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Properties of thin yttrium oxide dielectric films. Riemann, Ernest B. 1971

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PROPERTIES  OF THIN YTTRIUM  OXIDE D I E L E C T R I C  FILMS  by  ERNEST  B.  Eng.  (Physics)..,  A THESIS  B.  RIEMANN  McMaster  SUBMITTED IN  University,  P A R T I A L FULFILMENT  THE REQUIREMENTS FOR THE DEGREE  MASTER  in  OF A P P L I E D  the  We a c c e p t  this  Research  of  as  conforming  to  standard  Supervisor.  Members  of  Head  the  of  OF  Engineering  thesis  required  the  Committee  Department  Members  of  the  of E l e c t r i c a l THE U N I V E R S I T Y  OF  SCIENCE  Department  Electrical  1969  Department Engineering  OF B R I T I S H  December,  1971  COLUMBIA  the  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r  an advanced degree a t the U n i v e r s i t y 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 f r e e l y  a v a i l a b l e f o r r e f e r e n c e and  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e f o r s c h o l a r l y purposes may by h i s r e p r e s e n t a t i v e s .  study.  c o p y i n g of t h i s  be g r a n t e d by the Head of my  thesis  Department or  I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n  of t h i s t h e s i s f o r f i n a n c i a l  g a i n s h a l l not be a l l o w e d w i t h o u t  written permission.  Department o f 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  'ABSTRACT A study has been made of the properties of thin yttrium oxide dielectric films prepared by the electron beam evaporation of high purity Y  2 3 powder* U  Films deposited on freshly cleaved NaCl crystals and on polished n-type silicon were examined in the electron microscope.  The specimens were o  found to be polycrystalline, with a crystal size of the order of 100 A. The structure was found to be essentially the same as found for bulk 2^3* Y  D.C. conduction measurements were made on films of various thicknesses. The characteristics \rete found to be bulk-limited, with the conductivity decreasing at lower pressures.  An activation energy of 0.6 eV was found.  The conduction mechanism was believed to be Poole-Frenkel emission of electrons from donor centers into the ^O^ conduction band.  The donor  centers were believed to be i n t e r s t i t i a l yttrium atoms rather than oxygen vacancies because of the pressure  dependence observed in conductivity.  Step response/measurements were,made, and the results explained on the oasis of a loss peak with a most probable relaxation time of 200 seconds.  The relaxation of oxygen atoms dissolved in the anion defective  Y^O^ lattice was assumed to be the mechanism.  The results of step response  and A.C. bridge loss measurements indicated that different relaxation mechanisms^are dominant i n different frequency ranges. 3tnte:rnal photoemission measurements were made on Al-Y^O^-Al sandwiches.  The energy barrier between the electrodes was found to be trapezoidal,  with barrier heights of 3.14 and 3.72 eV.  TABLE OF CONTENTS  Page  ABSTRACT.....  •  *  TABLE OF CONTENTS  i i  LIST OF ILLUSTRATIONS  .  iv-  ACKNOWLEDGEMENT  vi  I.  Introduction........  II.  Sample Preparation  ."  I I I . Electron Microscopy of Thin  IV.  •• i • 3  Films.  7  1.  Introduction  7  2.  Procedure  3.  Results..  4.  Analysis  12  5.  Discussion  17  •  •• 8  Conduction i n Thin Y ° 3 Films 2  1.  Introduction. . . .  19  2.  Experimental procedures.  27  3.  Experimental results  27  4. . Discussion... V.  34  Step Response and Loss Factor i n ^2 3 U  1.  Introduction  44  2.  Experimental procedures  46  3.  Results  4. VI.  8  3.1  Step response....  46  3.2  Loss factor  52  Discussion..  52  B a r r i e r Height Determination by Interanl Photoemission..... 1.  Introduction  54  2.  Experimental Procedures  57  3.  Experimental Results  .".  • • 58  Page 4.  Discussion  64  APPENDIX.... REFERENCES  67 .'  71  LIST  OF I L L U S T R A T I O N S Page  II.  1  MIM  Structure  6  II.  2  MIS  Structure  6  III.  3  Freshly  III.  4  Recrystallized . Y ^  III.  5  Diffraction  structure  III.  6  Diffraction  pattern  III.  7  Reflection  Y 0  deposited  2  .  film  3  film of  . .... 9  : recrystallized  after  further  electron diffraction  9  film  .  9  recrystallization.  from ^ O ^  on n - t y p e  10 polished  silicon  10  III.  8  Diffraction  III.  9 Jh +k +i 2  2  2  pattern  vs.  ring  of  Au f i l m  diameter  ...  1  Trap p o t e n t i a l w e l l . .  IV.  2  Poole-Frenkel lowering  IV.  3  Energy  IV.  4  D.C.  IV.  5  Log  IV.  6  Determination  IV.  7  Effect  IV.  8  Determination  IV.  9  D.C.  IV.  10  Determination  of  6.....  IV.  11  Determination  of  activation  IV.  12  Reproducibility  of  V.  1  Al-Y^O^-Al  step  response  charging  V.  2  Al-^O^-Al  step  response  discharging  V.  3  Log  V S . log  :  I  vs.  of  /V  for of  Q  of  of  trap  energy b a r r i e r  Simmons'  ..  22  model  24  characteristics different  28  temperatures  8  polarity  Conduction  (I/I )  21  diagram for  Conduction  13  for Y ^  TV.  band  10  4680  29  A )  . . reversal  activation at  (d =  on D . C .  (t/r ) Q  conduction.  32  energy  Low P r e s s u r e  D.C.  30  33  (p = 50u)  35 36  energy..  conduction  for  37  current  (p = 50  uHg)  current.  after  38 47  current.  discharge  ....  48 3V  step.....  50  Page V.  4  Dielectric  losses  vs.  VI.  1  Simplified  MIM  VI.  2  Monochromator  calibration  VI.  3  Monochromator  intensity  VI.  4  Monochromator  calibration  VI.  5  Photoresponse  of  VI.  6  VI.  7  band  frequency  51  structure  54  curve  (deuterium  calibration (200 0 - 5 0 0 0  source)  (visible  56  range)  59 60  A°)  A l - Y ^ - A l  61  Fowler P l o t s  for A l - Y ^ - A l  63  Y 0  shape  64  2  3  barrier  A.l  M0S  C Hysteresis  (f=0.1Hz)  68  A.2  M0S  C Hysteresis  (f=0.05Hz)  69  A. 3  MOS  C Hysteresis  ( f = 0 . 0 1 H z ) . .•  .  v  70  ACKNOWLEDGEMENT  I  wish  encouragement  to  and g u i d a n c e  Grateful Council  in  the  acknowledgement  for supporting Thanks  D.C.  t h a n k my r e s e a r c h s u p e r v i s o r ,  are  this  also  course is  work w i t h due  conduction measurements,  t o Mr. and M i s s  vi  of  given  this  L.  L.  Young,  his  Research  Scholarship.  Wong f o r Morris  for  investigation.  to the N a t i o n a l  a Science B.  Dr.  doing for  some  typing  of this  the thesis.  •I.  INTRODUCTION  High q u a l i t y thin d i e l e c t r i c films are v i t a l to the f a b r i c a t i o n of many s o l i d state devices.  The films provide i n s u l a t i o n , and are used for  d i f f u s i o n masking, surface passivation and hermetic sealing. Si-jN^, AlpO^,  T a 2  ^5  anc  To date,  Si0  2 >  * evaporated SiO have been the p r i n c i p a l d i e l e c t r i c s  used i n e l e c t r o n i c devices.  It i s desirable to f i n d other  dielectric  materials that give better performance, higher r e l i a b i l i t y and lower cost. A number of attributes are d e s i r a b l e i n a d i e l e c t r i c used for device f a b r i c a t i o n . Some of these are: (1)  Good i n s u l a t i n g properties (low pinhole density, high breakdown f i e l d strength-, high p e r m i t t i v i t y , low  losses.)  (2)  Low  i o n i c mobility at adequate operating f i e l d s and, temperatures.  (3)  Low  surface-state density when deposited on semiconductor material.  (4)  Ease of production. In this t h e s i s , the properties of thin yttrium oxide  films have been investigated.  dielectric  Previous work by C a m p b e l l ^ had shown these  films to have low losses and i n t e r e s t i n g d i e l e c t r i c properties. In the next chapter, the techniques  used i n sample preparation  are discussed. Chapter III i s concerned with the study of thin yttrium oxide films by electron microscopy, i n order to determine t h e i r physical structure. Chapter IV deals with the D.C. films, and how  these properties may  conduction properties of these  be understood by considering the structure  of the 2 ° 3 c r y s t a l l a t t i c e . Y  In Chapter V, the r e s u l t s of step response and A.C. are given.  loss measurements  2  Chapter VI the Al-Y^O^ i n t e r f a c e Finally, for  in  deals  with  the  i n Al-Y^O^-Al Chapter  f u r t h e r research are  VII  given.  energy  barrier height  determination  at  devices.  the  concluding  remarks  and  recommendations  •  I I , SAMPLE PREPARATION  The y t t r i u m o x i d e f i l m s were e v a p o r a t e d i n an e l e c t r o n beam apparatus w i t h a 1 0 - i n c h low as 10 ^ t o r r w i t h o u t 9kW w a t e r - c o o l e d  d i f f u s i o n pump c a p a b l e o f r e a c h i n g p r e s s u r e s l i q u i d nitrogen cooling.  e l e c t r o n gun p r o v i d e d  the compressed Y^O^ powder.  as  A Brad-Thomson t y p e 776 W  t h e e l e c t r o n beam used f o r h e a t i n g  I t was p o s s i b l e t o a p p l y beam powers o f up t o  800 w a t t s ( f o r 20 kV a c c e l e r a t i n g v o l t a g e and 40 ma beam c u r r e n t ) t o an a r e a 2  as s m a l l as 25 mm. Campbell^. boron n i t r i d e  .  The e v a p o r a t i o n  p r o c e d u r e was s i m i l a r t o t h a t used by  99.99% p u r i t y y t t r i u m o x i d e powder was packed f i r m l y i n t o a c r u c i b l e before  i n s e r t i o n i n t o t h e vacuum system.  The  m a t e r i a l was o u t g a s s e d f o r f i v e minutes w i t h a low power e l e c t r o n beam. -5 When t h e vacuum r e a c h e d 1 X 10 t o r r , oxygen was b l e d i n t o t h e system and _5 the p r e s s u r e was h e l d a t 5 x 10 valve.  torr by t h r o t t l i n g back t h e h i g h vacuum  The f i l m t h i c k n e s s was m o n i t o r e d d u r i n g e v a p o r a t i o n by d e p o s i t i n g  Y^O^ s i m u l t a n e o u s l y 5 MHz r a t e .  on t h e s u b s t r a t e and a q u a r t z c r y s t a l o s c i l l a t i n g a t a  The mass d e p o s i t e d  on t h e c r y s t a l d e c r e a s e d t h e o s c i l l a t i n g  f r e q u e n c y , w h i c h was mixed w i t h t h e o u t p u t o f a v a r i a b l e o s c i l l a t o r s e t near 5 MHz.  The f r e q u e n c y d i f f e r e n c e was a l i n e a r f u n c t i o n o f f i l m  assuming c o n s t a n t  f i l m density.  The c o n s t a n t  o f p r o p o r t i o n a l i t y was found  by measuring t h e t h i c k n e s s o f a number o f d e p o s i t e d The  thickness,  films with a Talysurf .  equation d * 3.24Af  where d = f i l m t h i c k n e s s  (&)and Af = change i n f r e q u e n c y ( H z ) , was found t o  be a c c u r a t e w i t h i n 10% by comparison w i t h T a l y s u r f measurements. P o s t - d e p o s i t i o n t h i c k n e s s measurements were made by T a l y s u r f o r A  Made by T a y l o r Hobson L t d .  Angstrometer. The T a l y s u r f m e c h a n i c a l movement  of  is  a mechanical  a stylus  The A n g s t r o m e t e r interference be m e a s u r e d reflecting  with  measures  of  monochromatic  light  and  a FlzeaU flat  in  a l u m i n u m was  measurement.  deposited  The t h i c k n e s s  is  t  H film  D  = distance  B o t h methods  contact with on  given  ambient hours  for  at  between  crucible  surface  of  substrate  considered  deposition  the  films  the  A layer  film  to  the film  of  to  highly  facilitate  by  _ d  _X  D  2  (1)  during  evaporation. P  o W  position of  ^  e r  a n c  the  substrates  and s i l i c o n w a f e r s .  were  about to  found  to  +100  JL  cool  slowly  then baked  encountered with  in  the  of  c o n t r o l l e d by  the  air  first  be s p a t t e r i n g  T h i s was  ^ beginning  over  to  were a l l o w e d  The f i l m s  T h e c a u s e was  Two t y p e s glass  caused by  between  film.  insulating  to be a c c u r a t e  Some p r o b l e m s w e r e  t h e ^2^3 into  the  plane.  1  h a d many p i n h o l e s . the  5890 i )  amplified  fringes  f i f t e e n minutes.  150°C.  the  a reference  displacement  (Na y e l l o w ,  the  step  were  After  to  measures  thickness  d = fringe X = 5890  respect a fringe  .  where  device that  evaporation,  in  for  an  sixteen  films,  material  first  oxygen  which from  fusing  then r o t a t i n g  the the  cruicible. were  used,  Dottf C o r n i n g  The f o r m e r were c l e a n e d w i t h  7059  propyl  aluminosilicate alcohol,  chromic o  acid  and d i s t i l l e d w a t e r ,  t h i c k was system.  evaporated Aluminum,  onto  indium  then the  dried in substrate  air. in  A metal  an E d w a r d s  and g o l d were u s e d .  film  typically  diffusion  pump  The 99.999% p u r i t y  Al  2000  A  vacuum wire  was cleaned i n KOH  s o l u t i o n before placement on the tungsten heater w i r e .  The aluminum was melted c a r e f u l l y and a small quantity was evaporated w i t h the shutter i n place between the heater and substrate. to b o i l o f f .  This allowed i m p u r i t i e s  The shutter was opened f o r the evaporation, then shut again  before a l l the aluminum had evaporated to minimize the evaporation of tungsten and other i m p u r i t i e s from the heater wire. high as 1500 2/min were found to give good f i l m s .  Evaporation rates as The thickness was  monitored w i t h another quartz c r y s t a l o s c i l l a t o r . S i m i l a r precautions were used i n evaporating the other metals,  except  that propyl a l c o h o l was used f o r cleaning. Y^O^  f i l m s of varying thicknesses were then evaporated onto the metal  f i l m s , using deposition rates i n the 100 to 1000 & per minute range.  Higher  rates were found to y i e l d h i g h l y stressed f i l m s that cracked on c o o l i n g . Metal counterelectrodes of various areas and thicknesses were then evaporated onto the oxide f i l m .  For i n t e r n a l photoemission  s t u d i e s , the  counterelectrode f i l m s were made between 100 and 150 A* t h i c k .  For other  measurements, more durable counterelectrodes of s e v e r a l thousand angstroms thickness were employed. The s t r u c t u r e s discussed above are i l l u s t r a t e d i n F i g . 1. The other substrates used were 0.3-0.6ft-cm n-type p o l i s h e d s i l i c o n wafers one inch i n diameter, purchased from the Monsanto Company. oxide f i l m s were evaporated onto the s i l i c o n s l i c e s as before.  Yttrium  A l a y e r of  antimony doped gold one to two thousand angstroms t h i c k was evaporated onto the unpolished (reverse) s i d e of the wafer.  The antimony was d r i v e n i n t o the  s i l i c o n by d i f f u s i o n at 400°C i n a hydrogen  atmosphere of 500 mm Hg pressure  + f o r f i v e minutes.  The r e s u l t i n g h e a v i l y doped n  contact t o be made to the s i l i c o n .  r e g i o n permitted ohmic  6  metal  7059  glass  substrate Fig.  MIM  1  Structure  metal  n  type  silicon  wafer  "+  -  /  AuSb Fig. MIS  2  Structure  counterelectrodes  counterelectrode  7  III.  ELECTRON MICROSCOPY O f  THIN.Y 0  FILMS  Introduction  1.  A polycrystalline which  it  can be  shown  material  yields  = diffraction E camera  Lx d  ring  Bragg's  spacing  law  n  E an i n t e g e r  6  E angle  of  for  5  in  crystal  diffraction  the  a  o  is  lattice,  indices  the  {hkl}  lattice  Combining  sin  (1)  lattice .  is where  6,  incident the  (2)  beam and  the  crystal  interplanar  spacing  ik  I  plane.  d corresponding  to  a  is  d where  where  1  between  a cubic  Miller  for  diameter  nX = 2d  set  pattern  constant  B interplanar  In  diffraction  that Dd = 2 L X ,  D  a ring  a  o  1  + k  2 +  <  2  3 )  constant,  eq.  (l)  and  gives  (3)  a  ^2U^  D  =  +  k  2  +  l  »  2  W  h  r~2~ is  a straight  line  of  slope  Two t e c h n i q u e s area  diffraction  the lens  area  area of and  aperture  the  Q  were used  when / h to  object  intermediate  that lens  in  can be  the  image p l a n e s  ( 4 )  2  2 +  is  1  diffraction  with  an  objective  seen.  h  plotted  against  patterns:  D.  selected  diffraction.  a r e a method b e g i n s (located  c  + k  obtain  and r e f l e c t i o n e l e c t r o n  The s e l e c t e d selected  a /2LX  i  In are  image of lens  normal  the  image p l a n e )  operation,  conjugate  film.  foci,  so  the that  The  defines objective an  8  enlarged image of the film is produced.  To obtain a diffraction pattern,  the focal length of'the intermediate lens i s decreased  Until  the objective  back focal plane is conjugate to the intermediate lens image plane.  A  diffraction pattern then appears at the intermediate lens image plane. While the intermediate lens focal length is being decreased, the image of the object gradually shrinks to a point, and a diffraction pattern forms around i t . In the reflection diffraction technique, no image can form since only diffracted electrons can reach the image screen. 2.  Procedure Yttrium oxide films (~200 % thick) were evaporated onto freshly  cleaved NaCl crystals.  After cooling, the films were floated off the water-  soluble substrate in d i s t i l l e d water and picked up with copper electron microscope grids. The films were then examined by transmission electron microscopy and diffraction. In order to  check the influence of the substrate on crystal  structure, a fairly thick (~2000 &) film of yttrium oxide was evaporated on . polished n-type silicon and the structure Was examined by reflection electron diffraction. 3.  Results Fig. 3 shows the photograph of a diffraction pattern obtained with  an accelerating voltage of 75kV, using the selected area diffraction technique. The film was found to be polycrystalline bordering on amorphous,with random o (2) crystal orientation and a crystal size of about 75 A or more. Ifi was found that individual crystals could not be resolved, probably  Fig. 3 Freshly deposited  Fig.  «  Recrystallized Y 0  film.  Fig. 5 film.  D i f f r a c t i o n Structure of R e c r y s t a l l i z e d film  Fig.  Fig.  7  Reflection electron  diffraction  from Y 0 , on n - t y p e p o l i s h e d  silicon  8  Diffraction of gold  pattern film  11  because of d i f f r a c t i o n by c r y s t a l s of s e v e r a l o r i e n t a t i o n s stacked v e r t i c a l l y i n the f i l m . When the f i l m s were heated w i t h an intense e l e c t r o n beam, they were observed to r e c r y s t a l i z e .  An attempt was made to f i n d the r e c r y s t a l l i z a -  t i o n temperature with a heating stage, but nothing W a s observed below 800°C, the thermal l i m i t of the stage.  F i g . A shows the s t r u c t u r e of a r e c r y s t a l l i -  zed f i l m at a magnification of ,X46,O0O. i s shown i n F i g . 5.  A d i f f r a c t i o n pattern for t h i s f i l m  The pattern was observed to be more d i s t i n c t ,  probably  because of reduced random s c a t t e r i n g of electrons from near-amorphous regions. The strong l i n e s have diameters i n the same r a t i o s as i n F i g . 3, but more rings can be resolved.  This pattern was photographed using lOOkV as the  a c c e l e r a t i n g p o t e n t i a l , r e s u l t i n g i n l a r g e r diameter r i n g s (due to the shorter e l e c t r o n wavelength.) than F i g . 3. A f t e r f u r t h e r r e c r y s t a l l i z a t i o n by the beam, the p a t t e r n of F i g . 6 was obtained.  The continuous d i f f r a c t i o n r i n g s of F i g . 5 are broken i n t o  rings of d i f f r a c t i o n spots because of the smaller number of c r y s t a l s i n the path of the beam. F i g . 7 shows a r e f l e c t i o n e l e c t r o n d i f f r a c t i o n p a t t e r n f o r y t t r i u m oxide deposited on polished n-type s i l i c o n .  The r i n g diameters again are i n  the same r a t i o s as the b r i g h t e s t r i n g s i n F i g . 5, but the s i z e of the o v e r a l l pattern i s reduced because of the proximity of the specimen and the photographic p l a t e i n the r e f l e c t i o n method. F i n a l l y , F i g . 8 shows the transmission d i f f r a c t i o n p a t t e r n f o r a t h i n gold f i l m that was used to determine the camera constant of the e l e c t r o n microscope f o r the p a r t i c u l a r c o n t r o l . s e t t i n g s used.  The value of the  camera constant v a r i e s w i t h the lens s e t t i n g s , and so the same s e t t i n g s must  12  be used i n the specimen d i f f r a c t i o n as f o r the c a l i b r a t i o n d i f f r a c t i o n .  The  a c c u r a c y o f the f i n a l r e s u l t s depends on the a c c u r a c y w i t h which  the  camera c o n s t a n t i s determined.  crystal  s t r u c t u r e of g o l d and  4.  A g o l d f i l m was  its lattice  used because the  c o n s t a n t are w e l l known.  Analysis The  equation  camera c o n s t a n t of the e l e c t r o n m i c r o s c o p e  was  determined  with  (4) to be  LX  = 5.82 + 0.02,  4.087 £ f o r the l a t t i c e c o n s t a n t of g o l d . ^  u s i n g the V a l u e o f  T a b l e 1 shows an a n a l y s i s o f the d i f f r a c t i o n p a t t e r n of y t t r i u m o x i d e based  on F i g . 5.  T h e ^ r i n g diameter  with a simple cubic s t r u c t u r e .  The  observed  A few  faint  rings  t o be c o n s i s t e n t  r i n g i n t e n s i t i e s were compared t o  e x i s t i n g data f o r p o l y c r y s t a l l i n e ^ O ^ agreement.  r a t i o s were found  powder and were found  t o be i n e x c e l l e n t  ( c o n s i s t e n t w i t h the c r y s t a l s t r u c t u r e ) were  i n the e l e c t r o n d i f f r a c t i o n but not i n the X-ray p a t t e r n .  n  F i g . 9 shows a p l o t of /h is a straight  l i n e p a s s i n g through  d a t a to the simple c u b i c s t r u c t u r e . determined  t o be  a  which i s i n e x c e l l e n t  '  + k  2  2  + 1  v s . r i n g diameter.  The  the o r i g i n , i n d i c a t i n g a good f i t of From F i g . 9 , the l a t t i c e  = 10.58 + 0.05  o agreement w i t h the v a l u e  constant  result the was  A,  10.605 +' 0.001 o b t a i n e d by  (4)  X-ray  diffraction.  2 and 3.  The  first  f o u r r i n g s of F i g . 3 and F i g . 7 a r e . a n a l y z e d i n T a b l e s  The  r i n g diameters were found  to be i n the same r a t i o s and  the same r e l a t i v e i n t e n s i t i e s as the b r i g h t w i t h i n experimental  error.  have  ^ r a c t i o n r i n g s of F i g . 5,  TABLE  1  ELECTRON D I F F R A C T I O N Ring Diameter (cm)  RESULTS  Ratio D  R  D  1.10  X-Ray R  2  h  k  l  intensity*  Intensity  1.55  1.41  1.99  2  110  f  2.20  2.00  4.00  4  200  m  -  2.69  2.45  6.00  6  211  b  14  3.12  2.84  8.08  8  220  vf  -  3.48  3.16  9.96  10  310  vf  -  3.80  3.46  12.0  12  222  vb!!  100  4.12  3.74  14.0  14  321  f  - .  4.40 '  4.00  16.00  16  400  vb  4.66  4.24  18.0  18  411  m  7  4.93  4.48  20.2  20  420  f  2  5.17  4.70  22.1  22  332  m  9  5.40  4.91  24.1  24  422  f  2  5.60  5.10  26.0  26  431 510  b  14  6.02  5.47  29.8  30  521  m  5  6.24  5.66  32.0  32  440  vb  61  6.43  5.84  34.1  34  530 433  f  3  6.60  6.00  36.0  36  600 442  vf  2  —  31  ( 5 )  TABLE 1  D(cm)  R  R  6.78  6.17  38,0  6.95  6.33  7.13  2  (Continued)  2  2  2  X-Ray hkl  I  I  38  6 U 532  m  8  40.1  40  620  vf  2  6.48  42.1  42  541  m  8  7.30  6.64  44.1  44  622  b  43  7.46  6.78  46.0  46  631  m  11  7.62  6.93  48.0  48  444  m  10  7.78  7.08  50.1  50  f  4  550 710 543 7.93  7.22  52.0  52  640  vf  3  8.08  7.36  54.2  54  633 552 721  m  6  8.23  7.46  55.8  56  642  f  4  * vf  very  faint  f  faint  m  medium  b  bright  vb  very  bright  16  TABLE 2 YgO^ o n N a C l . ' , Un re'cry's t a l l i z e d  D (cm)  R-  R  D  0.707  2  2 2 2 h +k +SL  Plane  Intensity  2.46  3.46  12  12  222  vb  2.84  4.03  -16.2  16  400  vb  4.02  5.64  31.7  32  440  b  4.73  6.67  44.4  44  622  vb  ±0.05  TABLE Y^O^ On  D (cm)  R=  -  D ,,  2  Silicon  2 2 2 h +k + £  Plane  12.0  12  222  vb  15.7  16  400  b  R  Q  3  Intensity  0.400  1.62  3.46  1.90  3.96  2.66  5.66  32 .0  32  440  b  3.12  6.65  44.2  44  622  m  ±0.05  ,  5.  Discussion Freshly prepared yttrium oxide films on sodium chloride and s i l i c o n  were found to have the same structure.  The films were p o l y c r y s t a l l i n e , with  a c r y s t a l s i z e of the order of 100 A°.  Thus, i t can be concluded that the  c r y s t a l structure of the substrate material has l i t t l e e f f e c t on the structure of the yttrium oxide films. The films were found to have a simple cubic structure with a l a t t i c e o constant of 10.58 + 0.05 A, which i s i n good agreement with the e x i s t i n g data for bulk  Y 2  0 . 3  Thus, i t i s evident that the metastable reduced oxide Y0 i s present in^ only small quantities or not at a l l i n the films. The results found are i n e s s e n t i a l agreement with those of Hass, Ramsey and T h u n ^ , who  examined the structure of I^O^  work on o p t i c a l coatings.  i n the course of t h e i r  However, their films were somewhat more amorphous  than those studied here, possibly because they did not evaporate i n an oxygen ambient.  Also, they evaporated from tungsten boats, a lower  process than electron gun evaporation. determination of I^O^  temperature  As a r e s u l t , t h e i r structure  showed a hexagonal l a t t i c e with a c/a r a t i o of  instead of the value of 1.56  accepted for the bulk material.  1.63  No such d i s t o r -  tions of the c r y s t a l l a t t i c e were observed i n this work. The unit c e l l of the Y^O^ oxygen i o n s ^ .  structure contains 32 yttrium and 48  The structure consists of subunits containing one cation  centered within a cube of eight anion s i t e s , of which only s i x are occupied. Half the cations are i n subunits which have the unoccupied anion s i t e s on the face diagonal, the other h a l f have unoccupied s i t e s on a body diagonal.  The  s u b u n i t s f i t t o g e t h e r so t h a t the unoccupied s t r i n g s along the <111>  anion s i t e s  d i r e c t i o n s ' o f the c r y s t a l .  form n o n i n t e r s e c t i n g  These s t r i n g s  pathways a l o n g which the d i f f u s i o n o f oxygen i o n s would meet w i t h little  resistance.  are unoccupied,  F u l l y o n e - f o u r t h of the a n i o n s i t e s i n the  provide relatively  sublattice  so t h a t a h i g h s o l u b i l i t y of CL i n Y„0„ would be  expected.  19  IV. 1.  CONDUCTION IN  FILMS  Introduction In  for  carrier  often true  thin  transport.  due t o for  insulating  the  films  trapping  more  current  density  in  than  'a  N  B current =  E  = 2(E  -  p  E )  This  particularly  is  is  thick.  following  expression  for  the  electron  E exp(-Eg/2kT).  (1)  effective density  of  states  in  conduction  and  valence  bands temperature  favourable  —18  2  normally  room-temperature values  2 cm / V s e c ,  a n d E = 10  6  V/cm,  of  the  19  A. vN N^ = 3 x current  10  -3 cm  density  is  ,  only  (7)  A/cm  activation  conduction  = bandgap  c  = insulator  y = 100  10  > 3eV),  conductivity  mobility  = 3eV,  carriers.  responsible  density  = carrier  V  the  (E  can be  insulator:  •y  For  currents  gives  concentration  ,N  mechanisms  field  T = absolute  about  theory  H carrier  C  of  a few h u n d r e d a n g s t r o m s  n  g  of  = aE = neuE = e y / N ^  E = electric J  a variety  and d e t r a p p i n g  an i n t r i n s i c  J  where  films,  F o r wide bandgap m a t e r i a l s  Semiconductor  E  THIN  , which observed  energies  for  is in  much l e s s thin  film  conduction  are  than  the magnitude  insulators. usually  of  the  Furthermore,  much s m a l l e r  the  than E  observed  /2,  so  s that  intrinsic The  to  the  conduction conductivity  unique nature  stoichiometrically  of  cannot be of  such  because  of  the  transport  vacuum d e p o s i t e d films. the  Compounds  differing  mechanism.  thin are  films  can be  difficult  evaporation  rates  to of  attributed evaporate the  consti-  20  tuent  atoms.  During  Often,  in  the  o f ^O^v  the e v a p o r a t i o n  coloration  that  researchers  associated  with  oxygen  with of  significant  defect  have  amorphous  or near-amorphous  it  that  trapping  densities Thus,  high  density  properties  of  of  a small  a high  it  films  betx^een m e t a l  for  insulators  likely  is  assumed  at  21  that  must be  conduction  /cm  3  or  In  have been  donor  reported  insulating centers,  studied with mechanisms  this  the since  evaporant these  Finally,  insulating  vacuum  centers  Evaporation  than  concentration.  exist.  evaporated  and a c c e p t o r  less  (from metal  than  effect  the  films  evaporated  makes  CdS,  (9)  films  will  and h e n c e defect  have  the  a  conduction  structure  have been proposed  b e e n shown t o  to metal)  100 A* t h i c k , is  a metal-insulator  to be Coulombic,  e l e c t r o n has  10  will  dis-  Contamination  defects.  slower  evaporated  a brown  color  .  film  somewhat.  for  in  mind.  insulating  counterelectrodes.  The S c h o t t k y the b a r r i e r  thin  of  to  dielectric films,  nature  is  The t u n n e l e f f e c t only  in  reduced  showed  attributed  magnitude  carrier  as  rapidly  a source, o f of  are  electrons  intrinsic  high  A number o f  trapped  densities  as  films  deposited  orders  density  films  the  Y^O^ h a v e  and  trap  traps  these  films  on b u l k  many  materials  likely  such  oxides,  could a l s o be  crucible material  can p r o d u c e  of  vacancies  crucible material  the  case  field  and w i l l  enhanced  interface.  then the  image  is  If  a possible not  be  thermionic the b a r r i e r  force barrier  mechanism  considered emission at  the  lowering  here.  over interface  for  an  be (2)  and  the  conduction  characteristic  is  e  J = AT  exp{-  V  6  s ^ kT  }  (3)  where  A =  = barrier  ii>  It  is  high  constant  unlikely defect  that  this  density,  space  charge  thick  films.  height  mechanism  unless  the  can  films  Frenkel  over to  the  Coulombic b a r r i e r  semiconductors In  are  e f f e c t s w o u l d be e x p e c t e d t o  The P o o l e - F r e n k e l e f f e c t , carriers  account  Fig.  1,  quite  for  conduction  thin,  dominate  since  the  or  field-assisted  of  a donor  in  films  trapping  with  and  conduction process  thermal  c e n t e r , was  emission  first  a  in  of  applied  by  .  the p o t e n t i a l w e l l  associated  with  a trap  of  depth E  f c  is  illustrated.  Fig. The n e x t  diagram  shows how t h e p o t e n t i a l  u n i f o r m e l e c t r i c f i e l d E. be d e t e r m i n e d by distribution The  to  1  finding  The b a r r i e r the  t h e maximum  Coulomb  distance in  the  b a r r i e r has  is  m o d i f i e d by  lowered i n  from the  energy the  is  potential  energy  center of  function.  the presence of  the  by  A<j>, w h i c h  potential  a can  X  Fig. 2 In the presence of the f i e l d E, this becomes 2 E J  n  =  4TTEX  - eEx  (4)  The dielectric constant e i s the high frequency value, since the electron motion i s too rapid for the l a t t i c e ions to follow. dE  e^  •~~r~ = 0, so , dx 4irex  At x , o  - eE = 0, or 2  o  X  Thus, A<f> i s A*  o  (5)  /4ireE  ./ST-  (6)  Frenkel assumed (as discussed later in this chapter) that the ionization potential E  of the solid was reduced by the amount A<j>, yielding the con-  duction law J  p  = neuE = euN E exp-{ [ ( E - B g  c  p F  ^)  ]/2kT} (7)  =  J  o  6 X P  (_  2kT- ' )  Mead (1962) ^ \  i n his work on Ta^O,. thin films, used the equation  J = G E exp{[(B ^-V)]/kT} Q  pF  (8)  to  explain  his  results.  enhanced thermal bandgap. E was was is  e m i s s i o n from t r a p s  He d e r i v e d  similar  twice  as  similar  to  (8)  that  large  to  He a s s u m e d  by  of  (as  of  assuming  the  that  that  the  effect,  seen by  except  c o n d u c t i o n mechanism  depth V i n  Schottky  can be  Frenkel's,  the  insulator  field-  forbidden  exponential  dependence o f  except  the b a r r i e r  comparing the  the  to be  (2)  that and  (6)).  His  of  is  B™/  coefficient  J  on  lowering  equation kT  .  Mead's  Jrr data too  gave a f i t large  for  of  21 and  that  the  the h i g h - f r e q u e n c y  Other workers found  27' f o r  values  of  d i e l e c t r i c constant  who u s e d  e about  d i e l e c t r i c constant.  (8)  four  to  explain  of  their  times  too  large  concluded that  (8)  did  These values  are  Ta20,..  results  have  were n e c e s s a r y  typically  to  fit  their  (12) data.  Hartman  o n ^^2^S  a n c  Although  *  al  films  the  c o u l d not  et  Schottky  explain  because  of  conduction  the v a r i a t i o n  the  adequately  d i f f i c u l t y with  equation of  not  gave  the  film  the  data  permittivity.  a .much b e t t e r  current with  fit  fit  thickness  for  that  e,  it  was  observed. (13) Simmons resolve  the  model w i t h  has  difficulty. deep  donor  suggested In  this  centers  a theory  theory,  of  Poole-Frenkel emission  Simmons  and s h a l l o w  considered  neutral  traps,  an  as  to  insulator  illustrated  below. If is  we a s s u m e  negligibly  equate *If  t h e number o f  eq.  (8)  emission . the  log  slope.  small  is  (eq. T vs.  that  compared  to  electrons  correct, (3))  t h e number  it  of  t h e number missing  electrons of  trapped  from donor  would be p o s s i b l e  to  and P o o l e - F r e n k e l e m i s s i o n  v^E p l o t s .  in  the  conduction  electrons,  centers  to  t h e n we  t h e number  d i f f e r e n t i a t e between by  The P o o l e - F r e n k e l s l o p e  the d i f f e r e n c e i n would be  band  twice  the  can of  Schottky  slope  of  Schottky  Fig. occupied traps,  N where  for E  exp{-(E  D  F  E  >> k T a n d E „ -  1J  E_  I  -E )/kT}  =  D  >>  r  donor  density  of  states  N^, = e f f e c t i v e  trap  density  of  states.  Solution  for  of  (9)  Thus,  the zero  at  F  Fermi energy  i D V ( E  =  zero  the  +  field,  +  \  k T ln  c  exp-{[E -E ]/kT}  = N  c  % / N  field  conductivity  gives  <> 0 1  free electrons  n = N  c  (9)  <VV  the number o f  T  kT:  exp{-(E^Ep)/kT>  = effective  E  and  -  r  3  is  F  exp-{[2E -(E +E )]/2kT} c  is  a  =  T  (11)  D  neu  o = eyN When an e l e c t r i c by  field  is  applied,  the P o o l e - F r e n k e l v a l u e .  energy  barrier  is  conduction band  not  the  Because  a f f e c t e d , so  c  /N  D  /N  1  donor energy  the  that  traps  are  t h e number  exp{[2E  c  barrier assumed of  -(E  +E  E ~E c  ID D  )]/2kT}(12)  is  lowered  to be n e u t r a l ,  free electrons  in  their  the  is  n = N v N /N /  c  D  T  exp{t(E -E )+(E -E )-3 c  T  c  D  p F  vaT)]/2kT}  (13)  Hence, a = a We s e e normally current  that  associated is  the  with  Q  exp(B vTT/2kT).  (14)  p F  conductivity the Schottky  varies effect  with at  the  field in  a  a neutral barrier.  manner The  J » aE = a E exp{B „vaY/2kT}  (15)  T3  O  rr  S t u a r t ^ ^ and H i l l et a l ^ ^ have explained t h e i r conduction data on SiO with equation (15).  The f i t f o r e was  found to be good i n the h i g h - f i e l d region  of conductivity. There are several d i f f i c u l t i e s with Simmons' theory. F i r s t , the c a l c u l a t i o n of the electron concentration using the Fermi l e v e l requires that the insulator be i n equilibrium. Poole-Frenkel emission, however, i s a non-equilibrium e f f e c t , and so the methods used to derive (15) are somewhat contradictory. It i s also u n r e a l i s t i c to assume that the trap energy b a r r i e r w i l l remain unaffected by the presence of an e l e c t r i c f i e l d . The b a r r i e r height for emission from traps i s smaller than that for emission from donors i n Simmons' model, and the trap b a r r i e r lowering should give the largest contribution to the conduction current. The major d i f f i c u l t y with equation (12) concerns the a c t i v a t i o n energy of the conduction process.  In commonly used insulators such as  SiOgj-SiO and Al^O^, as well as ^O^,  the energy difference between the  Fermi l e v e l and the insulator conduction band i s 3eV or more (the bandgap i s 6-8eV).  The Poole-Frenkel b a r r i e r lowering for E = 10^V/cm (near break-  down), and e  f  = 3 i s only 0.44  eV.  This amount of b a r r i e r lowering i s not  nearly large enough to allow a s i g n i f i c a n t number of donors below the Fermi energy to be ionized at room temperature.  The a c t i v a t i o n energies usually  observed for Poole-Frenkel currents are about 0.5 f i t t e d the results for SiO, and 0.6  eV was  eV.  Stuart found 0.4  found f o r 2^3 Y  fil™  8.  Thus, Simmons' theory suggests higher a c t i v a t i o n energies than are found i n p r a c t i s e .  eV  An e q u a t i o n  that  t h e methods  of  donors  that  are normally  is  total  the  define  Frenkel's  number  an o c c u p a n c y  The r a t e field  of  better  original  donors  release  = vibration  The r a t e  of  capture  c = J  (1  of  = current  s E capture we w o u l d  expect In  equal,  so  D  electrons  of  an i n s u l a t o r  considering with  shallow  room t e m p e r a t u r e .  If  occupied donors  from donors  lowering)  vexp-{[(E -E )-3 c  electrons  ~-f)N  at  and n ^ t h e number  f r e q u e n c y of  of  Consider  f o u n d by  we  can  by  R = f N  v  can be  electrons  (assuming P o o l e - F r e n k e l b a r r i e r  where  results  paper.  f i l l e d with  factor  of  gives  D  trapped  will  p F  will  in  the presence  of  a  be  v^E]/kT}  (17)  electrons.  be  J s / e , where  (18)  density cross-section  the occupancy  equilibrium,  the  of  empty  donors.  f  to be  field-dependent.  factor rates  of  For  electron capture  shallow  and  donors,  release  are  that  ^  If  we assume t h a t  is  small,  then  f  = ev e x p - { [ ( E - E ) c  t h e number 1,  and  of  the  D  -  electrons  current  J = neuE =  is  (l-f)N  e  p p  v^]}/Js  released given  (19)  from donors  by  the  field  by  eyE  2 • N e =  Solving  for  the  current  uEv  exp-{t(E -E )-6 c  D  p F  /E"]/kT}  (20)  gives HV  s  E  exp-{[(E - E j - B ^ ^ E j ^ k T } ^ c D "PF  (21)  .27  This equation i s s i m i l a r to Simmons', and i t gives the same slope on a l o g J vs.  p l o t as the Schottky conduction law.  v a r i a t i o n with the f i e l d i s v^E rather than E.  The  pre-exponential  This i s unimportant at high  f i e l d s , where the exponential term dominates. 2.  Experimental The D.C.  417 high-speed  Procedures conduction c h a r a c t e r i s t i c s were measured w i t h a K e i t h l e y  picoammeter i n s e r i e s w i t h a v a r i a b l e voltage supply..  Shielded cables were used to minimize t r a n s i e n t s . For the high temperature measurements, the sample was placed i n a Statham SD6 oven.  An iron-constantan  thermocouple was i n s t a l l e d near the sample and was used to measure the temperature. The conduction c h a r a c t e r i s t i c s were found to d r i f t over a period of time, probably because of step response e f f e c t s i n the d i e l e c t r i c m a t e r i a l . I t was  found necessary to wait f o r anywhere between a few minutes to an  hour (depending on the applied  Voltage)  l i m i t i n g value to w i t h i n a few percent.  f o r the conduction to approach i t s Space charge e f f e c t s or i o n i c  currents are a l s o a p o s s i b l e explanation of the observed 3.  drift.  Experimental Results The t h i n Y^O^  f i l m s were found to have b u l k - l i m i t e d conduction  c h a r a c t e r i s t i c s roughly s i m i l a r to those found f o r SiO f i l m s by S t u a r t . Fig.  In  4, l o g I i s p l o t t e d against vA/ f o r three d i f f e r e n t thicknesses of f i l m .  The p l o t s are l i n e a r i n the h i g h - f i e l d region where the voltage i s greater than about 15 v o l t s .  The f i l m s had aluminum counterelectrodes.  In F i g . 5, the v a r i a t i o n  of the conduction c h a r a c t e r i s t i c s w i t h  temperature i s p l o t t e d . . Higher currents were observed at higher  temperatures.  -6.00  SORTIV/VOLT)  Fig. 5 Log I vs. V ^ 1  2  for Different Temperatures(d = 4680A°.)  0.60-1  3/TCDEG. KELVINJ Fig. 6  104  Fig.  6 shows  3 in  the  a plot  of  8 (—)/(2.303 kT)  derived.from Fig.  A fit  5.  for  equation  • h »- #'  1  was  1  vs.  made w i t h  Fig.  6,  ex  and t h e  {2  (22)  relative permittivity  of  the  f i l m was  found  using 3 3  < > 23  TTEd  o The  film  thickness  M100 A n g s t r o m e t e r .  was  The r e f r a c t i v e  r  index of  a wavelength  = 3.2 a  Y  of  IBM  r e s u l t was 360  f o u n d by  computer w i t h This  gives  solving  iterative  was  found  to  Sloan  be  + 0.2  2^3  (24) o  6328 A ° t o  n = 1.75 This  t o b e 4680 + 200 A on t h e  The d i e l e c t r i c c o n s t a n t e  e l l i p s o m e t r y a t  measured  s i l i c o n was  n  determined  by  be  + 0.01  (25)  the e l l i p s o m e t r y .equation  on t h e  U.B.G.  methods.  the. p e r m i t t i v i t y 2 e  which  is  in  good agreement w i t h  c o n d u c t i o n measurements. measurements  is  function were  found  in  Fig.  The f o r w a r d  to be v i r t u a l l y  bulk-limited  rather  than  conductivity  observed  Xtfould b e e x p e c t e d f o r  is  3.05,  the Value  These metals  difference.  =  The e f f e c t  illustrated  counterelectrodes.  = n  r  of  of  polarity  7 for  were  Thus,  limited.  probably  due t o  on t h e  of  conduction the  an i n t e r n a l  d i f f e r e n t work  from  the  conduction  indium  their  large  work  characteristics  conductivity  The v e r y  found  g o l d and  s e l e c t e d because  emission  with  reversal  a film with  and r e v e r s e  identical.  contacts  the p e r m i t t i v i t y  slight field  ^O^  is  asymmetry  in  in  functions.  of  the oxide,  as  -8.00-,  -.9.00 -  a. tx u -10.00 o  -11.00-  -12.00 0.0025  T  r  T~ 0.0030  R  T  3/TtDEG. KELVINJ  Fig. 8 Determination  of  Activation  Energy  r  T  1 0.0035  34  The a c t i v a t i o n energy of the conduction process was found to be independent  of temperature,  as can be seen from the straight l i n e plot of  log I vs. — shown i n F i g . 8.  The a c t i v a t i o n energy was found to be 0.58 +  0.05eV. The low pressure D.C. conduction c h a r a c t e r i s t i c s are plotted f o r d i f f e r e n t temperatures  i n F i g . 9.  The pressure was about 50uHg.  The f i l m  o thickness was measured to be 3240 + 100 A with a Talysurf. The current was observed to decrease by several orders of magnitude over a period of a few hours after the pressure was reduced. plot of (3/2)/(2.303kT) based on the slopes of F i g . 9.  F i g . 10 shows a  The value of the  r e l a t i v e p e r m i t t i v i t y that was found to f i t the conduction c h a r a c t e r i s t i c s was E = 11.2 + 0.7, or roughly four times the high-pressure value.  The  a c t i v a t i o n energy was found from F i g . LV to be 0.63 + 0.05eV, almost the same as the high-pressure value. F i g . 12 gives the D.C. conduction of three d i f f e r e n t counterelectrodes on the same Y^O^ f i l m . v a r i a t i o n observed 4.  The r e p r o d u c i b i l i t y i s seen to be f a i r l y good.  The  can be attributed to thickness variations i n the thin f i l m .  Discussion The conduction c h a r a c t e r i s t i c s of thin Y^O^ films were found to f i t  equation (21) quite w e l l .  The non-linearity observed at low f i e l d s i s s i m i l a r  to that reported by Kartman et a l ^ (1966) and S t u a r t ^ (1967) f o r SiO f i l m s . The conductivity i n this region i s believed to be p a r t l y bulk-limited and p a r t l y ohmic.  This view i s supported by the fact that the current f o r a l l  three thicknesses begins to approach the same l i m i t i n g value at low applied 5 voltages.  In the h i g h - f i e l d region where  E a  p ii p  e (  3 ^ 1°  volts/cm, the  35  -12.00H  -13.00  T—i—r  3.00  ' I ' 4.00 1  i—|—i—i—I—i—|—i—i—i—i—I—i—i—i—i—I—r  5.00  6.00 7.00 SQRTIV/VOLT)  a.00  T  Fig. 9 D.C.  Conduction  at Low  Pressure  (P=50u)  1  1  |  1  9.00  I  1  1  1  10.00  0.40 - i  1/TlOEG. KELVIN) Fig.  10  37  -n.oo-i  31  -lO.OO-i  00  SQRTlV/VOLT) F i g . 12 Reproducibility  of  D.C.  Conduction  Current  (P=50uHg)  Poole-Frenkel  emission  process  The p o s s i b i l i t y movement  of  different  currents  at  the  little  effect  of  ions  i o n i c , c o n d u c t i o n was  through  same p o t e n t i a l .  on  Fig.  the  7 also  since  the d i f f e r e n t  interfaces  would  give  not  is  A fairly  possible,  Baking  the  vacancies the  likely  tion  reduced  diffusion  of  optical  ionic  for  at  the  give  conduction as  different  is  two  Schottky  had  unlikely.  a possible  the  the  electrode metal  conduction  metal-insulator  conduction,  present  drift  the  £^  m s  c  n  centers  films  in  ^-  a  s0  0.6eV below  oxygen  were  oxygen  evaporated  through  on o p t i c a l  the  (as  absorption  to  were used  and  the p a r t i a l l y  of  this  this  an oxygen  Thus,  Vacancies  change  the  slow  for  filling  conduction  to  interstitials  ambient. filling  a l ^ films,  on  during  subevapora-  that  baking  obtained  for  interstitials  f i l l e d by b a k i n g ) films.  The  e l e c t r o n beam of  in  that  properties  the value  of  found,  They found  both yttrium  time observed  the  the oxide  work).  (partly  et  earth  reduced cool-substrate  be e x p l a i n e d by  by  Hass  rare  not  electrons  or y t t r i u m  reduction of in  of  insulator  probably  d i d not  c o e f f i c i e n t , but  and oxygen  in  films.  properties  this  the  vacancies  dielectric losses,  film properties with a  Poole-Frenkel emission  on h e a t e d s u b s t r a t e s .  probably  atoms.  that  emission  on a h e a t e d s u b s t r a t e  substrates  deposited  in  the  They a t t r i b u t e d  cold  the  of  t h e i r work  deposited  is  concentration of  ( u n a f f e c t e d by baking)  ^2^2  currents  mechanism  reduced the  baking.  onto  films  Schottky  from donor  even though  by  films  sequent  high  films  course  only  so  barrier heights  different  the v a l e n c e band  band.  7 showed  However,  observed. The most  into  Fig.  eliminates  considered.  would be e x p e c t e d to  conduction process,  mechanism,  was  dominates.  vacancies  are  slow  evaporated with  oxygen  Contamination The b o r o n n i t r i d e unable  to  reach  Substantial  the v e r y  alkali  easily  7059  earth  —6  these  results  pathways  the exist  by  for  solution  crystal  of  substrate  al  , in  necessary  material glass,  for  is  donors.  and h e n c e  was  evaporation.  also  which has  of  unlikely, a low  since  concentration  t h e Y^O^ c o n d u c t i o n c h a r a c t e r i s t i c s  t h e i r work  found  that  and a low  of  since  The d i f f u s i o n  and i n  polycrstalline  no  Berard's  for  for  seconds  =  D  o  room  -19  of  x  1200  C.  y §  e  is  As  which  the  orders  provides the  the p o r o s i t y  temperature:  in ions  of  oxygen of  magnitude  the  Chapter can sites  diffusion  w o u l d make  gives  explained  ample  solubility of  crystal  defective  oxygen  solubility  Values  They  discussed  determining  on  single  diffusivity  n  inherently  sublattice  full  in  ^ (0.85eV).  along  several  worst-case  e x p ( - £ )  ~10  a temperature  films,  at  o  on t h e  available  c o u l d be  Assuming  ^igh  energy  In  assumed  d a t a were  even e a s i e r .  at  oxygen.  evaporated  »  3  structure  Gerard  constant  1000  s  diffusion  these materials.  open a n i o n  interstitial  Y^O^.  diffusion  activation  The u n u s u a l l y  i n ^2^3'  a  mechanism b a s e d  sublattice  of  on o x y g e n ^  ^2^2  t h e Y^O^ c r y s t a l  oxygen  lattice,  * Measured  source  a water-cooled block  temperatures  dependence of  a migration  in  readily.  constant  et  anion  migrate the  an u n l i k e l y  ions.  2 cm / s e c )  x 10  of  in  aluminosilicate  sesquioxides  (6.06  nature  held  is  understood. Berard  rare  high  contamination with  The p r e s s u r e not  cruicible material  c r u c i b l e was  t h e s e were C o r n i n g of mobile  by  in  the  oxygen  in  higher,  diffusion  following  results  II,  However, i f Berard's d i f f u s i o n constant i s too low by two orders of magnitude (as he indicated to be possible) and the average  activation  energy i n the thin films i s 0.6eV rather than 0.85eV, the d i f f u s i o n distance becomes x /-v/ Jt> x lO "*"^ xlO^ cm -  =  7700 A,  or more than the f i l m thickness.  Thus, oxygen d i f f u s i o n cannot be eliminated  as a possible cause of the reduced conductivity at lower pressures. and Vest  , i n t h e i r high temperature  (1400-1800 C) measurement of the  conductivity of bulk p o l y c r y s t a l l i n e Y^O^ amphoteric  semiconductor.  Tallan  found that the material was  an  The region of predominant hole conduction had  the conductivity  a = 1.3 x 10  3  P  3 / 1 6 Q 2  exp(-1.94/kT)  (26)  They explained their results by assuming the presence of f u l l y ionized Y vacancies.  In the films studied here, the trap density for holes i s probably  too great for hole conduction to occur.  Also, yttrium i n t e r s t i t i a l s  more l i k e l y to be present than yttrium vacancies.  They did observe  are a  strong dependence of a on the oxygen p a r t i a l pressure, as observed i n t h i s work. The donor centers from which Poole-Frenkel emission occurs are probably i n t e r s t i t i a l yttrium atoms.  The conduction process i s l i k e l y  determined by the i n t e r a c t i o n of yttrium i n t e r s t i t i a l s , oxygen vacancies and dissolved oxygen atoms.  Reducing  the oxygen p a r t i a l pressure would  reduce the number of oxygen atoms i n solution and increase the number of oxygen  Vacancies,  pressure.  and this may be the cause of the conductivity change with  The presence of more oxygen vacancies, which act as deep electron  traps,  would  r e d u c e t h e number  for  Poole-Frenkel emission.  are  closely  associated  (oxygen v a c a n c i e s ) from  as  would  of  If  electrons  oxygen  neutral  in  the  vacancies  defect  donor  levels  and y t t r i u m  available  interstitials  pairs> the p r e s e n c e o f  r e d u c e t h e number  of  donors  deep  available  for  traps  emission  to n  Then e q u a t i o n  = N  D  ( 21) w o u l d b e m o d i f i e d  -  D  N  (27  T  to  (28)  T h e empty because  donors  of  arguments  p r o d u c e d by N  their  close  leading  to  Equation partial  pressures,  found  at  the in  It  increased the  seems  equation  (28)  is  oxygen  not  that  Vacancy  oxygen still  trapping so  conductivity oxygen  data  (11.7  at  of  vs.  but  that  at  low p r e s s u r e  a change  of  reduced  the  3.2  reduced concentration of  oxide,  centers the  oxygen  diffusion.  the high value  concentration  the  as  vacancies\  rapid  conduction  the  act  valid.  a lower  explain  not  permittivity  at  atmospheric  oxygen  atoms  caused  some  the magnitude  and change  observed  doubtful. The Y^O^ f i l m s  quite  would  sufficiently  from the  r e f r a c t i v e index of  are  predict  does  likely  with  (21)  does  assuming  low p r e s s u r e s  pressure).  association  (28)  However,  vacancies  similar  conduction  to  those  of  were SiO  characteristics  found thin  that  fit  f  to have  conduction  i  B  l  m  the  is  made  in  the  following  o  equation  1  A comparison  s  2kT  table:  ) '  t  h  characteristics have  bulk-limited  TABLE 1  MATERIAL SiO Y 0 2  3  Activation Energy ' W  n  0.4eV  3.6  10~ amps.  0.6eV  3.05  10~ amps.  O J  _  I at E = , ..5 ,, 3x10 V/cm. t  5  8  Y^O^ has much smaller conduction currents at the same e l e c t r i c  field.  The higher a c t i v a t i o n energy and d i f f e r e n t doping levels are l i k e l y the cause of t h i s difference.  44  V.  STEP RESPONSE AND LOSS FACTOR IN  Y^  1. Introduction The transient currents produced by the response of a dielectric material between conducting electrodes often yields useful information about low frequency losses in the material and the nature of the processes responsible for those losses.  If <f>(t) is the relaxation function of a material after application  of a step in the potential across i t , the real and imaginary parts of the complex permittivity can be expressed by E'CW) = C~{/°°(j)(t)cosa)t dt + C } a ° o  (1)  1  e"Cw) where C  cl  and  (2)  = C~ {/ <t>(t)sinu)t dt + Guf }, a o 1  D  1  5 capacitance with vacuum between the capacitor plates,  C  =• capacitance at high frequencies,  G  = steady-state D.C.  co = angular  Conductivity,  frequency.  These equations are general, except for the reasonable assumption that linear superposition holds for the observed currents in the material. It has been found that a relaxation function of the form <)>(t) = AC t a  m  (19)  holds for many materials at a fixed temperature  . Use of this expression in  ( 2 ) yields, after a contour integration convergent for 2 cos(mTr/2)]  *  +  G/CJC  m > 0,  >  a  ,  (3)  For materials with a Cole-Cole distribution of relaxation energies, (20) *The Cole-Cole distribution function has the form -  \ J 1 F(s)ds = — 2TT  T./  sin aTr , r—7- r ds, cosn (l-a)s-cos arr  .  where a and a are constants. The distribution.is similar to the Gaussian distribution, but i t i s less peaked. Many materials have a Cole-Cole distribution of relaxation times.  the p e r m i t t i v i t y has been determined to be e  = ' - j e " - e+' { t e ^ O / U ^ ^ ) "  CO  1 }  e  .C" - yj— , a  Here the high-frequency d i e l e c t r i c constant i s  E  q  i s the s t a t i c  d i e l e c t r i c constant, T i s the most probable relaxation time and n = 1 - a, ' o r  where a i s a factor determining the d i s t r i b u t i o n width.  Both n and  a  Vary  between 0 and 1. The r e v e r s i b l e transient current <f>(t) flowing at a time t a f t e r a step i n voltage can be found by taking the inverse Fourier transform of (1) and (2) giving <t>(t) = ~ ir  TeCjw) exp(ju)t)dw o  (5)  On s u b s t i t u t i o n of (4) into (5), expanding i n a series and integrating, two l i m i t i n g cases a r i s e : > ( t ) = [te -e ) / T ] [ l / r ( n ) ] ( t / T )-<l-n) O o o  (6)  00  for t<<x , and o + (t) = [ C e - e , ) / T J [ n / r a - n ) 3 ( ^ - ) " 0  (7)  ( 1 + n )  0  o for t>>t,where x i s a c h a r a c t e r i s t i c time. o o  Hence, f o r a given material the  log (fi(t) vs. log ( t / t ) curve has a slope of s  1  = -(1-n) = -a  (8)  for times short compared to the most probable relaxation time t ,and a slope o  of  s  2  = -Cl+n) = -(2-a)  at times very long compared to T . o  (9)  At times near T , the curve bends over. q  This i s the dispersion region where a peak i n e"occurs. The d i e l e c t r i c loss factor for a Cole-Cole d i s t r i b u t i o n has been found  for the two l i m i t i n g cases to be e"Cu)  - (e -eJCiot ) sin(nTr/2) o *° o  (10)  n  f o r (urr )<<1, and o £  "( ) U  = (c -e ) ( ( 0 T j ' s i n ( n / 2 )  (11)  n  f f  O  0 0  0  at high frequencies where tox » 1 . 2.  Experimental  Procedures  Step response measurements were c a r r i e d out w i t h the same c i r c u i t used f o r conduction measurements, except f o r the a d d i t i o n of a switch.  Currents  were measured w i t h the K e i t h l e y 417 high-speed picoammeter. The time constant of the picoammeter input  c i r c u i t was small compared to the current decay  rates measured f o r the current ranges used. Capacitance  and l o s s measurements were made w i t h a General Radio  1615-A capacitance bridge i n the three-terminal mode. Measurements were made i n the 100 Hz-lOOkHz frequency range. 3.  Results 3.1  Step Response T y p i c a l r e s u l t s f o r charging and discharging currents are shown i n o  the double l o g p l o t s of F i g . 1 and 2 f o r an y t t r i u m oxide f i l m 1250 + 50 A thick.  The counterelectrode metals were aluminum and indium.  The two p l o t s  are very s i m i l a r f o r the same voltage step, except that the D.C. current eventually dominates the charging  conduction  characteristic.  In F i g . 3, a p l o t i s made of l o g ( l / I ) against log(t/,x ) f o r d i s Q  charge currents a f t e r a voltage step of 3 v o l t s .  o  I  and T  q  are the current  and time at the point where the 3 V o l t curve i n F i g . 2 bends over. the slopes determined i n the two regions are  From F i g . 3  -8.00-1  -9.00H  10.D0H  ll.DOH  12.00-  T  r  T — 1  r  1.00  T  1  f—  1  LOG2.00 IT/SEC)  1  1  1  1  3.00  Fig. 1 kl-Y^O^-Al  Step Response Charging Current  r~  1  1  1  1  4.00  Volts  T  1  T  1  1  1.00  1  1  Fig. kl-Y^O^-kl  1  1  1  1  2.00 L0GU7SECJ  Step  1  1  3.00  2  Response  Discharging  Current  1  1  1  1  4.00  0.014-1  0.012H  0.030H  o.ooaH  0.006H  0.004H  0.002H  -0.000-  11  10  u  niiuiimiii i 3 4 6 1  IIIHIIUM  2  ' ' ' | ' " l " H " l ' W i "I'"I'l'VlM'l i 10 2 3 4 6 . 10 2 3 4 6 30  11111IIIIHIII IIIIM'III'H  2  3 4  6  1  '  FREQUENCY  IKHZ J  Fig. 4 . D i e l e c t r i c Losses vs. Frequency  52  s, = -0.49 + 0.03 1 and s  2  = -1.49 + 0.03 f o r  t>>T  O <  f o r t«f  o  Use of equations  average value f o r n of 0.50 + 0.03.  (8) and (9) gives an  The c h a r a c t e r i s t i c time t was 200 seconds.  Use of the f o l l o w i n g parameters i n equation (11) gives the v a r i a t i o n of the high-frequency *  e e  d i e l e c t r i c loss with  frequency:  m  = 3 .'05 + 0.02  (opt real-measurements)  Q  = 12.4 + 1.0  (capacitance measurements)  n = 0.50 + 0.03 e"(f)  + 10%.  rr 3.2  (12)  -  Loss Factor The d i e l e c t r i c l o s s f a c t o r f o r a Y ^  f i l m 1950 + 80 1 t h i c k w i t h  indium and aluminum counterelectrodes i s shown i n F i g . 4. s i m i l a r to that found by C a m p b e l l ^ f o r ^O^  This r e s u l t i s  f i l m s , although the magnitude  of h i s d i s s i p a t i o n f a c t o r was somewhat smaller at low frequencies. 4.  Discussion The agreement between the l o s s f a c t o r c a l c u l a t e d from step response  measurements and that determined by bridge methods was only approximate. This suggests that  two d i f f e r e n t l o s s mechanisms are operative.  The mechanism responsible f o r the step response losses i s l i k e l y f i e l d - a s s i s t e d thermal hopping of oxygen atoms between i n t e r s t i t i a l s i t e s i n the ^2^3 l a t t i c e .  The step response data f i t a model that has a Cole-Cole  d i s t r i b u t i o n of r e l a x a t i o n energies.  An estimate of the most probable  relaxation  energy can be made using T  = v*" exp(E /kT) p 1  o  (13)  where  T v  Q  E most probable r e l a x a t i o n time s atomic v i b r a t i o n frequency  Ep = most probable r e l a x a t i o n energy. A reasonable estimate f o r v from o p t i c a l phonon spectra i s 10  Hz  at room temperature. This gives E  p  : 0.9leV.  A comparison, can be made w i t h the d i f f u s i o n r e s u l t s of Berard et a l (1968) who found an a c t i v a t i o n energy of 0.85 eV f o r the d i f f u s i o n of oxygen atoms i n Y^O^.  Considering the nature of the approximations made, the agree-  ment between the two a c t i v a t i o n energies i s q u i t e good.  Thus, the l o s s peak  may be due to the r e l a x a t i o n of oxygen atoms d i s s o l v e d i n the Y^O^  lattice.  Campbell (1970) found a strong dependence of d i e l e c t r i c losses on temperature i n h i s ^O^ f i l m s .  He f e l t that t h i s dependence was i n d i c a t i v e  of an a c t i v a t i o n energy process, but f o r the temperatures  considered (between  20 and 75 °C), the steep frequency dependence of e" precluded a f l a t d i s t r i b u t i o n of a c t i v a t i o n energies.  The proposed l o s s mechanism i s i n agreement  w i t h these conclusions. At higher frequencies, the losses were independent of frequency, i n d i c a t i n g that a d i f f e r e n t loss mechanism i s dominant.  This view i s support  by the poor agreement between the measured values of e" and the c a l c u l a t e d values predicted by the theory i n the i n t r o d u c t i o n at high frequencies. The s l i g h t l y higher high frequency losses found i n t h i s work (0.058 compared to 0.038 found by Campbell) may be caused by the use of d i f f e r e n t substrates or some s m a l l d i f f e r e n c e i n evaporation technique.  54  •VI.  1.  B A R R I E R HEIGHT DETERMINATION BY  Introduction  Internal the  INTERNAL PHOTOEMISSION  photoemission  energy b a r r i e r  at  the  is  the emission  From p h o t o c u r r e n t measurements  of  light,  the  photoexcited carriers  i n t e r f a c e between a m e t a l  insulator. incident  of  as  (or  semiconductor)  a function  energy  barrier height  may b e  given  ah a p p r o x i m a t e  classical  of  the  over  and  an  wavelength  determined.  (21) Fowler electric  effect  has  (.emission of  electrons  from a m e t a l  treatment  into  of  Vacuum) .  the The  photoexact  (22) quantum m e c h a n i c a l work, theory  the of  two  treatments  Fowler w i l l Consider  metal  theory  diode  the  is  given  give  essentially  be r e f e r r e d simplified  shown i n F i g .  by M i t c h e l l  .  For  identical  results,  energy band  structure  1.  E  of  a metal  -insulator-  Metal  2  insulator Fig.  The e f f e c t i v e work  function  insulator  and h e n c e s e m i - t r a n s p a r e n t . insulator  simpler  • * \ / \ ^ hv  1  the  the  this  c  Metal  and t h e  so  of  to.  4>  the Fermi l e v e l  the purposes  1  $ is  the  difference in  conduction band.  F o r an e l e c t r o n to be  c o n d u c t i o n band by  an i n c i d e n t  energy  between  Electrode 2 is  very  e x c i t e d from metal  photon  of  energy  hv,  the  1  thin . into  condition  (1)  h v + E > <j) must be met.  E is  the  initial kinetic  energy  of  the  electron.  The  lowest  55  photon energy for emission is given by hy - <j>,  (2)  which defines the photoelectric threshold. 2  For electron emission, the energy ~  of the electron motion perpendi-  cular to the emitting surface should exceed <}>.. other velocity components may be neglected.  In a f i r s t approximation, the  The condition for emission may  then be expressed as  The photoelectric yield is expected to be proportional to the incident light intensity, the number of electrons meeting condition ( 2 ) , the chance that the quantum hv w i l l be absorbed by the  electron velocity component  normal to the metal surface, and the probability that the electron w i l l be transmitted through the barrier at the metal insulator boundary . Fowler, using these assumptions, found that the photoresponse R (electrons per incident photon) was given by r> - 4_Trm k T , x Ro ' {e 2  for x = ( * g %  e  , e  2 x  9—  +  ,,«. (4)  3 x  - ...}  —0  * 0, and 2„2 4Trmk T  for x  2  • ,Tf  2  2  , -x  e  ~2x  , e  -3x  ,  \  -s  /t  0. For large values of x (say x > 8, a value easily met in practise), 2  the only significant term in the expansion is -y  in (5).  Thus, the photo-  current expected i s I = C(hv - <j>)  2  (6)  Monochromator  Calibration  Curve  (Deuterium  Source)  where C i s a constant.  A plot of the square root of the current against  the photon energy hv w i l l give a straight l i n e f o r large values of x. In the presence of att e l e c t r i c f i e l d , the b a r r i e r height  w i l l be  lowered by  because of the Schottky  2.  effect.  Experimental Procedures The photocurrents motor Drive  chopper £ ? e l w  were measured with the c i r c u i t shown below. specimen jj-j  Chart recorder  Monochromator  417 picoammeter  Lock-in Amplifier  EXT  Photodiode Light from the Bausch and Lomb p r e c i s i o n grating monochromator was chopped at a frequency of 2 2/3 Hz.  This low frequency was used because of  the long time constant of the picoammeter input i n i t s most s e n s i t i v e range. The currents developed i n the specimen were detected by the Keithley 417 picocammeter, amplified i n the Princeton HR-8 l o c k - i n amplifier and plotted on a Moseley Chart recorder.  The l o c k - i n amplifier was used i n the s e l e c t i v e  external mode, with the. external signal"'being, derived . from the output of a photodiode i n the path of the chopped l i g h t .  This  method of detection was found superior to the D.C. method because errors due to slow transient currents i n the d i e l e c t r i c f i l m were eliminated, as were some of the noise problems associated with measuring currents of l e s s than  10*"  amperes.  The setup was capable of detecting currents as small as  2 x 10~^ amperes, but the smallest currents capable of being measured i n Y^O^ -12 were about 5 x 10  amperes because of noise limitations.  The monochromator had a choice of two light sources and three gratings capable of covering the entire wavelength spectrum from 200 m i l l i microns to 3 . 6 microns. A calibration of the source intensity was made by illuminating an Eppley  silver-bismuth thermopile with light from the monochromator.  Chopping the light was found to reduce the average intensity by a factor of 2.  Photoemission measurements were made with the specimen in the same position  as the thermopile.  The thermopile voltages were measured with a Keithley 150 A  microvoltmeter and recorded with a Moseley chart recorder. A synchronous 1 RPH motor was used to drive the monochromator diffraction grating. run took 45 minutes.  A typical  The slow scan rate eliminated slow transient effects from  the data. The.monochromator entrance and exit s l i t s were set at 2.78 and 1.56 mm. width.  This permitted a band of wavelengths 10 millimicrons wide to pass  through the monochromator.  Narrower settings gave better spectral purity, but  the light intensity was too low. 3.  Experimental Results . The sensitivity of the thermepile used to make light intensity  measurements was 19.0uW/uV. Fig. 2 shows the spectral variation of the monochromator in the ultraviolet region•. The deuterium light source was used.  A similar calibration  in the visible range is given i n Fig. 3. The tungsten halogen lamp was the light source.  The calibration curve for the spectral region of interest for  * Made by Eppley Laboratories, Newport R.I., U.S.A.  500.00-1  400.00  £ 300.00H tx a* o cc  s  tn  200.00  loo.ooH  0 —I if 2000.00  i  »—i—I—r 3000.00  T—i—|—r 5000.00 ' 4000.00 WAVELENGTH IRNGSTRQHS)  '  i— 6000. 00  Fig. 3 Monochromator Intensity C a l i b r a t i o n ( V i s i b l e Range)  7.00-j  00 WAVELENGTH IflNGSTRCMSJ Fig. Monochromator  4  Calibration  (2000-5000 A ° )  Y^O^  photo-emission i s shown i n F i g . 4, which shows the incident photon  flux. Fig. aluminum M1M  5 shows the photoresponse of an aluminum-yttrium oxide-  structure.  with the Sloan  M-100  The insulating f i l m was measured to be 8 8 0 " ^ ° ^  Angstrometer.  The aluminum counterelectrode was  o about 100 A thick and had a transmission c o e f f i c i e n t of 0.04  for white l i g h t .  The response .was observed to f i r s t go negative, then p o s i t i v e with increasing v.  Since no p o t e n t i a l was applied across the i n s u l a t i n g  f i l m , the photoresponse must be due to two photocurrents, one from each (23)  electrode.  Schuermeyer  has suggested that the photoresponse can be  expressed as the sum of two currents of the Fowler type, giving R = c (hv-<f> ) - c (hv-<f> ) 2  2  where the constants c^ and, c are c  2  2  (8)  2  2  1  1  are d i f f e r e n t because the l i g h t  intensities  If <t> >~4>^i then for hv < Q^*  d i f f e r e n t i n the two metal films.  2  = 0; s i m i l a r l y , for hv < <}>, c^ = 0 also.  For cf>^ < hv  < <f>  2>  /|R| = »^(hv- j, ) (  (9)  l  The f i r s t points i n the negative portion of F i g . 5 were plotted i n F i g . 6 to give / J ~ .  The b a r r i e r height was found to be = 3.14  +0.06eV.  (10)  /cj(hv-<f> )  (11)  The p o s i t i v e current /lj=  2  was found using equation (8) and the result plotted i n Fig.  (6).  The  work function <j> was found to be 2  <t> = 3.72 + 0.07 eV. 2  (12)  The e l e c t r i c f i e l d i n the i n s u l a t o r i s  E  =  *2-*l  W  = (6.7 + 2.2) x 10  volts/cm.  The Schottky b a r r i e r lowering i s A<}> = 0.0056 + 0.00015 eV, which i s much smaller than the errors i n <fi 4.  and <j) , so i t may be neglected.  Discussion The b a r r i e r determined f o r ^O^ was found to have the following  shape:  <J> = 3.72 eV  tj> =3.14 eV  2  hv  Fig. 7 A simple explanation of the observed currents can be given. For c j ^ < hv  < <j»2» only ^  flows i n the i n s u l a t o r . Because the i n t e n s i t y  of l i g h t i n metal (1) i s low, and because  i s attenuated by the e l e c t r i c  f i e l d i n the i n s u l a t o r , the current observed i s small. When hv both  and  flow, but J  2  > ty^*  rapidly becomes dominant because i t i s .assisted  by the i n t r i n s i c f i e l d and the i n t e n s i t y of l i g h t i n metal (2) i s large. In the region hv plot.  or hv-v^,'  a curvature i s observed i n the Fowler  This i s due to the spread i n the occupation p r o b a b i l i t y of electron  energy states near the Fermi l e v e l because the temperature i s greater than absolute zero.  A more e x a c t model w o u l d h v > <j>, t h e e l e c t r o n s w i l l  be  P  injected into  factors  into  account.  the oxide with  the  When  energy  2  E = —  P  take other  + hv -  <(>, w h e r e  2  2 ^ was metal .was  the i n i t i a l surface.  electron kinetic  The o t h e r  done i n . F o w l e r ' s  electrons properties  than  components  derivation.  injected w i l l  energy w i t h  be hot  When h v  light  films the  in  the metal  will  films.  pay  a l s o be  these  into  factors  researchers(25,26,27,28)^  n  C2c The most p r o m i s i n g  The e f f e c t s  significant  simply be s c a t t e r e d back Some o f  Q  d a t a On A l - A ^ O ^ - A l . •  fairly  The b a r r i e r h e i g h t s bandgap i n s u l a t o r s . is  for  due t o  The o t h e r  p  for ^ O ^  time  to  f i l m was  by  found are  r e  hensive  appear  comparable  to  and l i k e l y  could  intensity  metal  just  inside  electrons  of  yet been developed.  to  fit  the  those  functions  had  50A o f  result.  the ^ O ^  fit  simple model  found  aluminum o  about  Carlo  w h i c h gave a good  The f i r s t  evaporated d i r e c t l y onto  effective b a r r i e r height  the  a number  model has  yields,  The d i f f e r e n c e i n work  air  the  the i n j e c t e d  e x p e r i m e n t a l e r r o r s w o u l d mask any  the p r e p a r a t i o n method.  a short  between  affects  scattering  Some o f  i n t e r n a l photoemission  large  light  the  transport  have b e e n o b t a i n e d w i t h Monte  experimental  the  of  it  as  27)  of  but  the  the m e t a l .  c o m  results  obtained  of  as  light  have b e e n c o n s i d e r e d by  calculations  The d a t a  account,  large,  different  The i n t e r f e r e n c e o f  The a b s o r p t i o n  must a l s o be c o n s i d e r e d .  insulator  -(j>--is s u f f i c i e n t l y  e l e c t r o n s , which have  thermal e l e c t r o n s .  to  o f momentum h a v e b e e n n e g l e c t e d ,  t h e m e t a l e l e c t r o d e s must be t a k e n i n t o of  a momentum n o r m a l  at  second o r d e r for  other  t h e two  f i l m was  ^2^3 film,  o  ^  n  so  to  well, effects.  wide barriers  exposed  e  a  surface. different  VII. T h e t h i n Y^O^ f i l m s the properties -The evaporation  to  curves.  for  insulating  of  The leading  essential  Y^O^  w  a  s  depositing  investigated device  a  of  reasonably  ionic mobility  was  losses,  may b e p o s s i b l e  to  the  found  films  simple,  found  to  h a v e many  excellent,  non-critical  and h y s t e r e s i s  in  were  to be q u i t e h i g h  improve  on a h e a t e d s u b s t r a t e  were  of  fabrication.  properties  low-frequency  It  CONCLUSIONS  in  to  in  t h e MOS  prevent  the  process.  the performance of  order  and  the  films,  capacitance the  films  reduction of  by  the  evaporant. A number o f desirable process  in  taken  t h e most p r o b a b l e  would of  data  then give  the  loss  order at  dependence of  check t h e mechanism  different  relaxation  temperatures frequency estimate  the  proposed.  would  Also,  reciprocal  be  conduction  would be u s e f u l .  against of  It  step  A  plot  temperature  t h e mean a c t i v a t i o n  energy  mechanism. investigation  would be d e s i r e a b l e . useful material  for  In  particular well  of  the p r o p e r t i e s  the  on m o d e l l i n g  emphasis  above  view  of  ease  of  double-dielectric device  F u r t h e r work  energies  to  can be s u g g e s t e d .  the pressure  a more a c c u r a t e  Further  with  experiments  know more a b o u t  i n Y^O^,  response of  to  other  on t h e h o t  the  the p h o t o e l e c t r i c  deposition,  of  i n MOS  structures  Y ^ O ^ may b e  a  fabrication.  internal  nature  of ^ O ^  photoeffect  is  necessary,  photoelectrons  at  light  threshold.  APPENDIX  Preliminary Au-^O^-Si curves. of  devices  Figs.  a voltage  while  inductance n-type  were  t h e MOS  meter.  silicon  generated  triangular  measuring  of  waveform  +.05fi - c m  frequencies.  Comparison  using  depletion  density  the high that  energies  about  state  devices  with  the  e l e c t r o n i c or i o n i c  motion  is  oxide  films  probably  the  cause  (as  and t h e A - C mechanism.  losses  across  film  model  C-V  71A  the  specimen  capacitance-  1500 + 2 0 0 A ° t h i c k  on  lower  capacitance,  as  scan  calculated a  surface  2 .  This  is  defect  Y^O^ appears density  charges  seems  frequency  of  application  (29) model• , indicated  surprisingly  low,  near  likely,  densities to be  considering  (i.e.,  and hence  a useful  x-rays)  higher  material  for  considerations.  o b s e r v e d may b e  either  the  more p r o n o u n c e d a t  higher  Thus, state  p l o t t e r by  t h e e l e c t r o n beam e v a p o r a t i o n  give  densities.  The h y s t e r e s i s  in  curves  differential  a Boonton  i d e a l MOS  3 x 10 / c m  involved  1 MHz  low  a Y20^  approximation  from s u r f a c e  the  and  o b s e r v e d was  would be e x p e c t e d t o  surface MOS  of  the  capacitance  resistivity.  11 state  in  on an X - Y  The s p e c i m e n h a d 0.4  t h e MOS  capacitance with  The h y s t e r e s i s  t h e MOS  of  showed h y s t e r e s i s  1-3  of  investigation  caused by  the  the Y20.j-Si  considering  observed),  s l o w movement  interface.  the s t r u c t u r e  the motion  of  oxygen  of  If  ionic  of  the  ions  is  68  C(pf)  -5 Fig. MOS  C Hysteresis  (Sweep  1 F r e q u e n c y = 0.1  Hz)  69  70  71  REFERENCES 1.  Campbell, K.C.  Thin S o l i d Films , 6(1970) pp. 197-202.  2.  Marshak, R.E., Fundamental' of Transmission Electron Microscopy , Wiley Interscience, p. 179 (1964). ~ '  3.  American I n s t i t u t e of Physics Handbook, McGraw-Hill (1967) p.  4.  Staritzky, E.,  5.  Hass, G., J.B. Ramsey and R. Thun, J . O p t i c a l Soc. Am., (1959).  6.  Berard, M.F. , CD. 643 (1968).  7.  Simmons, J.G., Handbook of Thin Film Technology, McGraw-Hill Co., 19 70, p. 14-3.  8.  M i l l e r , A. and A. Daane, J . Inorg. Nucl. Chem., 9, 27 p. 1955-60 (1965).  9.  Dresner, J . and F.V. Shalcross,  9-4.  A n a l y t i c a l Chemistry, 28(1956) p. 2023  Wirkus and D.R.  Wilder, J . Am.  2, 49 p. 116  Cer. S o c , 11, Vol. 51,  Solid-State Electron , 5, 205  10.  Frenkel, J . , Phys. Rev. 54, 647 (1938).  11.  Mead, C.A. Phys. Rev. J . , 128 p. 2088 (1962).  12.  Hartman, T.E., J.C. B l a i r and R. Bauer, JAP 37, p. 2468 (1968).  13.  Simmons, J.G. Phys. Rev. 3, 155  14.  Stuart, M., Phys. Stat. S o l i d ! , 23, 595  15.  H i l l , A.G., p. 278-95.  16.  A.M.  (1962).  (1967). (1967).  Phahle and J.H. Calderwood, Thin S o l i d Films 5(1970),  Archer, R.J. "Determination of the Properties of Films on S i l i c o n by the Method of Ellipsometry", J . Optical Soc. Am., Vol. 52, No. 9, . pp. 970-977, Sept. 1962.  17.  T a l l a n , N.M.  18.  F r o h l i c h , H., 'Theory of D i e l e c t r i c s , Oxford University Press, London, 1949.  ,19.  Baird, M.E.,  "20.  Cole, K.S. and R.H.  21.  Fowler, R.H., p. 358.  and R.W.  Vest, J . Amer. Cer Soc. 8, 49, p. 401 (1966).  Reviews of Modern"Physics, 1, 40, p. 219  (1968).  Cole, J . Chem Phys. 10, 98 (1942).  S t a t i s t i c a l Mechanics, Cambridge University Press, 1936 .  72  22.  Mitchell,  K.,  Proc.  23.  Schuermeyer,  24.  Goodman,  25.  Schuermeyer,  F.,  JAP  26.  Schuermeyer,  F.,  C.K.  F.,  Royal  J . Appl.  Soc.  Am., V o l .  Phys.  A.M., E l e c t r o c h e m .  37  (5)  Sdc. , V o l .  37 N o . Young  5,  p.  p.  1998  15 N o .  1998  and J . M .  146 p .  442  (1924).  (1966).  9 p.  276C  (1968).  (1966).  Blasingame,  JAP  39 N o .  3,  p.  (1968). 27.  Stuart,  R.  and F.  28.  Powell,  R.J.,  29.  G r o v e , A . S . , P h y s i c s and T e c h n o l o g y W i l e y and S o n s , 1967, p. 271.  JAP,  Wooten, 40 N o .  Phys. 13,  p.  Rev.  156 N o .  5093 of  2,  p.  364  (1967).  (1969). Semiconductor  Devices,  John  1971  

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