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A study of thermal effects in the reverse characteristics of germanium point contact diodes Burgess, Ronald Reginald 1957

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A STUDY OF THERMAL EFFECTS IN THE REVERSE CHARACTERISTICS OF GERMANIUM POINT CONTACT DIODES  by RONALD REGINALD BURGESS B.A., University of B r i t i s h Columbia, 19!?6  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 thesis as conforming to the standard required from candidates f o r the degree of MASTER OF SCIENCE  THE UNIVERSITY OF BRITISH COLUMBIA October, 19^7  ii.  ABSTRACT P r e v i o u s work on t h e r e v e r s e 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 Ge p o i n t c o n t a c t d i o d e s has shown t h e presence  o f a v o l t a g e maximum  ("turnover").  The p r e s e n t i n v e s t i g a t i o n i s an attempt t o e x p l a i n t h e f a c t t h a t t h e power dissipated  a t t h i s v o l t a g e maximum decreases  w i t h i n c r e a s i n g ambient tem-  perature.  U s i n g d i o d e s which were g i v e n r i g o r o u s t e s t s t o ensure  stability  o f o p e r a t i o n , a c c u r a t e r e v e r s e c h a r a c t e r i s t i c s were o b t a i n e d a t c a r e f u l l y c o n t r o l l e d ambient t e m p e r a t u r e s .  On t h e b a s i s o f a model i n v o l v i n g  surface  leakage c u r r e n t s as w e l l as t h e main b u l k f l o w , a c u r r e n t c h a r a c t e r i s t i c i n v o l v i n g two a c t i v a t i o n e n e r g i e s was proposed.  I t was shown t h a t t h i s  model was c a p a b l e o f g i v i n g t h e observed b e h a v i o r o f t h e t u r n o v e r nower. U s i n g parameters o b t a i n e d f r o m t h e s t a t i c c o n s t a n t - v o l t a g e p l o t s , t h e t h e o r e t i c a l dependence o f t h e t u r n o v e r power on ambient temperature  was  o b t a i n e d and was v e r y c l o s e l y t h e same form as t h a t found e x p e r i m e n t a l l y by Benzer o v e r a v e r y wide range o f temperature.  By a d j u s t i n g one parameter  (the d i s s i p a t i o n c o n s t a n t ) e x c e l l e n t agreement was o b t a i n e d between t h e t h e o r e t i c a l t u r n o v e r power and t h a t measured i n the p r e s e n t  experiments.  A s e r i e s o f p u l s e measurements e s t a b l i s h e d t h e f a c t t h a t t h e t h e r m a l  relaxation  t i m e o f t h e diode was l e s s than 1 yu.sec. The e x p e r i m e n t a l and t h e o r e t i c a l s t u d y p r e s e n t e d here shows t h a t a c o m p l e t e l y c o n s i s t e n t model f o r t h e t u r n o v e r phenomenon c a n be c o n s t r u c t e d i n terms o f a r e v e r s e c u r r e n t composed o f two components w i t h d i f f e r e n t a c t i v a t i o n e n e r g i e s ; p h y s i c a l l y t h e r e i s e v i d e n c e t h a t t h e s e components c o r r e s pond t o b u l k and s u r f a c e c u r r e n t f l o w .  In p r e s e n t i n g the  requirements  of  British  it  freely  agree for  that  this  for  I agree  for  purposes  Department o r by h i s  that  for reference  permission  scholarly  shall  r  this  be allowed, w i t h o u t  ^ v / s / g  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r S, C a n a d a . Date  /  Library  7  is  Columbia,  I  further  thesis  thesis  Head o f my understood  for  my w r i t t e n  s  University  copying of t h i s  It  of  s h a l l make  and s t u d y .  representative.  gain  of  the  may be g r a n t e d by t h e  copying or p u b l i c a t i o n of  Department  the  extensive  that  not  in partial fulfilment  an a d v a n c e d d e g r e e a t  Columbia, available  thesis  financial  permission.  iii.  TABLE OF CONTENTS  Chapter I  Page INTRODUCTION  I  1.1 Reverse c h a r a c t e r i s t i c s of gold-bonded Ge diodes  1  1.2 The phenomenon of turnover  6  1.3 The scope of the present work II  MEASUREMENT OF THE REVERSE CHARACTERISTICS 2.1 Devices  III  IV  10 11  investigated  2.2 Measurement and maintenance of a constant ambient temperature  12  2.3 Selection and forming of diodes  13  2.k Static d.c. measurements  15  THEORY AND PREDICTIONS OF THE TWO ACTIVATION ENERGY MODEL  18  3.1 Surface leakage current and the "Two b" model  18  3.2 General analysis of the "Two b" model  20  3.3 Comparison of t h e o r e t i c a l r e s u l t s with experiment  22  MEASUREMENT OF THE CONTACT TEMPERATURE AND THE THERMAL  2h  TIME CONSTANT U.l Transient e f f e c t s expected i n a diode I4.2 Attempted pulse measurement of t and A APPENDIX - AN ELECTRONIC TEMPERATURE REGULATOR  2it 26 27  iv.  LIST OF  ILLUSTRATIONS  Figure  Page  1  Hemispherical model of a gold-bonded diode  2  2  Dimensions involved i n thermal d i s s i p a t i o n  k  3  Form of the reverse c h a r a c t e r i s t i c s of a Ge point contact r e c t i f i e r  U  7  A possible form of the turnover power vs. temperature• relationship derived from the two b model  10  5  The arrangement f o r experimental purposes  12  6(a)  C i r c u i t used f o r dynamic display  13  6(b)  Typical dynamic display obtained on the C.R.T.  13  7  C i r c u i t used to pulse diodes  lh  8  C i r c u i t used f o r d.c. measurements  15  9  C i r c u i t used f o r simultaneous a.c. and d.c. measurements  16  10  Surface conduction layer on a point contact r e c t i f i e r  18  11  B(T) vs. T derived f o r the diode used  Facing 23  12  T„ vs. T„ derived f o r the diode used o a Voltage, temperature, and current wave forms expected  Facing 23  13  i n pulse experiments lk  C i r c u i t s used to measure thermal time constant  Plates Internal structure of a Ge point contact r e c t i f i e r  II  The reverse current-voltage c h a r a c t e r i s t i c s of the  IV  V VI  Facing 25 Facing Page  I  III  2$  diode used at various ambient temperatures. Reverse current vs. temperature f o r f i x e d reverse bias voltages on the diode used. Derived curve of turnover power vs. ambient temperature  1  15 17  for the diode used.  2k  The v a r i a t i o n of current at 1 v o l t , with temperature  26  C i r c u i t diagram f o r an electronic temperature regulator  27  V.  ACKNOWLEDGMENTS I w i s h t o g i v e my s i n c e r e t h a n k s t o P r o f e s s o r R. E. Burgess f o r t h e h e l p and c o n s i d e r a t i o n he gave t h r o u g h o u t t h i s i n v e s t i g a t i o n , and f o r t h e c o n s t r u c t i v e c r i t i c i s m and comments he o f f e r e d d u r i n g t h e p r e p a r a t i o n of t h i s  thesis. F a c i l i t i e s f o r t h i s r e s e a r c h were s u p p l i e d b y a Defense  Board  Research  grant. I gratefully  acknowledge  t h e a s s i s t a n c e r e c e i v e d i n t h e form o f  N a t i o n a l Research C o u n c i l awards t h r o u g h 1906-57.  Plate I  Internal structure of a Ge point contact  rectifier.  1.  CHAPTER I INTRODUCTION  1.1  Reverse Characteristics of Gold-Bonded Germanium Diodes Contact rectifiers u t i l i z i n g n-type Ge crystals and metallic wires  (cat whiskers) have been in practical use for over ten years.  Originally,  in order to make as rugged a unit as possible, the contact was welded, or "formed", by passing a current pulse of several tenths of an ampere i n the forward direction.  Later, Benzer (19ll9) found that such a pulse also stabi-  lized the reverse characteristic and increased the back resistance. Since thermal conversion and diffusion of impurities from the whisker to the Ge during the pulse were undoubtedly changing the Ge i n the immediate vicinity of the contact from n-type to p-type, manufacturers attempted to improve the back characteristic as much as possible by intentionally forming a p-n junction at the contact.  The gold-bonded Ge diodes i n use today represent  the results of such a deliberate attempt to u t i l i z e the forming pulse to produce a hemispherical p-n junction. In this case, the cat whiskers are typically gold alloyed with 1% gallium; hence the forming pulse produces the Au-Ge eutectic with i t s melting point of 360°C. regrows onto the original crystal.  As the diode cools some Ge  Since the gallium leaves the regrown  region strongly p-type, the contact i s essentially a hemispherical single crystal p-n junction. In the Hughes type 1N67A diode used i n the present thesis, the Ge wafer is about lxlx.U mm, and has a resistivity of about 2 ohm-cm.  2.  The whisker i s 2 m i l i n diameter, and hence the regrown p-region, with a r e s i s t i v i t y of about .1 ohm-cm., has a diameter of the order of 10 -25x10"^ cm. Under $0 v o l t s of reverse bias the current i n t h i s type i s l e s s than 50 microamps. Because of the small contact dimensions, very large f i e l d s w i l l be set up during normal reverse bias operation.  Since these f i e l d s are quite  sensitive to changes i n contact geometry, i t i s necessary to consider the following hemispherical model i n order to f i n d t h e i r order of magnitude.  The  heavily doped p region i s of radius r , and the n-region i s of r e s i s t i v i t y Q  f> with electron density n and mobility ^x.  Because of the appreciably lower  impurity density i n the n-region,we consider space charge e f f e c t s i n i t alone.  Fig. 1 Hemispherical model of a gold-bonded diode.  Since N » N we can write N -N = N . Moreover setting n= N • A D A D [ n  gives us  &  3.  Hence Poisson's equation i n the carrier-depleted part of the n-region becomes  4 ±  (2)  U  \ --  E  %(7ilL.il)  where € = P e r m i t t i v i t y of germanium.  When  I  a voltage V i s applied i n the  reverse d i r e c t i o n the region between the hemispheres r = r  and r = r ^ w i l l be  Q  swept c l e a r of mobile charge, while the r e s t of the diode w i l l remain unchanged.  (Since the p-layer w i l l be very t h i n i t s e l f , we may neglect the  hole-depletion space charge layer.) ()  So the necessary boundary conditions are  -- E (*.)  3  •- o  If we solve f o r the f i e l d at the junction surface E ( r ) = E ,'we f i n d the m' implicit relation Q  (U) For  V" = 4„ t~, -  A[ / / / -f 3/»>*e£~  jo- 2 ohm-cm.. V= 100  m  ^  s  6  VOltS  3  ^  -  o  a  j  t  i •  c  l(= (^^hjC c-nd  G-r.UiC.tl l  r = 2.5x10"^ o  c r a  .  thi6 gives E - 2* /o^ volts/cm. m r = if-*lo  1  cm.  Fields of t h i s order w i l l introduce several e f f e c t s not present i n the low f i e l d case: 1) A decrease i n electron mobility For electrons i n n-type Ge, i t has been determined (Ryder 1953) that t  v  d  c< E  for  E < 700 volts/cm.  * E^  "  700 < E < 3000  ~ const.  "  3000 < E < 7000  There i s no data available f o r f i e l d s larger than t h i s , however,  Shockley(1951)  has shown that v w i l l only be doubled i f E i s increased from 2000 to 60,000 d volts/cm.  a.  2) Breakdown At very high f i e l d s the c a r r i e r densities can increase very r a p i d l y with increasing f i e l d s , either by Townsend avalanche breakdown, or by Zener high f i e l d emission.  The voltage drop across such a broken down diode should  remain at e s s e n t i a l l y the breakdown value, increasing only slowly with increasing currents.  3 ) Punchthrough of the p region If the r e s i s t i v i t y of the p-region i s high enough, i t may  happen  that the hole-depletion space charge l a y e r w i l l reach from the n-region r i g h t through to the whisker, before breakdown has occurred.  In t h i s case,the  diode  would consist of the spreading resistance i n series with the punchedthrough p-layer (which w i l l have a voltage drop across i t independent of current).  Since the behavior of a semiconductor-metal contact i s i n general dependent upon i t s temperature, the steady-state c h a r a c t e r i s t i c s of a diode w i l l be determined, i n part at l e a s t , by the r i s e i n contact temperature due to the d i s s i p a t i o n of power.  I f one solves the thermal continuity equation  f o r the hemispherical model below (where k the metal whisker and k  i s the thermal conductivity of m i s the thermal conductivity of the Ge wafer), then  s (Torrey and Whitmer 191*8)  Fig. 2 Dimensions involved i n thermal d i s s i p a t i o n .  \  5. (5)  Cr-  v  )  y  (6)  R  -  -  ^  y  -  //  where: P  s  i s the power dissipated i n the spreading resistance  P^  i s the power dissipated i n the b a r r i e r  R  i s the thermal resistance of the Ge  =  ' z 77 £  S  R m  "  »  "  "  "  "  5  CL  whisker  77  Since f o r the case of reverse bias P,>  P  we can ignore the power dis-  sipated i n the spreading resistance and write  (-r-T,. )  (7)  -  -P  where P i s the t o t a l power dissipated i n the diode. k = .£S watt/cm-°C f o r Ge s k = m  2.8 2  L  =  1  = 10"3  b ^  "  11  "  So i f we take:  (McCarthy & Ballard  1955)  Au  mm. cm.  2.£xlO~  a = 10~3  cm.  3  cm.  then (we note i n c a l c u l a t i o n that the dominant term i s since the thermal conduction i s predominantly through the Ge)  **k -  (^-~-)  2 7 0  o  c  /  w  a  t  u  So f o r 1 milliampere reverse current at 100 volts,we would expect the contact temperature to r i s e by 27°C.  I f the spreading resistance i s small compared  to the b a r r i e r resistance, t h i s temperature r i s e should f a l l o f f as l / r through the Ge.  Such an increase i n contact temperature w i l l be important f o r f i e l d s  6. corresponding to the breakdown and constant velocity regions of the diode. It is also interesting at this point to examine the thermal relaxation time of the diode.  For the contact, at a temperature T, let there  exist a time ~c such that (8)  where T  d  T  dt  a  =  ^^° " C "- ~*) T 7  is the ambient temperature.  It can be shown (Torrey and Whitmer  19U8) that for a point at the centre of the contact (9)  ^  c  ~-  8 X  where  H  is the thermal diffusivity of germanium.  If we take a = 10~^ c.m.  then c  1.2 The Phenomenon of Turnover An outstanding feature of the steady-state d.c. reverse currentvoltage characteristics of Ge point contact rectifiers, first noted by Benzer (19U9),  is the property of turnover.  That is, as the reverse current is  increased,the voltage drop across the diode goes through a maximum and thereafter decreases with increasing current, thus producing a negative resistance which persists up to the highest currents obtainable.  This turnover voltage, which  at room temperature may be anything from a few volts to several hundred volts, is observed to decrease with increasing ambient temperature.  Since the  current at turnover is relatively insensitive to such changes, the power at turnover decreases with increasing ambient temperature over a wide range (Benzer 19ii9).  This constitutes the important difference between the static reverse  characteristic of a crystal diode and the static characteristic of a thermistor; for a thermistor the turnover power increases with increasing ambient temperature (Becker, Green and Pearson 19U6), while for a diode i t decreases with increasing ambient temperature.  7.  Fig. 3 Form o f the r e v e r s e characteristics of a Ge p o i n t c o n t a c t r e c t i f i e r . /So  iHEj^fnAL  I n a t h e r m i s t o r , t u r n o v e r can be e x p l a i n e d on t h e b a s i s o f the r a p i d decrease i n s e m i c o n d u c t o r r e s i s t a n c e (R °< e x p ( b / T ) ) as t h e t e m p e r a t u r e i s r a i s e d by s e l f h e a t i n g .  Over t h e range o f i n t e r e s t , t h e i s o t h e r m a l c u r r e n t -  v o l t a g e r e l a t i o n f o r a t h e r m i s t o r a t a b s o l u t e temperature T i s c l o s e l y  given  by (10)  X  -  c V  -  t>/r b,c are c o n s t .  I f we assume Newton's l a w o f c o o l i n g , t h e t h e r m i s t o r w i l l l o s e h e a t t o t h e surroundings (ID  a t temperature T  such t h a t , i n s t e a d y s t a t e , I V  A  =: Qpnst.  From t h e s e we can show t h a t a t t u r n o v e r , t h e temperature o f t h e t h e r m i s t o r and t h e power d i s s i p a t e d i n i t w i l l be g i v e n b y (12)  d.  U3)  v.  -  ^  |  -  X.  - (£-  i  IX.?'  ( i f b >> T as i s usual for thermistors)  7? h  Burgess (1905) has pointed out that f o r a diode, similar arguments based on the assumption of an exponential decrease of contact resistance with temperature (Benzer 191*9; Bennett and Hunter  1951;  Billig  1951)»  are untenable,  since they predict a turnover power which increases with increasing  (1955), involving  A more complex model proposed by Armstrong  temperature.  ambient  non-Newtonian cooling through the Ge wafer, was also shown to be unacceptable for the same reason. 1)  In f a c t , Burgess showed that:  Any c h a r a c t e r i s t i c of the form  W  -Z" -  °  v <= * I'  \  •"•'//  c = const,  i s unacceptable since the requirements that both turnover voltage and turnover power should decrease with increasing ambient temperature are incompatible. 2)  Any c h a r a c t e r i s t i c of the form  (15)  g  JT-  (T)  which, on the assumption of Newtonian cooling f a i l s to predict ,the required behavior of turnover power, cannot be made to do so by the assumption of nonNewtonian cooling i . e . by assuming  (16)  y  ( T - T .  -f o r some m > 0.  He also suggested the following current c h a r a c t e r i s t i c s , J  (17)  .  C  /  /  /  +  f  l  —  T  &  ZL -L  (  Ce*f>  ,  /  (~  6  .  -  T  )  ^  (~ --r)  j  0  (-r -T) o  \  C  B  f  i  nCBA^l /  / V  ,  \  )  CBA  =  1  __  ±  9.  (where A, B, T  q  are constants) which, when taken together with Newton's law  of cooling  ) - A  (T-T„  (W)  IV  w i l l give the required behavior of turnover voltage and power; but he pointed out that there i s no existing r e t i f i e r theory which w i l l predict any of these current c h a r a c t e r i s t i c s . It w i l l be shown l a t e r that with c e r t a i n r e s t r i c t i o n s constants b^, b^,  on the ''  , c^ , the current c h a r a c t e r i s t i c  (which has a possible physical interpretation to be discussed l a t e r ) w i l l predict the observed behavior of turnover power with ambient That t h i s i s possible can be seen simply as follows. such that one exponential term determines contact temperatures,  temperature.  If the constants are  the temperature dependence f o r low  while the .other term dominates at high temperatures,  we  may write (for b^ > b^ )  (20)  X  -  4^)  c e  X / r  i  f o r small T  for large T Hence, as i n the thermistor case above, we w i l l have regions of almost quadr a t i c dependence of turnover power on ambient  (22)  (23)  71  *  *  temperature.  /fi,^  f o r small T  IZ'/siL,,  f o r large T  Hence, f o r appropriate vaiues of the constants, we see that i t should be possible (as indeed i t i s ) to obtain a curve which has dP^/dT^ < 0 over an  10.  appreciable range of T , as shown below.  1.3  The Scope of the present work The object i n the experimental  work was to obtain a set of accurately  reproducible s t a t i c d.c. reverse current-voltage c h a r a c t e r i s t i c s for a goldbonded diode over a range of ambient temperature, and the associated isothermals, i n an attempt to f i n d some mathematical representation, i n p a r t i c u l a r the two b model mentioned above, for the dependence of current on contact temperature. Further confirmation of t h i s model was  attempted by comparing the predicted  curve of turnover power vs. ambient temperature (obtained from the  constants  taken from constant-voltage plots) with that a c t u a l l y measured experimentally. An investigation was also carried out to see i f i t was p o s s i b l e , by pulse techniques, to measure the constant o f p r o p o r t i o n a l i t y ,  A  i n Newton's law of  cooling, and also the thermal relaxation time t of the whole diode.  11.  CHAPTER II MEASUREMENT OF THE REVERSE CHARACTERISTICS  2.1  Devices investigated. In t h i s investigation the following types of commercial point-  contact r e c t i f i e r s were examined: 1)  Sylvania type  1N5UA diodes.  These were representative of the older type of diode,, and had a tungsten rather than a gold cat whisker.  They were characterized by a  rather high turnover current, and a f l a t turnover c h a r a c t e r i s t i c i . e . a small rate of change of voltage with current, over a wide range of current, near turnover.  This l a s t property made i t impossible to determine the  current at turnover with an uncertainty of l e s s than 10$. 2)  Transitron type 1N6?A diodes.  These were of the gold-bonded type, and when f i r s t used exhibited current-voltage c h a r a c t e r i s t i c s as s a t i s f a c t o r y as the Hughes diodes mentioned below.  However, there seemed to be no stable reverse c h a r a c t e r i s t i c , as the  voltage at a given current decreased 1-5% each time i t was measured. 3)  Hughes type 1N67A diodes.  These gold-bonded diodes were by f a r the most s a t i s f a c t o r y units found f o r the present work, and were the only ones used f o r quantitative measurements.  They were characterized by a turnover voltage of about 100 -  125 v o l t s at room temperature, and a turnover current of the order of 1 mA. After the c h a r a c t e r i s t i c had been traversed one or two times, the measurements were reproducible with a discrepancy of l e s s than 1%. A l l of these units were encapsulated  i n glass containers.  12.  2.2  Measurement and maintenance of a constant ambient temperature The diode being studied was strapped to the bulb of the thermometer  with an aluminum c l i p , which ensured good thermal contact between the two. The thermometer was then inserted into a quart vacuum f l a s k f i l l e d with transformer o i l , u n t i l the bulb was near the centre o f the f l a s k .  The high  thermal capacity of the transformer o i l made i t possible to dissipate much more power i n the diode than could have been done i f i t were i n a i r .  Further,  brass f i n s were soldered to both leads of the diode to conduct away the heat generated i n the contact as e f f i c i e n t l y as possible.  Fig, 5 The arrangement f o r experimental purposes.  Even though the diode was i n a vacuum f l a s k , the ambient temperature was observed to f a l l by as much as 5 G° during a current-voltage run at a high temperature  ( i t took about hS minutes to do such a run).  Hence i t was  necessary to b u i l d an electronic temperature c o n t r o l l e r (see Appendix). to the high negative c o e f f i c i e n t of resistance of the temperature  Due  sensitive  device (a small piece of n-type Ge with ohmic contacts), i t was not at a l l d i f f i c u l t to keep the diode within l / l O of a degree of any desired temperature. F i n a l l y , the o i l was kept c i r c u l a t i n g , v e r t i c a l l y as well as h o r i z o n t a l l y , by the i n s e r t i o n of a h e l i c a l glass s t i r r i n g rod.  With t h i s arrangement no  fluctuations due to temperature changes were observed.  13.  2.3  Selection and forming of diodes. In order to f a c i l i t a t e selection of the diodes f o r experimental  purposes, a dynamic display c i r c u i t was set up (Fig. 6). The diode was subjected to a s i x t y cycle a.c. voltage, the amplitude of which could be varied, and a small sampling r e s i s t o r was inserted i n series with the diode to give a signal proportional to the diode current. was  -A A/v~ v  2 o KM-  ->/y&-  O - / o o K-f2-  When the c h a r a c t e r i s t i c  P la.-fas  //o y/a.c-  ac. 5~ K -A-  Fig.  " Ays /•<? r< s  *£vfcA'5.c  6  (a) C i r c u i t used f o r dynamic display. (b) Typical dynamic display obtained on the C.R.T.  Vat  examined on an osc'illiscope, a c e r t a i n amount of h y s t e r i s i s was always present i n the reverse bias region, which was probably due to a relaxation e f f e c t i n the i n t e r n a l mechanism of the diode.  However, i t was found that the path  traversed when the reverse bias was increasing was almost i d e n t i c a l to the steady state d.c. c h a r a c t e r i s t i c .  Since the l e s s robust units "broke down"  almost immediately when subjected to this sort of treatment (the back resistance decreased and the turnover current increased to a p r o h i b i t i v e value), t h i s c i r c u i t provided a r e l a t i v e l y simple method of selecting a rugged diode with suitable turnover properties (a well defined turnover current, and a turnover power of less than 1^0 mW). Since the turnover current could not be determined with an uncert a i n t y of less than $% with the best diodes obtainable (and to considerably  lii. more than t h i s with the Sylvania diodes), i t was decided to see i f i t were possible to improve t h i s feature of the c h a r a c t e r i s t i c by reforming the contact i . e . by passing a large current pulse through the diode.  The method  used was quite simple (Fig. 7), and consisted of discharging a condenser through the diode, while observing i t s current-voltage c h a r a c t e r i s t i c on an oscilliscope.  A variable r e s i s t o r was inserted i n the c i r c u i t to control  the amount of power dissipated i n the diode, and a reversing switch was i n s t a l l e d to permit pulses of either p o l a r i t y to be applied. variable r e s i s t o r at lKft  , a series of three 300  With the  pulses (two i n the  forward d i r e c t i o n and one i n the reverse) apparently broke the a i r seal on one of the u n i t s , since i t s reverse c h a r a c t e r i s t i c decayed over a period of two days,until i t became ohmic with a resistance of 500 ohms.  Since t h i s  was the only e f f e c t noticed on any of the diodes so treated, the attempt at forming was abandoned.  Fig. 7 C i r c u i t used to pulse diodes.  Plate II  The reverse current-voltage c h a r a c t e r i s t i c s of the diode used at- various ambient temperatures.  15.  2.h  Static d.c. measurements The method used to obtain the s t a t i c d.c. reverse current-voltage  plots was quite simple.  Using the c i r c u i t of F i g . 8, the voltage drop across  the diode f o r a given current through i t was measured over a current range of 1=  .1 - 3 mA., the diode being allowed to reach a steady state each time the  current was increased. temperatures  This process was repeated f o r a number of ambient  between 25 and 85°G.  A t y p i c a l set of c h a r a c t e r i s t i c s i s given  i n Plate I I . With the Hughes type 1N67A used, any such measurements were reproducible to within 1% provided the following precautions were taken:  Fig. 8 C i r c u i t used f o r d.c. measurement s.  1) The temperature of the contact was not raised above the maximum value i t had had before the measurements were o r i g i n a l l y made. 2) The power dissipated was not greater than a c e r t a i n c r i t i c a l value (about 350 mW. with the diodes used) since the measurements were o r i g i n a l l y made.  That i s , i n spite of the precautions taken under 1) above, the  c h a r a c t e r i s t i c s would change i f the power dissipated i n the diode was greater than 350 mW. Hence, before any quantitative measurements were made, the diode current was raised to h mA., at an ambient temperature of 85°C. no d i f f i c u l t i e s were encountered  After such a "running-in"  due to c h a r a c t e r i s t i c s changing, provided  16. precaution 2) above was taken. A test was made to determine whether or not the c h a r a c t e r i s t i c s were dependent upon the impedence of the source feeding the diode.  Due to  the s t a t i s t i c a l nature of avalanche breakdown,one might expect t h i s to be so i f avalanche breakdown played an important part i n the turnover phenomena (Drews 1957).  Although the series r e s i s t o r was increased from  l$Kft to  lliOKft , no changes i n the c h a r a c t e r i s t i c s were noticed.  PL A Vg  s  Fig. 9 C i r c u i t used for simultaneous a.c. and d.c. measurements.  -A/VW-  'ot<Ji.  In an e f f o r t to obtain a more accurate measurement of the current at turnover, the c i r c u i t of figure 9 was set up. the a.c. bridge was balanced.  With the diode shorted out,  Then the diode was put i n the c i r c u i t and the  bridge brought back to balance by increasing the reverse bias on the diode. For  t h i s purpose a small a.c. sweep voltage was used i n an e f f o r t to stay on  the " l i n e a r " portion of the diode c h a r a c t e r i s t i c .  In t h i s way the current,  and voltage, at the point of zero a.c. resistance could be measured d i r e c t l y . However, due to the e f f e c t of some relaxation time of the diode, t h i s point lay at a current greater than the d.c. turnover current.  It moved towards  the d.c. turnover point as the bridge frequency was lowered, as one might expect, but at the lowest frequency available (10 cps.) i t was away.  s t i l l a good distance  Hence, t h i s technique could not be used, and i t was not found possible  broke-,  do-^i-vi  .-/-he  i-ry-to  S<i-rn  4~ -f he -  A / T  c c '  So  r-  \  -  \  V Io -»  = 51o°K 5" 1  •OOiSo  r *«  "i +0  .5a  £<i  7»  Plate I I I Reverse current vs. temperature f o r fixed reverse bias voltages on the diode used.  7r IT ('«  -I  17. to determine the turnover current with an uncertainty of l e s s than 5"$. F i n a l l y , an attempt to find the form of the temperature dependence of the current c h a r a c t e r i s t i c was made.  Using the same setup as i n F i g . 8,  plots of current vs. ambient temperature were made f o r several d i f f e r e n t voltages over as wide a range of ambient temperature as possible.  The power  was kept low enough so that i t was possible to neglect contact heating, and thus write T ^ T . a  Typical curves are given i n Plate I I I .  18.  CHAPTER I I I THEORY AND PREDICTIONS OF THE TWO ACTIVATION ENERGY MODEL  3.1  Surface leakage current and the "Two B" model. It has been shown (McWhorter and Kingston 195UXthat excess  reverse current i n p-n junctions can be caused by an n-type surface cond u c t i v i t y layer on the p-side of the junction.  Christensen (195k) has also  demonstrated that i t i s possible to produce both n-type layers on the p-side, and p-type layers on the n-side of a p-n junction, by suitable surface t r e a t ment.  We s h a l l consider the leakage current produced by such a p-type layer  on the surface of the Ge wafer i n a point-contact diode (Fig.10  )•  In order to simplify the problem, we s h a l l assume that the surface layer of thickness t has a constant r e s i s t i v i t y j> , and that the flow of current across the surface b a r r i e r i s described by the simple diode (2k)  ->  a  ( e  equation  - '  Fig. 10 Surface conduction layer on a p.c. r e c t i f i e r .  <S e The voltage drop across a c y l i n d r i c a l s h e l l of the surface layer w i l l be given by  c/A  (25) °1 a  t  19.  where I i s the current flowing through the surface layer at radius r f o r the applied voltage V.  Due to leakage across the surface barrier, the current  flowing r a d i a l l y across the layer w i l l decrease i n a c y l i n d r i c a l s h e l l by <~ / / '. T~  •-  (26) where J  Q  -2~<±  zr {^e  cA'c  i s the saturation current/cm  of the surface junction.  For large reverse voltages i t i s reasonable radius js/j  - i  u  to assume that even at the outer  and hence we can write  (27)  From these expressions we  J~  -  -  dZ  c/t  u  find  V"  (28)  --  y_'  +  /l &  ft  which can be immediately integrated to give  *i V'  (29)  +  z  C  * t Hence (30)  X  -  7rJr  ( h  z  o  - V  )  since the current must s a t i s f y the boundary condition We see that the t o t a l leakage current given by 1(0) (31)  ZT  L  -  ~rr J ~  c  U  I(tJ  - o  is s m c e  h> >>  a  We vrould not expect that t h i s leakage current should have the same activation energy as the bulk current, and i n f a c t , experiments on S i formed junction diodes enery i s 1.20 ev.  (Cutler and Bath 1957)  have shown that while the bulk a c t i v a t i o n  ev., the a c t i v a t i o n energy for the surface current i s only  0.62  20.  Since the temperature dependence of current at constant voltage can be expressed quite s a t i s f a c t o r i l y as the sum of two exponential terms (Plate III)  ,  ,  -r .Z~-  (32)  -t>.}r +  -J* -! " 7  a. e t  a,, a fens o f V  1  o. c  1* 2  0  z  b> b 1  a >a L  2  2  we postulate a current c h a r a c t e r i s t i c o f the form  (33)  h> > L  + A(s)  - A ( ' ) k '  In view of the argument given above, we can interpret kb^ as the bulk activation energy and kb^ as a surface activation energy (where k i s 'Boltzmann's constant).  Since at turnover the voltage i s constant, i t  should be s u f f i c i e n t f o r the present investigation into the behavior of turnover power with ambient temperature,  (3U)  f  +  \  -i, (c,G  7  to consider IT  + C\  -t,i  e  Jr \  )  The more general form (33) also predicts a decrease of turnover power with increasing ambient temperature,  but the algebra becomes quite complex and  nothing e s s e n t i a l l y new i s found. 3.2 General Analysis of the "Two B" model If the diode current i s given by (3U) above, then the two c o n t r i butions to the t o t a l current w i l l be equal at a temperature only i f -^> 2* c  c  A  s  stated i n section 1.2 above, t h i s i s necessary f o r turnover  power to decrease with increasing ambient temperature. law o f cooling, then i n the steady state;  If we assume Newton's  21.  (35)  ~r>  ~K <-  then  /) / / *• I d /  (36) a.  and hence from (3U) by d i f f e r e n t i a t i o n with respect to I  (37)/  ^  A t v ) T  /\/+Td\f \  2  \ ( 6 c, e ''' +  b c e. '  6  Lt/  t  l  z  clZ  -h dl Since f o r turnover we have  cd/ (38)  '  d  o  I  we f i n d  rf  (39)  -  C---7;)  ±  A_f_,5.  A£i.  ~ ts. /7~.  ••  £  6  A  ; T  If we set  (Uo)  / B ^ T )=  j^.c, e  we f i n d on d i f f e r e n t i a t i n g  hc  *  t  z  e  ( 39) that z  da) / - ±  ^  dT  '  '  ^  >.  J  d.  From (35) we also have  (u2)  J  ' a.  So f o r */ dP  - < o we must have o''*/  >  I HT  ' ^'o,  function of T i f c > c 1  2  /.  ), and T > T Q  Since  > 0 (B i s a monotone increasing w-,-  ' a  we must have  22.  (U3)  (  7  ~  > I  ) f ^ *  for  ^  <  0  Since -  _£LiL*_  £A,.r_Ju_l  at  If we evaluate t h i s at T =  T , which i s very close to the point where  Q  i s a maximum, we  find  (1*6) Hence f o r (^3)  to b e . s a t i s f i e d  >  Oxi)  **}>(+  til±L  )  or  This i s the necessary and s u f f i c i e n t condition for  d  P^  j'a'71_  <o  with t h i s  model.  3*3  Comparison of t h e o r e t i c a l r e s u l t s with experiment A straight substitution of the values of b^ and  obtained from  the plot of current at 50 v o l t s vs. temperature (Plate I I I ) , into equation (U8)  gives us the condition  that  23. -T  <  j 3/ /  3  £  "  f o r b i - 7U00°K  c^  b --10$0°K  K  2  i n order that turnover power can decrease with increasing ambient  temperature.  Since f o r t h i s diode  we see that the model i s consistent with regard to t h i s i n e q u a l i t y i . e . a diode e x h i b i t i n g ^5If now,  <o  does s a t i s f y the required r e s t r i c t i o n .  we take the parameters b-^, b , and T , obtained from the 2  x  constant-voltage p l o t of Plate I I I , and, from these, construct a curve of turnover power vs. ambient temperature, we fulness of the model.  F i g . 11 shows the v a r i a t i o n of the function B(T) f o r  the p a r t i c u l a r diode used.  F i g . 12 shows the v a r i a t i o n of contact temperature  at turnover, T , with ambient temperature; Q  the graph of F i g . 11.  s h a l l be able to assess the use-  obtained from equation (39) using  From t h i s relationship between T  against ambient temperature.  Q  and T  a  Such a p l o t i s given i n Plate IV.  we can plot  We  see  immediately the great s i m i l a r i t y between the shape of t h i s curve and the curve found by Benzer (19h9) f o r the v a r i a t i o n of turnover power i n the range -100°C <T <100°C. a  Moreover, by f i t t i n g the one adjustable parameter A, we  are able to get a remarkable agreement between the shape of t h i s predicted curve, derived from the isothermal c h a r a c t e r i s t i c , and the actual turnover power measured.  This consistency supports the use of such a model to describe  the phenomenon of turnover.  Plate IV Derived curve of turnover power vs. ambient temperature " f o r the diode  used.  2h. CHAPTER IV MEASUREMENT OF THE CONTACT TEMPERATURE AND THE THERMAL TIME CONSTANT U.1  Transient effects expected i n a diode. Consider a diode i n a steady state at ambient temperature T^, with  a voltage drop V-^ across i t , and a current 1-^ through i t , such that  If t h i s voltage i s suddenly decreased ( i n a time very much l e s s than the thermal time constant t of the diode) to ^2«V^, we should expect the current to behave i n the following manner.  F i r s t of a l l , i t w i l l f a l l to a value I  determined by the o r i g i n a l contact temperature T^ i . e .  (50)  T  7V  z  Al.V.)  +  The contact temperature w i l l f a l l o f f exponentially with decay t i m e t , by virtue of the equation  —  (51)  -  ~  ^ ~" ) t  AP  7  '  Since ^ I ^ \^1*  '^  le c u r r e n  by  -  71  CT-T*, )  1  ^  t  also f a l l o f f , but i n a manner detennined  J-  u n t i l steady state i s again reached.  (52)  Then  T.  f(S<~z)  T^-r  t  A-r^x  This f a l l o f f of current w i l l i n general not be exponential i . e . we w i l l not be able to f i n d a 1 such that the i n i t i a l f a l l of current w i l l be given by  ^  (53)  '  However, i f  d  _ r  X<*  (55)  dtcz)  and also  (  -n  Tj  /  (5-1) so  j  C'  t  (51*)  d  ^  from -  7 "  2  T  x JT,' -  (51)^(53)  It  jxF.  -It— vwvv  zf'o  a.  (a)  -vw^— i—"JOv-  +  / 3  £  /  >S/<JL  (b)  Figure lU  C i r c u i t s used to measure thermal time constant.  25. Hence, even though current i s a r a p i d l y varying function of temperature, i t i s possible f o r ir' to be much greater or much l e s s than t .  6c  ho-Jturi'  o -£  j  Cert  C t  -/-cm p .  ex/>ccrccf  de  F i g . 13 Voltage, temperature, and current wave forms expected i n pulse experiments.  Ca->J  The expected behavior of current i s i l l u s t r a t e d i n F i g . 13. By observing t h i s transient i t i s possible to determine T , A and X , i f the function i s known, as follows: 1)  T^ can be determined immediately from I^ using the constant  voltage  plot (-£-). Since I. , V , and T are known, a knowledge of T determines A, through X X 3. X Newton's law of cooling. 2)  3)  By making quantitative measurements on the current decay curve, i t i s  possible to reconstruct the contact temperature decay curve, by using the constant voltage p l o t .  From t h i s X. can be r e a d i l y obtained.  _J 5b  Plate V  1  I  s+  6£  -f-  7JT  The v a r i a t i o n of current at 1 v o l t , with temperature.  7"  26.  h»2  Attempted Pulse Measurements ofx and A The c i r c u i t of F i g . lii(a) was setup i n an e f f o r t to observe these  transient phenomena.  Seventy v o l t pulses of the order of  superimposed on a constant 1 v o l t bias.  10-100  ^*.sec. were  When the desired effects were not  found, the c i r c u i t of F i g . lli(b) was set up i n an e f f o r t to shorten the f a l l time of the voltage pulse.  Although t h i s f a l l time was reduced to 10  ^xsec.  no transient e f f e c t s were observed. 'This i s not too surprising  since i f we examine the constant-voltage  p l o t , we see that, to a f a i r approximation  over the range  50°C <  T  <100°C.  We see from Plate II that at an ambient  temperature of 2$°C the current flowing w i l l be 0.1 o . ince A i s of the order of 250 r i s e of the order of 2°C. If  X  ma. f o r a 70 v o l t pulse.  C/watt, t h i s w i l l produce a contact temperature  So we would expect t' to be of the order of  were of the order of 1 ^.sec. (Sec. 1.1  1:' just at the l i m i t of d e t e c t a b i l i t y . must have an upper bound of 1 usee.  It.  above) t h i s would put  Hence, we can conclude that  t  .  _  0  Plate VI  9  C i r c u i t diagram f o r an electronic temperature regulator  APPENDIX  An electronic temperature regulator For the purpose of maintaining a constant ambient temperature i n the i n t e r i o r of the vacuum f l a s k , i t was necessary to construct a rather sensitive temperature regulator (Plate VX).  The temperature sensitive device  used was a small piece of Ge. with ohmic contacts which was placed as close to the diode as possible.  This device was one arm of a 60 cycle 'Wheatstone  bridge; two of the remaining arms were f i x e d r e s i s t o r s of the same size .as the room temperature resistance of the Ge, and the l a s t was a.resistance •box by which the balance temperature of the bridge could be adjusted. . The signal from the bridge was grid of a phase sensitive detector V2.  amplified i n VI and put on to the The plate supply of this tube was  ••t a.c. voltage i n phase with the voltage supplied to the bridge.  Since  .-.he phase of the signal coming from the bridge changed as the bridge passed •irough balance, the voltage drop across V2 changed continuously as the bridge went through balance.  This voltage was then r e c t i f i e d i n V3 and  f i l t e r e d to give a d.c. voltage which was used as a bias f o r a Schmidt t r i g g e r circuit. As the o i l bath cooled down the voltage at point A would drop u n t i l i t reached 80 v o l t s .  At t h i s time Vit would cut o f f and V5 would begin to  conduct, thus closing the r e l a y and turning on the heater.  As the o i l  .warmed up the voltage at point A would increase u n t i l i t reached 82 v o l t s , at which point Vlj would again conduct and V5 would cut o f f , thus turning o f f the heater.  This voltage swing, which determined the s t a b i l i t y of the o i l bath  temperature was minimized by adjusting the plate load of Vl|. The swing i n ambient temperature of the o i l was l/lO°C f o r Ta long term d r i f t never exceeded 1°C i n eight hours.  observed  5>0°C, and  the  BIBLIOGRAPHY Armstrong, H.L. 1953, J . Appl. Phys., 2ij., 1332. Becker, J.A., Green, C.B., and Pearson, G.L., 19h7, B e l l . Syst. Tech. J . , 26, 170. Bennett, A.I., and Hunter, L.P., 1951, Phys. Rev., 81, 152. Benzer, S., 19ii9, J. Appl. Phys., 20, 80iu B i l l i g , E., 1951, Proc. Roy. Soc. A, 207, 156. Burgess, R.E., 1955, Proc. Phys. Soc. B, 68, 908. Christensen, H., 195U, Proc. I.R.E., U_2, 1371. Cutler, M., and Bath, H.M., 1957, Proc. I.R.E., h_5, 39. Debye and Conwell, 1952, Phys. Rev., 87, 1131. Drews, R.E., 1957, (Thesis, U.B.C. Physics Dept.). Haynes and Shockley, W., 1951, Phys. Rev., 81, 835. McCarthy and Ballard, 1955, Phys. Rev., 99, 110U. McWhorter,  A.L., and Kingston, R.H., 195U, Proc. I.R.E., U2, 1376.  Ryder, E.J., 1953, Phys., Rev., 90, 766. Shockley, W., 1951, B e l l . Syst. Tech. J . , 30, 990. Torry, H.C., and Whitmore, C.A., 19^8, "Crystal R e c t i f i e r s " (New York: McGraw-hill).  

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