i n a photon c o u n t i n g  may be o p e r a t e d  ( o r G i e g e r tube) mode b y p u l s i n g i t i n t o v e r y deep  d e p l e t i o n , beyond t h e p o i n t where avalanche  breakdown n o r m a l l y  occurs.  O p e r a t i o n above t h e breakdown v o l t a g e has been p r e v i o u s l y demonstrated, howe v e r , o n l y p-n photodiodes  have been o p e r a t e d  i n t h i s mode so f a r .  Further-  more, t h e r e has been no attempt t o o p t i m i z e t h e s e d e v i c e s as low l i g h t photon c o u n t i n g s e n s o r s , n o r has a m o n o l i t h i c imaging d e t e c t o r s been c o n s i d e r e d .  a r r a y o f such  The MOS photon c o u n t i n g s e n s o r i s shown t o have  an i n h e r e n t s e l f - q u e n c h i n g p r o p e r t y t h a t g r e a t l y s i m p l i f i e s i n t o such an a r r a y .  level  i t s incorporation  The proposed photon c o u n t i n g CCD (PC-CCD) has t h e  p o t e n t i a l f o r a c h i e v i n g a DQE t h a t i s independent o f t h e t o t a l ' i n t e g r a t e d s i g n a l and which i s n e a r l y e q u a l t o t h e photon-noise a c h i e v e d w i t h a n a l o g CCD imagers. packets  l i m i t e d DQE's b e i n g  A l s o , t h e l a r g e s i z e o f t h e s i g n a l charge  generated b y t h e photon i n d u c e d avalanche  h i g h c l o c k i n g r a t e s t o be used d u r i n g r e a d o u t ,  discharges should  enable  and make p o s s i b l e a h i g h  frame r a t e . The  f o l l o w i n g major problem areas i n t h e development o f a s u c c e s s f u l  PC-CCD imager were i d e n t i f i e d : (1)  m a x i m i z i n g t h e avalanche  initiation  probability  (2)  r e d u c t i o n o f t h e dark p u l s e r a t e t o an a c c e p t a b l e  level  192 (3)  achieving planar micro-plasma-free  (k)  prevention of optical coupling due to light emission during the  avalanche discharges  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 i n 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 required for operation i n the above-breakdown regime. The generation of triggering carriers by band to band tunneling through trap states is also examined.  There i s very l i t t l e existing data upon which  to base estimates for the dark generation due to this mechanism but by extrapolating data obtained with high f i e l d Esaki diodes, order-of-magnitude estimates can be made. Such estimates indicated that tunneling through  193  t r a p s w o u l d l i k e l y be the dominant s t e a d y s t a t e dark g e n e r a t i o n  mechanism  and t h a t , depending on t h e t r a p d e n s i t y , peak f i e l d s l o w e r t h a n 3 x 1 0 ^ may  be r e q u i r e d .  Vcm"  A c h i e v i n g the l o w e s t 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 m i n i m i z i n g t h i s t y p e o f dark  generation.  F o l l o w i n g t h e d e p l e t i n g p u l s e above breakdown, t h e r e i s a t r a n s i e n t s i t u a t i o n d u r i n g w h i c h t h e dark p u l s e r a t e may creased  be e i t h e r i n c r e a s e d or de- :  from i t s s t e a d y s t a t e v a l u e depending on t h e c o n d i t i o n s d u r i n g  and on t h e energy and c a p t u r e  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 .  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 r a p p i n g o r impact i o n i z a t i o n o f the t r a p s d u r i n g the a v a l a n c h e T h e o r e t i c a l expressions  A  t o charge  discharge.  are d e r i v e d t o d e s c r i b e the change i n p u l s e  during these t r a n s i e n t s .  reset  rate  A low d e n s i t y o f t r a p s i s r e q u i r e d t o m i n i m i z e  t h e 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 i n c r e a s e d c a r r i e r emmission f o l l o w i n g an a v a l a n c h e d i s c h a r g e . The  •  c o n t r o l o f f r i n g i n g f i e l d s and t h e p r e v e n t i o n  o f premature edge  breakdown i s d i s c u s s e d b r i e f l y , a l o n g w i t h t h e p r o c e s s i n g t e c h n i q u e s  used  t o p r e v e n t o r e l i m i n a t e l a t t i c e d e f e c t s t h a t might l e a d t o l o c a l i z e d  micro-  plasma breakdown. A r e v i e w o f t h e e x i s t i n g d a t a on l i g h t e m i s s i o n  during avalanche  breakdown i n d i c a t e s t h a t some form o f o p t i c a l b a r r i e r between t h e 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  gree o f 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 a r r a y s a r e The  experimental  i n v e s t i g a t i o n o f MOS  MOS initially.  s t r u c t u r e s t h a t breakdown a t  de-  described.  s t r u c t u r e s operating i n the  above-breakdown regime i s r e p o r t e d i n c h a p t e r d i r e c t e d p r i m a r i l y a t problems ( l ) and  individual  four.  T h i s i n v e s t i g a t i o n was  (2) above. t h e s i l i c o n s u r f a c e were s t u d i e d  An e x t e n s i o n o f t h e g a t e m e t a l o v e r the t h i c k f i e l d o x i d e  used t o p r e v e n t edge breakdown and t h e d e v i c e s s t u d i e d were r e s e t by  was inject-  19b  ing the charge into the substrate. ym was shown to be necessary.  A gate oxide thickness greater than 0.2  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 f i r s t to second level metal vias. In order to obtain appreciable delays to breakdown the surface-breakdown devices had to be pulsed from a reset condition corresponding to i n 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 f i e l d conditions that exist i n deep depletion.  The low interface state density measured on  the test samples indicates that i t w i l l not be possible to reduce this form of dark generation to an acceptable level by further reductions in the interface state density. Inverting the guard ring during reset results i n 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 photogate 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 i n 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 v e 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 t h a n 0.5, were 3 o r d e r s o f magnitude h i g h e r t h a n t h e maximum d e s i r e d dark p u l s e r a t e  of  -1-2 500 sec  cm  .  F o r t h e above reasons MOS s t r u c t u r e s t h a t breakdown at t h e  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 a v o i d e d by g o i n g t o an MOS s t r u c t u r e t h a t b r e a k s down i n t h e b u l k away from t h e S i - S i 0 2 i n t e r f a c e .  It  i s shown t h a t s u c h a s e l f -  q u e n c h i n g , b u l k - b r e a k d o w n MOS g a t e can be made by f o r m i n g a l i g h t l y  doped  n - c h a n n e l at t h e s i l i c o n s u r f a c e , as i n t h e b u r i e d c h a n n e l 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 v e r y low i n t h e b u l k - b r e a k d o w n s t r u c t u r e so t h a t t h e 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 a t t h e low (<100 K) operating temperatures.  F u r t h e r m o r e , w i t h a c o r r e c t l y doped n - c h a n n e l t h e  p o t e n t i a l minimum l i e s i n t h e b u l k o f t h e n - c h a n n e l away from t h e S i - S i O ^ i n t e r f a c e so t h a t t h e c a r r i e r s e m i t t e d b y i n t e r f a c e s t a t e s a r e u n a b l e t o 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 m o d e l i n g o f t h e com-  p l e t e d t e s t d e v i c e s i n d i c a t e d t h a t t h e 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 t h e p o t e n t i a l minimum was l o c a t e d a t t h e S i - S i O ^ i n t e r f a c e t h e d e e p l y d e p l e t e d c o n d i t i o n above breakdown. d i d , however,  in  The r e s u l t s o f t h e m o d e l i n g ,  c o n f i r m t h a t t h e degree o f premature edge-breakdown i n t h e  f a b r i c a t e d d e v i c e s w o u l d not be e x c e s s i v e . I n g e n e r a l , t h e b e h a v i o r o f t h e b u l k - b r e a k d o w n 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 t h e s u r f a c e - b r e a k d o w n 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 p o o r e r 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 , t h e p u l s e h e i g h t d i s t r i b u t i o n was v e r y s h a r p l y peaked. Only a v e r y weak t e m p e r a t u r e dependence o f t h e dark p u l s e r a t e was o b s e r v e d , s u g g e s t i n g 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 r d e r s o f magnitude h i g h e r t h a n t h a t p r e d i c t e d f o r t h e 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 f i e l d Esaki  12 diodes, provided a mid gap trap density of 10  13 -3 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 related to the number of resets, suggesting that the tunneling emission of triggering carriers in the high f i e l d region is increased following a reset. There i s , however, no apparent mechanism to explain the change in trap occupancy 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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Brews, IEEE Trans E l e c t r o n . Devices, ED-20, 380 (1973).  [3C  C.N. Berglund, IEEE Trans. E l e c t r o n . Devices, ED-13, 701 (1966).  [4C  R. Castagne, C.R. Acad. S c i . , B267, 866 (1968).  [5C  M. Kuhn, S o l i d - S t a t e E l e c t r o n . , 13, 873'(1970).  [ID  K.M. De Meyer, and G.J. Declerck, IEEE Trans. Electron.. Devices, ED-28, 313 (1981).  [2D  H. W. Hanneman, and L.J.M. Esser, P h i l i p s Res. Rep., 30, 56 (1975).  1  (l9lb).  2C-1+ APPENDIX A Electron and hole ionization coefficients in silicon For small electric f i e l d strengths the free carriers in a semiconductor  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 f i e l d 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 f i e l d strengths (-lO'V/cm in silicon) the carriers gain energy from the f i e l d faster than they can ld'se i t by emitting phonons. At these and higher fields the carriers are no longer i n equilibrium with the lattice and their energy relative to the band edge increases until they have acquired the threshold energy for impact ionization.  The electron and hole  ionization coefficients are used to describe the average distance a carrier w i l l 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 i s 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 i s independent of energy.  (h)  The mean-free-path for impact ionization is constant for electron energies 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 i n c l u d i n g o p t i c a l phonon absorption thereby enabling the temperature dependence 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 t o be determined.  They suggested that an average energy  l o s s per c o l l i s i o n <E > could be used i n place o f E^ i n B a r a f f ' s Theory, r  and give the f o l l o w i n g expression f o r the temperature dependence o f X and E r  ' r E  <E > jjp = r  tanh  X X  r_ 2kT  (Al)  where X i s the low temperature l i m i t t o the mean-free-path f o r o p t i c a l q  phonon generation.  They also give the f o l l o w i n g approximation  to Baraff's  numerical s o l u t i o n f o r the i o n i z a t i o n c o e f f i c i e n t s a ( c o r r e c t t o w i t h i n ±2% f o r 0 . 0 1 < r < 0 . 0 6 and 5 < x < l 6 ) ,  aX  =  exp  (il.5r  - 1.17r + 3.9x 10 * ) x + (l*6r - 11.9r + 1.75 x 1 0 ) 2  -1  2  +(-757r  where  r =  <E > — and x Ej r  2  - 2  2  E = —FT qcX  + 7 5 . 5 r - 1.92)  (A2)  , '  There i s considerable u n c e r t a i n t y as t o the exact magnitude and f i e l d v a r i a t i o n o f the e l e c t r o n 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  i o n i z a t i o n r a t e s 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 r a t e s , and the only ones that can be f i t t o B a r a f f ' s theory w i t h a reasonable value f o r the parameter X, the accepted value o f E =3/2 E , and the measured o p t i c a l phonon energy o f E = 0 . 0 6 3 eV. The i o n i z a t i o n rates were transformed t o the appror  p r i a t e temperature using Crowell's and Sze's m o d i f i c a t i o n t o B a r a f f ' 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 , 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  discriminator.  RAMP RATE CONT.  J_ ~  X ~  o driver output  AO  o  B  oC  INTEGRATOR CONT. PULS GEN..  209  O A  surface devices  co-£x>-4>o  o comp.  bulk devices  pulse counter 2  TIMING  surface dev. *1 R 2  *3 c C  2  3  10 100 10 .47 1 .47  bulk 100 10 10 1 .1 .1  210 68 n  r-WW  D o-  1—  2.7  2.7  pulse counter 1  PMI 1 CMP01  220P  com p.oDESCRIMIN ATOR  * low noise input o -O  E  -O  D  •*15 10 preset ointeg. o-  8 12 5 0053 9 4 10 3 7  •15 -15 o o 0  11  '3 I!  4.7; preset level 10  MC1741  CURRENT AMP. AND INTEGRATOR  211 APPENDIX C Methods used t o determine t h e d o p i n g p r o f i l e and i n t e r f a c e  state  density  (l)  Doping P r o f i l e  The d o p i n g p r o f i l e s were o b t a i n e d b y t h e w e l l known dC/dV - method based on t h e f o l l o w i n g f o r m u l a e ( l C )  v  =  € /C S  (C2)  S C  where N = d o p i n g d e n s i t y w = d e p l e t i o n l a y e r w i d t h ( i . e . , d i s t a n c e from t h e s e m i c o n d u c t o r s u r f a c e a t which t h e doping d e n s i t y i s determined) C . = space charge c a p a c i t a n c e p e r u n i t a r e a <J> = s e m i c o n d u c t o r s u r f a c e p o t e n t i a l The n e g a t i v e s i g n a p p l i e s f o r n-type s u b s t r a t e s and t h e p o s i t i v e s i g n f o r ptype.  E q u a t i o n s ( C l ) and (C2) a r e based on t h e d e p l e t i o n a p p r o x i m a t i o n ,  w h i c h becomes i n v a l i d f o r s m a l l v a l u e s o f w where t h e 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 l o n g e r be n e g l e c t e d i n comparison t o t h e d o p i n g d e n s i t y . T h i s l i m i t s t h e d e t e r m i n a t i o n o f t h e doping d e n s i t y t o v a l u e s o f w g r e a t e r . than 2  where  D  i s t h e e x t r i n s i c Debye l e n g t h [ 2 C ] .  1 qN  I n d e p l e t i o n t h e space charge c a p a c i t a n c e i s r e l a t e d t o t h e measured h i g h f r e q u e n c y MOS c a p a c i t a n c C„„ a c c o r d i n g t o  HF  212 p r o v i d e d t h e measuring frequency  i s h i g h enough t h a t t h e 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 t h e o v e r a l l c a p a c i t a n c e .  C  i s the oxide  capacitance  w h i c h , i n t h e case o f 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 t h e measured c a p a c i t a n c e i n s t r o n g a c c u m u l a t i o n .  I n o r d e r t o use Eq.  (Cl)  i t i s f u r t h e r n e c e s s a r y t o o b t a i n a r e l a t i o n s h i p between the s u r f a c e t i a l <f> and the a p p l i e d v o l t a g e V .  Berglund  £  f a c e p o t e n t i a l may  be determined  by  poten-  (3C)-has shown t h a t the s u r -  t o w i t h i n an a d d i t i v e c o n s t a n t by  inte-  g r a t i n g the measured C(V) curve from a p o i n t c o r r e s p o n d i n g t o s t r o n g accumulation, V  , toward d e p l e t i o n , 3,C C •  r  * y (  =  s  The a d d i t v e c o n s t a n t  j  v  ,  g  (v  c  I 1  v  +  o  K  I  (  C  4  )  x  acc  drops out when p e r f o r m i n g the d e r i v a t i v e i n ( C l ) .  I t i s customary t o use p u l s e d C-V  measurements i n o r d e r t o  prevent  t h e f o r m a t i o n o f an i n v e r s i o n l a y e r and enable t h e doping p r o f i l e t o be t a i n e d t o g r e a t e r depths. a d i f f e r e n t method was  ob-  Because o f the l a c k o f such measuring equipment,  used here.  Samples w i t h s e v e r a l 1 m m d i a MOS  capacitors  were mounted i n l 6 p i n DIP packages and c o o l e d t o 80K i n the c o l d chamber used f o r t h e d e v i c e t e s t i n g .  Under t o t a l darkness  charge c o l l e c t s so s l o w l y t h a t i t was by. p o i n t w i t h a c a p a c i t a n c e b r i d g e .  500  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 The m e a s u r i n g f r e q u e n c y used  was  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 measurements w i t h h i g h f r e q u e n c y C-V [40]. C  the i n v e r s i o n l a y e r  o b t a i n e d by combining q u a s i - s t a t i c  measurements, as d i s c u s s e d by Castagne  The d i f f e r e n c e between t h e q u a s i - s t a t i c (low f r e q u e n c y )  and t h e h i g h frequency  C-V  c a p a c i t a n c e C„„  capacitance  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  /. \  ss  (<p  s  )  u  where N  ss  C C . LF ox  C  ox  ox  LF  C HF ox HF  i s the interface state density per unit area per eV and C  ss  i s the  capacitance due to interface states. The interface state densities obtained from Eq. (C5) are only valid when the MOS sample is in depletion.  In i n -  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 no longer be determined.  ij) (V ), was obtained by plotting- l/C S  can  ss The constant in Eq. (Ch), needed to determine  §  versus (<j> - K ), which results in a SC  S  X  straight line in depletion (with uniformly doped samples).  l/C • goes to 0 sc  as <J> goes to 0 , therefore, the intercept gives K^. g  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 _2 current in response to a linear voltage ramp ( 1 0 Kuhn [5C].  displacement  V/sec), as described by  The displacement current was measured on a Keithley model 6 0 2  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 f i e l d distributions in the bulk breakdown devices The structure for which the solutions w i l l be derived i s shown in Fig. Dl  X  +L/2  -L/2  V„  ox  0-  -5*-  x  n-type  p-type  ~L y  FIGURE Dl  Device structure used for the two-dimensional model.  The method i s analogous to that described by Meyer and Declerck . [ID] for obtaining potential distributions i n BCCD structures, and uses the superposition 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 i n 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 distribution in the substrate cannot be accurately determined, particularly i f  215 the s u b s t r a t e d o p i n g d e n s i t y i s comparable t o t h a t o f t h e n - l a y e r as i t i s v i t h t h e b u l k breakdown d e v i c e s . I n t h e method d i s c u s s e d b e l o w , t h e s u p e r p o s i t i o n p r i n c i p l e i s u s e d throughout.  T h i s i n f a c t r e s u l t s i n a s i m p l e r s o l u t i o n as i t e l i m i n a t e s  t h e c o m p l i c a t e d m a t c h i n g c o n d i t i o n between t h e n - l a y e r and t h e  substrate  solutions. A z e r o g a t e s e p a r a t i o n i s assumed as shown i n F i g . D l . the d e p l e t i o n approximation  By making  and u s i n g , t h e 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 t o o b t a i n t h e s o l u t i o n f o r t h e e l e c t r o s t a t i c p o t e n t i a l as t h e  sum  o f two p a r t s ,  <i> , ( x , y )  '=  • (x,y) + <f>f. (x,y)  (Dl)  <t» (x,y)  =  <f> ( x , y ) + +Q (x,y)  (D2)  ox  X  where <|> (x,y) i s t h e s o l u t i o n t o the homogeneous "problem o b t a i n e d by h  t h e charge d e n s i t i e s e q u a l t o z e r o , i . e • 2 h V <f> (x,y)  =  0 , -d  5  setting  t o the problem,  < y  (D3)  w i t h boundary c o n d i t i o n , (D4) and <j>' one  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 =  dimensional  0, i . e . , t o t h e  problem,  , -d  -Biz) s  ox  <y < 0  0 < y  (D5)  (D6)  216 with boundary conditions d) (-d ) = ox ox  0  (D7)  4(o)  (D8)  P  T  *P (0)  -  x  a<lOX > (o) e .—r  H'SI .(o) = e —  p  i  v  By  s  fT  9y  . .  (D9) n  The additional boundary conditions needed to obtain d> and d> . are ox si r  <J> (x,w)  =0  (D10)  Si  . (x,w) — l y — =  (DH)  0  34 .(x,w) =  By  0  (D12)  The particular problem posed by Equations (D5)-(D9) is straight-forward. By using partial integration and the three boundary conditions, d> (x,y) and ox P  <i>.(x,y) can be expressed as si * P  C ' (x  ^(x.y)  = Jj 3  r  y)  =  C  l  (  y  +  1 f  7  p(y)dy - -  d  ox '• }  " ox d  < y K  y  yp(y) dy + -C  0  °  re.  ( D 1 3 )  1  y + d l  ox I  ,0<y  (D14)  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 i n Fig. Dl, however, there i s an easier solution based on conformal mapping techniques.  By using the trans-  formations, x'  =  x , y' ' J  z"  = In  =  y + d ox  { ] I Ify , Z z  z'  = x» + iy'  (D15)  217  the e l e c t r o s t a t i c s problem i s transformed t o that shown i n F i g . D 2 , f o r which the f o l l o w i n g s o l u t i o n can be obtained by i n s p e c t i o n ,  4> (x",y") h  =• V  (V - V ) y"  +  T  6  (D16)  T  i r  ^\\\X\\\\\\\\\\\\\\\X\\\ ^  L  + 00  —  V  CO  +00  TT  .  FIGURE D2  \  g  f  Device s t r u c t u r e a f t e r conformal transformation.  A f t e r applying the inverse transformation the s o l u t i o n becomes (V - V J  ry + d >  <f> (x y) h  ox  ;an  s  The constant C  [ x - L/2J  ry + d  - tan  Ix  1  ox  (D17)  + L/2j  can now be obtained from B.C. ( D l l ) , w s j l I  1  "  / \ j  -I7(e J s  3J (x,w) \ + "V" J  (D18)  x  and w i s determined by an i t e r a t i v e procedure from B.C. (DIO), which becomes w <j> (x,w) - -  yp(y) dy - — d e. ox 1  —s 6  p(y) dy  - {w + L  0  „ 13<j> (x,w) h  d  }  ox  J  3y =  where the d e r i v a t i v e of (D17), w i t h respect t o y, i s  0  (D19)  218 3<  T(x,y)  =  y  L/2) +  (x -  )S-1  (y + d  (x + L/2) + (y + d ) ^ - l  ox  Boundary c o n d i t i o n  (D20)  (x + L/2)  (x - L/2)  (D12) f o l l o w s  automatically  from B.C.  (DIO).  I n o r d e r t o s o l v e f o r P (w) and P, (0) e q u a t i o n s (3.2) - (3.5) were e h i n t e g r a t e d a l o n g a l i n e s t a r t i n g from a p o i n t  a t t h e p o t e n t i a l minimum  ( i n t h e b u l k o r a t t h e i n t e r f a c e ) and f o l l o w i n g t h e d i r e c t i o n o f t h e e l e c t r i c f i e l d vector electric  (see F i g u r e s  k.26  i n text).  The x and y components o f t h e  f i e l d were o b t a i n e d from t h e x and y d e r i v a t i v e s o f <|> . ( x , y ) , as  follows,  •  .  .  SX  •  3<f> (x,y) si  Mx,y)  dx  H  (x,y) 9x  +  —  e  y + d  ox  s  !2i  (D21)  ax  9* (x,y) s i  £ (x,y) y  3y  .  ^ >  +  dC^/dx can be o b t a i n e d from B.C. e.  _ i e  3x  w  + d  s  i j  o  (  y  i  y  t  ! i  0  (D22)  i  (D12) as f o l l o w s , 1-1 »,h,  v  (D23)  ( x ? v )  ox  '  9x  where t h e d e r i v a t i v e o f (D17) w i t h r e s p e c t 84> (x,y) 3x  )  to x i s  n  =  f  i ^ ^ ! (y + d  o x  - 1  )  +  (y  +  d  )  [(y d +  Q  x  )  ox'J  (D24)  

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