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A study of space-charge and avalanche multiplication processes in germanium Barker, Alfred Stanley, Jr. 1957

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A STUDY OF SPACE-CHARGE AND AVALANCHE MULTIPLICATION PROCESSES IN GERMANIUM  by ALFRED STANLEY BARKER JR. B.  A., U n i v e r s i t y o f B r i t i s h Columbia,  1955  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  i n the Department of Physics  We accept t h i s t h e s i s as conforming t o t h e required  THE  standard  UNIVERSITY OF BRITISH COLUMBIA September,  1957  (ii) ABSTRACT  PNP  s t r u c t u r e s have been i n v e s t i g a t e d and  v a r i o u s e f f e c t s encountered  the  d e s c r i b e d i n terms o f  fundamental aspects of c a r r i e r f l o w .  The c a p a c i t a n c e o f  a r e v e r s e b i a s e d j u n c t i o n i n a pnp s t r u c t u r e i s found  to  r i s e a b r u p t l y w i t h i n c r e a s e o f i t s r e v e r s e b i a s past the punch-through v o l t a g e .  T h i s e f f e c t a r i s e s from the  a d d i t i o n o f the c a p a c i t a n c e o f the second j u n c t i o n by  the  low r e s i s t a n c e c o n n e c t i o n o f the space charge column across the n r e g i o n .  An u n u s u a l phenomenon c a l l e d  "induced breakdown" i s found junction transistors.  t o occur i n c e r t a i n grown  Here the punch-through e f f e c t  the space-charge spreading from one  j u n c t i o n causes the  other j u n c t i o n t o s u f f e r avalanche  breakdown.  r e s i s t a n c e i s observed  diodes.  to  i n some pnp  of  Negative  T h i s i s shown  be a r e s u l t o f the c u r r e n t dependence of the hole  t r a n s m i s s i o n process o c c u r i n g i n the n-type t r a n s m i s s i o n r e g i o n combined w i t h the m u l t i p l i c a t i o n e f f e c t i n the h i g h f i e l d r e g i o n at the c o l l e c t o r j u n c t i o n . Current flow i n the t h i n base diode i s o f a space-charge l i m i t e d nature i n the n r e g i o n . t h a t the f i e l d to  I t i s shown  over most o f t h e n r e g i o n i s l a r g e enough  cause the hole m o b i l i t y to decrease  low f i e l d v a l u e .  The  many f o l d from i t s  s l o p e r e s i s t a n c e of a t y p i c a l  tends a s y m p t o t i c a l l y t o a constant value which i s approximately  c o n s i s t e n t w i t h the model based on a  diode  (iii) s a t u r a t e d d r i f t v e l o c i t y f o r holes i n the n r e g i o n .  In presenting the  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  r e q u i r e m e n t s f o r an advanced degree at the  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t freely  a v a i l a b l e f o r r e f e r e n c e and  agree t h a t p e r m i s s i o n f o r e x t e n s i v e for  s c h o l a r l y purposes may  study.  I further  copying of t h i s  be g r a n t e d by the Head o f  Department o r by h i s r e p r e s e n t a t i v e .  be a l l o w e d w i t h o u t my w r i t t e n  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada.  my  I t i s understood  t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r g a i n s h a l l not  thesis  financial  permission.  (iv) TABLE OF CONTENTS  Chapter I  Page 1  INTRODUCTION 1.1  P h y s i c a l Processes i n  Junction 1  Structures 1.2  Theory o f the I d e a l One-Dimensional PNP  II  3  Transistor  1.3  D e p l e t i o n Layer E f f e c t s  5  1. h  Space-Charge L i m i t e d  7  1.5  Avalanche M u l t i p l i c a t i o n  1.6  Variation of Transistor  Currents  8  Current G a i n  w i t h E m i t t e r Current DEPLETION LAYER PHENOMENA IN THIN BASE STRUCTURES 2.1  Measurements o f F l o a t i n g  12  Junction  Potential 2.2  Capacitance C h a r a c t e r i s t i c s  2.3  Current-Voltage C h a r a c t e r i s t i c s o f  2. h  PNP Diodes I n f l u e n c e o f Non-Ideal Geometry and Non-Uniform Base R e s i s t i v i t y  III  10  12 18  20 23  AVALANCHE PHENOMENA IN THICK BASE . . 3.1  STRUCTURES I n f l u e n c e o f M u l t i p l i c a t i o n on PNP  3.2  27  Diode P r o p e r t i e s  27  Induced Breakdown i n F l o a t i n g Junctions  31  (v)  Chapter IV  Page COMBINED ALPHA VARIATION AND AVALANCHE PHENOMENA.  .  h.l  Negative R e s i s t a n c e  h.2  E f f e c t o f J u n c t i o n Area on t h e Turnover C o n d i t i o n  V  SUMMARY AND OUTSTANDING PROBLEMS BIBLIOGRAPHY  33 33  35 8 13+ 2  ^3  (vi) LIST OF FIGURES Figure 1 2  F a c i n g Page Current and v o l t a g e conventions f o r a t h e o r e t i c a l pnp t r a n s i s t o r  3  Schematic diagram o f hole and e l e c t r o n flow  10  Dependence o f punch-through v o l t a g e on frequency o f alpha c u t o f f  12  h  C i r c u i t f o r punch-through measurements  13  5  Direct current c o l l e c t o r - e m i t t e r voltage  3  c h a r a c t e r i s t i c s f o r a pnp t r a n s i s t o r 6  Punch-through models  7  Schematic diagram o f a d e p l e t e d base  ih  15  pnp t r a n s i s t o r 8  D i s p l a y c i r c u i t t o demonstrate  13  limiting  potential distributions  16  9  Dynamic d i s p l a y of punch-through  17  10  C i r c u i t f o r j u n c t i o n capacitance measurement  18  11  Capacitance  vs. reverse bias f o r  c o l l e c t o r and e m i t t e r j u n c t i o n s Capacitance v s . r e v e r s e b i a s f o r c o l l e c t o r and e m i t t e r j u n c t i o n s o f a punch-through t r a n s i s t o r  18  13  T r a n s i s t o r data  22  1*+  Current-voltage c h a r a c t e r i s t i c f o r a pnp diode  22  12  15  Capacitance  vs. reverse bias f o r a  grown t r a n s i s t o r 16  25  Current through a pnp diode as a f u n c t i o n of the b i a s  17  19  28  C u r r e n t - v o l t a g e c h a r a c t e r i s t i c o f pnp diode 2N277  29  (vii) Figure  F a c i n g Page  18  Alpha as a j u n c t i o n of e m i t t e r c u r r e n t  30  19  Single junction current voltage c h a r a c t e r i s t i c and f l o a t i n g e m i t t e r potential  32  Current-voltage c h a r a c t e r i s t i c pnp diode 2N112  33  20 21  of  C i r c u i t r e p r e s e n t a t i o n o f an avalanche transistor  39  (viii) ACKNOWLEDGMENTS  I am Indebted t o P r o f e s s o r R. E . Burgess f o r h i s guidance o f t h i s i n v e s t i g a t i o n  and h i s many h e l p f u l  suggestions d u r i n g the p r e p a r a t i o n o f t h i s  thesis.  Support i n t h e form o f a B r i t i s h Columbia Telephone Company s c h o l a r s h i p and a Defence Research Board grant  i s gratefully  acknowledged.  1  CHAPTER I INTRODUCTION  S e c t i o n 1.1  P h y s i c a l Processes I n J u n c t i o n  Structures  At a pn J u n c t i o n i n t h e r m a l e q u i l i b r i u m t h e r e i s a space-charge double l a y e r s u b s t a n t i a l l y d e p l e t e d o f carriers.  The f i e l d  produced by t h i s double l a y e r has Just  the magnitude and d i r e c t i o n t o counteract tendencies  the d i f f u s i o n a l  o f the c a r r i e r s t o c r o s s the J u n c t i o n , so t h a t  the hole and e l e c t r o n c u r r e n t s v a n i s h .  When an e x t e r n a l  r e v e r s e b i a s i s a p p l i e d t o a pn J u n c t i o n , t h e parts o f the c r y s t a l away from the J u n c t i o n remain s u b s t a n t i a l l y n e u t r a l w h i l e the space-charge double l a y e r widens, i n c l u d i n g more i o n i c charge and thereby i n c r e a s i n g the p o t e n t i a l drop i n the c r y s t a l t o balance t h e e x t e r n a l l y a p p l i e d v o l t a g e .  As  charge must be d i s p l a c e d t o widen the space-charge r e g i o n , a Junction exhibits The  capacitance.  widening o f the space-charge l a y e r w i t h  reverse  b i a s causes the e l e c t r i c f i e l d a t the j u n c t i o n t o i n c r e a s e also with bias.  As a r e s u l t , a t some b i a s v o l t a g e , one o r  b o t h o f two phenomena may o c c u r .  The space-charge may extend  r i g h t across t h e c r y s t a l and t o u c h t h e c o n t a c t t o t h a t  region.  T h i s phenomenon i s known as punch-through, and t h e M a s necessary t o extend t h e space-charge across i s c a l l e d the punch-through v o l t a g e .  a given region  Any f u r t h e r i n c r e a s e s  2 i n b i a s produce a s t r o n g tendency f o r the p o t e n t i a l d i f f e r e n c e between the c o l l e c t o r and e m i t t e r to maintain a v a l u e n e a r l y e q u a l to the punch-through v o l t a g e and can cause a p p r e c i a b l e currents to flow.  The second p o s s i b i l i t y i s t h a t the  f i e l d at the j u n c t i o n may punch-through occurs) carriers i s possible.  i n c r e a s e t o such a v a l u e  t h a t impact i o n i z a t i o n by  electric  (before  energetic  Here an e l e c t r o n or hole a c c e l e r a t e d  by the f i e l d can achieve enough energy t o c r e a t e a secondary e l e c t r o n hole p a i r by d i r e c t c o l l i s i o n w i t h a v a l e n c e e l e c t r o n . These secondaries  may  i n t u r n g a i n enough energy  before  l e a v i n g the h i g h f i e l d r e g i o n t o e x c i t e f u r t h e r e l e c t r o n hole pairs. high  Thus a s m a l l primary c u r r e n t on passing through the f i e l d r e g i o n of a pn j u n c t i o n may  number of secondaries The  c r e a t e a tremendous  and be r e s p o n s i b l e f o r a l a r g e c u r r e n t .  c u r r e n t v o l t a g e c h a r a c t e r i s t i c s of germanium pn j u n c t i o n s  o p e r a t i n g under such avalanche m u l t i p l i c a t i o n c o n d i t i o n s show as much as a hundred f o l d i n c r e a s e i n c u r r e n t f o r a d o u b l i n g o f the r e v e r s e b i a s v o l t a g e . T h i s paper deals mainly w i t h e f f e c t s r e l a t e d t o the space charge r e g i o n s i n r e v e r s e b i a s e d pnp transistors.  The  junction  emphasis i s placed on i n t e r p r e t i n g the  v a r i o u s r e s u l t s i n terms of a simple  model.  The  remainder  o f Chapter I presents the u s u a l pn j u n c t i o n and  transistor  theories.  sets of  I n Chapters I I and I I I , two  phenomena are i n v e s t i g a t e d .  The  separate  d i v i s i o n of the phenomena  i n t o these s e t s i s q u i t e n a t u r a l .  The  e f f e c t s i n Chapter I I  a r e r e l a t e d t o d e p l e t i o n l a y e r widening, w h i l e those i n  CURRENT VOLTAGE CONVENTIONS FOR THEORETICAL PNP TRANSISTOR  N THEORETICAL DEVICE  L  EMITTER REGION'  BASE REGION  lib  Fiai  COLLECTOR REGION  3 Chapter III are related to avalanche multiplication.  In  Chapter IV negative resistance is discussed as a hybrid effect, depending on a combination of properties already Chapter V gives a summary and l i s t s outstanding  presented. problems. Section 1.2  Theory of the Ideal One-Dimensional PNP Transistor  Shockley (19^9) has developed the theory of current flow and potential distribution i n pn junction transistors.  The assumptions he makes are the following:  1)  non degenerate distributions for the electrons and holes  2)  predominance of diffusion currents as compared with drift currents  3)  low level injection  h)  one-dimensional geometry  5) long bounding p regions for a pnp transistor The theory has been amply borne out i n experiments with junction transistors. Using the current and voltage conventions shown i n figure 1, Shockley^ result for a pnp transistor with heavily doped p regions is  T =.-^QD ?b{cothw ( e ^ - i ) -Csckw (e^-T,)} ,n U U where /)= cross sectional area of the theoretical planar r  P  3  ( 1  2 )  t r a n s i s t o r , q = e l e c t r o n i c charge,W = hase w i d t h , Dp = hole diffusion constant,U  = d i f f u s i o n l e n g t h o f holes i n the base  ?b a t h e r m a l e q u i l i b r i u m c o n c e n t r a t i o n o f h o l e s i n the  base.  A l p h a , the e m i t t e r c o l l e c t o r c u r r e n t g a i n , i s an important performance index o f a t r a n s i s t o r .  I t i s d e f i n e d as c<=J ~^ c  s  le where Is  is  the c o l l e c t o r c u r r e n t t h a t flows when  If - V c » h l  , t h e n from equations  le- = 0  .  (1.1) arid ( 1 . 2 )  oC = SeckW.  (1.3)  Lb  I n any a c t u a l c i r c u i t \fe inaccessible  and Vc  may be  t o d i r e c t measurement because o f the base  resistance  rt  . n, a r i s e s  from the b u l k of r e l a t i v e l y h i g h  r e s i s t i v i t y m a t e r i a l t h a t base c u r r e n t s must flow through to r e a c h the base c o n n e c t i o n o f the t r a n s i s t o r .  I f the c i r c u i t  can be arranged so t h a t no base c u r r e n t i s drawn Vg may be measured d i r e c t l y (See f i g u r e 1 ) . open c i r c u i t e d base t r a n s i s t o r i s work w i t h from t h i s condition, I  c  =^e =1  point o f view.  Prom equations is  to f l o w ,  (l.^)  The pnp diode or  particularly attractive  to  I n the f l o a t i n g base  , so from equations  I = flqDpPbfCotkw + Cschv*/ \[£  and Vc,  h T  -l]  (1.1) and ( 1 . 2 ) '  (l.*0  a n d ( 1 . 5 ) , we note t h a t i f any c u r r e n t  the base must take up such a p o t e n t i a l t h a t  one  J u n c t i o n i s forward b i a s e d and the other i s r e v e r s e b i a s e d .  5 Section 1.3 Depletion Layer Effects Shockley (19^9) has shown that In an impurity semiconductor, regions of large gradient i n the fixed ionic charge do not' have a compensating accompaniment of carriers to produce neutrality.  At an abrupt pn Junction there is  such a large gradient.  The carriers are almost entirely  absent from a region about the junction leaving the fixed ionic charge which forms a double layer.  As the equations  which describe the situation are nonlinear, Shockley makes the assumption that depletion of carriers about the junction is complete to some depth on either side, where there is an abrupt change to neutrality.  When reverse bias is applied,  the p and n regions far from the junction remain neutral. Carriers are drawn away from the junction, so the carrier depletion region of ionic space charge widens to give an increased voltage drop i n the crystal.  Since the complete  depletion layer must contain zero net ionic charge, the ratio of the layer widths is the reciprocal of the impurity densities in the two regions.  For a step junction with the  p region much more heavily doped than the n region, the depletion layer spreads almost entirely into the n region with increase of reverse bias.  Assuming one dimensional  geometry, a simple double integration of Poisson's equation gives for the width of the depletion layer  (1.6)  where  = width of the d e p l e t i o n l a y e r , which i s mostly i n  the n r e g i o n , (^n  = net p o s i t i v e i o n d e n s i t y i n the n r e g i o n ,  Np = net negative i o n d e n s i t y i n the p r e g i o n , V reverse b i a s , (typically  = applied  = " b u i l t i n " p o t e n t i a l of the j u n c t i o n = .3 v o l t s f o r Np/Nn = 10* ) <j = e l e c t r o n i c 9  charge, 6 = p e r m i t t i v i t y of the semiconducting m a t e r i a l . The t o t a l p o s i t i v e charge s t o r e d i n the d e p l e t i o n l a y e r i s Q =«|Nvidinfl  .  Because there must be a displacement  of charge f o r a changedV  i n reverse b i a s , we may  evaluate  the dynamic capacitance of the d e p l e t i o n l a y e r .  C - i i = A|M"  e  ' = i l  (17)  which i s e x a c t l y equal t o the geometrical capacitance of the n r e g i o n d e p l e t i o n l a y e r . to N  ?  (We now neglect  as compared  ) I n a pnp t r a n s i s t o r w i t h h e a v i l y doped p r e g i o n s ,  a reverse bias on e i t h e r j u n c t i o n w i l l cause a d e p l e t i o n layer t o spread out from that j u n c t i o n i n t o the base according t o equation (1.6).  I f V i s increased s u f f i c i e n t l y ,  the d e p l e t i o n layer may extend r i g h t across the base and touch the f a r j u n c t i o n . •punch-through  1  The reverse voltage at which t h i s  occurs i s obtained simply from equation  Vot = «)N»W?  where Vpt  = the reverse v o l t a g e necessary t o spread the  (1.6)  ( 1 # 8 )  7 d e p l e t i o n l a y e r r i g h t across the base, Wo o f the t r a n s i s t o r .  i s n e g l e c t e d now  E a r l y (1952) has equations  the base w i d t h  s  as compared w i t h V^t  .  pointed out t h a t s i n c e Shockley's  d e s c r i b i n g t r a n s i s t o r a c t i o n depend onW  , the  l e n g t h of n e u t r a l base m a t e r i a l t h a t m i n o r i t y c a r r i e r s must d i f f u s e across t o r e a c h the c o l l e c t o r , d e p l e t i o n l a y e r widening w i t h consequent r e d u c t i o n of W (1.1)  account i n a p p l y i n g equations notes that the i n t r i n s i c  and  must be taken i n t o (1.2).  base r e s i s t a n c e  depends on W  He d e r i v e s a s m a l l - s i g n a l e q u i v a l e n t c i r c u i t elements which depend onW We  .  i n c l u d i n g two  hence on c o l l e c t o r  note a g a i n t h a t open c i r c u i t  leave us. f r e e o f and  and  Early also  voltage.  base measurements  and i t s p o s s i b l e v a r i a t i o n s w i t h c u r r e n t  voltage.  S e c t i o n l.k  Space Charge L i m i t e d  Currents  When v o l t a g e i s a p p l i e d between a m i t t e r c o l l e c t o r o f a f l o a t i n g base pnp forward  Junction i s  b i a s e d and the other r e v e r s e b i a s e d , and c u r r e n t  obeying equations diode  t r a n s i s t o r , one  and  (l.h)  and  (1.5).  I f the v o l t a g e across  i s i n c r e a s e d t o a value e q u a l t o the  v o l t a g e o f the r e v e r s e b i a s e d  flows the  punch-through  J u n c t i o n , the d e p l e t i o n l a y e r  of t h i s J u n c t i o n w i l l engulf the e n t i r e base up t o the forward  b i a s e d J u n c t i o n so t h a t a l l m a j o r i t y c a r r i e r s have  been removed from the base.  Greater a p p l i e d v o l t a g e can  only  be t a k e n up by an i n c r e a s e of p o s i t i v e charge d e n s i t y i n the base r e g i o n due  t o holes i n j e c t e d from the e m i t t e r .  Such  8  i n j e c t e d m i n o r i t y c a r r i e r c u r r e n t s must flow through t h e r e g i o n of space charge i n the base. o b t a i n i n g equations S h o c k l e y and  (1.1)  and  (1.2)  ions N  assumption used i n  are not  longer a p p l i c a b l e .  Prim (1953) have d e r i v e d a c u r r e n t  r e l a t i o n f o r such a case i n the Poisson's  The  pnp  diode.  voltage  They combine  e q u a t i o n w i t h p o s i t i v e space charge due  and i n j e c t e d holes  p , and  the c u r r e n t  e q u a t i o n which n e g l e c t s e l e c t r o n s and o f c u r r e n t i n the base. the h o l e s .  t o donor  density  d i f f u s i o n components  Constant m o b i l i t y i s assumed f o r  At h i g h c u r r e n t s where p^>  an analogue t o C h i l d ' s law but w i t h I«c  N  the authors f i n d  n  Y  a  ,  I n the  i n t r i n s i c base t r a n s i s t o r the space charge l i m i t e d d e n s i t y has  the simple  current  form  where ju i s the m o b i l i t y f o r h o l e s . Dacey ( 1 9 5 3 ) for  the pnp  has  I n t e g r a t e d Poisson's  space charge l i m i t e d diode,  assuming  equation constant  m o b i l i t y f o r the holes up t o a c r i t i c a l v a l u e o f f i e l d E . At g r e a t e r f i e l d s he assumes t h a t m o b i l i t y f o l l o w s an law.  Dacey takes  his f i e l d  Ryder's (195,3) work. equations  matched at E  E  dependence o f m o b i l i t y from  T h i s approach w i t h two yields a result  differential  practically  i d e n t i c a l w i t h the Shockley P r i m r e s u l t . Section 1.5 It  Avalanche M u l t i p l i c a t i o n i s w e l l known ( M i l l e r  1955)  t h a t impact  i o n i z a t i o n o f the c r y s t a l l a t t i c e atoms i s p o s s i b l e i n the  9 h i g h f i e l d r e g i o n o f a r e v e r s e b i a s e d pn j u n c t i o n . e n t e r i n g the h i g h f i e l d  r e g i o n a t t a i n enough energy t o  produce an e l e c t r o n hole p a i r by r a i s i n g a valence i n t o the conduction o f Townsend's ^  Carriers  band.  M i l l e r has  electron  found t h a t an  extension  mechanism t o i n c l u d e both e l e c t r o n s  and  holes' i o n i z i n g at d i f f e r e n t r a t e s agrees w e l l w i t h experiments and  t h e o r e t i c a l l y derived i o n i z a t i o n rates.  s i n g l e parameter M,  A  the m u l t i p l i c a t i o n f a c t o r , c o n v e n i e n t l y  d e s c r i b e s the cascading  r e l e a s e of c a r r i e r s which i s t a k i n g  place at d i f f e r e n t r a t e s i n d i f f e r e n t p a r t s o f the  Junction.  M i s the r a t i o o f the t o t a l c u r r e n t f l o w i n g through the J u n c t i o n t o the c u r r e n t one would expect i f no c a r r i e r s were being r e l e a s e d i n the  extra  Junction.  For r e v e r s e b i a s e d s t e p J u n c t i o n s , M i l l e r f i n d s t h a t the m u l t i p l i c a t i o n f a c t o r c l o s e l y f o l l o w s  the  empirical relation  n  =  L _  I-ALT where V = r e v e r s e b i a s v o l t a g e o f the J u n c t i o n , V y breakdown v o l t a g e , n i s a n u m e r i c a l n t o be about 3 f o r germanium pnp  parameter.  M i l l e r found  t r a n s i s t o r s and V b j t o  depend on the i m p u r i t y center d e n s i t y on the r e s i s t i v i t y s i d e of the  = body  high  Junction.  K i d d , Hasenberg, and Webster  (1955)  have s t u d i e d  t h e o p e r a t i o n o f t r a n s i s t o r s w i t h avalanche m u l t i p l i c a t i o n o c c u r i n g at the c o l l e c t o r j u n c t i o n . present  I n t h e i r paper they  a v e r y u s e f u l schematic diagram o f h o l e and  electron  SCHEMATIC DIAGRAM OF HOLE AND ELECTRON FLOW  IN A  P type emitter  PNP  TRANSISTOR  K TYPE BASE REGION Ip»*Ifc  ^  P type collector  \  pip  s .  <r  —  t  I I I J V  i  I l  /  ii  = (i-H*)I*-r1ls  flow -4->-Hole flow  Blechoin  y3-fraction of boles leaving emitter vrhich qet across base ^fraction ofle which is hole flow  FIG. 2  flow under such c o n d i t i o n s .  T h i s diagram i s reproduced i n  f i g u r e 2 w i t h one s m a l l leakage component o f c u r r e n t  omitted.  Prom t h i s diagram, we q u i t e g e n e r a l l y o b t a i n  I  6  =  (1.10)  Mis 4-L,  i - MoC  Ic = M(Is * "1$ I - Moc  (l.U)  where cK = the e m i t t e r c o l l e c t o r c u r r e n t g a i n , M = t h e c o l l e c t o r Junction m u l t i p l i c a t i o n factor. we take oc t o be the product the e m i t t e r e f f i c i e n c y  As i s customary  o f t h e t r a n s p o r t f a c t o r / 3 and  which a r e d e f i n e d i n t h e f i g u r e .  K i d d , Hasenberg, and Webster d e r i v e an e q u a t i o n i d e n t i c a l t o equation  almost  ( 1 . 1 0 ) and u s e i t t o e x p l a i n t h e  f e a t u r e s o f 'avalanche t r a n s i s t o r ' o p e r a t i o n , i n p a r t i c u l a r the f a c t t h a t the e f f e c t i v e a l p h a i s Hoc. S e c t i o n 1.6  The V a r i a t i o n o f T r a n s i s t o r C u r r e n t Operating  Gain  with  Conditions  Webster (195^) has shown t h a t t h e pn j u n c t i o n t r a n s i s t o r t h e o r y p u b l i s h e d by Shockley does not e x p l a i n v a r i a t i o n s o f e m i t t e r c o l l e c t o r c u r r e n t g a i n , oC. o f most t r a n s i s t o r s  The oC  i s observed t o r i s e , pass through a  maximum and then decrease w i t h i n c r e a s e o f e m i t t e r  current.  Webster has r e v i s e d Shockley*s assumption o f low l e v e l injection.  T h i s r e v i s i o n leads t o an e f f e c t w i t h two  consequences.  The m a j o r i t y c a r r i e r d e n s i t y i n the base  w i l l i n c r e a s e t o m a i n t a i n n e u t r a l i t y i n the h i g h l e v e l  11  i n j e c t i o n case.  This increase w i l l  produce an  electric  f i e l d i n the hase o f the r e g i o n which aids m i n o r i t y flow.  The  electric field  i s r e s p o n s i b l e f o r the  i n c r e a s e o f aC w i t h e m i t t e r c u r r e n t w h i l e the carrier  carrier  initial  majority  d e n s i t y i n c r e a s e i s r e s p o n s i b l e f o r subsequent  decrease o f #  and hence o f o C . 1-ex  i s a parameter more  s e n s i t i v e t o such changes than cc i t s e l f . terms which Increase w i t h c u r r e n t , 1 —oC  Neglecting  the  can show a t most  a h a l v i n g w i t h i n c r e a s e o f c u r r e n t a c c o r d i n g t o Webster's work.  DEPENDENCE OF PUNCH-THROUGH VOLTAGE ON F R E Q U E N C Y OF ALPHA CUTOFF FOR A PNP GERMANIUM STEP JUNCTION TRANSISTOR  BASE WIDTH  10"* C*.  FIG. 3  12 CHAPTER I I  DEPLETION LAYER PHENOMENA IH THIN BASE STRUCTURES  S e c t i o n 2.1  Measurements o f F l o a t i n g E m i t t e r P o t e n t i a l  The t r a n s i s t o r s used f o r punch-through experiments were s e l e c t e d from commercially germanium h i g h frequency u n i t s .  a v a i l a b l e s i l i c o n and F i g u r e 3 shows r e l a t i o n s  between some standard t r a n s i s t o r parameters f o r germanium pnp step j u n c t i o n t r a n s i s t o r s .  Any t r a n s i s t o r w i l l have a  r e p r e s e n t a t i v e point i n the space d e p i c t e d . l i e s above the dashed l i n e , avalanche  I f the point  w i l l occur a t the  r e v e r s e b i a s e d j u n c t i o n b e f o r e the space charge has reached across the base. the avalanche  T h e o r e t i c a l l y i f a reverse bias equal to  breakdown v o l t a g e Vtd  i s applied to a  j u n c t i o n , the c u r r e n t approaches i n f i n i t y . speaking  Practically  however, damage can occur to the j u n c t i o n because  of e x c e s s i v e heating before the b i a s reaches  Vu .  Thus  punch-through i s more l i k e l y t o be e x h i b i t e d by t r a n s i s t o r s w i t h a h i g h alpha c u t o f f frequency. D i r e c t c u r r e n t measurements were made on G e n e r a l E l e c t r i c f u s e d j u n c t i o n t r a n s i s t o r s types 2N123 and 2N137, and P h i l c o s u r f a c e b a r r i e r t r a n s i s t o r s type SB-100. c i r c u i t used i s shown i n f i g u r e h.  The  S t r i c t l y speaking the  meters i n t h i s c i r c u i t do not measure e x a c t l y the v o l t a g e across the e m i t t e r and c o l l e c t o r j u n c t i o n s .  However s i n c e  CIRCUIT USING  FOR THE  PUNCH-THROUGH M E A S U R E M E N T S FLOATING E M I T T E R P O T E N T I A L  EMITTER  BASE  COLLECTOR •WW-  P  P  N  s V e ) High resistance Voltmeter  FIG.4  DIRECT CURRENT COLLECTOR-EMITTER VOLTAGE CHARACTERISTIC FOR P N P TRANSISTOR TYPE 1N 137*18  -\4  V*lts  5«  F K 5 . 5  13 the above t r a n s i s t o r s a l l showed base c u r r e n t s o f l e s s one microampere over the range i n v e s t i g a t e d , and the  than  intrinsic,  base r e s i s t a n c e i s expected t o be tens or hundreds o f ohms, no c o r r e c t i o n s f o r  were r e q u i r e d .  The dependence o f f l o a t i n g e m i t t e r p o t e n t i a l on c o l l e c t o r p o t e n t i a l o f one t r a n s i s t o r type 2N137 i s shown i n f i g u r e 5.  T h i s curve i s t y p i c a l o f t h e curves  obtained  from a l l the t r a n s i s t o r s which e x h i b i t punch-through. onset o f punch-through i s c l e a r l y marked by the t o g e t h e r o f the c o l l e c t o r and  The  locking  e m i t t e r p o t e n t i a l s so t h a t  t h e i r d i f f e r e n c e i s a constant e q u a l t o the punch-through 1 v o l t a g e (Schenkel and S t a t z  195*).  The base f o r -V  c  <  p o t e n t i a l observed between the e m i t t e r and V t  has been p r e d i c t e d by Shockley  p  From e q u a t i o n ( 1 . 1 ) , i f l e  =0  Ve = tT In(i - <*) Thus, at 300°K KT volt.  = .026  (19*49).  (2.1) v o l t s and f o r oC - 0.98,  V  fc  =  -0.10  The v a l u e s o f i n t e r n a l c o n t a c t p o t e n t i a l measured  were -0.10  to  -0.16  0.98 and 0.998. potential for - \  consistent with values of The  < Vpt  oC between  s a t u r a t i o n of the f l o a t i n g e m i t t e r to values consistent with equation  (2.1) i n d i c a t e s freedom from channels  (Brown  1953).  As  channels would provide an u n d e s i r a b l e e x t r a c o n d u c t i n g path between c o l l e c t o r and e m i t t e r , such measurements form a c r i t e r i o n o f s u i t a b i l i t y of t r a n s i s t o r s f o r punchthrough  experiments.  PUNCH-THROUGH MODELS FOR A PNP TRANSISTOR WITH A PUNCH-THROUGH VOLTAGE O F 10 VOLTS <ionor i o n neutral base  ONE DIMENSIONAL  THREE DIMENSIONAL M O D E L  MODEL  4=-iov  iOV  iiv  ISV  c  J  FIG. 6  I t was found experimentally that the voltmeter connected between emitter and ground need not have a high resistance.  With a meter of i n t e r n a l resistance  5 0 0 0  ohms,  the collector-emitter voltage plot i s i d e n t i c a l for -V > Vpt c  to the one made with a 5 0 megohn meter.  The i n t e r n a l contact  p o t e n t i a l does not appear however f o r -Vc  Vpt . The space  charge column across the depleted base i s thus a low resistance connection between c o l l e c t o r and emitter. I t s a c t u a l resistance depends on the nature of the space charge limited currents (Shockley Prim 1 9 5 3 )  that flow when an attempt..  i s made to increase the c o l l e c t o r emitter p o t e n t i a l difference. The usual one dimensional model f o r punch-through (Schenkel & Statz  195*0  can be extended to three dimensions  to give a q u a l i t a t i v e idea of the potential d i s t r i b u t i o n i n the t r a n s i s t o r when -V > Vpt . c  With the one dimensional  model one wonders what the p o t e n t i a l of the base lead Is past punch-through, and how greater voltages than Vpt can be applied between c o l l e c t o r and base.  In figure 6 one and  three dimensional models of a t r a n s i s t o r are depicted.  A  section i n the centre of the three dimensional model Is imagined to behave l i k e the one dimensional model.  When  -Vc = Vpt there i s a column of space-charge joining the c o l l e c t o r and emitter.  Since, under these conditions, the  c o l l e c t o r emitter p o t e n t i a l difference i s simply proportional to a double i n t e g r a l of the charge density over t h i s column (neglecting small voltage drops i n the heavily doped end  SCHEMATIC DIAGRAM OF DEPLETED BASE P N P TRANSISTOR, A N O CORRESPONDING ELECTRIC FIELD AND POTENTIAL FIELD DISTRIBUTIONS IN THE BASE  FIO.7  15 r e g i o n s ) , a g r e a t e r p o t e n t i a l d i f f e r e n c e cannot between them.  exist  Once the e m i t t e r i s so connected t o  the  c o l l e c t o r i t seems i n t u i t i v e l y obvious t h a t f u r t h e r i n c r e a s e i n the r e v e r s e v o l t a g e a p p l i e d between c o l l e c t o r and w i l l cause space charge t o spread i n p a r t s c and d o f f i g u r e 6. equation  base  i n t o the base as p i c t u r e d  A c t u a l s o l u t i o n of  Poisson's  f o r the geometry o f a r e a l t r a n s i s t o r has not been  found n e c e s s a r y . I t i s i n t e r e s t i n g t o imagine a t r a n s i s t o r i n which the c o l l e c t o r and reversed biased.  emitter  junctions are  As the r e v e r s e b i a s of each j u n c t i o n i s  i n c r e a s e d , d e p l e t i o n l a y e r s w i l l spread w i l l f i n a l l y meet i n the c e n t r e . o f the base but V  c  = V  6  .  i n t o the base  That i s , the base has  locked  so t h a t t h e i r p o t e n t i a l d i f f e r e n c e i s Vyt . equation  together,  This result i s  i s solved quite generally  a t r a n s i s t o r w i t h base d e p l e t e d  o n l y one  been  emitter p o t e n t i a l s  (measured w i t h r e s p e c t t o base) are not  obvious i f Poisson's  of c a r r i e r s .  When  j u n c t i o n i s r e v e r s e b i a s e d , the p o t e n t i a l and  e l e c t r i c f i e l d are s e t e q u a l t o zero at the other for  and  Thus there i s d e p l e t i o n  punched through but the c o l l e c t o r and  for  equally  the punch-through c o n d i t i o n .  The  anywhere w i t h i n the base however.  The  f i e l d may  junction  be  zero  limiting potential  d i s t r i b u t i o n s occur when the f i e l d i s zero at a j u n c t i o n . S o l u t i o n s o f Poisson's  equation  f o r a one  t r a n s i s t o r are shown i n f i g u r e 7.  dimensional  P a r t a shows the  usual  s i t u a t i o n , a t r a n s i s t o r w i t h i t s base d e p l e t e d by space charge  DISPLAY CIRCUIT TO DEMONSTRATE LIMITING POTENTIAL DISTRIBUTIONS FOR A P H P PUNCH-THROUGH TRANSISTOR  C R O  • VcrKeal  Emitter  Horizontal  Base  Collector  1—WVW*—L-  -HAWW—t  P  J  «  N  9fNE WAVE OSCILLATOR IOOO CPS  P  SINE WAVE OSCILLATOR 30 CPS  Fie. 8  16 spreading  from a r e v e r s e b i a s e d c o l l e c t o r j u n c t i o n .  b, c and d o f f i g u r e 7 may shown. The  The  be r e a l i s e d w i t h the b i a s i n g  f i g u r e shows d e p l e t i o n i n t o the end  l i m i t i n g p o t e n t i a l d i s t r i b u t i o n s may  terms o f charge s t o r a g e .  Parts  p regions.  be d e s c r i b e d i n  A limiting potential distribution  occurs when a l l the n e g a t i v e  i o n i c charge needed t o  balance  the p o s i t i v e charge i n the base i s grouped at e i t h e r the c o l l e c t o r or e m i t t e r .  From the f o r e g o i n g , i t i s evident  t h a t f o r a r e c i p r o c a l t r a n s i s t o r , t h a t i s one which punches through the base on a p p l i c a t i o n o f a f i x e d r e v e r s e b i a s Vpt to either junction.  -Vpt  <lVd-\V | e  f^Vpt (2.2)  1  A dynamic d i s p l a y o f t h i s mathematical r e l a t i o n was  obtained  by b i a s i n g the c o l l e c t o r and e m i t t e r o f a t r a n s i s t o r s i n e wave generators  of d i f f e r e n t frequencies.  The  with circuit  used and the r e s u l t i s shown i n f i g u r e 8 . S t a f e y e v , T u c h k e v i c h and Yakovchuk (1956) have operated  the t r a n s i s t o r as an a m p l i f i e r w i t h b o t h j u n c t i o n s  reverse biased.  The  c o l l e c t o r s a t u r a t i o n c u r r e n t !<» i s  modulated by changes i n the r e v e r s e b i a s o f the  emitter.  As the e m i t t e r d e p l e t i o n l a y e r spreads i t sweeps away more o f t h e c a r r i e r s generated i n the base, r e d u c i n g I s the c o l l e c t o r .  S i g n i f i c a n t c u r r e n t g a i n i n the d e p l e t i o n  mode o f o p e r a t i o n i s obtained at e l e v a t e d temperatures where I s  i s larger. The  at  f a c t t h a t c o l l e c t o r and e m i t t e r p o t e n t i a l s  DYNAMIC  DISPLAY  DYNAMIC  Emitter P  OF  PUNCH-THROUGH  DISPLAY  Base  N  CIRCUIT  Collector  P Variable Fre^ueocy  Sine Wave oscillator  nfp OSCILLOSCOPE PATTERNS FOR DIFFERENT OSCILLATOR FREQUENCIES FOR A TRANSISTOR WITH V | * =10VOLTS  a.  »••  -Vc  io"* cps  FIG; 9  17 are locked o n l y w i t h i n c e r t a i n l i m i t s when the base i s d e p l e t e d i s shown a l s o by a dynamic punch-through d i s p l a y . S c h e n k e l and S t a t z (195 *) 1  shown i n f i g u r e 9 .  suggested t h e d i s p l a y c i r c u i t  At low f r e q u e n c i e s the u s u a l punch-  through t r a c e r e s u l t s (see part a ) . I f t h e frequency i s i n c r e a s e d , t h e t r a c e s shown i n parts b, c , d o f t h e f i g u r e are obtained.  I t i s e v i d e n t t h a t c o l l e c t o r and e m i t t e r  p o t e n t i a l s a r e not locked t o g e t h e r f o r - V > Vpt • c  emitter j u n c t i o n capacitance  i s responsible f o r the  behaviour o f t h e e m i t t e r p o t e n t i a l .  The e m i t t e r i s d r i v e n  negative by the low impedence generator reaches Vpt .  The  However, when -Vc  as soon as -Vc  decreases a g a i n Ve cannot  f o l l o w i t because the charge s t o r e d around t h e e m i t t e r j u n c t i o n must leak away g i v i n g an RG" decay o f Ve back t o M  See part b, f i g u r e 9 .  zero.  Quantitative description:is  d i f f i c u l t here as t h e r e i s no simple r e l a x a t i o n time f o r a junction. capacitance bias.  The leakage r e s i s t a n c e and the j u n c t i o n are both non-linear functions of the j u n c t i o n  At two k i l o c y c l e s the charge has not a l l leaked o f f  the e m i t t e r when V to  c  r e t u r n s t o zero but t h e charge has time  leak o f f b e f o r e t h e next sweep o f Vc.  as -V  c  At t e n k i l o c y c l e s  decreases from i t s maximum v a l u e , -Ve  s l o w l y by j u n c t i o n leakage.  -Vc  r e a c h the point where |V I - IVcl 6  decreases  drops r a p i d l y enough t o = Vj»t .  This  represents  a l i m i t i n g p o t e n t i a l c o n f i g u r a t i o n i n the base w i t h t h e field  e q u a l t o zero a t the c o l l e c t o r .  Now the c o l l e c t o r  drags the e m i t t e r downward w i t h i t t r a c i n g t h e s t r a i g h t  CIRCUIT FOR JUNCTION CAPACITANCE MEASUREMENT p  N  p SOURCE  J  IMPEPANCE BWOGE  FIG.IO  CAPACITANCE VS. REVERSE BIAS OF COLLECTOR AND EMITTER JUNCTIONS OF TYPE VTD110 TRANSISTOR* 167  zoo  fre^untj • too KiWcycUs  100  COUECTOR  EWITTER  O  JUNCTION  JUNCTION  < fco  4I  4Z  REVERSE  3  BIAS  F I G , II  -t—J—i—i  4  fc  volts  t  l i t  10  ao  p o r t i o n AB  i n part c o f the f i g u r e .  zero and-V sweep.  e  V  c  18  then r e s t s at  decays by j u n c t i o n leakage b e f o r e the  next  At f o u r hundred k i l o c y c l e s the f e a t u r e s o f the t r a c e  a r e the same as p a r t c ( s t r a y c a p a c i t a n c e d i s t o r t s the p i c t u r e ) except now  the e m i t t e r j u n c t i o n c a p a c i t a n c e does  not have time t o completely d i s c h a r g e b e f o r e the  collector  i s swept n e g a t i v e a g a i n . The V  c  - V  "operating point" f o r both junctions  €  r e v e r s e b i a s e d i s always s u b j e c t t o the c o n d i t i o n s imposed by the l i m i t i n g p o t e n t i a l d i s t r i b u t i o n s i n the base. the t r a c e s a b c d o f f i g u r e 9,  l i e i n s i d e the  Thus  boundaries  of t h e shaded r e g i o n o f the o s c i l l o s c o p e p a t t e r n o f f i g u r e S e c t i o n 2.2  Capacitance  The c i r c u i t  Characteristics  shown i n f i g u r e 10  was  used  to  measure the c a p a c i t a n c e o f a number o f r e v e r s e b i a s e d junctions i n t r a n s i s t o r s . at  30  k i l o c y c l e s and  100  difference i n results. for  Measurements were c a r r i e d out kilocycles with essentially  From e q u a t i o n  (1.7),  the c o l l e c t o r or e m i t t e r j u n c t i o n o f a one  u n i f o r m base t r a n s i s t o r .  no  C«c: (V + vp )  ^  0  dimensional  A In C - In V plot of t h i s  r e l a t i o n w i l l give a s t r a i g h t  line of slope - £ f o r V»vy . 0  S i n c e the c a p a c i t a n c e formula f o r t a p e r e d geometry and non-uniform equation  base r e s i s t i v i t y  (1.7),  i s much d i f f e r e n t  than  p l a n a r i t y and u n i f o r m base r e s i s t i v i t y  assured i n a t r a n s i s t o r whose  In C - In V plot i s a  s t r a i g h t l i n e o f s l o p e - % f o r l a r g e V.  Such p l o t s were  are  8.  CAPACITANCE  VS. R E V E R S E  BIAS FOR  COLLECTOR A N D EMITTER JUNCTIONS OF A P U N C H - T H R O U G H  TRANSISTOR  R E V E R S E BIAS  F I G .  Volts  12  made and used as an acceptance  t e s t f o r t r a n s i s t o r s t o be  used i n punch-through experiments.  F i g u r e 11 shows a t y p i c a l  c a p a c i t a n c e r u n on t h e c o l l e c t o r and e m i t t e r j u n c t i o n o f a G e n e r a l E l e c t r i c type VTD 110 t r a n s i s t o r .  The f a c t t h a t  the c o l l e c t o r j u n c t i o n c a p a c i t a n c e curve l i e s above t h e e m i t t e r curve i s due t o the l a r g e r collector.  The g e n e r a l p r a c t i c e  dot on a l l o y e d  e f f e c t i v e area o f t h e  i s t o make t h e c o l l e c t o r  s t r u c t u r e s l a r g e r than the e m i t t e r dot t o  improve the alpha o f the t r a n s i s t o r . at  low v a l u e s o f V as here  w i t h V.  The curves round o f f  i s not n e g l i g i b l e  compared  may be r e a d d i r e c t l y from t h e graph as  indicated  i n f i g u r e 11. F i g u r e 12 shows a c a p a c i t a n c e v o l t a g e p l o t o f t h e  c o l l e c t o r j u n c t i o n o f a t r a n s i s t o r which punches-through a t about 8 v o l t s .  The sudden i n c r e a s e i n c o l l e c t o r  c a p a c i t a n c e at the punch-through v o l t a g e i s due t o the e m i t t e r j u n c t i o n c a p a c i t a n c e suddenly b e i n g shunted the c o l l e c t o r c i r c u i t by the space-charge  connection  between t h e c o l l e c t o r and e m i t t e r r e g i o n .  A similar  i s o b t a i n e d f o r the e m i t t e r j u n c t i o n o f t h i s The  into  curve  transistor.  jump i n c a p a c i t a n c e at the punch-through v o l t a g e i s  g r e a t e r f o r t h i s arrangement as i t i s the c o l l e c t o r c a p a c i t a n c e t h a t i s b e i n g shunted  i n t o the c i r c u i t now  r a t h e r t h a n the e m i t t e r c a p a c i t a n c e .  The v a l u e o f  c a p a c i t a n c e added t o the c i r c u i t when punch-through i s reached  i s not t h e f u l l zero b i a s value f o r the j u n c t i o n  concerned.  D i f f e r e n t i a l capacitance i s equal t o the r a t e  20 o f change o f s t o r e d charge w i t h r e s p e c t t o r e v e r s e b i a s . However, a s m a l l change i n s t o r e d charge i s always p r o p o r t i o n a l t o a change i n d e p l e t i o n depth times From f i g u r e 6 part e we  an a r e a .  see t h a t when the e m i t t e r i s  touched by the space charge and f u r t h e r d e p l e t i o n i n t o the base o c c u r s , the f u l l e m i t t e r a r e a i s not brought i n t o the picture.  The  c a p a c i t a n c e "behavior past punch-through has  no simple dependence on v o l t a g e because o f the  complicated  n a t u r e o f the s o l u t i o n o f Poisson's e q u a t i o n f o r the geometry o f a r e a l t r a n s i s t o r .  exact  Curves s i m i l a r t o those  of  f i g u r e 12 were o b t a i n e d f o r the c o l l e c t o r and e m i t t e r j u n c t i o n s o f the other punch-through t r a n s i s t o r s t h a t were tested. S e c t i o n 2.3  C u r r e n t - v o l t a g e C h a r a c t e r i s t i c s o f PNP  The name pnp used as a two disconnected.  diode d e s i g n a t e s a pnp  t e r m i n a l d e v i c e w i t h the base  Diodes  transistor  left  D i r e c t c u r r e n t v o l t m e t e r ammeter measurements  were made on the G e n e r a l E l e c t r i c type 2N137 t r a n s i s t o r s used as pnp  diodes.  The c o l l e c t o r and e m i t t e r j u n c t i o n s  o f these t r a n s i s t o r s have a punch-through v o l t a g e o f 10 v o l t s , and an avalanche The  break-down v o l t a g e of w e l l over 200  volts.  2N137 has a power r a t i n g o f 100 m i l l i w a t s . W i t h t h e  t r a n s i s t o r immersed i n o i l at room temperature,  readings  were taken out t o 20 milliamps at 20 v o l t s or f o u r times the power r a t i n g .  Readings taken at g r e a t e r powers were not  s t a t i o n a r y and t h e r e was  observable  h e a t i n g o f the  21 t r a n s i s t o r case.  Measurements at higher c u r r e n t s were  c a r r i e d out w i t h a p u l s e r and c a l i b r a t e d o s c i l l o s c o p e . ten  microsecond  A  pulse f i f t y times a second was found  s u i t a b l e t o extend the readings t o t e n watts instantaneous power.  maximum  The c u r r e n t v o l t a g e c h a r a c t e r i s t i c  o b t a i n e d i s shown i n f i g u r e lh. For the 2N137 #18s Vpt = 8 v o l t s measured by the f l o a t i n g emitter c i r c u i t o f f i g u r e Wo as 1.2  10~3 c e n t i m e t e r s from t h e  manufacturer's  alpha c u t o f f  frequency.  S i n c e the 2NS37 has a u n i f o r m base r e s i s t i v i t y as i n d i c a t e d by i t s c a p a c i t a n c e v o l t a g e c h a r a c t e r i s t i c , t h e f i e l d w i l l be l i n e a r i n t h e d e p l e t i o n r e g i o n . / When the base i s f u l l y d e p l e t e d , i . e . when V = Vpt i s a p p l i e d t o the pnp diode, the average f i e l d i n t h e base i s E=  *  -  10* Volts/Cm.  At such h i g h f i e l d s , the Shockley Prim  (1953) r e s u l t  not a p p l i c a b l e as t h e authors d e r i v e the space  charge  l i m i t e d c u r r e n t on t h e b a s i s o f constant m o b i l i t y . v o l t s / c m . i s w e l l i n t o the r e g i o n where Ryder r e p o r t e d a many f o l d decrease o f m o b i l i t y .  is  10 ^ «,  (1953)  From 3  has  10^  v o l t s / c m . t o w e l l over 10 * v o l t s / c m . m o b i l i t y obeys an 1  E"  1  law a c c o r d i n g t o Ryder.  Since the f i e l d i s l i n e a r i n  the d e p l e t i o n r e g i o n b e f o r e V i s i n c r e a s e d t o the p o i n t where holes f l o o d i n t o the base, we note t h a t m o b i l i t y  TRANSISTOR TRANSISTOR  DATA  71* m  2NII3  TYPE  2NI37  PUNCH-THROUGH VOLTAGE (Measured) BASE WIDTH  3 0 Volts  .OOI3cm . S  Wo (fwn jUco)  26 volts  8 Volts  . 0014cn»  •OOI3cn, .  A R E A (from  IMPURITY DENSITY IN THE BASE Nr.  .4  •6I0"V  —  —  Capacitance whenV»Vj*.  S  .25 I O V  I O V  .09  |0V  F I G . 13 f  CURRENT VOLTAGE FOR  CHARACTERISTIC  PNP DIODE WHICH PUNCHES THROUGH AT 8 VOLTS  100  200  CURRENT  500 MWIiamperes  FIG. 14  400  22 w i l l f o l l o w t h e E " ^ law over most o f the base. assume the E*"^ law o r s a t u r a t e d d r i f t  I f we  v e l o c i t y law over t h e  whole base, then proceeding along t h e l i n e s o f the Shockley Prim  derivation  3" - fV*v  (2.3)  i ! V = -Cpn,+  ft)  (  2  h )  where J = c u r r e n t d e n s i t y , pm = mobile charge d e n s i t y (assumed t o be holes f o r the pnp d i o d e ) , v = average drift  v e l o c i t y (assumed t o be constant over t h e whole b a s e ) ,  V = the e l e c t r o - s t a t i c potential, ff = the fixed d e n s i t y , € = p e r m i t t i v i t y o f germanium.  charge  When the above  equations a r e combined and i n t e g r a t e d twice over t h e base w i t h t h e p o t e n t i a l and f i e l d s e t e q u a l t o zero at one junction  I f we n e g l e c t t h e s m a l l v o l t a g e drops i n the h e a v i l y doped p regions, equation (2.5) i s the voltage-current d e n s i t y c h a r a c t e r i s t i c o f t h e pnp d i o d e .  Equation (2.5) i s a  d i s p l a c e d ohms law, g i v i n g a s l o p e r e s i s t a n c e o f  Kflc =  dV = \A)O* A 41 ?.evfl  F o r 2H137 #18, Rfi per second data l i s t e d  C  (2.6)  = 10 ohms, u s i n g v = 6 10** c e n t i m e t e r s  from R y d e r s data f o r h o l e s , and t h e t r a n s i s t o r f  i n f i g u r e 13.  23 I n f i g u r e lk a current voltage p l o t o f pnp diode #18 i s shown. The slope r e s i s t a n c e does tend t o a value of 17 ohms at kOO m i l l i a m p s , however, the general features observed a r e not those o f a d i s p l a c e d ohms law.  This i s  q u i t e probably due t o changes i n e f f e c t i v e area A, i n equation (2.6).  As the emitter j u n c t i o n i n the pnp diode  i s forward biased, we expect the base emitter p o t e n t i a l d i f f e r e n c e t o be s m a l l .  Thus, as the c o l l e c t o r emitter  p o t e n t i a l d i f f e r e n c e i s increased, the d e p l e t i o n r e g i o n s t i l l spreads from the c o l l e c t o r , exposing more o f the emitter s u r f a c e , i n c r e a s i n g t h e area o f the emitter over which space-charge emmission i s p o s s i b l e . I n general the approach o f the d r i f t  velocity  to a constant value as the f i e l d increases w i l l lead t o a current-voltage c h a r a c t e r i s t i c beyond punch-through which e x h i b i t s a slope i n c r e a s i n g a s y m p t o t i c a l l y t o t h e constant value c a l c u l a t e d above. Section  Influence o f Non-Ideal Geometry and Non-Uniform Base R e s i s t i v i t y I n the one-dimensional planar t r a n s i s t o r model,  i f d e p l e t i o n i s complete t o some depth about a reverse b i a s e d j u n c t i o n , Poisson's equation may be i n t e g r a t e d t o give the p o t e n t i a l d i s t r i b u t i o n about the j u n c t i o n . I n Chapter 1, S e c t i o n 1.3 t h i s i n t e g r a t i o n i s c a r r i e d out and the formulae f o r the punch-through voltage and the d i f f e r e n t i a l capacitance derived f o r a one-dimensional planar t r a n s i s t o r o f uniform base  resistivity.  2h  I f the c o n c e n t r a t i o n o f donor i m p u r i t i e s i n the base o f a pnp planar t r a n s i s t o r i s N ( x ) , Poisson's  equation  may be I n t e g r a t e d twice t o o b t a i n  VM=I^sNfe)<Js  -° 5/ c  s j d s  ] (2  7)  where V (x) = 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 i n t h e n r e g i o n , dn = depth o f d e p l e t i o n i n t o t h e n r e g i o n , x = d i s t a n c e measured from t h e j u n c t i o n i n t o the n r e g i o n . has been s e t e q u a l t o zero at d  n  The f i e l d  where the d e p l e t i o n l a y e r  ends, V has i t s zero a t the j u n c t i o n .  I f v o l t a g e drops i n  r e g i o n s other than the d e p l e t e d n r e g i o n are n e g l e c t e d , the v o l t a g e a c r o s s the j u n c t i o n i s V = V ( W ) . 0  occurs when dn = W , 0  transistor.  Punch-through  where W5 i s t h e base w i d t h o f the  I f the s u b s c r i p t s c and e a r e used f o r t h e  c o l l e c t o r and e m i t t e r punch-through v o l t a g e s  Vpt 6  then  £ \ N(\Mo-oOdx  Thus a t r a n s i s t o r w i l l not be r e c i p r o c a l w i t h r e s p e c t t o punch-through v o l t a g e u n l e s s N(x) i s a c o n s t a n t , o r a t l e a s t symmetric about the c e n t r e of, the base. d i f f e r e n t i a l capacitance i s  f o r our v o l t a g e  The convention.  CAPACITANCE VS. REVERSE BIAS FOR TEXAS INSTRUMENTS GROWN JUNCTION SILICON TRANSISTOR TYPE 9 0 3  REVERSE BIAS FIG. 15  voiu  25  Jo £ so while t h e r e i s no simple dependence o f C on V,  the  c a p a c i t a n c e i s g i v e n by the g e o m e t r i c a l c a p a c i t a n c e of the d e p l e t i o n r e g i o n .  The  s l o p e of the  capacitance  v o l t a g e curve i s of i n t e r e s t .  JC_  -fl€ N(cU 2  =  ( 2  1 0 )  OjJ*  cJV  Thus, a n a l y s i s o f the s l o p e y i e l d s the i m p u r i t y d e n s i t y anywhere i n the base.  F i g u r e 15  shows the measured  c a p a c i t a n c e v o l t a g e dependence of a grown j u n c t i o n transistor.  Capacitance  measurements were c a r r i e d out t o  the avalanche break-down v o l t a g e o f each j u n c t i o n .  The  g r e a t e r n e g a t i v e s l o p e of the e m i t t e r j u n c t i o n curve as compared w i t h the c o l l e c t o r curve agrees  qualitatively  w i t h equation (2.10) and the r a t i o n of N at each end the base, p r e d i c t e d by the avalanche ( M i l l e r 1955)  breakdown v o l t a g e s  o f the r e s p e c t i v e j u n c t i o n s .  Quantative  a n a l y s i s of grown t r a n s i s t o r s i s v e r y d i f f i c u l t  as  d e v i a t i o n s from planar step j u n c t i o n behavior may t o non-uniform base r e s i s t i v i t y or non-planar Poisson's e q u a t i o n may  of  be  due  geometry  be s o l v e d q u i t e s i m p l y  i n the d e p l e t i o n r e g i o n o f a j u n c t i o n having the symmetry  o f any o r t h o g i n a l c u r v i l i n e a r c o - o r d i n a t e system.  The  26  c a p a c i t a n c e i s always j u s t the g e o m e t r i c a l c a p a c i t a n c e f o r t h a t geometry.  The  c a p a c i t a n c e v o l t a g e r e l a t i o n can  w r i t t e n down only as a p a i r o f parametric  be  equations  depending on a v a r i a b l e r e l a t e d t o the depth o f d e p l e t i o n . F o r example, at a h e m i s p h e r i c a l r e v e r s e b i a s e d j u n c t i o n o f radius  Pc w i t h the net donor d e n s i t y of the  surrounding  m a t e r i a l , N, a f u n c t i o n o f r a d i u s o n l y , the d e p l e t i o n r e g i o n i s h e m i s p h e r i c a l and c o n c e n t r i c w i t h the j u n c t i o n . N e g l e c t i n g the b u i l t - i n p o t e n t i a l and s m a l l p o t e n t i a l drops I n r e g i o n s other than the n r e g i o n , the b i a s V a c r o s s the j u n c t i o n i s  (2.11) where r region.  n  i s the r a d i u s o f the outer edge o f the d e p l e t i o n The  d i f f e r e n t i a l capacitance i s  C =.i lire 1  (2.12)  which i s the g e o m e t r i c a l c a p a c i t a n c e o f a h e m i s p h e r i c a l c a p a c i t o r o f i n n e r and outer r a d i i re and r . n  27 CHAPTER I I I  AVALANCHE PHENOMENA IN THICK BASE STRUCTURES  S e c t i o n 3.1  I n f l u e n c e o f M u l t i p l i c a t i o n on PNP Diode Properties Current v o l t a g e measurements were made on  Delco 2N277 power t r a n s i s t o r s . frequency o f t h e 2N277 i s 0.5  The alpha  cutoff  megacycles.  As such power  t r a n s i s t o r s u s u a l l y have low base r e s i s t i v i t i e s 5 ohm c e n t i m e t r e s ) they s h o u l d e x h i b i t  avalanche  m u l t i p l i c a t i o n r a t h e r than punch-through w i t h of s u f f i c i e n t l y  (perhaps  application  l a r g e r e v e r s e b i a s t o the c o l l e c t o r  j u n c t i o n (see f i g u r e  3 ) . Such was found t o be t h e  case f o r t h e c o l l e c t o r j u n c t i o n s o f the t h r e e Delco transistors  tested.  T e s t s were not made on r e v e r s e d  b i a s e d e m i t t e r j u n c t i o n s as t h e Delco t r a n s i s t o r i s designed t o d i s s i p a t e equations  (1.10) lL =  I  c  heat from the c o l l e c t o r o n l y .  and  (1.11)  , i f  I  e  From  =0,  (3.1)  =nis  Thus c o l l e c t o r j u n c t i o n c u r r e n t v o l t a g e measurements w i t h e m i t t e r l e f t f l o a t i n g should p r o v i d e d i r e c t evidence o f Such measurements were c a r r i e d out on the type 2N277 transistor  a t room temperature.  o c c u r r e d a t above 100  volts.  Avalanche  When V  breakdown  was g r e a t e r than  50 v o l t s the r e a d i n g s were found t o d r i f t  however,  M.  CURRENT THROUGH PNP DIODE 2N277 AS A FUNCTION OF THE BIAS APPEARING ON EACH JUNCTION SEPARATELY  •» .w . n J U N C T I O N BIAS  :  .04  F I G . 16  o Volts  28  sometimes as much as 10$ i n a minute. junction of a transistor  The c o l l e c t o r  i s not a good p l a c e t o observe  the p u r e l y j u n c t i o n e f f e c t o f m u l t i p l i c a t i o n ,  as t h e r e a r e  t r a n s v e r s e m a j o r i t y c a r r i e r c u r r e n t s i n the base which c a n make the c a r r i e r flow p e t t e r n through t h e m u l t i p l y i n g region very c u r r e n t - s e n s i t i v e .  Pnp diode  were made next on the 2N277 t r a n s i s t o r s .  measurements The c o l l e c t o r  r e g i o n was r e v e r s e b i a s e d w i t h r e s p e c t o f e m i t t e r and t h e base was l e f t d i s c o n n e c t e d .  At low v o l t a g e s where M i s 1  e s s e n t i a l l y the pnp diode s h o u l d obey Shockley's equations.  diffusion  F i g u r e 16 shows t h e c u r r e n t through t h e pnp  diode as a f u n c t i o n o f the b i a s on each j u n c t i o n s e p a r a t e l y . Shockley's equations  and (1.5) are each f i t t e d at one  point t o t h e a p p r o p r i a t e c u r v e . diode  As t h e v o l t a g e across the  i s i n c r e a s e d the f i e l d a t the r e v e r s e b i a s e d  c o l l e c t o r w i l l increase u n t i l m u l t i p l i c a t i o n take p l a c e .  The r i g h t s i d e o f f i g u r e  begins t o > '  16 shows the c u r r e n t  through the c o l l e c t o r as m u l t i p l i c a t i o n begins  and the  d i f f u s i o n equation breaks down. The diode  e m i t t e r j u n c t i o n s t i l l behaves as a Shockley  at the high currents.  Such behavior  i s an important  c o n f i r m a t i o n o f the f a c t t h a t i n t h e f l o a t i n g base pnp diode w i t h avalanche a t t h e c o l l e c t o r  j u n c t i o n , the emitter  end o f the base s t i l l obeys the d i f f u s i o n t h e o r y o f hole i n j e c t i o n and t r a n s p o r t . To d e s c r i b e t h e pnp diode w i t h avalanche  CURRENT  VOLTAGE  OF P N P DIODE  CHARACTERISTIC  TYPE  2N277  VOLTAGE ACROSS P N P DIODE  FIG.I7  #  4I  s/oits  29 m u l t i p l i c a t i o n t a k i n g p l a c e , It> equation  (1.10)  i s set e q u a l t o zero i n  to y i e l d  (3.2)  I c = Mis I This equation  McC  s t a t e s t h a t f o r breakdown i n the pnp  diode,  M does not have t o approach i n f i n i t y but o n l y i n c r e a s e t o a value such t h a t V\°c = 1 T h e breakdown at about Uo compared t o over 100 alone.  The  v o l t s i n the pnp  diode c o n f i g u r a t i o n ,  v o l t s f o r the c o l l e c t o r  p h y s i c a l reason  form o f e l e c t r o n s .  Delco t r a n s i s t o r s e x h i b i t e d  junction  i s a feed-back mechanism i n the  I f some m u l t i p l i c a t i o n i s going on at  the c o l l e c t o r , the e l e c t r o n s produced flow back i n t o the base.  As the base i s f l o a t i n g the c u r r e n t e n t e r i n g  the  e m i t t e r r e g i o n must step up so t h a t i t s s m a l l e l e c t r o n component l e a v i n g the base w i l l p i c k up the e l e c t r o n s g i v e n the base by the m u l t i p l i c a t i o n p r o c e s s .  When the  e m i t t e r c u r r e n t steps up however i t i s sending  many more  holes a c r o s s the base t o be m u l t i p l i e d .  Figure  shows the c u r r e n t v o l t a g e c h a r a c t e r i s t i c of one diode.  An attempt was  made t o f i t equation  graph u s i n g the low v o l t a g e constant  17 2N277 pnp  (3.2)  to the  values o f oL aud Xs  .  V a r i a t i o n s o f oC and I s w i t h c u r r e n t and v o l t a g e must be included f o r a better f i t . Is  I f temperature i s kept  should be a f u n c t i o n o f v o l t a g e o n l y .  Ml*  may  constant, be  determined from a separate c o l l e c t o r j u n c t i o n measurement (see equation  (3.1)).  A l p h a measurements  w  made on 2N277  ALPHA AS A FUNCTION OF EMITTER CURRENT FOR TRANSISTOR 2N277 *4I  FI6. I S  30  No. hi  Experimentally \ — ©C e x h i b i t s  are shown i n f i g u r e 18.  a decrease of greater than 2 t o 1.  This v i o l a t i o n of  Webster's r e s u l t s may be due t o a decrease of surface recombination v e l o c i t y w i t h increase of emitter current at the very s m a l l emitter c u r r e n t s . mentioned by R i t t n e r (195*+).  Such an e f f e c t has been  Webster's e m p i r i c a l form, f o r  the term which decreases w i t h current i s approximated to w i t h i n 5% by =  |-oc  (l-QCQ)  where ( l - °Co) = swfts. ,  I  0  le  +  (3.3)  Io  = l3flE> M  W  Dp (\  P  , s  = surface  recombination v e l o c i t y , As » e f f e c t i v e area f o r surface recombination.  This equation was compared w i t h the  observed values of 1—cC (see open c i r c l e s , f i g u r e 18). The f i t t i n g i s done at the high current region because of the p o s s i b l e surface recombination v e l o c i t y v a r i a t i o n s at low c u r r e n t .  I t i s evident that Webster 's r e s u l t  f u l l y describes the increase i n From Shockley's transistor with W/L^ «  Since W = Wo - d  w  success-  observed i n the 2N277.  d i f f u s i o n equations f o r a 1  , the dependence of W on c o l l e c t o r  voltage i s known, so i f the a c t u a l alpha i s taken t o be the product of an emitter current dependent term from Webster's work and a c o l l e c t o r voltage dependent term of  the form o f e q u a t i o n G . ^ ) ,  I  -OC  The  diode may  and  To  + Io  l €  (3.5)  f l - Vc f  dependences o f  v o l t a g e are now pnp  the f o l l o w i n g i s o b t a i n e d  , andoC on c u r r e n t and  known, so e q u a t i o n (3.2)  be compared w i t h pnp  d e s c r i b i n g the  diode measurements. 1— oC  0  f o r the alpha dependence of e q u a t i o n (3.5)  are  measurements of f i g u r e 18.  o b t a i n e d from the 1-oC  Vtd  the M term [ e q u a t i o n (l.£))] i s obtained by f i t t i n g (3.2)  at one  F i g u r e 17 (3.2) The  point t o the pnp  diode  shows the values o f Ic  for  equation  characteristic.  c a l c u l a t e d from e q u a t i o n  u s i n g the above mentioned oi  , Mis  , and M dependences.  q u e s t i o n a r i s e s whether such a f i t i s s i g n i f i c a n t .  For any p a r t i c u l a r t r a n s i s t o r i t appears t h a t o C and not o p e r a t i o n a l l y d e f i n e d . combinations  of  MoC or Klls  Measurements y i e l d .  The  o n l y way  M appears t o be to accept the form o f one  M are  only  to separateoC  and  or the other from  work done w i t h s p e c i a l t r a n s i s t o r s designed t o e l i m i n a t e some o f the e f f e c t s .  The f i t o f e q u a t i o n (3.2)  attempted  here has been made by a c c e p t i n g such forms and must be accepted i n t h i s S e c t i o n 3.2  light.  Induced Breakdown i n F l o a t i n g J u n c t i o n s  Miller  (1953)  has. found the avalanche  v o l t a g e o f a j u n c t i o n Vu  breakdown  , t o depend on the i m p u r i t y  d e n s i t y on the h i g h r e s i s t i v i t y s i d e of the j u n c t i o n .  SINGLE JUNCTION CURRENT VOLTAGE CHARACTERISTICS AND FLOATING EMITTER POTENTIAL AS A FUNCTION OF COLLECTOR REVERSE BIAS FOR A GROWN TRANSISTOR 2N167 *I4 Emitter Junction  20  'CollecTor Junction  40  JUNCTION  L&  REVERSE BIAS Volts  4-1  a  1  2.0  40  40  C O L L E C T O R R E V E R S E B I A S Volts  Fie.-19  32 I f t h i s i m p u r i t y d e n s i t y i s denoted by N  , Miller's  result  is  -.725"  Thus a grown j u n c t i o n t r a n s i s t o r different  may have a q u i t e  c o l l e c t o r and e m i t t e r breakdown v o l t a g e .  i s the current voltage c h a r a c t e r i s t i c  F i g u r e 19  o f t h e c o l l e c t o r and  e m i t t e r j u n c t i o n s o f a grown t r a n s i s t o r  type 2N167.  The  e m i t t e r j u n c t i o n avalanche breakdown v o l t a g e was measured as V? v o l t s .  The c o l l e c t o r  down a t 60 v o l t s . down however. curve o f f i g u r e  j u n c t i o n appeared t o break  The c o l l e c t o r  j u n c t i o n does not break  The e m i t t e r v o l t a g e , c o l l e c t o r  voltage  19, shows t h a t when the c o l l e c t o r  junction  i s r e v e r s e b i a s e d s u f f i c i e n t l y , punch-through occurs r a t h e r than avalanche breakdown.  As c o l l e c t o r  reverse  b i a s i s i n c r e a s e d beyond t h e punch-through v o l t a g e , t h e e m i t t e r i s f o r c e d n e g a t i v e w i t h r e s p e c t t o t h e base u n t i l i t s avalanche breakdown v o l t a g e i s reached.  Now t h e  space charge column across the base provides  a low  r e s i s t a n c e path l e t t i n g the e m i t t e r breakdown be seen a t the  collector.  o  CURRENT OF  VOLTAGE PNP  CHARACTERISTIC  DIODE  2NII2  VOLTAGE ACROSS DIODE Volts  FIG.20  CHAPTER IV  COMBINED ALPHA VARIATION AND AVALANCHE  S e c t i o n h,l  Negative  PHENOMENA  Resistance  F i g u r e 20 shows c u r r e n t v o l t a g e o s c i l l o s c o p e t r a c e s o b t a i n e d f o r a Raytheon t r a n s i s t o r type connected  as a pnp diode.  2N112  The d i s p l a y c i r c u i t used i s  s i m i l a r t o t h a t o f f i g u r e 9 except  t h a t v o l t a g e drop  ,across a 500 ohm r e s i s t o r p l a c e d i n s e r i e s w i t h t h e diode was used t o i n d i c a t e c u r r e n t .  The t r a c e shown i n  the f i g u r e was made at 30 c y c l e s per second and i s s i m i l a r t o those obtained f o r other 2N112 t r a n s i s t o r s . The  e m i t t e r and c o l l e c t o r j u n c t i o n s i n d i v i d u a l l y e x h i b i t e d  avalanche  breakdown at about 70 v o l t s , thus the r a p i d  i n c r e a s e i n c u r r e n t at 25 v o l t s f o r the pnp diode i s i n a c c o r d w i t h equation (3.2) and M i l l e r ' s formula f o r M [ e q u a t i o n ( \.°\ ) ] . The t r a c e s a l l c l e a r l y showed a turnover point and a r e g i o n o f n e g a t i v e r e s i s t a n c e . For the pnp diode ( s e c t i o n 3.1)  I=iHs_  <»r.l)  S i n c e the e m i t t e r j u n c t i o n i n the pnp diode has o n l y a few tenths o f a v o l t drop a c r o s s i t , the v o l t a g e a c r o s s the pnp diode and the v o l t a g e across i t s c o l l e c t o r  3* 1  j u n c t i o n a r e assumed e q u a l and both denoted by V. and I I,  6  IfM  are f u n c t i o n s o f V o n l y andoc a f u n c t i o n o f V and  then from e q u a t i o n (U-.l)  F o r turnover  _0  or  dl  Thus e q u a t i o n ( ^ . 1 ) function of I .  can g i v e t u r n o v e r i f alpha i s a  To examine the turnover c o n d i t i o n  q u a n t i t a t i v e l y oc  i s assumed t o be a f u n c t i o n of I o n l y  g i v e n by e q u a t i o n ( 3 . 3 )  and I  s  i s assumed c o n s t a n t .  The  c o n d i t i o n f o r t u r n o v e r [ e q u a t i o n (*+.3)] becomes  (21  +Io)  2  The l e f t s i d e o f e q u a t i o n (h.h) j u n c t i o n o f I , asymptotic  to I  i s a monotonic i n c r e a s i n g =  .  S i n c e the  l e f t s i d e i s zero when I i s zero and i s monotonic i n c r e a s i n g i n I , f o r turnover t o be a t a l l a t t a i n a b l e the f o l l o w i n g must h o l d .  35 (\ - ^ o ) I o  >  4  Since I s = I c ( I e  I s = fi<\^Wo given  w  h  e  = 0  n  i n equation  )  , from equations  . v »hl ( 3 . 3 ) ,  (1.1),  (1.2)  Using the value o f Io  c o n d i t i o n (^.5)  becomes  >1  0  oC  .  c  (l-o^ )L\Nh 4 Wo* where  Is  (if.6)  i s the low c u r r e n t v a l u e o f <yC , Nn  0  i m p u r i t y d e n s i t y i n the n-type base, n* i n t r i n s i c c a r r i e r d e n s i t y , Wo To conclude,  = n  n  = the p  n  = the  = the base w i d t h .  turnover  i n the pnp  diode i s  p r e d i c e d by the avaianche t r a n s i s t o r model d e s c r i b e d equations  (1.10) and  (1.11).  i n the h i g h frequency  appearance o f W  0  Turnover appears more l i k e l y  t r a n s i s t o r s such as the 2N112  than the low frequency  by  rather  t r a n s i s t o r s , because of the  i n the denominator o f the  left  side  o f c o n d i t i o n (*+.6) T h i s c r i t e r i o n has not been r i g o r o u s l y d e r i v e d however as v o l t a g e dependence o f oC i g n o r e d and transistor  I —<^-o  has been  has not been reduced t o b a s i c  parameters.  S e c t i o n H-.2  E f f e c t of J u n c t i o n Area on the Turnover Condition  F i g u r e 20 i n d i c a t e s t h a t turnover c u r r e n t i n the pnp  occurs  at a lower  diode when the c o l l e c t o r i s made negative  36 w i t h r e s p e c t t o the e m i t t e r . t h a t the e l e c t r i c f i e l d  Webster (I95h) has shown  i n the base r e g i o n at the  emitting  j u n c t i o n i s r e s p o n s i b l e f o r the i n i t i a l r i s e o f a l p h a emitter current.  S i n c e the f i e l d  with  i s r e l a t e d to current  d e n s i t y , the area of the e m i t t i n g j u n c t i o n i s a s i g n i f i c a n t parameter i n the turnover The  equations.  s u b s c r i p t s N and R are now  d i s t i n g u i s h two  cases.  used t o  Normal o p e r a t i o n (N): the  i s n e g a t i v e w i t h r e s p e c t t o the e m i t t e r .  collector  Reverse  o p e r a t i o n (R): the e m i t t e r i s negative w i t h r e s p e c t the c o l l e c t o r .  The  to  area of the e m i t t i n g j u n c t i o n i s  i n c l u d e d by r e w r i t i n g I o , (the c u r r e n t at which the has caused I-oC as  To  t o drop t o 2 / 3  o f i t s low  current  field  value)  » the c u r r e n t d e n s i t y r e s p o n s i b l e f o r the f i e l d  at  the e m i t t i n g j u n c t i o n , times the a r e a of the e m i t t i n g junction.  Thus f o r normal and r e v e r s e o p e r a t i o n ,  Io  becomes  ION = JoAe IOR = Jo Ac Where Ag  = emitter area, A At the turnover  equation  (h.h)  becomes  (2 I , +Io )* N  c  = collector  area.  c u r r e n t f o r normal o p e r a t i o n I T  ,  37 An order o f magnitude c a l c u l a t i o n i n d i c a t e s t h a t the turnover  c u r r e n t f o r normal o p e r a t i o n ,  hundred times s m a l l e r than Now i f \~<^v  IOM  and I s  or l o  R  IT  , i s five  .  a r e the same t o t h e f i r s t (,k,h)  order f o r b o t h normal and r e v e r s e o p e r a t i o n , equation may be examined f o r r e v e r s e o p e r a t i o n .  The f o l l o w i n g i s  found t o hoIdJ  (l - *£Q) JQ AC I T  < IS  (*+8)  (2IT<-T<A)* using  IOM, I°R ^  ^  T  , and  /lc >  Ae  So t h e r e v e r s e c u r r e n t v o l t a g e  characteristic  s h o u l d have a p o s i t i v e slope r e s i s t a n c e (see e q u a t i o n  (^.2))  at t h e c u r r e n t where the normal c h a r a c t e r i s t i c i s t u r n i n g over.  Since W  T  in  1  B  ( e q u a t i o n (^.2)) i s monotonic i n c r e a s i n g I  , t h i s means t h a t turnover w i l l occur a t a g r e a t e r  c u r r e n t f o r r e v e r s e o p e r a t i o n as compared w i t h normal operation.  Thus t h e n o n - r e c i p r o c i t y i n turnover  current  e x h i b i t e d by the 2N112 i s e x p l a i n e d by the c o l l e c t o r e m i t t e r a r e a r a t i o which i s g r e a t e r than 1 f o r t y p i c a l alloyed structures.  38 CHAPTER V  SUMMARY AND OUTSTANDING'PROBLEMS  An attempt has "been made i n t h e course  o f the  above work t o understand t h e v a r i o u s phenomena i n v e s t i g a t e d i n terms o f simple models based on t h e s o l i d s t a t e p h y s i c s aspect  of transistors.  T h i s approach i s q u i t e d i s t i n c t  from s y n t h e s i s o f e q u i v a l e n t c i r c u i t s from e l e c t r i c a l measurements. I n Chapter I I , t h e e m i t t e r base p o t e n t i a l o f a pnp t r a n s i s t o r i n the f l o a t i n g e m i t t e r c o n d i t i o n i s d e s c r i b e d i n terms o f Shockley's d i f f u s i o n equations f o r voltages  l e s s t h a n t h e punch-through v o l t a g e , and I n terms  o f t h e low r e s i s t a n c e space-charge column across t h e n r e g i o n once t h i s r e g i o n has been punched through. The  c o l l e c t o r j u n c t i o n capacitance d i s c o n t i n u i t y  o f a pnp d e v i c e which punches through i s e x p l a i n e d a l s o i n terms o f t h e low r e s i s t a n c e space charge column. emitter capacitance  i s switched  by t h e space charge r e g i o n .  The  i n t o the c o l l e c t o r  circuit  The dynamic d i s p l a y o f  punch-through f o r d i f f e r e n t f r e q u e n c i e s shows a c o m p l e t e l y d i f f e r e n t aspect  of t h i s capacitance  effect.  I n t h e t h i n base pnp diode, punch-through before s i g n i f i c a n t current flows.  occurs  Once the n-type r e g i o n  i s d e p l e t e d o f the m a j o r i t y c a r r i e r s n o r m a l l y  present,  CIRCUIT  R E P R E S E N T A T I O N OF A N  AVALANCHE TRANSISTOR EMITTER  COLLECTOR.  CURRENT GENERATORS  FIG. 21  39 g r e a t e r a p p l i e d p o t e n t i a l s cause a space charge hole flow a c r o s s the n r e g i o n . s l a b 10  F o r an n-type germanium  c e n t i m e t e r s t h i c k o f 20  r e s i s t i v i t y , an average  limited  ohm  centimeter  e l e c t r i c f i e l d o f io"*  present when d e p l e t i o n i s accomplished.  volts/cm. i s  The  occurs at the n e g a t i v e s i d e o f the s l a b .  high f i e l d  The  drift  v e l o c i t y o f h o l e flow under such c o n d i t i o n s f o l l o w s a n o n - l i n e a r m o b i l i t y law over most o f the n r e g i o n , g i v i n g r i s e t o a c u r r e n t v o l t a g e c h a r a c t e r i s t i c which a s y m p t o t i c a l l y approaches a constant s l o p e r e s i s t a n c e . Non u n i f o r m r e s i s t i v i t y and non i d e a l geometry o f the n r e g i o n i n a pnp s t r u c t u r e are shown t o r e s u l t i n a p r e d i c t a b l e non r e c i p r o c i t y o f punch-through v o l t a g e and capacitance-bias  characteristic.  I n Chapter  I I I induced breakdown o f a f l o a t i n g  j u n c t i o n i s d e s c r i b e d i n terms o f punch-through and d i f f e r e n t avalanche collector  the  breakdown v o l t a g e s o f the e m i t t e r and  j u n c t i o n s f o r a pnp s t r u c t u r e w i t h a non  uniform  n region. The t h i c k base pnp diode c u r r e n t v o l t a g e measurements agree w e l l w i t h equations d e r i v e d from a simple model of c u r r e n t flow i n the pnp transistor.  avalanche  The measured alpha v a r i a t i o n s o f the t h i c k  base s t r u c t u r e agree w i t h Webster's a n a l y s i s . The t h i c k base t r a n s i s t o r and pnp diode might be r e p r e s e n t e d by the c i r c u i t  of f i g u r e 21.  each r e p r e s e n t a c u r r e n t stream.  The  generators  These c u r r e n t s a r i s e  ko from h o l e t r a n s p o r t a c r o s s the base, m u l t i p l i c a t i o n i n the h i g h f i e l d r e g i o n , and the scavanging o f thermallygenerated c a r r i e r s by the c o l l e c t o r d e p l e t i o n r e g i o n .  The  b a s i c avalanche t r a n s i s t o r equations (1.10) and (1.11)  may  be d e r i v e d d i r e c t l y from the f i g u r e .  T h i s model w i l l  d i s p l a y t u r n o v e r and n e g a t i v e r e s i s t a n c e f o r the pnp  diode  c h a r a c t e r i s t i c i f alpha i s a s u i t a b l e f u n c t i o n of c u r r e n t . In  the course o f i n v e s t i g a t i o n t h r e e new  effects  have been observed and e x p l a i n e d : i)  ii)  iii) The  The d i s c o n t i n u i t y of j u n c t i o n c a p a c i t a n c e f o r a pnp s t r u c t u r e at the v o l t a g e where the n r e g i o n i s punched through Induced breakdown of a f l o a t i n g j u n c t i o n i n a grown pnp d e v i c e on a p p l i c a t i o n o f s u f f i c i e n t r e v e r s e b i a s t o the other junction Negative r e s i s t a n c e over a c o n s i d e r a b l e c u r r e n t range f o r c e r t a i n pnp diodes f o l l o w i n g q u e s t i o n s are important w i t h  r e s p e c t t o a f u r t h e r understanding and more d e t a i l e d d e s c r i p t i o n of the space-charge  and  avalanche  m u l t i p l i c a t i o n processes and t h e i r e f f e c t on t h e b e h a v i o r of  the pnp  structure. What i s the temperature  of  drift  and f i e l d dependence  v e l o c i t y f o r h o l e s i n n-type germanium?  Thence  what i s the form of the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c o f t h e space-charge  l i m i t e d pnp and p i p diodes?  I f i n c o n d i t i o n s of space-charge  l i m i t e d flow  t h e r e occurs avalanche m u l t i p l i c a t i o n at the c o l l e c t o r  end  hi o f the base r e g i o n , what are the d i s t r i b u t i o n s of the r e s u l t i n g p o t e n t i a l and c a r r i e r d e n s i t i e s i n the base? What are the d e t a i l e d processes which determine the v a r i a t i o n o f ( i ) hole i n j e c t i o n e f f i c i e n c y hole c u r r e n t d e n s i t y and transmission potential?  K  ( i i ) the v a r i a t i o n o f h o l e  w i t h c u r r e n t d e n s i t y and Under avalanche c o n d i t i o n s are  collector these  parameters s i g n i f i c a n t l y m o d i f i e d by the r e t u r n i n g electrons?  with  BIBLIOGRAPHY Brown, W. L., "N-Type S u r f a c e C o n d u c t i v i t y on P-Type Germanium," Phys. Rev., August  91,  pp.  518-527,  1953  Dacey, G. C., "Space-Charge L i m i t e d Hole Current i n Germanium," Phys. Rev., June  90,  pp.  759-763,  1953  E a r l y , J . M., " E f f e c t s o f Space-Charge Layer Widening In J u n c t i o n T r a n s i s t o r s , " Proc IRE, UO, pp.  1*K)1- 1*K>6,  November  1952  K i d d ,ffl.C., Hasenberg, W., Webster, W. M. "Delayed C o l l e c t o r Conduction, A New E f f e c t i n Junction Transistors," RCA Rev.,  16,  pp.  16-33,  March  1955  M i l l e r , S. L., "Avalanche Breakdown i n Germanium," Phys. Rev.,  99,  PP.  123*+-12^1,  August  1955  Ryder, E . J . , " M o b i l i t y o f Holes and E l e c t r o n s i n High E l e c t r i c F i e l d s , " Phys. Rev., June  90,  pp.  766-769,  1953  S c h e n k e l , H., S t a t z , H., "Voltage Punch Through and Avalanche Breakdown and t h e i r E f f e c t on the Maximum Operating V o l t a g e s f o r J u n c t i o n Transistors," Proc 1  Nat'1 E l e c t r o n i c s  195*  Conf.,  10,  pp.  61U-625  ^3 Shockley, W.,  "The Theory o f P-N J u n c t i o n s i n  Semiconductors and P-N J u n c t i o n T r a n s i s t o r s , " B e l l S y s . Tech. J r . , Shockley, W.,  28,  pp.  ^35-^89,  and Prim, R. C., "Space-Charge L i m i t e d  E m i s s i o n i n Semiconductors," Phys. Rev., Stajeyev,  J u l y 19^9  90,  pp.  753-758,  June  1953  V. I . , Tuchkevlch, V. M., Yakovchuck, N.  S.,  "Operation of a T r a n s i s t o r i n Conditions  of  Depletion," J . Tekh. F i z . ,  26,  pp.  15-21, 1956  Webster, W. M., "On the V a r i a t i o n o f J u n c t i o n T r a n s i s t o r Current-Amplification Factor with Current," Proc IRE,  1*2,  pp.  91^-920,  Emitter  June  195*+  

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